You eam $10 per hour working as a manager at a grocery store. You are required to work at the grocery store at least 8 hours per week. You also teach music lessons for $15 per hour. You need to earn at least $120 per week, but you do not want to work more than 20 hours per week. a. Write a system of linear inequalities that represents the situation. Use z for hours worked at the grocery store and y for hours teaching music lessons. Inequality for hours at grocery store: Inequality for total earnings: Inequality for total work hours: b. Identify and interpret a solution of the system. (4, 10): You can work 4 hours at the grocery store and spend 10 hours teaching music lessons. O (9, 1): You can work 9 hours at the grocery store and spend 1 hour teaching music lessons. (12, 10); You can work 10 hours at the grocery store and spend 10 hours teaching music lessons (12, 2): You can work 12 hours at the grocery store and spend 2 hours teaching music lessons. C. Can you you work 8 hours at the grocery store and teach 1 hour of music lessons? You work 8 hours at the grocery store and teach 1 hour of music lessons.​

Answer:

4/7 > 2/10

Step-by-step explanation:

4/7 is close to 1/2

2/10 is close to 0

4/7 > 2/10

Answer:

$2.91

Step-by-step explanation:

There are 2 dollar bills. That's 2 dollars right there.

There are 2 quarters. That's 50 cents.

There are 2 dimes. That's 20 cents.

There are 2 nickels. That's 10 cents.

There is 1 penny. That's 1 cent.

2.00

0.50

0.20

0.10

0.01

+

___

2.91

That's how you get your answer.✌️

Answer:

convert the lengths to meters

10dm=1m

1dm=0.1m

hence, firs ribbon

2m+0.1m=2.1m

Second Ribbon

3m and 9dm

convert 9dm into Metres we get 0.9m

hence, 3m+0.9m=3.9m

Third Ribbon

6m+0.4m=6.4m

Answer:

Step-by-step explanation:

If we are looking for the ratio of the area of the inner square to the area of the outer square, that means that we need the areas of each of these squares, and we need to find the areas without any numbers. But that's ok; the answer they want is not a number answer. The answer will have a's and b's in it instead of numbers.

First the area of the inner square. Here we go:

Look at the triangle in the lower left corner of this coordinate plane. It is a right triangle. The height of it is b. That's because the height is a "y" thing and the y-coordinates of each of those sets of coordinates is b and 0. The height is then b - 0 = b.

The length of the base is a - b. That's because the length is an "x" thing and the x-coordinates of each of those sets of coordinates is (a - b) and 0. The length is then a - b - 0 = a - b.

Now we need the length of the hypotenuse which also serves as one of the sides of the inner square. Using Pythagorean's Theorem, we can find the length of the hypotenuse, which I will label as "?":

\(?^2=b^2+(a-b)^2\) and

\(?^2=b^2+a^2-2ab+b^2\) and

\(?^2=a^2-2ab+2b^2\) so

?, the length of the hypotenuse, is

\(?=\sqrt{a^2-2ab+2b^2}\) and now we can use that to find the area of the inner square. The formula for a square's area is

\(A=s^2\) so

\(A=(\sqrt{a^_2}-2ab+2b^2})^2\) which gives us finally:

\(A=a^2-2ab+2b^2\) **

Now for the outer square. Those blue triangles you see are all congruent. We can use the side lengths for the triangles we found above to find the length of a side of the outer square. One side of the outer square is made up of one base length of these triangles and one height. We found the base length to be (a - b) and the height to be b; therefore, the length of one side of the outer square is b + (a - b) which is just "a". That's is, just a length of "a". The area is found by multiplying this side length by itself, so the area of the outer square is

A = a²

The ratio of the area of the inner to the outer is:

\(\frac{A_i}{A_o}:\frac{a^2-2ab+2b^2}{a^2}\) and that does not reduce.

Answer:

A

Step-by-step explanation:

Edmentum

We have to determine the 3% per year first, and then multiply it by 25 (The total ammount of years):

So $11250 is the yearly interest, and now for 25 years it would be:

So, in 25 years you would need to pay $281250 on interest.

Given statement solution is :- It takes approximately 1.122 seconds for the ball to reach its maximum height.

To find the time it takes for the ball to reach its maximum height, we need to determine the vertex of the parabolic function given by the equation h(t) = \(-4.9t^2 + 11t + 7.\)

The vertex of a parabola in the form y = \(ax^2 + bx\) + c is given by the formula t = -b / (2a).

Comparing the equation h(t) = \(-4.9t^2 + 11t + 7\) to the standard form, we have:

a = -4.9

b = 11

Using the formula for the vertex, we can calculate the time it takes to reach the maximum height:

t = -11 / (2 * -4.9)

t = -11 / -9.8

t ≈ 1.122

Therefore, it takes approximately 1.122 seconds for the ball to reach its maximum height.

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The solution of the inequality by method of interval is x = [5,∝) and x = [-2,0]∪[8,-∝).

The first inequality is (x² - 25)/(x + 10) ≥ 0

⇒ x² - 25 ≥ 0

⇒ x² ≥ 25

∴ x ≥ 5

Thus the domain of the given inequality from method of interval is x = [5,∝).

The second inequality is (x + 2)(x² - 64)/(x² + 45) ≤ 0

⇒ (x + 2)(x² - 64)≤ 0

Either (x + 2)≤ 0 or (x² - 64)≤ 0

Either x ≤ -2 or x ≤ 8

Thus , the combined domain of the given inequality from method of interval is x = [-2,0]∪[8,-∝) .

Therefore, the solution of the inequality by method of interval is x = [5,∝) and x = [-2,0]∪[8,-∝).

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Answer:45 meters i think

Step-by-step explanation:

it looks like the same but ones flipped

Answer:

4/25 foot²

Step-by-step explanation:

Refer to attachment*

Consider the attachment first for a better understanding, now after considering the attachment you will gotta know that, the height of the parallelogram is just same as the width of the rectangle i.e (2/5) foot and but for the base of the parallelogram we can subtract the base of one triangle from the length of the rectangle, so it will give us (3/5) - (1/25) = (2/5), so now we have breadth as well as height of the parallelogram, so now, as area of a parallelogram is given by it's height times it's base, so we will be having

\({:\implies \quad \sf Area_{(Parallelogram)}=\dfrac{2}{5}\times \dfrac25}\)

\({:\implies \quad \boxed{\bf{Area_{(Parallelogram)}=\dfrac{4}{25}\:\: sq.\:\:foot}}}\)

Hence, Option D) is correct

Well, we have another method for it, we can subtract the area of both the triangles from the area of rectangle, and now,as their base of the triangle is (1/5) foot and height is same as the width of rectangle i.e (2/5) foots, so its area will be (1/2) times base times height, but as here are two triangles, so multiplying the area of one triangle by 2 will vanish 2, so now we just have

\({:\implies \quad \sf Area_{(Parallelogram)}=\bigg(\dfrac{2}{5}\times \dfrac{3}{5}\bigg)-\bigg(\dfrac{1}{5}\times \dfrac{2}{5}\bigg)}\)

\({:\implies \quad \sf Area_{(Parallelogram)}=\dfrac{6}{25}-\dfrac{2}{25}}\)

\({:\implies \quad \boxed{\bf{Area_{(Parallelogram)}=\dfrac{4}{25}\:\: sq.\:\:foot}}}\)

This also, proves that the correct answer is D)

The overtime rate of pay is K10.25.

The overtime rate of pay can be calculated by multiplying the basic rate pay by the time-and-a-quarter factor. In this case, the basic rate pay is K8.20.

To determine the overtime rate of pay, we need to calculate one-quarter (1/4) of the basic rate pay, and then add that amount to the basic rate pay. One-quarter of K8.20 is calculated as (1/4) * K8.20 = K2.05.

By adding the calculated overtime amount to the basic rate pay, we get the overtime rate of pay: K8.20 + K2.05 = K10.25.

Therefore, the overtime rate of pay is K10.25.

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It will take approximately 4.08 years for an investment of P8,000 to amount to P16,000 at a 10% interest rate compounded monthly.

Using the compound interest formula, we can determine how long it will take for an investment of P8,000 to grow to P16,000 at a monthly interest rate of 10%:

Where: A = the ultimate sum (in this case, P16,000);

\(A = P(1 + r/n)^(nt)\)

P is equal to the principal ($8,000 in this case).

r = the yearly interest rate (decimalized as 10% or 0.10)

n is the number of times each year (monthly, thus 12) that interest is compounded.

t is the number of years.

By rearranging the equation to account for t, we get at: \(t = (1/n) * log(A/P) / log(1 + r/n)\)

By entering the specified values, we obtain:

\(t = (1/12) * log(16,000/8,000) / log(1 + 0.10/12)\)

When we calculate this statement using a calculator, we see that t is roughly 4.08 years (rounded to the next hundredth).

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Answer:

24 because you have to subtract

Answer:

y = 25x + 200

Step-by-step explanation:

y =  the total cost of the party

x = the number of guests

75/3 = 25

25 is the cost per guest.

Helping in the name of Jesus.

Answer: The y-intercept is 5

Step-by-step explanation:

If Sophie adds x oz of water, the volume of the new syrup will be (25 + x) oz. The syrup she starts with already contains 0.20 • (25 oz) = 5 oz of sugar, and if she adds water to it, that amount doesn't change.

She wants to end up with a syrup containing 10% sugar, so that the starting 5 oz makes of 10% of the total (25 + x) oz of syrup. So

5 / (25 + x) = 0.10

5 = 0.10 (25 + x)

5 = 2.5 + 0.10x

2.5 = 0.10x

x = 2.5 / 0.10

x = 25 oz

Answer:

25oz

Step-by-step explanation:

Answer:

15.9% of the data will be greater than 235.3.

Step-by-step explanation:

Use a calculator with statistical functions.  In this case you'll need the cumulative normal distribution:  normcdf(.

Evaluate the following:  normcdf(235.3, 10000,186.4, 48.9):

We get:  0.159, or 15.9%

15.9% of the data will be greater than 235.3.

The range of value X > 284.2 of data will be greater than 235.3.

A Z-Score is a statistical measurement of a score's relationship to the mean in a group of scores.

We know that the upper 2.5% of data would be 97.5% of data.

We will use a z-score formula to solve our given problem.

\(\rm z=\dfrac{x-\mu}{\sigma}\)

Where; z = z-score,

x = Random sample score,

\(\mu\) = Mean,

\(\sigma\) = Standard deviation.

We will use a normal distribution table to find a z-score corresponding to 97.5% area or 0.975.

We can see from the normal distribution table that the z-score corresponding to the area of 0.975 is 1.96.

\(\rm 1.96=\dfrac{x-186.4}{48.9}\\\\1.96 \times 48.9 =x-186.4\\\\x = 186.4 +95.84\\\\x=282.84\)

Hence, the range of value X > 284.2 of data will be greater than 235.3.

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9514 1404 393

Answer:

  13 costumes

Step-by-step explanation:

The amount of fabric used is the product of the amount per costume and the number of costumes.

  A = na . . . . . A = total area; n = number of costumes; 'a' = area per costume

  46 2/3 = n(3 1/2)

  n = (46 2/3)/(3 1/2) = (140/3)/(7/2) = (140/3)(2/7) = 40/3 = 13 1/3

Apparently there is some waste, as Emerson used more fabric than necessary to make 13 costumes.

The product of -22/5 × - 1/3 is 12/15

A product in math is defined as the result of two or more numbers when multiplied together. For example if 5 is multiplied by 2 , the product is 10 i.e 5 × 2 = 10 , 10 is the product where 5 and 2 are the factors. Also 5×4 = 20, 20 is the product and the 5 and 4 are the products.

The division of this of the product with any of the factors will give the other factors.

To solve -2 2/5 × -1/3

we first change the mixed fraction to improper fraction.

We then multiply -12/5 with -1/3

-2 2/5 = -12/5

-12/5 × -1/3

= 12/15

therefore the value of -2 2/5 × -1/3 is 12/15

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the answer is (6,1) aka. 3rd answer

a) The point which is closest to the yz-plane is B=(-16,0,10).

b) The distance from the yz-plane to this point is 16.

c) The point farthest from the xy-plane is C=(-9,16,16).

d) The distance from the xy-plane to this point 16.

e) None of the given points have a y-coordinate of 0, so there is no point that lies on the xz-plane.

a) To find the point closest to the yz-plane, we need to find the point with the smallest x-coordinate, since the yz-plane is defined by x=0. The point with the smallest x-coordinate is B=(-16,0,10), so B is closest to the yz-plane.

b) The distance from the yz-plane to point B can be found using the formula for the distance between a point and a plane, which is given by:

distance = |ax + by + cz + d| / √(a² + b² + c²)

where a, b, and c are the coefficients of the plane equation (which are 1, 0, and 0 for the yz-plane), d is the constant term (-0 in this case), and (x, y, z) are the coordinates of the point. Substituting the values for B, we get:

distance = |-16(1) + 0(0) + 10(0) + 0| / √(1² + 0² + 0²) = 16

So the distance from the yz-plane to point B is 16.

c) To find the point farthest from the xy-plane, we need to find the point with the largest z-coordinate, since the xy-plane is defined by z=0. The point with the largest z-coordinate is C=(-9,16,16), so C is farthest from the xy-plane.

d) The distance from the xy-plane to point C can be found using the same formula as before, but with the coefficients of the plane equation being 0, 0, and 1, and the constant term being 0. Substituting the values for C, we get:

distance = |0(0) + 0(0) + 1(16) + 0| / √(0² + 0² + 1²) = 16

So the distance from the xy-plane to point C is 16.

e) To find the point that lies on the xz-plane, we need to find the point with y-coordinate 0, since the xz-plane is defined by y=0. None of the given points have a y-coordinate of 0, so there is no point that lies on the xz-plane.

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Applying the Pythagorean Theorem

we have that

x^2=576+100

x^2=676

therefore

he net income for the year is $16,550.

Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)

Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500

Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800

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Answer:

No

Step-by-step explanation:

For this problem let the ratio stand for pages: minutes. Emeline can type at a ratio of 10:4. Simplify by dividing by the greatest common factor. In this case, that is 2. So, the final ratio is 5:2. Merle's ratio is 15:5. Simplify this ratio the same way, using 5 as the GCF, to make a final ratio of 5:3. Since 5:2 is not the same as 5:3, they are clearly not equal ratios.

Answer:

8

Step-by-step explanation:

a² + b² = c²

c² = a² + b²

c² = 5² + (√39)²

c² = 25 + 39

c² = 64

c = 8

Answer:

no answer of this question

The values of x and z° are x = 14 and z = 12° , respectively.

In geometry, an angle is a measure of the amount of rotation between two intersecting lines or line segments. It is typically measured in degrees or radians. Angles are important concepts in geometry as they help us to understand and describe the relationships between different geometric figures.

An angle is formed by two rays or line segments that share a common endpoint called the vertex of the angle. The rays or line segments are referred to as the sides of the angle. The size of an angle is determined by the amount of rotation between the two sides, measured in degrees or radians.

Vertical opposite angles are congruent, which means that:

6x - 6 = 9x - 48

Simplifying this equation, we get:

3x = 42

Dividing both sides by 3, we get:

x = 14

Now we can use the value of x to find the measure of the adjacent angle z:

z = 180 - (6x - 6 + 9x - 48)

Simplifying and substituting x = 14, we get:

z = 180 - (6(14) - 6 + 9(14) - 48)

z = 180 - (84 - 6 + 126 - 48)

z = 180 - 168

z = 12°

Therefore, the values of x and z are x = 14 and z = 12° , respectively.

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For the given figure we used the angles of intersecting lines, the values of x is 14 while the value of z° is 102°.

In geometry, an angle is a measure of the amount of rotation between two intersecting lines or line segments. It is typically measured in degrees or radians. Angles are important concepts in geometry as they help us to understand and describe the relationships between different geometric figures.

An angle is formed by two rays or line segments that share a common endpoint called the vertex of the angle. The rays or line segments are referred to as the sides of the angle. The size of an angle is determined by the amount of rotation between the two sides, measured in degrees or radians.

Since the vertical opposite angles are equal, we can set them equal to each other and solve for x:

6x - 6 = 9x - 48

Subtracting 6x from both sides, we get:

-6 = 3x - 48

Adding 48 to both sides, we get:

42 = 3x

Dividing by 3, we get:

x = 14

Now, we can find the value of angle z:

angle z + (6x - 6) = 180                     [Linear pair]

Substituting x = 14, we get:

angle z + 78 = 180

Simplifying, we get:

angle z = 180 - 78

angle z = 102°

Therefore, x = 14 and angle z = 102°.

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