solve
2r - 22 = 4(r-3)

The perimeter of ΔNOP is equal to 25.6 units.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangles, we have the following:

ΔNOP ≅ ΔKLM

OP/ML = x/KL

x = (OP × KL)/ML

x = (8 × 7)/5

x = ON = 11.2 units.

For the perimeter of ΔNOP, we have;

Perimeter of ΔNOP = OP + NP + ON

Perimeter of ΔNOP = 8 + 6.4 + 11.2

Perimeter of ΔNOP = 25.6 units.

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The following is the right response for whatever bus has the smallest spread between the travel times: Bus 14, with an IQR of 6.

The dot plot, which depicts the frequency with which each observation appears in the data set, is the first thing we take into account.

The difference between the data set's third and first quartiles is represented by the interquartile range, which is the next factor we take into account.

Because it ignores outliers, the interquartile range is a better indicator of spread than a data set's range.

We have the following for classes of 15 students:

Since the first seven students make up the first half, the first quartile is represented by the fourth dot, which represents the first half's median.

The final seven students make up the second half, thus the eleventh dot—the first half's median—is in the first quartile.

The following are the Bus 14 quartiles:

[tex]Q_1=12\\\\Q_3=18[/tex]

Hence the IQR is of:

[tex]IQR=Q_3-Q_1\\\\IQR=18-12\\\\IQR=6[/tex]

The following are the Bus 18 quartiles:

[tex]Q_1=9\\\\Q_3=16[/tex]

Hence the IQR is of:

[tex]IQR=Q_3-Q_1\\\\IQR=16-9\\\\IQR=7[/tex]

Bus 14 is therefore the more reliable bus as a result of its lower IQR.

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The complete question is,

The endpoints of the rainbow are 2√60 cm apart.

The given equation for the rainbow is in vertex form, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

In this case, the vertex is (1, 6), which means that the parabola is shifted horizontally by 1 unit to the right and vertically by 6 units upwards from the standard parabola y = ax^2.

Since the height of the rainbow is 6 cm, this means that the highest point of the parabola is at y = 6, which occurs at the vertex (1, 6).

To find the distance between the endpoints of the rainbow, we need to find the x-intercepts of the parabola. These occur where y = 0. Therefore, we need to solve for x in the equation:

0 = -0.1(x - 1)^2 + 6

-6 = -0.1(x - 1)^2

-6/-0.1 = (x - 1)^2

60 = (x - 1)^2

±√60 = x - 1

x = 1 ± √60

Since we are looking for the distance between the endpoints, we need to subtract the smaller x-value from the larger one:

Distance between endpoints = (1 + √60) - (1 - √60)

Distance between endpoints = 2√60

Therefore, the endpoints of the rainbow are 2√60 cm apart.

The given equation in the question is wrong, the correct equation is:

y = -0.1(x - 1)^2 + 6.

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(b) The volume of the medium box is 5832 cubic inches.

In mathematics, a ratio is a comparison of two quantities or numbers. It is expressed as the quotient of one number divided by another, and is often written as "a:b" or "a/b". Ratios are used to compare the sizes of two or more quantities, and they can be used to solve problems involving proportions and percentages.

For example, if a recipe calls for a ratio of 2 cups of flour to 1 cup of sugar, this means that for every 2 cups of flour used, 1 cup of sugar should be used as well. Similarly, if a company has a debt-to-equity ratio of 2:1, this means that for every $2 of debt, the company has $1 of equity.

(a) Let x be the length of the sides of the original box. Then the volume of the box is x^3 = 216, so x = 6.

When the length, width, and height are all tripled, the new side length of the medium box is 3x = 18.

The ratio of the sides of the medium box to the original box is 18:6, or simplified, 3:1.

The area of the base of the original box is. [tex]x^2 = 6^2 = 36[/tex]square inches.

The area of the base of the medium box is. [tex](3x)^2 = 18^2 = 324[/tex] square inches.

The ratio of the 5832 of the bases of the medium box to the original box is 324:36, or simplified, 9:1.

The volume of the medium box is. [tex](3x)^3 = 18^3 = 5832[/tex]cubic inches.

The ratio of the volumes of the medium box to the original box is 5832:216, or simplified, 27:1.

(b) The volume of the medium box is 5832 cubic inches.

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The current outdoor temperature is 37.89°C, which is less than the highest temperature limit, i.e., 47.8°.

Both Celsius and Fahrenheit have different zero points and the temperature increments also vary quite differently. 100 degrees separate freezing and boiling on the Celsius scale, but for Fahrenheit the difference is 180 degrees. This means Celsius is 1.8 times larger than Fahrenheit.

To determine whether the medication has been exposed to temperatures higher than 47.8°C, we need to convert the outdoor temperature from Fahrenheit to Celsius. The conversion formula is:

°C = (°F - 32) x 5/9

Using this formula, we can get the temperature in Celsius form,

°C = (100.2 - 32) x 5/9

   = 37.89°C

Since the outdoor temperature is lower than the maximum temperature the medication can be exposed to, it is safe to assume that the medication has not been exposed to temperatures higher than 47.8°C.

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Probability about at least one customer arrives at the shop while a one-minute interval is almost 0.632 or 63.2%.

The probability that at least one customer arrives at the shop during a one-minute interval can be calculated using the Poisson distribution, which is commonly used to model the arrival of events over a given time period.

Let's assume that the average number of customers arriving at the shop per minute is [tex]l[/tex]. Poisson probability mass function is;

[tex]P(X = k) = (e^{-l} * l^k) / k![/tex]

where X is the random variable representing the number of customers arriving in a one-minute interval, and k is the number of customers that arrive.

To find the probability of at least one customer arriving, we need to calculate the probability of X being greater than or equal to 1. That is,

[tex]P(X > = 1) = 1 - P(X = 0)[/tex]

When [tex]l[/tex] is relatively small, we can use approximation:

[tex]P(X = 0) = e^{-l[/tex]

Therefore,

[tex]P(X > = 1) = 1 - P(X = 0)[/tex]

[tex]≈ 1 - e^{-l[/tex]

We don't have the value of [tex]l[/tex], but assuming an average arrival rate of 1 customer per minute (i.e., [tex]l[/tex] = 1), we get:

[tex]P(X > = 1) = 1 - e^{-1[/tex]

≈ 0.632

Therefore, the probability about  at least one customer arrives at the shop while a one-minute interval is almost 0.632 or 63.2%.

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Answer:

9ft

Step-by-step explanation:

I'm not sure, sorry if this didn't help you have a good day

The proof for the given proportion or two equivalent ratios given as (y+x):(y-x) = k:1 is shown below

What is a proportion?

On ratio and fractions, proportion is based. Two ratios are equal when they are represented as a fraction (a/b), a ratio (a:b), and then a proportion. A and B are two integers. Two sets of supplied numbers are said to be directly proportional if they increase or decrease in the same ratio for both sets. The symbols "::" or "=" are used to indicate proportions. If the ratio between the first and second is equal to the ratio between the second and third, then any three quantities are in continuing proportion.

Given that (y+x) : (y-x) = k : 1

We know that product of extremes = product of means

Extremes=(y+x) and 1

Means=(y-x) and k

(y+x) . 1   = (y-x) . k

y + x = ky - kx

y - ky = -kx - x

y - ky = - x(k + 1)

-(y - ky) = x(k + 1)

ky - y = x(k + 1)

y(k - 1) = x(k + 1)

y=[tex]\frac{x(k+1)}{(k-1)}[/tex]

Hence proved.

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The relative frequency of a B grade is 0.25 or 25%.

The relative frequency of a B grade is the fraction or proportion of the total number of students who received a B grade in the class.

Relative frequency of a B grade = (Number of students who received a B grade) / (Total number of students in the class)

Substituting the given values, we get:

In this case, we know that out of 100 students, 25 students received a B grade. So the relative frequency of B grade is:

25/100

Relative frequency of a B grade = 25 / 100 = 0.25

Therefore, the relative frequency of a B grade is 0.25 or 25%.

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After Tuesday, Andy still had 5/18 of his candy bar left.

What is the fraction?

A fraction is a mathematical representation of a part of a whole, where the whole is divided into equal parts. A fraction consists of two numbers, one written above the other and separated by a horizontal line, which is called the fraction bar or the vinculum.

If Andy ate 7/12 of his candy bar on Monday, then the fraction of the candy bar that was left after Monday is:

1 - 7/12 = 5/12

So, on Tuesday, he ate 1/3 of the remaining candy bar, which is:

(1/3) * (5/12) = 5/36

Therefore, the fraction of the candy bar that was still there after Tuesday is:

5/12 - 5/36 = (15/36) - (5/36) = 10/36 = 5/18

Hence, after Tuesday, Andy still had 5/18 of his candy bar left.

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The company must produce and sell at least 857 bottles of juice in a day to break-even, given the given expenses and selling price per bottle.

Let's denote the number of bottles of juice sold in a day as "x".

The total cost of production and business expenses :

Total cost = Business expenses + (Cost per bottle of juice) x (Number of bottles produced and sold)

Total cost = $1200 + $1.10x

The revenue generated from selling "x" bottles :

Revenue = (Selling price per bottle of juice) x (Number of bottles produced and sold)

Revenue = $2.50x

The company will break-even when revenue equals total cost, so we can set two expressions equal to each:

[tex]\\$2.50x = $1200 + $1.10x\\$2.50x - $1.10x = $1200\\$1.40x = $1200\\x = $1200 / $1.40\\[/tex]

x ≈ 857

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Thus, the probability that two custard-filled donuts are selected in a row) 11/46.

sampling without replacement is the process of selecting a subset of observations at random; once an observation is chosen, it cannot be chosen again. sampling with replacement, whereby one observation may be chosen more than once and a subset of observations is chosen at random.

Given data:

two-dozen (24) donuts

probability = favourable outcome / total outcome

probability (1st custard-filled donut) = total custard-filled donut / total donuts

probability (1st custard-filled donut) = 12/24

probability (1st custard-filled donut) = 1/2

Now,1 is already taken, now total donuts left are 23 with 11 custard-filled donut.

probability (2nd custard-filled donut) = total custard-filled donut / total donuts

probability (2nd custard-filled donut) = 11/23

Now,

probability (two custard-filled donuts in a row) = 1/2 * 11/23

probability (two custard-filled donuts in a row) = 11 / 46

Thus, the probability that two custard-filled donuts are selected in a row) 11/46.

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According to the information, the number of people who likes folk song is 90, and the number of people who likes modern song 80. So, the total number of people in the survey is 250.

Let the number of people who like modern songs be 8x, and the number of people who like folk songs be 9x.

From the given information, we know that:

50 people like both modern and folk songs

40 people like only folk songs

The total number of people who like at least one type of song is (8 + 9)x - 50 = 17x - 50

80 people like none of the songs

Therefore, we can write the following equation:

(8x + 9x) - 50 - 40 + 80 = 17x

Simplifying this equation, we get:

17x - 10 = 17x

Thus, x = 10.

So, the number of people who like folk songs is 9x = 9(10) = 90.

Similarly, the number of people who like modern songs is 8x = 8(10) = 80.

The total number of people in the survey is the sum of the number of people who like modern songs, the number of people who like folk songs, and the number of people who like none of the songs.

So, the total number of people in the survey is:

80 + 90 + 80 = 250.

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An analysis of future events performed by the probability of those events and the potential outcomes is called probabilistic analysis.

Probabilistic analysis involves using mathematical models and statistical techniques to estimate the likelihood of different outcomes, given a set of assumptions and inputs. It is commonly used in risk management, financial analysis, and project management to evaluate the potential impact of different scenarios and make informed decisions. By quantifying the probabilities of different outcomes, probabilistic analysis helps decision-makers identify the best course of action and manage uncertainty and risk.

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The surface area is given below:

Surface area refers to the total area that the surface of an object occupies. It is a measure of how much-exposed area there is on the outside of the object.

The surface area of an object can be calculated by adding up the areas of all of its faces or surfaces.

The formula for surface area varies depending on the shape of the object. For example, the surface area of a rectangular prism can be calculated by adding up the areas of all six of its faces, while the surface area of a sphere can be calculated using a different formula.

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In table 9.1, the marginal cost of producing the seventh unit of output is equal to $8.
Marginal cost refers to the additional cost incurred when producing one more unit of output. To find the marginal cost of producing the seventh unit of output, follow these steps:

1. Locate the total cost column in table 9.1.
2. Identify the total cost of producing 6 units of output.
3. Identify the total cost of producing 7 units of output.
4. Subtract the total cost of producing 6 units from the total cost of producing 7 units.

The difference you get from step 4 is the marginal cost of producing the seventh unit of output.

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Answer:

To do this you have to multiply 3.14 times the diameter, so 14 x 3.14 = 43.96 which is the diameter you cn round it!

Step-by-step explanation:

The flour will fit into two of the container is 144 inches.

What is the volume of cuboids?

A cuboid is a six-sided solid known as a hexahedron. Quadrilaterals make up its faces. Cuboid is short for "like a cube". A cuboid is similar to a cube in that a cuboid can become a cube by varying the lengths of the edges or the angles between the faces.

Here, we have

Given: Mrs. Hanson is filling containers in her bakery with flour.

we have to find how much flour will fit into two of the containers.

Volume of cuboid = length × breadth × height

Length = 6 inches

Breadth = 3 inches

Height = 8 inches

The flour will fit into two of the containers = length × breadth × height

= 6 ×3 × 8

= 144 inches

Hence, The flour will fit into two of the container 144 inches.

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The equivalent sum to the given equation is -9c - 20.

An algebraic expression is consists of variables, numbers with various mathematical operations.

Equivalent sums refers to addition or subtraction from the other number to maintain the same total value.

= 9c-12-15c-8-3c

To find the equivalent sum, first we can simplify this expression by first combining like terms:

= 9c - 15c - 3c - 12 - 8

= (9c - 15c - 3c) - (12 + 8)   (grouping the like terms)

Solving the expression for terms c and  for constant terms,

= -9c - 20

Therefore, the equivalent sum is -9c - 20.

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(a) The linear density (mass/length) rho has SI units of kg/m. Since rho = a + bx, the SI units of a must be kg/m and the SI units of b must be kg/m^2.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod:
m = ∫₀ᴸ ρ(x) dx
Substituting in ρ(x) = a + bx:
m = ∫₀ᴸ (a + bx) dx
m = [ax + (1/2)bx²] from 0 to L
m = aL + (1/2)bL²
Therefore, the mass of the rod in terms of a, b, and L is m = aL + (1/2)bL².

(a) In this problem, rho (ρ) represents linear density, which has units of mass per length. In SI units, mass is measured in kilograms (kg) and length in meters (m). Therefore, the units of linear density are kg/m. Since ρ = a + bx, the units of a and b must be consistent with this equation. The units of a are the same as those of ρ, so a has units of kg/m. For b, since it is multiplied by x (which has units of meters), b must have units of kg/m² to maintain consistency in the equation.

(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod (from x=0 to x=L). Let's set up the integral:

Mass (M) = ∫(a + bx) dx, with limits from 0 to L

Now, we can integrate:

M = [a * x + (b/2) * x²] evaluated from 0 to L

Substitute the limits:

M = a * L + (b/2) * L²

So, the mass of the rod in terms of a, b, and L is:

M = aL + (bL²)/2

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We get a probability of 3/8 or 0.375.

To find the probability of two successes (i.e., drawing two red balls) out of three draws from an urn containing 14 balls (7 of which are red), we can use the binomial probability formula:

[tex]P(X = 2) = (n\ choose\ x) * p^x * (1-p)^{(n-x)[/tex]

where

n is the total number of draws (3 in this case),

x is the number of successes (2 in this case),

p is the probability of a success on any given draw (7/14 or 1/2 in this case),

and (n choose x) is the number of ways to choose x items out of n items.

Plugging in the values, we get:

[tex]P(X = 2) = (3\ choose\ 2) * (1/2)^2 * (1/2)^{(3-2)} = 3/8[/tex]

Therefore, the probability of getting two red balls out of three draws is 3/8 or 0.375.

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d) there must be at least 30 trials.

For quadrilateral ABCD x=85 and angle B= 23°.

A quadrilateral is a polygon with four sides and four angles. It is a closed figure and can have different shapes and sizes, depending on the length of its sides and the angles between them.

(a) Supplementary equation used to solve for x:

∠A + ∠C = 180°

(b) All math used to calculate for x:

∠A + ∠C = 180°

(x - 5) + (x + 15) = 180 (substitute the given values for ∠A, ∠C)

2x - 10 = 180

2x = 170

x = 85

(c) Correct value for x:

x = 85

(d) Plugging x into expressions for angles A, C, D:

∠A = x - 5 = 2(85) - 5 = 165

∠C = x + 15 = 85 + 15 = 100

∠D = x - 13 = 85 - 13 = 72

(e) All math used to calculate the measures of angles A, C, D:

∠A + ∠B + ∠C + ∠D = 360° (sum of angles in a quadrilateral)

165 + ∠B + 100 + 72 = 360

∠B = 23

Therefore, the measures of the angles are:

∠A = 165°

∠B = 23°

∠C = 100°

∠D = 72°

(f) All math used to calculate the measure of angle B:

∠B = 360 - ∠A - ∠C - ∠D

∠B = 360 - 165 - 100 - 72

∠B = 23°

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The correct answer is: Fast Chicken, because it has a smaller median.

What is median?

Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude. To find the median, you need to arrange the values in order from smallest to largest and then find the middle value.

Based on the information provided, the drive-thru restaurant with less wait time is Fast Chicken, as it has a smaller median wait time of 12.5 minutes compared to the median wait time of 12 minutes for Super Fast Food. The mean wait time is not given, and even if it were, the median is a better measure of central tendency to compare in this scenario, as the box plots suggest some potential outliers.

Therefore, the correct answer is: Fast Chicken, because it has a smaller median.

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Answer:

I dont know the answer to be honest..

JUST KIDDING.. ill answer this step by step lol

To solve the inequality 9/x + 81 > 45, we can follow these steps:

Step 1: Subtract 81 from both sides of the inequality to isolate the fraction on the left-hand side:

9/x + 81 - 81 > 45 - 81

9/x > -36

Step 2: Take the reciprocal of both sides of the inequality to eliminate the fraction:

1 / (9/x) < 1 / (-36)

x/9 < -1/36

Step 3: Multiply both sides of the inequality by 9 to get rid of the fraction in the numerator:

9 * (x/9) < 9 * (-1/36)

x < -1/4

So, the solution to the inequality 9/x + 81 > 45 is x < -1/4. This means that x must be less than -1/4 for the inequality to be true.

The simplifies Boolean function of the given function F(x, y, z) = xy'z + (x + z' + xz')' is F(x, y, z) = xz' + yz

Hence, the correct option is A.

To simplify the Boolean function F(x, y, z) = xy'z + (x + z' + xz')', we can use De Morgan's laws and distributive property.

First, let's simplify the second term (x + z' + xz')' using De Morgan's law:

(x + z' + xz')' = x'z(z + x')

Now, we can substitute this simplified term back into the original expression and apply distributive property:

F(x, y, z) = xy'z + x'z(z + x')y'

= xy'z + x'y'z + x'zy'

= z(x'y' + xy') + xy'z

= z(x + y') + xy'z

= xz' + yz

Therefore, the simplified Boolean function is F(x, y, z) = xz' + yz, which corresponds to option A.

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To determine the effect of the interaction of the number of pages and cover type on cost, a statistical analysis would need to be performed using data on the number of pages, cover type, and cost. The analysis would likely involve running a regression model that includes both the number of pages and cover type as predictor variables, as well as an interaction term between the two.

 To answer your question, the effect of the interaction between the number of pages and cover type on the cost can be determined through a step-by-step process:

1. Identify the base cost of each cover type (e.g., hardcover, paperback, etc.).
2. Determine the cost per additional page for each cover type.
3. Calculate the cost for a specific number of pages and cover type by adding the base cost and the cost of additional pages.

For example:
- Base cost for hardcover: $5.00
- Base cost for paperback: $3.00
- Cost per additional page for hardcover: $0.10
- Cost per additional page for paperback: $0.05

Now, let's say you want to find the cost of a 100-page hardcover book:

1. Start with the base cost of a hardcover: $5.00
2. Multiply the number of pages (100) by the cost per additional page for hardcover ($0.10): 100 * $0.10 = $10.00
3. Add the base cost and the cost of additional pages: $5.00 + $10.00 = $15.00

So, the cost of a 100-page hardcover book is $15.00.

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The sum of the expression is 3.5x+6.8.

Given that are two expressions, we need to find the sum of the expressions,

The expression is a mathematical statement which is constructed by putting arithmetical operations, variables and numbers together.

So, finding the sum.

(-4.25x + 9) and (8x - 2.2)

Putting the sign of addition,

= (-4.25x + 9) + (8x - 2.2)

Opening the brackets,

= -4.5x + 9 + 8x - 2.2

Combining the like terms.

= 8x-4.5x + 9-2.2

Operating the like terms,

= 3.5x+6.8

Hence, the sum of the expression is 3.5x+6.8.

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Answer:

it A or B

Step-by-step explanation:

the other two C and D dont make sense to what the question is asking