One year, Alex bought an antique car for his birthday. During the first year he owned it, the
value of the car gained 10%. During the second year, the value of the car gained another
15% from the previous year. If the value of the car is now $37,950.00, how much did Alex
originally pay for his car?

DeMoivre's theorem says

(2 (cos(12°) + i sin(12°)))⁵ = 2⁵ (cos(5×12°) + i sin(5×12°))

… = 32 (cos(60°) + i sin(60°))

… = 32 (1/2 + √3/2 i )

… = 16 + 16√3 i

Answer:

(C) The value of r indicates that the number of sales decreases as the price increases.

ED2021.

The best statement, given the correlation coefficient of -0.63 is: value of r indicates that the number of sales decreases as the price increases.

A negative correlation coefficient has a negative sign, and implies a negative relationship between two variables.

This means that, as one variable decreases, the other variable increases.

Thus, a correlation coefficient of -0.63 shows a negative relationship between prices of smartphones and the number of sales.

Therefore, the best statement, given the correlation coefficient of -0.63 is: value of r indicates that the number of sales decreases as the price increases.

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Answer:

The number of hits would follow a binomial distribution with [tex]n =10,\!000[/tex] and [tex]p \approx 4.59 \times 10^{-6}[/tex].

The probability of finding [tex]0[/tex] hits is approximately [tex]0.955[/tex] (or equivalently, approximately [tex]95.5\%[/tex].)

The mean of the number of hits is approximately [tex]0.0459[/tex]. The variance of the number of hits is approximately [tex]0.0459\![/tex] (not the same number as the mean.)

Step-by-step explanation:

There are [tex](26 + 10)^{6} \approx 2.18 \times 10^{9}[/tex] possible passwords in this set. (Approximately two billion possible passwords.)

Each one of the [tex]10^{9}[/tex] randomly-selected passwords would have an approximately [tex]\displaystyle \frac{10,\!000}{2.18 \times 10^{9}}[/tex] chance of matching one of the users' password.

Denote that probability as [tex]p[/tex]:

[tex]p := \displaystyle \frac{10,\!000}{2.18 \times 10^{9}} \approx 4.59 \times 10^{-6}[/tex].

For any one of the [tex]10^{9}[/tex] randomly-selected passwords, let [tex]1[/tex] denote a hit and [tex]0[/tex] denote no hits. Using that notation, whether a selected password hits would follow a bernoulli distribution with [tex]p \approx 4.59 \times 10^{-6}[/tex] as the likelihood of success.

Sum these [tex]0[/tex]'s and [tex]1[/tex]'s over the set of the [tex]10^{9}[/tex] randomly-selected passwords, and the result would represent the total number of hits.

Assume that these [tex]10^{9}[/tex] randomly-selected passwords are sampled independently with repetition. Whether each selected password hits would be independent from one another.

Hence, the total number of hits would follow a binomial distribution with [tex]n = 10^{9}[/tex] trials (a billion trials) and [tex]p \approx 4.59 \times 10^{-6}[/tex] as the chance of success on any given trial.

The probability of getting no hit would be:

[tex](1 - p)^{n} \approx 7 \times 10^{-1996} \approx 0[/tex].

(Since [tex](1 - p)[/tex] is between [tex]0[/tex] and [tex]1[/tex], the value of [tex](1 - p)^{n}[/tex] would approach [tex]0\![/tex] as the value of [tex]n[/tex] approaches infinity.)

The mean of this binomial distribution would be:[tex]n\cdot p \approx (10^{9}) \times (4.59 \times 10^{-6}) \approx 0.0459[/tex].

The variance of this binomial distribution would be:

[tex]\begin{aligned}& n \cdot p \cdot (1 - p)\\ & \approx(10^{9}) \times (4.59 \times 10^{-6}) \times (1- 4.59 \times 10^{-6})\\ &\approx 4.59 \times 10^{-6}\end{aligned}[/tex].

Step-by-step explanation:

xx is the Roman number of 20

Answer:

Yes D is the correct answer :)

Answer:

Yes, D

Step-by-step explanation:

Answer:

multiply the numerator together and denominator together

Answer:

D) a = - 5/2

Step-by-step explanation:

2x -5y - 7 = 0

5y = 2x - 7

y = 2/5 x - 7

the slope of this line is therefore 2/5 (factor of x).

the perpendicular slope is then (exchange y and x and flip the sign) -5/2, which is then a and the factor of x.

Answer:

Induction produces an electromagnetic field in a coil to transfer energy to a work piece to be heated. When the electrical current passes along a wire, a magnetic field is produced around that wire

Step-by-step explanation:

Answer:

Both ways are correct

If you multiply the cost by 8% and add, you will still get 108% as your total.

Answer:

Both ways are correct

Step-by-step explanation:

Father's way is ( 40 × 0.08 ) + 40 = $43.2

Mothers way is 40 × 1.08 = $43.2

Answer:

We Reject the Null, H0 and conclude that the volume of juice filled by old machine varies more than volume filled by new machine

Step-by-step explanation:

Given the data:

Old machine: 8.2, 8.0, 7.9, 7.9, 8.5, 7.9, 8.1,8.1, 8.2, 7.9

Sample size, n = 10

Using calculator :

s1² = 0.37889.

New machine: 8.0, 8.1, 8.0, 8.1, 7.9, 8.0, 7.9, 8.0, 8.1

Sample size, n = 9

s2² = 0.006111

Hypothesis :

H0 : s1² = s2²

H1 : s1² > s2²

New machine :

s2² = 0.006111 ; n = 9

Using the Ftest :

Ftest statistic = larger sample variance / smaller sample variance

Ftest statistic = 0.37889 / 0.006111

Ftest statistic = 62.0

Decision region :

Reject H0 ; If Test statistic > Critical value

The FCritical value at 0.05

DFnumerator = 10 - 1 = 9

DFdenominator = 9 - 1 = 8

Fcritical(0.05, 9, 8) = 3.388

Since 62 > 3.388 ; Reject H0 and conclude that volume filled by old machine varies more than volume filled by new machine

Answer:

Step-by-step explanation:

x = 0, 1/5

Answer:

1

Step-by-step explanation:

list the numbers that are odd or greater than 2

1,2,3,4,5,6

aka every single outcome

therefore the answer is just 1

Answer:

5/6

Step-by-step explanation:

The possible outcomes are 1,2,3,4,5,6

Odd numbers are 1,3,5

Greater than 2 are 3,4,5,6

Good solutions are 1,3,4,5,6  = 5 outcomes

P( odd or greater than 2) = good solutions / total

                                          = 5/6

Answer:

101 is the answer of the question

Answer:

101 degrees

Step-by-step explanation:

First you add all the percentages

39 + 28 + 30 + 3 = 100%

To find the number of degrees of basketball you multiply 28% by 360 because it’s a circle.

28/100 * 360 = 10,080/100 = 100.8 ~ 101

Answer:

a) 75.8% of students would score less than 550 in a typical year.

b) The comparable standard would be a minimum ACT score of 22.2.

c) 0.0139 = 1.39% probability that a randomly selected student will score over 700 on the SAT math test.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Question a:

SAT, so mean of 480 and standard deviation of 100, that is, [tex]\mu = 480, \sigma = 100[/tex]

The proportion is the p-value of Z when X = 550. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{550 - 480}{100}[/tex]

[tex]Z = 0.7[/tex]

[tex]Z = 0.7[/tex] has a p-value of 0.758.

0.758*100% = 75.8%

75.8% of students would score less than 550 in a typical year.

b. What would the engineering school set as comparable standard on the ACT math test?

ACT, with a mean of 18 and a standard deviation of 6, so [tex]\mu = 18, \sigma = 6[/tex]

The comparable score is X when Z = 0.7. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.7 = \frac{X - 18}{6}[/tex]

[tex]X - 18 = 0.7*6[/tex]

[tex]X = 22.2[/tex]

The comparable standard would be a minimum ACT score of 22.2.

c. What is the probability that a randomly selected student will score over 700 on the SAT math test?

This is 1 subtracted by the p-value of Z when X = 700, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{700 - 480}{100}[/tex]

[tex]Z = 2.2[/tex]

[tex]Z = 2.2[/tex] has a p-value of 0.9861.

1 - 0.9861 = 0.0139

0.0139 = 1.39% probability that a randomly selected student will score over 700 on the SAT math test.

Answer:

Option C. 6.5

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle B = 80°

Side opposite B (b) = 10

Angle C = 40°

Side opposite C (c) =?

We can obtain the value of c by using the sine rule as illustrated below:

b / Sine B = c / Sine C

10 / Sine 80 = c / Sine 40

Cross multiply

c × Sine 80 = 10 × Sine 40

Divide both side by Sine 80

c = (10 × Sine 40) / Sine 80

c = 6.5

Thus, the value of c is 6.5

Answer:

The first three terms in the geometric sequence are 18, 24, 32.

Step-by-step explanation:

A number when added to [tex]x,y,z[/tex] that yields consecutive terms of a geometric sequence is an unknown number [tex]t\in \mathbb{Z}[/tex]

Given

[tex]x = 1, y = 7, z = 15[/tex]

We know

[tex]\alpha _1 = 1+t[/tex]

[tex]\alpha _2 = 7+t[/tex]

[tex]\alpha _3 = 15+t[/tex]

Recall that a geometric sequence is in the form

[tex]\boxed{a_n = a_1 \cdot r^{n-1}}[/tex]

Therefore, once  [tex]\alpha_1, \alpha_2, \alpha_1[/tex] are consecutive terms,

[tex]15+t = (1+t) r^{3-1} \implies 15+t = (1+t) r^2[/tex]

To find the ratio, for

[tex]\dots a_{k-1}, a_k, a_{k+1} \dots[/tex]

we know

[tex]\dfrac{a_k}{a_{k-1}} =\dfrac{a_k}{a_{k-1}} =r[/tex]

Therefore,

[tex]\dfrac{(7+t)}{(1+t)} =\dfrac{(15+t)}{(7+t)} \implies (7+t)^2 = (15+t)(1+t)[/tex]

[tex]\implies 49+14t+t^2=15+16t+t^2 \implies -2t=-34 \implies t=17[/tex]

The ratio is therefore

[tex]r=\dfrac{4}{3}[/tex]

Therefore, the first three terms in the geometric sequence are 18, 24, 32.

Answer:

By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?

By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.

Explanation:

Applying the derivative to f gets us

f(x) = -8x - 3

f ' (x) = -8

The fact that f(x) being linear directly means that the derivative is simply the slope value. No matter what we replace x with, the result is always -8.

Answer:

f'(6) = -8

Step-by-step explanation:

f(x)=-8x-3

First find the derivative of the function

f'(x) = -8

This is a constant so  when x=6 it will be -8

f'(6) = -8

Answer:

3/8

Step-by-step explanation:

The value of 37.5% reduced to the lowest terms is 15/40.

A fraction is written in the form p/q, where q ≠ 0. Fractions are of two types they are proper fractions and improper fractions. Fractions can also be converted into percentages by multiplying them by 100.

We know e can convert percentages into decimals and fractions by dividing the percentage value by hundred.

Given we have to convert 37.5% as a fraction which is,

= 37.5/100.

= 375/1000.

= 75/200.

= 15/40.

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Answer:

y = -3x/2 + 5/2

Step-by-step explanation:

Well, basically what you do is modify it so that y is on one side.

3x+2y = 5

2y = 5-3x

y = (5-3x)/2

y = 5/2 -3x/2

So, the answer is the second option.

Answer:

B

Step-by-step explanation:

3x + 2y = 5

Our goal is this form:

y = mx + b

- move 3x to right anc change its sign

2y = -3x + 5

- divide each member by 2

y = -3/2 x + 5/2

Answer:

????

Step-by-step explanation:

as in y = 4.95 + 3.99 or points? if so just draw a horizontal line at 8.94

Answer:

0.25 = 25% probability that the two brothers will end up in the starting line up

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the players are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Desired outcomes:

Matthew plus another forward from a set of 3.

Tony plus another two guards from a set of 5.

So

[tex]D = C_{3,1}C_{5,2} = \frac{3!}{1!2!} \times \frac{5!}{2!3!} = 3*10 = 30[/tex]

Total outcomes:

Two forwards from a set of 4.

Three guards from a set of 6.

So

[tex]T = C_{4,2}C_{6,3} = \frac{4!}{2!2!} \times \frac{6!}{3!3!} = 6*20 = 120[/tex]

What is the probability that the two brothers will end up in the starting line up?

[tex]p = \frac{D}{T} = \frac{30}{120} = 0.25[/tex]

0.25 = 25% probability that the two brothers will end up in the starting line up

Answer:

might be wrong too

Step-by-step explanation:

hope u like it

10-[5-{6+2(7-7-4)}]=10-[5-{6+2×(-4)}]=10-[5-2]=10-3=7

The measure of the interior angle at vertex E can be determined by using the properties of triangles. In a triangle, the sum of all interior angles is always 180 degrees.

Therefore, to find the measure of the interior angle at vertex E, we need to subtract the measures of the other two angles at vertices A and B from 180 degrees. Let's assume that the measures of the angles at vertices A and B are a and b degrees, respectively. Then, the measure of the interior angle at vertex E can be calculated as follows: Interior angle at vertex E = 180 degrees - (measure of angle at vertex A + measure of angle at vertex B) Now, let's refer back to the given answer choices: A. 50 B. 90 C. 30 D. 150 Without additional information or a diagram, it is not possible to determine the exact measures of the angles at vertices A and B. Therefore, we cannot directly calculate the measure of the interior angle at vertex E. In order to solve this problem, we need more information about the triangle or a diagram that shows the relative positions of the vertices.

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