5s • 2 to the power of 3 + (h-1)to the power of 2

What is the value of the expression when: h= 4 and s = -1?

A -49
B -31
C 49
D 164

Answer:

20 mpg

Step-by-step explanation:

Given:

A passenger car will go 310 miles on 15.5 gallons of gasoline in city driving. What is the rate in miles per gallon?

Solve:

To find the rate in miles per gallon we have to divide.

Knowing that "Per" means "Each/One"

Hence, to find miles per gallon we divide :

Miles by Gallons

⇒ 310/15.5

Solving using long division format: ( Multiply both by 10 first)

[tex]155\overline{|\smallspace3100}\:\:\:\:[/tex]

Divide 310 by 155 to get 2:

[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace2\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 155\overline{|\smallspace3100}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\underline{\emptyspace3\emptyspace1\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

Divide 0 by 15.5 to get 0.

[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace2\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\\ 155\overline{|\smallspace3100}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\underline{\emptyspace3\emptyspace1\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

Hence, the rate is 20 mpg.

~kavinsky

The number 25×10 to the power of -3 written in the standard form is 2.5×10⁻⁴.

The given number is;

25×10 to the power of -3

This can be written as;

= 25×10⁻³

Now, as per the standard form, the number should contain only one digit to the left of decimal.

Thus, shifting one decimal to the left of the 5 and converting the power by adding one to the current power,.

The number becomes;

= 2.5×10⁻⁴.

Thus, the number written in the standard form is 2.5×10⁻⁴.

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Answer:

Step-by-step explanation:

(5n - 3)/2=n-0.3

Then we solve for n.

Multiply the whole thing by 2.

5n-3=2n-0.6

Add 0.6

5n-2.4=2n

Add 2.4

5n=2n+2.4

Subtract 2n

3n=2.4

Divide by 3

n=0.8

The most appropriate choice for speed will be given by

Speed of the car of Lewis family = 38 miles/hours

What is speed?

Distance travelled by an object per unit of time is called speed.

If d is the distance travelled and t is the time taken, then speed is calculated by-

Speed = [tex]\frac{d}{t}[/tex]

Here, speed is a scalar as the direction is not taken into account.

Distance drove by  Lewis family to the river = 45.6 miles

Time taken by the Lewis family to go to the river  = 1.2 hours

Speed of the car of Lewis family = [tex]\frac{45.6}{1.2}[/tex]

                                                      = 38 miles/hour

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Given:

The diameter of the sphere is 1.3 inches.

The surface area of the sphere is given as,

Answer: area covered with sprinkles is 5.3 square inches

Answer: b

Step-by-step explanation:

Answer:

t=44 hrs.

Step-by-step explanation:

1. a. you are asked to find the total hours the 2 girls work in a week.

b. it needs to be a greater number than 26

2. variables: h= hours per week

t= total hrs.

3. h= hrs. per week

t= total hrs.

4. 44=26+h

-26 -26

18=h

5. 44=26+18

44=44

6. The total hours the two work in a week is 44 hours.

The value of sin(O) will at the range of 0° to 90° consistently increase. This makes option D the correct options.

In trigonometry, the first basic functions are the sin, cos and tan.

In a right angle triangle the sin is represented as the ratio of opposite to hypotenuse. cos is represented as the ratio of the adjacent to hypotenuse, while tan is the ratio of opposite to adjacent or ratio of sin to cos.

Plotting the graph of sin functions, the pattern forms a sinusoidal pattern which bears its maximum value at sin 90degrees and the minimum value at sin 0 degrees.

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The y-intercept of the line that passes through points (-2,6) and (1,6) in an ordered pair is ( 0,6 ).

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

The slope of a line is expressed as change in y over change in x.

Slope m = (y₂-y₁)/(x₂-x₁)

Given the data in the question;

Point A ( -2,6 )

Point B ( 1, 6 )

First, we determine the slope of the line.

Slope m = (y₂-y₁)/(x₂-x₁)

Slope m = ( 6 - 6 )/( 1 - ( -2) )

Slope m = ( 0 )/( 1 + 2) )

Slope m = ( 0 )/3

Slope m = 0

Now, we can determine the y-intercept b, using the slope and coordinates of 1 point.

y = mx + b

6 = (0)(1) + b

Solve for b

6 = 0 + b

b = 6

Therefore, the coordinates of the y-intercept is ( 0,6 ).

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Answer:

False

Step-by-step explanation:

The dependent variable changes, the size of the order will change depending on how many employes want a shirt.

|-3| means "the absolute value of 3", which is a way of saying how far away from zero the number -3 is on the number line.

The definition of absolute value goes like this:

[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]

In other words, if the number [tex]x[/tex] inside the absolute value bars is already positive or zero, we leave it alone. If instead [tex]x[/tex] is negative, we multiply it by -1 to recover the positive version of that number.

Since -3 is negative, it follows that |-3| = -(-3) = 3. So the expression 3 |-3| is equivalent to 3 • 3 = 3² = 9.

Answer:

10%

Step-by-step explanation:

this is because the total number is supposed to be 100%

and 60%+20%=90%. 100%-90%=10%.

So 10% is the final answer

Answer:

Step-by-step explanation:

1/2 to 1 day is 2 1/2

11/3 x 11/3 = 121/9

13.4 books

Part a

The experimental probability that landing on red is equal to

P=277/500

P=0.554

Part b

The theoretical probability that landing on red is equal to

P=5/10

P=0.5

Part c

the answer is the first option

The correct equation to solve for x is 2(2x-15)=2x-8 , and the value of x is 11 .

in the question ,

from the given figure , we can see that RL=LQ   and PK=KQ which means

that L and K are the mid points of sides RQ and PQ respectively .

The Mid Point Theorem states that

If the line segment adjoining the mid points of any of the sides of the triangle then the line segment is said to be parallel to the third  side and is half of the length of  third side .

which means LK parallel to RP and RP/2=LK  ( ... by mid point theorem)

Substituting the values of LK = 2x-15  and RP = 2x-8 .

(2x-8)/2=2x-15

Multiplying both sides by 2

2x-8 = 2(2x-15)

So, the equation to solve for x is 2(2x-15)=2x-8

Simplifying further

2x-8 = 4x-30

4x-2x= 30-8

2x = 22

x = 11

Therefore , the correct equation to solve for x is 2(2x-15)=2x-8 , and the value of x is 11 .

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Answer:

y = (1/3)x + 4

Step-by-step explanation:

(0, 4) and (-3, 3)

(x₁, y₁)         (x₂, y₂)

        y₂ - y₁           3 - 4           -1            1

m = ------------- = ------------ = --------- = --------

         x₂ - x₁          -3 - 0         -3           3

y - y₁ = m(x - x₁)

y - 4 = (1/3)(x - 0)

y - 4 = (1/3)x - 0

   +4            +4

----------------------------

y = (1/3)x + 4

I hope this helps!

The error in the solution is adding 9 and 2 before the multiplication and the new expression is (2 x 3) +  9

The equation and the steps are given as

9 + 2 x 3 = 11 x 3 = 33

The above solution is incorrect

This is so because the product has a higher order of precedence

So, it must be evaluated first

So, the correct solution is

9 + 2 x 3 = 9 + 6 = 15

To rewrite the expression such that the product is done first, we introduce the use of brackets

So, we have

9 + (2 x 3)

This gives

(2 x 3) +  9

Hence, the result of the products is (2 x 3) +  9

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Answer:

.24 as a fraction is 6/25

Step-by-step explanation:

1) Let convert our decimal into a percentage so we could write it in the not simplified fraction of 0.24:

.24 = 24% = 24/100

2) Now since we have 24/100, we could now simplify:

24/100 = 12/50 = 6/25

We can't simplify anymore.

Answer: 6/25

Step-by-step explanation:

Think of

Answer:

a₂ = 12.5 m/s²

Step-by-step explanation:

Applying the 2º Newton's Law:

∑F = m * a

F₁ = m₁ * a₁

F₁ = m₁ * 12.5

F₁ = 12.5m₁

F₂ = m₂ * a₂

2F₁ = 2m₁ * a₂

a₂ = F₁ / m₁

So:

a₂ = 12.5m₁ / m₁

a₂ = 12.5 m/s²

Answer:

x = + or - 8

Step-by-step explanation:

2x^2 = 128

solve for x

hope this helped have a great day ^^

Using the normal distribution and the binomial distribution, it is found that:

a) 43.25% of 10 year old's cannot go on this ride.

b) There is a 0.7814 = 78.14% probability that at least two of them will be able to ride Batman the Ride.

c) There is a 0.1062 = 10.62% probability that the first 10 year old you see who can ride Batman the Ride is the 3rd 10 year old who enters the park.

d) There is a 0.0834 = 8.34% probability that the 5th 10 year old you see who can ride Batman the Ride is the 12th 10 year old who enters the park.

The z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In the context of this problem, the mean and the standard deviation are given as follows:

[tex]\mu = 55, \sigma = 6[/tex]

For item a, the proportion is the p-value of Z when X = 54, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (54 - 55)/6

Z = -0.17.

Z = -0.17 has a p-value of 0.4325.

Hence the percentage is of 43.25%.

The formula for the probability of x successes is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

For item b, the parameters of the binomial distribution are given as follows:

p = 0.5675, n = 4.

Hence:

Hence:

P(X >= 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.3615 + 0.3162 + 0.1037 = 0.7814.

Which is the probability.

For item c, the probability is given as follows:

p x P(X = 0 with n = 2).

Hence:

p = 0.5675 x (0.4325)² = 0.1062.

For item d, the probability is given as follows:

p x P(X = 4 with n = 11). (inverse binomial).

Hence:

0.5675 x (11!)/(5! x 6!) x (0.5675)^4 x (0.4375)^7 = 0.0834.

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iven:

here are givren the expression:

xplanation:

o find the coefficient of the given expression, we need to use the binomial expansion formula:

So,

From the formula of binomial expansion:

then,

After using the above formula in the given binomial, the expansion will be:

inal answer:

ence , the coefficient of the given term is shown below:

Answer: 0.0625

Step-by-Step Explanation: positive exponents = multiply the number by itself however many times the exponent demands.

negative exponents:  multiply the reciprocal of the base number by itself however many times the exponent demands.

y = x - 3

y = - x -1

They intersect at

Answer: z=23/9

Step-by-step explanation:

I will use cross multiplication

[tex]\frac{1}{9} =\frac{z}{23} \\23(1)=9(z)\\23=9z\\\frac{23}{9} =\frac{9z}{9} \\z=\frac{23}{9}[/tex]

I hope this helps.

Answer:

x - intercept = - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

x - 2y = 7 ( subtract x from both sides )

- 2y = - x + 7 ( divide through by - 2 )

y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{7}{2}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then

y = - 2x + c ← is the partial equation of the perpendicular line\to find c substitute (- 3, 4 ) into the partial equation

4 = 6 + c ⇒ c = 4 - 6 = - 2

y = - 2x - 2 ← equation of perpendicular line

to find the x- intercept let y = 0 into the equation and solve for x

- 2x - 2 = 0 ( add 2 to both sides )

- 2x = 2 ( divide both sides by - 2 )

x = - 1

the x- intercept of the perpendicular line is - 1 or (- 1, 0 )

Answer:

35.45

Step-by-step explanation:

C=2πA=2·π·100≈35.44908

To find the equation that does not belong with the other three we have to solve each equation.

Given the equation:

Dividing by 4 at both sides:

7:

Simplifying on the left:

10:

:

27:

4 :

5

In consequence, the equation that does not belong with the other three is:

because its solution, 4, is different from the solution to the other equations (2).

If we change the 5 in the equation by a 10 and solve the equation we get:

And now the equation (with a 10) belongs with the other three