What is the difference of (-2x + 9) and (3x - 4)?
A: -5x + 5
B: x + 5
C: -5x - 13
D: x+ 13

Answer:

y ≤ -1/3x + 1

Step-by-step explanation:

find the slope and y-intercept and write equation in form of

y = mx + b;  m = slope and b = y-intercept

if you start at (0,1) and move down and to the right to (3,0) you get a slope equal to -1/3

we can see by looking at the graph that the y-intercept is 1

therefore, y ≤ -1/3x + 1

Answer:

126 blue marbles, 24 white marbles

Step-by-step explanation:

The ratio of blue marbles to white marbles is 21 to 4. From this, we have this equation:

\(21x + 4x = 150\)

\(25x = 150\)

\(x = 6\)

So we have 21 × 6 = 126 blue marbles and 4 × 6 = 24 blue marbles.

126/24 = 21/4

Answer:

Step-by-step explanation:

16

The scale is 1 : 30. A rectangle is shown. The length of the rectangle is labeled 3 inches. The width of the rectangle is labeled 4 inches. Show your work to determine the area of the room in square feet.First, we need to convert the measurements of the rectangle from inches to feet, since the question asks for the area in square feet. 3 inches = 3/12 feet = 0.25 feet 4 inches = 4/12 feet = 0.33 feet Now, we can use the scale to determine the actual dimensions of the room. If 1 inch on the drawing represents 30 inches in real life, then: 1 foot on the drawing represents 30 feet in real life So, the length of the room is: 1 foot on the drawing = 30 feet in real life 3 inches on the drawing = 3/12 feet = 0.25 feet in real life 0.25 feet x 30 = 7.5 feet And the width of the room is: 1 foot on the drawing =

The calculated volume of the dilated prism is 141.75 cubic feet

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

The volume is calculated as

Volume = Base area * Heigth

For the dilated prism, we have

Volume = Base area * Heigth * Scale factor³

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

Volume = 6 * 7 * (3/2)³

Evaluate

Volume = 141.75

Hence, the volume of the dilated prism is 141.75 cubic feet

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Answer:

Step-by-step explanation:

If the tip varies directly with the number of guests, it means that an increase in the amount of tip would be as a result of an increase in the number of guests and a decrease in the amount of tip would be as a result of an decrease in the number of guests.

If we introduce a constant of proportionality, k , the relationship would be

t = kg

Given that

When t = 18, g = 10, then

18 = k × 10

k = 18/10 = 1.8

Therefore, the equation representing the relationship is

t = 1.8g

Answer:

answer is a

Step-by-step explanation:

The probability that a randomly chosen college student exercises in the morning or afternoon is 0.76

We have given that the M be the event that the student exercises in the morning and A be the event that the student exercises in the afternoon.

To find : The probability that a randomly chosen college student exercises in the morning or afternoon

P(M) = 0.25+0.37 = 0.62

P(A) = 0.14+0.37 = 0.51

P(M and A) = 0.37

Now,

P(M or A) = P(M) + P(A) - P(M and A)

                = 0.62 + 0.51 - 0.37

                = 0.76

Hence, Option last 0.76 is the correct choice.

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(Answer is bolded, and underlined)

If we imagine that point D is on the negative side of the X axis, because right now, it is on the positive, and we need its reflection. If we flip it over, it becomes a -5, and the Y axis will stay the same, so the answer is

(-5, -3)

Answer:

(5, 3)

Step-by-step explanation:

If you kind of 'flip' the figure of=ver the x-axis, you'll see that every coordinate has the same numbers but has different positive and negative signs. If you flip the figure over the x-axis, point D will be in the first quadrant. Since the first quadrant is (positive, positive), then you change the signs to (positive, positive.)

John Kemeny, while chair of the Mathematics Department at Dartmouth College, wanted to determine the probability of having at least one day without mail in a ten-year period. around 0.0025.

Assuming the number of letters he received each day followed a Poisson distribution.

To calculate this probability, he applied the Poisson distribution twice. First, he found the probability of having at least one day without mail in 3000 days, assuming each year had approximately 300 days of mail delivery. The probability he found was approximately 0.0025.

Let's denote the average number of letters John Kemeny received per day as λ. Since he received an average of ten letters each day, we have λ = 10.

To find the probability of having at least one day without mail in 3000 days, we can use the Poisson distribution. The Poisson distribution provides the probability of a certain number of events occurring in a fixed interval, given the average rate of occurrence.

The probability of having no mail on a particular day can be calculated using the Poisson distribution formula:

\(P(X = 0) = (e^(-λ) * λ^0) / 0!\)

Since we want to find the probability of having at least one day without mail, we can find the complement of this probability:

P(at least one day without mail) = \(1 - P(X = 0)\)

For a single year, with approximately 300 days of mail delivery, we can calculate the probability of at least one day without mail using the given λ:

P(at least one day without mail in a year) = \(1 - P(X = 0) = 1 - (e^(-λ) * λ^0) / 0!\)

Substituting λ = 10, we get:

P(at least one day without mail in a year) =\(1 - (e^(-10) * 10^0) / 0!\)

Now, to find the probability of at least one day without mail in ten years (3000 days), assuming each year has 300 days of mail delivery, we raise the yearly probability to the power of 10:

P(at least one day without mail in ten years) = \([1 - (e^(-10) * 10^0) / 0!]^10\)

Evaluating this expression, we find that the probability John Kemeny calculated was approximately 0.0025.

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The given statement can be formulated as follows: A batch of 150 iPads is inspected by choosing a sample of four iPads. Eight of the 150 iPads do not conform to specifications.

How many samples of four contain exactly one non-conforming iPad?

Let's solve the given problem step by step.

Step 1: We have 8 non-conforming iPads and 142 conforming iPads in the batch of 150 iPads. We need to find the number of ways to choose 4 iPads that include exactly one non-conforming iPad.

Step 2: We choose one non-conforming iPad in 8 ways and choose 3 conforming iPads in 142C3 ways, where nCk is the number of ways to choose k objects from n distinct objects without regard to order.

Thus the total number of ways to choose 4 iPads with exactly one non-conforming iPad is given by:

=8 × 142C3

\(8 \times \frac{142 \times 141 \times 140}{3 \times 2 \times 1}\)

= 2,107,280

Therefore, there are 2,107,280 samples of four that contain exactly one non-conforming iPad.

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Answer:

\( \huge{ \boxed{ \bold{ \tt{14x + 14}}}}\)

Option E is the best choice.

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☯ Question : Simplify

☯ Available options :

☐ 12x + 16

☐ 24x + 48

☐ 10x + 2

☐ 14x + 48

☑ 14x + 14

☐ 9x + 5

✎ Step - by - step explanation :

Distribute 4 through the parentheses

\( \dashrightarrow{ \sf{12x + 8 + 2(x + 3)}}\)

Distribute 2 through the parentheses

\( \dashrightarrow{ \sf{12x + 8 + 2x + 6}}\)

Combine like terms. Only coefficients of like terms can be added or subtracted

\( \dashrightarrow{ \sf{12x + 2x + 8 + 6}}\)

\( \dashrightarrow{ \sf{14x + 8 + 6}}\)

Add the numbers : 8 and 6

\( \dashrightarrow{ \boxed{ \sf{14x + 14}}}\)

Hope I helped!

Have a wonderful time ツ

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Answer:

18

Step-by-step explanation:

1. Put them in order (15, 17, 19, 21, 24, 25, 38, and 39)

2.Then find the median, which would be 22.5

3. The lower quartile is the median of the first 4, and the upper would be the median of the upper four.

4. If it's an odd amount of number the lower would be the numbers under the median.

5. You'd get 17 and 19 so add the together then divide by 2.

6. You get 18.

Answer:

6\(\sqrt{5}\)-4\(\sqrt{7}\)

Step-by-step explanation:

3\(\sqrt{5} -2\sqrt{7} +3\sqrt{5} -\sqrt{28}\\6\sqrt{5}-2\sqrt{7} -2\sqrt{7} \\6\sqrt{5}-4\sqrt{7}\\=2.8334\)

Answer:

The 3rd one!

Step-by-step explanation:

Pls give brainliest i rlly rlly need it—..

The area of the surface obtained by rotating the circle \(x^2 + y^2 = r^2\) about the line y = r is π²r² square units.

To find the area of the surface obtained by rotating the circle

\(x^2 + y^2 = r^2\) about the line y = r, we can use the method of cylindrical shells.

The circle \(x^2 + y^2 = r^2\) is centered at the origin (0, 0) with a radius r. The line y = r is the line y-axis but shifted up by r units.

When we rotate the circle about the line y = r, it forms a 3D shape called a torus or a donut shape.

Consider a small strip on the circle at a distance y from the line y = r.

This small strip is at a distance r - y from the y-axis.

The length of this strip is the circumference of the circle at y, which is 2πy (since the circumference of a circle is 2π times its radius).

The width of this strip is the change in x, which we can denote as dx.

The area of this small strip is then given by the product of its length and width, which is 2πy dx.

Now, to find the total surface area, we integrate this area over the range of y values from -r to r (since the circle is symmetric about the y-axis):

Total Surface Area = ∫[from -r to r] 2πy dx

Now, we need to express y in terms of x using the equation of the circle \(x^2 + y^2 = r^2:\\y^2 = r^2 - x^2\)

y = ±√(r² - x²)

Since we are considering the upper half of the circle, we take the positive square root:

y = √(r² - x²)

Now, we can rewrite the integral with respect to x:

Total Surface Area = ∫[from -r to r] 2π√(r² - x²) dx

To solve this integral, we can make a trigonometric substitution:

Let x = r sin(θ), then dx = r cos(θ) dθ.

When x = -r, θ = -π/2, and when x = r, θ = π/2.

Now the integral becomes:

Total Surface Area = ∫[from -π/2 to π/2] 2π√(r² - (r sin(θ))²) (r cos(θ)) dθ

Total Surface Area = 2πr² ∫[from -π/2 to π/2] √(1 - sin²(θ)) cos(θ) dθ

Now, we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

√(1 - sin²(θ)) = cos(θ)

Total Surface Area = 2πr² ∫[from -π/2 to π/2] cos²(θ) dθ

Now, use the trigonometric identity: cos²(θ) = (1 + cos(2θ))/2

Total Surface Area = 2πr² ∫[from -π/2 to π/2] (1 + cos(2θ))/2 dθ

Total Surface Area = 2πr² [θ/2 + (sin(2θ))/4] [from -π/2 to π/2]

Total Surface Area = 2πr² [(π/2 + sin(π) - (-π/2 + sin(-π)))/4]

Since sin(π) = 0 and sin(-π) = 0:

Total Surface Area = 2πr² [(π/2 - (-π/2))/4]

Total Surface Area = 2πr² (π/2)

Total Surface Area = π²r²

So, the area of the surface obtained by rotating the circle \(x^2 + y^2 = r^2\) about the line y = r is π²r² square units.

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We are given the following equation:

To solve for "x" we will take arccos to both sides:

Solving the operations:

This is for the first quadrant. Dividing both sides by 2:

For the second quadrant we have:

Dividing both sides by 2:

For the third quadrant we have:

Dividing by 2:

For the fourth quadrant:

Dividing by 2:

Therefore, the values of "x" are:

Answer:

Step-by-step explanation:

66 mile per hour .

(a) No, a triangle cannot have two obtuse angles. (b) No, a triangle cannot have two right angles.
(c) If no angle of a triangle measures more than 60°, then the triangle is an acute triangle.


(a) In a triangle, the sum of all three angles must be 180°. Since two obtuse angles would sum to more than 180°, it is not possible for a triangle to have two obtuse angles.
(b) In a triangle, the sum of all three angles must be 180°. Since two right angles would sum to 180°, it is not possible for a triangle to have two right angles.
(c) In an acute triangle, all three angles are less than 90°. If no angle of a triangle measures more than 60°, then all three angles are less than 90°, making it an acute triangle.

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Answer:

0.19

Step-by-step explanation:

the easiest way to solve for this is 4.75/25 (division). This is assuming I read this right and your asking the price of each individual pencil

0.19 dollars is the unit price.

As we can see that a pack of 25 pencils costs 4.75 dollars

So the cost for 1 pencil would be 4.75/25

=0.19

A group of friends or a group of something

An example of to pack is putting collectibles in a box to be stored away. An example of to pack is putting your child's lunch in a lunch box for them to take to school.

An example of to pack is placing what you'll need for a weekend trip in a piece of luggage.

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.

Answer:

128 <33

Step-by-step explanation:

6 ÷ 3 + 32 • 4 - 2 = 128

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Answer:

6

Step-by-step explanation:

Based on the information given if She divided the place mat into 6 equal parts to color the name for the parts will be the 6 parts she divided to color reason been that division or separation of the place mat into 6 equal Parts to color means that the place mat that was divided by Madison into 6 equal parts have the same size or equal size .

Therefore the name for the parts will be 6.

When we divide a shape with each part has same size then all the parts are called as equal parts of a whole. Thus the name of equal parts of the mat made by the Madison is sixths.

Equal parts of a whole-

When we divide a shape with each part has same size then all the parts are called as equal parts of a whole.

For example, a shape is divided into two equal parts then the name of the equal parts is halves. If  a shape is divided into three equal parts then the name of the equal parts is thirds.

Here in the question, given-

The mad made by the Madison has 6 part.

The size and shape of each part is same.

When Madison divides the mat in 6 equal part of this mat than each part will have 1/6 part mat of the original size mat. As by the definition of the equal parts of a whole we can conclude that if a shape is divided into 6 equal parts then the name for the parts is sixths.

Hence, the name of equal parts of the mat made by the Madison is sixths.

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Step-by-step explanation:

Distributive property

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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The consumption bundle that will not be the consumer's choice, given the assumptions of choosing the optimal bundle, is option B) 30 snacks and 12 meals. To determine the optimal consumption bundle, we need to consider the consumer's budget constraint and maximize their utility.

Given that the price of snacks is $4 and the price of meals is $10, and the consumer has $240 remaining on their meal card, we can calculate the maximum number of snacks and meals that can be purchased within the budget constraint.

For option A) 5 snacks and 20 meals, the total cost would be $4 × 5 + $10 × 20 = $200. Since the consumer has $240 remaining, this bundle is feasible.

For option B) 30 snacks and 12 meals, the total cost would be $4 × 30 + $10 × 12 = $240. This bundle is on budget constraint, but it may not be the optimal choice since the consumer could potentially consume more meals for the same cost.

For option C) 20 snacks and 16 meals, the total cost would be $4 × 20 + $10 × 16 = $240. This bundle is also on budget constraint.

Since options A, C, and D are all feasible within the budget constraint, the only bundle that will not be the consumer's choice is option B) 30 snacks and 12 meals. The consumer could achieve a higher level of utility by reallocating some snacks to meals while staying within the budget constraint. Therefore, the correct answer is option B.

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Answer:

92

Step-by-step explanation:

Based on the data above, The five-number summary is 0.00, 0.17, 0.5, 1.43, 292.00.

The following data represent the dividend yields (in percent) of a random sample of 26 publicly traded des.

The following data represents the dividend yields (in percent) of a random sample of 26 publicly traded des:

0.5 0.8 1.75 0.04 0.18 0.35 3.69 0 0.95 0 0.17 1.83 1.33 0 0.54 1.14 0.41 159 21 2.41 292 3.18 3.03 1.43 0.58 0.13 0 0.19

Here, the five-number summary is given by:

Minimum value = 0.00

First Quartile (Q1) = 0.17

Median (Q2) = 0.5

Third Quartile (Q3) = 1.43

Maximum value = 292.00

Therefore, the five-number summary is 0.00, 0.17, 0.5, 1.43, 292.00.

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Answer:

x represents per mile fee