What is the solution set of -|x| =
-8?

Given:

44, 38, 21, 37, 48, 43, 28

To find the box-and-Visker plot representing the given data:

Let us write it in ascending order.

21, 28, 37, 38, 43, 44, 48.

The median of the given data is 38.

The median of the first three terms is 28.

The median of the last three terms is 44.

The lowest of the given data is 21.

The highest of the given data is 48.

Hence, the correct option c.

Answer:

(4y-3)2=72

8y-6=72

8y=72+6

8y=78

y=78/8

y=9,75

The area of a shape is the amount of space the shape can take. The following are the results of the computations:

A. Number of cans that can fit along the lengths of the boxes

Given that:

\(d = 76mm\) ---- the diameter of the can

\(L_1 = 36cm\) -- the length of the first box

\(L_2 = 50cm\) -- the length of the second box

The number of cans (n) is calculated by:

\(n = \frac{Length}{diameter}\)

For the first box:

\(n_1 = \frac{L_1}{d}\)

\(n_1 = \frac{36cm}{76mm}\)

Convert mm to cm

\(n_1 = \frac{36cm}{76cm\times 0.1}\)

\(n_1 = \frac{36cm}{7.6cm}\)

\(n_1 = 4.736...\)

Remove the decimal part (do not approximate)

\(n =4\)

For the second box

\(n_2 = \frac{L_2}{d}\)

\(n_2 = \frac{50cm}{76mm}\)

Convert mm to cm

\(n_2 = \frac{50cm}{7.6cm}\)

\(n_2 = 6.578..\)

Remove the decimal part (do not approximate)

\(n_2 = 6\)

Hence, 4 cans can fit the along the lengths of the first box, while the second box can take 6 cans, along its length.

B. Number of cans that can fit along the widths of the boxes

Given that:

\(W_1 = 25cm\) -- the width of the first box

\(W_2 = 20cm\) -- the width of the second box

The number of cans (n) is calculated by:

\(n = \frac{Width}{diameter}\)

For the first box:

\(n_1 = \frac{W_1}{d}\)

\(n_1 = \frac{25cm}{76mm}\)

Convert mm to cm

\(n_1 = \frac{25cm}{7.6cm}\)

\(n_1 = 3.2894...\)

Remove the decimal part (do not approximate)

\(n_1 =3\)

For the second box

\(n_2 = \frac{W_2}{d}\)

\(n_2 = \frac{20cm}{76mm}\)

Convert mm to cm

\(n_2 = \frac{20cm}{7.6cm}\)

\(n_2 = 2.631...\)

Remove the decimal part (do not approximate)

\(n_2 = 2\)

Hence, 3 cans can fit the along the width of the first box, while the second box can take 2 cans, along its width.

C. Number of cans that can fit on the bases of the boxes

First, we calculate the area of the base of the can.

The base of the can is circular; so the area is:

\(Area = \pi r^2\)

Where:

\(r = \frac d2 = \frac{76mm}{2} =38mm = 3.8cm\)

So, we have:

\(Area = 3.14 \times 3.8^2\)

\(Area = 45.3416cm^2\)

Next, calculate the areas of the base of the box

The boxes are rectangular ; so, the area is:

\(Area=Length \times Width\)

For the first box;

\(A_1 =36cm \times 25cm\)

\(A_1 =900 cm^2\)

For the second box;

\(A_2 = 50cm \times 20cm\)

\(A_2 = 1000cm^2\)

So, the number of cans on the bases is:

\(n = \frac{Area\ of\ base}{Area\ of\ can}\)

For the first box:

\(n_1 = \frac{900cm^2}{45.3416cm^2}\)

\(n_1 = 19.85\)

Remove the decimal part (do not approximate)

\(n_1 = 19\)

For the second box;

\(n_2= \frac{1000cm^2}{45.3416cm^2}\)

\(n_2 = 22.05\)

Remove the decimal part (do not approximate)

\(n_2 = 22\)

Hence, 19 cans can fit the base of the first box, while the base of the second box can take 22 cans.

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Answer:

n = m - a

Step-by-step explanation:

Given that:

The expression of the formula  a = m - n

where;

a = actual cost of an item

m = original price

n = amount of coupon in dollars

The objective is to solve for the amount of the coupon.

In order to determine the amount of the coupon, we need to make n which is the amount of coupons in dollars the subject of the formula from the given expression.

So if a = m - n

a + n = m

n = m - a

Answer:

y=0+-7 (I think)

Step-by-step explanation:

find slope: -7-(-7)/-5-(-3):

y=0+b: -7=b

check: -7=0*-3+-7

-7=-7 which is true.

Answer:

A. \( {5}^{ \frac{1}{4} } \)

Step-by-step explanation:

\( \huge \sqrt[4]{5} = {5}^{ \frac{1}{4} } \)

Answer:

164 teachers

Step-by-step explanation:

212+386=598

762-598=164

Answer:

144 teachers

Step-by-step explanation:

I added the parents and students together to get 212 + 386 = 598  then subtracted 598 from 762 to get 144 teachers at the fair

It will take the golf ball 12 seconds to hit the ground using the kinematic equation for vertical motion.

To determine the time it takes for the golf ball to hit the ground, we can use the kinematic equation for vertical motion:

\(h = ut + (1/2)gt^2\)

Where:

h is the height (0 feet, as the ball is on the ground)

u is the initial velocity (192 feet per second)

g is the acceleration due to gravity (-32 feet per second squared, considering downward direction)

t is the time we want to find

Plugging in the given values, we get:

\(0 = (192)t + (1/2)(-32)t^2\)

Simplifying the equation, we have:

\(-16t^2 + 192t = 0\)

Factoring out t, we get:

t(-16t + 192) = 0

Setting each factor equal to zero, we have:

t = 0 (not applicable in this case)

-16t + 192 = 0

Solving for t, we get:

-16t = -192

t = 12

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The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

The time it takes for the golf ball to hit the ground can be determined using the equation of motion. We can use the formula:

h0 = 0

v0 = 192

g = 32.2

a = 16.1

b = 192

t1 = 0

t2 = -b / a

t(-16t + 192) = 0

Setting each factor equal to zero, we have:

t = 0 (not applicable in this case)

-16t + 192 = 0

Solving for t, we get:

-16t = -192

t = 12

t2 >= 0:

   time_to_hit_ground = t2

   time_to_hit_ground = t1

The time it takes for the golf ball to hit the ground is approximately", round(time_to_hit_ground, 2 seconds.

The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

Since time cannot be negative in this context, we discard the negative solution. Therefore, the time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

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Answer:

51.86

Step-by-step explanation:

Answer:

C.  37.5

Step-by-step explanation:

From inspection of the given triangle, we can see that the straight line that divides the triangle into two smaller triangles is an angle bisector since it divides the angle into two congruent angles.

Angle Bisector Theorem

An angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

\(\implies x:15=40:16\)

Solve for x:

\(\implies \dfrac{x}{15}=\dfrac{40}{16}\)

\(\implies \dfrac{x}{15}=2.5\)

\(\implies x=2.5\times 15\)

\(\implies x=37.5\)

Answer:

Cone: 100ft^3

Sphere: 200ft^2

Step-by-step explanation:

Firstly, the volume of a cone is 1/3 of the volume of the cylinder. It's literally in the formula:

\(V_{cone} = \frac{h \pi r^2}{3}\\\textrm{As you can notice, }\pi r^2\textrm{ is the area of the base, like in the cylinder formula}\\\)

So we can just instantly tell that the volume of the cone is 100feet^3.

Not for the sphere - we can assume that if the height is the same, it's equal to two radiuses, or simply - to the diameter. Let's use the formula for the volume of a sphere, but substitute one of the radiuses with \(\frac{h}{2}\)

\(V_{sphere} = \frac{4\pi r^3}{3} = \frac{2\pi r^2 h}{3} = \frac{2h\pi r^2}{3} = 2\cdot V_{cone}\)

So we can instantly tell that the volume of the sphere is 200feet^3

Answer:

12, 14, 16, 18

Step-by-step explanation:

(x + (x+2) + (x+4) + (x+6))/4 = 15

^ solve algebraically

you'll get (4x+12)/4 = 15

then: 4x + 12 = 60

then 4x = 60-12

then 4x = 48

then x = 12

x is 12 so then do substitution

so you get

12 + (12+2) + (12+4) + (12+6)

12, 14, 16, 18

Based on a survey of 400 non-fatal accidents, where 173 involved faulty equipment, the point estimate for the population proportion (p) of accidents that involved faulty equipment is 173/400 = 0.4325.

To calculate the point estimate for the population proportion, we divide the number of accidents involving faulty equipment (173) by the total number of accidents surveyed (400).

This gives us a ratio of 0.4325, which represents the estimated proportion of accidents involving faulty equipment in the population.

A point estimate is a single value that serves as an approximation or best guess for an unknown population parameter.

In this case, the population proportion (p) represents the proportion of all accidents that involved faulty equipment. The point estimate of 0.4325 suggests that approximately 43.25% of non-fatal accidents may involve faulty equipment based on the sample data.

It's important to note that this point estimate is subject to sampling variability and may not perfectly reflect the true population proportion. To obtain a more precise estimate with a measure of uncertainty, one would need to consider confidence intervals or conduct hypothesis testing using statistical methods.

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Answer:

-48

Step-by-step explanation:

Substitute 6 in for j and -4 for k

5k =jk

5(-4) + (6)(-4)

-20 + (-24)

-48

Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Mean width of fabric = 23 millimeters

Standard deviation = 0.06 millimeters

The mean width of fabric specified a ove represents the average length of the width of all fabrics being produced in the factory. The mean width could have been obtained by taking the average of the width length of all fabrics produced in the factory. This means that not all fabrics have a width of 23 millimeters but the average width length of all fabrics produced is 23 millimeters.

Since all fabrics do not have the same width length, the standard deviation helps us determine how dispersed or spread out the different widths of fabrics are from the mean value. With a low standard deviation value of 0.06 millimeters, it shows that the various widths of fabric are closer to mean value.

The required integral is \($\boxed{\frac{1}{3} \ln |x^3+39| + C}$,\) where $C$ is the constant of integration.

Given Integral: \($$\int \frac{x^2}{x^3+39}dx$$\)

Let \($u=x^3+39$.\)

Differentiating both sides with respect to x we get

               \($$\frac{du}{dx}=3x^2$$$$du=3x^2dx$$\)

Dividing both sides by

                         \($3(x^3+39)$\)

we get \($$\frac{du}{3(x^3+39)}=dx$$\)

Substituting \($u=x^3+39$\) and \($dx = \frac{du}{3(x^3+39)}$\)

we get, \($$\int \frac{x^2}{x^3+39}dx\)

                           \(= \int \frac{1}{3u}du$$$$\Rightarrow \frac{1}{3} \ln |u| + C$$$$= \frac{1}{3} \ln |x^3+39| + C$$\)

Therefore, the required integral is \($\boxed{\frac{1}{3} \ln |x^3+39| + C}$,\) where $C$ is the constant of integration.

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Answer:

total angle inside quadrilateral = 360°

x+2x+90+30 = 360

3x = 360-120

3x = 240

x = 80°

Answer:

Step-by-step explanation:

if we have 42 students which are divided in group of 4 we will have

42/4=10 groups and 2 students left

if we would have a group out of 3 students, we will have 14 groups and 14 chaperones

a group will have 3 students and one chaperone

42 students and 14 chaperones

Answer:

the 3rd one

Step-by-step explanation:

The answer to this question is none of the given options (A, B, C, D, or E).To find the maximum perimeter of a square that can fit inside a circle of radius 5 cm, we need to consider that the diameter of the circle is equal to the diagonal of the square.

This means that the side of the square will be equal to the radius of the circle multiplied by the square root of 2 (since the diagonal of a square is the side length times the square root of 2).

So, the side length of the square will be 5 cm x √2 = 7.07 cm. And since a square has four sides of equal length, the perimeter of the square will be 4 x 7.07 cm = 28.28 cm.

However, this perimeter is greater than the circumference of the circle with radius 5 cm, which is 2 x π x 5 cm = 31.42 cm. This means that the square cannot fit entirely inside the circle.

Therefore, the answer to this question is none of the given options (A, B, C, D, or E).

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\(\\ \rm\rightarrowtail x^2-3x-10=0\)

\(\\ \rm\rightarrowtail x^2-5x+2x-10=0\)

\(\\ \rm\rightarrowtail x(x-5)+2(x-5)=0\)

\(\\ \rm\rightarrowtail (x+2)(x-5)=0\)

\(\\ \rm\rightarrowtail x=-2\;or\:5\)

Given,

\(\small\bold{x² – 3x – 10 =0}\)

Taking LHS,

\(\small\bold\red{ → }\small\bold{x^2 – 5x + 2x – 10}\)

\(\small\bold\red{ → }\small\bold{ x(x – 5) + 2(x – 5)}\)

\(\small\bold\red{ → }\small\bold{ (x – 5)(x + 2)}\)

The roots of this equation, x² – 3x – 10 = 0 are the values of x for which (x – 5)(x + 2) = 0

Therefore,\( \small\bold{x – 5 = 0 \: or \: x + 2 = 0}\)

\(\small\bold\red{ → }\small\bold{x = 5 \: or \: x = -2 }\)

Answer:

The rules for standard form are

Small numbers can also be written in standard form. However, instead of the index being positive (in the above example, the index was 3), it will be negative. The rules when writing a number in standard form is that first you write down a number between 1 and 10, then you write × 10(to the power of a number)

I hope this helps

Answer:

False

Step-by-step explanation:

Please Mark me brainliest

Step-by-step explanation:

40 ÷ 4 ( 4 sides) = 10

So each side measures 10inches

Answer:

10

Step-by-step explanation:

beacue 10x4

Polynomials are algebraic expressions consisting of terms that include real numbers, variables, and positive integer exponents. Each term in a polynomial has a variable raised to a non-negative integer power, and the coefficient of each term is a real number. Polynomials are classified by the degree of their highest power. If two or more terms in a polynomial have the same variable raised to the same power, they can be combined into a single term.

1. -x² + x - x² + 1

Combine like terms: -x² + x - x² + 1 = -2x² + x + 1

This polynomial has degree 2 because the highest power of the variable is 2.

2. x² + x + 2x³ - x

Rearrange terms: 2x³ + x² + x - x = 2x³ + x²

This polynomial has degree 3 because the highest power of the variable is 3.

3. 4x + x + x - 2

Combine like terms: 4x + x + x - 2 = 6x - 2

This polynomial has degree 1 because the highest power of the variable is 1.

4. 3x² + 4 - 3x² - 1

Combine like terms: 3x² - 3x² + 4 - 1 = 3

This polynomial has degree 0 because there is no variable term.

Therefore, the four given polynomials have degrees 2, 3, 1, and 0, respectively.

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Answer: 4597

Step-by-step explanation:

Answer:

The answer is 4,597

Step-by-step explanation:

\((32+47)*(83-24)-4x^{3}\)

add the numbers

\(79(83-24)-4x^{3}\)

subtract the numbers

\(79*59-4x^{3}\)

evaluate the power

\(79*59-64\)

multiply the numbers

\(4661-64\)

subtract the numbers

\(4597\)

Answer:

700 milliliters of solution B

Step-by-step explanation:

Joe has 2 solutions that contain alcohol and is mixing them with each other he uses 500 milliliters less of solution A than solution B

A = B - 500

Solution A is 14% alcohol and solution B is 19% alcohol

14%A +19%B = 161 mm

0.14A + 0.19B = 161

Substitute for B - 500 for A in the equation below:

0.14A + 0.19B = 161

0.14(B - 500) + 0.19B = 161

0.14B - 70 + 0.19B = 161

Collect like terms

0.14B + 0.19B = 161 + 70

0.33B = 231

B = 231/0.33

700 milliliters

A = B - 500

A = 700 - 500

A = 200 milliliters

Therefore, he uses 700 milliliters of solution B

Answer:

Recipe 3 has the greatest honey to oats ratio amongst the 4 recipes.

Step-by-step explanation:

Complete Question

Mr. Anderson has 4 recipes for granola. Recipe 1

A 2-column table with 3 rows is titled Recipe 1. Column 1 is labeled Honey (tablespoons) with entries 5, 10, 15. Column 2 is labeled Oats (cups) with entries 2, 4, 6.

Recipe 2

A 2-column table with 3 rows is titled Recipe 2. Column 1 is labeled Honey (tablespoons) with entries 6, 10, 14. Column 2 is labeled Oats (cups) with entries 3, 5, 7.

Recipe 3

A 2-column table with 3 rows is titled Recipe 3. Column 1 is labeled Honey (tablespoons) with entries 3, 6, 9. Column 2 is labeled Oats (cups) with entries 1, 2, 3.

Recipe 4

A 2-column table with 3 rows is titled Recipe 1. Column 1 is labeled Honey (tablespoons) with entries 8, 10, 12. Column 2 is labeled Oats (cups) with entries 4, 5, 6.

Which recipe has the greatest ratio of honey to oats?

Solution

Computing the ratio of honey to oats for each of recipes

Recipe 1

Honey | 5 | 10 | 15

Oats | 2 | 4 | 6

Honey to Oats ratio = (5/2) = (10/4) = (15/6) = 2.5 to 1.

Recipe 2

Honey | 6 | 10 | 14

Oats | 3 | 5 | 7

Honey to Oats ratio = (6/3) = (10/5) = (14/7) = 2 to 1.

Recipe 3

Honey | 3 | 6 | 9

Oats | 1 | 2 | 3

Honey to Oats ratio = (3/1) = (6/2) = (9/3) = 3 to 1.

Recipe 4

Honey | 8 | 10 | 12

Oats | 4 | 5 | 6

Honey to Oats ratio = (8/4) = (10/5) = (12/6) = 2 to 1.

Recipe 3 evidently has the greatest honey to oats ratio amongst the 4 recipes.

Hope this Helps!!!

Answer: Recipe 3

Step-by-step explanation:

Time taken by the smaller hose to fill the pool on its own = 75 minutes

Time taken to fill the swimming pool by the larger hose and smaller hose working together = 30 minutes

Time taken by the larger hose to fill up the swimming pool = 50 minutes

Let 'x' be the time taken by the smaller hose to fill the swimming pool on its own.

In 30 minutes, the larger and smaller hoses together can fill the swimming pool. So in 1 minute, it can fill up 1/30 of the swimming pool.

In 50 minutes, the larger hose can fill up the swimming pool on its own. So the larger hose can fill up 1/50 of the pool in 1 minute.

It takes 'x' minutes for the smaller hose to fill up the pool on its own. So in 1 minute, the smaller hose alone can fill up 1/x of the pool.

Hence 1/30 = 1/x +1/50

⇒ 1/30 = (50+x)/50x

⇒ 30 = 50x/(50+x)

⇒ 30 (50 + x) = 50x

⇒ 1500 + 30x = 50x

⇒ 20x = 1500

⇒ x = 1500/20

⇒ x = 75 minutes.

Thus the smaller hose alone takes 75 minutes to fill up the pool.

The question is incomplete. Find the complete question below:

Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 50 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?

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Answer:

68 in.

Step-by-step explanation:

Multiply 4 by 8 and get 32

Multiply 6 by 6 and get 36

Add 38 and 36

=68

Answer:

92 square inches.

Step-by-step explanation:

4 × (6+8) + (6×6)