(08.01 MC)
The function h(x) is a continuous quadratic function with a domain of all real numbers. The table
x h(x)
-6 12
-57
-4 4
-3 3
-24
-1 7
What are the vertex and range of h(x)?

Answer:

3071.6 ft

Step-by-step explanation:

In this situation,

We can use sine law,

in which Sin angle = opposite side/ hypotenuse

Similarly

In triangle ABC

SIn A=BC/AC

Sin 19°=1000/AC

Doing criss cross multiplication:

AC= 1000/(Sin 19°)

AC=3071.55 ft

Therefore, the distance I ski down the mountain is 3071.6 ft

The diagram is below.

==============================================

Work Shown:

sin(angle) = opposite/hypotenuse

sin(19) = 1000/x

xsin(19) = 1000

x = 1000/sin(19)

x = 3071.553487

x = 3071.6

Refer to the diagram below.

Note that the angle of depression ACD is equal to the angle of elevation BAC because of the alternate interior angles theorem.

Answer:

Step-by-step explanation:

12 14 33 35========1,234,000,124,581.

Answer:

16

Step-by-step explanation:

(|7 − 3 x 5| ÷ 4)³ + √64

(|7 − 3 x 5| ÷ 4)³ + √64

(|7 − 15| ÷ 4)³ + √64

(|7 − 15| ÷ 4)³ + √64

(8 ÷ 4)³ + √64

(8 ÷ 4)³ + √64

2³ + √64

8 + 8

16

Answer:

16

Step-by-step explanation:

To solve, use PEMDAS as it applies to the expression.

First, you must carry out what is in the parenthesis.

Multiply (3*5 = 15), then subtract (7 - 15 = -8). The two little vertical lines surrounding (7 - 3 x 5) mean absolute value. This means that you will write -8 as +8.

Continuing on in the parenthesis, carry out (8 ÷ 4 = 2).

Next, we must do exponents.

We see that everything in the parenthesis is being raised to the power of three (cubed). Since we've solved what was in the parenthesis, we simply need to carry out ([tex]2^{3}[/tex] = 8).

Now, we need to quickly carry out [tex]\sqrt{64}[/tex]. Square roots are just whatever number can be multiplied by itself to get, in this case, 64.

[tex]\sqrt{64} = 8[/tex].

Finally, we must add what remains.

8 + 8 = 16.

So, (|7 - 3 x 5) | ÷ [tex]4)^{3}[/tex] + [tex]\sqrt{64}[/tex] = 16.

The graph that displays the line of best fit for the data is the one where the line with the best fit goes through the points.

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The numeral 7,001 eight is equal to 3585 in base ten.

To convert the numeral 7,001 in base eight to base ten, we need to multiply each digit by the corresponding power of eight and sum them up.

Starting from the rightmost digit, we have:

[tex]1 * 8^0 = 1\\0 * 8^1 = 0\\0 * 8^2 = 0\\7 * 8^3 = 3584[/tex]

Adding these values together, we get:

1 + 0 + 0 + 3584 = 3585

Therefore, the numeral 7,001eight is equal to 3585 in base ten.

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The break-even sales (units) when the variable costs are decreased by $4 is approximately 47,714 units.

To find the break-even sales (units) when the variable costs are decreased by $4, we need to calculate the new unit variable costs and then use the break-even formula.

Fixed costs (F) = $334,000

Unit selling price (P) = $22

Unit variable costs (V) = $19

Change in unit variable costs = $4

New unit variable costs (V') = V - Change in unit variable costs

= $19 - $4

= $15

Now, let's calculate the break-even sales (units) using the formula:

Break-even sales (units) = Fixed costs / (Unit selling price - Unit variable costs)

Break-even sales (units) = $334,000 / ($22 - $15)

= $334,000 / $7

= 47,714.29

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Step-by-step explanation:

1. Answer is 2

2. Answer is -3

3. Answer is 4

Answer:

i) -5x + 3/2

ii) x = 11

iii) x + 9/2

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Answer:

34.45%

Step-by-step explanation:

A tree diagram shows all possible outcomes of two or more events.

Each branch is a possible outcome and is labelled with the probability of that outcome.

Draw lines (branches) to represent the first event (main meal). Write the outcomes on the ends of the branches: "sandwich" and "slice of pizza". Write the given probabilities on the branches.

Draw the next set of branches to represent the second event (side).  Write the outcomes on the ends of the branches: "chips" and "veggies with hummus". Write the given probabilities on the branches.

We assume that the events in this scenario are independent, so the probability of the first event happening has no impact on the probability of the second event or the third event happening.  Therefore, to find the probability of each combination of events, multiply along the branches.

Sandwich and chips = 35% × 47% = 16.45%

Sandwich and veggies with hummus = 35% × 53% = 18.55%

Slice of pizza and chips = 65% × 47% = 30.55%

Slice of pizza and veggies with hummus = 65% × 53% = 34.45%

Therefore, the probability that Sophie selects a slice of pizza and veggies is 34.45%.

The probability that Sophie selects a slice of pizza and veggies is 34.45%.

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

The probability of pizza and veggies  is calculated as

P = Pizza * Veggies

Substitute the known values in the above equation, so, we have the following representation

P = 65% * 53%

Evaluate

P = 34.45%

Hence, the probability that Sophie selects a slice of pizza and veggies is 34.45%.

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Answer:

Step-by-step explanation:

Answer:

f(0) = 1

f(1) = 21.1

Step-by-step explanation:

Do as the problem says:

[tex]f(0)=4^{2.2(0)}=4^0=1\\f(1)=4^{2.2(1)}=4^{2.2}\approx21.1[/tex]

The line that intersects two of the planes is : Line X

The line that intersects one of the planes is : Line Z

The line that that has points on three of the planes shown is Line Y

From this figure you can see that there are 3 different levels and 3 different lines. One line intersects two planes (line X), another line intersects only one plane (line Z). Line Y, on the other hand, has points in all three planes.

A line y has points A and B in all three planes.

A plane is simply a plane that can be intersected by a straight line connecting any two points on the plane.

Therefore, we can conclude from the figure

A line that intersects two planes is: line x

A line that intersects one of the planes is: line Z

A line with points on the three planes shown is Line Y. 

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Answer:

Step-by-step explanation:

We must simplify and rearrange the variables to divide x in order to determine the comparable inequality to the supplied inequality, -4(x + 7) 3(x - 2).

Below are the steps to solve the problem:

-4(x + 7) < 3(x - 2)

Expanding the equation:

-4x-28<3x-6

Gather the variable term on one side and constants on the other:

Adding -4x and 28 on both sides:

-4x + 4x - 28 + 28 < 3x + 4x - 6 + 28

=>0 < 7x + 22

To make the coefficient of x positive, we divide the entire inequality by 7:

0/7 < (7x + 22)/7

=> 0 < x + 22/7

Answer:

5n - 8 = 37

5n = 45

n = 9

The number is 9.

Answer:

Step-by-step explanation:

First, we multiply 2×2 then the answer we obtain we add to it 6 which in total gives us 10

Step-by-step explanation:

a. 4/64= 1/16 for red marble

b. 40/64= 5/8 black marbles

c. 20/64= 5/16 blue marble

d. highest: black marble

e. lowest: red marble

a. The distribution of X is a normal distribution.

b. The median giraffe height is also 19 feet.

c. The Z-score for a giraffe that is 22 foot tall is 3.

d. The probability that a randomly selected giraffe will be shorter than 18.9 feet tall is less than -0.1.

f. The 80th percentile represents the value below which 80% of the data falls.

a. The distribution of X is a normal distribution (or Gaussian distribution) with a mean of 19 feet and a standard deviation of 1 foot. This can be denoted as X ~ N(19, 1).

b. The median of a normal distribution is equal to its mean.

c. To find the Z-score for a giraffe that is 22 feet tall, we can use the formula: Z = (X - μ) / σ, where X is the observed value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get Z = (22 - 19) / 1 = 3.

d. To find the probability that a randomly selected giraffe will be shorter than 18.9 feet tall, we need to calculate the area under the normal curve to the left of 18.9. This can be done using the Z-score and a standard normal distribution table or a calculator.

Alternatively, we can use the Z-score formula from the previous question. The Z-score for 18.9 feet can be calculated as Z = (18.9 - 19) / 1 = -0.1. We can then look up the corresponding probability in the standard normal distribution table or use a calculator to find the probability that Z is less than -0.1.

e. To find the probability that a randomly selected giraffe will be between 18.6 and 19.5 feet tall, we need to calculate the area under the normal curve between these two values.

Again, we can use the Z-score formula to standardize the values and then find the corresponding probabilities using a standard normal distribution table or a calculator.

f. To find the height at the 80th percentile, we can use the standard normal distribution table or a calculator to find the Z-score that corresponds to the 80th percentile.

Once we have the Z-score, we can use the formula Z = (X - μ) / σ to solve for X. Rearranging the formula, we have X = Z * σ + μ. Plugging in the values for Z (obtained from the percentile) and μ (mean) and σ (standard deviation), we can calculate the height at the 80th percentile.

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The probability that all four cards are clubs is approximately 0.0026. Option A.

To understand why, let's break down the calculation. In a well-shuffled deck, there are 13 clubs out of 52 cards.

When dealing the first card, there are 13 clubs out of the total 52 cards, so the probability of getting a club on the first draw is 13/52.

For the second card, after the first club has been removed from the deck, there are now 12 clubs left out of the remaining 51 cards. Therefore, the probability of getting a club on the second draw is 12/51.

Similarly, for the third card, after two clubs have been removed, there are 11 clubs left out of the remaining 50 cards. The probability of drawing a club on the third draw is 11/50.

Finally, for the fourth card, after three clubs have been removed, there are 10 clubs left out of the remaining 49 cards. The probability of drawing a club on the fourth draw is 10/49.

To find the probability of all four cards being clubs, we multiply the probabilities of each individual draw:

(13/52) * (12/51) * (11/50) * (10/49) ≈ 0.0026.

This calculation takes into account the fact that the deck is being dealt without replacement, meaning that the number of available clubs decreases with each draw.

The third option, 1/4, is incorrect because it assumes that each card dealt is independent and has an equal probability of being a club. However, as cards are drawn without replacement, the probability changes with each draw. So Option A is correct.

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Note the complete question is

A 52-card deck contains 13 cards from each of the four suits: clubs ♣, diamonds ♦, hearts ♥, and spades ♠. You deal four cards without replacement from a well-shuffled deck so that you are equally likely to deal any four cards.

What is the probability that all four cards are clubs?

A.) 13/52 ⋅ 12/51 ⋅ 11/50 ⋅ 10/49 ≈0.0026

B.) 13/52 ⋅ 12/52 ⋅ 11/52 ⋅ 10/52 ≈0.0023

C.) 1/4 because 1/4 of the cards are clubs

The purchasing power in five years will be $15,476.

To predict the purchasing power in five years, we can substitute the value of X as 5 into the equation y = 20000(0.95)^X.

Plugging in X = 5, we have:

[tex]y = 20000(0.95)^5[/tex]

Calculating the expression, we find:

[tex]y ≈ 20000(0.774)[/tex]

Simplifying further, we get:

[tex]y ≈ 15480[/tex]

Rounding the result to the nearest dollar, the predicted purchasing power in five years would be approximately $15,480.

Therefore, the closest option to the predicted purchasing power in five years is $15,476.

So the correct answer is:

$15,476.

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Rounding to the nearest dollar, the predicted purchasing power in five years is approximately $15,480.

To predict the purchasing power in five years using the given equation, we substitute the value of x (representing the number of years) as 5 and calculate the result.

The equation provided is: y = 20000(0.95)^x

Substituting x = 5 into the equation, we have:

y = 20000(0.95)⁵

Now, let's calculate the result:

y ≈ 20000(0.95)⁵

≈ 20000(0.774)

y ≈ 20000(0.774)

≈ 15,480

This means that, according to the given equation, the purchasing power of $20,000, with an inflation rate of five percent, would be predicted to be approximately $15,480 after five years.

By changing the value of x (representing the number of years) to 5, we can use the preceding equation to forecast the buying power in five years.

The example equation is: y = 20000(0.95)^x

When x = 5 is substituted into the equation, we get y = 20000(0.95).⁵

Let's now compute the outcome:

y ≈ 20000(0.95)⁵ ≈ 20000(0.774)

y ≈ 20000(0.774) ≈ 15,480

This indicates that based on the equation, after five years, the purchasing power of $20,000 would be estimated to be around $15,480 with a five percent inflation rate.

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Answer:

0

Step-by-step explanation:

Use the following models to show the equivalence of the fractions 35 and 610 a) Set model

Answer:

x=3

Step-by-step explanation:

You can get the answer by substituting the value of x in the equations, your aim is to find a number that will make both equations equal zero.

The person's expenditure is $1,755. (30 words)

To find the expenditure, we need to determine the person's income first. Since the income tax is 13% of the income and is given as $585, we can calculate the income. Dividing the income tax by the tax rate gives us the income. So, $585 divided by 0.13 equals $4,500, which is the person's income.

Now, we can calculate the expenditure. Given that the expenditure is 75% of the income, we can multiply the income by 0.75 to find the expenditure. So, $4,500 multiplied by 0.75 equals $3,375. Therefore, the person's expenditure is $3,375. (120 words)

In summary, the person's expenditure is $3,375. To find this, we first determined the person's income by dividing the given income tax of $585 by the tax rate of 13%, resulting in an income of $4,500.  

Then, we calculated the expenditure by multiplying the income by 0.75 since the expenditure is stated to be 75% of the income. Thus, the person's expenditure is $3,375.

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Answer:

[tex]f(x) = - 3 {x}^{2} - 6x - 1[/tex]

The first mechanic worked for 12 hours, and the second mechanic worked for 8 hours.

Let's assume the first mechanic worked for x hours. Since the first mechanic charged $75 per hour, their earnings can be represented as 75x dollars.

Similarly, the second mechanic worked for (20 - x) hours, and at a rate of $95 per hour, their earnings can be represented as 95(20 - x) dollars.

According to the problem, the combined earnings of both mechanics are $1800. Therefore, we can write the equation:

75x + 95(20 - x) = 1800

Simplifying this equation, we get:

75x + 1900 - 95x = 1800

-20x = -100

x = 5

Substituting x back into the equation, we find that the first mechanic worked for 5 hours, and the second mechanic worked for (20 - 5) = 15 hours.

Therefore, the first mechanic worked for 5 hours, and the second mechanic worked for 15 hours.

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The correct answer is an option (d): Impossible.

Both the geometric mean and harmonic mean require positive values. However, in the given set of values, we have negative values (-11 and -14), which makes it impossible to calculate the geometric mean and harmonic mean. Therefore, the correct answer is that it is impossible to calculate the geometric mean and harmonic mean for the given values.

Answer:

it 10:579

Step-by-step explanation:

it is the anser

Juan could have a maximum of 3 quarters.

1. Let's assume Juan has x quarters.

2. The value of x quarters in dollars would be 0.25x.

3. We are given that Juan has 18 dimes, which have a value of 0.10 * 18 = $1.80.

4. The combined value of Juan's dimes and quarters should be less than or equal to $2.75.

5. We can write the equation: 0.25x + 1.80 ≤ 2.75.

6. Subtracting 1.80 from both sides of the equation, we have: 0.25x ≤ 2.75 - 1.80.

7. Simplifying, we get: 0.25x ≤ 0.95.

8. Dividing both sides of the inequality by 0.25, we have: x ≤ 0.95 / 0.25.

9. Evaluating the expression, we find: x ≤ 3.8.

10. Since Juan cannot have a fraction of a quarter, the maximum number of quarters he could have is 3.

11. However, we need to check if the combined value of the dimes and quarters is at least $0.20.

12. If Juan has 3 quarters (0.25 * 3 = $0.75) and 18 dimes ($1.80), the combined value is $0.75 + $1.80 = $2.55.

13. Since $2.55 is less than $2.75, Juan can have 3 quarters.

14. Therefore, the maximum number of quarters Juan could have is 3.

Note: There are no possible solutions where Juan has more than 3 quarters and still satisfies the conditions.

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