Letters a, b, c, and d are angle measures.

Lines f and g are intersected by line n. At the intersection of lines n and g, clockwise from the top, the angles are: a, 75 degrees, blank, b. At the intersection of lines n and f, clockwise from the top, the angles are blank, blank, d, c.

Which should equal 105° to prove that f ∥ g?

a
b
c
d

39 subjects were tested in this simple one-way ANOVA.

The df for F distribution is (treatment df, error df)

Using given information

Treatment df = 7

Error df = 31

Total df= 7+31 = 38

Again, total df = N-1, N= number of subjects tested

Then, N-1 = 38

=> N= 39

One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.

The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.

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The correct answer is d) f^(-1)(x) = x/3, as it represents the Inverse relationship of y = 3x.

To find the inverse of a function, we need to switch the roles of x and y and solve for the new y.

The given function is y = 3x.

To find its inverse, let's swap x and y:

x = 3y

Now, solve this equation for y:

Dividing both sides of the equation by 3, we get:

x/3 = y

Therefore, the inverse function of y = 3x is f^(-1)(x) = x/3.

Among the given options:

a) f^(-1)(x) = 1/3x

b) f^(-1)(x) = 3x

c) f^(-1)(x) = 3/x

d) f^(-1)(x) = x/3

The correct answer is d) f^(-1)(x) = x/3, as it represents the inverse relationship of y = 3x.

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The cost of installing a fence around an 80 ft. wide and 120 ft. deep rectangular lot, with the fence priced at $3.25 per linear foot, will be $1,300.

To determine the cost of installing a fence around a rectangular lot, you need to calculate the total length of the fence required and then multiply that by the cost per linear foot. The given dimensions of the lot are 80 feet wide and 120 feet deep.
First, calculate the perimeter of the rectangular lot. The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length (or depth) and W is the width. In this case, the perimeter is P = 2(120) + 2(80) = 240 + 160 = 400 feet.
Next, multiply the total length of the fence by the cost per linear foot, which is $3.25. So, the cost of installing the fence is 400 feet × $3.25 per linear foot = $1,300.

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The perimeter of a rectangle is 30 inches. The length of the rectangle is twice as long as the width. What are the dimensions (length and width) of the rectangle?

Given :

Need to find :

Solution :

First we will make an equation and then we will calculate the dimensions of the rectangle using the formula.

Length is twice as long as it's width

Let us assume width as x then length = 2x

We know,

\( \star \: \large\boxed{ \sf{ Perimeter \: of \: a \: rectangle = 2l + 2w = 2(l + w)}}\)

Where,

Substituting the values in the above formula

\( \small\bf{ 30 = 2(2x + x)}\)

\( \small\rm{30 = 2(3x)} \)

\( \small\rm{30 = 6x} \)

\( \small\rm{ \cancel\dfrac{30}{6} = x} \)

\( \small\boxed{ \rm{x = 5}} \)

Substituting the value of x = 5

Length = 2x = 2 × 5 = 10 inches

Breadth = x = 5 inches

Final Answer :

NOTE :

\( \rule{90mm}{3pt} \)

Answer:

\( \\ \)

Step-by-step explanation:

It is given that, the perimeter of a rectangle is 30 inches and the length of the rectangle is twice as long as the width and we've to find the dimensions of the rectangle.

So, Let us assume the width of the rectangle is x inches, therefore the length will be 2x inches

\( \\ \)

Before solving it, first we have to know this formula :

\( \\ {\longrightarrow \pmb{\frak {\qquad 2(Length + Width) =Perimeter_{(Rectangle) }}}} \\ \\\)

\({\longrightarrow \pmb{\sf {\qquad 2(2x + x) =30}}} \\ \\\)

\({\longrightarrow \pmb{\sf {\qquad 4x + 2x =30}}} \\ \\\)

\({\longrightarrow \pmb{\sf {\qquad 6x =30}}} \\ \\\)

\({\longrightarrow \pmb{\sf {\qquad x = \frac{30}{6} }}} \\ \\\)

\({\longrightarrow \pmb{\frak {\qquad x =5}}} \\ \\\)

Therefore,

So, we have to find the length of the rectangle :

\( \\ {\longrightarrow \pmb{\frak {\qquad Length =2(x)}}} \\ \\\)

\({\longrightarrow \pmb{\frak {\qquad Length =2(5)}}} \\ \\\)

\({\longrightarrow \pmb{\frak {\qquad Length =10 \: inches}}} \\ \\\)

Therefore,

The required solution of the given simultaneous equation is x = -4/27 and y = 56/27.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Given equation,
y=-14x - - - - - - - -(1)

x+2y=4 - - - - - -- - - -(2)

Put the above value of y in equation 2,
x + 2(-14x) = 4
x - 28x = 4
-27x = 4
x = -4/27

Now,
form expression of y,
y=-14x
y = -14(-4/27)
y = 56/27

Thus, the required solution of the given simultaneous equation is x = -4/27 and y = 56/27.

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The given statement is FALSE.

If one or more data items are much greater than the other items, the median, rather than the mean, is more representative of the data.

When one or more data items are much greater than the other items, these extreme values can greatly influence the mean.

When you have a skewed distribution, the median is a better measure of central tendency than the mean

The median and mean can only have one value for a given data set. The mode can have more than one value

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Answer:

Step-by-step explanation:

P(t)=t³-1 at t = 1 has the value P(1) = (1)³ - 1 = 0

P(-1)=(-1)³-1  =  -2

P(0) = 0³ - 1  =  -1

P(2) = 2³ - 1 = 7

P(-2) = (-2)³ - 1 = -9

The probability of the weight loss falling between 8 pounds and 11 pounds is 1/2

Variation of weight = Between 6 to 12.

It is required to ascertain the percentage of the overall range that corresponds to that interval in order to calculate the chance that the weight reduction will fall between 8 pounds and 11 pounds.

Calculating the total range of weight -

Range = Higher weight - Lower weight

= 12 - 6

= 6

Similarly, calculating the total range of weight for 8 pounds and 11 pounds

Range = Higher weight - Lower weight

= 11 - 8

Calculating the probability -

Probability = Range of interest / Total range

= 3 / 6

= 1/2.

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Complete Question:

Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost between 8 pounds and 11 pounds

a. 1/2

b. 1/4

c. 2/3

d. 1/3

We can help if you don't show the scatterplot.

The standard deviation of the distribution of sample means (that is, the standard error, sigma_m) is; 2.9698

From the complete question written below, we are given that;

Mean Number; M = 103.4

Standard deviation; σ = 21

Sample size; n = 50

Now, in statistics, the formula for the standard error of mean is;

σM = σ/√n

Plugging in the relevant values gives us;

σM = 21/√50

σM = 2.9698

The z score typical average difference between the mean number of seats is;

z = (103.4 - 99.2)/( 2.9698 )

z = 1.41

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Complete Question is;

There are 559 full-service restaurants in Delaware. The mean number of seats per restaurant is 99.2. [Source: Data based on the 2002 Economic Census from U.S. Census Bureau.]

Suppose that the true population mean mu = 99.2 and standard deviation sigma = 21 are unknown to the Delaware tourism board. They select a simple random sample of 50 full-service restaurants located within the state to estimate mu. The mean number of seats per restaurant in the sample is M = 103.4, with a sample standard deviation of s = 18.2. The standard deviation of the distribution of sample means (that is, the standard error, sigma_m) is_.

The factors of the polynomial x^3-9x^2+27x-27 are (x -3), (x - 3) and (x - 3)

The polynomial you provided is x^3-9x^2+27x-27. If you know one of the factors of this polynomial, we can use that to find the remaining factors.

One factor of this polynomial is (x-3) as it gives remainder zero when divided by (x-3)

quotient is  x² - 6x + 9

remainder is zero

So the remaining factors are (x-3) and x² - 6x + 9

Alternatively, we can factor the remaining quadratic polynomial  x² - 6x + 9

by using Factor theorem or by using difference of squares

x² - 6x + 9 = (x - 3)²

So the remaining factors are (x-3) and (x - 3)

So the original polynomial can be factored as (x-3)(x-3)(x-3) = (x-3)³

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Answer:

2nd option

Step-by-step explanation:

one-and-a-half = 1 1/2

Audio files sold one-and-a-half times as many songs than download tunes

Answer : value of x and y in the matrix equation is:

x = -3

y = +4, -4

Step-by-step explanation :

The matrix expression is:

\(\left[\begin{array}{ccc}x+4\\y^2+1\end{array}\right]+\left[\begin{array}{ccc}-9x\\-17\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

First we have to add left hand side matrix.

\(\left[\begin{array}{ccc}(x+4)+(-9x)\\(y^2+1)+(-17)\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

Now we have to add left hand side terms.

\(\left[\begin{array}{ccc}x+4-9x\\y^2+1-17\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

\(\left[\begin{array}{ccc}4-8x\\y^2-16\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

Now we have to equating left hand side matrix to right hand matrix, we get:

\(\Rightarrow 4-8x=28\text{ and }y^2-16=0\\\\\Rightarrow 8x=4-28\text{ and }y^2=16\\\\\Rightarrow x=-3\text{ and }y=\pm 4\)

Therefore, the value of x and y in the matrix equation is -3 and +4, -4 respectively.

Answer:

D is wrong. The correct answer choice is C ( x=-3 and y= +4, -4)

Step-by-step explanation:

Math unit test review

Answer:

The answer is -3<x≤2

The probability of selecting exactly one defective calculator out of the 6 sent to the local high school is 0.29166.

The probability of selecting exactly one defective calculator out of the 6 sent to the local high school can be calculated using the binomial probability formula. The binomial probability formula is \(P(x) = nCx * p^x * q^(n-x)\). For this problem, n = 6 (the number of calculators sent to the local high school), x = 1 (the number of defective calculators selected), p = 4/12 (the probability of selecting a defective calculator from the shipment of 12 calculators), and q = 8/12 (the probability of selecting a non-defective calculator from the shipment of 12 calculators). Plugging these values into the formula gives \(P(x) = 6C1 * 4/12^1 * 8/12^5\), which simplifies to 0.29166. This means that the probability of selecting exactly one defective calculator out of the 6 sent to the local high school is 0.29166.

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Answer:

D

Step-by-step explanation:

Your answer is Toys and treats

this is a cool shape. it has 7 sides.

here's a formula: the sum of interior angles in a shape with x number of sides is 180*(x-2)

in this case, x is 7

so, we have 180*(7-2) = 900 as the sum of all interior angles

so 139 + 121 + 125 + 126 + 158 + 120 + x = 900

now you solve for x (but i'll do it because you are lazy)

789 + x = 900

x = 111

woohooo

Becca made a total of 24 rolls and 12 biscuits.

Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.

Becca made 2 trays of rolls and biscuits, with 12 rolls and 6 biscuits in each tray. To find the total number of rolls and biscuits, we need to multiply the number of rolls and biscuits per tray by the number of trays, and then add them together:

Total rolls = 2 trays × 12 rolls per tray = 24 rolls

Total biscuits = 2 trays × 6 biscuits per tray = 12 biscuits

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Answer:

Step-by-step explanation:

To find the normal plane and osculating plane, we first need to find the required derivatives.

x = 5t, y = t^2, z = t^3

dx/dt = 5, dy/dt = 2t, dz/dt = 3t^2

So, the velocity vector v and acceleration vector a are:

v = <5, 2t, 3t^2>

a = <0, 2, 6t>

Now, let's evaluate them at t = 1 since the point (5, 1, 1) is given.

v(1) = <5, 2, 3>

a(1) = <0, 2, 6>

The normal vector N is the unit vector in the direction of a:

N = a/|a| = <0, 1/√10, 3/√10>

Using the point-normal form of the equation for a plane:

normal plane equation = 0(x-5) + 1/√10(y-1) + 3/√10(z-1) = 0

Simplifying this equation we get:

5x + 2y + 3z = 30

The osculating plane can be found using the formula:

osculating plane equation = r(t) · [(r(t) x r''(t))] = 0

where r(t) is the position vector, and x is the cross product.

At t = 1, the position vector r(1) is <5, 1, 1>, v(1) is <5, 2, 3>, and a(1) is <0, 2, 6>.

r(1) x v(1) = <-1, 22, -5>

r(1) x a(1) = <12, -6, -10>

v(1) x a(1) = <-12, 0, 10>

Substituting these values into the formula, we get:

osculating plane equation = (x-5, y-1, z-1) · <12, -6, -10> = 0

Simplifying this equation we get:

3x - 15y + 5z = 5

Therefore, the equations for the normal plane and osculating plane at (5, 1, 1) are:

(a) 5x + 2y + 3z = 30

(b) 3x - 15y + 5z = 5

Answer:

a) Each individual act will last 5 minutes.

b) Each group act will last 10 minutes.

Step-by-step explanation:

I think this is right

Answer:

The degree is 6 and there are 2 terms

Answer:

(a) Coefficient of x

5

=−6

    Coefficient of x

2

=0

(b) Degree of polynomial = highest degree of monomial with non-zero coefficient =7

(c) Constant term = Coefficient of x

0

=−6

(d) Number of terms =4

Step-by-step explanation:

Answer:

Variable B is the area of triangular base.

B = 38.5 \(in^{2}\).

Variable h is the height of pyramid.

In the given prism, h is 9 inches.

The volume of prism is 346.5 \(in^{3}\).

Step-by-step explanation:

Please refer to the attached image for the detailed labeling of all the sides.

\(\triangle ABC\) is the triangular base of the prism.

BC is the base of triangular base of the prism.

AP is the height of triangular base.

Area of triangular base is represented by B and is calculated by following formula of area of a triangle.

\(Area = \dfrac{1}{2} \times \text{Base}\times \text{Height}\)

\(\Rightarrow \dfrac{1}{2} \times 11 \times 7\\\Rightarrow 38.5\ in^{2}\)

Hence, B = 38.5 \(in^{2}\).

Height of prism, h = 9 in

h is represented as side BE in the attached image.

It is know that volume of prism is given as :

V = Bh

Putting values of B and h:

\(V = 38.5 \times 9\\\Rightarrow V = 346.5\ in^{3}\)

Answer:

The formula for volume of a prism is V = Bh.

The variable B stands for the ✔ area of the base.

In this prism, B equals ✔ 38.5  in.².

The variable h stands for ✔ height.

In this prism, h is ✔ 9 in.

The volume of the prism is ✔ 346.5  in.³.

Explanation:

The answer above mine is correct. I hope this helps!

Answer:

43.30 km^2

Step-by-step explanation:

Since the shape is a regular polygon, the sides of the triangle are equal (10km) now find the area on the triangle using herons formula

Working:

Side is 10

Perimeter= 30km

Semiperimeter (s) = 15km

Formula= √s(s-a)(s-b)(s-c)

= √15(15-10)(15-10)(15-10)

= √15*5*5*5

=5√5*15

=5√75

= 5*8.66

= 43.3 km^2

Answer:

43.3

Step-by-step explanation:

since it is a regular polygon thus it is a equilateral triangle where all sides are the same and all angles are 60

use formula 1/2 x a x b x sin C where a and b are sides and C is the angle

1/2 x 10 x 10 x sin 60 = 43.30

or method 2 is using Pythagoras theorem by drawing a perpendicular height to length 10km

h = \(\sqrt{10^{2} - (10/2)^{2} } = \sqrt{75} \\\)

area of triangle = 1/2 x 10 x \(\sqrt{75}\) = 43.30

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