A recipe says to use 3 cups of flour to make 48 cookies. What is the constant of proportionality that relates the number of cookies made, y, to the number of cups of flour used, x ?

Answer:

3.507 x 107 in scientific notation.

Answer:

3.507 x 10^7 is the answer to your question.

The average velocity for the time period is -15 feet per second

The velocity of the ball = 31 feet / seconds

The function of the height is

y = 31t - 23t^2

Time period beginning when t = 1 and lasting .01 s, .005 s, .002 s, .001 s

The average velocity = f(1.01) - f(1) / 1.01 - 1

f(t) = 31t - 23t^2

f(1.01) = 31(1.01) - 23(1.01)^2

= 31.31 - 23.46

= 7.85 feet per second

Similarly

f(1) = 31(1) - 23(1)^2

= 31 - 23

= 8 feet per second

The average velocity =  7.85 - 8 / 1.01 - 1

= -0.15 / 0.01

= -15 feet per second

Hence, the average velocity for the time period is -15 feet per second

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\(8^{3} \cdot 8^{-7} =8^{-4}=\boxed{\frac{1}{8^4}}\)

Using degree of freedom,

Two degrees of freedom would we report when we report the results of our study is (2,24).

Degree of freedom:

The statistical degrees of freedom (DF) indicate the number of independent values that can be changed in the analysis without violating the constraints.

degrees of freedom is the number of independent values that can be estimated in a statistical analysis. It can also be thought of as the number of values that are free to vary when estimating the parameters

DF = N – P

Where:

N = sample size

P = the number of relationships

We given that,

Number of groups , k = 3

Number of total participants, n = 27

Degrees of freedom for F-test is F(k-1,n-k)

= F(3-1 , 27-3)

= F(2,24)

Hence, (2,24,) are required two degrees of freedom.

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Answer:

The answer is A, because $7.00 is more than 5% commission on ticket sales.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

Cards C and E

Step-by-step explanation:

Remember that irrational numbers cannot be written as a fraction of two integers:

Is 10 irrational? No, because 10 can be written as a fraction (ex. 10/1, 20/2, etc.)

Is 6/5 irrational? No, because it is a fraction.

Is π irrational? Yes, because it can't be written as a fraction as its digits continue infinitely without repetition.

Is 11/4 irrational? No, because it is a fraction.

Is 8.25635... irrational? Yes, because the ellipsis shows the digits continue infinitely without repetition, otherwise there would be a bar over the digits to show repetition

Is -7 irrational? No, because it can be written as a fraction (ex. -7/1, -14/2, etc.)

Is 6.31(bar) irrational? No, because the bar shows that the digits 3 and 1 repeat.

Therefore, only cards C and E are irrational.

The cards that represent irrational numbers are C (π) and possibly E (8.25635), as π is a well-known irrational number and E is a decimal with multiple digits. The other options represent rational numbers.\

The cards that show irrational numbers are:

C. π (pi) - π is an irrational number representing the ratio of a circle's circumference to its diameter.

E. 8.25635 - This number is not known to be irrational based on the given information, but as it is a decimal with multiple digits, it could potentially be irrational.

The other options, A, B, D, F, and G, represent rational numbers, either whole numbers or fractions, and are not considered irrational.

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Answer:

The domain of 2(x-2)+4 is all real numbers, as well as for 2-(x-2)+4

Step-by-step explanation:

The probability that you pick exactly 2 juniors is 15/30 x 14/29 x 13/28 x 12/27, or 0.081.

1. Probability of picking the first junior: 15/30

2. Probability of picking the second junior: 14/29 (14 remaining juniors out of 29 total students after the first pick)

3. Probability of picking the third non-junior: 13/28 (13 remaining non-juniors out of 28 total students after the second pick)

4. Probability of picking the fourth non-junior: 12/27 (12 remaining non-juniors out of 27 total students after the third pick)

Therefore, the probability of picking exactly 2 juniors is

15/30 x 14/29 x 13/28 x 12/27

= 0.081.

The probability of picking exactly 2 juniors out of 4 slips of paper from a hat with the names of all 30 students in your statistics class is 0.081. This is calculated by taking the probability of picking the first junior (15/30) and multiplying it by the probability of picking the second junior (14/29, since there are 14 remaining juniors out of 29 total students after the first pick), the probability of picking the third non-junior (13/28, since there are 13 remaining non-juniors out of 28 total students after the second pick), and the probability of picking the fourth non-junior (12/27, since there are 12 remaining non-juniors out of 27 total students after the third pick).

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Answer:

The cake cost $6.00

Step-by-step explanation:

Let c = the cost of the cake

Let t =  the cost of the tea

c = 2t

c + 5t = 21  Substitute 2t for c

2t + 5t = 21  Combine like terms

7t = 21  Divide both sides by 7

\(\frac{7t}{7}\) = \(\frac{21}{7}\)

t = 3  

A cup of tea costs $3.00

c = 2t  Substitute 3 for t

c = 2(3)

c = 6

A cake costs $6.00

Answer:

Cake: £6

Step-by-step explanation:

1c = 2t             Eq. 1

1c + 5t = 21      Eq. 2

c = cost of a cake

t = cost of a cup of tea

Replacing Eq. 1 in Eq 2:

2t + 5t = 21

7t = 21

t = 21/7

t = 3

From Eq. 1:

c = 2t

c = 2*3

c = 6

Check:

From Eq. 2:

c + 5t = 21

6 + 5*3 = 21

6 + 15 = 21

The rate at which the end of the person's shadow is moving from the lamppost is 4ft/sec.

Let us consider the the distance of the person from the bottom of the lamppost is = xft

therefore the length of shadow is = yft

then the formula is

x + y/15 = y/6

or, 6(x + y) = 15y

=> 6x + 6y = 15y

=> 9y = 6x

therefore, y = 2x/3

Differentiation of both sides w.r.t t

dy/dt = 2/3 × dx/dt

we know that,

dx/dt = 6 ft/sec

then,

dy/dt = 2/3 × 6 => 4 ft/sec

The rate at which the end of the person's shadow is moving from the lamppost is 4ft/sec.

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The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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Considering the Empirical Rule, it is found that the distribution of the average July 1st temperature in Pittsburgh, PA, is approximately normal.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is given as follows:

In this problem, the mean and the standard deviation are given as follows:

Within one standard deviation of the mean, the bounds are given as follows:

The percentage of temperatures in this range is:

(4 + 12 + 5)/(1 + 2 + 2 + 4 + 12 + 5 + 2 + 2 + 1) x 100% = 68% (approximately).

Within two standard deviation of the mean, the bounds are given as follows:

Hence the percentage is:

(2 + 2 + 4 + 12 + 5 + 2 + 2)/(1 + 2 + 2 + 4 + 12 + 5 + 2 + 2 + 1) x 100% =94% (approximately)

100% of the measures will be within three standard deviations of the mean. All of the percentages are close to the percentages established by the Empirical Rule, hence it can be said the distribution is normal.

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Answer:

12

Step-by-step explanation:

Answer:

82 cm is the area of trapezoid

Answer:

c.$71.80

Step-by-step explanation:

did the debt management quiz

Answer:

Infinitely many solutions

Step-by-step explanation:

Step by Step Solution

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System of Linear Equations entered :

[1] 3x + y + 2z = 5

[2] 2x + 3y + 3z = 3

[3] x - 2y - z = 2

Solve by Substitution :

// Solve equation [3] for the variable x

[3] x = 2y + z + 2

// Plug this in for variable x in equation [1]

[1] 3•(2y+z +2) + y + 2z = 5

[1] 7y + 5z = -1

// Plug this in for variable x in equation [2]

[2] 2•(2y+z +2) + 3y + 3z = 3

[2] 7y + 5z = -1

// Solve equation [2] for the variable z

[2] 5z = -7y - 1

[2] z = -7y/5 - 1/5

// Plug this in for variable z in equation [1]

[1] 7y + 5•(-7y/5-1/5) = -1

[1] 0 = 0 => Infinitely many

Answer: $30.50

Step-by-step explanation:

To find a discount, the formula is, List price - (List price x (percentage / 100))

The outward flux of the vector field F across the boundary of the region D, which is the cube bounded by the planes x = ±1, y = ±1, and ±1, can be found using the divergence theorem.

The outward flux is the integral of the divergence of F over the volume enclosed by the boundary surface.The first step is to calculate the divergence of F. The divergence of a vector field F = P i + Q j + R k is given by div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z. In this case, div(F) = ∂/∂x(5y - 4x) + ∂/∂y(-4z - 5y) + ∂/∂z(-3y - 2x). Simplifying these partial derivatives, we have div(F) = -4 - 2 - 3 = -9.

Applying the divergence theorem, we can relate the flux of F across the boundary surface to the triple integral of the divergence of F over the volume enclosed by the surface. Since D is a cube with sides of length 2, the volume enclosed by the surface is 2^3 = 8.

Therefore, the outward flux of F across the boundary of D is given by ∬S F · dS = ∭V div(F) dV = -9 * 8 = -72. The negative sign indicates that the flux is inward.

In summary, the outward flux of the vector field F across the boundary of the cube D, as described by the given vector components, is -72. This means that the vector field is predominantly flowing inward through the boundary of the cube.

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After answering the provided question, we can conclude that t = 1.833 is standard deviation the critical value for a one-tailed t-test with 9 degrees of freedom and a significance level of 0.05.

A statistic that communicates the fluctuation or variance of a number set is the standard deviation. A high standard deviation indicates that the values seem to be more dispersed, whereas a low standard deviation indicates that the values are closer to the established mean. The standard deviation is a measure of how far the data varies from the mean (or ). So when standard deviation is small, the data tends to cluster around the mean; when it is huge, the data is more dispersed. The standard deviation represents the average variability of something like the data set. It displays the average deviation from the mean of each score.

To decide whether the new manufacturing technique should be used, we must first determine whether the standard deviation of the drug concentration in the new process is less than 4 g/l. A hypothesis test can be used with the following null and alternative hypotheses:

H0 (null hypothesis): In the new process, the standard deviation of drug concentration is 4 g/l.

Alternative hypothesis (Ha): In the new process, the standard deviation of drug concentration is less than 4 g/l.

For the standard deviation, we can use a one-tailed t-test with a

\(t = (n - 1) * s^2 / \sigma^2\\s = \sqrt(1/(n-1) * \sum(xi - x\bar)^2) = 0.004 g/l\\t = (n - 1) * s^2 / \sigma^2 = (10 - 1) * 0.004^2 / 4^2 = 0.0007\)

t = 1.833 is the critical value for a one-tailed t-test with 9 degrees of freedom and a significance level of 0.05.

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Answer:

180

Step-by-step explanation:

(10×11)+(10×7)=110+70

The area of the kite is expressed as 1/2 × (Product of its diagonals)

In this case, we have;

Therefore, when we substitute the diagonals in the formula, we get;

When simplified, we get;

Therefore, the area of the kite is 180 ft².

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Answer:

17, -5, and 10

Step-by-step explanation:

In a nutshell, for this problem, the coefficients are the numbers that go in front of the variables.

The expression \left(\(4g^{3}h^{4}\right)^{3}\)) can be simplified to \(64g^{9}h^{12}.\)

To simplify this expression, we raise each term inside the parentheses to the power of 3. For 4\(g^{3}\), we have \(4^{3}\) = 64 and \((g^{3})^{3}\)= \(g^{9}\), so we get \(64g^{9}\). Similarly, for \(h^{4}\), we have \((h^{4})^{3} = h^{12}\).

Combining these simplified terms, we have \(64g^{9}h^{12}\) as the final simplified form of the expression \left\((4g^{3}h^{4}\)\right)^{3}.

In summary, raising the expression\(4g^{3}h^{4}\) to the power of 3 simplifies to \(64g^{9}h^{12}\).

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Answer: what’s the question? :D

Step-by-step explanation:

The correlation between your daily calorie intake and your GPA is not likely to be immediately apparent, and it would require further investigation to determine whether there is a positive or negative correlation, or no linear relationship between the two variables.

It is difficult to predict the correlation between your daily calorie intake and your GPA as they are not obviously related variables. However, it is possible that there may be a weak or indirect relationship between the two variables.

          If a person is consuming a well-balanced diet with the right amount of nutrients, vitamins, and minerals, they may have the energy and focus necessary to perform well academically. In this case, there may be a positive correlation between calorie intake and GPA. Alternatively, if a person is consuming an excessive amount of calories from unhealthy foods, they may be more likely to experience health problems that could impact their academic performance. In this case, there may be a negative correlation between calorie intake and GPA.

      On the other hand, there may be no direct linear relationship between the two variables, and other factors such as sleep, stress, exercise, and overall health may have a greater impact on academic performance than daily calorie intake.

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The absolute value functions for each graph are given as follows:

1. y = |x - 2|.

2. y = |x - 2| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The leading coefficient a does not influence the vertex of the absolute value function.

For the first graph, the vertex is at the coordinates (2,0), hence the equation is given as follows:

y = |x - 2|.

For the second graph, the vertex is at the coordinates (2,-2), hence the equation is given as follows:

y = |x - 2| - 2.

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Answer:

B and D

Step-by-step explanation:

Area of B = 2 x 6 = 12 units^2

Area of D = 3 x 4 = 12 units^2

The study is investigating the relationship between the exposure to the suspected drug during pregnancy and the risk

of delivering a malformed infant. This study design is a case-control study design.

The resultant data are: forty mothers have taken the suspected drug during their pregnancies. Of these mothers, 35

have delivered malformed infants. In addition, 10 other infants are born with malfunctions," then the answer would be

as follows:

The type of study design that is described in this scenario is a case-control study design.

A case-control study design is a type of observational study design that compares people with a particular condition

(cases) to people without that condition (controls) to determine whether there is a relationship between the exposure

to a suspected risk factor and the development of the condition.

In this scenario, the cases are the 35 mothers who delivered malformed infants, and the controls are the 5 mothers

who did not deliver malformed infants. The study is investigating the relationship between the exposure to the

suspected drug during pregnancy and the risk of delivering a malformed infant. Therefore, this study design is a case

control study design.

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