Find the constant of variation and the missing value when y varies directly with x.
If y = 35 when x = 7, find x when y = 49.

The initial age of 10 years and the spaceship speed of 0.60•c, gives the Andrea's age at the end of the trip as 18 years.

The time dilation using the Lorentz transformation formula is presented as follows;

\(t' = \frac{t}{ \sqrt{1 - \frac{ {v}^{2} }{ {c}^{2} } } } \)

From the question, we have;

The spaceship's speed, v = 0.6•c

∆t = Rest frame, Courtney's time, change = 10 years

Therefore;

\(\delta t' =\delta t \times \sqrt{1 - \frac{ {(0.6 \cdot c)}^{2} }{ {c}^{2} } } = 8\)

The time that elapses as measured by Andrea = 8 years

Andrea's age, A, at the end of the trip is therefore;

A = 10 years + 8 years = 18 years

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9???????????????????????????????

Answer:

I'm going to guess that you are trying to find z. If so, Z is 9.

Step-by-step explanation:

Z + 18 = 27

Subtract 18 on both sides

Z + 18 = 27

Z - 18 = - 18

Z = 9

Answer:

y=−252x

Step-by-step explanation:

Answer:

9x^3

Step-by-step explanation:

5x^3 + 4x^3

Since these are like terms

x^3 (5+4)

9x^3

Answer:

\(9x^3\)

Step-by-step explanation:

\(5x^3 + 4x^3\)

Add the like terms.

\(=9x^3\)

Answer:

The answer will be 10 , the last item .

Answer:

As cd=de;

9x-25=6x+8

solve for X

replace the value of X into the other equations

Answer:

see explanation

Step-by-step explanation:

given the legs CD and DE are congruent , then

CD = DE , that is

9x - 25 = 6x + 8 ( subtract 6x from both sides )

3x - 25 = 8 ( add 25 to both sides )

3x = 33 ( divide both sides by 3 )

x = 11

Then

CD = 9x - 25 = 9(11) - 25 = 99 - 25 = 74

DE = 6x + 8 = 6(11) + 8 = 66 + 8 = 74

showing CD = DE

CE = 10x - 73 = 10(11) - 73 = 110 - 73 = 37

In testing whether each individual independent variable (xs) in a multiple regression equation is statistically significant in explaining the dependent variable (y), one uses the t-test.

The t-test is a statistical test that helps determine the significance of each independent variable in a multiple regression model. It assesses whether the coefficient associated with each independent variable is significantly different from zero.

To perform the t-test, individual t-statistics are calculated for each independent variable. The t-statistic measures the ratio of the estimated coefficient of an independent variable to its standard error. It indicates how many standard deviations the estimated coefficient is away from zero.

The null hypothesis for each t-test states that the corresponding independent variable has no effect on the dependent variable, meaning its coefficient is equal to zero. The alternative hypothesis states that the independent variable does have a significant effect, implying that its coefficient is not equal to zero.

By comparing the calculated t-statistics with critical values from the t-distribution, one can determine whether to reject or fail to reject the null hypothesis for each independent variable. If the absolute value of the t-statistic is greater than the critical value, it indicates that the independent variable is statistically significant in explaining the dependent variable.

In summary, the t-test is utilized to assess the statistical significance of each individual independent variable in a multiple regression equation. It helps determine whether the coefficients associated with the independent variables are significantly different from zero, indicating their impact on the dependent variable.

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Answer:

27. x=7/20; 28. m= 3.7; 29. a= 5.8

30. x= 6; 31.x= 46

Step-by-step explanation:

27.

\(x + \frac{2}{3} = \frac{9}{ 10} \)

you are going to carry the 2/3 over the equal sign. This will make the 2/3 negative so...

\(x = \frac{9}{10} - \frac{2}{3} \)

now calculate it by finding the LCM of 10 and 3 ....this will be 30....you can just multiply the 10 and 3

now

30 into 10 goes 3 times....you will multiply this 3 with the 9 to get 27

30 into 3 goes 10 times...you will multiply this 10 with the 2 to get 20

\(x = \frac{27 - 20}{30}\)

\(x = \frac{7}{30} \)

Hopefully you understand

28.

\(1.2 = m - 2.5\)

\(1.2 + 2.5 = m\)

carry the 2.5 over the equal sign to get the m by itself...this is because you are trying to find m

when the negative number goes over the equal sign it will become positive...this is why you add it to the 1.2

m= 3.7

you can do the other on your own

the error in 30 is that the 7 should not be added to the 13 but subtracted

..this is because when you carry the positive number over the equal sign it will become negative..hence you subtract it

\(x + 7 = 13\)

\(x = 13 - 7\)

\(x = 6\)

and for 31...the 12 should not be subtracted but added since when it goes over the equal sign it will become positive.

\(34= y - 12\)

\(34 + 12 = y\)

\(y = 46\)

Answer:

answer is 75

Step-by-step explanation:

6÷8x100=75%

from 58 to 66 its have 6 colums..thats why 6/8

Answer:

Step-by-step explanation:

5) Domain: -3<=x<=2

Range: 4<=y<=-3

6)  Domain: {-3,-2,-1,0,1,2}

Range: {4,3,2,1,0,-1,-2,-3}

Do you need number 7 too?

:]

Answer: there parallel

The correct statement is: P(A and B) <= 0.3 * 0.5 = 0.15.

The probability of A and B both occurring is denoted by P(A and B). If A and B are independent events, then the probability of both events occurring is given by the product of their individual probabilities, that is P(A and B) = P(A) * P(B). Therefore, P(A and B) = 0.3 * 0.5 = 0.15.

To understand why this statement is correct, we need to understand the concept of independence and multiplication rule of probability.  When two events are independent, the occurrence of one event does not affect the occurrence of the other. In other words, the probability of one event occurring is not affected by the occurrence of the other event.
The multiplication rule of probability states that if two events A and B are independent, then the probability of both events occurring together is given by the product of their individual probabilities, that is P(A and B) = P(A) * P(B).
In this case, we are given that events A and B are independent, and their individual probabilities are P(A) = 0.3 and P(B) = 0.5. Therefore, we can calculate the probability of both events occurring together as follows:
P(A and B) = P(A) * P(B)
= 0.3 * 0.5
= 0.15
This means that the probability of both events occurring together is less than or equal to 0.15. This statement is correct because the multiplication of probabilities can never result in a probability greater than the smaller of the two individual probabilities.

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The unknow angles are as follows:

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

Therefore,

m∠4 = 72 degrees

Hence,

m∠1 + m∠4 = 180 (angle on a straight line)

m∠1 = 180 - 72

m∠1 = 108 degrees

m∠2 = m∠4 (vertically opposite angles)

Vertical angles are the angles formed when two lines intersect each other. Vertical angles are congruent.

Therefore,

m∠2 = 72 degrees

m∠5 = m∠1 (corresponding angles)

Corresponding angles are angles that occur on the same side of the transversal line and are equal in size.

m∠5 = 108 degrees.

m∠7 = m∠5(vertically opposite angles)

m∠7 = 108 degrees

m∠8 = m∠2 (alternate exterior angles)

Alternate exterior angles are congruent.

m∠8 = 72 degrees

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Answer: B is right

Step-by-step explanation: Check the file for steps

Using Conditional Probability,

the probability that the sum of the numbers appearing on the two dice is 8, if 3 appears on the first is 1/5.

We have given that,

Two dice are thrown. Let S be the sample space S={1,2,3,4,5,6×{1,2,3,4,5,6}

Total number of possible outcomes (n(S)) =36

Let A ≡ the event that the sum of the numbers coming up is 8

and B ≡ the event of occurrence of 3 on the first die.

A ≡{(3,5),(6,2),(4,4),(5,3),(2,6)}

favourable cases for A (n(A) )= 5

B≡{(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)}

favourable cases for B (n(B)) = 6

Now, A int B = { (3,5 ) } = 1

favourable cases for AnB (n(An B) )= 1

Probability of event A occur (P(A)) = 5/36

Probability of event B occur (P(B)) = 6/36

Probability of event B occur (P(AnB)) = 1/36

we have to calculate probability the sum of the numbers appearing on the two dice is 8, if 3 appears on the first i.e., P(A/B) --> Conditional Probability

Required probability, P(A/B) = P(ANB)/ P(B)

=> P(A/B) = 1/36/5/36 = 1/5

Hence, the required probability is 1/5.

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The range of the given graph is [5, ∞).

Range.

Range refers the set of possible output values, and if we have the graph, then the set of all possible y values on the graph is defined as the range.

Given,

Here we have the graph.

Through the given graph we have to find the range of the line.

As per the definition of range, we have identified that the range take the value of y axis.

While we lookin into the given graph, we have identified that the starting point of the line is

=> (0, 5)

In this point 0 refers the x coordinate and 5 refers the y coordinate. So, the starting range is 5.

And the end of the line is not pointed.

So, we can consider that this line goes infinitely.

So, the range of the graph is  [5, ∞).

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The correct statements regarding the domain and the range of the function in this problem are given as follows:

B. The domain is the set of all real numbers.

C. The range is the set of all real numbers.

The function in this problem is defined for all real values, and assumes all real values, hence options B and C are the correct options for this problem.

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Hence, the equation for the tangent plane to the surface at the point (1, 1, 1) is 3x + 3y + 7z - 13 = 0.

To find the equation for the tangent plane to the surface at the point (1, 1, 1), we need to find the gradient vector of the surface equation at that point. First, let's differentiate the surface equation with respect to each variable:

∂/∂x \((x^2 + xyz + y^2 + 3z^2)\) = 2x + yz

∂/∂y \((x^2 + xyz + y^2 + 3z^2)\) = xz + 2y

∂/∂z \((x^2 + xyz + y^2 + 3z^2)\) = xy + 6z

Now, evaluate the partial derivatives at the point (1, 1, 1):

∂/∂x \((x^2 + xyz + y^2 + 3z^2)\) = 2(1) + (1)(1)

= 3

∂/∂y \((x^2 + xyz + y^2 + 3z^2)\) = (1)(1) + 2(1)

= 3

∂/∂z \((x^2 + xyz + y^2 + 3z^2)\) = (1)(1) + 6(1)

= 7

Therefore, the gradient vector at the point (1, 1, 1) is given by:

∇F = (3, 3, 7)

The equation for the tangent plane can be written as:

3(x - 1) + 3(y - 1) + 7(z - 1) = 0

Simplifying:

3x + 3y + 7z - 13 = 0

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There is a fundraiser for the marching band. One answer to the problem is 46 t-shirts & 82 yearbooks equal $2822. The best choice is B.

A fundraising event is a gathering where money is raised for a cause, charity, or nonprofit organization (also known as a fundraiser).

The yearbook costs $26 and T-shirts $15.

The group must fund $2800.

Create a model that illustrates how many yearbooks and T-shirts must be sold.

Determine three T-shirt and sweatshirt combinations that satisfy the model, then graph the model.

Let x = no. of $15 t-shirt

Let y = no. of $26 yearbook

The equation

15x + 26y = 2800

Therefore, the correct option is B, 46 t-shirts and 82 yearbooks.

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Answer:

The temperature goes down 2 degrees for every hour

Step-by-step explanation:

The equivalent function in the form y = ab^x is \(F(t)=2,298.1(0.7)^t\)

Give the exponential function in a general sense as y = ab^x

We are to write it in the form \(f(t) = ab^t\)

This can be further expressed as;

\(F(t) = 6700(0.7)^{3t}\\F(t) = 6700(0.7^3)(0.7^t)\\F(t)=2,298.1(0.7)^t\)

Hence the equivalent function in the form y = ab^x is \(F(t)=2,298.1(0.7)^t\)

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The mathematical relationship that is based on marginal analysis that associates dollars spent on advertising and sales generated; sometimes used to help establish an advertising budget is known as Return on Advertising Spend (ROAS).Return on Advertising Spend (ROAS) is an analytical approach to measure the financial effectiveness of advertising campaigns by dividing the revenue earned from an ad campaign by the amount spent on that ad campaign.

The formula for calculating ROAS is: ROAS = Revenue from ad campaign / Cost of ad campaignROAS is used to analyze the efficacy of a particular advertising campaign. It is often used as a benchmark to compare different ad campaigns. It helps to make decisions about how to allocate advertising budgets in a more effective manner. If the ROAS is high, it indicates that the advertising campaign has been successful, and investing more in such an ad campaign is profitable. In contrast, if the ROAS is low, it means that the campaign is not performing well, and a change in strategy may be required.

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Answer:

Y= 60 degrees.

Step-by-step explanation:

A traingle's three angles always equals 180 degrees. since the singular line on the triangle on the right mean the side are equal, the angles are also equal. 180 divided by 3 equals 60 degrees.

The given expression "the square of a number is 3 less than four times the number" is represented as x² = 3 - 4x and the values of number could be: x1= 0.645 , x2= -4.645

In mathematics, when we refer "square of a number" we mean that the exponent of that number is 2. So we express it mathematically as:

x²

When we express "3 less than" of a number we mean that the number 3 is subtracting that number. So we express it mathematically as: 3 -

x² = 3 -

When we express "four times the number" we mean that the number is exactly 4 times greater than a number or that it contains it 4 times. So we express it mathematically as: 4x

x² = 3 - 4x

Organizing the values, we have a quadratic equation: x² + 4x – 3 = 0

Where:

Solving the quadratic question we get the values for the (x) number

x= {- b ± √ [b² - (4* a*c)]} / (2 *a)

x= {- 4 ± √ [4² - (4* 1*-3)]} / (2 * 1)

x= {- 4 ± √ (16 + 12)} / 2

x= {- 4± √ 28} / 2

x= (- 4 ± 5.29 ) / 2

x1= (- 4 + 5.29 ) / 2

x1= (1,29) / 2

x1= 0.645

x2= (- 4 - 5.29 ) / 2

x2= (9.29) / 2

x2= -4.645

We can check the values, replacing them into the equation:

(x1)² = 3 - 4(x1)

(0.645)² = 3 - 4*(0.645)

0.42 = 0.42

(x2)² = 3 - 4(x2)

(-4.645)² = 3 - 4*(-4.645)

21.58 = 21.58

It is an algebraic equation where the polynomial formed has three terms, one variable has an exponent 2, another in which the variable has exponent 1 and the last term without any variable. Its standard form is:

ax²+ bx + c = 0

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a. 195 households obtained news from television but not from newspapers or the Internet.

b. 270 households obtained news from newspapers but not from television or the Internet.

c. 934 households obtained news from television or newspapers.

d. 66 households did not acquire news from television, newspapers, or the Internet.

a. To find the number of households that obtained news from television but not from newspapers or the Internet, we need to subtract the number of households that obtained news from television and either newspapers or the Internet from the total number of households that obtained news from television.

724 (total households that obtained news from television) - 412 (households that obtained news from television and newspapers) - 185 (households that obtained news from television and the Internet) = 127 households that obtained news from television but not from newspapers or the Internet.

b. To find the number of households that obtained news from newspapers but not from television or the Internet, we need to subtract the number of households that obtained news from newspapers and either television or the Internet from the total number of households that obtained news from newspapers.

545 (total households that obtained news from newspapers) - 412 (households that obtained news from television and newspapers) = 133 households that obtained news from newspapers but not from television or the Internet.

c. To find the number of households that obtained news from television or newspapers, we need to add the number of households that obtained news from only television, only newspapers, and both television and newspapers.

724 (households that obtained news from television) + 545 (households that obtained news from newspapers) + 412 (households that obtained news from television and newspapers) = 1681 households that obtained news from television or newspapers.

d. To find the number of households that did not acquire news from television, newspapers, or the Internet, we need to subtract the number of households that obtained news from any of these sources from the total number of households surveyed.

1000 (total households surveyed) - 1681 (households that obtained news from television or newspapers) = 319 households that did not acquire news from television, newspapers, or the Internet.

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The population mean, or average score for the population on a certain variable, is symbolised as follows:μ = ( Σ Xi ) / N.

The mean of a data set is the sum of all values ​​divided by the total number of values, often called the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean", it is the most commonly used measure of central tendency. This result is obtained by dividing the total number of values ​​in the data set by the sum of all those values. Both raw data and data combined into frequency tables can be used in calculations. Mean refers to the average of a number. The calculation is simple: divide by the number of numbers when you added all the numbers. the total divided by the number.

The population mean or population mean score for  a given variable is symbolized as follows:μ = ( Σ Xi ) / N. The symbol 'μ' represents the population mean.

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Step-by-step explanation:

n=3

1. 12=4×n

=12/4=n

=3=N

3.n×12=36

n=36/12

n=3

n=4

2. 12=n×3

12/3=n

3=n

n= 9

4. 4×n=36

n=36/4

9=n

hope it helps

The speeds of the car are 35 km/hr and 25 km/hr, if a car starts from A and another car starts from B at the same time. If both cars travel in the same direction, they cross in 8 hours, but if these cars travel in opposite directions, they meet each other in 1 hour 20 mins. A and B have a distance of 80 km.

Let the speed of the car at A be \(v_1\)

the speed of the car at B be \(v_2\)

In the first case, they travel in the same direction, the relative velocity is given by \(v_1-v_2\)

\(v_1-v_2\) = \(\frac{80}{8}\)

\(v_1-v_2\) = 10 -----(i)

In the second case, they travel in the opposite direction, the relative velocity is given by \(v_1+v_2\)

\(v_1+v_2\) = \(\frac{80}{1\frac{1}{3} }\)

\(v_1+v_2\) = \(\frac{80*3}{4}\)

\(v_1+v_2\) = 60 ------(ii)

Add equations (i) and (ii)

\(2v_1\) = 70

\(v_1\) = 35 km/hr

From equation (i)

\(v_2\) = 25 km/hr

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Answer:

10 root 2

Step-by-step explanation:

Refer to attachment.

Hope it helps.