What is the area of the figure?

A figure can be broken into a rectangle and triangle. The rectangle has a base of 5 feet and height of one-third feet. The triangle has a base of 3 and two-thirds feet and height of 2 feet.
5One-third ft2
6 and two-thirds ft2
7 ft2
9 ft2

plzzzz help in a test!!! i only have 18 pts sry!!!

The value of the square root of 7 is,

⇒ √7 = 2.645

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

WE have to given that;

To find the value of the square root of 7 .

Since, the square root of 7 is,

⇒ √ 7

⇒ 2.645

Thus, The value of the square root of 7 is,

⇒ √7 = 2.645

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The curved surface area of the cylinder is 23. 7cm²

The circumference of a cylinder is expressed as;

C = 2πr

Now, substitute the value, we have;

4 = 2×3.14 ×r

Multiply the values

r = 4/6.28 = 0. 73

Now, the formula for the curved surface area of a cylinder is expressed as;

Area = 2πrh

Now, substitute the values, we get;

Area = 2 ×3.14 × 0.63 × 6

Multiply the values, we get;

Area = 23. 7cm²

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Answer:

1.0000

Step-by-step explanation:

because if it ends with a zero it will go on forever

For the given data, the range, variance, and standard deviation is 1.47, 0.1716, and 0.414, respectively.

To find the range, subtract the minimum value from the maximum value in the set of data. The minimum value is 0.48 and the maximum value is 1.95, so the range is: 1.95 - 0.48 = 1.47.

To find the sample variance, follow these steps.

1. Calculate the mean of the data set.

2. Subtract the mean from each value in the data set.

3. Take the summation of the squares of the result.

4. Divide the sample size minus 1.

Upon calculation, the sample variance is 0.1716.

Lastly, to find the sample standard deviation, take the square root of the sample variance: √0.1716. = 0.414.

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Answer:

0.0783

Step-by-step explanation:

The probability of getting the first success on xtg trial ; this is a geometric distribution :

P(x) = p(1−p)^x−1

The probability of being a universal donor , p = 0.15

The probability of obtaining someone who is a universal donor on 5th trial will be :

P(5) = 0.15(1 - 0.15)^(5 - 1)

P(5) = 0.15(0.85)^4

P(5) = 0.15(0.52200625)

P(5) = 0.0783009375

P(5) = 0.0783

The coordinate points of smaller and larger x -value from the origin is (-7, 0 ) and (7, 0) respectively.

The given point which is 7 unit from the origin, is equivalent to the radius of a circular curve.

The general equation is written as follows;

\(x^2 + y^2 = 7^2\)

The corresponding positive and negative values of x are obtained when y = 0

\(x^2 + 0 = 7^2\\\\x^2 = 49 \\\\x = +/- \ \ \sqrt{49} \\\\x = +/- \ 7\)

The coordinate of smaller x -value becomes;

(x, y) = (-7, 0)

The coordinate of larger x-value becomes;

(x, y) = (7, 0)

Thus, the coordinate points of smaller and larger x -value from the origin is (-7, 0 ) and (7, 0) respectively.

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Answer:

- 0.964

Step-by-step explanation:

Given that Coefficient of determination (R^2) = 0.93

Slope of regression line = - 5.26

The linear correlation Coefficient =?

The Coefficient of determination (R^2) is used to obtain the proportion of explained variance of the regression line. It is the square of the linear correlation Coefficient (R).

Hence. To obtain the linear correlation Coefficient (R) from the Coefficient of determination (R^2); we take the square root of R^2

Therefore,

R = √R^2

R = √0.93

R = 0.9643650

R = 0.964

However, since the value of the slope is negative, this depicts a negative relationship between the variables, hence R will also be negative ;

Therefore, R = - 0.964

The linear correlation coefficient of the data is: -0.96

Recall:

Thus, given:

Coefficient of determination of a set of data points = 0.93

Slope of the regression line = -5.26

Therefore:

R² = 0.93

R = √0.93

R = 0.96

Since the slope the regression line is negative, R will be negative in this case.

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Answer:

See attached graph

Step-by-step explanation:

We need to convert the polar coordinates into Cartesian coordinates using the rules \(x=r\:cos\theta\) and \(y=r\:sin\theta\) (see table in attached file).

The converted points will start to resemble a circle with a horizontal pole and a diameter of 4, so by connecting the points, we get our equation \(r=4\:cos\theta\).

Answer:

lily can make nine necklace and 3 beads are still left

The value of tα/2 of the t-test is 2.898

A t-test is a statistical test that is used to compare the means of two groups. tα/2 refers to the t critical value from the t-distribution table that corresponds to α/2

Given:  n = 18 and a 99% confidence interval

We have to find the critical t value for 99% confidence level and sample size of 18

Degrees of freedom = n - 1 = 17

α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

In the t table (check the attached image), we have to check the value against the column 0.005 and for 17 degrees of freedom.

The value obtained from the table is 2.898

Therefore, tα/2 = 2.898

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Answer:

The researcher did not state that the p-value is conditional on the null hypothesis being true.

Step-by-step explanation:

The p-value or the assumed value represent the probability in which the test results that are received would be atleast extreme in that the null hypothesis would be correct

Here the wrong thing would be that researcher would not stated the p value is in conditional form based on the null hypothesis being true

Therefore the correct option is A.

Answer:

\(x=-\frac{4}{5}\)

Step-by-step explanation:

\(6=\frac{3}{4}(10x+16)\\\mathrm{or,\ }6\times 4=3(10x+16)\\\\\mathrm{or,\ }24=30x+48\\\\\mathrm{or,\ }-24=30x\\\\\mathrm{\therefore}\ x=-\frac{4}{5}\)

Answer:

75 mph

Step-by-step explanation:

The speed of Raymond from San Antonio to Dallas is given by S = 75 mph

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the speed of Raymond from San Antonio to Dallas be S

Let the distance between San Antonio to Dallas be represented as D

Now , the value of D = 390 miles

Let the time taken for Raymond to travel D miles be T = 5.2 hours

Now , the speed is = Distance / Time

On simplifying , we get

The speed of Raymond from San Antonio to Dallas S = D / T

The speed of Raymond from San Antonio to Dallas S = 390 / 5.2

The speed of Raymond from San Antonio to Dallas S = 75 mph

Hence , the speed is 75 miles per hour

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Answer:

A) 12%

Step-by-step explanation:

Lets assume a random diameter to work with. I will use a diameter of 10.

Circumference = πD

Circumference = π * 10

Circumference = 31.415

Decreasing the circumference by 12%

31.415 * 0.12 = 3.769

31.415 - 3.769 = 27.64

To find out what percent the diameter is reduced by we will find out the new diameter with the new circumference

Circumference = πD

27.64 = π * D

D = 27.64 / π

New Diameter = 8.8

OldD - NewD

10 - 8.8 = 1.2

1.2/10 = 0.12

The diameter decreased by 12%

The diameter of the circle decreased by 12% due to decrease of circles circumference by 12%.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

The diameter is the longest line that can be drawn inside a circle.

Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.

Let's say the diameter of the circle is D

Circumference of circle = πD

12% of Circumference = (12/100) × πD

⇒ 0.12πD

So new circumference will be

πD -  0.12πD = 0.88πD

Now let say new diameter after decreasing circumference is d

Circumference of new circle will be

πd = 0.88πD

d = 0.88D

% decrement = (change/original) × 100

diameter decrease = (D - 0.88D)/D × 100

⇒ 12% hence it will be correct answer.

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Answer:

a) 13.9%.

b) If the nuber of patient files in this study were increased to 100, the margin of error would be decreased.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

35 random patient files and finds that 27 of these patients are using this same toothpaste.

This means that \(n = 35, \pi = \frac{27}{35} = 0.7714\)

a. What is the margin of error for a 95% confidence interval to the nearest tenth of a percent?

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(M = 1.96\sqrt{\frac{0.7714*0.2286}{35}}\)

\(M = 0.139\)

As a percent, a margin of error of 13.9%.

b. If the number of patient files in this study were increased to 100, what would happen to the margin of error?

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

This means that the margin of error is inversely proportional to the sample size. As n increases, n decrease. Then:

If the nuber of patient files in this study were increased to 100, the margin of error would be decreased.

Answer:

a) 13.9%.

b) If the number of patient files in this study were increased to 100, the margin of error would be decreased.

Step-by-step explanation:

if y=a(b)^t is an exponential decay function, then b must be less than one

Answer:

a)  ( 31.92 < μ < 33.88 )  

The confidence interval is not very different from the confidence interval given in the question

b) ( 31.74 ,  34.66 )

Step-by-step explanation:

n = 250

x ( mean ) = 32.9

std = 6.9

95% confidence interval

df = n - 1 = 250 - 1 = 249

a) construct confidence interval estimate

calculate for the margin of error

= \(t_{0.05/2} ,_{250-1} ( \frac{s}{\sqrt{n} } )\) ( using excel function:  T.INV.2T(0.025,249) )

= 2.255 ( 6.9 / 15.81 )

= 0.98

Hence the confidence interval for the population

= ( x - 0.98 < μ < x + 0.98 )

= ( 31.92 < μ < 33.88 )  

The confidence interval is not very different from the confidence interval given in the question

b) when n = 19

x = 33.2 and std = 2.6

margin of error = \(t_{0.05/2} ,_{19-1} ( \frac{s}{\sqrt{n} } )\) = 2.45 * ( 2.6 / 4.36 )  = 1.46

confidence interval

= ( 33.2 - 1.46 , 33.2 + 1.46 )

= ( 31.74 ,  34.66 )

Using the hypergeometric distribution, it is found that there is a 0.19704% probability that the balls have the same number.

The balls are chosen without replacement, hence, the hypergeometric distribution is used.

Hypergeometric distribution:

P (X = x) = h (x, N, n, k)

              = \(\frac{C_{k, x} C_{n - k, n - k} }{C_{N, n} }\)

\(C_{n, x} = \frac{n!}{x!(n - x)!}\)

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this problem:

There are 3 balls, hence .

For each number, there are 3 balls, hence .

3 balls are selected, hence .

For each ball, the probability is P(X = 3). There are 8 balls, hence we have to find 8P(X = 3).

P (X = x) = h (x, N, n, k)

              = \(\frac{C_{k, x} C_{n - k, n - k} }{C_{N, n} }\)

P (X = 3) = h (3, 30, 3, 3) = 0.0002463

0.0002463 x 8 = 0.0019704

0.0019704 = 0.19704% probability that the balls have the same number.

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WXYZ must be a square, all the sides must have a length of 5.

The vertices of the quadrilateral are:

W(-1, 1), X(3, 4), Y(6,0), and Z(2, -3)

Distance can be calculated using the formula derived from Pythagoras theorem. In coordinate geometry, the distance formula is:

\(\sqrt{[(x_2 -x_1)^2 + (y_2 - y_1)^2]}\)

We have to prove that WXYZ is a square.

Using the distance formula :

\(WX = \sqrt{(-1-3)^2+(1-4)^2}\\ \\WX = \sqrt{16 + 9}\\ \\WX = \sqrt{25}\\ \\WX = 5\)

Since WXYZ must be a square, all the sides must have a length of 5.

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The given question is incomplete, complete question is:

Select the correct answer from each drop-down menu.

Given: W(-1, 1), X(3, 4), Y(6,0), and Z(2, -3) are the vertices of quadrilateral WXYZ.

Prove: WXYZ is a square.

Using the distance formula, I found that

…

A. all four sides have a length of 5

B. all four sides have different lengths

C. only 2 sides have the same length

D. all four sides have a length of 10

The values of x and y vary directly. Hence, we can write

Here, k is the constant of proportionality.

Substitute x=0.1 and y=0.9 in the above equation and solve for k.

Put the value of k in y=kx.

Therefore, y=9x.

The maximum displacement is 5 centimeters.

The time required for one oscillation is π seconds.

The frequency is 1 / π Hz.

Equation to model the motion of the object is x(t) = 5 × cos(2t)

The maximum displacement from equilibrium can be determined by observing that the object is pulled down 5 centimeters from its rest position.

In simple harmonic motion, the amplitude represents the maximum displacement from equilibrium.

The period of oscillation is given as π seconds.

The period (T) is the time required for one complete oscillation.

The frequency (f) is the reciprocal of the period and represents the number of oscillations per unit time.

Thus, the frequency is the inverse of the period: f = 1 / T.

To model the motion of the object, we can use the equation for simple harmonic motion:

x(t) = A×cos(ωt + φ)

A = 5 centimeters (maximum displacement),

T = π seconds (period),

f = 1 / π Hz (frequency).

To find ω, we can use the relation ω = 2π / T:

ω = 2π / π = 2 radians/second.

The equation to model the motion of the object is:

x(t) = 5 × cos(2t)

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Explanation:

Since all of the elements of B are part of A, then we can say that B is a part of A or B is a subset of A.

Answer:

The answer is B ⊂ A. Option 1.

Answer:

Draw a circle and cut it into three

Step-by-step explanation:

By using the figure below, the value of line segment PT is equal to 54 units.

In Mathematics, the midpoint of a line segment with two endpoints can be calculated by adding each point on a line segment together and then divide by two (2).

Since T is the midpoint of PQ, we have the following:

Line segment PT = Line segment TQ

7x + 5 = 9x - 9

9x - 7x = 9 + 5

2x = 14

x = 14/2

x = 7.

Now, we can determine the value of PT:

PT = 7x + 5

PT = 7(7) + 5

PT = 54 units.

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Complete Question:

Use the figure to the right to find the value of PT. T is the midpoint of PQ PT=7x+9 and TQ=9x-5

Answer:

5.333...

Step-by-step explanation:

You devide 8 by 15 and get the decimal form of this fraction.

It is 5.3 repeating

Answer and Step-by-step explanation:

The number 0.533333333 is the decimal for 8/15. You know this because to find the decimal for a fraction you divide. So, you divide 8 by 15. When you do that you get, 0.533333333.

Hope this helped you out! Have a wonderful day!

Answer:11

Step-by-step explanation:

Therefore , the solution of the given problem of  probability comes out to be the right response is thus: "Drawing a red card or a Queen from a regular deck of cards is an overlapping occurrence."

The primary objective of statistical inference, a branch of mathematics, is to determine the chance that a claim is true or that a specific event will occur. Chance can be represented by any number between 0 and 1, in which 1 typically represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.

Here,

Because the Queen of Hearts and Jack of Spades are not face cards or nines,

the occurrences "Drawing a Queen of Hearts or Jack of Spades from a standard deck of cards" and "Drawing a face card or a 9 from the a standard deck of cards" do not overlap.

A Queen of Hearts is both a red card and a queen, and a diamond is a type of red card and a club is a type of card, so the occurrences "Drawing a Diamond or a Club from a Standard Deck of Cards" and "Drawing a Red Card or a Queen from a Standard Deck of Cards" overlap.

The right response is thus: "Drawing a red card or a Queen from a regular deck of cards is an overlapping occurrence."

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