E(y) = Var(y) for a Poisson distribution, the variance of y is equal to the value of E(y) .
To calculate the variance of y, follow these steps:
Recall that for a Poisson distribution, the mean (first moment) is equal to the variance. So, if the first moment of x is less
than the first moment of y by 8, we can write: E(x) = E(y) - 8.
We are also given that the second moment of x is 60% of the second moment of y:
[tex]E(x^2) = 0.6 × E(y^2).[/tex]
Recall that for a Poisson distribution, the second moment is given by [tex]E(X^2) = E(X)² + E(X)[/tex]. Thus, we can write equations
for x and y using this relationship: [tex]E(x^2) = E(x)² + E(x) and E(y^2) = E(y)² + E(y).[/tex]
Plug the expressions from step 1 into the equation from [tex]E(x^2) = (E(y) - 8)² + (E(y) - 8).[/tex]
Plug the expressions from step 2 into the equation from[tex]0.6 × E(y^2) = (E(y) - 8)² + (E(y) - 8).[/tex]
Solve for [tex]E(y^2)[/tex] from the equation in [tex]E(y^2) = (10/6) × ((E(y) - 8)² + (E(y) - 8)).[/tex]
Substitute [tex]E(y^2)[/tex] back into the equation for the second moment of y from [tex]E(y^2) = E(y)² + E(y).[/tex]
Solve for E(y) from the equation in
Since E(y) = Var(y) for a Poisson distribution, the variance of y is equal to the value of E(y) .
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Send Halp What is the interest rate if the investment is $1,000 at 16% simple interest for 20 yrs?
Answer:
The interest rate is already given as 16%. If you want to calculate the total interest earned on the investment, you can use the formula:
Simple Interest = (Principal x Rate x Time)/100
Where:
Principal = $1,000
Rate = 16%
Time = 20 years
Substituting the values, we get:
Simple Interest = (1000 x 16 x 20)/100 = $3,200
Therefore, the total interest earned on the investment is $3,200.
Step-by-step explanation:
From midnight to 2:00 am, the temperature dropped 1.15°C each hour. If the temperature at 2:00 am was 3.7°C, what was the temperature at midnight?
Answer:
6 degrees Celsius
Step-by-step explanation:
The temperature at 2am was 3.7 degrees C.
Since the temp dropped 1.15 degrees each hour, at 1am the temp was 3.7+1.15 = 4.85 degrees
So at midnight, 12am, the temp was 4.85+1.15 = 6 degrees Celsius
Please help me find the surface area.
Answer:
Step-by-step explanation:
The number of toy trucks in Mike's toy collection is 2/5 of the number of toy cars a,Express the number of toy cars as a fraction of the number of toy trucks. b,What is the ratio of the number of toy trucks to the total number of toy trucks and toy cars? c,What fraction of the total number of toy trucks and toy cars is the number of toy cars?
The number of toy cars to the number of trucks is 5/2,the number of toy trucks is 2/7 of the total number of toy cars and toy trucks and the number of toy cars is 5/7 of the total number of toy cars and toy trucks.
EquationsLet's represent the number of toy cars as 'c' and the number of toy trucks as 't'.
From the problem, we know that:
t = 2/5c
Express the number of toy cars as a fraction of the number of toy trucks:
c = 5/2t
c/t = (5/2t)/t = 5/2
Therefore, the number of toy cars is 5/2 times the number of toy trucks.
The total number of toy cars and toy trucks is:
c + t
Substituting t = 2/5c, we get:
c + (2/5)c = 7/5c
So the ratio of the number of toy trucks to the total number of toy cars and toy trucks is:
t/(c + t) = (2/5c) / (7/5c) = 2/7
Therefore, the number of toy trucks is 2/7 of the total number of toy cars and toy trucks.
The fraction of the total number of toy cars and toy trucks that is the number of toy cars is:
c / (c + t)
Substituting t = 2/5c, we get:
c / (c + 2/5c) = c / (7/5c) = 5/7
Therefore, the number of toy cars is 5/7 of the total number of toy cars and toy trucks.
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Please Help me I don't get it. (DON'T ANSWER IT IF YOU DON'T KNOW, I'M TIRED OF PEOPLE ANSWERING IT FOR NO REASON TO GET POINTS)
Answer: 1/8 or 0.125 in decimal form
Step-by-step explanation: Reduce the expression by cancelling the common factors.
HELPPP! WHOEVER GETS THE ANSWER GET POINT PLS!
7. Alonzo and Mandy are selling raffle tickets at school for a fundraiser. Alonzo sells 5 tickets less than three times what Mandy sells. Together they sell a total of 43 tickets. Let n equal the number of tickets Mandy sells. Use an equation to determine the number of tickets Alonzo sells. Show how you arrived at your answer.
That we know that Mandy sells 12 tickets, we can use the first equation to find out how many tickets Alonzo sells: a = 3n - 5 = 3(12) - 5 = 31
Alonzo sells 31 tickets.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
Let's use algebra to solve the problem:
Let's start by defining some variables:
Let n be the number of tickets Mandy sells.
Let a be the number of tickets Alonzo sells.
We know that:
Alonzo sells 5 tickets less than three times what Mandy sells. So we can write:
a = 3n - 5
Together they sell a total of 43 tickets. So we can write:
a + n = 43
We have two equations with two variables, so we can solve for a by substituting the first equation into the second equation:
(3n - 5) + n = 43
4n - 5 = 43
4n = 48
n = 12
Now that we know that Mandy sells 12 tickets, we can use the first equation to find out how many tickets Alonzo sells:
a = 3n - 5 = 3(12) - 5 = 31
Therefore, Alonzo sells 31 tickets.
So the answer is: Alonzo sells 31 tickets.
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select all the expressions equivalent to 80-20x
Answer:
where is the pic
Step-by-step explanation:
Ellie uses 27 yards of fabric for 48 doll dresses she uses that same amount for one dress how many yards of fabric does use for one
Ellie uses approximately 0.5625 yards or 9/16 of a yard of fabric for one doll dress, which can be useful in calculating the total cost of fabric required for a certain number of doll dresses.
Given that Ellie uses 27 lengths of fabric for 48 doll dresses, we can calculate the amount of fabric she uses for one dress by dividing the total yards of fabric by the number of dresses.
Dividing 27 by 48, we get 0.5625 yards, or approximately 9/16 of a yard, for one doll dress. This means that each dress requires a little more than half a yard of fabric.
This information can be useful in calculating the cost of fabric required to make a certain number of doll dresses. If we know the cost of fabric per yard, we can multiply it by the number of yards required to determine the total cost of fabric. In this case, if the cost of fabric is $5 per yard, the cost of fabric for one doll dress would be approximately $2.81.
In conclusion, Ellie uses approximately 0.5625 yards or 9/16 of a yard of fabric for one doll dress.
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Fourth-grade students recorded the distance it takes to get from home to the nearest grocery store. The distance in miles is recorded on the line plot. Which is the most common distance from home to the grocery store?
Using the line plot graph, we can conclude that the 5th distance that is 5/4 is the most common distance from home to the grocery store.
Define line plot?A line plot is a type of graph that shows the frequency of each value together with the data using symbols above a frequency number-line. It is used to organise the information simply and is very easy to comprehend.
In the given graph we can see that the distance values are given.
So, in the first instance the number of times the distance is used = 2.
The 2nd distance has been used = 3.
The 3rd distance has been used = 2.
The 4th distance has been used = 4.
The 5th distance has been used = 5.
The 6th distance has been used = 2.
The 7th distance has been used = 2.
The 8th distance has been used = 2.
Hence, we can conclude that the 5th distance that is 5/4 is the most common distance from home to the grocery store.
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Assume all lines that appear parallel, are parallel. Solve for y.
The value of y is 10. we canget this answer by using fact ratios of the corresponding sides are equal. Using this fact, we can set up the proportion
what is corresponding sides?
In geometry, corresponding sides are sides in two or more figures that are in the same relative position or location. For example, if you have two triangles ABC and DEF, and AB is corresponding to DE, BC is corresponding to EF, and AC is corresponding to DF, then AB and DE are corresponding sides, BC and EF are corresponding sides, and AC and DF are corresponding sides.
In the given question,
To solve for y, we need to use the fact that line wt and line ye are parallel to each other. This means that the ratios of the corresponding sides are equal. Using this fact, we can set up the following proportion:
wt/ty = we/yc
Substituting the given values, we get:
(8 + x + 6)/16 = 10/y
Simplifying and solving for y, we get:
y = (160)/(14 + x)
Now we need to use the fact that the sum of the lengths of two sides of a triangle is always greater than the length of the third side. Using this fact for triangle ATY, we get:
AT + TY > AY
Substituting the given values, we get:
x + 6 + 16 > y
Simplifying and substituting y with its expression, we get:
x + 22 > (160)/(14 + x)
Multiplying both sides by (14 + x), we get:
x² + 22x + 14x + 352 > 160
Simplifying and rearranging, we get:
x² + 36x - 192 > 0
Now we can solve this quadratic inequality to get the range of possible values for x:
(x - 4)(x + 48) > 0
The solutions are x < -48 or x > 4. Since x represents a length, we can ignore the negative solution. Therefore, we have:
x > 4
Substituting this value into the expression we derived for y, we get:
y = (160)/(14 + x) = (160)/(14 + 4) = 10
Therefore, the value of y is 10.
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Dorothy bought an energy drink for $2.34 and a bag of chips for $1.82
She paid with a $50 bill. How much change should Dorothy have
received?
Dorothy should have received $45.84 in change.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
To find out how much change Dorothy should have received, we need to first calculate the total cost of the energy drink and the bag of chips:
Total cost = Cost of energy drink + Cost of the bag of chips
Total cost = $2.34 + $1.82
Total cost = $4.16
Next, we need to subtract the total cost from the amount paid by Dorothy to get the change:
Change = Amount paid - Total cost
Change = $50 - $4.16
Change = $45.84
Therefore, Dorothy should have received $45.84 in change.
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A principal wants to know if students at a particular high school are in favor of a new dress code at their school. The principal is not able to ask the opinion of every student at the school, so she needs to select an appropriate sample of the students to represent the high school.
Select which sample of students the principal should choose.
The principal should then survey the selected students to gather their opinions on the new dress code.
To answer your question, the principal should choose a sample of students that is both representative and random. This will ensure that the opinions gathered are an accurate reflection of the entire high school population.
How the principal can achieve this:
Determine the sample size:
The principal should decide on a suitable sample size based on the total number of students in the high school.
A larger sample size will yield more accurate results, but it may not be feasible to survey too many students.
To ensure representativeness, the principal should divide the high school population into different strata, such as grade levels or other relevant demographic categories.
This will help ensure that the sample includes a balanced mix of students from different backgrounds and groups.
Select a random sample:
Within each stratum, the principal should choose a random sample of students.
The principal should then survey the selected students to gather their opinions on the new dress code.
By following these steps, the principal can select an appropriate sample of students that will provide an accurate representation of the high school's overall opinion on the new dress code.
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which of the following statements are true? the resample can contain serial numbers that are not in the original sample. the original sample can contain serial numbers that are not in the resample. because the sample size is small, the histogram of the resample might look very different from the histogram of the original sample. the resample has either zero, one, or more than one copy of each serial number. the original sample has exactly one copy of each serial number for every german plane. the resample has exactly the same sample size as the original sample.
The true statements about the sample are a, c, d and e.
Serial codes in the resample may differ from those in the initial sample. The histogram of the resample may vary significantly from the histogram of the initial sample due to the small sample size. The number of copies of each serial number in the resample can be zero, one, or more. Furthermore, each serial number for every German aircraft is present in the initial sample precisely once.
Using resampling methods like bootstrapping or permutation tests, a new resample is created by arbitrarily selecting some of the initial sample. Therefore, depending on the precise resampling technique employed, the sample amount of the resample may be the same as the initial sample or it may be smaller or bigger.
Complete Question:
which of the following statements are true?
a. the resample can contain serial numbers that are not in the original sample.
b. the original sample can contain serial numbers that are not in the resample.
c. because the sample size is small, the histogram of the resample might look very different from the histogram of the original sample.
d. the resample has either zero, one, or more than one copy of each serial number.
e. the original sample has exactly one copy of each serial number for every German plane.
f. the resample has exactly the same sample size as the original sample.
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Given â–³rst ~ â–³rqp. triangle p q r. side p q is 8 centimeters and side p r is 12 centimeters. triangle s r t. side s t is x centimeters and side r t is 18 centimeters. what is the value of x?
The required simplified value of x in the △RQP (triangle RQP) is given as x = 12 centimeters.
Similar triangles:
Two triangles are similar if their corresponding sides have the same ratio and if the corresponding pairs of angles are equal. Two or more figures having the same shape but different sizes are called similar figures. Consider a hula hoop and a bicycle wheel, both objects are similar in shape because they have the same shape. Similar triangles are those triangles that have similar properties, i.e. angles and proportionality of sides.
Here,
△RST ~ △RQP
So, the Property of similar triangle states that the ratio of the corresponding side of the triangle is equal.
PQ/ST = PR/RT
From the given data n the question,
8/x = 12 / 18
⇒ x = 8 × 18 / 12
⇒ x = 12
Thus, the required simplified value of x in the △RQP is given as x = 12.
Complete Question:
Given △RST ~ △QRP. Triangle P Q R. Side P Q is 8 centimeters and side P R is 12 centimeters. Triangle S R T. Side S T is x centimeters and side R T is 18 centimeters. What is the value of x?
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Jordan wants a collapsible puppy pen that gives his puppy at least 35 square feet of area and at Least 10 feet of diagonal length. Should Jordan buy the pen shown? Explain.
Using area formula, we can find that the diagonal length is not 10ft. So, Jordan should not buy the pen.
Define area of square?A square's area is a measurement of the volume or surface that it takes up. It is equivalent to the two sides' combined lengths. Since the product of a square's two sides determines its size, the area is expressed in square units.
Here in the question,
Jordan wants an area that is of 35 ft² and 10ft diagonal length.
Now in the figure,
Dimensions of the pen are:
Length, l = 6ft.
Width, w = 6ft.
Height, h = 6ft.
So, it's a square.
Area that the puppy pen will provide = l × w
= 6 × 6
=36ft².
Diagonal of the pen is: (As per Pythagoras theorem)
√ (6² + 6²)
= √ (36+36)
= √ 72
= 8.48
The pen does provide 35ft² of area as it has 36ft², but it does not have a diagonal length of 10ft.
Therefore, Jordan should not buy the puppy pen.
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The complete question is:
Jordan wants a collapsible puppy pen that gives his puppy at least 35 square feet of area and at Least 10 feet of diagonal length. Should Jordan buy the pen shown? Explain.
We may determine that the diagonal length is not 10 feet using the area formula. Jordan shouldn't buy the pen.
Define area of square?The volume or area that a square occupies is determined by its area. It is equal to the sum of the lengths of the two sides. The area is given in square units since a square's size is determined by the product of its two sides.
Jordan requests a 35ft² square foot area with a 10-foot diagonal.
Now look at the figure.
The pen is the following size:
Length, l = 6ft.
Width, w = 6ft.
Height, h = 6ft.
So, it's a square.
The area that the puppy kennel will offer
= 6 × 6
=36ft².
Diagonal of the pen is:
= √ (6² + 6²)
= √ (36+36)
= √ 72
= 8.48
The pen has 36ft² square feet, so it does offer 35ft² square feet, but it lacks a 10 foot diagonal.
Jordan shouldn't purchase the Puppy pen as a result.
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The complete question is attached below,
A school has 800 students. The staff plans to order a bag for each student. They ask 120 randomly selected students which color bag they prefer. Based on this sample, how many bags of each color should the staff order? Show your work.
Blue 48
Black 54
Gray 18
The staff should order 48 blue bags, 54 black bags, and 18 gray bags for a total of (48 + 54 + 18) = 120 bags
To determine the number of bags of each color that the staff should order, we need to use the information from the sample of 120 students and make an inference about the entire population of 800 students.
If we assume that the sample of 120 students is representative of the entire population, we can use the proportions from the sample to estimate the number of bags of each color that the staff should order.
Let's use the following proportions from the sample:
40% of the students prefer blue bags (0.40 x 120 = 48)
45% of the students prefer black bags (0.45 x 120 = 54)
15% of the students prefer gray bags (0.15 x 120 = 18)
Therefore, based on this sample, the staff should order 48 blue bags, 54 black bags, and 18 gray bags for a total of (48 + 54 + 18) = 120 bags.
However, it's important to note that this is just an estimate based on a sample, and there may be some variability or uncertainty in the actual preferences of the entire population.
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The math club is planning a meeting. They are planning to serve cookies and brownie bites and want to have one dessert per person. They expect an attendance of a total of 75 people. Cookies (c), come in packs of 12 each, and the brownie bites (b) come in packages of 15. What is the equation for the total number of packages of each dessert that the club treasurer needs to purchase in order to have a dessert for each person who attends? b+ 12 15 75 C= If the treasurer buys 1 package of brownie bites, how many packages of cookies are needed according to this equation? packages of cookies Is this value a reasonable value in this
Equation for the total number of dessert packages needed for a math club meeting with cookies and brownie bites; 5 packages of brownie bites and 15 packages of cookies needed to serve one dessert per person for a total of 75 attendees.
What is the equation for the total number of dessert packages needed for a math club meeting with cookies and brownie bites?We can use the following equation to calculate the total number of packages of each dessert that the club treasurer must purchase:
Total packages of brownie bites (b) + Total packages of cookies (c) = Total number of attendees (75)
We know that brownie bites come in packages of 15, so the total number of packages of brownie bites the treasurer needs to purchase would be:
b = ceil(75/15) = 5
where "ceil" refers to the ceiling function, which rounds to the nearest integer. In this case, we need at least 5 packages of brownie bites to have one dessert per person.
To find the number of packages of cookies needed, we can substitute the value of b into the equation:
c + 12b = 75
c + 12(5) = 75
c + 60 = 75
c = 15
However, this value is not reasonable since 15 packages of cookies would provide 180 cookies, which is more than 2 cookies per person. Therefore, the treasurer would need to adjust the number of packages of cookies based on the actual number of cookies in each package to ensure that they have exactly one dessert per person.
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for the previous example, which statements are accurate conclusions? group of answer choices the proportion of drinkers in the population of ca college students is not 0.60. there is a statistically significant difference between the proportion of drinkers in the american adult population (0.60) and the proportion of drinkers in the population of ca college students. a larger proportion of ca college students drink alcohol compared to the adults nationwide. when we compare the american adult population to the population of ca college students, there is a 0.06 difference in the proportion of drinkers.
The following statements are accurate conclusions:
The proportion of drinkers in the population of California college students is not 0.60.There is a statistically significant difference between the proportion of drinkers in the American adult population (0.60) and the proportion of drinkers in the population of California college students.A larger proportion of California college students drink alcohol compared to adults nationwide.The null hypothesis is: The proportion of California college students who currently drink alcohol is the same as the proportion nationwide (p = 0.60).
The alternative hypothesis is: The proportion of California college students who currently drink alcohol is different from the proportion nationwide (p ≠ 0.60).
p in the hypotheses represents the proportion of college students who currently drink alcohol.
The Z-score is calculated as:
Z = (0.66 - 0.60) / 0.023 = 2.61
The P value can be obtained from a standard normal distribution table or calculator:
P = 0.0045 (for a two-tailed test)
We reject the null hypothesis and come to the conclusion that there is a statistically significant difference between the proportion of drinkers in the population of California college students and the proportion of drinkers in the American adult population because the P value (0.0045) is less than the significance level (which is not stated in the question) (0.66).
For the given question:
The following statements are accurate conclusions:
The proportion of drinkers in the population of California college students is not 0.60.There is a statistically significant difference between the proportion of drinkers in the American adult population (0.60) and the proportion of drinkers in the population of California college students.A larger proportion of California college students drink alcohol compared to adults nationwide.The result that "There is a 0.06 difference in the proportion of drinkers when we compare the US adult population to the population of CA college students" is untrue since the hypothesis test is not concerned with proportional differences.
The complete question is:-
Normal Distribution Calculator Drag the orange flag left or right to change the Z-score Alternatively, enter a Z-score into the textbox and click enter. Enter 8 -1 Z-score: -1.000 0 Z-score The area to the left of the Z value is 0.1587 The area to the right of the Z value is 0.9413 Question 1 6 pts California College Students Who Drink According to the Centers for Disease Control and Prevention, 60% of all American adults ages 18 to 24 currently drink alcohol. Is the proportion of California college students who currently drink alcohol different from the proportion nationwide? A survey of 450 California college students indicates that 66% currently drink alcohol. The null hypothesis is (Select] The alternative hypothesis is Select] p in the hypotheses represents [Select) The standard error is 0.60(1-0.60) 450 = 0.023 The Z-score is (Select] The P value is Select) The conclusion is Select Question 2 4 pts For the previous example, which statements are accurate conclusions? The proportion of drinkers in the population of CA college students is not 0.60. There is a statistically significant difference between the proportion of drinkers in the American adult population (0.60) and the proportion of drinknes in the population of CA college students A larger proportion of CA college students drink alcohol compared to the adults nationwide When we compare the American adult population to the population of CA college students, there is a 0.06 difference in the proportion of drinkers
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std study: a 2008 cdc study estimated that 26% of young women between the ages of 14 and 19 in the u.s. were infected with at least one of the most common sexually transmitted diseases (human papillomavirus [hpv]), chlamydia, herpes simplex virus, and trichomoniasis). is the percentage higher in your community? suppose that we plan to select a random sample of 100 young women in your community. if we use the national figure of 26%, we estimate that the standard error is about 0.04 for results from random samples of 100 young women. when we select a random sample of 100 young women in your community, we find that 20% are infected with at least one of the most common stds. which gives the best interpretation of the 95% confidence interval to estimate the percentage of young women in your community who are infected with at least one of the most common stds?
Be 95% confident that the true percentage of young women infected with at least one STDs in your community is between 12% and 28% based on the random sample of 100 young women in your community.
The national estimate for the proportion of young women in the United States who are infected with at least one of the most prevalent sexually transmitted diseases is 26% based on the information provided. The study also predicts that the standard error for findings from 100 young women's random sample will be 0.04 percent.
It is discovered that 20% of 100 young women in your community who were chosen at random are infected with at least one of the most prevalent STDs. A 95% confidence interval can be used to calculate the proportion of young women in your community who have at least one of the most frequent STDs.
If the same sample is obtained multiple times, the true value will, in 95% of cases, fall within the computed interval, according to a 95% confidence interval. The range of 12% to 28% is the predicted 95% confidence interval for the proportion of young women in your town who have at least one of the most prevalent STDs.
We therefore have a 95% confidence level that the true percentage of young women infected with at least one of the most prevalent STDs in your community is between 12% and 28% based on the sample of 100 young women in your community. This indicates that there is a chance that the proportion could be either higher or lower than the 26% national estimate.
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on a roadway with eight 11 ft lanes (four in each direction), a horizontal curve is designed with a radius of 1176 ft, and a concrete wall is built at 70 ft from the center line, what is the sight distance for the driver?
The sight distance for the driver on the given road with the mentioned conditions is calculated to be approximately 860.8 ft.
To calculate the sight distance for the driver, we need to use the horizontal curve sight distance formula. The formula is:
SD = 2/3 × ((h + R)² / (2 × R - f))
Where:
SD = sight distance
h = height of driver's eye above the roadway surface (in feet)
R = radius of the curve (in feet)
f = distance from the driver's eye to the object or obstacle (in feet)
First, we need to determine the height of the driver's eye. A typical height for a driver's eye above the roadway surface is 3.5 feet. Therefore, we will assume that h = 3.5 ft.
Next, we need to determine f, which is the distance from the driver's eye to the concrete wall. Since the wall is located 70 feet from the center line of the roadway, we can determine f as follows:
f = (W / 2) + S
Where:
W = width of the roadway (in feet)
S = distance from the center line to the wall (in feet)
Substituting the given values, we get:
f = (8 × 11 / 2) + 70 = 114 ft
Now, we can plug in the values for h, R, and f into the sight distance formula:
SD = 2/3 × ((3.5 + 1176)² / (2 × 1176 - 114))
Simplifying the formula, we get:
SD ≈ 860.8 ft
Therefore, the sight distance for the driver on this roadway with a horizontal curve of radius 1176 ft and a concrete wall built at 70 ft from the center line is approximately 860.8 ft.
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For problems 8 and 9, find the length of the missing side of each right triangle. Round your
answers to the nearest tenth, if necessary. (2 points each)
Answer:
8. c ≈ 7,2 cm
9. b ≈ 6,7 in
Step-by-step explanation:
Use the Pythagorean theorem for each of these problems:
8.
[tex] {c}^{2} = {6}^{2} + {4}^{2} = 36 + 16 = 52[/tex]
[tex]c > 0[/tex]
[tex]c = \sqrt{52} ≈7.2[/tex]
.
9.
[tex] {b}^{2} = {7}^{2} - {2}^{2} = 49 - 4 = 45[/tex]
[tex]b > 0[/tex]
[tex]b = \sqrt{45} ≈6.7[/tex]
the height h (in feet) above the water of a cliff diver is modeled by h=-16t^2+10t+26 where t is time (in seconds). how long is the diver in the air?
Step-by-step explanation:
When the diver hits the water at Height = 0 , the diver is no longer in the air .
0 -16t^2 + 10t + 26 Use Quadratic Formula
a = -16 b = 10 c= 26
to find the positive value of t = 1.625 s
The points P(1. -2) and Q(7, 1) lie on the circumference of a circle. Show that the centre of the circle lies on the line 4x + 2y = 15
Answer:
Sure, I can help you with that geometry problem! To find the center of a circle given two points on its circumference, we need to find the perpendicular bisector of the line segment connecting those two points. Let's first find the midpoint of line segment PQ. Midpoint M = ( (1+7)/2 , (-2+1)/2 ) M = (4, -1/2) The slope of the line PQ is: Slope of PQ = (1-(-2)) / (7-1) Slope of PQ = 3/2 The slope of the perpendicular bisector of PQ is the negative reciprocal of the slope of PQ. Slope of perpendicular bisector = -2/3 Now we can find the equation of the perpendicular bisector of PQ in point-slope form using the midpoint M:
The radii of two cylinders are in the ratio of 4:5and their height are in the ratio 7:6 find the ratio of their lateral surface area
Answer:
Let the radii of two cylinders be 4x and 5x and their heights be 7y and 6y respectively. The lateral surface area of a cylinder is given by the formula 2πrh where r is the radius and h is the height. The lateral surface area of the first cylinder is 2π(4x)(7y) = 56πxy. The lateral surface area of the second cylinder is 2π(5x)(6y) = 60πxy. Therefore, the ratio of their lateral surface area is 56πxy : 60πxy which can be simplified to 14:15. Hence, the ratio of their lateral surface area is 14:15.
Ally needs 90 meters of tape for a project. Tape comes in different size rolls. If she bought 50 meters, 22.86 meters, and an 18.288-meter roll, how much tape will she have in all? ___________ meters
Ally will have 91.148 meters of tape in all if Ally needs 90 meters of tape for a project.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.
Ally needs a total of 90 meters of tape for her project. She bought three rolls of tape, one with 50 meters, another with 22.86 meters, and the last one with 18.288 meters. To find the total amount of tape she has, she needs to add the length of all three rolls together.
Adding the length of the first two rolls, we get:
50 meters + 22.86 meters = 72.86 meters
Then adding the length of the third roll to the sum above, we get:
72.86 meters + 18.288 meters = 91.148 meters
Therefore, Ally will have 91.148 meters of tape in all.
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the city of raleigh has 10600 registered voters. there are two candidates for city council in an upcoming election: brown and feliz. the day before the election, a telephone poll of 350 randomly selected registered voters was conducted. 135 said they'd vote for brown, 191 said they'd vote for feliz, and 24 were undecided. the target population for this survey is:
The target population for this survey is the registered voters in the city of Raleigh who are eligible to vote in the upcoming city council election.
The target population for a survey refers to the specific group of people that the survey is intended to represent or provide information about. In this case, the survey was conducted to gather information about the voting preferences of registered voters in the city of Raleigh for the upcoming city council election. Therefore, the target population for this survey would be the registered voters in the city of Raleigh who are eligible to vote in this election.
It's important to note that the target population is not the same as the sample population. The sample population refers to the group of people who actually participated in the survey, while the target population refers to the larger group of people that the sample population is intended to represent. In this case, the sample population was the 350 randomly selected registered voters who participated in the telephone poll.
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Please Help Me Answer These
Answer:
1) 100m^2 3) 96cm^2 4) 36 inches
Step-by-step explanation:
1) 10*10=100[tex]m^{2}[/tex]
2)
3) 12*8=96[tex]cm^{2}[/tex]
4)9*4=36 inches
Which equation is the inverse of y = 2x² - 8?
X+8
Oy=2
O y=
+√√√x+8
2
NIX
-8
Oy=+√√√2+8
y=±₁
O y-√x +4
An equation which is the inverse of y = 2x² - 8 include the following: B. [tex]y= \pm \sqrt{\frac{x+8}{2} }[/tex]
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
f(x) = y = 2x² - 8
x = 2y² - 8
2y² = x + 8
By dividing both sides of the equation by 2, we have the following:
y² = (x + 8)/2
By taking the square root of both sides of the equation, we have the following:
y = √[(x + 8)/2]
[tex]y= \pm \sqrt{\frac{x+8}{2} }[/tex]
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Which statement is true for the absolute values of points P and Q on the number line? Responses A |−8| ≤ 6|−8| ≤ 6 B |6| > |−8||6| > |−8| C |−8| > |6||−8| > |6| D |−8| < |6||−8| < |6| Question 2 Which absolute value statement is TRUE? Responses A |−6| > |−8||−6| > |−8| B |−10| < |−5||−10| < |−5| C |−8| < |3||−8| < |3| D |−9| > |−8||−9| > |−8|
For the given statements the correct answer is B |6| > |−8| and C |−8| < |3|.
What is statement?
In mathematics, a statement is a declarative sentence that is either true or false, but not both. Statements are often expressed using variables, symbols, or mathematical notation, and they can describe mathematical objects, relationships, properties, or operations.
For the first question, the correct response is:
B |6| > |−8|
This is true because the absolute value of a number is always positive, and it represents the distance of that number from zero on the number line. So, the absolute value of 6 is greater than the absolute value of -8, because 6 is further away from zero than -8 on the number line.
For the second question, the correct response is:
C |−8| < |3|
This is true because the absolute value of -8 is greater than the absolute value of 3. Absolute values tell us the distance from zero on the number line, and the distance between -8 and 0 is greater than the distance between 3 and 0.
Therefore for the given statements the correct answer is B |6| > |−8| and C |−8| < |3|.
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Puppy fencing comes in sizes thatal 12 feet, 24 feet, and 30 feet in length. Which length would be the best fort pen? How much, if any, will have to B cut off to fit the pen?
If you want a square pen with each side measuring 6 feet:
- Perimeter = 6 feet x 4 = 24 feet
- The best length would be 24 feet, as it exactly matches the perimeter.
- No fencing needs to be cut off in this case, as the chosen fencing length fits the pen perfectly.
To determine the best length for the puppy pen, you will first need to know the dimensions of the desired pen. Assuming the pen is a square, follow these steps:
1. Measure the length and width of the area you want to fence.
2. Calculate the perimeter of the pen by adding the lengths of all four sides (since it's a square, the length and width are equal, so just multiply one side by 4).
3. Compare the perimeter to the available fencing lengths (12 feet, 24 feet, and 30 feet).
4. Choose the fencing length that is closest to, but not less than, the calculated perimeter.
5. Calculate the excess length by subtracting the perimeter from the chosen fencing length. This is the amount that needs to be cut off.
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