Tara created a scatter plot for the same data. She fit the line y = 3.6x + 17.6 to the data in 8. Interpret the slope of the line fit to Tara's data.​

Answer:

[tex] {3}^{2} + {4}^{2} = {5}^{2} [/tex]

[tex] {(3 \times 2)}^{2} + {(4 \times 2)}^{2} = {(5 \times 2)}^{2} [/tex]

[tex] {6}^{2} + {8}^{2} = {10}^{2} [/tex]

3-4-5 is a Pythagorean triple.

Multiplying each of these numbers by 2, we obtain 6-8-10, which is a Pythagorean triple.

Answer:

Step-by-step explanation:

Sol'n,

Here,

The length of all sides of sq= height = h

Height of triangle=h

Base length of triangle=b

Now, We know that,

The entire figure is a trapezium,

so, Area of Trap.= 1/2 * h(length of diagonal one + length of diagonal 2)

or, 80 = 1/2 * h* {h +(b+h)}[ since here, the length of second diagonal is sum of the base and length of one side of sq]

or, 160 = h (2h+b)

2h^2 + hb - 160 = 0....(I)

Hence, I is the required eqn....

The Equation for Area of figure is area of Figure, h² + 1/2(h)(b) = 80

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given:

We have the figure consist of one square and one right triangle.

Now, Area of Figure,

= Area of square + area of Triangle

[tex]\dfrac{= \text{length} \times \text{width +}}{\times \text{base} \times \text{height}} =[/tex]

[tex]= 16 \times 12 + \dfrac{1}{2} \times 10 \times 20[/tex]

[tex]= 192+ 100[/tex]

[tex]=292 \ \text{unit}^2[/tex]

and, if the square with height, h, units and a right triangle with height, h units, and a base length, b units.

Then, area of Figure = h² + 1/2(h)(b) = 80 square units.

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[tex]\textit{volume of a rectangular prism}\\\\ V=Lwh ~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=150\\ w=120\\ V=288000 \end{cases}\implies 288000=(150)(120)h \\\\\\ \cfrac{288000}{(150)(120)}=h\implies 16=h[/tex]

Using only addition, how can you use eight '8's to get 1,000? 8 added 125 times=1000. 888+88+8+8+8=1000.

Answer: 68

Step-by-step explanation:

All the angles of a triangle add up to 180

so 32 + 80 + x = 180  or 180-32-80=x

x = 68

Answer:

x= 68

Step-by-step explanation:

80+ 32+ x= 180

112 +x= 180

x= 180-112

x= 68

We can be 90% confident that the true average number of sick days for an employee who is 28 years old falls between 4.31 and 9.85 days per year, based on the provided data

First, we can plug in the value of 28 for Age in the regression line equation to get the estimated average number of sick days for an employee who is 28 years old:

Next, we can use the standard error to calculate the margin of error for a 90% confidence interval:

Finally, we can construct the confidence interval by adding and subtracting the margin of error from the estimated average number of sick days:

Confidence interval = 7.079032 ± 2.767462 = (4.31157, 9.84649)

Therefore, we can be 90% confident that the true average number of sick days for an employee who is 28 years old falls between 4.31 and 9.85 days per year, based on the provided data.

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Complete Question:

The estimated regression line and the standard error are given. Sick Days=14.310162−0.2369(Age) se=1.682207 Find the 90% confidence interval for the average number of sick days an employee will take per year, given the employee is 28. Round your answer to two decimal places.

Employee 1 2 3 4 5 6 7 8 9 10

Age 30 50 40 55 30 28 60 25 30 45

Sick Days 7 4 3 2 9 10 0 8 5 2.

Answer:  [tex]12\frac{1}{2}[/tex] inches

Step-by-step explanation:

set common denominators.

[tex]3\frac{1}{5}[/tex] = [tex]3\frac{4}{20}[/tex]

add up all sides =  [tex]3\frac{4}{20}[/tex] + [tex]3\frac{4}{20}[/tex] + [tex]3\frac{1}{20}[/tex] + [tex]3\frac{1}{20}[/tex] = [tex]12\frac{10}{20}[/tex] = [tex]12\frac{1}{2}[/tex]

Answer:

12.5 inches

Step-by-step explanation:

To find perimeter you must plus all the sides. To add fractions they must have the same denominator which we can change by finding the common denominator.

Answer:

4 cm by 9

Step-by-step explanation:

Let's assume that the length of the rectangular ink pad is x cm and the width is y cm.

We know that the perimeter of a rectangle is the sum of the lengths of all sides, which in this case is given as 26 cm. Therefore, we can write:

2(x + y) = 26

x + y = 13

We also know that the area of a rectangle is the product of its length and width, which in this case is given as 36 square cm. Therefore, we can write:

xy = 36

We now have two equations with two variables. We can solve for one variable in one equation and substitute it into the other equation to solve for the other variable.

Let's solve for y in the first equation:

y = 13 - x

We can substitute this expression for y into the second equation:

x(13 - x) = 36

Expanding the left side of the equation, we get:

13x - x^2 = 36

Rearranging terms, we get:

x^2 - 13x + 36 = 0

This is a quadratic equation that can be factored as:

(x - 4)(x - 9) = 0

Therefore, the solutions for x are x = 4 and x = 9. We can plug these values back into the equation y = 13 - x to find the corresponding values of y:

If x = 4, then y = 13 - x = 9.

If x = 9, then y = 13 - x = 4.

Therefore, the dimensions of the rectangular ink pad are 4 cm by 9 cm or 9 cm by 4 cm.

Answer:

**9 cm by 4 cm** or **4 cm by 9 cm**.

Step-by-step explanation:

Let's call the length of the ink pad "l" and its width "w". We know that the perimeter of a rectangle is given by the formula `2(l+w) = 26` which simplifies to `l+w = 13`. We also know that the area of a rectangle is given by the formula `lw = 36`.

We can use these two equations to solve for "l" and "w". Let's solve for "w" in terms of "l" using the first equation: `w = 13 - l`. We can substitute this expression for "w" into the second equation to get: `l(13-l) = 36`. Expanding this expression gives us a quadratic equation: `l^2 - 13l + 36 = 0`. We can solve this equation using the quadratic formula: `l = (13 ± sqrt(13^2 - 4(1)(36))) / (2(1))`. This simplifies to `l = (13 ± 5) / 2`. So we have two possible values for "l": `l = 9` or `l = 4`.

If we use `l = 9`, then we can find "w" using the expression we derived earlier: `w = 13 - l = 4`. So the dimensions of the ink pad are **9 cm by 4 cm**.

If we use `l = 4`, then we get `w = 13 - l = 9`. So another possible set of dimensions is **4 cm by 9 cm**.

Therefore, there are two possible sets of dimensions for the ink pad: **9 cm by 4 cm** or **4 cm by 9 cm**.

PLEASE MARK ME AS BRAINLIEST !!!

A) Where the calibration of the graph represents a unit each, the approximate coordinates of the points  of intersection of the two graphs is (4.5, 3)

This means that after after a given number of days, the area covered by both types of mold were the same.

b) given the function, the number days it takes for the mold to cover 1000 square millimeters is 46 days.

A) this is observed by exploring the graph.

b) Let A(d) = 1000
⇒ 1000 = 100 x [tex]e^{0.05d}[/tex]

If we divide both sides by 100 to simplify, we will get

[tex]e^{0.05d}[/tex] = 10

To solve for d we need to compute the natural log of both sides, so we get

ln [tex]e^{0.05d}[/tex] = ln (10)

Recall that ln (eˣ) = x so

ln [tex]e^{0.05d}[/tex] = ln (10)

⇒ 0.05d = ln (10)

Divide both sides by 0.05

d = ln10/0.05

d = 2.30258509299/0.05

d = 46.0517018599

d ≈ 46 days.

thus,

it will take about 46 days for the mold to cover 1000 millimeters.

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Answer:

x= 6

x= 1

Step-by-step explanation:

First we must factor the equation by finding two numbers which when multiplied equal 6, and when added equal -7

-6 * -1 = 6 and -6 - 1 = 7, so our numbers are -6 and -1.

We will then write this factored form as (x - 6)(x - 1)=0

Because of the zero product property (anything multiplied by zero will equal zero), we know that either x - 6 equals zero, or x - 1 equals zero.

This means there will be two solutions.

First, we will do x - 6 = 0. We can simply move the 6 to the other side by adding 6 to both sides. This gets x = 6.

Then, we will do x - 1 = 0. By adding 1 to both sides, we will get x = 1

So finally, we know that x = 6 and x = 1

True. Stokes' theorem states that if we have a surface r whose boundary is a curve c, and f is a vector field, that provided that c and r are oriented compatibly, the circulation of f around c is equal to the flux of the curl of f through r.

Stokes' theorem states "for surface R whose boundary is a curve C, and F is a vector field, then provided that C and R are oriented compatibly, the line integral of F around C is equal to the surface integral of the curl of F over R."

This theorem relates the circulation of a vector field around a closed curve to the flux of its curl through the enclosed surface.

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Answer:

C. 5, 9, 12

Step-by-step explanation:

There is a rule in the triangle that if you add any 2 sides measure of the triangle, it must be bigger than the measure of the 3rd side.

Let's Check

A. 19, 6, 13

19 + 6 > 13

6 + 13 = 19

19 + 13 > 6

This is not meet the rule, so this option is wrong.

B. 10, 1, 8

10 + 1 > 8

1 + 8 < 10

This is not meet the rule, so this option is wrong.

C. 5, 9, 12

5 + 9 > 12

9 + 12 > 5

5 + 12 > 9

This meets the rule, so this option is correct.

Answer:

189.36 metres

Step-by-step explanation:

We can use trigonometry to solve this problem.

Let's draw a diagram to help visualize the situation:

```

          |

          |

          |90m

          |

          |

          |

-----------|--------------------

          x

```

We can see that the angle of depression is the angle formed by a horizontal line from the top of the cliff to the boat, and a line of sight from the top of the cliff to the boat. We can also see that the height of the cliff is 90 meters.

Using trigonometry, we can find the distance x between the boat and the foot of the cliff:

tan(26.2°) = opposite / adjacent

tan(26.2°) = 90 / x

To solve for x, we can rearrange the equation:

x = 90 / tan(26.2°)

x ≈ 189.36 meters

Therefore, the boat is approximately 189.36 meters from the foot of the cliff.

The number 0. 07129813 corrected to 2 decimal places is 0.07

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

0.07129813

Corrected to 2 decimal places means that we leave only two digits after the decimal points

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

0.07129813  = 0.07

Hence, the solutuion is 0.07

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To find the limit of cos(x)/(1-sin(x)) as x approaches (π/2)+, we can use l'Hospital's Rule.

First, we can take the derivative of both the numerator and denominator with respect to x: lim cos(x)/(1 − sin(x)) x → (π/2)+ = lim [-sin(x)/(cos(x))] / [-cos(x)] x → (π/2)+ = lim sin(x) / [cos(x) * cos(x)] x → (π/2)+

Now, plugging in (π/2)+ for x, we get: lim sin(π/2) / [cos(π/2) * cos(π/2)] x → (π/2)+ = 1 / (0 * 0) = undefined

Since the denominator approaches 0 as x approaches (π/2)+, and the numerator is bounded between -1 and 1, the limit does not exist.

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The statements that are true about Triangle HNR are;

a. The value of x is 2,

b. The value of y is 6 and

e. The length of KH is 7.6

To find the value of y for triangle HRN, we have to pick out coordinates that have y value in them and they are;  KR = (0.5y + 3.2) and KW = (2y - 8.9). The centroid divides the medians of a triangle into segments with a 2:1

KW : KR = 1:2

(2y - 8.9)/ (0.5y + 3.2) = 1/2

We multiply KW by 2 for the cross exchange, it becomes

4y - 17.8 = 0.5y + 3.2

3.5y = 21

We divide 3.5 and 21 by 3.5 to find the value of y

y = 6

We can then look for the length of KN which is

0.5 x 6 + 3.2 = 6.2

Therefor KR is 6.2

To find the value of x, we take the coordinates that have x in them.

KN = (5x -5.2), KT = (7.1x - 11.8)

7.1 x - 11. 8/ 5x - 5.2 = 1/2
14.2x - 23.6 = 5x -5.2

9.2x = 18.4

x = 2

To find the length of KN, we say

KN = 5 × 2 - 5.2 = 4.8

To find the value of w, we take the coordinates with w values and they are  KD = (9w -23.2) and KH = (4.5w - 5.9).

(9w -23.2)/(4.5w - 5.9) = 1/2

18w - 46.4 = 4.5w - 5.9

13.5w = 40.5

w = 40.5/13.5

w = 3

The length of KH becomes

4.5 × 3 - 5.9

KH = 7.6

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The correct interpretation of the 95% confidence interval is that if Peggy were to repeat her sampling process many times and calculate a 95% confidence interval each time

Approximately 95% of those intervals would contain the true population means the height of young women aged 18 to 24 in the US. In other words, we can be 95% confident that the true population means height falls within the interval that Peggy calculated from her sample of 2,000 young women.

The correct interpretation is that there is a 95% chance that the true population mean height falls within the calculated interval.

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Answer:

a) The mode is 6 (which occurs the most times--18).

b) Since there are 50 observations, the median is the value halfway between observations 25 and 26 when the data are arranged in order. That value is 6.

c) (4(2) + 5(10) + 6(18) + 7(14) + 8(6))/50 =

312/50 = 6.24 peas/pod

The probability that a randomly selected passenger car gets more than 35 mpg is approximately 38.4%.

To find the probability that a randomly selected passenger car gets more than 35 mpg, we need to use the normal distribution with a mean of 33.7 mpg and a standard deviation of 4.4 mpg.

First, calculate the z-score for 35 mpg using the formula:

z = (X - μ) / σ

where X is the value (35 mpg), μ is the mean (33.7 mpg), and σ is the standard deviation (4.4 mpg).

z = (35 - 33.7) / 4.4
z ≈ 0.295

Now, we use a z-table or calculator to find the probability for a z-score of 0.295. The table shows the probability to the left of the z-score, so we need to find the complement to get the probability of a car getting more than 35 mpg.

P(Z > 0.295) = 1 - P(Z ≤ 0.295)
P(Z > 0.295) ≈ 1 - 0.616
P(Z > 0.295) ≈ 0.384

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Answer:

Step-by-step explanation:

To solve this problem, we need to use the distributive property to simplify the expression inside the parentheses first, then combine like terms:

2x + 6 + 5x - 7 = 4x - 8

7x - 1 = 4x - 8 (combine like terms)

7x - 4x = -8 + 1 (subtract 4x from both sides)

3x = -7 (combine constants)

x = -7/3

Therefore, the solution to the equation 2(x + 3) + 5(x - 1) = 4(x - 2) - 8 is x = -7/3.

The solution to the given proportion is x = 6

A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio may be written as: 1: 3 (for every one boy, there are three girls).

To determine if a connection is proportional, examine the ratios between the two variables. The connection is proportionate if the ratio is always the same. The connection is not proportional if the ratio changes.

To solve the proportion, we state:

x/3 = 6/3

x / 3 = 2

x = 2 x 3

x = 6

Thus, the solution to the proportion is x = 6

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Solve the given proportion.

x/3 = 6/3

a) The length of its edge is; 8 units.

b) The volume of the sphere is; 268.083 cubic units.

c) The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage is 52.4 %.

A. We have been given that the volume of the cube is 512 cubic units.

We have to find the length of its edge. So, Let the length of an edge of a cube be a units.

Then, the volume of the cube = (length of edge)3

the volume of the cube = 512 cubic units.

So, (length of edge)3 = 512 cubic units

So,Length of edge = Cube root of 512 cubic units = 8 units

Thus, the diameter of the sphere = 8 units.

Hence, the radius of the sphere = 8 / 2 = 4 units

B. The volume of the sphere = (4 / 3)πr36

= (4 / 3) × π × 4^3

= 4/3 × 3.14 × 64= 268.08 cubic units

C. The fraction of the cube that is taken up by the sphere = volume of sphere/volume of cube

= 268.08 / 512= 67 / 128

So, the percentage of the cube taken up by the sphere is,

= (67 / 128) × 100= 52.34% (approx)

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Answer:

[tex]x = \sqrt{ {17}^{2} - {15}^{2} } = \sqrt{289 - 225} = \sqrt{64} = 8[/tex]

So x = 8 = 8.0

An expression that is equivalent to ∛18⁴ is (b) (18)³/⁴

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

∛18⁴

Applying the law of indices, we have

∛18⁴ = (18⁴)¹/³

Evaluate

So, we have

∛18⁴ = (18)³/⁴

Hence, the solution is (18)³/⁴

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To solve this expression, we can first simplify the expression inside the parenthesis by combining like terms:

(x + 2y) + (x + 2y)^2 = (x + 2y) + x^2 + 4xy + 4y^2

Now we can distribute the A to each term inside the parenthesis:

A(x + 2y) + A(x^2 + 4xy + 4y^2)

Next, we can simplify each term:

A(x + 2y) = Ax + 2Ay

A(x^2 + 4xy + 4y^2) = Ax^2 + 4Axy + 4Ay^2

Putting these simplified terms back together, we get:

Ax + 2Ay + Ax^2 + 4Axy + 4Ay^2

This is the final simplified expression.

Answer: 3.5 cm

Step-by-step explanation:

SA for cone = [tex]\pi[/tex]rs + [tex]\pi[/tex]r²        r=radius=9     s=slant height (not height)

A(cone) = 9[tex]\pi[/tex]s + 81[tex]\pi[/tex]

SA for a cylinder = 2[tex]\pi[/tex]rh +2[tex]\pi r^{2}[/tex]      r=6     h = 18

A(cyl) = 2([tex]\pi[/tex])(6)(8) + 2([tex]\pi[/tex])6²

           = 96[tex]\pi[/tex] + 72[tex]\pi[/tex]

           =168[tex]\pi[/tex]

Set the 2 areas equal to each other to solve for slant height

9[tex]\pi[/tex]s + 81[tex]\pi[/tex] = 168[tex]\pi[/tex]

9[tex]\pi[/tex]s=87[tex]\pi[/tex]

s=87/9

this is slant height, now you use pythagorean to solve for h

(87/9)²=9²+h²

h=3.5

Answer:

  A.  The graph of function g is the graph of function f shifted 6 units up.

Step-by-step explanation:

You want to know how the graph of g(x) = f(x) +6 differs from the graph of f(x).

Adding 6 to the function value will cause the y-coordinate of the point on the graph to be increased by 6. When the y-coordinate is increased, the point moves up.

The graph of g(x) = f(x) +6 is the graph of function f shifted 6 units up, choice A.

<95141404393>

The requried equation is true, which means that y = x is indeed the solution to the equation.

When Sherron inputs the equation 5 + 6x = 9y + 2 + 3(1 - y), we can simplify it as follows:

5 + 6x = 9y + 2 + 3 - 3y

5 + 6x = 6y + 5

6y = 6x

y = x

So the solution to the equation is y = x.

We can also check the solution by substituting y = x back into the original equation:

5 + 6x = 9y + 2 + 3(1 - y)

5 + 6x = 9x + 2 + 3(1 - x)

5 + 6x = 9x + 2 + 3 - 3x

5 + 6x = 6x + 5

Thus, the equation is true, which means that y = x is indeed the solution to the equation.

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Answer:

62.1156924

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

Calculate 256 to the power of \frac{3}{4} and get 64.