scores on the act college entrance exam follow a bell-shaped distribution with mean 21 and standard deviation 5. wayne’s standardized score on the act was −0.6. what was wayne’s actual act score?

Answer:

Step-by-step explanation:

A squiggly line can refer to a variety of different shapes or patterns. To create an equation using cosine that resembles a squiggly line, you can use a combination of sine and cosine functions with different frequencies and amplitudes. Here's an example equation that produces a squiggly pattern:

y = A * cos(B * x) + C * sin(D * x)

In this equation, A, B, C, and D are constants that you can adjust to modify the shape and characteristics of the squiggly line. By experimenting with different values for these constants, you can create various squiggly patterns. Keep in mind that the specific equation may vary depending on the exact shape and features you have in mind for the squiggly line.

The required angular speed of the propeller in 4000 rev per min π radians per sec is approximately 133.333 radians per second.

Given that a 80-horsepower outboard motor at full throttle will rotate its propeller at exactly 4000 revolutions per min.

We need to find the angular speed of the propeller in 4000 rev per min π radians per sec

.To find the angular speed of the propeller in 4000 rev per min π radians per sec, we know that1 revolution = 2π radiansTherefore,4000 revolutions

= 4000 × 2π radians

= 8000π radians

∴ Angular speed of propeller in 4000 rev per min π radians per sec

= (8000π radians/minute)/(60 sec/minute)

= (8000π/60) radians per second

= 133.333 radians per second (approx)

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Answer:

Step-by-step explanation:

You can have an infinite number of ratios are equivalent to 3:8 if you multiply this fraction by a fraction equivalent to   1 ( for example 2/2   3/3   4/4....)

3/8 x 2/2 = 6/16

3/8 = 0.375

6/16= 0.375

Answer:the other person got to it before me

Step-by-step explanation:

So, the teacher can give out the jerseys in 840 ways.

The teacher wants to divide the 12 students into 3 teams, each with at least one girl and one boy.

One possible way to count the number of ways to divide the students is to use the stars and bars method.

For the first team, we have 5 stars and 2 bars, so the number of ways to pick 6 students is:

(5+2)!/(5!2!) = 7

For the second team, we have 4 stars and 1 bar, so the number of ways to pick 6 students is:

(4+1)!/(4!1!) = 5

For the third team, we have 3 stars, so the number of ways to pick 6 students is:

(3+0)!/(3!0!) = 4

Then we can multiply the number of ways to pick students for each team together to find the total number of ways to divide the students:

7 * 5 * 4 = 140

Then, as the jerseys are indistinguishable, we just have to multiply the number of ways to divide the students by the number of ways to distribute jerseys:

140 * 3! = 840

Therefore, the teacher can give out the jerseys in 840 ways.

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Answer:

\($\frac{5\sqrt{2} }{2}$\)

Step-by-step explanation:

\(x: \text{opposite side of the angle of 45\º}\)

\(5: \text{hypotenuse of the right triangle}\)

\($\sin(\theta)=\frac{\text{opp}}{\text{hyp}} \Rightarrow \sin(45\º)=\frac{x}{5} $\)

\($\text{Once }\sin(45\º)=\frac{\sqrt{2} }{2} $\)

\($\frac{\sqrt{2} }{2} =\frac{x}{5} \Rightarrow 2x=5\sqrt{2} \Rightarrow x=\frac{5\sqrt{2} }{2} $\)

You can just remember that 5 is the diagonal of a square of side length x.

\($5=x\sqrt{2} \Rightarrow x=\frac{5}{\sqrt{2} } \Rightarrow x=\frac{5}{\sqrt{2} } \cdot \frac{\sqrt{2} }{\sqrt{2} } = \frac{5\sqrt{2} }{2} $\)

Answer:

Not 100% sure if this is correct but wouldn't it be 8%? because there is a 4% interest rate and its 2 years. 4%+4%=8%. let me know if I'm wrong...

What is the domain of the set of ordered pairs above

c {-1 ,0, 5, 10}

Answer:

c {-1 ,0, 5, 10}

Step-by-step explanation:

The statements which are true regarding the students whose results on 9 tests are as shown are; The median of Nadia's data is equal to the median of Ben's data.

Nadia had the highest score on a test.

According to the task content, it follows that the results of the students in discuss are indicated by means of a box plot as in the attached image.

Consequently, it follows from observation that the median of Nadia and Ben as indicated in the attached box plot is 92 in both cases as indicated by the vertical line in both boxes.

Additionally, the highest score by Nadia is 100 while that for Ben is; 99.

Hence, Nadia had the highest score on a test.

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Answer:

? that makes no sense

Step-by-step explanation:

Answer:

n × 6 + 17 ≤ 21

Answer:

the value to be written is -2

Step-by-step explanation:

The first thing we will do here is to set the divisor equals to zero

The divisor is the denominator

Thus, we have x + 2 = 0

This indicates that x = -2

The term to be written in front of the coefficients is -2

Answer:

73.75

Step-by-step explanation:

comment and heart if this was helpful

For a taxable income of $1,80,900, the effective tax rate is 21.11%.

Marginal tax is the tax rate applied to an individual’s last dollar of income. It is the additional tax that must be paid on any additional income earned. In other words, it is the tax rate that applies to an individual’s income after all deductions. For example, if an individual’s income is $50,000 and the marginal tax rate is 25%, then the individual must pay an additional $12,500 in taxes on top of the $25,000 in taxes already paid on their $50,000 income.

Marginal tax rates are progressive, meaning that as an individual’s income increases, the marginal tax rate will increase as well. The marginal tax rate is important to understand because it helps individuals determine how much additional income they will need to earn in order to make up for the taxes they will have to pay on that income. It is also important to understand how marginal tax rates can affect tax planning strategies.

To determine the effective tax rate for a taxable income of $180,900, calculate the sum of the marginal tax rates for each tax bracket that the $180,900 falls into. The taxable income of $180,900 is greater than $89,075 and less than $170,050. The marginal tax rates for these two tax brackets are 22% and 24%, respectively. The sum of the marginal tax rates is 46%. Divide the sum by the taxable income of $180,900 to get the effective tax rate of 21.11%. Round the final answer to the nearest hundredth to get 21.11%.

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Answer:

D is correct but this is the math section, please put these in the history section

Answer:

Looks good to me

Step-by-step explanation:

"The Court took the position that school officials could not prohibit only on the suspicion that the speech might disrupt the learning"

The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

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Answer:

28

Step-by-step explanation:

3x² - 2x + 7

→ Substitute x = 3

3 × 3² - 2 × 3 + 7 ⇔ 3 × 9 - 6 + 7 ⇔ 27 - 6 + 7 ⇔ 21 + 7 ⇔ 28

The pair of equations whose lines are perpendicular is (d) y = 1/6x + 3; y = -6x - 3

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

The pair of equations

By definition;

The slopes of perpendicular lines are opposite reciporcals

So, we have

(a) -1/3 and -3 false

(b) -3 and -6 false

(c) 3 and 3 false

(d) 1/6 and -6 true

Hence, the equations are (d) y = 1/6x + 3; y = -6x - 3

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Answer:

387 i think

i just divided 1162 by 3

Answer:

P ≈ 43.6 cm

Step-by-step explanation:

the perimeter (P) is the sum of the 2 radii and the arc

arc length = circumference of circle × fraction of circle

                 = 2πr × \(\frac{135}{360}\)

                 = 2π × 10 × 0.375

                 = 20π × 0.375

                 ≈ 23.6 cm ( to 1 decimal place )

Then

P = 23.6 + 10 + 10 = 43.6 cm

Answer:

13

Step-by-step explanation:

∠Q ≅ ∠ P ⇒ RP = RQ = 13

{(2, -1), (4, -2), (6, -3), (8, -4)}

In this relation, each point has a unique x coordinate. None of the x coordinates repeat themselves.

For something like choice A, we have x = 1 repeated. The input x = 1 leads to multiple outputs (y = 1 and y = 0 simultaneously).

The same situation happens in choice C also. This time x = 1 and x = 2 repeat themselves.

Choice D has x = 3 and x = 4 repeat themselves.

A function is only possible if each x input leads to exactly one y output.

average rate of change = -1

Average rate of change formula:

The range is from 1 to 3.

b= 3, a = 1

From the given function, x is greater than 1 when f(x) = -x + 2

when x = 3

f(3) = -3 + 2 = -1

when x = 1

f(1) = -1 + 2 = 1

Answer:

they're are more cows than chickens, they're less chickens than cows, the number of cows is 25 more than the number of chickens

Step-by-step explanation:

hope this helped love!

Answer:

49 degrees

Step-by-step explanation:

the answer is 49 degrees

Answer:

15 deg

Step-by-step explanation:

Sine and cosine are co-functions, so

sin x = cos(90 - x)

sin 25 = cos(90 - 25)

sin 25 = cos 65

y + 50 = 65

y = 15

Answer:

-15/16

Step-by-step explanation:

Both of the 7/16's cancel each other out.

Answer:

7/15

Step-by-step explanation:

easy as 1 2 3 na na naaaaaa he he he

Answer:

• Account A has a principal of $100

• Account B has a principal of $700

• Account B earned you the most interest in the first month.

Explanation:

Account A

• Simple Interest = $0.95

• Time = 3 months = 3/12 years

• Interest Rate=3.8%

We know that:

Account B

• Simple Interest = $21

• Time = 15 months = 15/12 years

• Interest Rate=2.4%

We know that:

Next, we determine the account that earned you the most interest in the first month.

Account A (Interest in the First Month)

Account B (Interest in the First Month)

We see that Account B earned you the most interest in the first month.

Speed is the change of distance per unit time

The ball will be rolling at a rate of about 10 inches per minute after 18 minutes.​

The function that represents the speed of the ball is given as:

\(f(x) = 1.1(1.13)^x\)

At the 18th minute, it means that:

\(x = 18\)

So, we substitute 18 for x in f(x)

\(f(18) = 1.1(1.13)^{18\)

Evaluate the above expression

\(f(18) = 9.92\)

Approximate

\(f(18) = 10\)

Hence, the ball will be rolling at a rate of about 10 inches per minute after 18 minutes.​

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Answer:

The probability that fewer than 60 false alarms are received is 0.0643.

Step-by-step explanation:

Let X denote the number of false alarms received at a certain fire station in a year.

The mean rate of false alarms in a day is 0.20.

Then the mean rate of false alarms in a year will be: \(365\times 0.20=73\).

Then the random variable X follows a Poisson distribution with parameter λ = 73.

The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large.

If X follows Poisson (λ) and λ is large then the distribution of X can be approximated but he Normal distribution.

The mean of the approximated distribution of X is:

μ = λ

The standard deviation of the approximated distribution of X is:

σ = √λ

Thus, if λ is large, then X follows N (μ = λ, σ² = λ).

Compute the mean and standard deviation of X as follows:

\(\mu=\lambda=73\\\\\sigma=\sqrt{\lambda}=\sqrt{73}=8.544\)

Compute the probability that fewer than 60 false alarms are received as follows:

\(P(X<60)=P(\frac{X-\mu}{\sigma}<\frac{60-73}{8.544})\)

                  \(=P(Z<-1.52)\\\\=0.06426\\\\\approx 0.0643\)

Thus, the probability that fewer than 60 false alarms are received is 0.0643.

Chance is a term used to represent the percentage of time a specific result is expected to occur when the same basic procedure is repeated over and over again, where each repetition is independent.

Chance is a term that is used to describe the probability that a certain outcome will occur given a set of fundamental instructions repeated again with each repetition being independent.

Ultimately, this means the number of times a result of an event occurs when repeated over a number of times is chance.

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The probability that at least one of the selected chips is defective is approximately 0.7852.

To find the probability that at least one of the selected chips is defective, we can use the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring. In this case, the event we are interested in is "at least one of the chips is defective". To find the probability that a randomly selected chip is not defective, we can use the fact that the probability of a chip being defective is 0.02. Therefore, the probability that a chip is not defective is: P(not defective) = 1 - P(defective) = 1 - 0.02 = 0.98. Since we are selecting 444 chips for inspection and assuming that the chips are independent, the probability that none of the chips are defective is: P(none defective) = (0.98)^444

Using the complement rule, the probability that at least one of the selected chips is defective is: P(at least one defective) = 1 - P(none defective)

= 1 - (0.98)^444

= 0.7852 (rounded to four decimal places)

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According to the recursive formula, the value of f(6) is 243.

A mathematical rule that takes one or more inputs, runs a series of operations on them, and produces a single output is known as a function. To put it another way, a function is a mapping between an input and an output in which there is only one output for each input.

Using the given recursive formula, we can find the value of f(6) by repeatedly applying the formula until we reach the desired value.

f(1) = 1 and

f(n)=3f(n−1)           (given in the question)

f(2) = 3f(1) = 3(1) = 3

f(3) = 3f(2) = 3(3) = 9

f(4) = 3f(3) = 3(9) = 27

f(5) = 3f(4) = 3(27) = 81

f(6) = 3f(5) = 3(81) = 243

Therefore, the value of f(6) is 243.

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Question-

If f(1) = 1 and f(n) = 3f(n−1) then find the value of  f(6).