The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 9 cm and the width is 6 cm, how fast is the area of the rectangle increasing?

The results of the two-sample t-test, there does not appear to be enough evidence to support the claim that the mean FICO score of borrowers with high-interest mortgages is different than the mean FICO score of borrowers with low-interest mortgages.

To test the claim that the mean FICO score of borrowers with high-interest mortgages is different than the mean FICO score of borrowers with low-interest mortgages, we can perform a two-sample t-test.

Using the given data, we can calculate the test statistic as follows:

t = (492 - 508) / sqrt((49^2 / 19) + (38^2 / 26)) = -1.57

The degrees of freedom for this test are 19 + 26 - 2 = 43. Using a t-table or calculator and a significance level of 0.2, we can find the critical value to be approximately ±1.301.

Since the absolute value of the test statistic (1.57) is less than the critical value (1.301), we fail to reject the null hypothesis. This means that we do not have enough evidence to support the claim that the mean FICO score of high-interest mortgage borrowers is different than the mean FICO score of low-interest mortgage borrowers at the 0.2 significance level.

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T-Mobile charges a base fee of $15 per month plus $0.05 for each minute. 300 minutes long would you need to call for them to charge the same amount.

Given that,

T-Mobile charges a base fee of $15 per month plus $0.05 for each minute you are on the phone for any long-distance call, while Verizon has a basic rate of only $10 per month but charges $0.10 for long-distance calls.

We have to find how long would you need to call for them to charge the same amount.

We can write the equation as

15+0.05x=0.10x

0.05x-0.10x=-15

-0.05x=-15

0.05x=15

x=15/0.05

x=300 minutes

Therefore, 300 minutes long would you need to call for them to charge the same amount.

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 complete question:

For any long-distance call T-Mobile charges a base rate of $15 per month plus $0.05 a minute

that you are on the phone, while Verizon charges a base rate of only $10 per month, but charges

$0.10 per minute for long distance calls. Write the equation that represents the total cost for one month of long distance calls for each company, where y is total cost and x is the amount of minutes used:

T-Mobile:

Verizon:

Using an algebraic method, determine how many minutes the two plans will cost the same.

According to the information, the vertex at the top left of the parallelogram is (4, 8.25). Thus, the other two vertices of the parallelogram are (2, 5), (9, 5), (7, 8), and (4, 8.25).

To find the vertex of the parallelogram we can use the point-slope form of a line: y - y1 = m(x - x1), where,

For the side sloping up from left to right, we can use the point (2, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:

Simplifying, we get:

To find the point where this line intersects the top side of the parallelogram, we can use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (2, 5) is 5 units away from the intersection point in the x-direction, so we can add 5 to the x-coordinate to find the intersection point. Plugging in x = 7 into the equation above, we get:

Therefore, the vertex at the top right of the parallelogram is (7, 8).

For the side sloping down from left to right, we can use the point (9, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:

Simplifying, we get:

To find the point where this line intersects the top side of the parallelogram, we can again use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (9, 5) is 5 units away from the intersection point in the x-direction, so we can subtract 5 from the x-coordinate to find the intersection point. Plugging in x = 4 into the equation above, we get:

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The angles that are 118 degrees are ∠1 , ∠3, ∠5 and ∠7.

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

Therefore, let's find the angle relationship in the line and find the angles that are 118 degrees.

Hence,

∠3 = 180 - 62 = 118 degrees(angles on a straight line)

∠1 ≅ ∠3 (vertically opposite angles)

∠7 ≅ ∠3 (alternate interior angles)

∠5 ≅ ∠7 (vertically opposite angles)

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The total surface area of the clubhouse including the floor is approximately 95.98 square feet.

We have,

The surface area of a square pyramid can be found by adding the area of the base to the sum of the areas of the four triangular faces.

Since the base is a square, its area is 6^2 = 36 square feet.

Each triangular face is an equilateral triangle with a side length of 6 feet, so its area can be found using the formula.

A = (√(3)/4) x s²,

where s is the length of a side.

The area of each triangular face.

A = (√(3)/4) x 6² = 9 √(3) square feet.

The total surface area is then:

A = 4 x 9 √(3) + 36

A = 36 √(3) + 36  ≈ 95.98 square feet

(rounded to the nearest hundredth)

Therefore,

The total surface area of the clubhouse including the floor is approximately 95.98 square feet.

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The order of given numbers from least to greatest is -2.66<-2.43<2.045<2.55.

The given numbers are [tex]-2\frac{2}{3}, 2\frac{5}{9},[/tex] 2.045 and -2.43.

Ascending order means to arrange numbers in increasing order, that is, from smallest to largest.

Here, -2.66, 2.55, 2.045 and -2.43.

-2.66<-2.43<2.045<2.55

Therefore, the order of given numbers from least to greatest is -2.66<-2.43<2.045<2.55.

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Answer:

C. The value of a car at the end of a year is 8 percent less than the value at the beginning of the year.

Step-by-step explanation:

An exponential function models situations in which a quantity grows or decays by a constant percentage or factor over equal intervals of time.

Let's analyze each situation:

A. The number of fish in a tank increases by five per month.

This situation represents a constant increase (addition) of fish every month. It can be modeled by a linear function, not an exponential function.

B. The number of people in a city increases by 100 every year.

This situation also represents a constant increase (addition) in the number of people per year. It can be modeled by a linear function, not an exponential function.

C. The value of a car at the end of a year is 8 percent less than the value at the beginning of the year.

This situation represents a constant percentage decrease (multiplication) in the value of the car each year. It can be modeled by an exponential function (e.g., V(t) = V_0 * (1 - 0.08)^t, where V(t) is the value of the car after t years and V_0 is the initial value of the car).

D. The value of a phone drops $100 per year.

This situation represents a constant decrease (subtraction) in the value of the phone per year. It can be modeled by a linear function, not an exponential function.

The equivalent Expression of 8[tex]0^{1/2[/tex] is √80.

We have the expression as 8[tex]0^{1/2[/tex]

We know that

[tex]a^{1/2[/tex] = √a

So, 8[tex]0^{1/2[/tex]

= √80

= √ 2 x 2 x 2 x 2 x 5

= 2 x 2 √5

= 4√5

Thus, the equivalent expression is √80.

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Answer:

for times it would = 34600 but for adding it would be 3,470

then subtracting would be 3,450 then dividing would be 346

Step-by-step explanation:

HOPE THIS HELPSSS

The 46th term of the sequence is 324.

We have,

To find the 46th term of the sequence, we need to determine the pattern or rule that generates the terms.

Since the difference between consecutive terms is a constant value of 7, we know that this is an arithmetic sequence with a common difference

of 7.

To find the 46th term, we can use the formula for the nth term of an arithmetic sequence:

a(n) = a(1) + (n - 1) d

where a(1) is the first term, d is the common difference, and n is the term number we want to find.

Using the given information, we have:

a(1) = 9

d = 7

n = 46

Plugging these values into the formula, we get:

a (46) = 9 + (46 - 1)7

a (46) = 9 + 45 (7)

a(46) = 9 + 315

a(46) = 324

Therefore,

The 46th term of the sequence is 324.

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The 99% confidence interval estimate of the mean skull width is given as follows:

(126.8 mm, 140.76 mm).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The sample in this problem is given as follows:

128.1, 138.2, 125.7, 132.3, 143.2, 134.7, 138.8, 129.3.

Inserting these values into a calculator, the parameters are given as follows:

[tex]\overline{x} = 133.78, s = 5.64, n = 8[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 8 - 1 = 7 df, is t = 3.5.

The lower bound of the interval is given as follows:

133.78 - 3.5 x 5.64/sqrt(8) = 126.8 mm.

The upper bound of the interval is given as follows:

133.78 + 3.5 x 5.64/sqrt(8) = 140.76 mm.

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The missing test scores were both 8.3. The standard deviation for the test scores was 21.66. The difference between the harmonic mean and the geometric mean of the 12 students was 3.26.

The sum of the scores of the 10 students is 63. The average score of the 10 students is

(63 + x + x) / 12 = 8.3

Solving for x, we get

x = 8.3 * 12 - 63 - 13.8 - 10.4

x = 100.6 - 63 - 13.8 - 10.4

x = 13.4

Therefore, each missing script has a score of 13.4.

To find the standard deviation, we first need to find the variance

Find the mean

(2.7 + 6.3 + 4.1 + 6.4 + 3.5 + 4.7 + 13.8 + 79 + 12.1 + 10.4 + 13.4 + 13.4) / 12 = 11.0

Subtract the mean from each score and square the result

(2.7 - 11)², (6.3 - 11)², (4.1 - 11)², (6.4 - 11)², (3.5 - 11)², (4.7 - 11)², (13.8 - 11)², (79 - 11)², (12.1 - 11)², (10.4 - 11)², (13.4 - 11)², (13.4 - 11)²

Add up the squared differences

5697.36

Divide by the number of scores minus one, to get the variance

5697.36 / 11 = 517.03

Take the square root of the variance to get the standard deviation

√(517.03) = 22.76

Therefore, the standard deviation for the test scores is 22.76.

The harmonic mean is calculated by dividing the number of scores by the sum of the reciprocals of the scores, and then taking the reciprocal of the result

12 / (1/2.7 + 1/6.3 + 1/4.1 + 1/6.4 + 1/3.5 + 1/4.7 + 1/13.8 + 1/79 + 1/12.1 + 1/10.4 + 1/13.4 + 1/13.4) = 5.04

The geometric mean is calculated by taking the product of all the scores, and then taking the nth root of the product, where n is the number of scores

(2.7 * 6.3 * 4.1 * 6.4 * 3.5 * 4.7 * 13.8 * 79 * 12.1 * 10.4 * 13.4 * 13.4)^(1/12) = 8.30

Therefore, the difference between the harmonic mean and the geometric mean is

5.04 - 8.30 = -3.26

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Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

Answer:

Step-by-step explanation:

Connect N and L to create a triangle. Connect P and L so that you also form a rectangle. Connect P and H to create a semicircle. Finally, connect H and K to create another rectangle, and another triangle. Use rectangle area formula, triangle area formula, and semicircle area formula to solve for the area.

We can conclude here that we have sufficient evidence that the mean score is not equal to 571.

The test statistic here is computed as:

= (589 - 571) / 46/✓26

= 1.9953

Now the p-value for n-1 = 25 degrees of freedom here is computed from the t-distribution tables as:

p = 2P( t25 > 1.9953 ) = 2*0.0285 = 0.0570

0.05 < P-value < 0.1

As the p-value here is 0.0570 < 0.1 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here.

Therefore we can conclude here that we have sufficient evidence that the mean score is not equal to 571.

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The solution is::

a. 120 ways can they​ arrive.

b. 6 can Eduardo arrive first and Tyrone ​last

c. 0.05 is the probability that Eduardo will arrive first and Tyrone last.

Here, we have,

a) The ways Eduardo, Sarah, Maria, Jim, and Tyrone can arrive to the party is

5! = 5×4×3×2×1 = 120

The logic behind it is

5 different people can arrive first, after that

4 different people can arrive second, when first and second arrived is known,

3 different people can arrive third, then

2 different people can arrive fourth

only 1 person left to be fifth.

b) Using the same logic, when first and last arrived is known, there is

3!=3×2×1=6 ways they can arrive in this case.

c)  The probability that Eduardo will arrive first and Tyrone last is

the division of the ways Eduardo arrive first and Tyrone ​last by the ways 5 people can arrive = 6/120 = 0.05

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complete question:

Eduardo, Sarah, Maria, Jim, and Tyrone have all been invited to a dinner party. They arrive randomly and each person arrives at a different time.

a. In how many ways can they​ arrive?

b. In how many ways can Eduardo arrive first and Tyrone ​last?

c. Find the probability that Eduardo will arrive first and Tyrone last.

The value of {g} on solving the given expression is 84.

The given expression is -

(16/4)(3x7) = g

We can solve for {g} as -

g = 16/4 x (3 x 7)

g = 4 x 21

g = 84

Therefore, the value of {g} on solving the given expression is 84.

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{Complete ques is -

Solve for g . Make sure to show your work.

(16/4)(3x7)=g}

The solutions for the given equation are x=−1,1,√2,−√2. Therefore, option B is the correct answer.

The given equation is x⁸-4x⁷+3x⁶+8x⁵-15x⁴+4x³+9x²-8x+2=0.

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Here, (x⁸-4x⁷+8x⁵+4x³)+3x⁶-15x⁴+9x²+2=0

(x-1)⁵(x³+x²-2x-2)=0

(x-1)⁵(x²-2)(x-1)=0

(x-1)⁵=0, (x²-2)=0 and (x-1)=0

x=±1 x=±√2 and x-1

Exact Form: x=−1,1,√2,−√2

Therefore, option B is the correct answer.

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Answer:

12

Step-by-step explanation:

4(5)-8

20-8

12

a) The amount at the end of 1 year is given as follows: $10,170.

b) The amount at the end of 2 years is given as follows: $11,492.10.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

P = 9000, r = 0.13, n = 1.

Hence the equation for the balance at the end of t years is given as follows:

[tex]A(t) = 9000(1.13)^t[/tex]

After one year, the balance is given as follows:

[tex]A(1) = 9000(1.13)^1 = 10170[/tex]

After two years, the balance is given as follows:

[tex]A(2) = 9000(1.13)^2 = 11492.1[/tex]

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Will ran longer.

Given that Will ran across the diagonal of a square field of the side 40 yd and the James ran across the diagonal of a rectangular field with a length of 25 yards and a width of 35 yards.

We need to find who ran longer,

So for the same we will simply apply Pythagoras theorem to find the length of the diagonal of the fields, whose diagonal will be longer he will run longer,

So, Will ran = √40²+40²

= √3200 = 56.56 yards

James = √25²+35²

= 43 yards

Since Will's diagonal is longer so he ran longer.

Hence, Will ran longer.

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Answer:

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

Use of identities:

Simplify the given expression as below:

By comparing we see that:

The equation of the line in point-slope form is given as follows:

y - 60 = 0.5(x - 40).

The point-slope equation of a line is given as follows:

y - y* = m(x - x*).

In which:

The point in this problem is given as follows:

(40, 60).

The intercept is (0, 40), meaning that when x increases by 40, y increases by 20, hence the slope m is given as follows:

m = 20/40

m = 0.5.

Thus the equation is:

y - 60 = 0.5(x - 40).

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(i) [tex]\lim_{x \to \pi/3}[/tex] f(x) = 1 + √3.

(ii) [tex]\lim_{x \to \frac{\pi}{4}} f(x)[/tex] does not exist.

For λ = 2.5, the function f(x) will be continuous at x = 0.

Given the function is,

f(x) = 1.5, when x = 0

    = 1 -2 sin x, when x < π/4

    = 1 + 2 sin x, when x > π/4

    = 1 + (sin λx/sin 5x)

Now,

[tex]\lim_{x \to \pi/3}[/tex] f(x) = [tex]\lim_{x \to \pi/3}[/tex] (1 + 2 sin x) [Since, π/3 > π/4]

                    = 1 + 2 sin (π/3)

                    = 1 + 2√3/2 = 1 + √3

Hence, [tex]\lim_{x \to \pi/3}[/tex] f(x) = 1 + √3.

Now left hand limit is,

[tex]\lim_{x \to \frac{\pi^+}{4}}[/tex] f(x) = [tex]\lim_{x \to \frac{\pi^+}{4}}[/tex] (1 + 2sin x) = 1 +2 sin(π/4) = 1 + 2*(1/√2) = 1 + √2

and right hand limit is,

[tex]\lim_{x \to \frac{\pi^-}{4}}[/tex] f(x) = [tex]\lim_{x \to \frac{\pi^-}{4}}[/tex] (1 - 2 sin x) = 1 - 2*(1/√2) = 1 - √2

Since left hand limit and right hand limit are not equal so value of [tex]\lim_{x \to \frac{\pi}{4}} f(x)[/tex] does not exist.

[tex]\lim_{x \to 0}[/tex] f(x) = [tex]\lim_{x \to 0}[/tex] (1 + (sin λx/sin 5x)) = 1 + [tex]\lim_{x \to 0}[/tex] ((sin λx/λx)/(sin 5x/5x))*(λ/5) = 1 + λ/5

Since f(x) is continuous at x = 0.

So, [tex]\lim_{x \to 0}[/tex] f(x) = f(0)

1 + λ/5 = 1.5

λ/5 = 1.5 - 1 = 0.5

λ = 2.5

Hence the value of λ will be 2.5.

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The teaspoons of juice that are in the can is 4

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Teaspoons = Pineapple/Recipe

Substitute the known values in the above equation, so, we have the following representation

Teaspoons = 12/3

Evaluate

Teaspoons = 4

Hence, the number of teaspoons is 4

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a. WXYZ is a kite

b.In the kite mWQZ = 90° because XZ bisects WY

c. WY = 24 mm because WQ = QY

A kite is a quadrilateral that has two pairs of consecutive equal sides and perpendicular diagonals.

a. From the figure, we see that WXYZ is a kite

b. To determine mWQZ, we use the property of a kite which says that the diagonals of a kite intersect at right angles. Since XZ and WX are the diagonals of the kite, they thus intersect at right angles.

Since a right angle is 90° and the angle of intersection is mWQZ, thus mWQZ = 90°

So, mWQZ = 90° because XZ bisects WY

c. To determine WY, we know that WY is the shorter diagonal of the kite. Since one of the properties of a kite says that the longer diagonal bisects the shorter diagonal. So, XZ bisects WY. So, WY = WQ + QY. Since XZ bisects WY, WQ = QY.

So, WY = WQ + QY

= QY + QY

= 2QY

= 2(12 mm)

= 24 mm

So, WY = 24 mm because WQ = QY

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The number which is not the part of the solution set to the inequality below is 27.

Given inequality is,

w - 10 ≤ 16

WE have to find the solution for the inequality.

Adding both side of the inequality with 10,

w - 10 + 10 ≤ 16 + 10

w ≤ 26

So the solution of the inequality consists of all the points which are less than or equal to 26.

So it contains 11, 15 and 26.

It does not contain 27.

Hence the solution does not contain 27.

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Answer:

use coordinate plane

Step-by-step explanation:

To find the inverse of an equation or graph, you can reflect the graph in the line y = x by switching the x and y coordinates of each point on the graph1. You can also find the equation for the inverse function by switching x and y in the original equation and solving for y12. To check if a graph has an inverse, you can use the horizontal line test: if any horizontal line intersects the graph only once, then the graph has an inverse1.

Considering that the surface area and the volume of the cylinders are equal, the surface areas are given as follows:

108π ft².

250π ft².

Here, we have,

the surface area and the volume of a cylinder:

For a cylinder of radius r and height h, the surface area is given by:

S = 2πr(h + r).

The volume is given by:

V = πr²h.

For item 14, the parameters are given as follows:

r = 6 ft, h = x ft.

Hence we solve for x equaling the surface area and the volume as follows:

V = S

36πx = 12π(x + 6)

3x = x + 6

2x = 6.

x = 3.

Hence the surface area is:

S = 12π(3 + 6) = 108π ft².

For item 15, the parameters are given as follows:

r = 10 ft, h = x ft.

Hence we solve for x equaling the surface area and the volume as follows:

V = S

100πx = 20π(x + 10)

5x = x + 10

4x = 10.

x = 2.5.

Hence the surface area is:

S = 20π(2.5 + 10) = 250π ft².

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