A triangular prism has the dimensions shown at theright. What is the volume of the prism? Round to thenearest tenth if necessary.

Given that the side of the square is 1.6 yards.

The area of the square is

Substitute a=1.6, we get

We need to convert yards to inches.

We know that

Taking square on both sides, we get

Multiplying by 2.56 on both sides, we get

Rounding to the nearest tenth, we get

Hence the area of the given square is 3317.8 square inches.

Looking at the triangle, the reference angle is 30 degrees. The hypotenuse of the triangle is c. The opposite side of the triangle is 7 and the adjacent side is a.

We would determine the hypotenuse, c by applying the sine trigonometric ratio which is expressed as

Sin# = opposite side/hypotenuse

Sin 30 = 7/c

cSin30 = 7

c = 7/Sin 30 = 7/0.5

c = 14

We would determine the adjacent side, a by applying the tangent trigonometric ratio which is expressed as

Tan# = opposite side/adjacent side

Tan 30 = 7/a

aTan30 = 7

a = 7/Tan 30 = 7/0.5774

c = 12.12

Given:

The number is:

Find-:

The scientific notation

Explanation-:

The scientific notation is:

So, the scientific notation is:

The mass of a human cell In scientific notation is 1X 10^10 kg.

What is Scientific notation?

Given that mass of a human cell= is 0.000000000001 kg

In scientific notation = 1X 10^10 kg

The mass of a human cell In scientific notation is 1X 10^10 kg.

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From the statement, we know that:

• a jar contains 100 tickets for a drawing,

• among those tickets are 7 winning tickets.

We must find the odds in favour of winning.

The odds in favour of winning are:

Odds in favour = Number of successes : Number of failures

In this case, we have:

• Number of successes = 7,

• Number of failures = 100 - 7 = 93.

So we have:

7:93

Answer: Take home pay

75.49%

$1,283.39

Step-by-step explanation:

Gross pay

$1,700.00

ChevronIncome taxes

10.95%

$186.09

Federal Income Tax

12%

$123.27

Iowa State Tax

6.25%

$62.82

ChevronFICA taxes

7.16%

$121.72

Social Security

5.8%

$98.65

Medicare

1.36%

$23.07

ChevronPre-tax

6.4%

$108.80

Commuter Parking

6.4%

$108.80

Post-tax

0%

$0.00

Take home pay

75.49%

$1,283.39

The probability of selecting or having a marble to be either a blue marble or a stone marble is 0.8076.

Given, a bag contains 6 blue glass marbles, 5 yellow glass marbles,

12 blue stone marbles and 3 yellow stone marbles.

Probability of selecting a marble and having that marble to be either blue marble or a stone marble = ?

we know that,

Glass marbles:

n(B) = 6 and n(Y)= 5

Stone marbles:

n(B) = 12 and n(Y) = 3

Probability = Number of favorable outcomes/Total number of outcomes.

Probability of selecting a marble and having that marble to be either blue marble or a stone marble:

total number of blue marbles = 18

total number of stone marbles = 15

total number of marbles in the bag = 26

⇒ 18+15-12/26

⇒ 33-12/26

⇒ 21/26

= 0.8076

Hence the probability of selecting a marble and having that marble be either a blue marble or a stone marble is 0.8076.

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5.2187 x 10^−3, 2.05 x 10^7, and 3.40 x 10^3 multiply all the terms. There will be 9 significant digits in the final result.

Given that,

5.2187 x 10^−3, 2.05 x 10^7, and 3.40 x 10^3 multiply all the terms.

We have to find how many digits should be significant for the product.

Multiplication is the action of adding a number to itself for the specified number of times. For instance, 3 × 4 denotes the addition of 3 to itself 4 times, and the opposite is true for the other number.

The multiplication of the given numbers is

=5.1287 × 10⁻³ × 2.05 × 10⁷ × 3.40 × 10³

=5.1287 × 2.05 × 3.40 × 10⁽⁻³⁺⁷⁺³⁾

= 35.747039 × 10⁽⁻³⁺⁷⁺³⁾

= 35.747039 × 10⁷

= 3.5747 × 10⁸

Given that the digit "3" comes before the decimal and the number "10" has a power of 8. As a result, there are 9 significant digits in total (8 + 1).

Therefore, There will be 9 significant digits in the final result.

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Answer:

the answer is 18 because if Jill put 18 on display she would have 2 left

Let's say "n" is the last denominator

A rule that the sequence could follow is

With 2 as the first value of n, this means that the next term will be 1/2(2)=1/4 and so on.

The next 3 terms in the sequence will be

1/2(8)=1/16

1/2(16)=1/32

1/2(32)=1/64

Answer:

105

Step-by-step explanation:

Let x, y and z be the 3 numbers in the order first, second and third

x + y + z = 180

Second number y is 3 times the smallest number and third number z is 7 times the smallest number. So smallest number has to be x

so y = 4x

z = 7x

x + y + z = x + 4x + 7x = 180

12x = 180

x = 15

Largest number = 7 x 15 = 105

2 units left of 16 is 14

The sum is:

16 + (-2) = 16 - 2 = 14

tank is 1/3 full

after he buys 9 gallons of gas it is 5/6

How many gallons can Jim's tank hold?

9 gallons = 1/2 tank

18 gallons is the capacity of the tank

The experimental probability of rolling such that the number is more than 3 is 0.44.

The proportion of outcomes where a specific event occurs in all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.

When a dies is rolled 200 times, the results are:

Frequency     Outcome

     1                     32

     2                    36

     3                    44

     4                    20

     5                    30

     6                    38

Therefore,

The experimental probability that a number is more than 3 after rolling will be:

= The sum of outcome above 3 / total outcome

= ( 20 + 30 + 38 ) / ( 32 + 36 + 44 + 20 + 30 + 38 )

= 88/ 200

= 0.44

Hence, the probability that the number is more than 3 is 0.44.

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Answer:

Domain: [1, 7]

Range: [-4, 2]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Answer:

y = -800x + 294000

286,000

Step-by-step explanation:

To write the equation, you need the slope and the y-intercept.  

The slope is -800

You find the slope by the change in y over the change in x

[tex]\frac{288400 - 294000}{7 - 0}[/tex] = [tex]\frac{15600}{7}[/tex] = -800

Now we will find the y -intercept.  I will use the slope and the point (0, 294,000) to find this.  I could have used the other point given. They will both work.

slope (m) = -800

x = 0

y = 294000

y = mx + b

294000 = -800(0) = b

294000 = b

The equation is

y = mx + b

y = -800x + 294000

2014

y = -800x + 294000

y = -800(10) + 294000

y =-8000 + 294000

y  = 286,000

The statement which is true is Option(D) The output value of the function is 8 when the input value is -2.

An expression, rule, or regulation that establishes a relationship between one variable (the independent variable) and another variable (the dependent variable) is referred to as a function in mathematics.

Given function:

H(x) = -x + 6

In Option A, the input value is -2 so the output of the function will be,

H(x) = -x + 6 = -(-2) +6 = 2+ 6 = 8 ,which is not equal to the given output value 4.

Hence, the statement is false.

Similarly in Option B and C, the input values are 1 and x.

H(x) = -x + 6 = -1 +6 = 5 ≠ 7

H(x) = -x + 6 ≠ 6

The given output values are not equal to the output values calculated.

So both statements are false.

In Option D the input value is -2 and the output value is 8 which is a correct statement as calculated in Option A.

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we know that

Erica

The sequence in minute is

15,30,60,120,240,480,960

This is a geometric sequence

where

r=30/15=2 ----> common ratio

the recursive formula For n>1 is equal to

Find out the explicit formula

where

a1=15

r=2

Naomi

we have the sequence in hours

3 3.5 4 4.5 5 5.5 6

This is an arithmetic sequence

where

d=3.5-3=0.5 ----> the common difference

the recursive formula For n> 1 is equal to

Find out the explicit formula

where

a1=3

d=0.5

substitute

The answer is true

the number 8 is a whole number

so

is an integer

a number that can be written without a fractional component is an integer

A natural number is an integer greater than 0

The correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q is a.

Step 1 x² + 10x + 24 − 1 = 0 − 1

Step 2 x² + 10x + 23 = −1

Step 3 (x + 5)² = −1 and

d.

Step 1 x² + 10x + 24 + 1 = 0 + 1

Step 2 x² + 10x + 25 = 1

Step 3 (x + 5)² = 1

Factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.

a² + b² + 2ab = (a + b)²

Given: x² + 10x + 24 = 0

= x² + 2x × 5 + 24

so b² has to equal 25 = 5²

Now, x² + 10x + 24 = 0

x² + 2x × 5 + 24 + 1 = 0 + 1

simplifying the above equation, we get

x² + 2x × 5 + 25 = 1

(x + 5)² = 1

Therefore, the correct answer is option

a.

Step 1 x² + 10x + 24 − 1 = 0 − 1

Step 2 x² + 10x + 23 = −1

Step 3 (x + 5)² = −1 and

d.

Step 1 x² + 10x + 24 + 1 = 0 + 1

Step 2 x² + 10x + 25 = 1

Step 3 (x + 5)² = 1

The complete question is:

Which of the following tables shows the correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q?[p and q are integers] (5 points)

Select one:

a.

Step 1 x² + 10x + 24 − 1 = 0 − 1

Step 2 x² + 10x + 23 = −1

Step 3 (x + 5)² = −1

b.

Step 1 x² + 10x + 24 − 2 = 0 − 2

Step 2 x² + 10x + 22 = −2

Step 3 (x + 5)² = −2

c.

Step 1 x² + 10x + 24 + 2 = 0 + 2

Step 2 x² + 10x + 26 = 2

Step 3 (x + 5)² = 2

d.

Step 1 x² + 10x + 24 + 1 = 0 + 1

Step 2 x² + 10x + 25 = 1

Step 3 (x + 5)² = 1

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The Solution:

Given:

We are required to find the range of a side (s).

So,

Similarly,

Therefore, the correct answer is (25.5, 34.5)

33,300  is standard form of the given question .

What does basic math standard form mean?

Definition of Standard Form?

Thirteen million, three hundred = 33,300

Two thousand, six hundred and forty = 2640

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The range of the function, y = 16x, is 60, where y is 960.

The range of the function, y = 16x, are the possible values that x can assume to meet the value of y.

Usually, the range of a function is the output value.

Since the value of y = 960, the range of the function will be 60 (960/16).

The capacity of the dispenser = 960 ounces

The capacity of the juice containers = 16 ounces

The function that models the situation is y = 16x

Where y = 960

x = 60 (960/16)

Thus, the implication is that the range of the function or the number of 16-ounce containers that can fill the dispenser with a capacity of 960 ounces is 60.

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Given :

An employee pays $450 towards health insurance

The second employer pays $475.

So, the ratio of employers contributions to the employees contributions=

EXPLANATION

The system that represents the solutions to x>3 and y≤ 2 is the OPTION A