Step 2: What factor is used to convert feet per minute into
miles per minute?

Answer:

0.89

Step-by-step explanation:

The probability of Larry making the next free throw is, 0.89

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one

Now, we can assume that Larry Bird has a 89% chance of making any given free throw.

Since, each free throw is an independent event, the fact that he made 10 free throws in a row does not affect the probability of him making the next free throw.

Therefore, the probability of Larry making the next free throw is also 89%.

Thus, the probability of Larry making the next free throw is, 0.89

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Answer:

The volume is 1539.38

Step-by-step explanation:

Answer:

384.7 cubic inches

Step-by-step explanation:

formula to find Volume of a Cylinder:  

V = π · r² · h

7 is the diameter, so r = 3.5

V = π (3.5)² · 10

V = π (12.25)(10)

V = π · 122.5

V ≈ 384.7 in³

===========================================================

Explanation:

For each expression in the parenthesis of choice A, focus only on the leading terms. Those would be the terms to the very left. The leading terms 3x^2 and 2x^6 multiply to 6x^8. This is the leading term of the final expansion and it's of degree 8. Any degree 8 polynomial will have 8 roots according to the fundamental theorem of algebra. Some of those roots may be complex numbers, or they may be purely real numbers.

Choice B can be ruled out because the leading term 3x^4 is raised to the 4th power to get (3x^4)^4 = 81x^16 as the leading term of the final expansion. This polynomial has 16 roots, but we want 8 roots instead.

Choice C is a similar story to choice B. In this case, we have (4x^2)^3 = 64x^6 as the leading term when you expand everything out. This 6th degree polynomial has 6 roots.

And finally, choice D can be ruled out as well. We follow the same steps as choice A. The leading terms from each parenthesis group multiply to 6x^8*3x^2 = 18x^10 showing we have 10 roots (due to the 10th degree polynomial).

Answer:

3.65 through 3.74

Step-by-step explanation:

The coordinates of the trapezoid  RSTU with vertices R(-13, 7), S(-1, 7), T(-1, -5), and U(-13,-9) after dilation with scale factor of k= 1/4 are

Data gotten from the question

Dilation refers to an increment or reduction in dimension and location of a preimage to get a new image

The coordinate of the image of dilation is gotten using the formula

x₂ = kx₁ - x₀(k - 1) for x coordinate

y₂ = ky₁ - y₀(k - 1) for y coordinate

definition of terms

terms with subscript 2 is corresponding to the image

terms with subscript 1 is corresponding to the preimage

terms with subscript 0 is corresponding to the center of dilation

\k = scale factor

R(-13, 7) ⇒ R'(-7, -2)

x₂ = 1/4 * -13 - -5(1/4 - 1) = -7

y₂ = 1/4 * 7 - -5(1/4 - 1) = -2

S(-1, 7)  ⇒ S' (-4, -2)

x₂ = 1/4 * -1 - -5(1/4 - 1) = -4

y₂ = 1/4 * 7 - -5(1/4 - 1) = -2

T(-1, -5) ⇒ T' (-4, -2.5)

x₂ = 1/4 * -1 - -5(1/4 - 1) = -4

y₂ = 1/4 * -5 - -5(1/4 - 1) = -2.5

U(-13,-9) ⇒ U' (-7, -6)

x₂ = 1/4 * -13 - -5(1/4 - 1) = -7

y₂ = 1/4 * -9 - -5(1/4 - 1) = -6

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Answer:

22.9508% increase

Step-by-step explanation:

I used my calculator

Answer:

  about 840.4 ft²

Step-by-step explanation:

You want the surface area of a regular pentagon with a side length of 16 ft and a slant height of 10 ft.

The area of the 5-sided base is ...

  A = 1/4(√(5(5 +2√5))s² . . . . for side length s

The area of the 5 triangular faces is ...

  A = 5×(1/2)sh

Using s = 16 ft and h = 10 ft, we find the total surface area to be ...

  SA = 1/4(√(5(5 +2√5))(16 ft)² +5/2(16 ft)(10 ft) ≈ 840.4 ft²

The surface area of this pentagonal pyramid is about 840.4 square feet.

__

Additional comment

The problem statement says the figure has a hexagonal base. We only count five sides, so have worked the problem as though it has a pentagonal base.

Either way, the figure cannot exist. The lateral area of such a figure must exceed the base area. In this figure, the base area is about 10% greater than the lateral area, meaning the points of the triangular faces cannot meet to form a pyramid.

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Answer:

1⁷/15

Step-by-step explanation:

2¾(3⅜-1½)

using the rule of BODMAS

change the fractions in the bracket into improper fraction

2¾(27/8-3/2)

find LCM of the fractions in the bracket

2¾(27-12)/8

2¾(15/8)

convert the other mixed fraction to an improper fraction

11/8(15/8)= 5.15625~ 5.2

The amount tied up in AR is $69434.12

The Gross Revenue, GR = $495,958.02

From the question:

The Annual Revenue, AR = 14% of GR

AR = (14/100) x $495,958.02

AR = 0.14 x $495,958.02

AR = $69434.12

The amount tied up in AR is $69434.12

All five answers are (1) 285.7 ft2 (2) 1056 cm2 (3) 105 mm3 (4) 108 cm3 (5) 628 mm3 in accordance with the provided assertion.

In mathematics, volume refers to the amount of space present within a specific 3D object. As an example, the dimensions of a fish aquarium are three feet long, one foot broad, and two feet height.

By increasing the length, width, and height, or 3x1x2, which also equals six, the volume is determined. Consequently, the fish tank has a 6 cubic foot size.

(1) The lateral area of a cone can be calculated using the formula L = πrℓ, where r is the radius and ℓ is the slant height. Using the given values, we have:

L = π(7)(13) ≈ 285.7 ft²

Rounding to the nearest tenth, the answer is 285.7 ft².

(2) A = B + (1/2)Pl, where B is the base area, P is the base circumference, l is the slope height, and A is the surface area, can be used to determine the surface area of a square pyramid. Since the pyramid's foundation is square, we have:

B = (24)² = 576 cm²

The perimeter of the base is 4 times the base length, so we have:

P = 4(24) = 96 cm

Now we can use the formula to find the surface area:

A = 576 + (1/2)(96)(16) = 1056 cm²

Therefore, the surface area of the square pyramid is 1056 cm².

(3) The volume of a rectangular prism can be calculated using the formula V = lwh,

where

l is the length

w is the base

h is the height

V is the volume.

Substituting the given values, we have:

V = (5)(7)(3) = 105 mm³

Therefore, the volume of the rectangular prism is 105 mm³.

(4) The formula V = (1/3)Bh, where B is the base area, h is the height, and V is the volume, can be used to determine the volume of a square pyramid. Since the pyramid's foundation is square, we have:

B = (9)² = 81 cm²

Now we can use the formula to find the volume:

V = (1/3)(81)(4) = 108 cm³

Therefore, the volume of the square pyramid is 108 cm³.

(5) The volume of a cone can be calculated using the formula V = (1/3)πr2h, where r is the radius, h is the height, and V is the volume. Substituting the given values, we have:

V = (1/3)π(10)²(6) ≈ 628.3 mm³

Rounding to the nearest whole number, the answer is 628 mm³.

Therefore, the volume of the cone is 628 mm³.

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The slope between points (17,8) and (17,24) is (B) undefined.

We know that the slope of a line passing through two points (a,b) and (c,d) is given by,

m = (d-b)/(c-a)

So here given points are (17,8) and (17,24)

Then, a=17, b=8, c=17, d=24

Now the slope between these two points is given by,

m = (24-8)/(17-17) = 16/0

So the slope value does not exist or infinity.

Hence the slope between the points (17,8) and (17,24) is Infinity or undefined.

Thus, the correct option is (B).

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Answer:

x = 6

Step-by-step explanation:

Since M is the midpoint of KL , then

KM = ML , that is

2x + 7 = 8x - 29 ( subtract 8x from both sides )

- 6x + 7 = - 29 ( subtract 7 from both sides )

- 6x = - 36 ( divide both sides by - 6 )

x = 6

Answer: x=1

Step-by-step explanation:

Answer:

IMS (Infinitely Many Solutions)

Step-by-step explanation:

1. Combine like terms (2/3x + 1/3x) Equation: 1x = x

2. 1x is just x, so the final equation is x = x. When you get an answer like this, it means there are infinitely many solutions.

Answer:

its -4! good luck bestie!!!

Step-by-step explanation:

Answer: The slope of line b is -4

Step-by-step explanation:

Usually I'd use the formula \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\) to find the slope.

Remember the coordinates of the origin are (0, 0) so subtracting them means nothing and instead we will just do y/x of (2, -8)

\(\frac{-8}{2} =-4\)

The slope is -4

Answer:

vertex B' is at (1, 1)

Step-by-step explanation:

Let us revise the rules of translation of a point

Let us use the rules to solve our question

∵ Vertex A = (-5, 2)

∵ Vertex A' = (2, -2)

→ The coordinates of the two points changed which means the

  quadrilateral is translated horizontally and vertically

∵ The x-coordinate of A = -5

∵ The x-coordinate of A' = 2

→ Which means it moves to the right, so use the first rule above

∴ the rule of translation is T (x, y) → (x + h, y)

∴ x → x + h

∵ x = -5 and x + h = 2

∴ -5 + h = 2

→ Add 5 to both sides

∴ -5 + 5 + h = 2 + 5

∴ h = 7

∴ The quadrilateral is translated 7 units right

∵ The y-coordinate of A = 2

∵ The y-coordinate of A' = -2

→ Which means it moves down, so use the 4th rule above

∴ the rule of translation is T (x, y) → (x, y - k)

∴ y → y - k

∵ y = 2 and y - k = -2

∴ 2 - k = -2

→ Add K to both sides

∴ 2 - k + k = -2 + k

∴ 2 = -2 + k

→ Add 2 to both sides

∴ 2 + 2 = -2 + 2 + k

∴ 4 = k

∴ The quadrilateral is translated 4 units down

→ Let us find B'

∵ T (x, y) → (x + h, y - k) is the rule of translation

∵ B = (-6, 5)

∵ h = 7 and k = 4

∴ B' = (-6 + 7, 5 - 4)

∴ B' = (1, 1)

∴ vertex B' is at (1, 1)

Quadrilateral ABCD is translated 7 units right and 4 units down. If vertex B is at (-6, 5), then vertex B′ is at (1, 1)

Answer:

5.75

Step-by-step explanation:

\(5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4} = 5.75 \\ \)

a) Contribution (objective value) = $132.14

b) The firm earns $132.14 at the optimal solution.

c) An additional hour of time available for the third machine is worth $0.14 to the firm.

d) An additional 5 hours of time available for the second machine will increase the objective value by $3.69.

The best result obtained from using computer software to solve the LP problem is: X1 = 11.43, X2 = 12.86, X3 = 5.71

b) The number of unused hours at the ideal solution is:

Machine 1 still has 8.57 hours of time left.

There are no hours left on Machine 2 at the moment.

There are still 94.29 hours left on Machine 3.

c) The shadow price of the third limitation is worth an extra hour of time available for the third machine. With the exception of increasing the right-hand side of the third constraint by one unit, we can solve the LP problem using the same constraints to determine the shadow price. Using LP to solve this issue, we discover that the shadow price for the third constraint is

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Answer:

17.1

Step-by-step explanation:

Plug in -1 for x, this gets you -4.

Solve 2^-4 and get .0625.

Add .0625 to 17 and get 17.0625.

The question says answer to the nearest tenth so you round the 6 up to a 1 giving you 17.1

D.  When multiple tests are done in analysis of variance, the family error rate is the family error rate is the probability of making one or more type 1 errors among the tests in the set.

It is also known as the familywise error rate (FWER). This is because when multiple tests are conducted simultaneously, the probability of making at least one type 1 error increases, and the FWER is used to control this error rate. To control the FWER, researchers use methods such as the Bonferroni correction or the Holm-Bonferroni correction, which adjust the significance level of each test to maintain the desired overall error rate.

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the Area of the triangle is 212.3 m².

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The perimeter will be P = sum of all three side.

Side a = 21 meters, b=31 meters, c = 18 meters

s = p/2 = 70/2 = 35

A =  √(s)(s-a)(s-b)(s-c)

A = √35*4*14*23

A = 212.3 m²

Hence the Area of the triangle is 212.3 m².

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The statement that best describes the infοrmatiοn presented in the chart is: "The number οf hurricanes was increasing but has decreased in recent years."

Hurricanes, knοwn generically as trοpical cyclοnes, are lοw-pressure systems with οrganized thunderstοrm activity that fοrm οver trοpical οr subtrοpical waters. They gain their energy frοm warm οcean waters.

The chart shοws the number οf hurricanes οf categοry 1 οr higher that οccurred during specific series οf years, and it indicates that the number οf hurricanes increased frοm 13 in 1980-1989 tο 23 in 2000-2009, and then decreased tο 10 in 2010-2017.

Therefοre, the chart suggests that the number οf hurricanes was increasing, but it has decreased in recent years. The chart dοes nοt prοvide any infοrmatiοn abοut tοrnadοes in Finleyville οr the relatiοnship between the number οf hurricanes and temperature.

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The statement that best describes the information in the graph is: "The number of hurricanes has increased but decreased in recent years." The graph shows that the number of Category 1 or greater hurricanes increased from 1980 to 2009, but decreased from 2010 to 2017.

The point (-2,2), we need to evaluate each case

In this case, for the real part we need to obtain -2

For the imaginary part, we need to obtain 2

As we can see the complex number that is shown in the graph is

ANSWER

A.

a) We were told that relationship between the value of the car and its age is linear. This means that it can be represented with a linear equation such as

y = mx + c

y is the dependent variable and in this case, it is the value of the car, V

x is the independent variable and in this case, it is the age of the car, a

The above equation is the slope intercept form equation where

m represents slope

c represents y intercept

The formula for determining slope is expressed as:

m = (y2 - y1)/(x2 - x1)

We were told that a 5 year old car is worth 14000. This means that

When x1 = 5, y1 = 14000

Also, the same car is worth 11400 after 2 years. This means that the car is worth 11400 after 7 years. Thus,

when x2 = 7, y2 = 11400

Thus,

slope, m = (11400 - 14000)/(7 - 5) = - 2600/2

m = - 1300

We would find the y intercept, c by substituting m = - 1300, x = 5 and y = 14000 into the slope intercept equation. Thus,

14000 = - 1300 * 5 + c

14000 = - 6500 + c

c = 14000 + 6500

c = 20500

Thus, by substituting m = - 1300 and c = 20500 into the slope intercept equation, the linear equation representng this scenario is

y = - 1300x + 20500

By replacing with the given variables,

V = - 1300a + 20500

b) When the car was new, it means that a = 0. By substituting a = 0 into the equation, we have

V = - 1300 * 0 + 20500

V = 20500

The value of the car was $20500 when it was new

To know which function has the largest value for f(3), we need to substitute x=-3 in each function:

A. f(x)=2x-5

f(-3)=2(-3)-5=-11

B. f(x)=2-4x

f(-3)=2-4(-3)=14

C. f(-3)=6-3^(-3)

f(-3)=6-1/27

f(-3)=161/27

D. f(x)=2^(x)+10

f(-3)=2^(-3)+10

f(-3)=1/8+10=81/8

The largest value for f(-3) is 14, The answer is B f(x)=2-4x

Answer:

the first one is 84

Step-by-step explanation:

subtract 145-61 then you get 84for the missing angle.

Answer:

1. 84,  2. 7.31

Step-by-step explanation:

1. 145-61=84

2. 16x+4-3x+11=110

13x+15=110

13x=95

x=7.31

a) The parameter of interest is the percentage of mail items received at the dorm that are considered packages. This can be denoted as p, where p is the proportion of packages out of all mail items received at the dorm. A confidence interval would be most appropriate for this inference procedure.

b) The parameter of interest is the difference in the average number of packages sent from online retailers to a neighborhood in Champaign and the average number of packages sent from online retailers to a neighborhood in Urbana. This can be denoted as μ1 - μ2, where μ1 is the average number of packages sent to Champaign and μ2 is the average number of packages sent to Urbana. A hypothesis test would be most appropriate for this inference procedure.

c) The parameter of interest is the difference in store pick-up rates between all cookies and all cakes sold by the bakery. This can be denoted as p1 - p2, where p1 is the proportion of cookies that are picked up in store and p2 is the proportion of cakes that are picked up in store. A confidence interval would be most appropriate for this inference procedure.

d) The parameter of interest is the association between the weight of the package and the delivery time. This can be denoted as ρ, where ρ is the correlation coefficient between the weight of the package and the delivery time. A hypothesis test would be most appropriate for this inference procedure.

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Answer:

45

Hope this helps!

Answer:

0.0037

Step-by-step explanation:

In scientific notation, if the exponent is negative, you shift the decimal to the left to find the number in standard form.