Your friend thinks that the equation k-3.5=21, is he correct? explain.

Answer: each soda costs $1.5 and each hotdog costs $3.

Step-by-step explanation:

If H is the price for one hotdog and S is the price for one soda, we have the equations:

for Jack.

3*H + 2*S = $12

For Angie.

1*H + 4*S = $9

Now we can isolate one of the variables in one of the equations and then replace it in the other equation, let's isolate H in the second equation:

H = $9 - 4*S

now we replace it in the first eq

3*H + 2*S = $12

3*($9 - 4*S) + 2*S = $12

$27 - 12*S + 2*S = $12

-10*S = $12 - $27 = -$15

S = $15/10 = $1.5

Now we can replace it in the equation for H and get:

H = $9 - 4*$1.5 = $3

So each soda costs $1.5 and each hotdog costs $3.

Answer: One hotdog cost $3 and One soda costs $1.5

Step-by-step explanation:

Let hotdogs be denoted by h

Let sodas be denoted as s

Jack bought 3 hotdogs and 2 sodas for a total of $12. This can be written as:

3h + 2s = 12

Angie bought 1 hotdog and 4 sodas for $9. This can be written as:

h + 4s = 9

3h + 2s = 12

h + 4s = 9

1 × (3h + 2s = 12)

3 × (h + 4s = 9)

3h + 2s = 12

3h + 12s = 27

Subtract the equation

-10s = -15

s = -15/-10

s = 1.5

One soda cost $1.5

Since h + 4s = 9

h + 4(1.5) = 9

h = 9 - 6

h = 3

One hotdog costs $3

The series converges by the Alternating Series Test. The given series can be tested for convergence or divergence using the Alternating Series Test. First, we need to identify the sequence bn, which in this case is bn = (-1)^n * ((n^3 + 4n)^-1).

Next, we need to evaluate the limit of bn as n approaches infinity. This can be done using the limit comparison test by comparing bn to a known convergent series.

Since bn is decreasing and positive for all n > 2, we can use the comparison series 1/n^3.

lim (bn/1/n^3) = lim n^3/(n^3 + 4n) = 1

Since the limit is a finite nonzero number, and the comparison series 1/n^3 converges, we can conclude that the given series also converges by the Alternating Series Test.

Therefore, the answer is: The series converges by the Alternating Series Test.

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Answer:

- Please see the attached picture for full solution!:)

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When the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have a property of equal intervals.

Therefore, when the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have a property of equal intervals.

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When it comes to printing full-color pictures, it usually involves using the CMYK color model which stands for cyan, magenta, yellow, and black.

These colors are combined in different amounts to create a wide range of colors and shades. Therefore, the answer to your question is three plus black. The colors cyan, magenta, and yellow are combined to produce a wide range of colors, while the black is added to enhance contrast and to create darker tones.

This combination of colors provides a more accurate and vibrant representation of the original picture. It is important to note that there are other color models used for printing such as RGB (red, green, and blue) which is used for digital displays, but for printing purposes, CMYK is the most common.

In conclusion, full-color pictures are printed using three colors (cyan, magenta, and yellow) plus black to enhance contrast and create darker tones. This combination of colors provides a more accurate and vibrant representation of the original picture.

This model consists of four ink colors: cyan (C), magenta (M), yellow (Y), and key (black, K). These four inks are combined in various proportions to produce a wide range of colors in the final print. Therefore, the correct answer would be four colors (CMYK), including black.

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Yes, there is statistical evidence of a linear relationship between shoe size and height.

Yes, at the 5% significance level, there is statistical evidence of a linear relationship between shoe size and height, as the p-value linked with the coefficient for height is less than 0.05.

The slope of the regression line is positive, showing that as height grows, so does shoe size.

The coefficient of determination (R-squared) is quite tiny, indicating that height can explain only a small amount of the variability in shoe size, but this does not rule out the existence of a statistically significant linear link between the two variables.

The modified R-squared value is negative, indicating that adding the height variable did not improve the model's overall fit.

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Answer: Yes, there is evidence at the 5% significance level

Step-by-step explanation:

Took the test.

Fluctuations in aggregate demand and​ short-run aggregate supply bring fluctuations in real GDP around potential​ GDP.

Short-Run Supply of Aggregates:

The ratio of the actual GDP supply to the price level under constant nominal wage rates, other resource prices, and potential GDP is known as the short-term total supply. A rise in the price level will enhance the supply of real GDP when the nominal wage rate and the prices of other variables remain constant. The upward sloping short-term aggregate supply curve (SAS).

The supply of real GDP will rise in the short run if the price level rises.

The SAS curve is steeply sloping. Firms can boost production when the price level rises without an increase in the pay rate.

Adjustments to Potential GDP:

The LAS and SAS curves all trend to the right as potential GDP rises.

The potential GDP will rise if the following scenarios materialize:

Full employment now entails more labour.

capital growth: Technological advancement has occurred.

Modifications to the Money Wage Rate:

Aggregate Demand decreases and drifts to the left in the short run.

The entire amount of goods and services that Canadians, businesses, governments, and foreigners want to buy is known as real GDP demand Y.

This amount is the total of net exports X-M, investment I, public spending G, and consumer spending C.

Therefore, Y=C+I+G+X-M

total demand curve The ratio of real GDP demand to price level is known as aggregate demand.

The AD curve's descending slope is caused by two factors:

Impact of Wealth:

An increase in price level will result in less actual wealth while all other factors remain constant (currency, stocks, etc.).

Real GDP is now less in demand.

Similar to how prices fall while other factors remain the same, real wealth, real GDP, and demand all increase.

Intertemporal substitution effect:

When all other factors remain constant, rising prices will cause the real worth of the dollar to decline and interest rates to rise.

People borrow less as interest rates go up, which lowers real GDP demand. Similar to this, a decline in price will raise the currency's real value and lower interest rates. People borrow more money and spend more when interest rates are lower, which boosts real GDP demand.

Aggregate demand:

When aggregate demand increases, curve AD shifts to the right.

When aggregate demand decreases, curve AD shifts to the left.

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Answer:

True.

Explanation:

When solving equations with unknowns on both sides, it is generally recommended to first deal with the variable terms before dealing with the constant terms. This involves simplifying the equation by combining like terms and isolating the variable on one side of the equation. Once the variable is isolated, you can then solve for its value.\(\)

Answer:

x= 4, y= -1

Step-by-step explanation:

3x -5y= 17 -----(1)

y= x -5 -----(2)

Substitute (2) into (1):

3x -5(x -5)= 17

Expand:

3x -5x +25= 17

-2x= 17 -25

-2x= -8

x= -8 ÷(-2)

x= 4

Substitute x= 4 into (2):

y= 4 -5

y= -1

Answer:

y= -1

x= 4

Step-by-step explanation:

Plug in for y

3x - 5(x-5) = 17     Use the distributive property

3x - 5x + 25 = 17      Combine like terms

-2x + 25 = 17        Subtract  25 from both sides

-2x = -8         Divide by -2 on both sides

x = 4          Plug in for x

y = (4) - 5       Solve for y

y = -1

I hope this helps and please mark me as brainliest!

Answer:

<————• -72

Step-by-step explanation:

I have attached an image that explains my steps. First multiply each side by 4 to get x alone. If you are dividing or multiplying by a negative number, you switch the direction of the sign. The number line should show -72 and a FILLED in circle due to the equals to sign with an arrow pointing left.

Answer:

12 liters per min

Step-by-step explanation:

Math

27/4 = x

9/16      1

27/4=(9/16)x

Divide both sides by 9/16

12=x

Answer:

77.5 square units

Step-by-step explanation:

set up a proportion first.

\( \frac{2}{5} = \frac{31}{x} \)

then, cross multiply

2x = 155

divide by 2

x = 77.5

The area of the base of the larger prism is approximately 193.75 square units.

If two prisms are similar, then their corresponding sides are proportional. Let the smaller prism have a base area of 31 square units, and let the corresponding side of the larger prism have length x.

Since the ratio of similarity is 2:5, we have:

x / s = 5/2

where s is the length of the corresponding side of the smaller prism. Solving for x, we get:

x = (5/2) x s

We know that the area of the base of a prism is given by the formula:

A = s²

Substituting the value of s in terms of x, we get:

A = ((5/2) x s)²

A = (25/4) x s²

Substituting the value of s² in terms of the area of the smaller prism, we get:

A = (25/4) x 31

A = 775/4

A = 193.75 square units

Therefore, the area of the base of the larger prism is approximately 193.75 square units.

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The general solution of the damped spring-mass system with the given parameters is y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)]. By applying the initial conditions y(0) = 1 and y'(0) = 0, the specific solution can be obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t).

The equation for the damped spring-mass system can be expressed as my'' + cy' + ky = 0, where m is the mass, c is the damping coefficient, and k is the spring constant. In this case, m = 1 kg, c = 3 kg/s, and k = 2 kg/\(s^2\).

To find the general solution, we assume a solution of the form y(t) = e^(rt). By substituting this into the equation and solving for r, we get \(r^2\) + 3r + 2 = 0. Solving this quadratic equation gives us the roots r1 = -2 and r2 = -1.

The general solution is then given by y(t) = c1e^(-2t) + c2e^(-t). However, since we have a damped system, the general solution can be rewritten as y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)], where √7/2 = √(3/4).

By applying the initial conditions y(0) = 1 and y'(0) = 0, we can solve for the coefficients c1 and c2. The specific solution is obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t). This satisfies the given initial value problem.

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Step-by-step explanation:

y = 4x - 1

2x + 2y = 3

2x + 2(4x - 1) = 3

2x + 8x - 2 = 3

10x = 3 + 2

x = 5/10

x = 1/2

y = 4x - 1

y = 4(1/2) - 1

y = 2 - 1

y = 1

(x,y) = (1/2 , 1)

The quadratic parent function is represented by the equation F(x) = \(x^{2}\), so, the correct answer is D.

A quadratic function is a type of mathematical function that can be written in the form:

f(x) = a\(x^{2}\) + bx + c

where a, b, and c are constants and x are the variable. The highest power of x in a quadratic function is 2, which is why it is called a "quadratic" function.

The graph of a quadratic function is a curve called a parabola. The shape of the parabola depends on the value of the coefficient a. If a is positive, the parabola opens upward and has a minimum point, and if a is negative, the parabola opens downward and has a maximum point.

Quadratic functions are used in many areas of mathematics and science, such as physics, engineering, and finance. They are also used in computer graphics to create curves and surfaces.

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Answer:

it is 24inches

Step-by-step explanation:

33/11=3

3x8=24

Answer:

A.

Step-by-step explanation:

Cubic because the highest exponent is 3.

The classification of the polynomial P(x) = x^3−1 by degree is; Cubic. Hence, option A is correct.

Generally, polynomials take the form,

P(x) = ax^n + bx^(n-1) + cx^(n-2).... + z

where:

a, b....= arbitrary constants

x = variable

n = highest power of the variable in the polynomial

The given polynomial is P(x) = x^3−1

The classification of the polynomial P(x) = x^3−1 by degree is; Cubic.

Cubic function is one that has the highest exponent is 3.

Hence, option A is correct.

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The principal plus interest which gives the amount in the account after each year are;

Simple interest is the product of the principal amount, the rate and the time of investment

The amount Brayden deposited in the savings account, P= $2,700

The interest on savings account, R = 0.3% simple interest

The simple interest formula is, I = P•R•T

The interest in the account after each year is therefore;

1st year = $2,700×0.3%×1 = $8.7

The interest in 2 years, I = 2×$8.7 = $17.4

3 years, I = $8.7 × 3 = $26.1

4 years, I = $8.7 × 4 = $34.8

5 years, I = $8.7 × 5 = $43.5

The amount in the account after each of the 5 years are therefore;

1st year, A = $2,700 + $8.7 = $2,708.7

2nd year, A = $2,700 + $17.4 = $2,717.4

3rd year, A = $2,700 + $26.1 = $2,726.1

4th year, A = $2,700 + $34.8 = $2,734.8

5th year, A = $2,700 + $43.5 = $2,743.5

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(a) If the curl of F is zero, then F is conservative.

(b)  the line integrals of F over curves C1 and Cs which start and end at the same point are equal.

(c) the same curve in the opposite direction are equal.

(d) the line integral of F over a simple closed curve C is zero.

What is the linear function?

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

(a) A vector field F is conservative if it is the gradient of a scalar potential function f, i.e., F = ∇f.

To check if a vector field is conservative, we can compute the curl of F. If the curl of F is zero, then F is conservative. Mathematically, this can be expressed as curl(F) = 0.

(b) If things are "nice," i.e., all curves are simple curves in a simply connected region D and all functions are continuously differentiable on D, then the line integrals of F over curves C1 and Cs which start and end at the same point are equal. Mathematically, this can be expressed as ∫C1 F · dr = ∫Cs F · dr.

(c) If things are "nice," then the line integrals of F over curves C1 and -Ci, the same curve in the opposite direction, are equal. This result holds even if we do not know that F is conservative. Mathematically, this can be expressed as ∫C1 F · dr = -∫Ci F · dr.

(d) If things are "nice," then the line integral of F over a simple closed curve C is zero. This result holds if and only if F is conservative. Mathematically, this can be expressed as ∮C F · dr = 0 if and only if F is conservative.

Hence, (a) If the curl of F is zero, then F is conservative.

(b)  the line integrals of F over curves C1 and Cs which start and end at the same point are equal.

(c) the same curve in the opposite direction are equal.

(d) the line integral of F over a simple closed curve C is zero.

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Answer:

Step-by-step explanation:

Since 8 increases by 5 to be 13 I would say that s=15 and y=11

Alos s is the hypotenuse which is the longest side of the triangle

To estimate the project's beta, we need to make assumptions and use available data. Given the information provided for a publicly traded firm in the same line of business, including the debt outstanding, number of shares, stock price per share, book value of equity per share, and the beta of equity, we can calculate an estimate of the project's beta.

The beta measures the systematic risk of an investment relative to the overall market. To estimate the project's beta, we can use the leveraged beta approach. Since the project will be financed with equity, we assume that the project's beta will be equal to the equity beta of the publicly-traded firm in the same line of business. Therefore, the estimated beta of the project would be 1.19, based on the given information.

It is important to note that this estimation relies on the assumption that the project's risk profile and systematic risk are similar to that of the publicly-traded firm used as a reference. Additionally, this approach assumes that the project is solely financed with equity and does not take into account any potential debt financing or other factors that may affect the project's beta.

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Answer:

31/20

Step-by-step explanation:

You need to plug in x as y-3.

so instead of 10x+10y=1 it is 10(y-3)+10y=1

Then just simplify the equation to find the value of y

Answer:

it is which of the following is a reactant

Step-by-step explanation:

Answer:

4.95

Step-by-step explanation:

espero que te ayude

The sample is Stratified Random Sample

A large company surveys 100 employees by taking random samples of 101010 managers and 909090 non- managerial employees.

To find the what type of sample is this?

Now, According to the question:

"A stratified random sampling involves dividing the entire population into homogeneous groups called strata (plural for stratum). Random samples are then selected from each stratum. ... A random sample from each stratum is taken in a number proportional to the stratum's size when compared to the population. "

The managers group (101010) is one strata of sampling, and the other group of non-managerial employees (909090) is another strata. We're taking one sample from each group .

Hence, the sample is Stratified Random Sample

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Answer:

It is a rhombus.

Step-by-step explanation:

We have the four equations:

3x - y = -4

3y - x = 4

3y = x + 12

y = 3*x - 4

First, we need to write all of them in slope-intercept form, so they are easier to read.

We get:

y = 3*x+ 4

y =  (1/3)*x + 4/3

y = (1/3)*x + 12/3

y = 3*x - 4

First, we can see that:

y = 3*x+ 4 and y = 3*x - 4

are parallel lines, because they have the same slope.

y =  (1/3)*x + 4/3 and y = (1/3)*x + 12/3  also are parallel lines, because they have the same slope.

Then this is a parallelogram.

Now, here we have two slopes, 3 and 1/3.

Remember that for a line y = a*x + b

A perpendicular line would be written as:

y = -(1/a)*x + c

From this we can see that there are no perpendicular lines in our set of lines.

Then this can not be a square nor a rectangle.

It can not be a trapezoid, because we would need 3 different slopes to make a trapezoid, and here we have only two.

Then this can only be a rhombus.

Below you can see the graph of the four lines to see which quadrilateral they form.

Answer:

3.5 units

Step-by-step explanation:

Base × Height = Area, so 10 Base × 3.5 Height = 35 units^2

Answer:

3.5 units

Step-by-step explanation:

Answer:

im pretty sure it's

Step-by-step explanation:

all the angles added should be 180, so you subtract 62 and 94 from 180 to get 24.

Answer:£872

Step-by-step explanation:

The hospital must cut the number of overtime hours by approximately 2.91% in order to stay within budget.

To determine the required percentage reduction in overtime hours, we need to consider the impact of the nurses' hourly rate increase and the limited budget increase for overtime wages.

Let's assume the current budget for nurses' overtime wages is denoted by B, and the total number of overtime hours worked is denoted by H. The current overtime rate per hour is R.

With the 5% hourly rate increase, the new overtime rate per hour becomes 1.05R. Considering the limited budget increase of 3%, the new budget for overtime wages is 1.03B.

To calculate the required percentage reduction in overtime hours, we can set up the following equation:

(1.05R) * (1 - x) * H = 1.03B

where x represents the required percentage reduction in overtime hours.

Simplifying the equation, we have:

(1 - x) * H = (1.03B) / (1.05R)

Now, let's solve for x:

1 - x = (1.03B) / (1.05R * H)

x = 1 - [(1.03B) / (1.05R * H)]

Here, we can see that the required percentage reduction in overtime hours, represented by x, depends on the values of B, R, and H.

It's important to note that without knowing the specific values of B, R, and H, we cannot calculate the exact percentage reduction. However, based on the provided information, we can determine the maximum percentage reduction that the hospital must make to stay within budget.

By assuming that B, R, and H are constant, we can use the given constraints to calculate an approximate percentage reduction. Based on the constraints of a 3% budget increase and a 5% hourly rate increase, the hospital would need to reduce the number of overtime hours by approximately 2.91% to maintain a balanced budget.

Please keep in mind that this approximation may vary depending on the specific values of B, R, and H.

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