Write 23/6 as a mixed number.

The triangle's surface area is 630 cm²

What is the Pythagorean theorem in plain English?

Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.

Given that

hypotenuse is 53 cm

base is 28 cm

and it is a right angle triangle

Area = 1/2 x Base x height

So by using Pythagorean theorem we can find its height

Height² + Base² = Hypotenuse²

Height² + 784 = 2809

Height² = 2024

Height = 45 cm

Area = 1/2 x 28 x 45

Area = 630 cm²

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Dr. Kirmser's monthly gross pay = $ 29345.65

Employers and workers are both subject to the Social Security tax, which is used to pay for the country's Social Security program. Federal Insurance Contributions Act (FICA)-mandated payroll taxes or Self-Employed Contributions Act-mandated self-employment taxes are the two ways that Social Security tax is collected (SECA).

Here we have

In 2009, Dr. Kirmser's gross pay was $381,318.60.

Social Security tax = 6.2%     [ Maximum: $106,800 ]  

=> 6.2% = 6.2/100 = 0.062  

Medicare tax = 1.45%  

=> 1.45% = 1.45/100 = 0.0145  

From the above information,

Total tax on salary =0.062 + 0.0145 = 0.0765

In 2009, Dr. Kirmser's gross pay was $381,318.60.

Tax can be calculated on Gross pay = 0.0765 × $381,318.60

= 29170.827  

As we know

Net pay = gross salary - deductions

=> Monthly gross pay = $381,318.60 - $29170.827 = $ 352147.773

Therefore,

Dr. Kirmser's monthly gross pay = 352147.773 ÷ 12 = $ 29345.65

Hence,

Dr. Kirmser's monthly gross pay = $ 29345.65

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If a person substitutes 2 ounces of lean meat by cooked lentils, the lentils that the person need to eat is ½ cup  as both are protein.

Lean meat and lentils are among the sources of proteins in the food intake. Protein is found throughout the human body such as in muscle, skin, hair, bone, skin, hair, and every other body part or tissue. It manufactures the enzymes that power chemical reactions and the hemoglobin that carries oxygen in your blood. Protein is required by the body to help your body repair and make new cells. The foods that contain high content of proteins include lean meat, eggs, dairy products, lentils, etc.  A half cup of cooked lentils provides 9 grams of protein, and 2 ounces of lean meat provides 8 grams of proteins. As the amount of protein provided by both is similar, a person can substitute one with another and maintain their protein intake.

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The percentage error of the mass of a bag of sugar that weighs 10.00kg is 0.1%

The mass of a bag of sugar that weighs = 10.00 kg

The possible error measurements are 10.01, 10.02 etc

The least count error in the measurements = 0.01

The percentage of error = (The least count error in the measurements / The mass of a bag of sugar that weighs ) × 100

Substitute the values in the equation

The percentage of error = (0.01 / 10) × 100

Divide the terms

= 0.001 × 100

Multiply the terms

= 0.1%

Hence, the percentage error of the mass of a bag of sugar that weighs 10.00kg is 0.1%

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The simple interest accumulated on the principal at 12% rate for 4 years is $3,840.

Simple interest formula is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given the data in the question;

First, convert the interest rate from percent to decimal.

Interest rate r = 12%

Interest rate r = 12/100

Interest rate r = 0.12

Plug the given values into the above formula and solve for interest I.

I = P × r × t

I = $8000 × 0.12 × 4

I = $3,840

Therefore, the interest earned is $3,840.

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Answer: 29

Step-by-step explanation: 3 times 7 = 21 + 8 = 29

Answer:

7=3x+8

x=-1/3

Step-by-step explanation:

we just replace f(X) with 7

7=3x+8

-8.    -8

-1=3x

/3. /3

-1/3=x

Hopes this helps please mark brainliest

Answer:

2x2+1+3-12

4+1+3-12

5+3-12

8-12

-4x

Answer:

-2

Step-by-step explanation:

9e-7=7e-11

9e-7e= -11+7

2e= -4

e= -4÷2

e= -2

The average speed in miles per hour is 1.67 miles/hour

What is her average speed?

Average speed is calculated by dividing distance by time (eg miles/hour).

Given that, Noreen can walk 1/3 mile in 12 minutes.

We need to find her average speed.

We know that the total distance covered divided by the total time taken is called the average speed of Noreen.

Mathematically, it is given by :

v=d/t

t = 12 minutes = 0.2 hours

v=(1/3 mile)/0.2 hours

v = 1.67   miles/hour

So, the average speed of Noreen is 1.67  miles/hour. Hence, this is the required solution.

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The percent error in the weight of the envelope is 7.69%.

Given that Harper weighs it at home as 10.4 ounces and then when she gets to the post office, the clerk weighs it at 9.6 ounces.

The percentage error will be:

= Change in value / Original value × 100

= (10.4 - 9.6) / 10.4 × 100

= 0.8 / 10.4 × 100

= 7.69%

The percentage is 7.69%.

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The slope of the line is 10.

Given:

The graph shows the distance traveled by an Olympic-level sprinter over time during a race.

The line begins at the line begins at the origin and passes through the point (2,20).

slope between (0,0) and (2,20).

slope m = y2 - y1 / x2 - x1

= 20 - 0 / 2 - 0

= 20/2

= 10.

Therefore the slope of the line is 10.

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Answer:True

Step-by-step explanation:

The required rate of return for DAK Corporation is 12.34%.

What is the required rate?

The minimal profit (return) an investor will seek or expect in exchange for taking on the risk of investing in a stock or other type of security is known as the required rate of return (RRR). RRR can also be used to determine a project's potential profitability in relation to its funding costs.

Here, we have

Given Information

Beta =   1.25

The yield on 30-year T bonds (rf)=     5.65%

Return on S&P (rM) =    11%

Required Return for DAK = rf + Beta*(rM - rf)

= 5.65% + 1.25*(11% - 5.65%)

=  12.34%

Hence,  the required rate of return for DAK Corporation is 12.34%.

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The principal amount in account A was $250.09 and in account B it was $600.

Account B earned you the most interest the first​ month because $1.2 is higher than $0.7711.

What is the simple interest?

Simple interest is a quick and easy way to calculate the interest charge on a loan. Simple interest is calculated by multiplying the daily interest rate by the principal by the number of days between payments.

The formula for simple interest is expressed as

                I = PRT/100

Where, P = the principal or initial amount of money invested.

            R = interest rate

            T = time

On account A,

     I = $6.94

    R = 3.7%

    T = 9 months = 9/12 = 0.75 years.

Using the formula:

         I = PRT/100

         [tex]6.94 = \frac{P(3.7)(0.75)}{100} \\\\6.94 = 0.02775P\\\\P=250.09[/tex]

On account B,

    I = $39.60

    R = 2.4%

    T = 33 months = 33/12 = 2.75 years

Using the formula:

     I = PRT/100

     [tex]39.60= \frac{P(2.4)(2.75)}{100} \\\\39.60 = 0.066P\\\\P=600[/tex]

To find the account that earned more interest in the first month we have to divide the interest by the number of months.

For account A,

                6.94/9 = $0.7711

For account B,  

                39.60/33 = $1.2

Hence, the principal amount in account A was $250.09 and in account B it was $600.

Account B earned you the most interest the first​ month because $1.2 is higher than $0.7711.

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In linear equations, $ 309.914 will abram receive on his 16th birthday .

What are examples of linear equations?

Let “M” be amount of money in account.

Let “y” be number of full years passed.

1.2/2 = 0.6(%) - interest for every 6 months

y = 16

Money in the account in 16 years:

M = 2,000(1.006)2y

    = 2,000(1.06)32

        = 2000 * 0.154957

         = $ 309.914

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Answer:

16/9, 4/3, 1, 3/4, and 9/16

Step-by-step explanation:

1.) Plug these x values into the equation. You will get: 16/9, 4/3, 1, 3/4, and 9/16.

Answer:

16/9, 4/3, 1, 3/4, and 9/16

Step-by-step explanation:

1.) Plug these x values into the equation. You will get: 16/9, 4/3, 1, 3/4, and 9/16.

Answer: 7.62m

Step-by-step explanation:

[tex]300in(\frac{2.54cm}{1in})( \frac{0.01m}{1 cm} )[/tex]

[tex]7.62m[/tex]

Answer: Making them into improper fractions will really help you with subtracting mixed fractions! For example 2[tex]\frac{1}{5} \\[/tex] - 1[tex]\frac{1}{4}[/tex].

Making them into improper fractions will turn the expression into [tex]\frac{11}{5}[/tex] - [tex]\frac{5}{4}[/tex].

Turn the denominators into the greatest common multiple, so the greatest common multiple of 5 and 4 is 20. Meaning you multiply  [tex]\frac{11}{5}[/tex] by 4 and [tex]\frac{5}{4}[/tex] by 5.

You now have [tex]\frac{44}{20} -\frac{25}{20}[/tex], which is much easier to work with. Simply subtract the numerators, and you should get [tex]\frac{19}{20}[/tex].

Hope this helps :)

If Q(t)= C/4t - 1 an equation for Q-¹(t) is y = C + t/4t.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

Given,

Q(t) = C/4t -1

Put a "y" in place of the "Q(t)":

y = C/4t -1

Change the t and y since each (t, y) has a corresponding (y, t) companion.

t = C/4y -1

Distribute t by multiplying into the bracket to find y.

t × 4y -1 = C

t × 4y - t = C

Add both sides of the equation together now.

t × 4y = C +t

4t divided by both sides

y = C + t/4t

If Q(t)= C/4t - 1 an equation for Q-¹(t) is y = C + t/4t.

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The factorization of given expression would be,

(4a^2)^2 - (b^2)^2= (4a^2 + b^2)(4a^2 - b^2)

In this question, we have been given an expression 16a^4 − b^4

We need to factor given expression using the polynomial identity

(x^2 - y^2) = (x − y)(x + y)

We write given expression as,

16a^4 − b^4 = (4a^2)^2 - (b^2)^2

Using the above polynomial identity,

16a^4 − b^4

= (4a^2)^2 - (b^2)^2

= (4a^2 + b^2)(4a^2 - b^2)

Therefore, the factorization of given expression would be,

(4a^2)^2 - (b^2)^2= (4a^2 + b^2)(4a^2 - b^2)

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Answer: the answer is number 6

Answer:

170%

Step-by-step explanation:

increase in price = 216 - 80 = $136

x : 100 = 136 : 80

x = 100 * 136 / 80

x = 10 * 136/8

x = 1360 / 8

x = 170 %

Answer:

170%

Step-by-step explanation:

80+170%=$216

The coordinates of point J so that GH is the hypotenuse of the right triangle formed by joining the three points will be (3,-8).

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

Given is a coordinate grid with the points G (-5, -8) and H (3, 7) plotted on it. In order for GH to be the hypotenuse of the right triangle created by joining the three points, point J is plotted.

Thus, the coordinates of point J so that GH is the hypotenuse of the right triangle formed by joining the three points will be (3,-8).

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The intermediate step of equation x^{2}+32x+116=0 is (x + 16)² = 140

In this question, we have been given an equation  x^{2}+32x+116=0

We need to find the intermediate step in the form (x + a)^2=b as a result of completing the square for the given equation

We can write given equation as,

x^{2}+32x= -116

Take the coefficient of x

k = 32

Divide it by 2

k/2 = 16

Square both sides

(k/2)^2 = 256

Add 256 to both sides of x² + 32x = -116

x² + 32x + 256 = -116 + 256

(x + 16)² = 140

Therefore, the intermediate step of equation x^{2}+32x+116=0 is (x + 16)² = 140

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Answer:

A) g(x) = 14x + 30

B) The last explanation

No, because her rate of change is $12 per week which is less than William's rate of change.  

Step-by-step explanation:

A:

At the beginning William as 30 dollars (0,30)  Week zero he has 30.  Then each week, his balance goes up 14 dollars

g(x) = 14x + 30  

B:

Jennifer's bank account is increasing by 12 dollars a week, but William's is increasing 14 dollars a week.

Answer:

44,000 shares in a blue-chip company

Step-by-step explanation:

So since Johnson had 22,000 shares in a blue-chip company and it split 2:1, we multiple the beginning number of shares by 2 because they split into 2 different shares.

22,000*2=44,000

Answer:

LM = 18

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{LM}{QM}[/tex] = [tex]\frac{LN}{QP}[/tex] ( substitute values )

[tex]\frac{LM}{12}[/tex] = [tex]\frac{15}{10}[/tex] ( cross- multiply )

10 LM = 180 ( divide both sides by 10 )

LM = 18

Answer:7:2 or 7 to 2

Step-by-step explanation:

Answer:

7 : 2 7/2 we can use two

Step-by-step explanation:

7 : 2 can't simplified

Answer:

(0,2)

It increases at the beginning. From 0 to 2 on the x axis