Ava’s runs at a rate of 15 kilometers per hour. What is Ava’s speed in meters per minute?

Answer:

0.279

0.613

-0.44

Step-by-step explanation:

The Zscore that seperates the middle 22% of the distribution ; could be obtained thus. The midpoint is the mean and the probability to either the right or left could be obtained.

To obtain the Zscore that seperates the middle 22% is equivalent to :

The probability to the left of the distribution :

P(x < (0.5 + 0.22/2) = p(x < 0.61)

Using the Z probability calculator :

P(x < 0.61) is equivalent to a Zscore of 0.279

α = 0.27

Z(1 - α) = Z(1 - 0.27) = Z0.73 = p(Z < 0.73) = 0.613

P(x < 0.33) = - 0.44 (Z probability calculator)

Answer: C. 752

Step-by-step explanation: Just took the Sequences and Series Unit Test

The sum of the arithmetic value sequence is S = 752

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the sum of the arithmetic sequence be S

Let the number of terms in the AP = 16

Now , the value of AP is

A = 16∑ ( 6t - 4 )

So , when t = 1

a₁ = 6 - 4 = 2

when t = 2

a₂ = 12 - 4 = 8

And , the common difference of the AP , d = 8 - 2 = 6

And , Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

So , when n = 16

S₁₆ = ( 16/2 ) [ 2 ( 2 ) + ( 15 ) 6 ]

S₁₆ = ( 8 ) [ 4 + 90 ]

S₁₆ = 8 x 94

S₁₆ = 752

Hence , the sum of AP is 752

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Step-by-step explanation:

Hey there!

Given expression is;

\( = {x}^{4} - {y}^{2} \)

The values of x and y is 3 and -6 respectively.

Put their values.

\( = {3}^{4} - {( - 6)}^{2} \)

= 81 - 36

= 45 is answer.

Hope it helps..

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

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

a) The terminal point is 0.896 radius length.

b) The value returned is -0.896.

We have,

The circle's radius is 3 units long and the terminal point is located at (−2.69,−1.33)

a. Since the circle's radius is 3 units long, we divide the x-coordinate by 3:

x-coordinate of terminal point: -2.69

Number of radius lengths to the right: -2.69 / 3 ≈ -0.896

However, since the angle is measured from the 3-o'clock direction, we consider it to be in the clockwise direction.

Thus, the number of radius lengths to the right is

Number of radius lengths to the right: -(-0.896) = 0.896

Therefore, the terminal point is 0.896 radius length.

b. Using Trigonometry

cos(h) = x-coordinate of terminal point / radius length

cos(h) = -2.69 / 3 ≈ -0.896

c. As, θ = h. From the given information, we have:

θ ≈ -0.896 radians

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Answer:

A, C, E are your answers

Step-by-step explanation:

The solution is Option A , Option C and Option E.

The simple interest at a principal of  $150 and annual rate of 4 % for 2 years is $ 12

What is Simple Interest?

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) 100

Given data ,

Let the principal be P = $ 150

Let the annual rate be R = 4 %

Let the time be T = 2 years

Now , the simple interest is calculated as SI = PRT / 100

Substituting the values in the equation , we get

Simple Interest = ( 150 x 4 x 2 ) / 100

Simple Interest = ( 150 x 2 ) / 25

Simple Interest = $ 12

So , the value of Simple Interest is $ 100

Now ,

a)

$300 at 2% for 2 years

Simple Interest = PRT / 100

Substituting the values in the equation , we get

Simple Interest = ( 300 x 2 x 2 ) / 100

Simple Interest = $ 12

c)

$400 at 3% for 1 year

Simple Interest = PRT / 100

Substituting the values in the equation , we get

Simple Interest = ( 400 x 3 x 1 ) / 100

Simple Interest = $ 12

e)

$50 at 48% for 6 months

Simple Interest = PRT / 100

Substituting the values in the equation , we get

Simple Interest = ( 50 x 48 x ( 1/2 ) ) / 100

Simple Interest = 48 / 4

Simple Interest = $ 12

Therefore , the Simple Interest is $ 12

Hence , The solution is Option A , Option C and Option E.

The simple interest at a principal of $150 and annual rate of 4 % for 2 years is $ 12

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Answer:

Assume that the formula is true for the (k+1)term

Step-by-step explanation:

I learned this in class a couple weeks ago in intermediate algebra

The multiplication expression with eight rational factors are ''positive''.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Jared writes a multiplication expression with eight rational factors. Half of the factors are positive and half are negative.

Since, Multiplication of four positive numbers are always gives a positive number and multiplication of four negative numbers are always gives a positive number.

Hence, The multiplication expression with eight rational factors are positive.

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Answer: y=5

Step-by-step explanation:

114+7y+y+26=180

8y+140=180

    -140   -140

8y=40

8     8

y=5

Answer: Option(C) is correct option

Explanation:

Margin of error is the factor that occurs in survey for determining random sampling error. It indicates about confidence interval (CI) through describing difference occurring in poll result and actual population value.If there is high margin of error, then confidence is low because poll result will not reflect the actual population result collected through survey.

According to the question, researcher would try to get small margin of error so that lower confidence interval can be acceptable because large confidence interval(CI) will indicate more margin of error.

Other options are incorrect because small margin of error cannot produce increment in confidence or usage of large confidence.Large confidence interval will result in large margin of error. Thus, the correct option is option(c).

The recursive formula for p(n) is; p(n) = p(n-2) + p(n-3) for n >= 3. Case 1: The last square is painted white. If the last square is painted white, then the second to last square must be painted gold.

There are p(n-2) ways to paint the remaining n-2 squares of the checkerboard subject to the restriction.

Case 2: The last square is painted gold. If the last square is painted gold, then the second to last square can be painted either white or gold. If the second to last square is painted white, then there are p(n-3) ways to paint the remaining n-3 squares of the checkerboard subject to the restriction.

If the second to last square is painted gold, then there are p(n-2) ways to paint the remaining n-2 squares of the checkerboard subject to the restriction.

Therefore, the recursive formula for p(n) is: p(n) = p(n-2) + p(n-3) for n >= 3

with initial conditions p(1) = 2 and p(2) = 3.

The base case for the recursion is p(1) = 2 and p(2) = 3, which are the number of ways to paint a 1 x 1 checkerboard and a 1 x 2 checkerboard subject to the restriction, respectively.

The recursive formula counts the number of ways to paint a 1 x n checkerboard subject to the restriction by considering the last column of the checkerboard.

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Answer:

y=x-7

Step-by-step explanation:

we know the y intercept is -7 since when x was 0 g(x) is -7

We write it in slope intercept form which is y=mx+b

m- slope

b- y- intercept

To find slope we do y2-y1/x2-x1

-5+7/2-0

2/2

1

1 is the slope so we just keep it X on the equation and the equation will be

y=x-7

Hopes this helps please mark brainliest

The height of the projectile after 4 seconds is 421.28 ft.

The projectile is in the air for 8.015 seconds.

The horizontal distance traveled by the projectile is 881.77 ft.

The maximum height of the projectile is 464.1 ft.

To solve this problem, we can use the kinematic equations of motion for a projectile.

Let's assume that the initial height of the projectile is zero.

What is the height of the projectile after 4 seconds:

We can use the equation:

\(y = yo + vot + 1/2at^2\)

where

y = height of the projectile

yo = initial height (zero in this case)

vo = initial vertical velocity = 220 sin(60°) = 190.53 ft/sec

a = acceleration due to gravity \(= -32.2 ft/sec^2\) ( negative since it acts downwards)

t = time = 4 sec

Plugging in the values, we get:

\(y = 0 + (190.53)(4) + 1/2(-32.2)(4)^2 = 421.28 ft\)

Therefore, the height of the projectile after 4 seconds is 421.28 ft.

Long is the projectile in the air:

The time of flight of a projectile can be calculated using the equation:

t = 2vo sinθ / g

where θ is the launch angle and g is the acceleration due to gravity.

Plugging in the values, we get:

t = 2(220 sin(60°)) / 32.2 = 8.015 sec

Therefore, the projectile is in the air for 8.015 seconds.

Horizontal distance traveled by the projectile:

The horizontal distance traveled by the projectile can be calculated using the equation:

\(x = xo + vot + 1/2at^2\)

where

x = horizontal distance traveled

xo = initial horizontal position (zero in this case)

vo = initial horizontal velocity = 220 cos(60°) = 110 ft/sec

a = acceleration due to gravity (zero in the horizontal direction)

t = time = 8.015 sec

Plugging in the values, we get:

\(x = 0 + (110)(8.015) + 1/2(0)(8.015)^2 = 881.77 ft\)

Therefore, the horizontal distance traveled by the projectile is 881.77 ft.

Maximum height of the projectile:

The maximum height of a projectile can be calculated using the equation:

\(ymax = yo + (vo^2 sin^2 \theta ) / 2g\)

Plugging in the values, we get:\(ymax = 0 + (190.53^2 sin^2(60\degree )) / (2)(32.2) = 464.1 ft\)

Therefore, the maximum height of the projectile is 464.1 ft.

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h = hours till they're 58 miles apart

Check the picture below.

so they're travelling in opposite directions, however the combined distances is 58 miles at say "h" hours, by the time that happend Hopi has been walking "h" hours and Brittany has also being walking "h" hours too.

Since the combined distance is 58 miles than if Hopi has covered "m" miles then Brittany covered the slack of "58 - m".

\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Hopi&m&15&h\\ Brittany&58-m&14&h \end{array}\hspace{5em} \begin{cases} m=(15)(h)\\\\ 58-m=(14)(h) \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{substituting on the 2nd equation}}{58-(\stackrel{m}{15h})=14h}\implies 58=29h\implies \cfrac{58}{29}=h\implies \boxed{2=h}\)

Answer:

152 cubic centimeters.

Explanation

To find the volume of the composed figure, we divide it into two as shown below:

This divides the figure into two rectangular prisms with the following dimensions:

• 8cm by 8cm by 2cm

• 4cm by 3cm by 2cm

The volume of any rectangular prism is obtained using the formula:

Therefore, we add the volume of the two prisms:

The solution to the variables are x = 7 and y = 4

From the question, we have the following parameters that can be used in our computation:

Shape = Triangle

The marks on the triangles imply that

So, we have the following representation

3x - 5 = 5y - 4

3x - 5 = y + 12

Substitute 3x - 5 = y + 12 in 3x - 5 = 5y - 4

y + 12 = 5y - 4

Evaluate the like terms

4y = 16

So, we have

y = 4

Substitute y = 4 in 3x - 5 = y + 12

3x - 5 = 4 + 12

So, we have

3x = 21

This gives

x = 7

Hence, the values are x = 7 and y = 4

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Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

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Answer:

B. $56.24

Step-by-step explanation:

74.99 x 7.5%=5.62425

5.62425 x 10= 56.24

The expression can be written as 5/4. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

There are four basic mathematical operations which are applicable for all the real number. The operations are as follows:

1.Addition(‘+’) operation gives the sum of the numbers.

2.Subtraction(‘-’) operation gives the difference of the numbers.

3.Multiplication(‘×’) operation gives the product of the numbers.

4.Division(‘÷’) operation gives the quotient of the numbers.

We are given -5/6 * -5/4 * 6/5

The expression can be rewritten as:

⇒-5/6 * -5/4 * 6/5

⇒-1 * -5/4 * 1   (as -5/6 * 6/5 = -1*1)

⇒ 5/4 * 1        

(as when two negative numbers are multiplied, we get positive number)

⇒ 5/4  (any number multiplied by 1 is the number itself)

Hence, the expression can be written as 5/4.

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The length of the apothem of the pentagon is approximately 11 meters.

Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons etc.

Here, we have,

To solve this problem, we can use the formula for the area of a regular pentagon:

A = (5/2) × s × a

Where A is the area of the pentagon, s is the length of one side, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).

We know that the area of the pentagon is 118.25 square meters and the length of one side is 4.3 meters. We can substitute these values into the formula and solve for the apothem:

118.25 = (5/2) × 4.3 × a

Divide both sides by (5/2) x 4.3:

a = 118.25 / ((5/2) × 4.3)

 = 118.25 / 10.75 ≈ 11 meters

Therefore, the length of the apothem of the pentagon is approximately 11 meters.

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Answer:

25 doughnuts

Step-by-step explanation:

for 15 workers,

the numbers of doughnuts =

5 doughnuts/3 workers × 15 workers

= 75/3 doughnuts

= 25 doughnuts

Answer:

25 doughnuts.

Step-by-step explanation:

5 doughnuts ÷ 3 workers × 15 workers

=75/3

=25 doughnuts.

The rate at which the energy pass through an area of 1.0 m² at 2.0 km is equal to 1.97 × 10⁹ J/s.

At a constant power, the intensity of a wave is inversely proportional to the distance from the source. Mathematically, the intensity of a wave with respect to the distance from a source can be modeled (represented) by this mathematical expression;

I ∝ 1/r²

Where:

Next, we would re-write the mathematical expression and then determine the intensity of a wave from source as follows;

I₁/I₂ = r₂²/r₁²

I₁ = I₂(r₂²/r₁²)

Note: We know that its intensity when it passed a point from the source is 2.0 km.

Substituting the given parameters into the formula, we have;

I₁ = 2.8 × 10⁶ × (53²/2²)

I₁ = 1.97 × 10⁹ J/m²s.

Now, we can calculate the rate of the energy by using this formula;

Power = intensity × area

Power = 1.97 × 10⁹ × 1.0

Power = 1.97 × 10⁹ J/s.

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The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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PART A: Linda has $4.41 more than Enrique after one year.

PART B: Enrique has $12.10 more than Linda after the second year.

PART A: After one year, we can calculate the amount of money each person has in their respective accounts.

For Linda's account:

Principal amount = $610

Interest rate = 1.2%

\(Interest $ earned = Principal $ amount \times (Interest rate/100) = $610 \times (1.2/100) = $7.32\)

\(Total $ amount after one year = Principal amount + Interest earned = $610 + $7.32 = $617.32\)

For Enrique's account:

Principal amount = $590

Interest rate = 3.9%

\(Interest $ earned = Principal amount \times (Interest rate/100) = $590 \times (3.9/100) = $22.91\)

Total amount after one year = Principal amount + Interest earned = $590 + $22.91 = $612.91

Comparing the two amounts, after one year Linda has more money.

The difference in the amount is:

$617.32 - $612.91 = $4.41

Therefore, Linda has $4.41 more than Enrique after one year.

PART B: After a second year, we need to calculate the amounts again.

For Linda's account:

Principal amount = $617.32

Interest rate = 1.2%

\(Interest earned = Principal amount \times (Interest rate/100) = $617.32 \times (1.2/100) = $7.41\)

Total amount after the second year = Principal amount + Interest earned = $617.32 + $7.41 = $624.73

For Enrique's account:

Principal amount = $612.91

Interest rate = 3.9%

\(Interest earned = Principal amount \times (Interest rate/100) = $612.91 \times (3.9/100) = $23.92\)

Total amount after the second year = Principal amount + Interest earned = $612.91 + $23.92 = $636.83

Comparing the two amounts, after the second year Enrique has more money.

The difference in the amount is:

$636.83 - $624.73 = $12.10

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Answer:

Step 1:  Determine why circle 1 is similar to circle 2

The reason why circle 1 is similar to circle 2 is that they both expand at the same rate.  While x grows larger, both circle 1 and circle 2 grow at a proportional rate.  Circle 2 grows is 5 times bigger than circle 1 given any value 5.

When x = 3:  circle 1 = 6 and circle 2 = 30

When x = 10:  circle 1 = 20 and circle 2 = 100

Answer:

Circle 2 is a dilation of circle 1 with a scale factor of 5.

Step-by-step explanation:

Took the quiz and got a perfect score :)

The inverse of f(x) = x^(7/9) using exponential notation is f(x) = x^(9/7)

An inverse function in mathematics is a function that "undoes" another function.

In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.

An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.

The given function is of the form

f(x) = x^(7/9), this is equivalent to ⁹√x⁷

say f(x) = y, then

f(x) = y = x^(7/9)

y = x^(7/9)

solving for the inverse, of y = x^(7/9)

y = x^(7/9)

y^(9/7) = x

interchanging the letters

y = x^(9/7)

hence the inverse function is solved to be f⁻¹(x) = x^(9/7)

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The width of the rectangular prism that has a volume of 440 cubic centimeters as shown in the image is: 5 cm

Recall;

Volume of rectangular prism is: \(V = length \times width \times height\)

From the image given, the dimension of the rectangular prism are:

Plug in the values into the volume formula:

\(x(x-3)(x+3) = 440\\\\\)

Find the value of x

\(x(x^2 - 9) = 440\\\\x^3 - 9x = 440\\\\x^3 - 9x - 440 = 0\)

Factorize

\((x - 8)(x^2 + 8x + 55) = 0\)

We can determine the value of x using one of the factors that will give us a positive value.

Thus:

x - 8 = 0

x = 0 + 8

x = 8

width(w) = x - 3

width (w) = 8 - 3

width (w) = 5 cm

Therefore, the width of the rectangular prism as shown in the image is: 5 cm

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