Darian drove 274.5 miles in 4.5 hours. What was his average speed (mph)?

Answer:

10a²b² is the answer

Hope this helps you :)

Answer:

isnt that 10ab??

Step-by-step explanation:

The number of ways can arrange the songs on the CD will be 3,628,800.

A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

Suppose Allen is going to burn a compact disk (CD) that will contain 10 songs.

Then the number of ways can arrange the songs on the CD will be given by 10 factorial.

⇒ 10!

⇒ 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

⇒ 3,628,800

Thus, the number of ways can arrange the songs on the CD will be 3,628,800.

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The molar quantity by the Avocado number:

\(\frac{1*10^3g}{3.95*10^{22} g} = 2.53*10^{24}\)  = 2.6 uranium atoms

The Avogadro's number, Nₐ uranium atoms have a mass of 238.03g.

We now calculate of the molar mass of uranium as 238.03⋅g⋅ mol⁻¹.

And thus moles of uranium

= 1000⋅ g / 238.03⋅g⋅mol⁻¹

= 4.20⋅mol.

And then multiply this molar quantity by the Avocado number:

4.20⋅mol × 6.022× 10²³⋅mol⁻¹

canceling out mol and mol⁻¹, we get:

= 4.20 × 6.022× 10²³

=  2.52924 ≈ 2.6 uranium atom.

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The mean cost of repairing the defective copiers is $500, indicating the average expense incurred by the company for repairs. The standard deviation of $433.01 represents the spread or variability of the repair costs around the mean. These calculations provide insights into the expected cost and the degree of uncertainty associated with the repair expenses for the randomly selected copiers.

To calculate the mean and standard deviation of the cost of repairing the defective copiers, we need to consider the probabilities associated with selecting different numbers of defective copiers.

Total number of copiers (N) = 10

Number of defective copiers (D) = 4

1. Mean Calculation:

The mean cost (μ) can be calculated by multiplying the probability of selecting a particular number of defective copiers by the cost of repairing each defective copier, and then summing up the results.

The probability of selecting 0 defective copiers is (6/10)*(5/9)*(4/8)*(3/7)*(2/6) = 0.1429.

The probability of selecting 1 defective copier is (4/10)*(6/9)*(5/8)*(4/7)*(3/6) = 0.2857.

The probability of selecting 2 defective copiers is (4/10)*(3/9)*(6/8)*(5/7)*(4/6) = 0.2857.

The probability of selecting 3 defective copiers is (4/10)*(3/9)*(2/8)*(6/7)*(5/6) = 0.1429.

The probability of selecting 4 defective copiers is (4/10)*(3/9)*(2/8)*(1/7)*(6/6) = 0.0476.

The mean cost is calculated as:

μ = (0.1429 * 0) + (0.2857 * $250) + (0.2857 * $500) + (0.1429 * $750) + (0.0476 * $1,000)

  = $500

2. Standard Deviation Calculation:

The standard deviation (σ) can be calculated by taking the square root of the sum of the squared differences between the cost and the mean, multiplied by the probabilities.

The standard deviation is calculated as:

σ = sqrt((0.1429 * (0 - $500)^2) + (0.2857 * ($250 - $500)^2) + (0.2857 * ($500 - $500)^2) + (0.1429 * ($750 - $500)^2) + (0.0476 * ($1,000 - $500)^2))

  = $433.01

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Answer:

x = -4.604

Step-by-step explanation:

Here, we want to get the value of x

We start by dividing through by 5

e^(2x + 11) = 30/5

e^(2x + 11) = 6

Writing this in natural logarithm form, we have;

ln 6 = 2x + 11

2x + 11 = 1.792

2x = 1.792-11

2x = -9.208

x = -9.208/2

x = -4.604

The value of x from the given equation is

x=-4.604

Given :

\(5e^{2x+11} =30\)

To solve for x , we need to get exponent 'e' alone

First we divide both sides by 5

\(e^{2x+11} =6\)

Now we write the given exponent in logarithmic form

Lets take ln on both sides

\(lne^{2x+11} =ln6\\(2x+11)lne=ln(6)\\\)

The value of ln(e) is 1

\((2x+11)=ln(6)\\2x+11=ln(6)\\subtract \; 11 \; on \; both \; sides\\2x=ln(6)-11\\Divide \; both \; sides \; by \; 2\\x=\frac{ln(6)-11}{2} \\x=-4.60412\)

The value of x from the given equation is

x=-4.604

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Answer:

Step-by-step explanation:

Answer:

3 × 4 + 2y = 22

12 + 2y = 22

2y = 22 - 12

2y = 10

y = 10/2

y = 5

Answer:

y = 5

Step-by-step explanation:

3x+2y= 22

3(4) + 2y = 22

12 + 2y = 22

2y = 10

y = 5

When the observed z-score is -2.15, we can find the p-value by looking up the value in a standard normal (z) table or using a calculator or software that provides p-values.

Step 1: Identify the z-score
The given z-score is -2.15.

Step 2: Find the p-value
To find the p-value, look up the z-score in a standard normal table or use a calculator. In this case, the p-value is approximately 0.0158.

So, the correct answer is:
c. 0.0158

This p-value represents the probability of observing a value as extreme or more extreme than the observed z-score in the standard normal distribution, assuming the null hypothesis is true.

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The equation of a line that passes through the point ( − 18 , 2 )with slope 1 will be

y=x+20

equation of a line that passes through the point ( x₁ ,y₁ )with slope m is

y-y₁ = m(x-x₁)

y-2=1(x-(-18))

y-2=x+18

y=x+20

coordinate geometry is a system that makes use of one or greater numbers, or coordinates, to uniquely determine the placement of the factors or other geometric factors on a manifold inclusive of Euclidean space.

The order of the coordinates is full-size, and they may be once in a while diagnosed through their function in an ordered tuple and sometimes via a letter, as in "the x-coordinate".

The coordinates are taken to be actual numbers in basic arithmetic, however may be complicated numbers or elements of a extra abstract system together with a commutative ring. the usage of a coordinate device permits troubles in geometry to be translated into issues approximately numbers and vice versa; that is the idea of analytic geometry

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Answer:

x = 2

Step-by-step explanation:

3(x - 1) = 23 - 5(x + 2) ← distribute parenthesis on both sides

3x - 3 = 23 - 5x - 10

3x - 3 = 13 - 5x ( add 5x to both sides )

8x - 3 = 13 ( add 3 to both sides )

8x = 16 ( divide both sides by 8 )

x = 2

Answer:

x=2

Step-by-step explanation:

Answer: 1665

Step-by-step explanation:

Prime factorization of the numbers:

15 = 3 × 5

45 = 3 × 3 × 5

37 = 37

LCM(15, 45, 37)

= 3 × 3 × 5 × 37

= 1665

Hope this helps!

The half life period is the time in which only half of the given population remains. It can be represented through this equation:

\(f(t)=a\times(1/2)^{\frac{t}{h}}\)

We're given:

For most questions like this, we would have to plug these values into the equation mentioned above. However, this question asks for the time elapsed after 3 half-lives.

This can be calculated simply by multiplying the given half-life by 3:

28 million years x 3

= 84 million years

84 million years

Answer:

Step-by-step explanation:

100cm/m=260cm/xm

cross multiply and solve:

100x=260

x=2.6

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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Each of the equations of parabolas should be matched with the x-intercepts of the parabolas as follows;

In Mathematics and Geometry, the x-intercept of any function refers to the point at which the graph of a function crosses the x-coordinate and the y-value of "f(x)" is equal to zero (0).

Next, we would determine the x-intercept of each of the equations of parabolas (quadratic functions) as follows;

y = x² + x - 12

0 = x² + x - 12

0 = x² + 4x - 3x - 12

0 = (x + 4)(x - 3)

Therefore, the x-intercept are (-4, 0) and (3, 0).

y = x² + 5x + 4

0 = x² + 5x + 4

0 = x² + 4x + x + 4

0 = (x + 4)(x + 1)

Therefore, the x-intercept are (-4, 0) and (-1, 0).

y = x² - 5x - 24

0 = x² - 5x - 24

0 = x² - 8x + 3x - 24

0 = (x - 8)(x + 3)

Therefore, the x-intercept are (-3, 0) and (8, 0).

y = -x² - 5x + 14

0 = -x² - 5x + 14

0 = -x² - 7x + 2x + 14

0 = (x - 7)(x + 2)

Therefore, the x-intercept are (-2, 0) and (7, 0).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

x=5

Step-by-step explanation:

multipy both sides of the equation by 3 to remove the denominator becomes

2+5x=27

subtract 2 from both sides since it's positive

5x=25

divide 5 from both sides

x=5

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A total of 5 glove prices meet the condition of having an absolute deviation from the mean of $8 or less.

To find the mean price, we need to sum up all the glove prices and divide by the total number of gloves.

Sum of glove prices = $55 + $42 + $28 + $39 + $82 + $25 + $40 + $32 + $45 + $38 + $52 + $34 = $512

Total number of gloves = 12

Mean price = Sum of glove prices / Total number of gloves = $512 / 12 = $42.67

To find the absolute deviation of each glove price from the mean, we subtract the mean from each price and take the absolute value.

Absolute deviation from mean for each glove = |Price - Mean price|

For example, for the first glove price of $55, the absolute deviation from the mean is |$55 - $42.67| = $12.33

We want the absolute deviation to be at most $8, so we need to find how many glove prices have an absolute deviation from the mean of $8 or less.

We can calculate the absolute deviation for each glove price and count how many are less than or equal to $8.

First row:

|$55 - $42.67| = $12.33

|$42 - $42.67| = $0.67

|$28 - $42.67| = $14.67

|$39 - $42.67| = $3.67

|$82 - $42.67| = $39.33

|$25 - $42.67| = $17.67

Out of the 6 glove prices in the first row, 2 have an absolute deviation from the mean of $8 or less.

Second row:

|$40 - $42.67| = $2.67

|$32 - $42.67| = $10.67

|$45 - $42.67| = $2.33

|$38 - $42.67| = $4.67

|$52 - $42.67| = $9.33

|$34 - $42.67| = $8.67

Out of the 6 glove prices in the second row, 3 have an absolute deviation from the mean of $8 or less.

Therefore, a total of 5 glove prices meet the condition

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The given condition is incomplete, the complete question is:

a baseball player wants to buy a new glove. the table shows the prices of several gloves. the player is willing to pay the mean price with an absolute deviation of at most $8. how many of the glove prices meet this condition?

Answer:

I think B 10 diamond and 12 circles

Step-by-step explanation:

Answer:

143

Step-by-step explanation:

Ben must bowl 143 in his third game to have an average of 160.

" Average is defined as the sum of all the numbers divided by total numbers of number."

Formula used

Average= (Sum of all the numbers) / Total numbers of number

According to the question,

Ben bowled in first two games = 144, 193

Total number of games= 3

Average = 160

'x' be the bowl in Ben's third game

Substitute the value in the formula we get,

160 = ( 144 + 193 + x) / 3

⇒337 + x = 480

⇒x= 480 - 337

⇒ x = 143

Hence, Ben must bowl 143 in his third game to have an average of 160.

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Inequality shows a relationship between two numbers or two expressions.

The solution for the inequality is x ≤ -2.

The graph is given below.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

Example:

2x > 4

We have,

x + 7 ≤ 5

Subtract 7 on both sides we get,

x + 7 - 7 ≤ 5 - 7

x ≤ -2

This inequality can be graphed as given below:

x is equal and less than -2.

Thus,

The solution for the inequality is x ≤ -2.

The graph is given below.

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Answer:

the ratio is 12:5

Step-by-step explanation:

48:20 divided in half 24:10 divided in half 12:5

The Solution:

Given the equation that modeled the population of fish after time (t) in years as below:

part 1:

We are to find the initial population of fish. This means we are to find the value of p when t = 0.

Part 2:

We are required to find the doubling time (t) for this population (Round the answer to the nearest tenth). This means we are to find t when P(t) = 500.

Note: double of 250 fish is 2x250 = 500 fish.

Dividing both sides by 3, we get

Taking the natural log of both sides, we get

The rule of inference being used here is Modus Tollens. Modus Tollens is a valid deductive argument form that states if a conditional statement "If P, then Q" is true and the consequent Q is false, then the antecedent P must also be false.

In the given scenario, the conditional statement is "If the guard dog doesn't know a person, then it barks."

The observation that the dog didn't bark (Q is false) leads to the conclusion that the dog must have known the person (the antecedent P is false).

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h= |x/3| equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .

Translation is the process of reworking text from one language into another to maintain the original message and communication.

The parent function is: g(x)=|x|

we stretch the parent function y = |x| by a factor of 3.

h= |x/3|

If the constant is between 0 and 1, we get a horizontal stretch

if the constant is greater than 1, we get a horizontal compression of the function.

Hence h= |x/3| equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .

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The radius of the hemisphere is approximately 5.7 inches.

The volume of a hemisphere is given by the formula:

V = (2/3)πr³

V is the volume of the hemisphere and r is the radius.

We are given the volume of the hemisphere as 885 in³.

Solving for r we get:

r = \([(3V)/(2\pi)]^{(1/3)\)

Substituting V = 885 in³, we get:

r = \([(3 \times 885)/(2\pi)]^{(1/3)\)

≈ 5.7 inches (rounded to the nearest tenth)

The radius of the hemisphere is approximately 5.7 inches.

The formula: gives the volume of a hemisphere.

V = (2/3)πr³

r is the radius and V is the hemisphere's volume.

The hemisphere's size is specified as 885 in3.

When we solve for r we get:

r = \([(3V)/(2\pi)]^{(1/3)\)

With V = 885 in3 we obtain:

r = [(3 x 885)/(2π)](Rounded to the nearest tenth) (1/3) 5.7 inches

As a result the hemisphere's radius is around 5.7 inches.

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Answer:

X-intercepts: (15, 0)

Y-intercepts: (0, -6)

Step-by-step explanation:

a) y = 1/2 √ −3(x + 1) + 4
- The function is multiplied by 1/2, indicating a vertical compression by a factor of 1/2.
- The function is multiplied by -3 inside the square root, indicating a horizontal compression by a factor of 1/3 and a reflection across the y-axis.
- The function is shifted 1 unit to the left, indicated by the (x + 1) inside the square root.
- The function is shifted 4 units up, indicated by the + 4 outside the square root.

a) y = (2(x − 1))^3 − 5
- The function is multiplied by 2 inside the cube, indicating a horizontal compression by a factor of 1/2.
- The function is shifted 1 unit to the right, indicated by the (x - 1) inside the cube.
- The function is shifted 5 units down, indicated by the - 5 outside the cube.

The transformations to f(x) = √x are as follows:
a) y = 1/2 √ −3(x + 1) + 4
- The function is multiplied by 1/2, indicating a vertical compression by a factor of 1/2.
- The function is multiplied by -3 inside the square root, indicating a horizontal compression by a factor of 1/3 and a reflection across the y-axis.
- The function is shifted 1 unit to the left, indicated by the (x + 1) inside the square root.
- The function is shifted 4 units up, indicated by the + 4 outside the square root.

The transformations to f(x) = x^3 are as follows:
a) y = (2(x − 1))^3 − 5
- The function is multiplied by 2 inside the cube, indicating a horizontal compression by a factor of 1/2.
- The function is shifted 1 unit to the right, indicated by the (x - 1) inside the cube.
- The function is shifted 5 units down, indicated by the - 5 outside the cube.

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