Simplify the expression. 35(12)(5)

If a business has 50 employees, who each earn more than $7000 per year in wages, the business's yearly FUTA tax payment, without considering the FUTA credit is $21,000.

If we consider the FUTA credit on the assumption that the business pays into a state unemployment insurance program, the FUTA payment is $2,100.

FUTA means the Federal Unemployment Tax Act, which levies 6% on the first $7,000 earned by employees on the employer.

However, employers who pay into their State Unemployment Tax Act (SUTA) are eligible for a FUTA credit of 5.4%, making the effective rate to be 0.6%.

Federal Unemployment Tax Act (FUTA) rate = 6%

FUTA tax credit = 5.4%

Effective FUTA rate after paying SUTA = 0.6%

The number of employees in the business = 50

The FUTA Wage Base = $7,000

The total FUTa wage base = $350,000 ($7,000 x 50)

FUTA tax payment without the credit = $21,000 ($350,000 x 6%)

FUTA tax payment with the FUTA credit = $2,100 ($350,000 x 0.6%)

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The given Mayan number which is : :|| :|| in decimal (base 10) is 42.

The Mayan number system is a base-20 system that uses three symbols: a dot (.), a horizontal bar (|), and a shell-like symbol (:). The symbol for zero is a shell-like symbol (:).

To convert the given Mayan number to decimal (base 10), we need to understand the positional value of each symbol. Each position in the number represents a power of 20, with the rightmost position being 20⁰, the next position to the left being 20¹, and so on.

The Mayan number given, : :|| :||, can be broken down as follows:

The leftmost position has no symbol, which represents a value of 0.

The second position from the left has two shell-like symbols (:), which represents a value of 2x20¹ = 40.

The third position from the left has two horizontal bars (||), which represents a value of 2x20⁰ = 2.

The given Mayan number in decimal (base 10) is 40 + 2 = 42.

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Complete question is:

Convert the following Mayan number to decimal (base 10).

: :|| :||

Answer:

5:20

Step-by-step explanation:

When working with the min hand

Starting from 12, each number of a clock adds an additional 5 mins until you reach the 12, where it starts at 0 again. So

1 = :05

2= :10

3 =:15

4 = :20

...and so on

When its 5:00, the hour hand is on the 5. As it moves towards 6:00, the hour hand will start to gradually get pulled towards the 6 until it becomes 6:00, where it will finally reach the 6.

The best statement that describes the amount of water in the pool is that it is decreasing during the time interval 4. That is option 3.

To determine the time interval of the water in the pool the following is carried out.

At 0 hour, the water is at the level of = 40 gallons

At 1 hour, the water decreased to = 25 gallons.

At 2 hours, the water decreased to = 10 gallons.

The water remained at a constant level till 4 hours.

Therefore, the amount of water in the pool is that it is decreasing during the time interval 4.

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Answer:

The correct answer is "0.9332".

Step-by-step explanation:

Given that:

\(\mu=12.30\)

\(\sigma=0.20\)

So,

= \(P(X>12)\)

= \(1-P(X<12)\)

= \(1-P(\frac{X-\mu}{\sigma} < \frac{12-12.30}{0.20} )\)

= \(1-P(Z<-\frac{0.3}{0.20} )\)

= \(1-P(Z<-1.5)\)

= \(1-0.0668\)

= \(0.9332\)

Okay so you put -6 in where y is then solve and youll get your answer

-8x-7(-6)=-6

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.

Answer:

The additive inverse of the number -10 1/4 is +41/4

The additive inverse of any number is such a number added to the given number to get zero.

Let the additive inverse of the given number be "x", hence:

-10 1/4 + x = 0

x = 0 - (-10 1/4)

x = 10 1/4

x = 41/4

Hence the additive inverse of the number -10 1/4 is +41/4

2 1/4 miles => 1 week

1 mile => 1 ÷ 9/4

( 9/4 is an improper fraction of 2 1/4 )

12 1/2 miles => ( 1 ÷ 9/4 ) × 25/2

= 50/9

= 5 5/9 weeks

( 25/2 is an improper fraction of 12 1/2 )

Therefore, it will take 5 5/9 weeks for the company to replace the stretch of road.

( you can round it off to 6 weeks if the qn specify to give to the nearest whole number )

The value of the expression is 16x(x+1) / 10x² -14x -12

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

The given expression is

16/(x-2)  ÷ 4/(x+1) + 6/x

Simplify this to have

16 / (x-2) ÷ (10x + 6) / (x+1)(x)

this implies that 16/(x-2) * (x+1)(x)/(10x +6)

16(x² + x)/(x-2)(10x+6)

Therefore the value of the expression is

16x(x+1) / 10x² -14x -12

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The experimental probability that the next spin falls in a black region is given as follows:

0.205 = 20.5%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

205 out of the previous 1000 trials fell in the black region, hence the experimental probability is given as follows:

p = 205/1000

p = 0.205.

p = 20.5%.

The problem asks for the experimental probability that the next spin falls in a black region.

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Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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Answer:

L'(6,8)

Step-by-step explanation:

If i had to take a guess what i would is subtract 4 from each x number and add 3 to each y number and then reflect over the line y=4 so then that would give me each distance. And by the looks it seems L'(6,8) is the farthest from he origin (0,0)

The zeros of the cubic equation x³ + 21x + 342 are approximately 0.5957, -11.5378, and 11.9421.

The zeros of the cubic equation y³ + 6y + 2 are approximately -0.7937, 1.1968, and -0.4031.
The zeros of the cubic equation y³ + 3y + 2 are approximately -0.7937, 1.1968, and -0.4031.

We have,

1.

x³ + 21x + 342:

p = 0

q = 342

Δ = -(4(0)³ + 27(342)²) = -370728

u = ∛((-342/2) + √(-370728/108)) = ∛((-171) + √(-3421)) ≈ 6.6286

v = ∛((-342/2) - √(-370728/108)) = ∛((-171) - sqrt(-3421)) ≈ -6.0329

x₁ = 6.6286 + (-6.0329) ≈ 0.5957

x₂ = -(6.6286 + (-6.0329))/2 + (6.6286 - (-6.0329)) x √(3)/2 ≈ -11.5378

x₃ = -(6.6286 + (-6.0329))/2 - (6.6286 - (-6.0329)) x √(3)/2 ≈ 11.9421

2.

y³ + 6y + 2:

p = 0

q = 2

Δ = -(4(0)³ + 27(2)²) = -216

u = ∛((-2/2) + √(-216/108)) = ∛((-1) + √(-2)) ≈ 0.7937

v = ∛((-2/2) - √(-216/108)) = ∛((-1) - √(-2)) ≈ -1.5874

y₁ = 0.7937 + (-1.5874) ≈ -0.7937

y₂ = -(0.7937 + (-1.5874))/2 + (0.7937 - (-1.5874)) x √(3)/2 ≈ 1.1968

y₃ = -(0.7937 + (-1.5874))/2 - (0.7937 - (-1.5874)) x √(3)/2 ≈ -0.4031

3.

y³ + 3y + 2:

p = 0

q = 2

Δ = -(4(0)³ + 27(2)²) = -216

u = ∛((-2/2) + √(-216/108)) = ∛((-1) + √(-2)) ≈ 0.7937

v = ∛((-2/2) - √(-216/108)) = ∛((-1) - √(-2)) ≈ -1.5874

y₁ = 0.7937 + (-1.5874) ≈ -0.7937

y₂ = -(0.7937 + (-1.5874))/2 + (0.7937 - (-1.5874)) x √(3)/2 ≈ 1.1968

y₃ = -(0.7937 + (-1.5874))/2 - (0.7937 - (-1.5874)) x √(3)/2 ≈ -0.4031

Therefore,

The zeros of the cubic equation x³ + 21x + 342 are approximately 0.5957, -11.5378, and 11.9421.

The zeros of the cubic equation y³ + 6y + 2 are approximately -0.7937, 1.1968, and -0.4031.
The zeros of the cubic equation y³ + 3y + 2 are approximately -0.7937, 1.1968, and -0.4031.

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g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8

The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.

Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).

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The expression for the area that includes an exponent is 6² + (6 × 2) + 24

Area of the entire figure is 72 square inches

The dimension of the entire figure is 9 inches by 8 inches

From the question, we are to write an expression for the area of the entire figure

Area of the entire figure = Area of green shape + Area of white shape + Area of blue shape

Area of the entire figure = 6² + (6 × 2) + 24 square inches

The expression is 6² + (6 × 2) + 24

Thus,

Evaluating

Area of the entire figure = 6² + (6 × 2) + 24

Area of the entire figure = 36 + 12 + 24

Area of the entire figure = 72 square inches

b. The dimension of the entire figure

Width of the entire figure = Length of the green square + Width of the white rectangle

Width of the entire figure = 6 inches + 2 inches

Width of the entire figure = 8 inches

Then,

Length of the entire figure = Length of the white rectangle + Width of the blue rectangle

First, we will determine the width of the blue rectangle

Using the formula,

Area = l  × w

Where l is the length

and w is the width

24 = (2 + 6) × w

24 = 8 × w

w = 24/8

w = 3 inches

Therefore,

Length of the entire figure = 6 inches + 3 inches

Length of the entire figure = 9 inches

Hence, the dimension is 9 inches by 8 inches

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The exponential regression equation is y = 11.37 * 3.87ˣ

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

(-4,0.05), (-3, 0.20), (-2, 0.75)

To calculate the exponential regression equation that best fits the data shown, we use a graphing tool

An exponential function is represented as

y = abˣ

From the graphing tool, we have

a = 11.37

b = 3.87

substitute the known values in the above equation, so, we have the following representation

y = 11.37 * 3.87ˣ

Hence, the exponential regression equation is y = 11.37 * 3.87ˣ

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Answer: It would be

As x -> positive infinity, h(x)-> positive infinity, and as x->negative infinity, h(x)-> negative infinity.

Answer:

D

Step-by-step explanation:

The solution of the expression, \(x^{\frac{9}{7} }\) is \(\sqrt[7]{x^{9} }\).

An expression is a combination of numbers, variables, functions such as addition, subtraction, multiplication or division etc.

Therefore, let's rewrite the expression to it's equivalent expression.

An equivalent expression is an expression that has the same value or worth as another expression, but does not look the same.

Therefore, using indices rule

\(x^{\frac{9}{7} }\) = \(\sqrt[7]{x^{9} }\)

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To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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Answer:

2. 8n. 8n. 8n. 8n

Step-by-step explanation:

\(2 {(8n)}^{4} = 2. 8n. 8n. 8n. 8n\)

Equivalent expressions are expressions with equal value.

The equivalent expression of \(\mathbf{2\cdot(8n)^4}\) is \(\mathbf{2\cdot(8n)\cdot(8n)\cdot(8n)\cdot(8n)}\)

The expression is given as:

\(\mathbf{2\cdot(8n)^4}\)

Apply law of indices

\(\mathbf{2\cdot(8n)^4 = 2\cdot(8n)\cdot(8n)\cdot(8n)\cdot(8n)}\)

The above equation means that:

\(\mathbf{2\cdot(8n)\cdot(8n)\cdot(8n)\cdot(8n)}\) is equivalent to \(\mathbf{2\cdot(8n)^4}\)

Hence, the correct option is (d) \(\mathbf{2\cdot(8n)\cdot(8n)\cdot(8n)\cdot(8n)}\)

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Answer:

y = 6

Step-by-step explanation:

\(\sqrt{(10-3)^2 + (y+18)^2} = 25 \\ 49 + y^2 + 324 + 36y = 625 \\\)

y^2 + 36y - 252 = 0

(y-6)(y+42) = 0

y = 6 (accettable)

y = -42 (not accettable)

Answer: 1.15

Step-by-step explanation:

23/20 = 1 3/20 = 1.15

Answer:

y = 5n + 200

Step-by-step explanation:

y = mx + b

$5 will be added every day, so 5 is the m and n is the x.

$200 is an extra cost that doesn't repeat, so it's the b.

∠G+∠H+∠J=180 and ∠K+∠L+∠M=180 from the angle sum property of triangle, ∠H=∠L (3rd Angle Theorem) and ∆GHJ≅∆KLM from ASA congruency theorem.

In the given question we have to prove ∆GHJ congrurnce ∆KLM.

Given that: ∠G≅∠K, ∠J≅∠M, \(\over{HJ}\) ≅ \(\over{LM}\).

As given that;

∠G≅∠K

∠J≅∠M

\(\over{HJ}\) ≅ \(\over{LM}\)

So from the angle sum property of triangle

∠G+∠H+∠J=180................(1)

∠K+∠L+∠M=180.................(2)

Now equation equation 1 and 2

∠G+∠H+∠J=∠K+∠L+∠M

As we know that ∠G=∠K, ∠J=∠M

So now the expression is

∠G+∠H+∠J=∠G+∠L+∠J

After solving ∠H=∠L (3rd Angle Theorem)

Since, ∠H=∠L, HJ=LM and ∠G=∠K, so from the theorem Angle Side Angle(ASA) congruency,

∆GHJ≅∆KLM

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Answer:

168

Step-by-step explanation:

Let the area of the square be \(x\).

\(\frac{4}{7}x-\frac{5}{6}\left(\frac{3}{7}x \right)=36 \\ \\ \frac{4}{7}x-\frac{5}{14}x=36 \\ \\ \frac{8}{14}x-\frac{5}{14}x=36 \\ \\ \frac{3}{14}x=36 \\ \\ \frac{1}{14}x=12 \\ \\ x=168\)

Answer:

A

Step-by-step explanation:

13/8, 1 3/4, 9/5

a) The distance of the stone above ground level at time t :

d(t)= -4.9t² + 950

b) It takes 13.92 seconds the stone to reach the ground

c)  With 136.42 m/s velocity the stone strikes the ground.

d) If the stone is thrown downward with a speed of 8 m/s, it will take 13.13 seconds to reach the ground

Here, a  stone is dropped from the upper observation deck of a tower, 950 m above the ground.

(a)  the distance of the stone above ground level at time t would be,

d(t)  = 0.5 (-9.8) t² + v(0) t + d(0)

      = (-4.9)t² + 0t + 950

      = -4.9t² + 950

(b) Now we find the time the stone takes to reach the ground.

i.e., the value of 't' when d = 0

Substituting d(t) = 0 in the above equation.

-4.9t² + 950 = 0

t² = (-950) / (-4.9)

t² = 193.88

t = 13.92 seconds

(c) We need to find the velocity the stone takes to strike the ground

i.e., the velocity when t  = 13.92 seconds

v(t) = v(0) + gt      

v(13.92) = 0 + (9.8)(13.92)

v = 136.42 m/s

(d) here, v(0) = -8 m/s  

Velocity is negative because stone is being thrown downward.

d(t) = 0

(-4.9)t² + v(0) t + d(0) = 0

(-4.9)t² -8t + 950 = 0

Using the quadratic formula we solve above equation for,

t = -14.76, 13.13

We can disregard the negative solution

So, we get t = 13.13 seconds.

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