Hours worked in a week - 32; Total Pay - $160.00; What is the hourly rate?

9514 1404 393

Answer:

  3 in

Step-by-step explanation:

Ratios of corresponding sides are equal, so we have the proportion ...

  x/(5 in) = (6 in)/(10 in)

  x = (5 in)(6/10) = 3 in

The missing side (x) is 3 in.

{x = 2y

{x + y = 9

{x = 2y

{2y + y = 9

{x = 2y

{3y = 9 / : 3

{y = 3

{x = 2 · 3

x = 6 and y = 3

Answer:

D

Step-by-step explanation:

im thinking its d, because prime factorisation is a way of expressing a number as a product of its prime factors.

a isn't correct since 9 isn't is a prime number.

b isn't correct because you wouldn't use decimals typically.

c isn't correct because 1 is not a prime number.

d is the only correct solution since all the numbers listed are prime numbers.

Answer:

n | 0 | 0 1

| y 2 | 2 y 3 | 3 años

Step-by-step explanation:

Answer:

Area = 80

Step-by-step explanation:

area = a^2 = 4^2 = 16 = square

area = wl = 12*8 = 96 = rectangle

rectangle - square

96 - 16 = 80

Answer:

first question: reflection on the y axis

second question: reflection on the x axis

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

2 pounds of fudge ÷ 1 pounds servings = 2 servings

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Answer: 8

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

it simplifies to [tex]x^{4}[/tex]

Step-by-step explanation:

3(2-x)=9

this is the answer to the statement

The expression three times the quantity two decreased by x is nine is - 1

A quantity two decreased by x can be expressed thus :

Multiplying the quantity by 3 :

The expression can be written Mathematically as thus : 3(2 - x) = 9

The expression can be expanded further as :

3(2 - x) = 9

6 - 3x = 9

Collect like terms

-3x = 9 - 6

-3x = 3

x = (3 ÷ -3)

x = - 1

Therefore, the expression equates to - 1

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9514 1404 393

Answer:

Step-by-step explanation:

If P is the perimeter of the larger triangle, then 3/5P will be the perimeter of the smaller one. The difference in perimeters is ...

  P -3/5P = 40 in

  2/5P = 40 in

  P = (5/2)(40 in) = 100 in

  3/5P = 3/5(100 in) = 60 in

The smaller triangle perimeter is 60 in; the larger is 100 in.

Answer:

0.48

Step-by-step explanation:

[tex]0.6*0.8 = 0.48[/tex]

The angle at which the leaning tower of Pisa deviates from the vertical is approximately 5.31 degrees.

To find the angle at which the leaning tower of Pisa deviates from the vertical, we can use the concept of tangent function.

First, we need to calculate the distance that the top of the tower is displaced from the vertical axis. This can be done using the Pythagorean theorem, which states that the displacement (d) is equal to the square root of the height of the tower (h) squared plus the amount the tower is out of plumb (p) squared:

d = √(h² + p²)

d = √(179² + 16.5²)

d = 180.14 ft

Next, we can use the tangent function to find the angle of deviation (θ):

tan(θ) = p/h

tan(θ) = 16.5/179

θ = tan⁻¹(16.5/179)

θ ≈ 5.31 degrees

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Step-by-step explanation:

Given line y=1/3x-4

slope of given line m=1/3

Slope of required line :

m=1/3

As lines are parallel then slope of lines are equal.

Using point slope form:

y-y1=m(x-x1)

p(x1,y1)=(9,8)

y-8=1/3(x-9)

3y-24=x-9

x-3y-9+24=0

x-3y+15=0

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Step-by-step explanation:

the correct aanswer is 3 is correct answermark me bbrainleast plz

Answer:

d is the answer

Step-by-step explanation:

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Answer:

[tex]\displaytstyle \theta \approx \left\{16.3249^\circ, 59.6388^\circ, 196.3249^\circ, 239.6388^\circ\right\}[/tex]

Or, their exact solutions:

[tex]\displaystyle \theta = \left\{\arctan\frac{2-\sqrt{2}}{2} , \arctan\frac{2+\sqrt{2}}{2}, 180^\circ + \arctan\frac{2-\sqrt{2}}{2}, 180^\circ + \arctan\frac{2+\sqrt{2}}{2}\right\}[/tex]

Step-by-step explanation:

We want to solve the equation:

[tex]\displaystyle 2\sec^2 \theta = 4\tan \theta + 1[/tex]

For 0° ≤ θ ≤ 360°.

Recall that tan²(θ) + 1 = sec²(θ). Substitute:

[tex]\displaystyle 2\left(\tan^2 \theta + 1\right) = 4\tan \theta + 1[/tex]

Distribute:

[tex]\displaystyle 2\tan^2\theta + 2 = 4\tan\theta + 1[/tex]

Isolate:

[tex]\displaystyle 2\tan^2\theta - 4\tan\theta + 1 = 0[/tex]

This is in quadratic form. Thus, we can solve it like a quadratic. Let u = tan(θ). Hence:

[tex]\displaystyle 2u^2 - 4u + 1=0[/tex]

The equation is not factorable. Therefore, we can consider using the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}[/tex]

In this case, a = 2, b = -4, and c = 1. Substitute and evaluate:

[tex]\displaytstyle \begin{aligned} u &= \frac{-(-4)\pm\sqrt{(-4)^2 - 4(2)(1)}}{2(2)} \\ \\ &= \frac{4\pm\sqrt{8}}{4} \\ \\ &= \frac{4\pm2\sqrt{2}}{4} \\ \\ &= \frac{2\pm\sqrt{2}}{2}\end{aligned}[/tex]

Therefore:

[tex]\displaystyle u = \frac{2+\sqrt{2}}{2} \approx 1.7071\text{ or } u = \frac{2-\sqrt{2}}{2}\approx 0.2929[/tex]

Back-substitute:

[tex]\displaystyle \tan\theta = \frac{2+\sqrt{2}}{2} \text{ or } \tan \theta = \frac{2-\sqrt{2}}{2}[/tex]

Take the inverse tangent of both equations. Hence:

[tex]\displaystyle \theta = \arctan\frac{2+\sqrt{2}}{2} \approx 59.6388^\circ\text{ or } \theta = \arctan\frac{2-\sqrt{2}}{2}\approx 16.3249^\circ[/tex]

The same value of tangent occurs twice in every full rotation. Hence, by reference angles, the other two solutions are:

[tex]\displaystyle \theta = 180^\circ + \arctan\frac{2+\sqrt{2}}{2} \approx 239.6388^\circ \\ \\ \theta = 180^\circ + \arctan\frac{2-\sqrt{2}}{2} \approx 196.3249^\circ[/tex]

In conclusion, the four solutions are:

[tex]\displaystyle \theta = \left\{\arctan\frac{2-\sqrt{2}}{2} , \arctan\frac{2+\sqrt{2}}{2}, 180^\circ + \arctan\frac{2-\sqrt{2}}{2}, 180^\circ + \arctan\frac{2+\sqrt{2}}{2}\right\}[/tex]Or, approximately:

[tex]\displaytstyle \theta \approx \left\{16.3249^\circ, 59.6388^\circ, 196.3249^\circ, 239.6388^\circ\right\}[/tex]

When both quantities in a rate are fractions, the strategy to write the rate as a unit rate is to divide both the numerator and denominator of the rate by their greatest common factor (GCF) to simplify the fraction.

To write the rate as a unit rate:

1. Identify the rate, which is a fraction with a numerator and a denominator.

2. Find the greatest common factor (GCF) of the numerator and denominator.

3. Divide both the numerator and denominator by the GCF to simplify the fraction.

4. The resulting simplified fraction is the unit rate.

For example, if the rate is 3/6, the GCF of 3 and 6 is 3. Divide both the numerator and denominator by 3:

3/6 ÷ 3/3 = 1/2

So, the unit rate of 3/6 is 1/2.

By converting the rate to a unit rate, we make it easier to compare the rate for a single unit of one quantity to a single unit of the other quantity, making it more convenient for comparison and analysis.

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Answer:

60

Step-by-step explanation:

5(x + 7)

when x is equal to 5, then

Answer:

11

Step-by-step explanation:

(y+5)-(y-6)

y+5-y+6(opening the bracket)

5+6

11

Answer:

11

Step-by-step explanation:

(y+5) - (y-6) = y + 5 - y + 6 =

0y + 11 = 11

Remember, y - y = 1y - 1y = 0y or 0,  and - (y-6) = -1 (y-6) = -y + 6

Answer:

A. 75 km²

Step-by-step explanation:

The area of a triangle

A =1/2 ab sin C  where a and b are the lengths of the sides and C is the included angle

A = 1/2 (14)(11) sin (77)

A = 75.0264949885

[tex] - 15 + 8x = x + 3 \\ 8x - x = 3 + 15 \\ 7x = 18 \\ \\ x = \frac{18}{7} \\ \\ x = 2.571[/tex]

We put the unknown on one side, and the other end is empty of the unknown , When it turns to the other side, its sign changes.

As for the number with the unknown, it becomes the denominator with the number without the unknown.

I hope I helped you^_^

Answer:

1.60934 per hour

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Answer:

1.60934 per hour

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Answer:

5(n+7)=8

Step-by-step explanation:

Answer:

Yes. It is a rational number.

Here, we want to solve for the number of servings 10 pounds of egg whites can make

Number of servings 10 pounds of egg whites can make is approximately 27 servings

1 pound = 16 ounce

10 pounds = 160 ounce

Quantity of egg whites available = 10 pounds

Quantity of egg whites per serving = 6 oz

Number of servings 10 pounds can make = Quantity of egg whites available / Quantity of egg whites per serving

Recall,

10 pounds = 160 oz

= 160 oz / 6 oz

= 26.67

Approximately,

27 servings

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9514 1404 393

Answer:

  70

Step-by-step explanation:

If we consider the terms to have decreasing powers of x, then the middle term is the one with x^4y^4 as its variables. The full value of that term is ...

  (8C4)(2x)^4(3y)^4 = 70(6xy)^4

Substituting for x and y, this is ...

  70(6(1/3)(1/2))^4 = 70(1^4) = 70

The middle term is 70 when (x, y) = (1/3, 1/2).

_____

The value of nCk is n!/(k!(n-k)!). Then 8C4 is 8!/(4!)^2 = (8·7·6·5)/(4·3·2·1) = 70.

Step-by-step explanation:

500 divided by 3 __

__ + 3645 = __

__ - 240 = __

Answer:

-2

Step-by-step explanation:

Simply plug 3 into the equation and follow the order of operations.

2(3 - 4) + (3(3)) - (3^2)

2(-1) + (9) - (9)

= -2

Answer:

{6, 8, 10, 12, 14, 16, 18, 20, ...}

Step-by-step explanation:

even natural numbers >/= 6.

Thus this has no upper limit and the set is thus infinite.

The set of even natural numbers greater than or equal to 6 is

" The natural numbers are those numbers used for counting and ordering. Numbers used for counting are called cardinal numbers."

We know the natural numbers are:

{1, 2, 3, 4, 5, 6, 7,..........}

Now, the set of even natural numbers are:

{2, 4, 6, 8, 10...........}

Therefore, the set of even natural numbers greater than or equal to 6 is

{6, 8, 10, 12,..............}

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