Use the distributive property to simplify the expression
6(8x+5)

Answer:

The surface area of a sphere is given by the formula:

surface area = 4 * pi * r^2

Where r is the radius of the sphere.

Using this formula, the surface area of an orange with a radius of 3.5 cm is:

surface area = 4 * pi * (3.5 cm)^2

= 4 * pi * 12.25 cm^2

= 49.0307 cm^2

The volume of a sphere is given by the formula:

volume = (4/3) * pi * r^3

Where r is the radius of the sphere.

Using this formula, the volume of an orange with a radius of 3.5 cm is:

volume = (4/3) * pi * (3.5 cm)^3

= (4/3) * pi * 42.875 cm^3

= 113.097 cm^3

Step-by-step explanation:

Given ,

To Find : The Surface Area and the volume of a spherical orange

In order to find the surface area of a spherical orange we use the formula,

[tex]SA = 4\pi r^{2}[/tex]

[tex]SA = 4X\frac{22}{7} X 3.5X3.5[/tex]

[tex]SA =[/tex] [tex]154cm^{2}[/tex]

And now to find the volume of a sphere

[tex]V = \frac{4}{3} \pi r^{3}[/tex]

[tex]V = \frac{4}{3} X \frac{22}{7} X (3.5)^{2}[/tex]

[tex]V[/tex] [tex]= 179.59cm^{2}[/tex]

Hence, the surface area is 154[tex]cm^{2}[/tex]and the volume of a sphere is [tex]179.59cm^{2}[/tex]

x=5 is the value of the x that is the solution of the given inequality.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

>,< and not equal to are types of inequality.

x=5 is the value of the x that is the solution of the given inequality.

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Answer:

1.5 kilograms

Step-by-step explanation:

You need to convert grams to kilograms, this means you must divide the mass value by 1000 to find your answer.

1,500/1,000 = 1.5

Answer:

For 1500 grams in kilogram we get 1.5 kg

Step-by-step explanation:

to convert a gram into a kilogram we have to divide the gram term by 1000

the range of the function shown in the graph -1 [tex]\leq[/tex] y[tex]\leq[/tex] 1.

All real numbers fall within the domain of the sine and cosine functions. Both the sine and cosine functions have a range of [1,1]. An angle's sine and cosine have the same absolute value as their respective reference angles.

An illustration of the function's range in the graphs of cos and sine

The cosine function's graph appears as follows: The range of the function y=cos(x) is 1y1, and the domain is all real numbers (cosine is defined for any angle measure).

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The number of adults at the public pool that day is 284 and the number of children is 147.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Let x be the number of adults and y be the number of children who used the swimming pool.

Total number of people used the swimming pool = 431

x + y = 431

Daily price for adults = $2.00

Daily price for children = $1.50

Total amount for admission = $788.50

2x + 1.5y = 788.5

We got two linear equations here :

x + y = 431 and 2x + 1.5y = 788.5

x + y = 431 ⇒ x = 431 - y

Substituting this in second equation,

2(431 - y) + 1.5y = 788.5

862 - 2y + 1.5y = 788.5

-0.5y = -73.5

y = 147

x = 431 - 147 = 284

Hence the number of adults is 284 and the number of children is 147.

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It would change to about 9. 960 atmospheres

Following the Boyle's law of gases which states that the product of pressure and volume is exactly a constant for an ideal gas.

This is represented as;

PV = K

then,

P₁V₁ = P₂V₂

From the information given, we have that;

Now, substitute the values

8. 9(4. 7) = P₂(4. 2)

mulitply the values

41. 83 = P₂(4. 2)

Divide both sides by 4.2

P₂ = 9. 960 atmospheres

Hence, the value is 9. 960 atmospheres

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Answer:

0.07

Step-by-step explanation:

lets make a chart first

           small | medium | large

hot     |   5      |     48     |    22

cold   |   8      |       1      |     5

1. add all the hot drinks

5+48+22=75

2. find 5/75,

5/75=0.0666666

it is this answer x≥

3

8

I don't know the step by step solution

Answer:

u = 8

Step-by-step explanation:

calculate the slope of the line passing through the 2 give points using the slope formula, then equate to the given slope.

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 5 ) and (x₂, y₂ ) = (5, u )

m = [tex]\frac{u-5}{5-(-5)}[/tex] = [tex]\frac{u-5}{5+5}[/tex] = [tex]\frac{u-5}{10}[/tex] , then equating the 2 expressions gives

[tex]\frac{u-5}{10}[/tex] = [tex]\frac{3}{10}[/tex] ( cross- multiply )

10(u - 5) = 30 ( divide both sides by 10 )

u - 5 = 3 ( add 5 to both sides )

u = 8

Step-by-step explanation:

(u - 5)/(5 + 5)= 3/10

(u - 5)/10= 3/10

10u - 50 = 30

10u = 80

u = 8

According to question, we can say that there are 128 quarters in the machine.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

N  = the  number of dollars  2N  the  number of  quaters.....so  we  have

25(2N)  + 1N   =   96

1.50N  =  96

so, by fraction we have -

N  =  96  / 1,50   =  64   dollars

2(64)   =    128  quarters

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Answer:

According to arithmetic progression, natural numbers can be written down as 1, 2, 3, 4, 5, 6, 7, and 8 to 100. Basically, the sum of the first 100 natural numbers is equal to 5050.

Answer:

Answer:

(0,1)

Step-by-step explanation:

In scenerio 1, the money in the retirement account at 62 years old is         $1,267,250.76

In scenerio 2, the money in the retirement account at 62 years old is         $ 633,625.38.

Scenerio 1:

a) 6% of salary = Salary * 6% = $6,100 * 6% = $366

b) Total amount the company paid monthly = 6% of salary = Salary * 6% = $6,100 * 6% = $366

c) The money in the retirement account at 62 years old can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity given as follows:

FV = M * (((1 + r)^n - 1) / r) ................................. (1)

Where:

FV = Future value = Money in the retirement account at 62 years old = ?

M = Monthly payment = Contribution you + Contribution by the employer = $366 + $366 = $732

r = Monthly interest rate = Annual interest rate / 12 = 6.28% / 12 = 0.0628 / 12 = 0.0052

n = number of months = Number years * Number of months in a year = (Retirement age – Age when hired) * 12 = (62 - 25) * 12 = 37 * 12 = 444

Substituting all the values into equation (1), we have:

FV = $732 * (((1 + 0.0052)^444 - 1) / 0.0052)

FV = Money in the retirement account at 62 years old = $1,267,250.76

d) Amount of money you put into the account = 6% of salary * number of months = $366 * 444 = $162,504

e) Amount of money your employer put into your account = Amount of money you put into the account = $162,504

f) Amount your account gained in interest over the years = FV – (Amount of money you put into the account + Amount of money your employer put into your account) = $1,267,250.76 – ($162,504 + $162,504) = $942,242.76

Scenario 2:

a) 3% of salary = Salary * 3% = $6,100 * 3% = $183

b) Total amount the company paid monthly = 3% of salary = Salary * 3% = $6,100 * 3% = $183

c) Using equation (1), we have:

M = Monthly payment = Contribution you + Contribution by the employer = $183 + $183 = $366

Substituting all the values into equation (1), we have:

FV = $366 * (((1 + 0.0052)^444 - 1) / 0.0052)

FV = Money in the retirement account at 62 years old = $633,625.38

d) Amount of money you put into the account = 3% of salary * number of months = $183 * 444 = $81,252.00

e) Amount of money your employer put into your account = Amount of money you put into the account = $81,252

f) Amount your account gained in interest over the years = FV – (Amount of money you put into the account + Amount of money your employer put into your account) = $633,625.38 – ($81,252 + $81,252) = $471,121.38

The difference in the amount of money at age 62 between scenarios 1 and 2 = Money in the retirement account at 62 years old in scenarios 1 + Money in the retirement account at 62 years old in scenarios 2 = $1,267,250.76 - $633,625.38 = $633,625.38

Difference in the amounts of money you put into retirement between scenarios 1 and 2 = $366 - $183 = $183

Amount got from your employer in scenario 1 than 2 = $366 - $183 = $183

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Answer: The measure of the angle is 35, the measure of its supplement is 145, and the measure of its complement is 55

Answer:

the answer is 28

Step-by-step explanation:

Maeda scored 24 points and if 4 less then jill

x is variable

x-4=24 add 4 on both sides

x=28

The initial amount is 610 and the growth factor is 7.54.

What is an exponential function?

An exponential function has the form f(x) = a*b^x, where a is the initial amount, also called the y-intercept, and b is the growth factor.

In the function f(X) = 610 • 7.54, the initial amount is a = 610, and the growth factor is b = 7.54.

Hence, the initial amount is 610 and the growth factor is 7.54.

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The initial amount is 610 and the growth factor is 7.54.

An exponential function has the form f(x) = a*b^x, where a is the initial amount, also called the y-intercept, and b is the growth factor.

A growth factor is a naturally occurring substance that stimulates a cell to grow, divide, and differentiate. Growth factors are typically proteins or peptides that bind to specific receptors on the surface of cells, triggering signaling pathways that lead to cell proliferation and survival.

In the function f(X) = 610 • 7.54, the initial amount is a = 610, and the growth factor is b = 7.54.

Hence, the initial amount is 610 and the growth factor is 7.54.

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Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.

A function is a relationship between a collection of sources or one product for each input. Simply described, a function is a group of equations linked to a single, distinct output. A declaration, rule, or law that specifies the relationship between two variables is known as a function in mathematics (the dependent variable). When a rules of this kind is employed, there is just one output. by photographer Alex Federspiel. This sentence provides a y=x2 example. Any input for x has only one output for y. Since x is indeed the input value, y is, by definition, a function of x.

Here,

Given :

f(x) = 3x²-3x - 8

g(x) = -x - 7

To find : fog)(-8)= ?

Thus,

We find

=> F(g(x)) => 3g(x)² -3g(x) - 8

=> f(-x-7) =3⋅(-x-7)²-3⋅(-x-7)-8

At x =-8

=> 3(-8-7)² - 3(-8-7)-8

=> 3(225)-3(15) -8

=> 675 - 45 -8

=> 622

Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.

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Answer:

m<1=50

m<2=130

m<3=50

m<4=130

m<5=40

m<6=40

m<7=90

m<8=140

Step-by-step explanation:

Answer: The function you provided describes an experiment in which a coin is tossed, a number cube is rolled, and a letter is picked from the word "framer". The outcome of the experiment is represented by the ordered triple (tails, 5, m).

P(tails, 5, m) refers to the probability of the outcome (tails, 5, m) occurring. To find this probability, you would need to know the probability of each individual event:

The probability of getting tails is 1/2,

The probability of getting a 5 on a number cube is 1/6

and probability of getting letter "m" in the word "framer" is 1/6

So P(tails, 5, m) = (1/2) * (1/6) * (1/6) = 1/72

It is to be noted that in order for the inverse function to exist, the function must be one-to-one, meaning each y value has one unique x value, meaning the random variables in question should be independent. But in this case the events are dependent on one another.

Step-by-step explanation:

The measure of angle E if The measure of angles is 2x + 13, 11x - 6 and 89°, is 37°.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.

Given:

The measure of angles is 2x + 13, 11x - 6 and 89°,

Use the exterior angle theorem and find the value of x as shown below,

2x + 13 + 89 =  11x - 6

2x + 102 = 11x - 6

9x = 108

x = 12

Thus, the measure of ∠ E = 2 × 12 + 13

∠ E = 24 + 13

∠ E = 37°

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343200 fts distance travelled in an hour

5720 ft was travelled in 1 minute and,

95.33 ft distance was travelled in 1 second.

The mile is a customary unit of measurement in the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is often referred to as the international mile or statute mile to distinguish it from other miles.

The British imperial and American customary systems of measurement both use the foot as a unit of length, denoted by the standard symbol: ft. An other sign that is frequently used is the prime symbol, ′. One foot is precisely equal to 0.3048 meters as of the International Yard and Pound Agreement of 1959.

5,280 feet per mile, sometimes known as a statute mile, is a unit of measurement (1.609 km). It derives from the mille passus, or "thousand paces," of the Romans, which was equivalent to 5,000 Roman feet.

65 miles per hour

so 65 * 5280 = 343200 ft travelled in 1 hr

in one minute distance travelled = 343200/60 = 5720  fts

and in one second distance travelled = 5720/60 = 95.33 fts.

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Proportion is the ratio of the two equal fractions. It compares the part of a whole to another part of another whole. Option c is the correct option which is, The test provides convincing evidence the proportion is greater than 90% but the actual proportion is equal to the 90%.

What is proportion?

proportion is the ratio of the two equal fraction. It compare the part of a whole to other part of of the another whole.

Given

Options for the following question are,

A) The test does not provide convincing evidence that the proportion is greater then 90 percent but the actual proportion is greater then 90 percent.

B) The test does not provide convincing evidence  the proportion is greater than 90% but the actual proportion is equal to the 90%.

C)The test provides convincing evidence the the proportion is greater than 90% but the actual proportion is equal to the 90%.

D)The test provides convincing evidence that the proportion is greater then 90 percent but the actual proportion is greater then 90 percent.

E) All type 1 error is not possible for this hypothesis test.

The Null Hypothesis for the given question is,

The proportion of all washers produced with the specified diameter is equal to 90 percent. The Null Hypothesis for the given case is true and actual proportion is equal to 90 percent.

Hence, option c is the correct option which is, The test provides convincing evidence tha the proportion is greater than 90% but the actual proportion is equal to the 90%.

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Answer:

the 2 positive of number is

Step-by-step explanation:

2_:3+23*3⅔+09=2465

[tex](x- (\frac{-5+71i }{4}))[/tex] and [tex](x- (\frac{-5-71i }{4}))[/tex] are factors of the quadratic expression.

2x^2 + 5x + 12

Consider given quadratic expression.

2x^2 + 5x + 12

Let f(x) = 2x^2 + 5x + 12

Assume f(x) = 0

2x^2 + 5x + 12 = 0

using the Quadratic Formula where

a = 2, b = 5, and c = 12

[tex]x = \frac{-b\pm \sqrt{b^2 - 4ac} }{2a} \\\\\\x = \frac{-5\pm \sqrt{5^2 - 4(2)(12)} }{2\times2} \\\\\\x = \frac{-5\pm \sqrt{25 - 96} }{4} \\\\\\x = \frac{-5\pm \sqrt{-71} }{4}[/tex]

The discriminant b^2 - 4ac < 0.

So, there are two complex roots.

[tex]x = \frac{-5\pm71i }{4}[/tex]

This means, [tex](x- (\frac{-5+71i }{4}))[/tex] and [tex](x- (\frac{-5-71i }{4}))[/tex] are factors.

2x^2 + 5x + 12

=  [tex](x- (\frac{-5+71i }{4}))[/tex] × [tex](x- (\frac{-5-71i }{4}))[/tex]

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By using the fact that the interior angles should add up to 360°, we will see that:

C = 142°

We know that for any polygon of N sides, the sum of the interior angles is equal to:

S = (N - 2)*180°

In this case, the polygon has 4 sides, then:

S = (4 -2)*180° = 360°

Then we can write the equation:

A + B + C + D = 360°

Replacing the known angles we get:

68° + 43° + C + 107° = 360°

And now we can solve this for C.

C = 360° - 107° - 43° - 68°

C = 142°

That is the measure of the angle BCD.

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Answer:

There was a discount of 20% on the pair of pants.

Step-by-step explanation:

10% of $34 would be $3.40 meaning 20% would be double, which is $6.80.

If we subtract 20% or $6.80 from the original price $34, we get 34 - 6.80 = 27.20

Answer:

24d^5

Step-by-step explanation: