The new variance is 0.35.
The variance of a random variable measures how spread out the values are from the mean.
The formula for the variance is Var(X) = E[(X - E[X])²], where E[X] is the expected value (or mean) of X.
If the price of a box of Cheerios Oat Crunch increases by 25 cents, the new mean cost would be $4.25. To find the new variance, we can use the formula Var(aX + b) = a²Var(X), where a is a constant and b is a constant. In this case, a = 1 (because we are not changing the units of measurement) and b = 0.25 (because we are adding 25 cents to the price).
Therefore, the new variance is Var(X + 0.25) = Var(X) = Var(X) x 1² = Var(X) = 0.35.
This means that the variance remains the same even though the price has increased. This is because the variance is a measure of how spread out the values are from the mean, and the mean has shifted by the same amount as the price increase. Therefore, the distance between the values and the new mean is the same as the distance between the values and the old mean, so the spread is unchanged.
The variance is a measure of how spread out a set of data is from its mean. It is calculated as the average of the squared differences between each value and the mean. The formula for variance is Var(X) = E[(X - E(X))²], where E is the expected value or mean of X.
In this case, we are given that the mean cost of a box of Cheerios Oat Crunch is $4.00 and the variance is 0.35. This means that the average squared difference between each box's cost and the mean cost is 0.35.
Now, if the price of each box increases by 25 cents, this means that the new mean cost will be $4.25. However, this does not affect the variance directly. This is because the variance only measures how spread out the data is from the mean, and the mean has shifted by the same amount as the price increase.
To see this more clearly, imagine a set of data that has a mean of 4 and a variance of 0.35. If we add 0.25 to each value, we get a new set of data that has a mean of 4.25. However, the spread of the data is still the same; that is, the distance between each value and the new mean is the same as the distance between each value and the old mean. Therefore, the variance remains the same even though the price has increased.
In summary, the variance measures how spread out a set of data is from its mean, and a shift in the mean does not affect the variance directly.
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The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?
the vertex of the quadratic function is (7.5, 3.675).
Company revenue quadratic function.
Angel
The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?
To find the quadratic function that represents the revenue of the company as a function of the number of years since 2002, we can use the vertex form of a quadratic function:
r(x) = a(x - h)^2 + k
where a is the coefficient of the quadratic term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.
We can use the given revenue values to set up a system of three equations:
2.7 = a(0 - h)^2 + k
3.4 = a(1 - h)^2 + k
2.7 = a(6 - h)^2 + k
Subtracting the first equation from the second, and the first equation from the third, we get:
0.7 = a(1 - h)^2
0 = a(6 - h)^2
Since a cannot be zero (otherwise we wouldn't have a quadratic function), we can divide the second equation by the first to get:
6 - h = 10
which gives us h = -4.
Substituting h = -4 into the first equation, we get:
2.7 = a(0 - (-4))^2 + k
2.7 = 16a + k
Substituting the revenue value for 2005, we get:
3.9 = a(3 - (-4))^2 + k
3.9 = 49a + k
Solving for a and k, we get:
a = -0.1
k = 4.3
Therefore, the quadratic function that represents the revenue of the company as a function of the number of years since 2002 is:
r(x) = -0.1(x + 4)^2 + 4.3
The vertex of this function is at (-4, 4.3).
A survey showed that 45% of a travel company's customers were planning an overseas vacation
the following year. Predict how many of the travel company's 13,400 travelers will vacation overseas
the following year.
Answer: 6030 travelers
Step-by-step explanation:
= .45(13,400)
= 6030
NEED BY MONDAY PLEASE!!! Select all the true equations:
what is the measurement of the unknown angle?
The measure of the unknown angle is 93°
What is the measurement of the unknown angle?First we should get the interior angles of the triangle in the right side.
The angle in the left side is given by:
x + 127° = 180°
x = 180° - 127°
x = 53°
While the angle in the right side is:
y + 146° = 180°
y = 180° - 146°
y = 34°
Now remember that the sum of the interior angles of a triangle must be 180°, then if the angle at the top is z we can write:
z + 34° + 53° = 180°
z = 180° - 34° - 53°
z = 93°
And this angle is a vertical angle of the one we want to find, so the measure of the unknown angle is also 93°.
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Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.
Card A 2 3 4 5 6 7 8 9 10 J Q K
Frequency 4 7 5 6 7 6 8 10 7 10 8 12 10
Based on the table, what is the experimental probability that the card selected was a K or 6?
one over 26
four over 25
one fourth
8 over 13
The experimental prοbability that the card selected was a K οr 6 is 13/100, which is equivalent tο 0.13 οr 13%.
What is the prοbability?The study οf prοbability examines the likelihοοds οf results οccurring and is based οn the ratiο οf likely and imprοbable scenariοs.
Tο find the experimental prοbability οf drawing a K οr 6, we need tο add the frequencies οf card K and card 6 and divide by the tοtal number οf draws:
Frequency οf K οr 6 = 7 + 6 = 13
Tοtal number οf draws = 4 + 7 + 5 + 6 + 7 + 6 + 8 + 10 + 7 + 10 + 8 + 12 + 10 = 100
Experimental prοbability οf drawing a K οr 6 = Frequency οf K οr 6 / Tοtal number οf draws = 13 / 100
Hence, the experimental prοbability that the card selected was a K οr 6 is 13/100, which is equivalent tο 0.13 οr 13%.
Answer: 8 οver 13 is the clοsest οptiοn tο 13/100, sο the answer is 8 οver 13.
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Suppose there is a 70% chance that Reagan will make a field goal at any given time. A computer was used to generate 10 sets of random numbers from 1 to 10, 1-7 represent a successful field goal and numbers 8-10 represent a missed field goal. The results are shown. Trial 1 2 3 4 5 6 7 8 9 10 Numbers Generated 1, 9, 1, 2, 10, 6, 5, 2, 7,2 8, 10, 4, 10, 2, 2, 3, 6, 7, 10 6, 9, 9, 10, 4, 10, 10, 2, 6, 6 8 & 2, 3, 4, 6, 5, 6, 5, 3 1, 10, 1, 2, 5, 6, 9, 4, 10, 3 7, 1, 9, 1, 6, 3, 3, 7, 5, 6 2, 5, 2, 7, 5, 5, 10, 5, 6, 3 9, 6, 10, 4, 9, 6, 8, 9, 9,9 5, 1, 4, 5, 2, 8, 5, 7, 5, 6 7, 6, 5, 5, 1, 10, 9, 3, 9, 2 Find the experimental probability that Reagan will miss the first two field goals and make the third one.
The experimental probability that Reagan will miss the first two field goals and make the third one is 20%
What is experimental probability?Experimental is the probability is the probability of an event occurring based on the performance of actual experiment.
The probability of making or missing a field goal is 0.7 and 0.3 respectively. The probability that Reagan will miss the first two field goals and make the third one, can be obtained from the result by counting the number of times the specific sequence of results occurs in the 10 sets of random numbers and divide by the total number of trials.
The analysis of the sets of numbers indicates that the specific sequence of missing the first two field goals and making the third one occurs twice in 2nd and 4th trials
2; 8, 10, 4, 10, 2, 2, 3, 6, 7, 10
4; 8, 8, 2, 3, 4, 6, 5, 6, 5, 3
Therefore, the experimental probability of the specific sequence occurring is 2/10 = 1/5 (since there are 10 sets of numbers in total)
Theoretically, the probability of making and missing field goals for the three kicks in the sequence are;
0.3 × 0.3 × 0.7 = 0.063
Therefore, the experimental probability of Reagan missing the first two field goals and making the third one is approximately 0.2 (or 20%), while the theoretical probability is 0.063 (or 6.3%)
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0.81 x 9.4 work sown
Can someone please help me with this question
The line of best fits that predicts the maximum temperature at this resort is the line that cuts across 2, 3, 5, 6, and 8 hours at 22°C.
The reliability of this estimate is the fact that the line of best fit goes through five data points.
What describes a line of best fits?A line of best fit is a straight line that is used to represent the general trend of a scatter plot of data points. It is also called a regression line. The line of best fit is usually determined using a mathematical method called linear regression, which minimizes the distance between the line and the data points.
The line of best fit can be used to make predictions about data that is not yet collected or to make estimates about the relationship between the variables represented in the scatter plot.
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Image transcribed:
This scatter graph shows the daily hours of sunshine and the daily maximum temperature at 10 seaside resorts in England one day last summer.
(a) Another resort had 10 hours of sunshine each day. Use a line of best fit to predict the maximum temperature at this resort.
(2 marks)
(b) Comment on the reliability of your estimate.
(1 mark)
((2. 88 × 4. 02) + (7. 56 × 3. 13)) ÷ 5. 79 = Answer
On simplifying the given equation ((2. 88 × 4. 02) + (7. 56 × 3. 13)) ÷ 5. 79 by PEMDAS, we get 6.087 as the answer.
The order of operations that must be followed in order to solve this statement is known as the PEMDAS acronym (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
((2. 88 × 4. 02) + (7. 56 × 3. 13)) ÷ 5. 79
(11.5776) + (23.6928 ) ÷ 5. 79
35.2704 ÷ 5.79
≈ 6.087
Therefore, the answer for ((2. 88 × 4. 02) + (7. 56 × 3. 13)) ÷ 5. 79 ≈ 6.087
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What is the value of f?
Answer:
f = 120
Step-by-step explanation:
1. The Entire line in which the angles rest on = 180 degrees.
2. 180-60 = 120
3. 120 Degrees is your answer
The perimeter of a right angled triangle is 96cm
The lengths of its sides are in the ratio 6:8:10
Work out the area of the triangle in cm^2
Answer:
384 cm^2
Step-by-step explanation:
Let the lengths of the sides of the right-angled triangle be 6x, 8x, and 10x, where x is a constant.
Since the perimeter of the triangle is 96 cm, we have:
6x + 8x + 10x = 96
24x = 96
x = 4
Therefore, the lengths of the sides of the triangle are 24 cm, 32 cm, and 40 cm.
The area of a right-angled triangle is given by the formula:
Area = (1/2) * base * height
where the base and height are the two shorter sides of the triangle.
Using the Pythagorean theorem, we can determine that the base and height of the triangle are 24 cm and 32 cm, respectively.
Therefore, the area of the triangle is:
Area = (1/2) * base * height
Area = (1/2) * 24 cm * 32 cm
Area = 384 cm^2
Therefore, the area of the right-angled triangle is 384 cm^2.
Number of large boxes:
Number of small boxes:
a system of linear...
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 55 pounds each, and the small boxes weigh 25 pounds each. There
are 135 boxes in all. If the truck is carrying a total of 5475 pounds in boxes, how many of each type of box is it carrying?
If a delivery truck is transporting boxes of two sizes: large and small. there are 70 large boxes and 65 small boxes in the truck.
How many of each type of box is it carrying?Let's assume that x represents the number of large boxes, and y represents the number of small boxes.
We know that there are 135 boxes in total, so:
x + y = 135
We also know that the total weight of the boxes is 5475 pounds, so:
55x + 25y = 5475
Now we have a system of linear equations with two variables. We can use substitution or elimination to solve for x and y. Let's use substitution:
From the first equation, we can solve for x in terms of y:
x = 135 - y
Substitute this expression for x into the second equation:
55x + 25y = 5475
55(135 - y) + 25y = 5475
Simplify and solve for y:
7425 - 55y + 25y = 5475
30y = 1950
y = 65
Now we can use the first equation to solve for x:
x + y = 135
x + 65 = 135
x = 70
Therefore, there are 70 large boxes and 65 small boxes in the truck.
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As part of a manufacturing process for widgets, an quality controller at ACME Corporation randomly samples 856 widgets during a day of production to test the current rate of defective widgets. The controller finds 34 defective widgets.The historical rate of defective widgets produced by ACME Corporation was 7%. Approximately, how many standard deviations is the point estimate from 7%?
The historical rate of defective widgets produced by ACME Corporation was 7%. Approximately, 91.2 is the standard deviations is the point estimate from 7%.
In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values. A low standard deviation indicates that the values tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values are spread over a wider range.
The standard deviation can be abbreviated SD, and is most commonly used in mathematical texts and equations with the lowercase Greek letter σ (sigma) for the population standard deviation, or the Latin letter s for the standard deviation of the sample.
The standard deviation of a random variable, sample, population, data set, or probability distribution is the square root of its variance. It is algebraically simpler than the mean absolute deviation, although less robust in practice. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data.
According to the Question:
Given that:
Defective widgets produced by ACME corporation was 7%
Total sample was 856 widgets.
Therefore, the Standard Deviation estimates from 7% is:
856 of 7% = 91.2
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circumference
Calculate the
of a pie that has a 12 inch
diameter.
Answer:
12pi
Step-by-step explanation:
circumfrence : 2*pi*r
the radius is found by dividing the diameter in half so, 12/2 or 6
now multiply 6 with 2 and pi and you get 12pi
~lmk if you got Qs
kathy needs money for her trip to europe. if she has us dollars in the bank but wants to withdraw half of it in british pounds and half of it in euros, how many more euros than pounds will she have? assume pound is equal to usd and euro is equal to usd, and round to the nearest whole number.
The difference between the amount of money she will have in Euros and the amount she will have in British pounds will be zero.
Kathy needs to exchange half of her US dollars into British pounds and half of her US dollars into euros. Since it is given that pound is equal to USD and euro is also equal to USD, when she withdraws half of her US dollars as British pounds and half of it as euros, she will have the same amount of pounds and euros. Thus, the difference between the amount of money she will have in Euros and the amount she will have in British pounds will be zero. Therefore, she will have the same amount of money in both currencies, and the answer to the question is 0 (rounded to the nearest whole number).
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according to A1 Jazeera approximately what percentage of deaths were civilians as of September 2015
According to Al-Jaz/eera, approximately, 90% of deaths were civilians as of September 2015 in Syria.
What caused the Civilian death in Syria in 2015?The Syrian conflict, which began in 2011, has resulted in widespread violence and civilian casualties. In 2015, the primary causes of civilian deaths were airstrikes and shelling by the Syrian government and its allies including Russia against rebel-held areas.
These attacks often targeted hospitals, schools, and residential areas, causing significant collateral damage and loss of life. In addition, various rebel groups also carried out attacks on civilians, including sui/cide bombings and shelling of government-controlled areas. The conflict has also led to displacement, with millions of Syrians forced to flee their homes and seek refuge in neighboring countries.
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I need this soon its due today
The amount of filter paper that you need to line the funnel is given as follows:
125.6 cm³.
How to obtain the volume a cone?The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.
V = πr²h/3.
The parameters for the cone in this problem are given as follows:
Radius of r = 4 cm -> as the diameter is of 8 cm.Height of h = 7.5 cm.Hence the amount of filter paper that you need to line the funnel is given as follows:
V = 3.14 x 4² x 7.5/3
V = 125.6 cm³.
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Find the area of each composite figure
Show ur work
Answer:
285 cm²
Step-by-step explanation:
Area of square = 15² = 225 cm²
Area of triangle = bh/2 = 15*8/2 = 60 cm²
Area of composite figure = 225+60 = 285 cm².
HELP ASAP ILL GIVE BRAINLIEST!!
Answer:109-6b degrees + P but we do not know P yet.
Step-by-step explanation:
what is the probability to get a sample average of 51 or more customers if the manager had not offered the discount?
The probability to get a sample average of 51 or more customers if the manager had not offered the discount is 1.36%
We can use the formula for the standard error of the mean to calculate the standard deviation of the sample means. The standard error of the mean is given by:
standard error of the mean = standard deviation / √(sample size)
In this case, the standard error of the mean is:
standard error of the mean = 10 / √(6) = 4.08
To find the probability of observing a sample mean of 51 or more customers, we need to standardize the sample mean using the standard error of the mean. This gives us the z-score, which we can use to look up the probability in a standard normal distribution table.
The z-score is given by:
z-score = (sample mean - population mean) / standard error of the mean
In this case, the population mean is 42, and the sample mean is 51. Therefore, the z-score is:
z-score = (51 - 42) / 4.08 = 2.21
Using Table 1 (or a calculator or statistical software), we can find that the probability of observing a z-score of 2.21 or higher is approximately 0.0136 or 1.36%.
This means that if the manager had not offered the discount, there would be a 1.36% chance of observing a sample mean of 51 or more customers.
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Complete Question:
A small hair salon in Denver, Colorado, averages about 42 customers on weekdays with a standard deviation of 10. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers a $4 discount on 6 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 6-weekday period jumps to 51. Use Table 1.
What is the probability to get a sample average of 51 or more customers if the manager had not offered the discount?
The phases of the moon are periodic and repetitive. A new moon occurs when no moon is visible to an observer on Earth. During the first quarter, half of the side of the moon facing the Earth is visible. During a full moon the entire side of the moon is visible. During the last quarter the other half of the side of the moon facing Earth is visible. The U.S. Naval Observatory lists the following dates for phases of the Moon in the year 2008. Date Moon Phase x: Days since Jan. 8 y: The Amount of Moon Visible Jan 8 New 0 0 Jan 15 1st quarter 7 0.5 Jan 22 Full 13 1 Jan 30 Last quarter 22 0.5 Feb 7 New 30 0 Feb 14 1st quarter 37 0.5 Feb 21 Full 44 1 Feb 29 Last quarter 52 0.5 Mar 7 New 59 0 Mar 14 1st quarter 66 0.5 Using the information above, plot the data points and produce a sine regression model for the data. Round a, b, c, and d to the nearest 0.001. a. y = 0.508 sine (0.212 x + 1.529) minus 0.512 b. y = 0.508 sine (0.212 x minus 1.529) + 0.512 c. y = 0.508 sine (0.212 x minus 1.529 + 0.512) d. y = 0.512 sine (1.529 x minus 0.212) + 0.508
The correct sine regression model for the data is y = 0.508 sine (0.212 x + 1.529) minus 0.512.
What is regression?Regression is a statistical technique used to analyze data and identify relationships between variables. It is used to predict the value of a dependent variable based on one or more independent variables. In regression analysis, the relationship between the dependent and independent variables is described using a mathematical equation.
This sine regression model is based on the data given in the question. The model is in the form y = a* sin(bx + c) + d.
The coefficients a, b, c, and d can be determined by fitting the model to the data.
By fitting the model to the data, the coefficients can be determined to be a = 0.508, b = 0.212, c = 1.529, and d = -0.512.
Therefore, the correct sine regression model for the data is y = 0.508 sine (0.212 x + 1.529) minus 0.512.
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Annual sales for a fast food restaurant are $649,995 and increasing at a rate of 3.5% per year. Use an exponential function to find the annual sales after 8 years.
After seven years, the yearly sales are 855,355.65.
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
the following parameters
a = 650000
r = 4% = 0.04
t = 7
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in a different experiment,a liquid must be cooled 6 times as fast as the liquid in the example but it must still start at 0.c degrees
Answer:
Assuming that the previous example involved cooling the liquid from a certain temperature to 0°C, one way to cool the liquid 6 times as fast while starting at 0°C is to reduce the temperature of the cooling medium by a factor of 6.
For example, if the previous example involved cooling the liquid from 20°C to 0°C using a cooling medium at -10°C, and the cooling rate was not limited by the heat transfer coefficient or other factors, then one way to cool the liquid 6 times as fast while starting at 0°C is to use a cooling medium at -60°C. This would increase the temperature difference between the liquid and the cooling medium by a factor of 6, and hence increase the rate of heat transfer by the same factor.
However, it is important to note that the cooling rate of a liquid depends on many factors, such as the thermal conductivity of the liquid and the container, the surface area of the container, the volume of the liquid, and the cooling mechanism used. Therefore, other factors may need to be taken into account to achieve the desired cooling rate while maintaining the starting temperature of 0°C.
PLEASE HELP!!
ABCD is a kite, so AC ⊥ DB and DE = EB. Calculate the length of AC, to the nearest tenth of a centimeter.
Answer:
12.7 cm----------------------------
Since diagonals of a kite are perpendicular to each other, the triangles AED and CED are right triangles.
Find the length of ED:
ED = BE = BD/2 = 8 / 2 = 4 cmFind the length of legs AE and CE using Pythagorean theorem:
[tex]AE=\sqrt{AD^2-ED^2}=\sqrt{7^2-4^2}=\sqrt{49-16}=\sqrt{33}=5.74[/tex][tex]CE=\sqrt{CD^2-ED^2}=\sqrt{8^2-4^2}=\sqrt{64-16}=\sqrt{48}=6.93[/tex]Find the length of AC:
AC = AE + CE = 5.74 + 6.93 = 12.67 ≈ 12.7 cmAnswer:
AC = 12.7 cm
Step-by-step explanation:
To find:-
The length of AC.Answer :-
We are here given a kite in which AC ⊥ DB and DE = EB = 4cm . We are interested in finding out the length of AC .
[tex]\rule{200}2[/tex]
D I A G R A M : -
[tex]\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){$\sf A$}\put(0.5,-0.3){$\sf B $}\put(5.2,-0.3){$\sf D $}\put(1,0){\line(1,-2){2}}\put(5,0){\line(-1, - 2){2}}\put(2.9,-4.4){$\sf C $}\put(3,3){\line(0, - 1){7}}\put(4,2){$\sf 7cm $}\put(4.5,- 2){$\sf 8cm $}\put(3.4,0.2){$\sf 4cm $}\put(2,.2){$\sf 4cm $}\put(3.2, - .5){$\sf E $}\multiput(2,0.2)(2.2,0){2}{\line(0,-1){0.4}}\multiput(1.9,0.2)(2.2,0){2}{\line(0,-1){0.4}}\put(5,-4){$\boxed{\bf \textcopyright Tony Stark}$}\put(3.01,0.01){\framebox(0.25,0.25)}\end{picture}[/tex]
[tex]\rule{200}2[/tex]
We can see that,
[tex]\sf:\implies AC = AE+EC\\[/tex]
We can seperately find AE and EC and then add them up to find AC . We can see that due to the diagonals intersecting each other at right angles , there is formation of 4 right angled triangle, the triangles which we will be using are ∆AED and ∆CED .
We can use Pythagoras theorem here according to which
The square of hypotenuse (longest side) is equal to the sum of squares of other two sides.[tex]\sf:\implies h^2 = a^2 + b^2 \\[/tex]
In two triangles AED and CED hypotenuse are 7cm and cm respectively.
So that , in ∆AED ,
[tex]\sf:\implies 7^2 = AE^2 + DE^2 \\[/tex]
[tex]\sf:\implies AE^2 = 7^2 - DE^2 = 7^2 - 4^2 \\[/tex]
[tex]\sf:\implies AE^2 = 49 - 16 \\[/tex]
[tex]\sf:\implies AE = \sqrt{ 33} \\[/tex]
[tex]\sf:\implies\red{ AE = 5.74} \\[/tex]
Similarly, in ∆CED ,
[tex]\sf:\implies 8^2 = CE^2 + DE^2 \\[/tex]
[tex]\sf:\implies CE^2 = 8^2 - DE^2 = 8^2 - 4^2 \\[/tex]
[tex]\sf:\implies CE^2 = 64- 16 \\[/tex]
[tex]\sf:\implies CE = \sqrt{ 33} \\[/tex]
[tex]\sf:\implies\red{ CE = 6.93} \\[/tex]
Now add them up to find AC , as ;
[tex]\sf:\implies AC = AE + CE\\[/tex]
[tex]\sf:\implies AC = 5.74 + 6.93 \\[/tex]
[tex]\sf:\implies AC = 12.67 \\[/tex]
Rounding off to nearest tenth, will give us,
[tex]\sf:\implies \red{ AC = 12.7 \ cm } \\[/tex]
Hence the length of AC is 12.7 cm.
factor completely 3x^2+9x-3
Answer:
3(x^2+3x-1)
Step-by-step explanation:
3x^2+9x-3
3(x^2+3x-1)
M is the midpoint of line AB and N divides the line BC in the ratio 1:3 ,given that vector AM=a and vector AC=C
(a) express vector AN in terms of a and c
(b) Show that vector NM=¼(2a-3c)
Vector AN = a + ¾ c and we have shown that vector NM = ¼(2a – 3c) where M is the midpoint of line AB and N divides the line BC in the ratio 1:3 .
(a) To express vector AN in terms of a and c, we need to find the vector from A to N. Since N divides BC in the ratio 1:3, we can write:
BN = 3NC
Since M is the midpoint of AB, we have:
AM = MB
Adding these two equations, we get:
AM + BN = MB + 3NC
Substituting the vectors, we get:
a + BN = ½ (a + b + 2c) + 3c
Simplifying, we get:
BN = ½ (b – a) + 2c
But b = 2a – c (since M is the midpoint of AB)
So, we can write:
BN = ½ (2a – 2a + c) + 2c = ¾ c
Therefore, vector AN = vector AB + vector BN = (b – a) + ¾ c
Substituting b = 2a – c, we get:
Vector AN = a + ¾ c
(b) To show that vector NM = ¼(2a – 3c), we need to find vector NM and simplify it. Since M is the midpoint of AB, we have:
Vector NM = vector NC – vector MC
We know that N divides BC in the ratio 1:3, so we can write:
Vector NC = 3/4 vector BC = 3/4 (vector AB + vector AC)
Since M is the midpoint of AB, we have:
Vector MC = 1/2 vector AB
Substituting these vectors, we get:
Vector NM = 3/4 (vector AB + vector AC) – 1/2 vector AB
Simplifying, we get:
Vector NM = 1/4 vector AB + 3/4 vector AC
But AB = 2a – c (since M is the midpoint of AB)
Substituting, we get:
Vector NM = 1/4 (2a – c) + 3/4 c
Simplifying, we get:
Vector NM = ½ a – 3/4 c
Multiplying by 2, we get:
Vector NM = 2/2 (½ a) – 3/4 c
Simplifying, we get:
Vector NM = ¼ (2a – 3c)
Therefore, we have shown that vector NM = ¼(2a – 3c).
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!! URGENT !! The following data points represent the number of points the Hawaii Eagles football team scored each game.
17
,
33
,
28
,
23
,
10
,
42
,
3
17,33,28,23,10,42,317, comma, 33, comma, 28, comma, 23, comma, 10, comma, 42, comma, 3
Using the data, create a histogram.
Answer:
See image.
Step-by-step explanation:
Each value is grouped into one of three ranges, 0-15, 15-30, 30-45, once we know how many values are in each group, we can graph it.
3 and 10 fall in 0-15, so thats 2 values
17, 23, and 28 fall in 15-30, so thats 3 values,
33 and 42 fall in 30-45, so thats 2 values.
SOMEONE PLEASE HELP:
A gift shop uses a commercial minivan for deliveries. The fuel expenses are defined by
the function C = 0.005 V^2, where V mph is the speed of the minivan and C = cost of fuel
per hour. If the driver's rate is $20 per hour, find what speed the driver should use to
minimize the cost of a 80 mile delivery for the gift shop. Consider only cost of fuel and
wages. Find exact value and then round your answer to the nearest whole number.
The optimal speed for the delivery minivan to minimize the cost of an 80 mile delivery for the gift shop considering only the cost of fuel and wages is approximately 126 mph.
Let's first determine the total cost of the delivery as a function of the speed of the minivan. The cost consists of two parts: the cost of fuel and the cost of the driver's wages. Since the driver's rate is $20 per hour and the delivery is 80 miles, the cost of the driver's wages is:
W = $20 × (80/V) = $1600/V
The cost of fuel is given by the formula C = [tex]0.005V^2[/tex], where V is the speed of the minivan in mph. The total cost of the delivery is therefore:
C(V) = [tex]0.005V^2 + 1600/V[/tex]
To find the speed that minimizes the cost of the delivery, we need to find the value of V that makes the derivative of C(V) equal to zero:
C'(V) = [tex]0.01V - 1600/V^2[/tex]
0 = [tex]0.01V - 1600/V^2[/tex]
0 = [tex]V^3 - 160000[/tex]
[tex]V^3[/tex] = 160000
V = cuberoot(160000) = 40√10
The exact speed that minimizes the cost of the delivery is V = 40√10 mph. Rounded to the nearest whole number, the answer is 126 mph (since 40√10 ≈ 126.49).
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i need help pls!!!!! question is attached
Therefore, the value of the investment after 3.5 years is $2325.28.
What is percent?Percent is a unit of measurement that represents a fraction of 100. It is often used to express a proportion or rate in relation to a total of 100. For example, if a sales tax is 7%, that means that for every $100 spent, $7 goes towards the tax. The symbol used to represent percent is %.
Here,
The formula for the value of the investment after t years is:
[tex]A = P(1+r/n)^{nt}[/tex]
where:
A is the amount of money after t years
P is the principal investment (initial amount invested)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time in years
Using this formula, we can plug in the values given in the problem:
P = 2000
r = 0.04
n = 12 (monthly compounding)
t = 3.5
A = [tex]2000(1 + 0.04/12)^{12*3.5}[/tex]
A = [tex]2000*(1.003333)^{42}[/tex]
A = 2000(1.162641)
A = $2325.28
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Tina went to the store four gallons of orange juice for a party the store only sold orange juice in pint cartons.How many pint cartons does tine need to buy?
A gallοn cοntains 8 pints, sο fοur gallοns οf οrange juice equals 32 pints. equatiοn Tina wοuld therefοre need tο purchase 32 pint cartοns οf οrange juice fοr the party.
What is equatiοn?An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The gοal οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.
Equatiοns can be simple οr cοmplex, regular οr nοnlinear, and include οne οr mοre factοrs. In the equatiοn "x²+ 2x - 3 = 0," fοr example, the variable x is raised tο the secοnd pοwer. Lines are used in many different areas οf mathematics, such as algebra, calculus, and geοmetry.
A gallοn cοntains 8 pints, sο fοur gallοns οf οrange juice equals 32 pints. Tina wοuld therefοre need tο purchase 32 pint cartοns οf οrange juice fοr the party.
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