The probability of incurring a loss when it rains is:P (loss | raining) = 80%So, there is a 20% chance that the food truck will not have incurred a loss when it rains.
The P (not raining | not loss) = 90% × 30% = 27%.Thus, the probability that it had not rained on that randomly selected day given that the food truck did not incur a loss is 27%.
The chance of not raining on a given day in Seattle can be calculated as follows:When it does not rain, there is a 10% probability that the food truck will incur a loss, as given in the statement. Similarly, when it rains, there is an 80% chance that the food truck will incur a loss on that day.
To calculate the probability that the food truck will not have incurred a loss on that day, we must first calculate the probability that the food truck will have incurred a loss on that day.Suppose the probability of rain is 70%, so the chance that it won't rain will be: P (not raining) = 100% - 70% = 30%When it rains, there is a 80% probability that the food truck will have incurred a loss, as given in the statement.
The probability of not incurring a loss when it does not rain is:P (not loss | not raining) = 100% - 10% = 90%The probability of not raining when the food truck does not incur a loss can be calculated as follows:P (not raining | not loss) = P (not loss | not raining) × P (not raining)P (not loss | not raining) = 90%P (not raining) = 30%
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2. Bucky walked 85 feet. His friend in Canada wanted to
know how many meters he walked.
Given that 1 foot = .3048 meter, how many meters
did Bucky walk?
The distance that Bucky walked is 25.908 meters
What is distance ?
Distance is a numerical measurement of how far apart two objects or points are in space. It is a scalar quantity, which means that it is defined only by its magnitude and not by its direction. Distance can be measured using various units, such as meters, feet, kilometers, miles, and so on, depending on the system of measurement being used.
Distance is an important concept in mathematics, physics, and other fields that deal with spatial relationships. It is often used to describe the length of a path traveled by an object or the separation between two objects in space.
According to the question:
To convert feet to meters, we can use the conversion factor 1 foot = 0.3048 meter.
The distance that Bucky walked is given as 85 feet. To find the distance in meters, we can multiply the number of feet by the conversion factor:
Distance in meters = 85 feet x 0.3048 meter/foot
Simplifying this expression, we get:
Distance in meters = 25.908 meters
Therefore, Bucky walked 25.908 meters.
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Label the measures of all of the angles on the picture
below.
Remember that, if you know one angle is 64°, you can use
this to help you figure out the measure of all of the other
angles.
Answer:
6, 2, and 3 would all also be 64° angles. 1, 4, 5, and 8 would all be 116° angles.
Step-by-step explanation:
Since 64° and 5 make up a supplementary angle (180°) just do the equation 180°-64° to get 116°. From there know that 64° and angle 6 must be equal (using the same logic from supplementary angles) then angles 2 and 3 must also be equal. Then apply that to angle 5 (which is 116°) and angle 8, as well as angles 1 and 4.
This thinking of a number, which he calls n. He finds of the number and then subtracts 5.
Write an expression to represent TJ's number.
000000
K
40
C
The expression to represent TJ's number is 1/3n - 3 and this can be determined by using the arithmetic operations and the given data.
What does a math equation mean?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
For instance, the equation 3x + 5 = 14 contains two expressions, 3x + 5 and 14, which are separated by the 'equal' sign. When two expressions are joined by an equal sign, a mathematical statement is called an equation.
The following steps can be used in order to determine the expression to represent TJ's number:
According to the given data, the number TJ's thinking about is 'n'.
Now, TJ's find 1/3 of the number 'n'. That is
= 1/3n
Now, he subtracts that number obtained in the above step by 3.
= 1/3n - 3
So, the expression to represent TJ's number is 1/3 n - 3.
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The complete question is -
TJ is thinking of a number which he calls n. he finds 1/3 of the number and then subtracts 5. write an expression to represent tj's number.
chris needs to mix a 20% alcohol solution with a 60% alcohol solution to create 200 millileters of a 52% solution. how many millileters of each solution must chris use?
In the word problem , Chris takes 40 ml of 20% alcohol and 160 ml of 60% alcohol.
What is percentage?
Divide the A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.
Let the volume of 20% solution be x
Then volume of 60% solution is 200 - x
Alcohol in 20% solution = 0.2*x = 0.2x
Alcohol in 60% sol = 0.6(200-x) = 120 - 0.6 x
If the final solution is of 52% concentration, it means the volume of alcohol in it
= 200*0.52 = 104 ml
So we have the equation
=> 0.2x + 120 -0.6x = 104
=> 120-104 = 0.4x
=> 0.4x = 16
=> x = 40 ml
So he takes 40 ml of 20% alcohol and 160 ml of 60% alcohol.
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What are the following is equal to the square root of 18 X to the seventh power Y to the sixth power
the answer to the question is 5.20XY cubed.
How to solve the problem?
The square root of 18 X to the seventh power Y to the sixth power can be simplified using the laws of exponents and radicals. First, we can express 18 as a product of its prime factors: 18 = 2 x 3 x 3. Then, we can write X to the seventh power as X to the sixth power times X, and Y to the sixth power as Y to the third power squared.
So, we have:
Square root of 18 X to the seventh power Y to the sixth power
= Square root of (2 x 3 x 3) X to the sixth power X Y to the third power squared
= Square root of 2 X to the sixth power Y to the third power squared times 3
= Square root of 2 X to the sixth power Y to the third power squared times square root of 3
Using the laws of exponents and radicals, we can simplify the square root of 2 X to the sixth power Y to the third power squared as X cubed Y cubed, and we can approximate the square root of 3 as 1.73. Therefore:
Square root of 18 X to the seventh power Y to the sixth power
= X cubed Y cubed times square root of 3
= 3XY cubed times 1.73
= 5.20XY cubed (rounded to two decimal places)
So, the answer to the question is 5.20XY cubed.
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Determine whether these lines are parallel, perpendicular, or neither. y = 3x -x-3y = 4
We can conclude that the lines are perpendicular, the slopes are negative reciprocals of each other,
What are the slopes?
To determine if the lines are parallel or perpendicular, we need to put both equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
y = 3x -x
-3y = -x + 4 (divide both sides by -3)
y = (1/3)x - (4/3)
Now we can see that the slope of the first equation is 3, and the slope of the second equation is (1/3). If two lines are perpendicular, their slopes are negative reciprocals of each other, meaning that one slope is the negative inverse of the other. The negative reciprocal of 3 is -1/3, and the negative reciprocal of 1/3 is -3. Since the slopes are negative reciprocals of each other, we can conclude that the lines are perpendicular.
The slope of a line can be positive, negative, zero or undefined. A positive slope indicates that the line is slanting upward from left to right, while a negative slope indicates that the line is slanting downward from left to right. A slope of zero indicates that the line is horizontal, while an undefined slope indicates that the line is vertical.
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Please show working out
the area of the first sector piece is approximately 42.4115 square . and area of the second sector piece is approximately 149.03 cm².centimeters.
what is area of circle?
The area of a circle is given by the formula,where A is the area of the circle, r is the radius of the circle, and π (pi) is a mathematical constant that is approximately equal to 3.14159.In words, the area of a circle is equal to pi times the square of its radius.
In the given question,
The area of a sector of a circle is given by the formula:
A = (θ/360) * πr²
where:
θ is the angle at the center of the circle (in degrees)
r is the radius of the circle
π is the mathematical constant pi (approximately equal to 3.14)
In this case, the angle at the vertex of the sector piece is 60 degrees, and the radius is 9 cm. Therefore, the area of the sector piece is:
A = (60/360) * π * 9²
A = (1/6) * π * 81
A = 13.5π
A ≈ 42.4115 cm²
So the area of the sector piece is approximately 42.4115 square centimeters
A = π(8.4 cm)²
A = 221.76 cm²
Next, we need to find the fraction of the circle that corresponds to the given angle. The total angle of a circle is 360 degrees, so the fraction of the circle that corresponds to an angle θ in degrees is:
f = θ/360
Plugging in the given angle of 242 degrees, we have:
f = 242/360
f = 0.6722
So the area of the sector piece is:
A_sector = f * A
A_sector = 0.6722 * 221.76 cm²
A_sector = 149.03 cm²
Therefore, the area of the sector piece is approximately 149.03 cm².
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The area of the sector of for the given radius is 1. 42.4 cm² and 2. 152.9 cm².
What is sector of a circle?A sector of a circle is an area that is bounded by two circle radii and the arc that runs between them. The length of the arc is proportional to the circumference of the circle, and the angle formed by the radii is known as the sector's central angle. The formula A = (θ/360)πr² may be used to determine the area of a sector, where r denotes the radius of the circle, denotes the constant pi, and denotes the central angle in degrees.
The area of a sector can be calculated using the formula:
A = (θ/360)πr²
1. For r = 9 and theta = 60 we have:
A = (60/360)π(9)² ≈ 42.4 cm²
2. For r = 8.4 and theta = 242 we have:
A = (242/360)π(8.4)² ≈ 152.9 cm²
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What is 2. 314 repeating as a fraction in simplest form
Carmen is trying to choose between two bike rental companies where h
is the number of hours rented and y
is the cost, in dollars. Company A charges a $30
fee and $2
for each hour rented, which can be represented by the equation y=2h + 30
. Company B charges a $10
fee and $4
for each hour rented, which can be represented by the equation y = 4h + 10
.
Carmen is comparing two bike rental companies, A and B. Company A charges a flat rate fee of $30 and $2 per hour, while company B charges a flat rate fee of $10 and $4 per hour.
Carmen can use mathematical equations to compare the costs of the two companies and make an informed decision.
The equation for the cost of renting from Company A is y=2h+30, where y represents the total cost in dollars and h represents the number of hours rented. The equation for the cost of renting from Company B is y=4h+10, where y represents the total cost in dollars and h represents the number of hours rented.
To compare the cost of renting from Company A and Company B for a specific number of hours, Carmen can substitute the value of h into each equation and solve for y. For example, if Carmen plans to rent a bike for 5 hours, the cost of renting from Company A would be y=2(5)+30=$40, and the cost of renting from Company B would be y=4(5)+10=$30. In this case, renting from Company B would be the more cost-effective option.
Carmen can also use algebraic methods to determine the break-even point, or the point at which the cost of renting from Company A is the same as the cost of renting from Company B. To find the break-even point, Carmen can set the two equations equal to each other and solve for h:
2h+30=4h+10
2h=20
h=10
This means that if Carmen plans to rent a bike for 10 hours or less, it would be more cost-effective to rent from Company B. If she plans to rent a bike for more than 10 hours, it would be more cost-effective to rent from Company A.
Another method of comparing the two companies is to graph the two equations on the same coordinate plane. The x-axis can represent the number of hours rented (h), and the y-axis can represent the total cost in dollars (y). Carmen can plot the two equations and visually compare the graphs to determine which company is more cost-effective for a specific number of hours rented.
In summary, Carmen can use mathematical equations, algebraic methods, and graphing to compare the costs of renting from Company A and Company B based on the number of hours rented. By comparing the costs, she can make an informed decision about which company to rent from based on her budget and the duration of the rental period.
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What is the decimal expansion of the following fraction?
1/22
A.0.045
B.0.22
C.1.22
D.0.045
The answer is either A or D, 0.045
Lucy recently asked the servers at her restaurant to only give straws to customers who request them. she thinks that about half of the customers will ask for straws but hopes that the rate will be less than half. she randomly selects 100 customers and finds that 43 of them ask for a straw. to determine if these data provide convincing evidence that the proportion of customers who will ask for a straw is less than 50%, 150 trials of a simulation are conducted. lucy is testing the hypotheses: h0: p = 50% and ha: p < 50%, where p = the true proportion of customers who will ask for a straw. based on the results of the simulation, what is the estimate of the p-value of the test? a. 0.0333 b. 0.05 c. 0.0733
d. 0.11
Answer:
Because the P-value of 0.0733 > , Lucy should fail to reject H0. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%.
A yard cleanup service charges a $365 fee plus $14.75 per hour. Another cleanup service charges a $250 fee plus $20.50 per hour. How long is a job for which the two companies' costs are the same?
Answer:
20 hours
Step-by-step explanation:
[tex]\text{x} = \text{number of hours}[/tex]
A yard cleanup service charges a $365 fee plus $14.75 per hour.
[tex]365 + 14.75x[/tex]
Another cleanup service charges a $250 fee plus $20.50 per hour.
[tex]250 + 20.50x[/tex]
How long is a job for which the two companies' costs are the same?
[tex]365 + 14.75x = 250 + 20.50x[/tex]
[tex]365 - 250 = 20.50x - 14.75x[/tex]
[tex]115 = 5.75x[/tex]
x = 20
The relationship between the amount of time a car is parked, in hours, and the cost of parking, in dollars, can be described with a function. a. Identify the independent variable and the dependent variable in this function. b. Describe the function with a sentence of the form "________________ is a function of ________________." c. Suppose it costs $3 per hour to park, with a maximum cost of $12. Sketch a possible graph of the function. Be sure to label the axes.
a. The independent variable in this function is the amount of time a car is parked, measured in hours. The dependent variable is the cost of parking, measured in dollars.
b. "The cost of parking is a function of the amount of time a car is parked."
c. Here is a possible graph of the function:
^
|
$12 +--------/-----
| /
| /
| /
$3 o
|
|
|
+--------------->
Time
In this graph, the vertical axis represents the cost of parking in dollars, and the horizontal axis represents the amount of time a car is parked in hours. The graph shows a linear relationship between the two variables, with a slope of $3 per hour, up to a maximum cost of $12. This means that the cost of parking increases by $3 for each additional hour of parking, up to a maximum cost of $12.
what is the probability he gets exactly one rose given that at least one of the flowers he gets is pink
The probability that he gets exactly one rose given that at least one of the flowers he gets is pink is 4/7.
To calculate the probability that he gets exactly one rose given that at least one of the flowers he gets is pink, we need to use conditional probability. Let R be the event that he gets a rose and P be the event that he gets a pink flower. Then, we want to find P(R=1 | P≥1).
Using Bayes' theorem, we have:
P(R=1 | P≥1) = P(R=1 and P≥1) / P(P≥1)
We can calculate the probability of getting at least one pink flower as:
P(P≥1) = 1 - P(P=0)
Assuming the probabilities of getting a rose and a pink flower are independent, we can calculate the probabilities of getting exactly one rose and at least one pink flower as:
P(R=1 and P≥1) = P(R=1) * P(P≥1) = (2/5) * (1 - 3/5) = 2/5 * 2/5 = 4/25
P(P=0) = 3/5, since there are 3 flowers that are not pink out of a total of 5.
Therefore, we have:
P(R=1 | P≥1) = (4/25) / (1 - 3/5) = 4/7
So the probability that he gets exactly one rose given that at least one of the flowers he gets is pink is 4/7.
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A button machine produces one button in 0. 15 seconds. How many buttons are produced in 48. 6 seconds?
Answer: 324
Step-by-step explanation:
Ratio--> 1/0.15=x/48.6
Do the butterfly method of multiplying
0.15x=48.6
Divide by 0.15 on both sides
48.6/0.15=324
Please help I’m a bit stuck!!
Step-by-step explanation:
From n=1, to n=4, plug this in the sigma notation
The first four terms of this series are
-4,-8/3,-16/9,-32/27
b. Since -1<r<1, the series diverge
c. The sum of an infinite geometric series is equal to
[tex] \frac{a}{1 - r} [/tex]
Where a is the initial value and r is the rate
a=-4
r =2/3
[tex] \frac{ - 4}{1 - \frac{2}{3} } = \frac{ - 4}{ \frac{1}{3} } = - 12[/tex]
B CLEVELAND CAVALIERS LA CLIPPERS H 73 75 H 77 79 81 HEIGHT IN INCHES + + 83 85 #1: The LA Clippers have a greater variability of heights than the Cleveland Cavaliers. #2: The shortest team member is 76 inches. #3: The second quartile of the LA Clippers is equal to the second quartile of the Cleveland Cavaliers. #4: The median of the LA Clippers is approximately 80 inches. OManeuvering the Middle LLC, 2016
The given information can be summarized as follows:
Team: Cleveland Cavaliers
Height (in inches): 73, 75, 77, 79, 81
Range: 81 - 73 = 8
IQR: Q3 - Q1 = 81 - 75 = 6
Median: 79
Team: LA Clippers
Height (in inches): 76, 80, 83, 85
Range: 85 - 76 = 9
IQR: Q3 - Q1 = 85 - 80 = 5
Median: 81.5 (average of 80 and 83)
Using this information, we can evaluate the given statements:
#1: The LA Clippers have a greater variability of heights than the Cleveland Cavaliers.
This statement is true. The range of the LA Clippers' heights (9) is greater than the range of the Cleveland Cavaliers' heights (8).
#2: The shortest team member is 76 inches.
This statement is true. The LA Clippers have a player with a height of 76 inches, which is shorter than any player on the Cleveland Cavaliers.
#3: The second quartile of the LA Clippers is equal to the second quartile of the Cleveland Cavaliers.
This statement is false. The second quartile (or median) of the LA Clippers (81.5) is higher than the second quartile (or median) of the Cleveland Cavaliers (79).
#4: The median of the LA Clippers is approximately 80 inches.
This statement is true. The median of the LA Clippers is 81.5, which rounds to approximately 80 inches.
Given amplitude 5, period of pi and a vertical shift of 2, write a sine equation.
So, the final equation for the sine function is:
[tex]y = 5 sin(2x - \pi /2) + 2[/tex].
How to write general trigonometry equation?The general form of a trigonometric equation can vary depending on which trigonometric function is being used (sine, cosine, tangent, etc.), but the most general form is:
[tex]f(x) = A sin(Bx + C) + D[/tex]
where f(x) is the trigonometric function, A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift. The phase shift and vertical shift are optional components and may not always be present in a trigonometric equation.
If using cosine instead of sine, the equation would be:
[tex]f(x) = A cos(Bx + C) + D[/tex]
If using tangent, the equation would be:
[tex]f(x) = A tan(Bx + C) + D[/tex]
Other trigonometric functions, such as secant, cosecant, and cotangent, can also be used in trigonometric equations, but the general form would follow the same structure as above.
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Eric is going to flip a coin 2 times. what is the fractional probability that it will be one head and one tail (in any order)?
Answer:
2/4=1/2
Step-by-step explanation:
The height of an arrow shot
into the air can be represented
by the equation
h = -16t² + vt + h0
Where t is time in seconds and h = height in feet
The arrow is shot into the air with an initial
velocity of 112 feet per second by someone
that is holding the bow 5 feet off the ground.
What is the maximum height of the arrow?
Answer: The height of the arrow shot into the air can be represented by the equation:
h = -16t² + vt + h0
where t is the time in seconds, h is the height in feet, v is the initial velocity in feet per second, and h0 is the initial height in feet.
In this problem, the arrow is shot into the air with an initial velocity of 112 feet per second, and the bow is held 5 feet off the ground. Therefore, we have:
v = 112
h0 = 5
To find the maximum height of the arrow, we need to find the vertex of the parabolic function given by the equation. The vertex of a parabola of the form y = ax² + bx + c is given by the point (-b/2a, c - b²/4a).
In our case, the equation of the parabola is h = -16t² + 112t + 5. So we have:
a = -16
b = 112
c = 5
The t-value of the vertex is given by -b/2a. Therefore, we have:
t = -b/2a = -112/(2*(-16)) = 3.5
To find the maximum height, we substitute t = 3.5 into the equation:
h = -16t² + 112t + 5 = -16(3.5)² + 112(3.5) + 5 = 196
Therefore, the maximum height of the arrow is 196 feet.
Step-by-step explanation:
How will changes in the base pairs affect the structure of DNA?
changes in the base pairs can alter the overall shape of the DNA molecule, disrupt specific interactions between different regions of the DNA, and potentially affect the normal functioning of the DNA.
The structure of DNA is determined by the sequence of its base pairs. There are four types of base pairs in DNA: adenine (A), thymine (T), guanine (G), and cytosine (C). The base pairs form the rungs of the DNA ladder, with the backbone consisting of sugar and phosphate groups.
The sequence of base pairs determines the overall shape of the DNA molecule. The base pairs are held together by hydrogen bonds, which are relatively weak but collectively provide enough stability to maintain the double helix structure of DNA. The sequence of base pairs also determines the specific interactions between different regions of the DNA molecule, such as the interaction between the two complementary strands.
Changes in the base pairs can have a significant impact on the structure of DNA. For example, a substitution of one base pair for another can result in a different hydrogen bonding pattern, which can affect the stability of the double helix. This can result in a change in the shape of the DNA molecule, and can also affect the specific interactions between different regions of the DNA.
Insertions or deletions of base pairs can also have a significant impact on the structure of DNA. These types of mutations can disrupt the regular spacing of base pairs along the DNA molecule, which can cause kinks or bends in the DNA. This can also affect the specific interactions between different regions of the DNA, and can potentially interfere with the normal functioning of the DNA molecule.
In general, changes in the base pairs can alter the overall shape of the DNA molecule, disrupt specific interactions between different regions of the DNA, and potentially affect the normal functioning of the DNA.
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suppose the following table is gathered for a new study investigating childhood asthma.
Age at Interview Asthma? 0=No 1=Yes
18 0
16 0
16 1
17 1
14 1
13 1
15 0
16 1
19 1
12 0
16 0
13 1
13 1
18 1
13 0
what is the average age at interview?
The average age of the interviewees in the study investigating childhood asthma is 15.2 years.
To find the average age at the interview, you need to follow these steps. Here's how you can calculate it:
First, add up all the ages of the interviewees:18 + 16 + 16 + 17 + 14 + 13 + 15 + 16 + 19 + 12 + 16 + 13 + 13 + 18 + 13 = 228Next, count the total number of interviewees in the study:
15 interviewees
Finally, divide the sum of ages by the number of interviewees: 228 ÷ 15 = 15.2
Therefore, the average age calculated in the study while investigating childhood asthma is approximately 15.2 years.
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Help with number 2 please
Answer:
7 cm
Step-by-step explanation:
You want the edge length of a cube whose space diagonal is 7√3 cm.
Face diagonalThe square of the face diagonal of a cube of edge length s is ...
d² = s² +s² = 2s²
Space diagonalThe square of the space diagonal is found by applying the Pythagorean theorem again. The space diagonal is the hypotenuse of a right triangle whose legs are one cube edge and the face diagonal.
D² = s² +d² = s² +2s² = 3s²
D = √(3s²) = s√3
So, we want to find s when D = 7√3:
s√3 = 7√3
s = 7
The edge length of the cube is 7 cm.
Solve It:
2 step equation:
Mr. Nelson is taking his students on a field trip to an observatory. The Observatory charges a $100 trip fee, plus $6.50 per student. If Mr. Nelson spent $327.50, how many students did he take on the trip?
Answer: 35
Step-by-step explanation:
Let's assume that Mr. Nelson took "x" students on the trip.
According to the problem, the observatory charges a trip fee of $100, which Mr. Nelson had to pay regardless of how many students he took.
In addition to that, he also had to pay $6.50 per student. So the total cost of the trip can be expressed as:
Total cost = $100 + ($6.50 * number of students)
We know from the problem that the total cost of the trip was $327.50. So we can set up an equation:
$327.50 = $100 + ($6.50 * x)
Now we can solve for "x" by first subtracting $100 from both sides:
$327.50 - $100 = $6.50x
$227.50 = $6.50x
Finally, we can solve for "x" by dividing both sides by $6.50:
x = $227.50 ÷ $6.50
x ≈ 35
Therefore, Mr. Nelson took approximately 35 students on the field trip.
Simplify (5/2x -16/5)-(-35/3x1/7x21)
Answer:
Before we can simplify this expression, we need to first find a common denominator for all the fractions. The prime factorization of the denominators is:
2 × 5
3 × 7 × x
Therefore, a common denominator is:
2 × 5 × 3 × 7 × x = 210x
Using this common denominator, we can rewrite the expression as:
[(5 × 21) / (2 × 5 × x) - (16 × 42) / (5 × 2 × 21 × x)] - [(-35) / (3 × x × 7 × 21)]
Simplifying each fraction, we get:
[105 / (10x) - 672 / (210x)] - [-5 / (3 × 7 × x × 21)]
Combining the two fractions and simplifying, we get:
[105 - 672] / (10x) + [5 / (3 × 7 × x × 21)]
= -567 / (10x) + 1 / (3 × 7 × x)
= (-567 × 21 + 10) / (210x)
= -11897 / (210x)
Therefore, the simplified expression is:
-11897 / (210x)
Write an equivalent expression in word form for 3/8x(1-1/3)
Answer:
1/4x
Step-by-step explanation:
1-1/3=3/3-1/3=2/3
3/8x(2/3)
6/24x
then simplify
1/4x
if 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie in
If 1,000 points are selected randomly inside the square with all points equally likely to be selected, points to lie inside the circle is 785.4 points.
We can find the answer by finding the ratio of the areas of the regions and then multiplying by the total number of points.
The square has an area of 1 (since it has sides of length 1).
The circle has a radius of 1/2 and an area of pi/4.
So the ratio of the areas is:
(π/4) / 1 = π/4
Therefore, we would expect:
(π/4) * 1000 = ( 3.14 / 4 ) 1000
(π/4) * 1000 = 1000 × ( 0.785 ) = 785 points
points to lie inside the circle. This is approximately 785 points.
Your question is incomplete but mos probably your full question was
If 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie inside the circle?
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An investment company is offering you two different policies.
a. Invest $1000, and it will grow by 10% per year.
b. Invest $3000, and it will grow by $150 per year.
Which investment is worth more after 1 year? Explain how
Investment a grows faster than investment b, and thus investment b is the better choice.
We can calculate the worth of each investment after 1 year by applying the given rates of growth.
a. For investment a, the initial investment of $1000 grows by 10% per year. Therefore, the worth of the investment after 1 year is:
1000 + 0.1*1000 = $1100
b. For investment b, the initial investment of $3000 grows by $150 per year. Therefore, the worth of the investment after 1 year is:
3000 + 150 = $3150
Comparing the two worths, we see that investment b worth more after 1 year, since $3150 is greater than $1100. Therefore, investment b is the better choice.
Alternatively, we can also calculate the growth rates of each investment and compare them directly. For investment a, the growth rate is 10% = 0.1, whereas for investment b, the growth rate is 150/3000 = 0.05 or 5%. Since 0.1 > 0.05, we can again conclude that investment a grows faster than investment b, and thus investment b is the better choice.
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1. This composite figure is created by placing a sector of a circle on a triangle. What is the area of this composite figure? Use 3.14 for . Round to the nearest hundredth. Show your work. Accessibility: Investigate 82% 10 cm 6 cm 8 cm. please ill be thankful and it needs the show your work but make it understandable please
So, the area of the composite figure is 96.57 square centimeters.
What is area?In geometry, area refers to the measure of the size of a two-dimensional surface or region. It is typically expressed in square units, such as square meters, square feet, or square centimeters.
To find the area of a shape, you need to measure the length and width of the shape and then multiply those measurements together. The formula for calculating the area of a rectangle, for example, is length x width. The formula for calculating the area of a circle is pi x radius squared, where pi is a mathematical constant, and the radius is the distance from the center of the circle to its edge.
by the question.
sure, I can help you with that!
To find the area of the composite figure, we need to find the area of each individual shape and then add them up.
First, let's find the area of the sector of the circle. We know that the radius of the circle is 6 cm, and the central angle of the sector is 82% of a full circle. Since a full circle has 360 degrees, we can find the central angle of the sector by multiplying 360 by 0.82:
[tex]Central angle of sector = 360 x 0.82 = 295.2 degrees[/tex]
The area of the sector can be found using the formula:
Area of sector = (central angle/360) x π x radius^2
Substituting the values, we know:
[tex]Area of sector = (295.2/360) x 3.14 x 6^2 = 56.57 cm^2[/tex]
Next, let's find the area of the triangle. We know that the base of the triangle is 8 cm, and the height is 10 cm. We can use the formula for the area of a triangle:
[tex]Area of triangle = 1/2 x base x height[/tex]
Substituting the values, we know:
[tex]Area of triangle = 1/2 x 8 x 10 = 40 cm^2[/tex]
Now, we can add the areas of the sector and the triangle to find the total area of the composite figure:
Total area = area of sector + area of triangle
[tex]Total area = 56.57 + 40 = 96.57 cm^2[/tex]
Rounding this to the nearest hundredth, we get:
[tex]Total area =96.57 cm^2[/tex]
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A floor is made up of parallelogram shaped tiles that each have a base length of 8.5 inches and a height of 3.5 inches what is the area of each tile ok in square inches
Answer:
The area of a parallelogram is given by the formula A = b × h, where b is the base length and h is the height. So, for each tile, the area is:A = 8.5 inches × 3.5 inches = 29.75 square inchesTherefore, the area of each tile is 29.75 square inches.
Step-by-step explanation: