50 points

Two siblings, sibling A and sibling B, are saving money for their summer vacation. The amount of money that sibling A has in their savings account, y, can be represented by the equation y = 10x + 25, where x represents the number of weeks. Sibling B's savings can be represented by the equation y = 5x + 50.

Based on the graph of this system of linear equations, after how many weeks will their savings accounts have the same amount of money?

2.5 weeks
5 weeks
15 weeks
75 weeks

The slope of a line perpendicular to 3x is \(-\frac{1}{3}\) .

What is slope ?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

What is perpendicular ?

The word perpendicular means at right angles and this is because when two lines meet, they form right angles. Perpendicular lines can face in any direction such as up and down, crossways, and side-to-side.

Have given,

Slope of the line  y=3x ,

you can compare it to  y=mx+c  form where  m  is the slope of the line.

y = 3x

differentiate respect of x

\(\frac{dy}{dx} = 3\)

Now, the slope of the line perpendicular to the line that has a slope of m is \(-\frac{1}{m}\)

The slope of a line perpendicular to 3x is \(-\frac{1}{3}\) .

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Total 6 students will be unable to complete the exam in the allotted time using probability.

It is a branch of mathematics. The possibility of the outcome of any random event is termed as probability. The range of the probability must be between o to 1.

Probability of completing in 90 minutes or less = P(x ≤ 90)

z = (x - μ)/σ

1.38= (90-79)/8

P(x ≤ 90) = P(z ≤ 1.38)

P(x ≤ 90) = P(z ≤ 1.38)

=0.91621

91.621% × 60 = 54.97

About 54 students will finish in the allotted time and  6 students will be unable to finish the exam in the allotted time.

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Answer:

250

Step-by-step explanation:

Compounded Continuously:

A=Pe^{rt}

A=Pe

rt

P=180 r=0.026 t=12

Given values

A=180e^{0.026(12)}

A=180e

0.026(12)

Plug in

A=180e^{0.312}

A=180e

0.312

Multiply

A=245.90784475

A=245.90784475

Use calculator (with e button)

A\approx 250

A≈250

Answer:

523.6 cm^3

Step-by-step explanation:

Volume of a sphere:

\( \frac{4}{3} \pi {r}^{3} \)

The diagram shows the diameter of the sphere is 10cm.

Radius (r) = 1/2 diameter

So r = 5 cm

Plug that into the formula above to get

\( \frac{4}{3} \pi \times{5}^{3} \)

= 523.6 cm^3

The solution of the differential equation with the given initial condition is: \(y = t² - 3e^(-t)\)

To find the solution `r(t)` of the differential equation with the given initial condition, the following format needs to be followed:r(t) = <__,__,__>

Section 10.7:

Problem 20 (1 point)

The differential equation is given as; \(dy/dt = 2t - y\)

and the initial condition is;

\(y(0) = -3\)

To solve the differential equation, we need to follow these steps;

Separate the variables y and t; \(dy = (2t - y)dt\)

Rearrange the terms by adding y on the right side;dy + y = 2tdt

Integrate both sides\(;∫(dy + y) = ∫2tdt\)

By integrating, we get;

\(y = t² - Ce^(-t)\)

Now, use the initial condition to solve for the constant C;

\(y(0) = (0)² - C(e^(-0)) \\= -3C \\= 3\)

Thus the solution to the differential equation is; \(y = t² - 3e^(-t)\)

Therefore, the solution of the differential equation with the given initial condition is: \(y = t² - 3e^(-t)\)

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Answer:

335

Step-by-step explanation:

multiply it by 2 and 3 respectively

Answer: y=-1 and x=2

Step-by-step explanation:

-9x+8y=-26

-9x-6y=-12

Subtract

14y = -14

Divide by 14

Y=-1

Substitute y=-1 into the equation

-9x-6(-1)=-12

-9x+6=-12

Subtract 6

-9x=-18

Divide by -9

X=2

In the most recent April issue of Consumer Reports, a study was conducted on the total fuel efficiency and weight of new cars to determine if there is a relationship between the two variables. To analyze this relationship, the appropriate statistical model would be A. Simple Linear Regression.

Simple Linear Regression is used to examine the relationship between a dependent variable (fuel efficiency in this case) and an independent variable (weight) when the relationship is expected to be linear. In this study, the researchers would use the data on fuel efficiency and weight for each car and fit a regression line to determine if there is a significant relationship between the two variables. The slope of the regression line would indicate the direction and strength of the relationship, and statistical tests can be performed to determine if the relationship is statistically significant.

In summary, the correct statistical model to analyze the relationship between the fuel efficiency and weight of new cars in the Consumer Reports study is A. Simple Linear Regression. This model would help determine if there is a significant linear relationship between these variables and provide insights into how changes in weight affect fuel efficiency. By fitting a regression line to the data and conducting statistical tests, researchers can draw conclusions about the strength and significance of the relationship.

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Answer:

Step-by-step explanation:

\((3, -4)=(x,y)\\y=3x+2\\\\m_1 =3\\In\: perpendicular\: line ;\\\\m_2 = \frac{-1}{m_1} \\m_2 = \frac{-1}{3} \\m_2 = -1/3\\\\Substitute \:new\:values\:into\: ;y=mx+b\\\\-4 = -\frac{1}{3} (3) + b\\-4 = -1 +b\\-4+1 =b\\-3 =b\\Substitute \:new\:values\:into\: ;y=mx+b\\y =-\frac{1}{3}x -3\)

Answer:

Sheet metal costs $20 per square foot.

Step-by-step explanation:

7.6x - 2.3x = 106

We are finding the value of x.

5.3x = 106

Divide both sides by 5.3.

x = 106 ÷ 5.3

x = 20

                                       Answer and Explanation

__________________________________________________________

__________________________________________________________

Sheet metal costs 20 dollars per square foot, and we can figure this out by multiplying the 20 by the numbers and subtracting them.

__________________________________________________________

\(7.6x-2.3x=106\) but what does x equal? ( 20 )

\(7.6\cdot20\) = \(152\)

\(2.3\cdot20\) = \(46\)

__________________________________________________________

\(152-46\) = \(106\)

Which is the same in the question, so x = 20.

__________________________________________________________

Hope this helps! <3

__________________________________________________________

Answer:

it issss 99+11d :)

Step-by-step explanation:

hope I helped

Answer:

99 + 11d

Step-by-step explanation:

11(9+d)

distribute the 11 into the ( )

99 + 11d

Hope this Helps!!!

In a multiple regression model, the variance of the error term e is assumed to be the same for all values of the independent variable. Therefore, the correct option is C) the same for all values of the independent variable.

In multiple regression, we use several independent variables to predict the values of the dependent variable. The model estimates the relationship between the independent variables and the dependent variable by calculating the coefficients of the independent variables.

The error term e represents the difference between the predicted value of the dependent variable and the actual value of the dependent variable.

The assumption of constant variance of the error term e is known as homoscedasticity. It means that the variance of the errors is the same for all levels of the independent variables.

This assumption is important because, if the errors have different variances across the levels of the independent variable, the model may not accurately capture the relationship between the independent variables and the dependent variable, leading to biased and unreliable results. so, the correct answer is C).

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The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.

The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:

(a) Local non-satiation:

This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.

(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:

MU1 = α * xi^(α−1) * x2^(β)

The marginal utility of x2 can be obtained as:

MU2 = β * xi^(α) * x2^(β−1)

Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.

(c) Quasi-concavity:

The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.

(d) Homotheticity:

The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.

In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.

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The solution to the system of inequalities is:

x ≥ -3.8 and

x ≤ 3

This can also be expressed as

-3.8 ≤ x ≤ 3

solving the first inequality:

-2x - 3x ≤ 19

Combining like terms, we get:

-5x ≤ 19

Dividing both sides by -5 :

x ≥ -3.8

So we have found that x is greater than or equal to -3.8.

From the second inequality:

-8x ≥ -24

Dividing both sides by -8:

x ≤ 3

So we have found that x is less than or equal to 3.

Therefore, the solution to the system of inequalities is:

-3.8 ≤ x ≤ 3

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The equation for a quartic function with zeros 4, 5, and 6 that passes through the point (7, 18) is given by \(y = \frac{3}{{7 - r^4}}(x - 4)(x - 5)(x - 6)(x - r^4)\), where \(r^4\) is the remaining zero of the quartic function. None of the provided options match this equation.

The equation for a quartic function with zeros 4, 5, and 6 that passes through the point (7, 18) can be found using the factored form of a quartic equation. First, let's start with the factored form of the quartic equation:

\(y = \frac{3}{{7 - r^4}}(x - 4)(x - 5)(x - 6)(x - r^4)\) , where \(r^{1}, r^2, r^3\) and \(r^{4}\) are the zeros of the function.

In this case, the zeros are 4, 5, and 6. So, we have:

\(y = \frac{3}{{7 - r^4}}(x - 4)(x - 5)(x - 6)(x - r^4)\)

To find the value of a, we can substitute the given point (7, 18) into the equation.

So, we have:

\(18 = \frac{3}{{7 - r^4}}(x - 4)(x - 5)(x - 6)(x - r^4)\)

Simplifying this equation, we get:

18 = a(3)(2)(1)(7 - \(r^4\)).

Next, we can simplify the right side of the equation:

18 = 6a(7 - \(r^4\)).
Now, we can divide both sides of the equation by 6 to solve for a:

3 = a(7 - \(r^4\)).
Dividing both sides by (7 - \(r^4\)), we get:

3/(7 - \(r^4\)) = a.

Now, we can substitute this value of a back into the factored form of the quartic equation:

y = (3/(7 - \(r^4\)))(x - 4)(x - 5)(x - 6)(x - \(r^4\)).

So, the equation for a quartic function with zeros 4, 5, and 6 that passes through the point (7, 18) is represented by the equation:

\(y = \frac{3}{{7 - r^4}}(x - 4)(x - 5)(x - 6)(x - r^4)\)

Unfortunately, the options provided in the question do not match this equation. Therefore, none of the options given is correct.

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The System Effectiveness is approximately 0.763.

To calculate the System Effectiveness, we need to multiply the values of Operational Readiness, Design Adequacy, Availability, Maintainability, and Mission Reliability.

System Effectiveness = Operational Readiness * Design Adequacy * Availability * Maintainability * Mission Reliability

Plugging in the given values:

System Effectiveness = 0.89 * 0.95 * 0.98 * 0.93 * 0.99

System Effectiveness ≈ 0.763

Therefore, the System Effectiveness is approximately 0.763.

The correct answer is a. 0.763.

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The population of rabbits by the year 2023  is 13985.

We have to use the following exponential function. This will be:

y = a b^t

In 2008 means, t=0

So we have 7100 = a b^0

a = 7100

y = 7100b^t

In 2013 means t = 2013-2008 =5

8900 = 7100 b⁵

b⁵ = 89/71

b = 1.046

So the equation will be

y = 7100 (1.046)^t

For 2023, t=2023-2008= 15

y = 7100(1.046)¹⁵

= 13985

The population is 13985.

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Step-by-step explanation: The solution to this system of equations will be where the two lines on the graph intersect with each other.

Notice that both of them intersect to the left of the y-axis which means our x - coordinate must be negative.

They also intersect above the x-axis so our y-coordinate must be positive.

So the only option with a negative x-coordinate

and a positive y-coordinate is (-1/4, 3/4).

Given the function:

Let's find the function after differentiating it 68 times.

To differentiate, let's take the derivative.

First derivative:

Second derivative:

Since 3 is the constant with respect to x, the derivative of 3cos(3x) with respect to x will be:

After the second differentiation, we have -sin, , the same will be applicable to the 68th time.

Therefore, for the 68th differentiation the exponent for the constant -3 will be 68.

Therefore, after differentiating the function 68 times, we have:

ANSWER:

Answer:

  720 kph

Step-by-step explanation:

The ratio of times is ...

  new time/original time = (1 2/3 h)/(5 h) = (5/3 h)/5 h) = 1/3

For the same distance, the ratio of speeds must be the inverse of this:

  new speed/original speed = s/240 = 1/(1/3) = 3

  s = 240(3) = 720 . . . . km/h

The aeroplane must travel at a speed of 720 km/h.

Answer:

720 km/h

Step-by-step explanation:

distance = 240*5=1200km

speed = distance/time

=1200/1.33 = 720 km/h

Answer:(192/9.6)÷7=20/7

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

If you cut them into halves then there will be twice as many pieces.

so you do:

6 x 2

= 12

Answer:

1:5

5:9

7:11

9:13

I think this is right in not sure though

Answer:

1.5

5.9

7.11

9.13

Step-by-step explanation:

I think that Is right also but I am not to sure

The solution to the system of equation 4y + x = 15 and x = 8y + 3 is (11, 1)

An equation shows the relationship between numbers and variables in an expression.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

Given that:

4y + x = 15

multiply by 2:

8y + 2x = 30    (1)

Also:

x = 8y + 3

8y - x = -3     (2)

Subtract equation 2 from 1 to solve using elimination method:

3x = 33

x = 11

put x = 11 in equation 2:

8y - 11 = -3

y = 1

The solution is (11, 1)

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The pair of lines perpendicular to RS are EA and FG.

A flat surface on which a straight line joining any two points on it would wholly lie is known as a plane.

What is plane?

A plane is a point, a line, and three-dimensional space's equivalent in two dimensions.

Main Body:

Given

E,F and G are on plane X. R and S are in both planes X and Y. EA and FG are parallel. AE and FG are vertical lines and are present on plane X. RS is present at the intersection of the 2 planes.

Explanation:

The lines which together could be perpendicular to RS are EA and FG.

We have to first draw both the planes according to the given information in question.

X is a vertical plane so draw a plane vertical on the horizontal plane that is Y plane. Now plot A and F And G in X plane and R,S in such a way that they  are in both plane so they will be at the intersection of both the planes. Now draw lines from A and F to form lines EA and FG.

Hence we can observe that lines EA and FD are perpendicular on line RS.

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Answer:

-5a + 10b - 5

Step-by-step explanation:

Simplify by combining like terms. Like terms are terms with the same amount of the same variables. Set the expression:

3a - 8a + 7b + 3b - 9 + 4

(3a - 8a) + (7b + 3b) + (-9 + 4)

(-5a) + (10b) + (-5)

-5a + 10b - 5 is your answer.

~

Answer:

Step-by-step explanation:

3a + 7b - 9 - 8a + 3b + 4 (Combine like terms)

(3a−8a) + (7b+3b) + (-9+4)

-5a +10b -5

Hope it helps!

Answer:

2/3*2/1

this is the answer

Answer:

2/3 × 2/1

Hope this helps :)

Explanation below.

Step-by-step explanation:

To find the multiplication expression, use the Keep, Change, Flip (KCF) method.