which shows graph (-3,5) and (4,-3) plotted correctly?​

The decay rate of a certain new cell phone is 0.333

For given question,

The average lifetime of a certain new cell phone is three years.

The manufacturer will replace any cell phone failing within two years of the date of purchase.

Also, the lifetime of these cell phones is known to follow an exponential distribution.

We need to find the decay rate.

We know that an exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time.

since the average lifetime of a certain new cell phone is three years, the decay rate would be 1/3 = 0.333

Therefore, the decay rate of a certain new cell phone is 0.333

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The point slope from the line with slope -3/7 that passes through the point (5,8) is y-8 = -3/7 ( x-5).

Two crucial constants are present in a linear function: the slope, which is represented by the letter m, and the y-intercept, which is represented by the letter b. Y = m x + b is the slope-intercept equation's formula. The point-slope equation is a different manner that we can occasionally express the equation of a line. It reads as follows y-y₀ = m(x-x₀).

Given that :

Slope m = -3/7

passes through the point p ( 5, 8 )

Equation is  y-y₀ = m(x-x₀)

y-8=-3/7 ( x-5)

here the point slope is y-8=-3/7 ( x-5)

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The plant's height after 24 months is 66 centimeters.

The equation relating H to M for this plant's growth pattern is:
H = 1M + 42

This equation shows that the plant's height (H) is equal to the number of months (M) times one centimeter, plus the initial height of 42 centimeters.

To find the plant's height after 24 months, we simply substitute M = 24 into the equation and solve for H:
H = 1(24) + 42
H = 24 + 42
H = 66

Therefore, the plant's height after 24 months is 66 centimeters.

Note that this equation assumes that the plant continues to grow at a constant rate of one centimeter per month.

In reality, the growth rate may vary depending on factors such as environmental conditions and the plant's health.

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Answer:

Paint required will be 2.06gallons

Step-by-step explanation:

The given dimensions are

Height - 8ft

Width - 7 \(\frac{11}{12}\) = 7.9ft

Length - 9. 83ft

To calculate the the amount of paint required to paint the walls we need to find the area of the walls

wall 1  = height * width of room= 8 * 7.9 = 63.28\(ft^2\)

wall 2 = height * length = 8*9.83 = 78.64 \(ft^2\)

The total area of the 4 walls will be = 2*(63 .28+78.64)= 283.84\(ft^2\)

ceiling area = 77.66\(ft^2\)

total area to be painted = 283.84 + 77.66 = 361.50\(ft^2\)

One gallon of paint covers 350 \(ft^2\) of area

so 361.50 \(ft^2\) area will be covered by = 361.5/350 = 1.03gallons of paint

also we need two coating so the paint required will be = 1.03 * 2 =2.06gallons

We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.

The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.

`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`

As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `

lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`

Since the limit of the ratio test is less than one, the given series converges.

The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).

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The cross product of the unit vectors j and k is i.

The cross product of two vectors a and b is defined as:

a x b = |a| |b| sin(theta) n

where |a| and |b| are the magnitudes of vectors a and b, theta is the angle between the two vectors, and n is a unit vector perpendicular to both a and b, with a direction given by the right-hand rule.

Here, j and k are unit vectors in the y and z directions, respectively. Since j and k are perpendicular to each other, the angle between them is 90 degrees, and the sin(theta) term in the cross product formula is equal to 1.

Thus, we have:

j x k = |j| |k| sin(90) n

Since j and k are unit vectors, their magnitudes are both equal to 1. Substituting these values into the equation above, we get:

j x k = 1 x 1 x 1 n = n

Therefore, the cross product of j and k is a unit vector n that is perpendicular to both j and k.

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Answer:

D.)

Step-by-step explanation:

Combine Like Terms:

=3x+3x+3x+2+2

=(3x+3x+3x)+(2+2)

=9x+4

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Answer:

the correct answer is D

Step-by-step explanation:

Answer:

it's your first answer of

y= (-7/8)x + 1/2

Answer:

x = 20

Step-by-step explanation:

The angles are same side interior angles so the add to 180

3x-10 + 5x+30 = 180

Combine like terms

8x +20 =180

Subtract 20 from each side

8x+20 -20 =180-20

8x = 160

Divide by 8

8x/8 =160/8

x = 20

Answer: x = 25

Step-by-step explanation:

When lines are parallel, the same side interior angles are supplementary, meaning they add up to 180 degrees. So to find x, you would add the two expressions and make it equal to 180 degrees.

3x - 10 + 5x + 30 = 180

8x - 20 = 180

8x = 200

x = 25

The answer is x=25

Answer:

(x∧2+4)(x∧2+8)

Step-by-step explanation:

Answer: the answer to this is true

Answer:

above sea level

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

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The surface area of the composite figure is 748 cm^2.

To find the surface area of a composite figure, we need to calculate the surface areas of each individual component and then add them together.

Let's break down the composite figure into its components:

There is a rectangular prism with dimensions 5 cm, 6 cm, and 4 cm. The surface area of a rectangular prism can be calculated using the formula: 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height respectively. So, the surface area of this rectangular prism is: 2(5)(6) + 2(5)(4) + 2(6)(4) = 60 + 40 + 48 = 148 cm^2.

There is a triangular prism with dimensions 20 cm (base), 12 cm (height), and 6 cm (slant height). The surface area of a triangular prism can be calculated by finding the areas of the two triangular bases and the three rectangular faces. The area of each triangular base is (1/2)(20)(12) = 120 cm^2, and the area of each rectangular face is (20)(6) = 120 cm^2. Therefore, the total surface area of the triangular prism is: 2(120) + 3(120) = 240 + 360 = 600 cm^2.

To find the surface area of the composite figure, we add the surface areas of the rectangular prism and the triangular prism: 148 cm^2 + 600 cm^2 = 748 cm^2.

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Answer:

A) y=(1/4)x-1, 4y=x-4

B) y=-2x

When the shape in the diagram rotates about the dashed line, shape 3, which is a cone with a cylindrical neck, forms a vertical section of a funnel. The correct answer is (C) Shape 3.

If the shape in the diagram rotates about the dashed line, the solid of the revolution formed will be a vertical section of a funnel, which corresponds to shape 3.

Shape 1 is a flat-top cone, which means it has a pointed top and a flat circular base. Rotating it about the dashed line would result in a solid with a pointed top and a flat circular base, resembling a cone. This does not match the description of a funnel, so shape 1 is not the correct answer.

Shape 2 is described as a 3D hexagon with a cylindrical hexagon on its top. Rotating it about the dashed line would not create a funnel shape but a more complex structure, which does not match the given description.

Shape 3 is a cone-shaped body with a cylindrical neck. When this shape is rotated about the dashed line, it will create a solid with a funnel-like shape, with a pointed top and a wider base. This matches the description provided, making shape 3 the correct answer.

Shape 4 is described as a 3D circle with a cylinder on top. Rotating it about the dashed line would not create a funnel shape, but rather a cylindrical shape with a circular base. In conclusion, the correct answer is C. Shape 3.

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Answer:  3082.2

Step-by-step explanation:

Answer: 3,082.2 ft

Step-by-step explanation:

You must apply the formula for calculate the perimeter of a circle, which is:

P=πd where,

P is the perimeter of the circle. (P=9,687 ft)

d is the diameter of the circle.

When you solve for d, you get:

d = P/π

d = (9,687 ft)/(22/7)

d = 3,082.2 ft

Therefore, the answer is: 3,082.2 ft

The approximate value of the system of equation is 3 which falls between 0.5 and 1

We should understand that to know the approximate value, we have to solve the systems of equations

The given equations are

y=-x+3

y=2x+1

when the various values of x are substituted in the two equations and the answers approximated to give exact value falls between 0.5 and 1 because the values of x at 0.5 =2.5.

When 2.5 is approximated gives 3 which is the value of y at x=1

In conclusion,  the approximate value of the system of equation is 3 which falls between 0.5 and 1.

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The final amount you will have in the account after 5 years of continuous compounding at an annual interest rate of 10% is approximately $824.36.

Using the formula for continuously compounded interest, we can calculate the final amount you will have in the account after 5 years:

\(A = P x e^(rt)\)

where:

P = $500 (the initial investment)

r = 0.10 (the annual interest rate as a decimal)

t = 5 (the time period in years)

Substituting the values into the formula, we get:

\(A = $500 x e^(0.10 x 5)\)

\(A = $500 x e^(0.50)\)

A = $500 x 1.6487 (rounded to 4 decimal places)

A = $824.36 (rounded to the nearest cent)

Therefore, the final amount you will have in the account after 5 years of continuous compounding at an annual interest rate of 10% is approximately $824.36.

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If you invest $500 at an annual interest rate of 10% compounded continuously, calculate the final amount you will have in the account after five years?

Answer:

  1.4×10¹⁸ m³

Step-by-step explanation:

You want 1.4×10⁹ km³ expressed in terms of m³.

1 km = 10³ m. Substituting that value for km in the given expression, we find the volume is ...

  1.4×10⁹ km³ = 1.4×10⁹×(10³ m)³ = 1.4×10¹⁸ m³

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Therefore, The given value of 1.4 × 109 km3 is converted into m3 by multiplying it with the conversion factor of (109 m3/km3), which gives 1.4 × 1018 m3.

The given value is 1.4 × 109 km3 to be converted into

m3.1 km = 1000 m.

Hence,

1 km3 = (1000 m)3 = 109 m3.

Therefore,

1.4 × 109 km3 = 1.4 × 109 × (109 m3/km3) = 1.4 × 1018 m3.

Hence, 1.4 × 109 km3 is equal to

1.4 × 1018 m3.

To convert

1.4 × 109 km3

into m3, the given value is multiplied by

(109 m3/km3), as 1 km3 = (1000 m)3 = 109 m3.

Therefore,

1.4 × 109 km3 = 1.4 × 109 × (109 m3/km3) = 1.4 × 1018 m3.

Hence, the conversion factor from km3 to m3 is 109, and this factor is multiplied by the given value. In the final answer, the value is expressed as 1.4 × 1018 m3.

Therefore, The given value of 1.4 × 109 km3 is converted into m3 by multiplying it with the conversion factor of (109 m3/km3), which gives 1.4 × 1018 m3.

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The dimension of pen that maximize the area is 150 ft by 150 ft.

What is the dimension of a area?

In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.

Given the perimeter of the rectangular is 600 ft.

Assume that the length of the rectangular be l and the breadth be b.

The perimeter of the rectangular is 2(l+b).

According the question:

2(l+b) = 600

Divide both sides by 2:

(l+b) = 300

l = 300 - b

The area of rectangular is A = lb

Substitute the value of l in the above equation:

A = (300 - b) b

A = 300b - b^2

The maximum value of a quadratic polynomial Ax^2+BX+C is at x = - B/(2A).

Compare Ax^2+BX+C  with 300b - b^2:

A = -1 and B = 300.

Putting A = -1 and B = 300 in b= - B/(2A).

b= - 300/(2×(-1))

b = 150.

Putting b =150 in l = 300 - b

l = 300 - 150

l = 150

The dimension is 150 ft × 150 ft.

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Answer:

143

Step-by-step explanation:

I think that's right

The equality of partial and Pearson correlations provides some insights into the relationship between X and Y, however, it is not sufficient to determine statistical significance, causality, range of scores.

The fact that the partial correlation is equal to the Pearson correlation does not automatically imply statistical significance. Statistical significance is determined by conducting hypothesis tests or calculating p-values, which require additional information such as sample size and significance level.

The statement (b) does not provide evidence of a causal relationship between X and Y. Correlation alone does not establish causality, as there may be other confounding factors or alternative explanations for the observed relationship.

The range of scores on X and Y cannot be inferred solely from the equality of partial and Pearson correlations. The range of scores depends on the actual data and variability within X and Y, which is not addressed in the statement.

The statement (d) suggests that the variable that was partialed out does not fully account for the correlation between X and Y.

However, it does not specify the nature of the variable or the method used for partial correlation. Further analysis and context are needed to draw conclusions about the role of the partialed-out variable.

In summary, while the equality of partial and Pearson correlations provides some insights into the relationship between X and Y, it is not sufficient to determine statistical significance, causality, range of scores, or the full explanation for the correlation observed. Additional analysis and considerations are necessary to make conclusions in these areas.

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Answer:

Step-by-step explanation:

1. 13/15

2.17/15

3.15/13

4.

5.

x=14

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Answer:

A length=24ft, width=15ft

Step-by-step explanation:

the side AB have x values of 5 and the side with CD have x values of 10 so the width from b to d or a to c is 5 so the width of the drawing is 5cm

the bottom side AC has y values of 8 and the top side BD has y values of 16 so they are 8 apart so the length of the rectangular drawing is 8cm

then the scale says that 1 cm = 3 ft so multiply the length and width each by 3 to get the answer that the length of the sail is 24ft and the width is 15ft

Hope this helps! :)

Answer: x = 6

Step-by-step explanation:

30 + 12 = x (5 + 2)

x (5 + 2) = 30 + 12

x (7) = 42

7x = 42

Divide both sides by 7

x = 6

Answer:

30+12=x(5+2)

or,42=7x

or,x=42÷7

So,x= 6

Answer:

C = 14π cm

Step-by-step explanation:

C = πd

or

C = 2πr

Simply use the 1st equation and plug in the diameter to find you answer.