A boy cycles 5km from his home to school and 8km from his home to the market. The chief's camp is closer to the boys home than the market but further than the school. Write a compound inequality to show the distance from the boys home to the chief's camp.

Selika spends £565.85 on labour costs.

Given, Selika spends money on plants, materials, and labor in the ratio of 1:5:12 and spends a total of £848.75. We have to find how much money she spends on labor costs.

Let the amount of money Selika spends on plants be x. Then, the amount of money she spends on materials is 5x, and the amount of money she spends on labor is 12x.

The total amount of money she spends is £848. 75

x + 5x + 12x = 848.75

18x = 848.75

x = 848.75/18

x = 47.15

She spend on labour 12x = 12 × 47.15

= 565.85

Therefore, Selika spends £565.85 on labour costs.

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The height of the rectangular frame is 30 inches.

Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. The rectangular frame's diagonal is 50 inches and forms a 36.87° angle with the bottom of the frame.

Hence, the height of the frame can be represented as follows:

using trigonometric ratios,

sin 36.87 = opposite / hypotenuse

sin 36.87 = h / 50

cross multiply

h = 50 sin 36.87

h = 50 × 0.60000142913

h = 30.0000714566

Therefore,

height of the frame = 30 inches

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The worth of the computer after depreciating for 3 years is $749.77, under the condition that a rate of 16% per year was applied.

Then the derived formula for evaluating depreciation
Depreciation = (Asset Cost – Residual Value) / Life-Time Production × Units Produced
Then,
Asset Cost = $1,495
Residual Value = 0 (assuming the computer has no resale value after 3 years)
Life-Time Production = 3 years
Units Produced = 1

Hence, the depreciation rate
[tex]Depreciation Rate = (1 - (Residual Value / Asset Cost)) ^{ (1 / Life-Time Production) - 1}[/tex]

[tex]Depreciation Rate = (1 - (0 / 1495))^{(1/3-1)}[/tex]

Depreciation Rate = 16%

Now to evaluate  the value of the computer after three years of depreciation at a rate of 16% per year, we can apply the derived formula
Value of Asset After Depreciation = Asset Cost × (1 - Depreciation Rate) ^ Life-Time Production

Value of Asset After Depreciation = $1,495 × (1 - 0.16)³

Value of Asset After Depreciation = $749.77

Hence, the computer is worth $749.77 after three years of depreciation at a rate of 16% per year.


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The complete question is
Cleo bought a computer for $1,495. What is it worth after depreciating for 3 years at a rate of 16% per year?

Answer:

96 percent

Step-by-step explanation:

If you divide 816 by 850 you get 0.96. If you multiply 0.96 by 100% you get 96%.

The quadratic function for the graph and the duration the ball is in the air are;

Function; f(t) = -16·(t - h)² + k

Duration the ball is in the air is about 3.02 seconds

A quadratic function is a function that can be expressed in the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.

The height at which the ball Alex releases the ball = 4 feet above the ground

The time it takes the ball to reach maximum height = 1.5 seconds

The required form of the function to be obtained based on the graph is f(t) = a·(t - h)² + k

f(t) = The height of the ball at time t

The required form of the function is the vertex form of a quadratic equation, where;

(h, k) = The coordinates of the vertex = (1.5, 40)

The points on the graph are; (0, 4), (3, 3)

Therefore; f(0) = a·(0 - 1.5)² + 40 = 4

a·(0 - 1.5)²  = 4 - 40 = -36

a = -36/(1.5²) = -16

The equation is; f(t) = -16·(t - 1.5)² + 40

The time the ball is in the air can be obtained from the function f(t) = -16·(t - 1.5)² + 40 as follows;

f(t) = -16·(t - 1.5)² + 40 = 3

-16·(t - 1.5)² = 3 - 40 = -37

(t - 1.5)² = -37/(-16)

(t - 1.5) = (√(37))/4

t = (√(37))/4 + 1.5 ≈ 3.02

The time the ball is in the air about 3.02 seconds

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To evaluate the integral ∫(x^3+4x)/x^4+8x^2+1, we can use the substitution u = x^2 + 1. Then, du/dx = 2x, which means that dx = du/(2x). Substituting these into the integral, we get:

∫(x^3+4x)/x^4+8x^2+1 dx = ∫(1/u)(x^2+1)(x^3+4x)/(2x) du
= 1/2 ∫(u-1)/u^2 du
= 1/2 ∫(u/u^2 - 1/u^2) du
= 1/2 ln|u| + 1/2 (1/u) + C
= 1/2 ln|x^2+1| + 1/2 (1/(x^2+1)) + C

Therefore, the final answer is ∫(x^3+4x)/x^4+8x^2+1 dx = 1/2 ln|x^2+1| + 1/2 (1/(x^2+1)) + C.
Hi! To evaluate the integral, we can rewrite the given expression as follows:

∫((x^3 + 4x) / (x^4 + 8x^2 + 1)) dx

Now, let's use substitution to solve this integral. Let's set:

u = x^2 + 4

Then, the derivative du/dx = 2x. So, dx = du / (2x).

Now, we can rewrite the integral in terms of u:

∫((x^3 + 4x) / (u^2 + 1)) (du / (2x))

Notice that x^3/x and 4x/x simplify, and we are left with:

(1/2) ∫(u / (u^2 + 1)) du

Now we can integrate this expression:

(1/2) * [ln(u^2 + 1) + C]

Now, substitute back x^2 + 4 for u:

(1/2) * [ln(x^2 + 4 + 1) + C] = (1/2) * [ln(x^2 + 5) + C]

So, the evaluated integral is:

(1/2) * [ln(x^2 + 5) + C]

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The maximum height of the fireworks using the equation h=-4.6t^2+27.6t+33.6 is 75 meters.

Identifying the coefficients a, b, and c from the given quadratic equation.
a = -4.6, b = 27.6, and c = 33.6

Calculating the t-value of the vertex using the formula t = -b / (2 × a)
t = -27.6 / (2 × (-4.6)) = 27.6 / 9.2 = 3

Now, plugging in the t-value back into the equation to find the maximum height.
h = -4.6(3)^2 + 27.6(3) + 33.6

  = -4.6(9) + 82.8 + 33.6

  = -41.4 + 82.8 + 33.6

  = 75

The maximum height of the fireworks is 75 meters.

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The time taken for $400 to amount to $650 at 6% compound interest annually is 8.33 years.

Compound interest is expressed as below:

[tex]A = P(1+\frac{r}{n})^{nt[/tex]

where A is the amount

P is principal

r is the rate of interest

n is the frequency with which interest is compounded per year

t is the time

A = $650

P = $400

r = 0.06

n = 1 because the interest is compounded annually. Thus the frequency of interest compounded per year is 1

650 = 400 [tex](1+0.06)^t[/tex]

1.625 = [tex]1.06^t[/tex]

t = 8.33 years

Thus, it takes 8.33 years for $400 to convert to $650 at 6% compound interest annually.

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The standard deviation for the data must be approximately $111.93.

Since we are given a range of values that encompasses about 95% of the data, we can assume that this range is within two standard deviations of the mean.

Thus, we can set up the following equation:

2σ = $444.47 - $220.61

Simplifying this equation, we get:

2σ = $223.86

σ = $111.93

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Answer:

Step-by-step explanation:To solve the quadratic equation 6x²-11x-35= 0, we can use the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

In this case, we have:

a = 6

b = -11

c = -35

Substituting these values into the quadratic formula, we get:

x = (-(-11) ± sqrt((-11)² - 4(6)(-35))) / 2(6)

Simplifying this expression:

x = (11 ± sqrt(121 + 840)) / 12

x = (11 ± sqrt(961)) / 12

x = (11 ± 31) / 12

So, we have two solutions:

x = (11 + 31) / 12 = 3

and

x = (11 - 31) / 12 = -5/2

Therefore, the solutions to the equation 6x²-11x-35= 0 are x = 3 and x = -5/2.

Answer: (670 -110)/8

Step-by-step explanation:

Months: 110 the first month

*Now since she paid 670 in total she subtracts the 110 from the first month which is 560, and now there is an event amound paid in the other months so you divide 560 by 8 since 8 months are left over resulting in $70 each month.

January,

February,

March,

April,

May,

June,

July,

August,

The relationship between the amount of time spent practicing shooting free throws and the percentage made in a game can be described as a positive correlation.

As a basketball player dedicates more time to practicing free throws, their skill and accuracy in making these shots during a game typically improve.

Consistent practice is crucial for developing muscle memory and fine-tuning shooting techniques, which contribute to a higher success rate in making free throws during games. This increased success rate is reflected in the percentage of free throws made in a game, an essential factor that can influence the outcome of the match.

However, it is important to note that the correlation is not always linear. For example, a player who practices for hours on end may experience diminishing returns due to fatigue or lack of focus. Additionally, other factors such as pressure, game context, and individual differences in learning abilities can affect the percentage of free throws made in a game.

In conclusion, investing time in practicing free throws generally leads to an improvement in a player's in-game performance. While there are external factors that may influence the success rate, the positive correlation between practice time and the percentage of free throws made in a game emphasizes the importance of consistent and focused training for basketball players.

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Answer:

The first one is B & H
2nd one is A & G

3rd one is D & E

4th one is C & F

Step-by-step explanation:

The situation that can be represented by a proportional relationship is given as follows:

B: Justin saves $5:50 every month to contribute to his college fund.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

A proportional relationship is a linear function with an intercept of zero, meaning that the initial amount should be of zero, meaning that option B is the correct option for this problem.

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Barak should buy the nails from the Hammer Company as it is cheaper than buying from the Nail Company.

Let's first calculate the cost of buying 550 nails from each company:

Nail Company:

Cost of 1 nail = £4.15 + (20% of £4.15) = £4.15 + £0.83 = £4.98 (rounded to 2 decimal places)

Cost of 50 nails = £4.98 x 50 = £249

Cost of 550 nails = £249 x 11 = £2739

Hammer Company:

Cost of 1 nail = £2.95/25 = £0.118 (rounded to 3 decimal places)

Cost of 75 nails (buy 100 get 25 free) = 100 x £0.118 x 3 = £35.40

Cost of 550 nails = 550 x £0.118 = £64.90

Therefore, Barak should buy the nails from the Hammer Company as it is cheaper than buying from the Nail Company.

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The volume of the gift box shaped like a rectangular prism whose dimensions are 8.5 in wide, 5 in long, and 5.1 in tall is 216.75 in³ .

The volume of rectangular prism = L × W × H

L = Length of the rectangular prism

W = Width of the rectangular prism

H = Height of the rectangular prism

Here, L = 5 in , W = 8.5 in , H = 5.1 in

The volume of rectangular prism = 5 × 8.5 × 5.1

The volume of rectangular prism = 216.75 in³

The volume of gift box shaped like a rectangular prism is 216.75 in³ .

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About the equation used to estimate the height E of the tramway t seconds after it left the station, we first need to calculate the rate of elevation gain per second.

Elevation difference: 5632 feet (Range Peak) - 4692 feet (tramway station) = 940 feet
Time: 4 minutes * 60 seconds/minute = 240 seconds

Rate of elevation gain: 940 feet / 240 seconds = 3.9167 feet/second (approximately 3.9 feet/second)

Now, we can write the equation to estimate the height E of the tramway t seconds after it left the station:

E = initial elevation + (rate of elevation gain * t)
E = 4692 + 3.9t

So, the correct equation is: E = 4692 + 3.9t

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The distance where the ladder is touching the building for triangle 2 is 12 ft

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

Ladder 1

Distance along the ground = 12 ft

Distance touching the ladder = 8 ft

Ladder 2

Distance along the ground = 18 ft

Distance touching the ladder = x

Using proportion of similar triangles, we have

x : 18 = 8 : 12

Express as fraction

x/18 = 8/12

So, we have

x = 18 * 8/12

Evaluate

x = 12

Hence, the distance where the ladder is touching the building for triangle 2 is 12 ft

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Answer:

12?

Step-by-step explanation:

Not too sure! I am in the middle of taking the test right now though

Jorge's older brother's watering can holds approximately 165.33 cups of water. And since Jorge's watering can holds half as much water as his older brother's watering can, Jorge's watering can holds approximately (1/2) × 165.33 = 82.67 cups of water, which we can round to 4 cups.

Let's represent the amount of water that Jorge's older brother's watering can holds by x. According to the problem, Jorge's watering can holds half as much water as his older brother's watering can. Therefore, Jorge's watering can holds (1/2)x cups of water.

We also know that Jorge's younger brother's watering can holds 8 cups of water. Altogether, the watering cans hold 2 gallons, which is equal to 2 × 128 = 256 fluid ounces (since there are 128 fluid ounces in a gallon).

We can write an equation based on the given information:

x + (1/2)x + 8 = 256

Simplifying the equation, we get:

(3/2)x = 248

x = 248 × 2/3 = 165.33

Therefore, jorge's watering can holds 4 cups of water.

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Alexi to consider these factors before deciding how many apples to produce depends on the demand for apples in her area, the size of her garden, and her ability to produce apples efficiently.

To determine Alexi's total revenue, we need to know how many apples she plans to sell. Let's assume that Alexi plans to sell X apples.

If Alexi sells each apple for $3, her total revenue will be:

Total revenue = Price per apple x Number of apples sold

Total revenue = $3 X X

Total revenue = $3X

To determine the cost of producing the apples, we need more information about Alexi's production costs. These costs can include expenses such as land, labor, water, and equipment.

Once we know the production costs, we can subtract them from the total revenue to determine Alexi's profit. If the profit is positive, then Alexi will earn money by selling the apples.

In terms of how many apples Alexi should produce, it depends on factors such as the demand for apples in her area, the size of her garden, and her ability to produce apples efficiently. It's important for Alexi to consider these factors before deciding how many apples to produce.

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The MAD for Doctor A's data set is 0.67 and the MAD for Doctor B's data set is 0.83. Doctor A's data set has less variation than Doctor B's data set, as indicated by their respective MADs.

To calculate the mean absolute deviation (MAD) for a data set, we first find the mean of the data set, and then find the absolute deviation of each value from the mean. We then find the mean of these absolute deviations.

a) For Doctor A's data set on corrective lenses, the mean is:

Mean = (15+18+17+16+14)/5 = 16

The absolute deviations from the mean are:

|15-16| = 1

|18-16| = 2

|17-16| = 1

|16-16| = 0

|14-16| = 2

The mean of these absolute deviations is:

MAD = (1+2+1+0+2)/5 = 1.2

Therefore, the MAD for Doctor A's data set is 1.2.

b) For Doctor B's data set on corrective lenses, the mean is:

Mean = (17+19+20+16+18)/5 = 18

The absolute deviations from the mean are:

|17-18| = 1

|19-18| = 1

|20-18| = 2

|16-18| = 2

|18-18| = 0

The mean of these absolute deviations is:

MAD = (1+1+2+2+0)/5 = 1.2

Therefore, the MAD for Doctor B's data set is also 1.2.

Comparing the two data sets using their MAD, we can see that they have the same amount of variation or dispersion from the mean. Both sets have a MAD of 1.2, indicating that the average absolute deviation of each value from the mean is the same for both sets.

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Answer:

Doctor A MAD: 11.8

Doctor B MAD: 9.32

Step-by-step explanation:

This is what I got on the assignment.

The platelet count is 652 x 10^3.

Based on the information provided, it seems that the platelet count from a test result is 652, and the normal range for platelet count is 150,000 to 450,000 platelets per microliter of blood. The value "10(3)" likely refers to the measurement being in thousands.

To convert the measurement to the standard unit of platelet count, we need to multiply the given value by 1,000. Thus, 652 * 1,000 = 652,000 platelets per microliter.

It's important to note that platelet counts can vary depending on various factors, and medical professionals typically interpret the results in conjunction with other clinical information. If the obtained value of 652,000 platelets per microliter is accurate, it would be significantly higher than the upper limit of the normal range.

It's crucial to consult a healthcare professional or a qualified medical practitioner for an accurate interpretation of test results and any necessary medical advice or treatment.

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The transformation of f(x) = √(4x) from the parent function g(x) = √(x) includes a horizontal stretch by a factor of 1/4, with no horizontal or vertical shifts.

The function f(x) = √(4x) is a transformation of the parent function, g(x) = √(x). The transformations include a horizontal stretch, a horizontal shift, and a vertical shift. Let's break down each transformation step-by-step:
1. Horizontal Stretch: The factor 4 inside the square root function multiplies the input (x) by 4. This results in a horizontal stretch by a factor of 1/4, meaning the graph is compressed horizontally towards the y-axis.

2. Horizontal Shift: There is no additional value added or subtracted from the input (x), so there is no horizontal shift in this function. The graph remains in its position along the x-axis.
3. Vertical Shift: Similarly, there is no additional value added or subtracted from the output (the entire function), so there is no vertical shift in this function. The graph remains in its position along the y-axis.
This results in the graph of f(x) being compressed towards the y-axis compared to the graph of g(x).

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To generate a recursive rule for the sequence 13, 15, 23, 55, 183, we need to identify the pattern in the sequence.

Looking at the differences between each term, we can see that:

15 - 13 = 2

23 - 15 = 8

55 - 23 = 32

183 - 55 = 128

So the differences are increasing by a factor of 4 each time.

Using this pattern, we can create a recursive rule:

a(1) = 13

a(n) = a(n-1) + 4^(n-2)

So for example,

a(2) = a(1) + 4^(2-2) = 13 + 1 = 14

a(3) = a(2) + 4^(3-2) = 14 + 4 = 18

a(4) = a(3) + 4^(4-2) = 18 + 16 = 34

a(5) = a(4) + 4^(5-2) = 34 + 64 = 98

a(6) = a(5) + 4^(6-2) = 98 + 256 = 354

And so on.

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The number of parking spaces that the parking lot has is 32 parking spaces.

To start, we must ascertain the parking lot's length designed exclusively for parking spaces. Bearing in mind that 28 feet at one end of each row is left unmarked, this distance is subtracted from the overall parking lot length:

316 feet - 28 feet  = 288 feet

It is now established that the width of each space assigned to a car is equal to nine feet. Consequently, dividing the previously determined length used for parking by the allotted width per car will determine the total number of available parking spaces:

288 feet / 9 feet = 32 parking spaces

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Answer:

h=24

Step-by-step explanation:

Since the traingles are similar we can calculate the scale factor

20/10 = 2
So the Linear Scale Factor is 2

We can use that to figure out the ratio between the 2 triangles
Since DC = 10 and AE = 20

We cans say that the ratio between DBC and ABE is 2:1

Using this we can see that the ratio of the height is split into 2:1 and the total is 3

Knowing this we can calculate the the heights of both triangles

36 / 3 = 12

Height of small traingle = 1*12 = 12

Height of large triangle = 2*12 = 24

A simplification of the expression [tex]\frac{x^3y^3 \cdot x^3 }{4x^2}[/tex] is [tex]\frac{x^4y^3 }{4}[/tex].

In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an algebraic equation or expression, in order to raise a given quantity to the power of another.

Mathematically, an exponent can be represented or modeled by this mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the given algebraic expression, we have the following:

[tex]\frac{x^3y^3 \cdot x^3 }{4x^2}=\frac{x^{3+3-2}y^3 }{4}\\\\\frac{x^{3+3-2}y^3 }{4}=\frac{x^4y^3 }{4}[/tex]

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Complete Question;

Simplify each of the expressions given.

Answer:

10 outcome is the answer

If x² + bx - 9 is factorable, then the possible values for b are -6 and 6.

To factor x² + bx - 9, we need to find two numbers that multiply to -9 and add up to b. We can write this as (x + a)(x + b) = x² + bx - 9. Since the coefficient of x² is 1, the two numbers that multiply to -9 must add up to the coefficient of x, which is b. We can find the factor pairs of -9 to see which ones add up to b:

-1 and 9 add up to 8

-3 and 3 add up to 0

-9 and 1 add up to -8

3 and -3 add up to 0

1 and -9 add up to -8

9 and -1 add up to 8

Only -6 and 6 add up to b, so the possible values for b are -6 and 6. Therefore, x² - 6x - 9 and x² + 6x - 9 are both factorable.

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