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To evaluate the expressions 2(y+6)/3 and (4y+64)/(-3) for y=-3, we substituted -3 for y and simplified. The first expression evaluates to 2, and the second evaluates to approximately -17.333.

To evaluate the expressions 2(y+6)/3 and (4y+64)/(-3) for y=-3, we can simply substitute -3 for y in each expression and simplify

2(y+6)/3 = 2(-3+6)/3

Now, simplifying by simple subtraction and then multiply,

= 2(3)/3 = 6/3 = 2

Therefore, when y=-3, the value of 2(y+6)/3 is 2.

Now, substituting the value of y =-3

(4y+64)/(-3) = (4(-3)+64)/(-3) = (-12+64)/(-3) = 52/(-3) = -17.333...

Therefore, when y=-3, the value of (4y+64)/(-3) is approximately -17.333.

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Step-by-step explanation:

its -7.4

because each gap means 0.1

Answer:

6,3,7

Step-by-step explanation:

this is because they are all obtuse angles please help me i have a brain fart on meidan  of 45, 52, 57, 42, 54, 58.

Answer:

36.6°

Step-by-step explanation:

If angles W and X are complementary, this means that they add up to 90°.

If angle X equals 53.4°, then we can subtract 90-53.4 to get the measure of angle W.

90-53.4

=36.6

Angle W=36.6°

Hope this helps! :)

The probability that an answer is Ann's given that it is correct is 0.43 or 43%.

Where P(A|C) is the probability that the answer is Ann's given that it is correct, P(C|A) is the probability that the answer is correct given that it is Ann's, P(A) is the probability that the answer is Ann's, and P(C) is the probability that the answer is correct.

We can use Bayes' theorem to calculate the probability that an answer is Ann's, given that it is correct:

P(A|C) = P(C|A) * P(A) / P(C)

We are given that Brandon answered 80% of the questions correctly, so the probability that the answer is correct is:

P(C) = 0.8(0.6) + 0.85(0.4) = 0.79

where 0.6 is the probability that Brandon answers a question correctly (since 40% fail), and 0.4 is the probability that Ann answers a question correctly.

We are also given that Ann usually gets 85% of the questions right, so the probability that the answer is Ann's is:

P(A) = 0.4

Finally, the probability that an answer is correct given that it is Ann's is simply:

P(C|A) = 0.85

These values are what we obtain when we apply Bayes' theorem to them:

P(A|C) = P(C|A) * P(A) / P(C)

P(A|C) = 0.85 * 0.4 / 0.79

P(A|C) = 0.43

The Bayes theorem is a mathematical formula that estimates the likelihood that an event will occur based on knowledge of comparable events that have already occurred. It is named after Reverend Thomas Bayes, an 18th-century statistician, who first formulated it.

The theorem is based on the concept of conditional probability, which is the probability of an event occurring given that another event has already occurred. Bayes' theorem provides a way to update the probability of an event based on new evidence or information. The formula for Bayes' theorem is: P(A|B) = P(B|A) * P(A) / P(B), where P(A|B) is the probability of event A given event B has occurred, P(B|A) is the probability of event B given that A has occurred, P(A) is the prior probability of A occurring, and P(B) is the prior probability of B occurring.

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Refer to the attached images.

The requried, rounding to the nearest gram, mass of the object is 95,297 g.

First, we need to find the volume of the rectangular prism:

Volume = length x width x height = 8 in x 7 in x 5 in = 280 cubic inches

Next, we need to convert the volume to cubic centimeters since the density is given in grams per cubic centimeter:

1 cubic inch = 16.3871 cubic centimeters

280 cubic inches = 280 x 16.3871 = 4594.628 cubic centimeters

Finally, we can calculate the mass of the object using the density formula:

Density = mass/volume

Density x volume

mass = 20.7 g/cm³ x 4594.628 cm³ ≈ 95,296.7 g

Rounding to the nearest gram, the mass of the object is 95,297 g.

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The price at which the company should sell its phones to get the maximum revenue is $250

Attaining peak yields is the preeminent rate of profits that a commerce or congregation can accumulate from its action, products, or amenities within a determined span.

It is where the firm or collective is accruing the most money achievable, harnessing its present facilities, marketplace appeal, pricing methods, along with other specifics.

In order to attain maximum revenue, an enterprise must focus on refining its sales and networking campaigns, developing its wares or services, determining and honing in on precise shoppers, and optimizing its expenses as well as costs efficaciously.

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The probability of a student having at least one sibling, based on the survey results is 0.8.

Daniel surveyed 120 students at his school and found that 96 of them have at least one sibling. This means that the probability of a student having at least one sibling, based on the survey results, is 96/120 or 0.8.

There are 425 students at Daniel's school, so if we multiply this number by the probability of having at least one sibling (0.8), we can estimate that approximately 340 students at the school have at least one sibling.

To estimate the number of students at Daniel's school who have at least one sibling, we can use this probability to make a prediction.

If we assume that the probability of a student having at least one sibling is the same for all students at the school, then we can apply this probability to the total number of students.

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Answer:

The answer for x is 28°

Step-by-step explanation:

x+62=90°

x=90-62

x=28°

The solution of the lines y = - x + 5 and y = 2x - 1 will be (2, 3).

Given that:

y = - x + 5

y = 2x - 1

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

If the slopes are different then the system has one solution.

The lines are drawn on the graph. And the solution of the lines will be (2, 3).

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The total surface area of the pyramid is  1,296 unit².

The lateral surface area (L.A) of the pyramid is 19.21 unit².

The volume of pyramid is 120 unit³.

The surface area of the pyramid is calculated as follows;

T.S.A = 2bh + b²

where;

In then diagram, we where given, base, b = 24 units, height = 15 units, then the surface area of the pyramid is calculated as follows;

T.S.A = 2 x 24 x 15  +  24²

T.S.A = 1,296 unit²

The lateral surface area is calculated as

L.A = √(b²/4 + h²)

L.A = √(24²/4 + 15²)

L.A = 19.21 unit²

The volume of pyramid is calculated as;

V = ¹/₃BH

V = ¹/₃ x 24 x 15

V = 120 unit³

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Answer: Gabriel is 10 years old.

Step-by-step explanation:

Let x represent Gabriel's age and x+2 represent Moussa's age.

x(x+2)=120

x^2+2x=120

x^2+2x-120=0

(Factor quadratic equation): (x-10)(x+12)=0

                                                  x=10, x=-12 --> (age can't be negative)

Gabriel is 10 years old.

The measures of the exterior angles of a triangle are 6x°, 8x°, and 10x°, and x equals 7.5°.

Angle is a figure formed by two straight lines or planes diverging from or meeting at a common point. It is a measure of the amount of rotation between two lines or planes and is usually measured in degrees or radians. Angles can be classified as right angles, acute angles, obtuse angles, straight angles, and reflex angles. Angles are also used in geometry to describe the shape of an object or the relationship between two lines or planes.

To solve for x in the measures of the exterior angles of a triangle, use the formula 180°=6x°+8x°+10x°. Rearranging to isolate x, we get x=180°/24x°=7.5. Therefore, x=7.5°.

Conclusion: The measures of the exterior angles of a triangle are 6x°, 8x°, and 10x°, and x equals 7.5°.

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The triangle has exterior angles measuring 90°, 120°, and 150° and value of x is 15.

What is Angle?

Angle is a figure formed by two straight lines or planes diverging from or meeting at a common point. It is a measure of the amount of rotation between two lines or planes and is usually measured in degrees or radians. Angles can be classified as right angles, acute angles, obtuse angles, straight angles, and reflex angles. Angles are also used in geometry to describe the shape of an object or the relationship between two lines or planes.

The sum of the exterior angles of any triangle is always 360 degrees.

Therefore, we can set up the equation: 6x° + 8x° + 10x° = 360°

Simplifying the left side of the equation, we get: 24x° = 360° Dividing both sides by 24, we get: x° = 15°

Therefore, the measures of the exterior angles of the triangle are: 6x° = 6(15°) = 90°

8x° = 8(15°) = 120°

10x° = 10(15°) = 150°

So the triangle has exterior angles measuring 90°, 120°, and 150°.

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The amount of wrapping paper for the gift is A = 279 inches²

Given data ,

To calculate the amount of wrapping paper Laura will need to wrap the gift, we need to find the total surface area of the gift.

The surface area of a rectangular box is given by the formula:

Surface Area = 2 x (length x width + length x height + width x height)

Given that the length of the gift is 6 inches, the width is 13.5 inches, and the height is 3 inches, we can substitute these values into the formula:

Surface Area = 2 x (6 x 13.5 + 6 x 3 + 13.5 x 3)

Surface Area = 2 x (81 + 18 + 40.5)

Surface Area = 2 x 139.5

The surface area of a rectangular box = 279 inches²

Hence , Laura will need 279 inches² of wrapping paper to wrap the gift

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Answer:

To find the lower bound of the mass of phosphorus in 1 liter of the fruit juice, we need to assume that all of the phosphorus is concentrated in just one liter of the juice. Therefore, the lower bound will be the mass of phosphorus in the entire bottle divided by the total volume of the bottle, which is 1.62 liters.

The mass of phosphorus per liter of juice is given by:

488 mg ÷ 1.62 L ≈ 301.2 mg/L

Rounding this to the nearest milligram, we get:

301 mg/L

Therefore, the lower bound of the mass of phosphorus in 1 liter of the fruit juice is approximately 301 mg.

The polynomial 2x³ − 5x² + 6x − 15 as a product of binomials is option (a) (x² + 3)(2x − 5).

To factor the polynomial 2x³ − 5x² + 6x − 15 into a product of binomials, we can use the technique of polynomial factorization by grouping.

Factor out the greatest common factor (GCF) from the first two terms and the last two terms separately

2x³ − 5x² + 6x − 15 = x²(2x − 5) + 3(2x − 5)

Notice that we have a common binomial factor of (2x − 5) in both terms. Factor out this common binomial factor

2x³ − 5x² + 6x − 15 = (2x − 5)(x² + 3)

Therefore, the polynomial 2x³ − 5x² + 6x − 15 can be factored as the product of binomials (2x − 5) and (x² + 3).

So, the correct option is (a) (x² + 3)(2x − 5).

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The answers based on the given information:

1. Output per worker (Y/L) is given as 100. Capital per worker (K/L) is given as 40,000.

2. Investment per worker (I/L) can be calculated using the savings rate (s). I/L = s * (Y/L). Since the savings rate is 20% (0.20), I/L = 0.20 * 100 = 20.

3. Depreciation per worker can be calculated using the depreciation rate (d) and capital per worker (K/L). Depreciation per worker = d * (K/L). Since the depreciation rate is 4% (0.04), Depreciation per worker = 0.04 * 40,000 = 1,600.

4. Net investment per worker can be calculated by subtracting depreciation per worker from investment per worker. Net investment per worker = (I/L) - Depreciation per worker = 20 - 1,600 = -1,580.

5. Since the net investment per worker is negative, capital per worker is decreasing.

7. If capital per worker is 360,000, net investment can be calculated by multiplying the savings rate by the new output per worker (assuming it stays the same) and then subtracting the depreciation. Net investment = (s * (Y/L)) - (d * 360,000) = (0.20 * 100) - (0.04 * 360,000) = 20 - 14,400 = -14,380.

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Answer:

8 sides and it's called an octagon.

Step-by-step explanation:

Let's begin by using the fact that the sum of the exterior angles of any polygon is always 360 degrees.

Let's call the measure of each interior angle "x". Then, you know that the measure of each exterior angle must be "x-90".

Using these expressions, you can find an equation for the sum of the exterior angles:

(number of sides) * (x-90) = 360

Simplifying this equation, you get:

number of sides = 360 / (x-90)

Now you just need to find a value of x that will make the number of sides an integer.

Since you know that the sum of the interior angles of any polygon is always (n-2)*180, where n is the number of sides, you can set up another equation:

(n-2)*180 = n*x

Simplifying this equation, you get:

n = 360 / (180-x)

You want both equations to give you an integer value of n, so you need to find a value of x that makes both denominators the same.

180-x = x-90

Solving for x, you get:

x = 135

Plugging this value of x into either equation gives you:

n = 360 / (180-135) = 360/45 = 8

So, the polygon has 8 sides and is called an octagon.

The volume of prism P is calculated as: 16.55 cm³.

Similar figures are defined as those figures that the same shape, but the sizes are different.

The parameters given are:

- Prism P and prism Q are similar.

- Ratio of the surface area of the prism P to Q = 1 : 3

We also have:

Volume of prism Q = 86 cm³

Scale factor of height of the prism would be square root of surface area of the prism.

Scale factor of volume of the prism would be the cube of the height of the prism.

Let volume of prism P be V(P)

Let the volume of the prism Q be V(Q).

Thus:

V(P) / V(Q) = 1 / (√3)³

V(P) = V(Q) / (√3)³

      = 86 / (√3)³

      = 16.55 cm³

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The requirements for a hypothesis test are satisfied.

To test the claim that the rate of polio is less for children given the Salk vaccine, we need to check if the requirements for a hypothesis test about two population proportions are met. The requirements are:

1. The samples are simple random samples and independent.
2. For each of the two groups, the sample size is at least 1000.

In this case, the study involved 401,974 children who were randomly assigned to two groups: the treatment group with 201,229 children and the placebo group with 200,745 children. This satisfies the first requirement, as the samples are simple random samples and independent. The sample size for both groups is also larger than 1000, meeting the second requirement.

Therefore, the requirements for a hypothesis test are satisfied, and we can proceed with testing the claim that the rate of polio is less for children given the Salk vaccine.

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Answer:

y=-5.3x+36.73

Step-by-step explanation:

We used a standard deviation to determine whether the bag filling machine was underfilling the bags at the 433 gram setting that is falls within the range of -2.76 to 2.76

To determine whether we should reject or fail to reject the null hypothesis, we will use a hypothesis test with a level of significance of 0.02.

Plugging in the values from the problem, we get:

t = (429 - 433) / (26 / √11)

t = -1.38

To determine whether we should reject or fail to reject the null hypothesis, we will compare the calculated t-value to the critical t-value from the t-distribution table.

Looking up the critical t-value with 10 degrees of freedom and a level of significance of 0.01, we find a value of ±2.76.

Since our calculated t-value of -1.38 falls within the range of -2.76 to 2.76, we fail to reject the null hypothesis.

This means that there is not enough evidence to conclude that the bag filling machine is underfilling the bags at the 433 gram setting.

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The required plant grew 9 centimeters in the sixth week.

Let x be the number of centimeters the plant grew in the sixth week.
To estimate x, we can use the formula for the mean (average) of a set of numbers:

mean = (sum of numbers) / (number of numbers)

We know the mean for 6 weeks is 9, so we can write:

9 = (13 + 6 + 10 + 5 + 11 + x) / 6

Multiplying both sides by 6, we get:

54 = 45 + x

Subtracting 45 from both sides, we get:

x = 9

Therefore, the plant grew 9 centimeters in the sixth week.

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The area of the original figure is 9 times the area of the figure that results

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

Scale factor = 3

This means that the area scale factor is

Area scale factor = 3²

Evaluate the exponent

So, we have

Area scale factor = 9

This means that the area of the original figure is 9 times the area of the figure that results.

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The volume of the orange traffic cones is 102.63 in³ respectively.

A cone is a recognizable three-dimensional geometric shape with a smooth and curving surface that is directed upward in mathematics. The

Greek word "konos," which denotes a peak or a wedge, is the source of the English word "cone."

The apex is the pointy end, while the base is the level area.

So, the cone volume is:

V=πr²h/3

Now, insert values as follows:

V=πr²h/3

V=π7²2/3

V=102.63

Therefore, the volume of the orange traffic cones is 102.63 in³ respectively.

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There were about 204 principals in attendance.

The correct option is (A).

The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations.

As per the given data:

The total number of people in the recent conference = 875

The total number of people in one exhibit room = 60

Number of teachers in one exhibit room = 46

Number of principals in one exhibit room = 14

To find out the total number of exhibit rooms:

= Total number of people in the conference / total people in one room

= 875 ÷ 60

= 14.58 = 15 {rounding off to the nearest integer}

Number of principals in one exhibit room = 14

Total number of principals in the conference:

= Number of rooms × Principals in one room

= 15 × 14 = 210 which is equal to 204 {approximate answer}

There were about 204 principals in attendance.

Hence, There were about 204 principals in attendance.

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Answer:

x = 10 cm

Step-by-step explanation:

The total surface area of rectangular prism = [tex]2 (lb + bh + lh)[/tex]

Given,

l = x cm

b = 11 cm

h = 9 cm

TSA = 598 cm

Plugging in the values we get,

[tex]598 = 2(11x + 99 + 9x)\\20x = 299-99\\x = 10[/tex]

Answer:

19%

Step-by-step explanation:

First, find how many water bottles were manufactured in March:

4,100 x 1.07 = 4387

Add 500 to the March number

4387 + 500= 4887

Then divide the April number by February

4887/4100= 1.19195

This means that there is a 19 percent increase of water bottles manufactured from February to April