write the expression 22^-2 in simplest form

Step-by-step explanation:

= f(g(x)) = g(f(x))

= f(x - 3) = g(5x)

= 5(x- 3) : 5x - 3

: 5x - 15

Answer:

$32.07

Step-by-step explanation:

I am not sure - are we seeing the full information about this problem ?

because the problem description is strangely vague and confusing, as it uses "total cost" two times for not the same thing ...

either total cost means including tax or not including tax. but it cannot mean both ...

I think the most likely understanding of this problem is that the first price is without tax, and now we need to calculate and add the extra 6% tax to get the really total price to be paid.

I will solve this now based on this assumption.

100% = $30.25

1% = 100%/100 = 30.25/100 = $0.3025

6% = 6×1% = 6×0.3025 = $1.815 ≈ $1.82

the total price is then calculated either by

100% + 6%

or by

106% = 100%×1.06 = 30.25×1.06 = $32.065 ≈ $32.07

in both cases we get the same result, of course.

Answer:

32.171

Step-by-step explanation:

Answer: it has a 20% increase

By definition, a Right triangle is a triangle that has an angle whose measure is 90 degrees (which is also called "Right angle").

You can identify that the triangle STU is a Right triangle, because:

The following is one of the Trigonometric ratios. It's called "Secant":

In this case you can identify that:

Then, substituting values, you get that the answer is:

Answer:

a= 12

Step-by-step explanation:

Use pythagorean theorem

a^2 + b^2 = c^2 where c is the hypotenuse

so 9^2 + a^2 = 15^2

81 + a^2 = 225

a^2 = 144

square root both sides to get a = 12

The money that will remain after he pays back the loan amount and interest is $320.

The cost a company pays a lender (creditor) for a loan is called interest. Although many other arrangements are available, interest payments are typically based on the remaining balance of a loan and paid on a monthly basis.

With he use of basic interest formula supplied.

A= P( 1+r)

A= (3000) + (1+ (00.6))

A= 3000* 1.06

A= 3180

hence $3180 will be due at the end of the year.

Amount remaining =(amount reserved- amount owed).

3500-3180

= $320

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complete question;

At the beginning of the year, Mr. Simms took

out a $3,000 loan from a bank that charges a

simple interest rate of 6%. He plans to save

$3,500, which he will use to pay back the entire

amount of the loan plus interest at the end of

the year.

Exactly how much money will remain after he

pays back the loan amount and interest?

Use: A = P(1 + r)

The Equation of circle is (x-2)² +(y+ 8)² = 7²

The standard form of a circle with center (h, k) and radius r is given by the equation:

(x-h)²  + (y-k)² = r²

In this equation, (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.

In this case, the center of the circle is (2, -8) and the radius is 7.

Plugging these values into the equation, we have:

(x- 2)² + (y- (-8))² = 7²

Simplifying further:

(x-2)² +(y+ 8)² = 7²

So, the equation in standard form for the circle with center (2, -8) and radius 7 is:

(x-2)² +(y+ 8)² = 7²

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Check the picture below.

The monthly payment amount is $217.42 and the finance charge is $413.02.

The payment amount and finance charge can be found by using the formula below

Payment amount formula: PMT = (P x R x (1 + R)^N) / ((1 + R)^N - 1)

Finance charge formula: Finance charge = Total payment - Loan amount

Where P = Loan amount

R = Interest rate per period

N = Number of periods

Given that a loan is made for $4800 with an APR of 12% and payments made monthly for 24 months

Therefore,P = $4800R = 12% / 12 = 1% per month

N = 24

Using the Payment amount formula above: PMT = (P x R x (1 + R)^N) / ((1 + R)^N - 1)

PMT = ($4800 x 0.01 x (1 + 0.01)^24) / ((1 + 0.01)^24 - 1)

PMT = $217.42

Hence, the monthly payment amount is $217.42 (rounded to two decimal places).

Using the finance charge formula above: Finance charge = Total payment - Loan amount

Total payment = Payment amount x Number of periods

Total payment = $217.42 x 24 = $5213.02

Finance charge = $5213.02 - $4800

Finance charge = $413.02

Hence, the finance charge is $413.02 (rounded to two decimal places).

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Answer:

I cannot see the number line mentioned here, but I'll explain how you multiply negative and positive using tiles and number line.

To multiply positive and a negative nunber, for instance, 2(–3), you'll think of it as 2 groups of negative one in three's. Using tiles you have

–1 –1

–1 –1

–1 –1

Two groups of negative one in three's, adding that up we have 6.

Using number line. See 2(–3), for instance, as moving twice in intervals of –3. If I am to multiply that, starting from 0, if I move once, I'll land at –3, if I move one more time, I'll land at –6. Since I am to move twice, that's the required answer.

The simplified expression of the expression given as (62)4 is 248

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

(62)4

Remove the bracket and rewrite the expression as a product expression

So, we have the following representation

(62)4 = 62 * 4

Evaluate the products

This gives

(62)4 = 248

The above expression cannot be further simplified

Hence, the solution is 248

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Answer:

on    e d g e n u i t y 2020, the answer is Set B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

According to the given statement  the value of sin x = 8/10

A mathematical field called trigonometry examines connections between triangles' sides and angles. Due to the fact that every straight-sided shape can be decomposed into a group of triangles, trigonometry can be found throughout all of  geometry.

To roof a home, to make the roof slant (in the case of single-family bungalows), to determine the height of a roof in buildings, etc., use trigonometry. The naval and aviation industries use it. It's applied to cartography (creation of maps). Trigonometry is also used in satellite navigation systems.

sin x = 4/5

We know that:

Sin x = opposite/Hypotenuse.

So,

When the triangle is enlarged, the opposite side will increase to an angle of 8, and the hypotenuse will increase to an angle of 10.

= 4/5 we multiply by 2 with 4 and 5 we get:

= 8/10

4/5 will result from simplifying 8/10. Thus, nothing has changed.

So the value of sin x = 8/10.

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Answer: The 9th term is 41990400

Step-by-step explanation:

As we can see here 25, 150, 900 to find the common ratio i'll divide 150 by 25 which gives me 6

to 25 times 6 is 150

150 times 6 is 900

T=Term

1t=25 2t=150 3t=900 4t=5400 5t=32400 6t=194400 7t=1166400 8t=6998400 9t= 41990400

900*6= 5400

5400*6=32400

32400*6= 194400

194400*6= 1166400

1166400*6= 6998400

6998400*6=41990400

The Type I error in this case would be if we conclude that the mean number of years Americans work before retiring is not 34, when in reality it is 34 years.

In statistical hypothesis testing, there are two different sorts of errors that might happen: type I and type II.

while the null hypothesis is wrongly rejected while it is true, this is referred to as a type I error, also referred to as a false positive.

The null hypothesis is mistakenly accepted when it is wrong, which is known as a type II error, or false negative.

This would mean that we have falsely rejected the null hypothesis (that the mean is 34 years) and made a mistake by assuming that the mean is different than it actually is. The Type II error would be if we conclude that the mean is 34 years, when in reality it is not 34 years. This would mean that we have falsely accepted the null hypothesis and made a mistake by assuming that the mean is the same as it actually is not.

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Answer:

A=314.16cm2

Step-by-step explanation:

A=πr2 this is the formula

Answer:

3.142cm^2

Step-by-step explanation:

A=πr^2

A=3.142×10^2

A=3.142×100cm^2

A=314.2cm^2

I believe you're asking about the one-sided limit,

\(\displaystyle \lim_{x\to-4^-}\frac{|x+4|}{x+4}\)

Recall the definition of absolute value:

• \(|x| = x\) if \(x\ge0\)

• \(|x| = -x\) if \(x < 0\)

Since we're approaching -4 from the left, we're effectively focusing on a domain of \(x<-4\) or \(x+4<0\). So, by the definition above, we have \(|x+4| = -(x+4)\). Then in the limit, we have

\(\displaystyle \lim_{x\to-4^-}\frac{|x+4|}{x+4} = \lim_{x\to-4^-}\frac{-(x+4)}{x+4} = \lim_{x\to-4^-}(-1) = \boxed{-1}\)

The smallest number of minutes that could have passed before the chemical was depleted is 1 minute.

If there are 562mm of the chemical left, we can find out the smallest number of minutes that could have passed by using the formula below;

v = u + at,

where: v = final velocity

u = initial velocity

a = acceleration

t = time

Since we are looking for the smallest number of minutes that could have passed, we will assume that the acceleration of the chemical is 0.

Thus, the formula becomes; v = u + 0 × t = u

Therefore, the velocity is equal to the initial velocity.

Assuming that the initial velocity of the chemical was 562mm of chemical per minute, the smallest number of minutes that could have passed before the chemical was depleted is 1 minute.

If we assume that the rate of depletion is constant, the chemical will be depleted after 1 minute since there is no acceleration.

So, the smallest number of minutes that could have passed before the chemical was depleted is 1 minute.

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Answer:

do like this i think answer is correct

's' and 't' represent free parameters that can take on any real values.

In the given system of equations:

x1 - x2 + 4x3 = -4

6x1 - 5x2 + 7x3 = -5

3x1 - 39x3 = 45

To solve this system, we can use the method of Gaussian elimination or matrix operations. Let's use Gaussian elimination:

Step 1: Write the augmented matrix for the system:

[1 -1 4 | -4]

[6 -5 7 | -5]

[3 0 -39 | 45]

Step 2: Perform row operations to transform the matrix into row-echelon form:

R2 = R2 - 6R1

R3 = R3 - 3R1

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 3 -51 | 57]

Step 3: Perform additional row operations to further simplify the matrix:

R3 = R3 - 3R2

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 0 0 | 0]

Step 4: Write the system of equations corresponding to the row-echelon form:

x1 - x2 + 4x3 = -4

x2 - 17x3 = 19

0 = 0

Step 5: Express the variables in terms of a parameter:

x1 = s

x2 = 19 + 17s

x3 = t

where s and t are parameters.

Therefore, the solution to the system is:

[x1] = [s]

[x2] = [19 + 17s]

[x3] = [t]

In the provided solution format:

[x1] = [s] []

[x2] = [19 + 17s] + s []

[x3] = [t] [__]

Here, 's' and 't' represent free parameters that can take on any real values.

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Given the letters in the word zombies. The number of ways can two of the letters be arranged such that one is a vowel and one is a consonant is 1260 ways.

The number of vowels in English alphabets are 5

The number of consonants are 21

Given the letters in the word zombies.

In the word zombies, the number of vowels are 3 and the number of consonants are 4

The number of ways can two of the letters be arranged such that one is a vowel and one is a consonant can be calculated by permutations and combinations.

The word zombies has 7 letters and the number of vowels are 3 and the number of consonants are 4

Number of ways can two of the letters be arranged such that one is a vowel and one is a consonant is (7! )/(4!)(3!) = 1260 ways.

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If you want to guarantee that two cards are from the same suit, you need only draw five cards (since there is no way you can draw five cards without at least two of them being the same suit)

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

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Answer:

Step-by-step explanation:

4) A photograph costs $20, so the cost of x photographs is 20x.

Similarly, the cost of y prints is $25.

So the total cost is 20x+25y, and this has to be less than or equal to 400, so C.

5) just plug each pair in.

For example for the first option, x=5 and y=10, and since 20(5)+25(10)=100+250. which is less than or equal to 400, it works.

The statement "cross-tabulation can only be used for two variables; each variable must have well-defined labels " is false

The cross tabulation is defined as the tool that is used in statistics to categorical data. We can also says that  that present the results of the entire group of respondents

The given statement is "cross-tabulation can only be used for two variables; each variable must have well-defined labels "

The cross tabulation method can be used to represent two or more variables. The cross tabulation table has x axis as one variable and y axis as another variables

The cross tabulation can be used for two or more variables

Therefore, the the given statement is false

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A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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Answer:

10(6)

Step-by-step explanation:

Hope it's right.....

The first step in solving the first equation is different from the first step of solving the second equation because,

In the first equation, start by squaring both sides to eliminate the radical, but in the second equation, start by adding 1 to both sides to isolate the radical.

Thus the option B is the correct option.

Algebraic expression are the expression which consist the variables, coefficients of variables and constants.

The algebraic expression are used represent the general problem in the mathematical way to solve them.

Given information-

The first equation given in the problem is,

\((x-1)^2=8\)

The above equation can be solve using the algebraic formula of whole square of two number as,

\((x-1)^2=8\\x^2+1^2-2x=8\\x^2-2x-8+1=0\\x^2-2x-7=0\)

The first equation can be solved by putting square root both side as,

\(\sqrt{(x-1)^2}=\sqrt{8}\\(x-1)=\sqrt{8}\\x=2\sqrt{3}+1\)

The second equation given in the problem is,

\(x^2-1^2=8\)

The above equation can be solve using the algebraic formula of difference of the square of two number as,

\(x^2-1=8\\x^2=8+1\\x^2=9\\x=\pm3\)

Hence, The first step in solving the first equation is different from the first step of solving the second equation because,

In the first equation, start by squaring both sides to eliminate the radical, but in the second equation, start by adding 1 to both sides to isolate the radical.

Thus the option B is the correct option.

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Answer:

B.

Step-by-step explanation:

Correct on Edgen. (2022)

The value x, in the joint variation, when w = 8 and y = 3/15, is calculated as: x = 8.

The formula for joint variation if x varies jointly with w and y, is:

x = kwy, where k is the constant of variation.

To solve for k, we can use the initial condition where x = 20 when w = 2/5 and y = 10:

20 = k(2/5)(10)

Simplifying, we get:

20 = 4k

Divide both sides by 4:

20/4 = 4k/4

k = 5

Now that we know k, we can use it to solve for x when w = 8 and y = 3/15:

x = (5)(8)(3/15)

Simplifying, we get:

x = 8

Therefore, when w = 8 and y = 3/15, the value of x is 8.

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Complete Question:

Given: x varies jointly with w and y. If x = 20 when w = 2/5 and y = 10, what is the value of x when w = 8 and y = 3/15?

Answer:

X=0 or no solution

Step-by-step explanation:

-2x+4=-3x+4

cancel equal terms on both sides of the equation

-2x=-3x

move the variable to the left-hand side and change its sign

-2x+3x=0

collect like terms

x=0