Challenge Andy and Emily each go to a hardware store to buy wire. The
table shows the cost y in dollars for x inches of the wire they need. Andy
needs 23 feet of the wire. Emily needs 15 yards of the wire. How much will
each of them spend for wire?

Answer:

y = 2/3x - 6

Step-by-step explanation:

Knowledge Needed

Slope-Intercept form: y = mx + b

Leave y and x as variables as it is easier for graphing.

m is the slope, or how much the y-value changes every timer the x-value increases by 1.

b is the y-intercept, or the x-value of the line when it has a x-value of 0 (when it hits the y-axis.)

Question

Using this information, lets first find the slope.

To find the slope, we can use the slope formula. Use any two sets of points to plug into the formula.

\(\frac{y_2-y_1}{x_2-x_1}\)

I'll use the points:

(3, -4)

and

(6, -2)

Because they are marked.

Plug in your two y-values into the numerator and two x-values into the denominator.

\(\frac{-2 - - 4}{6 - 3}\)

2/3

So, we have 2/3 as a slope. We can start writing the equation in slope-intercept form.

y = 2/3x + b

To solve for b, we can either examine the graph or solve it algebraically. However, if the graph is more complex we can't just look at it.

What is the x-value of the line when it touches the y-axis, or the bold vertical line?

-6

We know the y-intercept is -6.

y = 2/3x - 6

The mass of the original sample of phosphorus-32 was approximately 717.7 grams.

To solve this problem, we can use the radioactive decay formula:

A = Ao * 2^(-t/h)

Where:

A = resulting amount after time t

Ao = initial amount (at t=0)

t = time

h = half-life of the substance

In this case, we are given that the half-life of phosphorus-32 is 14.28 days. We want to find the initial mass, represented by Ao.

After approximately 57 days, 55 g of phosphorus-32 remain unchanged. Let's plug these values into the equation:

55 = Ao * 2^(-57/14.28)

To solve for Ao, we can isolate it by dividing both sides of the equation by 2^(-57/14.28):

55 / 2^(-57/14.28) = Ao

Using a calculator to evaluate 2^(-57/14.28), we find that it is approximately 0.07666.

Therefore, the initial mass, Ao, is:

Ao = 55 / 0.07666 ≈ 717.7 g

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Answer:

No

Step-by-step explanation:

The ratio of the first school is 5/2. The ratio of the second school is 7/8.

Answer: If two forecasters have unbiased forecasts, then they should have the same average error over many forecasts. In that sense, they would be equally good at forecasting.

Step-by-step explanation:

The statement that is true regarding evaluating the quality of a forecast is:

If both forecasters have an unbiased forecast, then they are equally good at forecasting.

Explanation:

A biased forecast can have a zero forecast error if the bias happens to offset the error in the forecast. However, a zero forecast error does not necessarily indicate that the forecast is unbiased.

In the mean squared error (MSE) evaluation, one single observation can make a very large difference because the errors are squared before they are averaged. Therefore, outliers can have a large impact on the MSE.

If we are evaluating the same forecaster, then the mean squared error is not always lower than the mean absolute error. It depends on the specific forecast and the distribution of errors.

However, if two forecasters have unbiased forecasts, then they should have the same average error over many forecasts. In that sense, they would be equally good at forecasting.

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Answer:

0.857142 infinity

Step-by-step explanation:

24/28 is an infinite decimal and would round to 0.86 by the nearest tenth

Answer:

s=6.2

Step-by-step explanation:

-3.1s=-19.22

divide -19.22 by -3.1 to get s

s=6.2

Answer:

1

Step-by-step explanation:

Answer:

(x/5)-6 and 3x(19)

Step-by-step explanation:

i have now attached the picture but it can be wrong!

The Riemann Hypothesis is a conjecture in mathematics that states that all non-trivial zeros of the Riemann zeta function lie on a specific line in the complex plane, known as the critical line.

This critical line is defined as the set of complex numbers with a real part equal to 1/2. Additionally, the hypothesis suggests that the only other zeros of the zeta function are the negative even integers.

The Riemann zeta function is an important mathematical function that arises in number theory and has connections to prime numbers. The Riemann Hypothesis has been a central problem in mathematics for over a century, and its truth or falsehood has significant implications for the distribution of prime numbers.

Despite extensive efforts, the hypothesis remains unproven, and its proof or disproof continues to be an active area of research.

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Answer:

x = 10, ∠ EHF = 110°

Step-by-step explanation:

7x and 11x are adjacent angles and sum to 180° , then

7x + 11x = 180

18x = 180 ( divide both sides by 18 )

x = 10

∠ EHF = 11x = 11(10) = 110°

Answer:

EHF = 110 deg

Step-by-step explanation:

From what it looks like 7x and 11x are being used as units of measurment. I can asssume a full circle adds up to 36x because 180deg adds up to 18deg.

If there were a number that was supposed to fill in for x it could be 0 because if the angles in this problem were 110 deg and 70 deg they would make 180 deg which is the straight line that the problem has.

A positive association occurs when an increase in one variable is generally associated with the increase in the second variable and a negative association occurs when one variable tends to decrease as the other increases.

An association is any relationship between two factors that produces them subordinate, i.e. knowing the value of one variable gives us some data around the possible values of the moment variable.

The objective of this variable is to utilize clear measurements and visualisations to investigate affiliations among different kinds of factors.

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Answer:

sin(x-60)-3

Step-by-step explanation:

The rule for translating a trigonometric function towards the right is y=f(x-a) so you substitute 60 for a which gives you y=sin(x-60).

Finally you subtract 3 from the whole function so the final answer should be y=sin(x-60)-3

Hope this helps.  

The orders are 1 stay the same. 2 change to 4, 3 change to 2, 4 change to 3, and 5 stays the same.

Multiple: 1/ 8 & 2/ 4  = 1 · 2/ 8 · 4  = 2/ 32  = 1 · 2/ 16 · 2  = 1/ 16   Multiply both numerators and denominators. Result fraction keep to lowest possible denominator (lowest=2). In the next intermediate step , cancel by a common factor of 2 gives 1/ 16 .  In words - one eighth multiplied by two quarters = one sixteenth.

Final result: 1/16

Answer:

200 cubic centimeter

Step-by-step explanation:

Answer:

201.1 cc

Step-by-step explanation:

r = d/2

v = πr^2 h

---------------------

r = 4/2

r = 2

v = π * (2^2) * 16

v = 3.14159 * 4 * 16

v = 201.06176

Rounded

v = 201.1 cc

--------------------

note:

if 3.14 is used for π

v = 200.96

which rounds to

v =201.0

Answer:

3, 6, 9, 12

4, 8, 12, 16

8, 16, 24, 32

15, 30, 45, 60

Step-by-step explanation:

multiply each number by itself

Answer:

m=7

Step-by-step explanation:

subract 35 from both sides to isolate the variable. Then you should be left with 5m=35. From there, divide both sides to isolate the variable even more, and you should be left with m=35/5 which is 7.

Answer: m=7

Step-by-step explanation:

\(5m+35=70\)

subtract 35 on both sides

\(5m+35-35=70-35\)

\(5m=35\)

divide 5 on both sides

\(35/5=7\)

\(m=7\)

Answer:

12

Step-by-step explanation:

bc u said that every by 12 that is only allow for every by 12 so its 12 ir 4

a. The width of the gap is 2cm

b. There are two ways Mr Goh can stack up 20 completed stools. And the lowest possible height is 4.8 metres.

Length of A = 3/8 × 64cm

Length of A = 24cm

Given that the volume of B and C is the same, then:

total length of B and C = 64cm - 24cm

total length of B and C = 40cm

length of B = 20cm and length of C = 20cm

a. The width of the gap in the stool is calculated by subtracting the width of B and C from the length of A

24cm - 22cm = 2cm

b. 20 completed stools can be stacked either standing or by it sides, so they can be stacked in two ways.

height of stacking 20 stools standing = 20 × (20 + 11)cm = 620cm

height of stacking 20 stools by its side = 20 × 24cm = 480cm

620cm = 6.2m

480cm = 4.8m

Therefore, the width of the gap is 2cm. There are two ways Mr Goh can stack up 20 completed stools. And the lowest possible height is 4.8 metres.

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Answer:

8 balloons

Step-by-step explanation:

We want to find how many she kept for herself.

She brought 24 balloons to the picnic.

She gave 1/3 to Karen.

She will be left with 2/3 of the balloons:

2/3 * 24 = 16

She will be left with 16 balloons.

She gave 1/2 of what was left to Tim. She will be left with 1/2 of the balloons:

1/2 * 16 = 8

She will be left with 8 balloons.

The f(5) for the given function f(x) is equal to 29.

We have,

f(x) = {x³     x< -3

         2x² -9   -3≤x<4

          5x+ 4       x≥4}

To determine f(5) for the function f(x), we need to evaluate the function at x = 5.

Let's consider the different cases based on the given piecewise definition of f(x):

For x < -3:

Since 5 is not less than -3, this case does not apply to the value we are evaluating.

For -3 <= x < 4:

Again, 5 does not fall within this range. Therefore, this case also does not apply.

For x >= 4:

Since 5 is greater than or equal to 4, this case applies. In this case, the function is defined as 5x + 4. So, substituting x = 5 into this equation, we get:

f(5) = 5(5) + 4

f(5) = 25 + 4

f(5) = 29

Therefore, f(5) for the given function f(x) is equal to 29.

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The x- and y-coordinates of the center of mass are; (20, 0)

The center of mass is the location where the sum of the relative position of the masses in a mass distribution is zero. It is the point where force can be applied on the distributed mass without causing a rotation of the system.

The mas of the steel plate = 800 g = 0.8 kg

The base length of the isosceles triangular plate = 20 cm = 0.2 m

The height of the isosceles triangular plate = 30 cm = 0.3 m

Considering a small strip of height, dx and width, I, we get

Area of small strip, dA = I·dx

Density of the plate for a unit thickness, ρ = M/A

Density of the small strip of mass dm = dm/dA

Considering the density of the plate as uniform, we get;

\(\displaystyle {\frac{dm}{dA} =\frac{M}{A}\)

Therefore;

\(\displaystyle {dm=\frac{M}{A}\times dA}\)

The area of the triangular plate, A = (1/2) × 0.2 m × 0.3 m = 0.03 m²

Mass of the plate, M = 0.8 kg

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx}\)

The width of the small strip, I, located at a distance x from the vertex of the triangular plate, using similar triangles, indicates;

\(\dfrac{I}{20} = \dfrac{x}{30}\)

\(I=20\times \dfrac{x}{30} = \dfrac{2}{3} \cdot x\)

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx} = \frac{0.8}{0.03}\times \dfrac{2}{3} \cdot x\cdot dx}\)

The center of mass, \(x_{cm}\), can be obtained with the formula; \(\displaystyle {x_{cm} = \dfrac{1}{M} \cdot \int\limits {x} \, dm }\)

Therefore; \(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx }\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx } = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0\)

\(\displaystyle {x_{cm} = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0=\frac{200}{9} \times \frac{0.027}{3} =0.2\)

The location of the x-coordinate center of mass, \(x_{cm}\) = 0.2 m = 20 cm from the vertex, which is the same location as the x-coordinate of the centroid of the plate of uniform density.

The plate is symmetrical about the x-axis, therefore, the y-coordinate of the center of mass is along the x-axis, which is \(y_{cm}\) = 0

The coordinate of the center of mass = (0.2, 0)

Part of the question requires the location of the coordinate of the center of mass of the triangular plate

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In conclusion, the present value of your return from this investment, when the stock price is 98, is approximately $1.965.

To find the present value of your return from the investment, we need to calculate the value of the European put option at time t=1/2 and then discount it back to the present value using the nominal annual interest rate of 6 percent compounded monthly.

(a) If S(1/2) = 102:
To calculate the value of the European put option at time t=1/2, we need to determine if it is in-the-money or out-of-the-money.

The strike price is K=100, and since the stock price is greater than the strike price (102 > 100), the put option is out-of-the-money. In this case, the put option has no intrinsic value.

The present value of your return from this investment would be $5, as the put option has no value. There is no profit or loss.

(b) If S(1/2) = 98:
Similar to the previous case, we need to determine if the put option is in-the-money or out-of-the-money. Since the stock price is less than the strike price (98 < 100), the put option is in-the-money.

The intrinsic value of the put option is given by the difference between the strike price and the stock price:

K - S(1/2) = 100 - 98 = 2.

To calculate the present value of your return from this investment, we need to discount the intrinsic value of the put option back to the present value. The nominal annual interest rate of 6 percent compounded monthly translates to a monthly interest rate of 6% / 12 = 0.5%.

Using the formula for the present value of a future cash flow:
Present Value = Intrinsic Value / (1 + Monthly Interest Rate)^(Number of Months)

Number of Months = 1/2 years * 12 months/year = 6 months.

Present Value = 2 / (1 + 0.005)^(6)
Present Value ≈ $1.965.

In conclusion, the present value of your return from this investment, when the stock price is 98, is approximately $1.965.

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Answer:

Step-by-step explanation: just learn

V= (4d^2 - 48d + 96) / (-36(d - 1)^2) will be the expression for the volume of the following prism when the dimensions of the prism are given.

The quantity of space a three-dimensional figure occupies is measured by its volume. It is determined by multiplying the object's length, breadth, and height, and is generally symbolized by the letter "V". For example, the volume of a cube with sides of length 3 units is 3 x 3 x 3 = 27 units.

The formula 4/3r3 may be used to determine a sphere's volume, where r is the sphere's radius. The area of the base times the height of the cylinder, or r2h, yields the volume of a cylinder.

It's important to remember that the volume of a three-dimensions figure varies depending on its shape and size.

How to solve?

V = (d - 2/3d - 9) * (4/d - 4) * (2d - 6/2d - 4)

V = (d - 2/3d - 9) * (4/d - 4) * (4d - 24/4d - 16)

V = ((d - 2)/(3d - 9)) * (4/d - 4) * (4d - 24/4d - 16)

V = ((d - 2)/(3d - 9)) * (4/(d - 4)) * (4d - 24/(4d - 16))

V = ((d - 2)/(3d - 9)) * (4/(d - 4)) * (4d - 24/(4d - 16))

= ((d - 2) * 4 * (4d - 24)) / ((3d - 9) * (d - 4) * (4d - 16))

= (4d^2 - 48d + 96) / (12d^2 - 48d^2 + 144d - 36)

= (4d^2 - 48d + 96) / (-36d^2 + 144d - 36)

= (4d^2 - 48d + 96) / (-36(d^2 - 4d + 1))

= (4d^2 - 48d + 96) / (-36(d - 1)(d - 1))

V= (4d^2 - 48d + 96) / (-36(d - 1)^2)

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Answer:

The Answer is 2

Step-by-step explanation:

70 - 20= 50 and if you divide by 25 you get 2. Because 25 times 2 = 50 hope it helps

Answer:

2

Step-by-step explanation:

Subtract 70 and 20

70 - 20

Simplify

50

Divide 50 by 25

50/25

Simplify

2

Answer:

ff

Step-by-step explanation:

Answer:

The price of rice per gram is 0.006$

Step-by-step explanation:

I. David wants to make 10 servings,

each require 75 g of rice and 5 spice. When ratio is 15:1

If rice : spice = 75 : x

15x = 75

x = 5

=> 5 * 15 : 1 * 5

= 75 : 5

So rice : spice is  75 : 5

II. When 1 serving require 75 : 5

So 10 servings is 10 * 75 : 5 * 10

= 750 : 50

So he must has 750 grams rice and 50 grams spice.

III. He must buy spice and rice which..

a) He has 40 grams spice, he'll buy for 10 grams spice.

b) He has no rice, he'll buy for 750 grams rice.

But the question only ask for price of rice which he spend 4.5$

=  \(\frac{4.5}{750}\)

= 0.006$

In 1 gram of rice he spend 0.006$

If 750 grams of rice, he'll spend 750 * 0.006$ = 4.5$ => true

That makes 0.006$ is the right answer.

Hope that help :)