The graph of the Function F(x) is shown below. What is the value of f^-1(1)

Answer:

original number:  27

reversed number:  72

Step-by-step explanation:

Let the tens place digit = a

Let the units place digit = b

⇒ Original two-digit number = 10a + b

⇒ Reversed two-digit number = 10b + a

If the reversed two-digit number is 9 less than 3 times the original number:

⇒ 10b + a = 3(10a + b) - 9

⇒ 10b + a = 30a + 3b - 9

⇒ 7b = 29a - 9

If the different of the two numbers is 45 (and the reversed number is larger than the original number):

⇒ (10b + a) - (10a + b) = 45

⇒ 10b + a - 10a - b = 45

⇒ 9b -9a= 45

⇒ 9(b - a)= 45

⇒ b - a= 5

⇒ b = 5 + a

Substitute  b = 5 + a  into  7b = 29a - 9  and solve for a:

⇒ 7(5 + a) = 29a - 9

⇒ 35 + 7a = 29a - 9

⇒ 44 = 22a

⇒ a = 2

Finally, substitute the found value of a into  b = 5 + a  and solve for b:

⇒ b = 5 + 2 = 7

Therefore,

Answer:

Part A)  Option c) 15.27 mm

Part B)   Option b) 12.05 mm

Step-by-step explanation:

The mean is also sometimes called the average

To find the mean, you add up every number in the data set, and you divide that sum by the total number of data points within the set.

A) What is the mean rainfall for the highland storms?

The sum of the data of Highlands storms

= 2*2 + 3*4 + 2*6 + 3*8 + 4*10 + 3*12 + 4*14 + 5*16 + 5*18 + 4*20 + 2*22 + 24 + 2*26 + 2*28 + 30 + 32 = 672

the total number of data = 44

Mean = 672/44 = 15.27 mm

So, the answer is option c) 15.27 mm

B) What is the mean rainfall for the lowland storms?

The sum of the data of Lowland storms

= 3*2 + 5*4 + 3*6 + 3*8 + 5*10 + 7*12 + 6*14 + 4*16 +2*18 + 20 + 2*22 + 24 + 2*28 = 530

the total number of data = 44

Mean = 530/44 = 12.05 mm

So, the answer is option b) 12.05 mm

Answer:

30 and 26

Step-by-step explanation:

Answer: I think it's 30km per hour.

Step-by-step explanation:

So first you have to find what speed the cyclist is going per hour. So first I did 90/3 and that gave me 30.

Answer:

f(x) = 3x^2 + 2

Step-by-step explanation:

Answer:

A quart is a little less then a liter

Step-by-step explanation:

An easy way to figure out liters to gallons, is that a quart is a little less than a liter and 4 liters is a little more than 1 gallon. To be exact, 1 liter is 0.264 gallon (a little more than a quart), and 4 liters is 1.06 gallons.

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Hope this helps you!

Answer:

A quart is a little less than a liter and 4 liters is more than 1 gallon. To be exact, 1 liter is 0.264 gallons (a little more than a quart), and 4 liters is 1.06 gallons.

Step-by-step explanation:

The new statement becomes "If the dog jumps in the lake, then it can't come in the house".

Legal syllogism is a legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.

We have a statement:

R → S: If the dog jumps in the lake, then it gets wet.

S > T: If the dog gets wet, then it can’t come in the house.

After applying the law of syllogism to form a new statement:

R→T:

If the dog jumps in the lake, then it can't come in the house.

Thus, the new statement becomes "If the dog jumps in the lake, then it can't come in the house".

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The area of the shaded region is [tex]154cm^2[/tex]

The formula for solving the area of a circle is:

[tex]\pi r^2[/tex]

Where [tex]\pi[/tex]= 3.14

r= 7cm

To find the area, we would input the values together

[tex]3.14 * 7^2[/tex]

= 3.14 * 49

= 153.86cm^2

Rounded to the nearest tenth would be:

154cm^2

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$16000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &5 \end{cases} \\\\\\ A=16000\left(1+\frac{0.05}{2}\right)^{2\cdot 5}\implies A=16000(1.025)^{10}\implies A\approx 20481.35[/tex]

$16000 for five years at 5% APR compounded semiannually gives an interest of 4481 dollars.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest compounded semiannually is,

A = P[1 + (r/2)/100]²ⁿ.

Where, A = amount, P = principle, r = rate and n = time in years.

Given,  $16,000 is deposited for five years at 5 % compounded semiannually.

A = 16000[1 + (5/2)/100]²ˣ⁵.

A = 16000[1 + 0.025]¹⁰.

A = 16000[1.025]¹⁰.

A = 16000×1.28.

A = 20481.

So, the interest earned is (20481 - 16000) = 4481 dollars.

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Answer:

3800

Step-by-step explanation:

Half way between 3700 and 3900

Answer:

3800

Step-by-step explanation:

it's plotted on the line between 3700 and 3900 and 3800 would be in the middle

Answer:

[tex]d > 12[/tex]

Step-by-step explanation:

[tex]23+d > 35[/tex]
[tex]d > 12[/tex] (subtract 23 on both sides)

If the first term is 25 and the common difference is 4. Then the 97th term of the sequence will be 409.

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

The sequence is given below.

25, 29, 33, ...., so on

Then the first term is 25. And the common difference is 4.

Then the 97th term will be given as

[tex]\rm a_n = a + (n - 1)d[/tex]

where

n = 97

a = 25

d = 4

Then we have

a₉₇ = 25 + (97 - 1)4

a₉₇ = 25 + 96 x 4

a₉₇ = 25 + 384

a₉₇ = 409

Then the 97th term of the sequence will be 409.

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Using the normal distribution, it is found that 25.14% of the batteries will last more than 420 hours.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

In this problem, we have that the mean and the standard deviation are given, respectively, by:

[tex]\mu = 400, \sigma = 30[/tex].

The proportion of the batteries will last more than 420 hours is one subtracted by the p-value of Z when X = 420, hence:

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

[tex]Z = \frac{420 - 400}{30}[/tex]

Z = 0.67

Z = 0.67 has a p-value of 0.7486.

1 - 0.7486 = 0.2514.

0.2514 = 25.14% of the batteries will last more than 420 hours.

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The area of the first, second, third, and fourth circles will be 56.72 cm², 36.3 ft², 167.33 m², and 188.6 yd² respectively.

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

Then the radius and diameter are given below.

[tex]\rm r_1 = 4 \dfrac{1}{4} = \dfrac{17}{4} = 4.25 \ cm\\\\\\r_2 = \dfrac{d}{2} = \dfrac{6\frac{4}{5}}{2} = \dfrac{34}{10} = 3.4 \ ft\\\\\\r_3 = \dfrac{d}{2} = \dfrac{14.6}{2} = 7.3 \ m\\\\\\r_4 = 7\dfrac{3}{4} = \dfrac{31}{4} = 7.75 \ yd[/tex]

Then the area of the circle is given as

Area = π × r²

Then the area of the first circle will be

Area = π × r₁²

Area = 3.14 × 4.25²

Area = 56.72 square cm

Then the area of the second circle will be

Area = π × r₂²

Area = 3.14 × 3.4²

Area = 36.3 square ft

Then the area of the third circle will be

Area = π × r₃²

Area = 3.14 × 7.3²

Area = 167.33 square m

Then the area of the fourth circle will be

Area = π × r₁²

Area = 3.14 × 7.75²

Area = 188.6 square yd

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Need mas

Find volume

Mass

As volume is same

Divide their densities to find ratio

Answer:

Problem 21:

Slope = -3
y-intercept = (0, 7)

Problem 23:

Slope = 1
y-intercept = (0, -2)

Problem 22:

Slope = [tex]\frac{2}{3}[/tex]
y-intercept = (0, 1)

Step-by-step explanation:

In the slope formula, the coefficient of x (the number times x) is the slope. The number added or subtracted from it is the y-intercept.

In problem 21, -3 is the coefficient of x, so thats the slope. 7 is what's being added, so that is the y-intercept.

In problem 23, 1 is the coefficient of x (a singular x is the same as 1, or -1 if the variable is negative), so thats the slope. -2 is what's being subtracted, so that is the y-intercept.

In problem 22, [tex]\frac{2}{3}[/tex] is the coefficient of x, so thats the slope. 1 is what's being added, so that is the y-intercept.

hope this helps!

Answer:

Below in bold.

Step-by-step explanation:

m < 3 = 59 degrees (alternate angles)

m < 2 = 180 - 59 = 121 degrees  ( adjacent angles)

Answer:

3pi/4

Step-by-step explanation:

can't really explain it that well, but I sure hope this helps!! :)

Answer:

26 in.

Step-by-step explanation:

» Concepts

The perimeter for a shape is the total distance around it measured in units. The formula to find the perimeter of a trapezoid is a + b + c + d, where a & b are the bases, and c & d are the lengths of the other sides.

» Solution

Adding up all the sides, we get:

26 inches

Answer:

I think it's y - 21 = 4 (x - 1)

Step-by-step explanation:

im sorry if it's wrong

Answer + Step-by-step explanation:

y = 2x + 1 represents a linear function then the its graph is a line

To draw the line we have to determine two points that lie on that line

If x = 0 → y = 2(0) + 1 = 1 then the point A(0,1) lies on the line

If x = 2 → y = 2(2) + 1 = 5 then the point B(2,5) lies on the line

Now all we have to do is joining the points A and B with a line

The line AB represents our graph

Answer:

I got -x/2+1/2. I'll get back to you in a lil bit.

Y = 1 - 2x

-1

y-1 = - 2x

÷ -2

y-1/-2 = x

f-1(x) = x - 1/-2

Let's make x = 7

7-1/-2 = - 3

Or

y = 1 - 2x

+2x

y + 2x = 1

-y

2x = 1-x

÷2

x. = 1-x/2

f-1(x) = 1 - x/2 is your answer

Let's make x=7

1-7/2 = - 3

Hope this helps!

Answer:

it's 4,8,8

Step-by-step explanation:

hope it helps

Answer:

6:1

Formula for this equation

Divide by 4

24 ÷ 4 = 6

4 ÷ 4 = 1

Answer:

A. is the correct answer tnx to the points

The function f(x) = 1/[(x-1)(x+4)] is a rational function with two vertical asymptotes and one horizontal asymptote, which is graphed below.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The function f(x) = 1/[(x-1)(x+4)] is a rational function with two vertical asymptotes and one horizontal asymptote.

The vertical asymptotes occur when the denominator, (x-1)(x+4), is equal to zero. This happens when x = 1 or x = -4.

Therefore, the graph will have two vertical asymptotes at x = 1 and x = -4.

The horizontal asymptote can be found by looking at the behavior of the function as x approaches positive or negative infinity. As x gets very large in either direction, the terms (x-1) and (x+4) become insignificant compared to x².

Hence, the correct option is (B) f(x) = 1/[(x-1)(x+4)].  

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Answer:

Step-by-step explanation:

4. Nicole can make 7 quarts of lemonade with 10 cups of sugar.

If 3/4 cup of sugar is used to make 1 quart of lemonade and 10 cups of sugar are available, then you multiply 3 times 10 (when multiplying fractions, you only multiply with the numerator, not the denominator) which will give you 30.

Now, you can write it as 30/4. Using simple division, you find that 30/4 is 7.5 (or 7 and 1/2), and because we're trying to find how many full quarts we can make using 10 cups of sugar, your answer will be 7.

5. Each person will get 0.83 repeating (or 5/6) boxes of raisins.

In this problem, we have 6 people and we have to share 5 boxes of raisins among all of them. We know that each person can't get 1 because there would have to be 6 boxes (1 for each person), so we have a fraction (or decimal, depending on where you're at).

Dividing 5/6, you'll simply get 5/6 because you can't simply this any further, but if you were to write this as a fraction, you'd get 0.83 repeating (over the 3).

6. Each class will receive 30 boxes of cracker jacks.

We know that there are 153 boxes of cracker jacks available, and this needs to then be split among 5 different classes. So, to find the answer, we have to divide 153 by 5. In doing that, we get 30.6, but because we're trying to find the whole number that the classes will receive, as you can't get a fraction of a box (at least, I assume), then each class will get 30 with 3 boxes remaining.