Steve had 48 chocolates but decided to
give 8 chocolates to each of his f
coworkers.
How many chocolates does Steve have
left?

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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9514 1404 393

Answer:

  105 ft

Step-by-step explanation:

Let x represent the height of the pole. Then (x -49) is the distance from the pole to the anchor point, and (x+14) is the length of the wire from the top of the pole to the anchor point.

The Pythagorean theorem gives us the relation ...

  (x +14)² = x² +(x -49)²

  x² +28x +196 = x² +x² -98x +2401 . . . . eliminate parentheses

  x² -126x +2205 = 0 . . . . . . . . put in standard form

  x² -126x +3969 -1764 = 0 . . . . "complete the square)

  (x -63) = ±√1764 . . . . . . add 1764, take the square root

  x = 63 +42 = 105 . . . . . . highest value root. The pole must be higher than 49 feet

The height of the pole is 105 feet.

Answer:

1)(8+18w)

2) -24d-20

3)6w-16

4) correct

5)-10d+2

Step-by-step explanation:

Answer:

1) 8 + 18w                                          11) - 48x - 24

2) 16d + 20                                       12) - 48 p - 18

3) 6v - 16                                           13) - 10 + 25m

4) - 24 + 16                                        14) - 9n + 36

5) 10d - 8                                           15) - 36k - 36

6) - 10 - 14j                                         16) - 9b + 6

7) - 9 + 24j                                         17) 5 + 3v

8) - 16 - 72v                                        18) - 72 + 18b

9) - 20f + 32                                       19) - 7x + 8

10) - 6 + 4p                                         20) 72 + 45t

Hope it helps!

Answer:

225 degrees

Step-by-step explanation:

It is: 5/8 of 360 = 225 degrees.

5/8 of a circle is equivalent to 225 degrees.

Given,

5/8 of a circle.

Now,

A full circle represents 360 degrees .

So,

1 complete circle = 360 degrees

Let 5/8 of a circle represents x degrees,

1 complete circle = 360 degrees

5/8 of circle = x degrees

Cross multiply,

x = 5/8 * 360

x = 225 degrees.

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Using basic geometry and applying the fence only on 3 sides, The required dimensions of the plot to have maximum area is 200 x 200.

A subfield of mathematics called geometry examines the dimensions, placements, angles, and sizes of objects.

In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.

fence length available = 600m

We only need to fence 3 sides. So length in each side = 600/3

=200m

So, Final dimension = 200 x 200

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Answer:

\(\boxed {\boxed {\sf \frac{ 243}{8} \pi , 95.3775, or \ 95.42587686 \ m^2 }}\)

Step-by-step explanation:

When given the central angle in degrees, the formula for sector area is:

\(A=\frac{ \theta}{360} * \pi r^2\)

where θ is the central angle and r is the radius.

We are given the diameter, so we must calculate the radius. The radius is half the diameter.

The diameter is 18 meters.

Now we know all the variables:

Substitute the values into the formula.

\(A=\frac{ 135}{360} * \pi (9)^2\)

Solve the exponent first.

\(A=\frac{ 135}{360} * (81 \ m^2) \pi\)

Solve the fraction.

\(A=\frac{ 3}{8} * (81 \ m^2) \pi\)

Multiply the two rational numbers.

\(A=\frac{243}{8} \pi \ m^2\)

The answer can be left like this, in terms of pi, or can be multiplied.

\(A=\frac{243}{8} *3.14 \ m^2\)

\(A= 95.3775 \ m^2\)

\(A= 95.42587685 \ m^2\)

The area is 243/8 π, 95.3775, or 95.42587685 square meters.

Answer:

8/13

Step-by-step explanation:

In a standard deck there are 52 cards. Let A denote the event of drawing a black card and B denote the event of drawing face card. We have to find P(A or B) or P(A∪B).

P(A∪B)=P(A)+P(B)-P(A∩B)

There are 26 black cards in a standard deck so,

P(A)=26/52.

There are 12 face cards in a standard deck so,

P(B)=12/52.

There are 6 cards that are black face cards.

P(A∩B)=6/52.

P(A∪B)=P(A)+P(B)-P(A∩B)

P(A∪B)=26/52+12/52-6/52

P(A∪B)=38/52-6/52

P(A∪B)=32/52

P(A∪B)=8/13

Thus, probability of drawing a black card or a face card is 8/13.

Answer:

12 constant terms and 12 variable terms

Step-by-step explanation:

The two cars must be approximately 177.34 feet apart from each other for Spiderman to have different depression angles to each car.

To find the distance between the two cars, we can use trigonometry and the concept of similar triangles. Let's denote the distance between Spiderman and the nearest car as d1 and the distance between Spiderman and the farther car as d2.

In a right triangle formed by Spiderman, the height of the hotel, and the line of sight to the nearest car, the tangent of the depression angle (52 degrees) can be used:

tan(52) = 600 / d1

Rearranging the equation to solve for d1:

d1 = 600 / tan(52)

Similarly, in the right triangle formed by Spiderman, the height of the hotel, and the line of sight to the farther car, the tangent of the depression angle (46 degrees) can be used:

tan(46) = 600 / d2

Rearranging the equation to solve for d2:

d2 = 600 / tan(46)

Using a calculator, we can compute:

d1 ≈ 504.61 feet

d2 ≈ 681.95 feet

The distance between the two cars is the difference between d2 and d1:

Distance = d2 - d1

Plugging in the values, we have:

Distance ≈ 681.95 - 504.61

Distance ≈ 177.34 feet

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Answer:

The APR of the loan was 18.30%.

Step-by-step explanation:

Given that a student has a total of $ 3000 in student loans that will be paid with a 48-month installment loan with monthly payments of $ 73.94, to determine the APR of the loan to the nearest one-half of a percent the following calculation must be done:

3,000 = 100

(73.94 x 48) = X

3,000 = 100

3,549.12 = X

3,549.12 x 100 / 3,000 = X

354,912 / 3000 = X

118.30 = X

118.30 - 100 = 18.30

Therefore, the APR of the loan was 18.30%.

Answer: The answer is 7

Step-by-step explanation:

Absolute value is the final amount of spaces it is from 0 so -7 and positive 7 are both 7 spaces from 0 so I claim that 7 is the absolute value making Amanda wrong!

Answer:

Step-by-step explanation:

1,506.75

Answer:

The answer is 1506.75

Step-by-step explanation:

Since they say the hourly rate is 71.75, and Lorna is working for 21 hours, then all we have to do is multiply 71.75 and 21 to get 1506.75.

Answer:

Step-by-step explanation:

360

Answer: thanks

Step-by-step explanation:

Answer:

y > 3x - 1

set y = 0

0 > 3x - 1

x > 1/3

points are [ 1/3,0]

set x = 0

y > 3(0) - 1

y > - 1

points are [0,-1]

second question

x + y ≤ - 2

set x = 0

y ≤ - 2

points are [0,-2]

set y = 0

x ≤ - 2

points are [-2,0]

So therefore A should be shaded.

Answer:

4equal to plus 5 eul is to be 9

Answer:

Option C

Step-by-step explanation:

The chi-square test of independence is used to determined whether there is a relationship between two categorical variable which in this study is to establish if there is a relationship between a customer's beverage preference and his/her income class (these are categorical variables).

The null hypothesis would be that no relationship exists between the variables while the alternative would be that there is a relationship between the two variables.

Answer:

12, 24, 36, 48, 60, 72, 84, 96

Step-by-step explanation:

The smallest natural number that is a common multiple of 3 and 4 is 12. The answer is all multiples of 12 less than 100.

Answer: 12, 24, 36, 48, 60, 72, 84, 96

Answer: 6 batches

Step-by-step explanation:

From the question, we are informed that one batch of cookies requires 2⁄3 cup of flour.

Therefore, the number of batches that can be made with 4 cups of flour will be:

= 4 / 2/3

= 4 × 3/2

= 12/2

= 6 batches

The equivalent expression for five eighths raised to the negative first power times forty-two hundredths raised to the second power is option B

(5/8)^-1 × (0.42)^2

= {1 ÷ (5/8)¹} × 0.42²

= {1 × (8/5)¹} × 0.42²

= (8/5)¹ × 0.42²

Therefore, the equivalent expression is eight fifths raised to the first power times the quantity one over forty-two hundredths raised to the second power

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Answer:

(1.6) (0.42)^2 C

Step-by-step explanation:

I had originally put B, but my teacher explained and said its C.

the first part of b is correct where it says 8/5, bc you need to flip it in order to not have a negative exponent (you cant have a negative exponent as an answer) but 0.42 is correct and iit does not need to be fliped, since there is no (8/5)(0.42)^2 option, you need to make the 8/5 into a decimal, it becomes 1.6 and so the answer is C

Answer:

t = 6.8 years

Step-by-step explanation:

The formula for compound interest is

\(A(t)=P(1+r/n)^n^t\), where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.

We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal).  We must solve for t and round to the nearest tenth:

\(5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t\)

x⁴ - 8x² + 17 is the function that represents the fog(x).

To find fog(x), we first need to find g(f(x)), which means we need to substitute the expression for f(x) into the expression for g(x):

g(f(x)) = g(x² - 4)

Now, we can substitute the expression for g(x) into the above expression:

g(f(x)) = (x² - 4)² + 1

Expanding the squared term, we get:

g(f(x)) = x⁴ - 8x² + 17

Therefore, fog(x) = g(f(x)) = x⁴ - 8x² + 17.

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Complete question:

f(x) = x² - 4 and g(x)= x^2 + 1  find fog(x).

Answer:

a³ = 8ab³ = 54abc² = 6abc = ? what exactly are you looking for?

Step-by-step explanation:

Answer: I got

-4.4c+1.1

Answer:

-4.4c+1.1

Step-by-step explanation:

Answer

Can someone give me the answer

Step-by-step explanation:

Spherical geometry is used in navigating between locations on the Earth's surface

The correct option for the statement that is true in plane geometry but not true in spherical geometry, is the first option;

Any two lines intersect in exactly one point

Reason:

Spherical geometry is the geometry that considers geometric objects on a spherical surface

While the basic terms in plane geometry are the lines and points, the basic terms in spherical geometry are the great circle and the point, such hat the line in plane geometry is equivalent to a great circle in spherical geometry

Therefore, the statement that is true in plane geometry but not true in spherical geometry is that any two lines intersect in exactly one point

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The Kaumajet Factory will allocate $7.20 of factory overhead to each unit of table lamp using the multiple production department factory overhead rate method with an allocation base of direct labor hours.

Two or more expressions with an Equal sign is called as Equation.

Predetermined overhead rate for Finishing Department = $550,000 / 500,000 direct labor hours = $1.10 per direct labor hour

Predetermined overhead rate for Production Department = $400,000 / 80,000 direct labor hours = $5.00 per direct labor hour

For one unit of table lamp, 2 hours of finishing and 1 hour of production are required, so the total direct labor hours for one unit of table lamp is 2 + 1 = 3 hours.

Finishing Department overhead cost per unit of table lamp = 2 hours * $1.10 per direct labor hour = $2.20

Production Department overhead cost per unit of table lamp = 1 hour * $5.00 per direct labor hour = $5.00

Total factory overhead cost per unit of table lamp

$2.20 + $5.00 = $7.20

Therefore, the Kaumajet Factory will allocate $7.20 of factory overhead to each unit of table lamp using the multiple production department factory overhead rate method with an allocation base of direct labor hours.

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The Kaumajet Factory produces two products-table lamps and desk lamps. It has two separate departments - Finishing and Production. The overhead budget for the Finishing Department is $550,000, using 500,000 direct labor hours. The overhead budget for the Production Department is $400,000 using 80,000 direct labor hours.

If the budget estimates that a table lamp will require 2 hours of finishing and 1 hour of production, how much factory overhead will the Kaumajet Factory allocate to each unit of table lamp using the multiple production department factory overhead rate methods with an allocation base of direct labor hours?

a. $4.91

b. $6.33

c. $7.20

d. $5.00