Given the function f(x) = 3x-7, which of the following represents f -1(x)?

Answer:

g(x)=x-2/x^2-9

If there is more than one value, separate them with commas.

Step-by-step explanation:

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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Answer:$31,500

Step-by-step explanation:

To calculate the total amount Mario will pay, including the loan amount and interest, for the loan from First Bank of Trust, we need to calculate the interest and add it to the loan amount.

The formula to calculate simple interest is:

Interest = (Loan Amount) x (Interest Rate) x (Loan Length)

Let's plug in the values given:

Loan Amount = $25,000

Interest Rate = 6.5% (or 0.065 as a decimal)

Loan Length = 4 years

Interest = $25,000 x 0.065 x 4 = $6,500

Now, let's calculate the total amount Mario will pay:

Total Amount = Loan Amount + Interest = $25,000 + $6,500 = $31,500

Therefore, the total amount Mario will pay, including the loan amount and interest, for the First Bank of Trust loan is $31,500.

The volume of the bag of nuts is the amount of nuts it can contain

The volume of the bag of nuts is 84.78 cubic inches

From the figure, we have the following parameters:

The volume of a cone is calculated using:

V = 1/3 πr^2h

Substitute the known values

V = 1/3  * 3.14 * 3^2 * 9

Evaluate the product

V = 84.78

Hence, the volume of the bag of nuts is 84.78 cubic inches

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Answer:

45 cm

Step-by-step explanation:

perimeter of a square is 4 equal sides. each is therefore 200 cm ÷ 4 = 50 cm each.

if each side is dilated by a factor of 0.9

then 50 cm × 0.9 = 45 cm

Answer:

5

Step-by-step explanation:

if primemenster buy n

the answer is

5

The inequality that represents the value of x is (b)  x > 80

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

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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Answer:

820.341

Step-by-step explanation:

(8.2×10^2)+(3.41×10^-1)​=

(8.2×100)+(3.41×0.1)=

820+0.341=

820.341

Answer:820.341

Step-by-step explanation:

(8.2x10^2)+(3.41x10^-1)

(8.2x10x10)+(3.41 x 1/10)

(8.2x100)+(3.41x0.1)

820+0.341=820.341

Step-by-step explanation:

9/32 or 0.28125

hehhehehehehehhehehehe

Answer:

Hello,

Step-by-step explanation:

\(\dfrac{\dfrac{3}{8} }{\dfrac{3}{4} } =\dfrac{0.375}{0.75}=\dfrac{375}{750} =\dfrac{1}{2} =0.5\\\\--------------------------------\\\\\dfrac{\dfrac{3}{8} }{\dfrac{3}{4} }=\dfrac{3}{8} * \dfrac{4}{3} \\\\\\=\dfrac{4}{8}\\\\=\dfrac{1}{2}\\\\=0.5\\\)

Answer:

Step-by-step explanation:

12nl-4=8 start by adding 4 to both sides.

12nl=12/l Divide both sides by l.

12n=12 then divide both sides by 12.

n=1/l

Answer:

N=625/3

Step-by-step explanation:

1) 0.25 ⋅ 1.44N=75

2) 0.36N=75

3) 0.36N/0.36 = 75/0.36

4) N= 625/3

Hope that helps

Have a good day

The z-scores are approximately -1.73 for part (a), -3.09 for part (b), 5 for part (c), and 10 for part (d).

To find the z-score, we need to use the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

a. M = 8, n = 12

z = (8 - 10) / (2 / √12) ≈ -1.73

b. M = 8, n = 30

z = (8 - 10) / (2 / √30) ≈ -3.09

c. M = 20, n = 4

z = (20 - 10) / (2 / √4) = 5

d. M = 20, n = 16

z = (20 - 10) / (2 / √16) = 10

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The equation that models the relationship between the number of guests, x, and the total charge, y is A. y = 450 + 125x. The base charge for a single guest is $450, and for each additional guest, the charge increases by $125. So, we add 125 times the number of additional guests to the base charge of $450.

The total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.

The interest you receive is referred to as compound interest. Using simple math, you can see how this works: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year.

A = P*(1 + r/n)\(^(^n^*^t^)\)

A is the total amount

P is the principal (initial amount borrowed), which is $1,000 in this case

r is the annual interest rate expressed as a decimal, which is 0.08 (8%)

n is the number of times the interest is compounded per year, which is usually 12 (monthly compounding) or 1 (annual compounding)

t is the time in years, which is 4 in this case

Assuming that the interest is compounded annually (n=1), we can plug in the values and simplify:

A = 1000*(1 + 0.08/1)¹⁴

= 1000(1.08)⁴

= 1000*1.3605

= $1,360.50

the total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.

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For question 4

(A u B)' = {3, 7, 9}

This implies the values that are not in either the spheres of A or B or both but are within the rectangle

For question 3

Recall that A' n B' = (A u B)'

Thus A' n B' = {3, 7, 9}

For question 2

A - B'

A = {1, 2, 4, 5, 8}

B = {0, 2, 4, 6}, then B' = {1, 3, 5, 7, 8, 9}

Thus, A - B' = {2, 4}

For question 1

A' = {0, 3, 6, 7, 9}

B = {0, 2, 4, 6}

A' u B = {0, 2, 3, 4, 6, 7, 9}

Answers:

5)

a.Highest- 96

Lowest-52

b.74

c. 70-80

d. 13

e. 7

6)

a. 89%

b. 51%

c. In the morning(89%)

Answer:

3 : 10

Step-by-step explanation:

2 kg = 2000g

600g peanuts : 2000 cashew nuts

600 : 2000

divide both sides by a common divisor ( 200)

600/200 : 2000/200

3 : 10

Answer:

10140.96 dollars

Step-by-step explanation:

Bob deposits 133 dollars at the end of every mounth in an account paying 5.9 percent interest compounded annually :

We khow that the interest is worth 5.9 percent

we can state :

Let At be the toatl amount after six years

At= 1596*6+94.16*6= 10140.96

Answer:

Step-by-step explanation:

\(\tt 10x+37+9x+1+5x+12=360^o\)

Add like terms:-

\(\tt 10x+9x+5x=360^o+37^o-1^o-12^o\)

\(\tt 10x+9x+5x=\bf 24x\)

\(\tt 360+37-1-12=\bf 384\)

\(\tt 24x=384\)

Divide both sides by 24:-

\(\tt \cfrac{24x}{24}=\cfrac{384}{24}\)

\(\tt x=16^o\)

Now, let's find m∠BCA:-

m∠BCA = 180-(10x-37)

\(\tt 180-(10(16)-37)\)

\(\tt 180-123\)

\(\tt 57^o\)

Therefore, m∠BCA = 57°.

________________________

Hope this helps!

Answer:

-------------------------------

Sum of exterior angles measures is 360°.

Set up the following equation and solve for x:

Find exterior angle measure at vertex C:

We know interior and exterior angles on the same vertex form a linear pair.

Find interior angle at vertex C, the ∠BCA:

The measure of the inscribed angle G in the circle is 85 degree.

An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.

The relationhip between an an inscribed angle and intercepted arc is expressed as:

Inscribed angle = 1/2 × intercepted arc.

Since the circle equals 360 degrees, we can determine the intercepted arc DF.

Hence:

Arc DF = 360 - ( 70 + 120 )

Arc DF = 360 - 190

Arc DF = 170°

Now, plug the value into the above formula:

Inscribed angle = 1/2 × intercepted arc.

Inscribed angle G = 1/2 × 170°

Inscribed angle G = 85°

Therefore, angle G has a measure of 85 degree.

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Answer:

-30 feet

Step-by-step explanation:

it is -30 feet because that one is closest to sea level because -42 feet is -12 feet more than -30 feet. plsss give me brainliest plssss

The probability that two cards will be drawn at random, without replacement, is 13/18.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our answer-

P(at least 1 green) = 1 - P(no green)

P(no green) = draw yellow on both draws

= P(draw yellow on 1st draw) * P( draw yellow on 2nd draw, given draw yellow on 1st draw)

= 5/9 * 4/8 = 20/72 = 5/18

P(at least 1 green) = 1 - 5/18

= 13/18

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No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Answer:

I'm not sure if this is exactly correct but I believe it would be 92%

Step-by-step explanation:

0.92 x 100= 92.

that's it ig

Answer:

1. WX = WY;WV =WZ

2. substitution property

3. SAS similarity theorem

Step-by-step explanation:

Complete steps of the proof are,

4) WX = WY

6) By definition of congruency, Put WZ = WV

9) By SAS congruency.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

Triangle WXY is isosceles with legs WX and WY

And, Triangle WVZ is isosceles with legs WV and WZ.

Now, For the proof of the ΔWXY – ΔWVZ;

The complete sentence of the table are,

4) WX = WY

6) By definition of congruency, Put WZ = WV

9) By SAS congruency.

Thus, Complete steps of the proof are,

4) WX = WY

6) By definition of congruency, Put WZ = WV

9) By SAS congruency.

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Answer:

Step-by-step explanation:

m∠X + m∠Z < 90°

m∠Y > 90°

∠X and ∠Y are complementary

m∠X + m∠Y < 90°