an auto mechanic earns $498.75 in 35 hours during the week. his pay is $2.50 more per hour on weekends. if he works 6 hours on the week, how much does he earn?

Answer:

a.) 4

b.) 6

c.) 25

d.) 21

e.) 14

f.) 30

g.) 15

h.) 30

i.) 16

Step-by-step explanation:

Basically just find what factor the numerator or denominator is changing by, and apply it to the rest of the fraction. For example,

Given: 2/? = 10/20

Find: ?

We see that the numerator is being multiplied by 5 to get 10, so we simply divide 20 by 5 to get our answer of 4.

? = 4

Answer:

a) 4

b) 6

c) 25

d) 21

e) 14

f) 30

g) 15

h) 30

i) 49

Step-by-step explanation:

Answer:

41.2

Step-by-step explanation:

By the alternate interior angles theorem, the angle of depression is congruent to the angle of elevation.

This means that tan(27)=21/x.

x(tan 27)=21

x=21/(tan 27), which is about 41.2

Given that cosθ = -2/8 and tanθ < 0, we can determine the values of sin(θ), tan(θ), cot(θ), sec(θ), and csc(θ). The calculated values are: sin(θ) = -√15/8, tan(θ) = √15/7, cot(θ) = -7/√15, sec(θ) = -4√15/15, and csc(θ) = -8/√15.

To find sin(θ), we can use the Pythagorean identity sin²(θ) + cos²(θ) = 1. Since we know cos(θ) = -2/8, we can substitute the value and solve for sin(θ).

Rearranging the equation, we get sin²(θ) = 1 - cos²(θ), and substituting the given value, we have sin²(θ) = 1 - (-2/8)² = 1 - 1/16 = 15/16.

Taking the square root, sin(θ) = ±√15/4. However, since tan(θ) < 0, we can conclude that sin(θ) must be negative.

Therefore, sin(θ) = -√15/4, which simplifies to -√15/8.

Next, we can determine tan(θ). Given that tan(θ) < 0, we know that the tangent function is negative in the specific quadrant where θ lies.

We can recall that tan(θ) = sin(θ)/cos(θ).

Substituting the values we found earlier, we have tan(θ) = (-√15/8) / (-2/8) = √15/2.

To calculate the remaining trigonometric functions, we can use their reciprocal relationships.

The reciprocal of tan(θ) is cot(θ), so cot(θ) = 1/tan(θ) = 1/(√15/2) = 2/√15 = 2√15/15.

The reciprocal of cos(θ) is sec(θ), so sec(θ) = 1/cos(θ) = 1/(-2/8) = -4/2 = -2.

Finally, the reciprocal of sin(θ) is csc(θ), so csc(θ) = 1/sin(θ) = 1/(-√15/8) = -8/√15.

In summary, the values of the trigonometric functions are:

sin(θ) = -√15/8, tan(θ) = √15/2, cot(θ) = 2√15/15, sec(θ) = -2, and csc(θ) = -8/√15.

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To find the point on the hyperbola xy = 8 that is closest to the point (3, 0), we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula:

Distance = √[(x2 - x1)² + (y2 - y1)²]

Let's denote the coordinates of the point on the hyperbola as (x, y). Substituting the given coordinates (3, 0) and the equation of the hyperbola xy = 8 into the distance formula, we get:

Distance = √[(x - 3)² + (y - 0)²]

Now, we need to minimize this distance. Since the distance is squared, we can minimize the square of the distance, which is:

Distance² = (x - 3)² + y²

To minimize this expression, we can take its derivative with respect to x and y and set them equal to zero. Let's differentiate Distance² with respect to x and y:

d(Distance²)/dx = 2(x - 3)

d(Distance²)/dy = 2y

Setting these derivatives equal to zero, we have:

2(x - 3) = 0 => x = 3

2y = 0 => y = 0

Therefore, the point on the hyperbola xy = 8 that is closest to the point (3, 0) is (3, 0).

Note that the distance from (3, 0) to any point on the hyperbola xy = 8 is always the same, which means the hyperbola is equidistant from the point (3, 0).

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Answer:

The best chart to show how your department's expenses compare to the total company's expenses, and hopefully save employee jobs, would be:

Pie Chart

Step-by-step explanation:

Answer:

umm is there a diagram for this?

Answer: The first answer choice

AKA: y = -1.74x + 46.6

Step-by-step explanation:

Answer:

I believe it's the second one

Answer:

25

Step-by-step explanation:

if you have 2 negative number and you have -55 and -80 you have to make them positive numbers and make an example like this- 80-55=25

Answer:

D.

Step-by-step explanation:

225 greeting cards

25 fathers day cards

How much would be expected to have fathers day cards be bought next year?

___________________________________________________________

Create a proportion of Fathers Day Cards bought and the amount of greeting cards bought.

\(\frac{45}{100} = \frac{x}{225}\)

You then would cross multiply, since we are finding x, let's isolate it. :

\(\frac{45*225}{100 * x}\)

\(10,125 = 100x\)

Divide both sides by 100 :

x = 101.25

We can round this to the nearest tenth, since the ones place is 1. It rounds down.

x = 100

The 90% confidence interval for the difference between the proportions of college graduates and individuals with some college who believe in the theory of evolution is (0.022, 0.220)

The sample size of respondents with some college education is 325, and 133 of them believe in the theory of evolution. The sample size of respondents who were college graduates is 228, and 121 of them believe in the theory of evolution.

Now, the sample proportions are:p1= 133/325 = 0.410p2 = 121/228 = 0.531The point estimate of the difference in proportions is:p1 - p2 = 0.531 - 0.410 = 0.121

To calculate the standard error of the sampling distribution of the difference of two proportions, use the following formula:\($$SE = \sqrt{ \frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}$$\)

Substituting the values, we get,\($$SE = \sqrt{ \frac{0.410(1-0.410)}{325} + \frac{0.531(1-0.531)}{228}}$$\)

Solving the above expression, we get,\($$SE = 0.0489$$\)

Using the formula of the confidence interval,\($$\text{Confidence Interval} = \text{point estimate} ± \text{margin of error}$$\)

Substituting the values,\($$\text{Confidence Interval} = 0.121 ± 1.645 \times 0.0489$$\)

Now, solving the above expression, we get the confidence interval as:\($$(0.022, 0.220)$$\)

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The equation of the javelin path h(t) = -16t^2+68t+6.5 is a quadratic function

The javelin hits the ground after 4.344 seconds

The equation of the javelin path is given as:

h(t) = -16t^2+68t+6.5

When it hits the ground, h(t) = 0.

So, we have:

-16t^2+68t+6.5 = 0

Using a graphing calculator, we have:

t = 4.344 and t = -0.094

Time cannot be negative.

So, we have:

t = 4.344

Hence, the javelin hits the ground after 4.344 seconds

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The following statements are proved using mathematical induction:

(b) Prove that for any positive integer n,6 evenly divides \(7^n -1\).

(c) Prove that for any positive integer n,4 evenly divides \(11^n-7^n\).

(e) Prove that for any positive integer n,2 evenly divides \(n^2-5n+2\).

(b) Prove that for any positive integer n, 6 evenly divides \(7^n - 1.\)

Step 1: Base case

Let's check if the statement holds true for the base case, n = 1.

For n = 1, we have  \(7^1 - 1 = 6\), which is divisible by 6. Therefore, the statement holds true for the base case.

Step 2: Inductive hypothesis

Assume that the statement is true for some positive integer k, i.e., 6 evenly divides  \(7^k - 1\).

Step 3: Inductive step

We need to prove that the statement holds true for the next positive integer, k + 1.

Consider the expression  \(7^{(k + 1)} - 1.\)

We can rewrite it as  \(7 * 7^k - 1.\)

Using the assumption from the inductive hypothesis, we know that \(7^k - 1\)is divisible by 6.

Since 7 is congruent to 1 (mod 6), we have \(7 * 7^k\) ≡ \(1 * 1^k\) ≡ 1 (mod 6).

Therefore,  \(7^{(k + 1)} - 1\) ≡ 1 - 1 ≡ 0 (mod 6), which means 6 evenly divides \(7^{(k + 1)} - 1.\)

By the principle of mathematical induction, we can conclude that for any positive integer n, 6 evenly divides  \(7^n - 1\).

(c) Prove that for any positive integer n, 4 evenly divides  \(11^n - 7^n.\)

Step 1: Base case

For n = 1, we have \(11^1 - 7^1 = 11 - 7 = 4\), which is divisible by 4. Therefore, the statement holds true for the base case.

Step 2: Inductive hypothesis

Assume that the statement is true for some positive integer k, i.e., 4 evenly divides  \(11^k - 7^k.\)

Step 3: Inductive step

We need to prove that the statement holds true for the next positive integer, k + 1.

Consider the expression  \(11^{(k + 1)} - 7^{(k + 1)}.\)

We can rewrite it as  \(11 * 11^k - 7 * 7^k.\)

Using the assumption from the inductive hypothesis, we know that \(11^k - 7^k\) is divisible by 4.

Since 11 is congruent to 3 (mod 4) and 7 is congruent to 3 (mod 4), we have  \(11 * 11^k\) ≡ \(3 * 3^k\) ≡ \(3^{(k+1)}\) (mod 4) and  \(7 * 7^k\) ≡ \(3 * 3^k\) ≡ \(3^{(k+1)}\) (mod 4).

Therefore,  \(11^{(k + 1)} - 7^{(k + 1)}\) ≡ \(3^{(k+1)} - 3^{(k+1)}\) ≡ 0 (mod 4), which means 4 evenly divides  \(11^{(k + 1)} - 7^{(k + 1)}.\)

By the principle of mathematical induction, we can conclude that for any positive integer n, 4 evenly divides \(11^n - 7^n.\)

(e) Prove that for any positive integer n, 2 evenly divides \(n^2 - 5n + 2.\)

Step 1: Base case

For n = 1, we have  \(1^2 - 5(1) + 2 = 1 - 5 + 2 = -2,\)  which is divisible by 2. Therefore, the statement holds true for the base case.

Step 2: Inductive hypothesis

Assume that the statement is true for some positive integer k, i.e., 2 evenly divides  \(k^2 - 5k + 2.\)

Step 3: Inductive step

We need to prove that the statement holds true for the next positive integer, k + 1.

Consider the expression  \((k + 1)^2 - 5(k + 1) + 2.\)

Expanding and simplifying, we get  \(k^2 + 2k + 1 - 5k - 5 + 2 = k^2 - 3k - 2.\)

Using the assumption from the inductive hypothesis, we know that 2 evenly divides  \(k^2 - 5k + 2\).

Since 2 evenly divides -3k, and 2 evenly divides -2, we can conclude that 2 evenly divides  \(k^2 - 3k - 2\).

By the principle of mathematical induction, we can conclude that for any positive integer n, 2 evenly divides  \(n^2 - 5n + 2\).

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The percent error in Jessica's calculation is 4.17%.

To calculate the percent error in Jessica's calculation, we can use the formula:

Percent Error = (|Measured Value - Actual Value| / Actual Value) * 100

Given that Jessica's measured value was 125 seconds and the actual value was 120 seconds, we can substitute these values into the formula:

Percent Error = (|125 - 120| / 120) * 100

Simplifying further:

Percent Error = (5 / 120) * 100

Percent Error = 0.0417 * 100

Percent Error = 4.17%

This means that Jessica's recorded time of 125 seconds differs from the actual time of 120 seconds by approximately 4.17% in relative terms. The positive sign indicates that Jessica's recorded time was greater than the actual time.

Percent error is a way to quantify the discrepancy between a measured value and the true value. It provides a measure of the accuracy of a measurement or calculation, allowing us to understand the degree of error or deviation involved.

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Answer:

Height= 4.5 Volume= 91.125

Step-by-step explanation:

The measure of angle 3 is 115°

Answer:

9) C: x=4, y=2rt3

10) A: XY/YZ

11) A: XY/XZ

Step-by-step explanation:

9 - that is a 30, 60, 90 triangle so the ratios will be a, root3a, 2a

10 - tan = opposite / adjacent

11 - cos = adjacent/hypotenuse

Answer:

9. (c)

10. (a)

11. (a)

................

Answer: 4, 2

Step-by-step explanation:

This is a sine/cosine wave.

we can see one full revolution from 0 to 4; this means that the period is 4.

the amplitude refers to how "high" or "low" the graph goes from its center.

we can see it hits a maximum of 2, (and a minimum of -2). Since the amplitude is the absolute value of this high/low value, it will always be positive. so the amplitude is 2

In conclusion:

Period = 4

Amplitude = 2

Answer:

5

Step-by-step explanation:

Answer:

d i think

Step-by-step explanation:

Answer: C

Step-by-step explanation:

our points are

(0, 64) and (17, 30)

slope = 30-64/17-0 = -34/17 = -2

y=-2x+64 aka C

We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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In regards to question A:

P(G) = 0.2

P(W) = 0.32

P(B) = 0.48

B: we can estimate that the friends will choose approximately 90 glass beads, 144 wood beads, and 216 brass beads if they select a total of 450 beads from the crate.

a. The probability model for choosing a bead can be represented by a discrete probability distribution, where the sample space consists of the three types of beads - glass, wood, and brass - and the probabilities of selecting each type are proportional to their respective frequencies. Let P(G) denote the probability of selecting a glass bead, P(W) denote the probability of selecting a wood bead, and P(B) denote the probability of selecting a brass bead. Then:

P(G) = \(\frac{60}{300}\) = 1 ÷ 5 = 0.2

P(W) = \(\frac{96}{300}\) = 8 ÷ 25 = 0.32

P(B) = \(\frac{144}{300}\) = 12÷ 25 = 0.48

b. To estimate the number of each type of bead that will be chosen if the friends select a total of 450 beads from the crate, we can use the probabilities calculated above to find the expected number of beads of each type. Let X_G, X_W, and X_B denote the random variables representing the number of glass, wood, and brass beads, respectively, that are selected out of the 450 total selections. Then:

E(X_G) = P(G) × 450 = (1 ÷ 5) × 450 = 90

E(X_W) = P(W) × 450 = (8 ÷ 25) × 450 = 144

E(X_B) = P(B) × 450 = (12 ÷ 25) × 450 = 216

Therefore, based on the frequencies in the table, we would expect approximately 90 glass beads, 144 wood beads, and 216 brass beads to be chosen if the friends select a total of 450 beads from the crate.

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Answer:

10cm

Step-by-step explanation:

Assuming the shape is a rectangle since it's already stated that it's a parallelogram, and the area is stated, we can use the Pythagorean theorem to find the length

\(a^{2} +b^2=c^2\), where c will be the length

isolate c

\(c^2=a^2+b^2\)

\(c=\sqrt{a^2+b^2}\)

substitute for a and b

\(c=\sqrt{8^2+6^2}\)

\(c=\sqrt{64+36}\)

\(c=\sqrt{100}\)

\(c=10\)

To find an explicit formula for the nth term of the sequence satisfying\(\(a_1 = 0\) and \(a_n = 2a_{n-1} + 1\) for \(n \geq 2\),\)  we can use recursive formula to generate the terms of the sequence.

Given:

\(\(a_1 = 0\)\\\(a_n = 2a_{n-1} + 1\) for \(n \geq 2\)\)

Using the recursive formula, we can generate the terms of the sequence as follows:

\(\(a_2 = 2a_1 + 1 = 2(0) + 1 = 1\)\\\(a_3 = 2a_2 + 1 = 2(1) + 1 = 3\)\)

\(\(a_4 = 2a_3 + 1 = 2(3) + 1 = 7\)\\\(a_5 = 2a_4 + 1 = 2(7) + 1 = 15\)\)

From the pattern, we observe that the nth term of the sequence is given by \(\(2^{n-2} - 1\).\)

Therefore, the explicit formula for the nth term of the sequence satisfying \(\(a_1 = 0\) and \(a_n = 2a_{n-1} + 1\) for \(n \geq 2\) is: \\\\\a_n = 2^{n-2} - 1.\]\)

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Answer:

18

Step-by-step explanation:

to make one third into a whole you have to mutiply by 3. So 1/3 x 3=1. To make it 6 you would multiply 3 x 6=18. 18 one third cup of servings are in 6 cups.

Since AE ≅FD and AC ≅BD are already given, we need to prove that Angle ADF and Angle CAE are also congruent.

Since we know that AE is parallel to FD and AD is also a straight segment that intersects both AE and FD, this will serve as our transversal segment. In this case, we have Angle ADF and Angle CAE as alternate interior angles. By definition, alternate interior angles are congruent. Hence, ∠ADF and ∠CAE are congruent with the reason that they are alternate interior angles.

From this, we can say that ΔAEC≅ ΔDFB is congruent by SAS Triangle Congruence Theorem stating that if two sides and an included angle are congruent to both triangles, then the two triangles are congruent.

Answer:

b (-1,-4 and (3,4

cgrshysvtdyt

Answer: 221.04 inches squared

Step-by-step explanation: