A $17,000 deposit in an account with an APR of 3.5%. The balance in the account after 20 year is approximately

Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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Answer:

3 3/4

Step-by-step explanation:

3.75 square ft per hr.

5/8 x 6 = 3.75

Answer:

1/3

Explanation:

P(Freshman | Boy)

⇒ Probability = Number of favorable outcomes ÷ Total number of possible outcomes

Answer:

\(\sf \dfrac13\)

Step-by-step explanation:

From the table:

\(\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}\)

\(\sf \implies P(Boy)=\dfrac{12}{30}\)

\(\sf \implies P(Freshman \cap Boy)=\dfrac{4}{30}\)

\(\begin{aligned}\sf P(Freshman|Boy) & = \sf\dfrac{P(Freshman \cap Boy)}{P(Boy)}\\\\ & = \sf\dfrac{4}{30} \div \dfrac{12}{30}\\\\ & = \sf\dfrac{4}{30}\times \dfrac{30}{12}\\\\ & = \sf \dfrac{4}{12}\\\\ & = \sf\dfrac{1}{3}\end{aligned}\)

Sorry if I didn't understand the question right-

Answer:

\(\frac{49}{6}\)

Step-by-step explanation:

The inverse of \(\frac{3}{7}\) is \(\frac{7}{3}\).

The inverse of \(\frac{2}{7}\) is \(\frac{7}{2}\).

Now we multiply:

\(\frac{7}{3}\) × \(\frac{7}{2}\) = \(\frac{49}{6}\)

Hope this helped :)

Answer: \(f^{-1} (x) = \sqrt{x} +1\)

Step-by-step explanation:

\(y = x^2 - 2x + 1\)

We know straight away the inverse will be a square root function. We also know that this inverse will have a restriction on the domain, (because you can only take the square root of a positive number).

So, to find the inverse, first we'll switch the x and y and solve for y:

\(x = y^2 - 2y +1\)

\(x = (y-1)^2\), (factor!)

±\(\sqrt{x} = y - 1\)

So, the inverse "function" is:

\(f^-1(x)\) = ±\(\sqrt{x} +1\)

But theres an issue here!

If we tried graphing this, this "function" would not pass the vertical line test, so its not really a function at all!

We need to restrict the domain to only include the values that are above the x axis.

So our final inverse function is:

\(f^{-1} (x) = \sqrt{x} +1\)

Answer:

50°

Step-by-step explanation:

Given that a triangle measures 180°.

∠U =40°

∠W=90°

Sum:130°

180°-130°=50°

The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

y - 3 = 1(x - (-1))

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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Answer:

Step-by-step explanation:

Set notation { } is used in this case, to represent the domain and the range.

The values that go into T are the domain while the values that come out of T are the range.

The domain comprises all x (independent) values while the range comprises all y (dependent) values.

This should be applied in the clear definition of the relation T.

To get the fractions that we can add together to give us 8, we will subtract a random fraction from 8.

Let us subtract 5/3 from

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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If he wants an average of 84, he needs to get at least 93 points.

Remember that the average value between 3 values A, B, and C is:

(A + B + C)/3

Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:

(76 + 83 + x)/3 = 84

159 + x = 252

x = 252 - 159

x = 93

So he needs to get at least 93 points in the next exam.

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Answer:

2+7t

Step-by-step explanation:

combine like terms

t+2+6t

2+7t

For one to isolate the variable by using equation rules. Inverse inequality sign if multiplying/dividing by negative. Steps to isolate variable in inequality: Simplify, move constants with inverse operations. Divide coefficient to isolate variable. Reverse direction if using negative number.

Inequalities require you to apply the same principles as those used in equations when isolating a variable. For example, if there is an inequality 3x - 5 < 7. one can isolate the variable, by first:

Add 5 to both sides to be: 3x < 12.

Then divide both sides by 3: x < 4.

So, the variable x is one that is isolated, and the solution to the inequality is one where x < 4.

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The value of the principal investment would be = $12,500.75

A principal investment is defined as the capital amount of money that is being deposited into an account with the purpose of receiving interest for a particular period of time.

The years of investment (t) = 9 years

The annual interest rate (r) = 3.9% = 3.9/100= 0.039

The total worth of the investment (A) = $17,757.16

Then, solve the equation for P

P = A / ert

P = 17,757.16 / e(0.039*9)

P = $12,500.75

Therefore, the principal amount that is needed which can be compounded continuously to get the total amount given = $12,500.75

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Answer:

For the third one,

3, 8, 15, 24, 35, 48, 63

For the fourth one,

4, 6, 10, 18, 30, 46, 66

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

(-3, 5) lie in the 2nd quadrant and it is given by point A

Answer:

B)  slope of the line   \(\frac{-5}{8}\)  ;Y- intercept is none

slope of the line   \(m = \frac{-5}{8}\)

Y- intercept is none

Step-by-step explanation:

Explanation:-

Given equation of the line   \(y = \frac{-5}{8} x\)

The equation of the straight line in slope - intercept form

                        y = m x + c

                        \(y = \frac{-5}{8} x+0\)

slope of the line   \(m = \frac{-5}{8}\)

Y- intercept is none

Step-by-step explanation:

distance = 90 km

time = 3 hours 15 min

= 3+ 15/60 hours

= 3+ 1/4 hours

= 13/4 hours

speed = distance/ time

= 90/ (13/4)

= 90 * 4 /13

= 27.69 km/ hr

Answer: 8

Step-by-step explanation:  9 x 8 = 72

Answer:

d. y minus 8 + 2 less-than-or-equal-to negative 2 + 2

Step-by-step explanation:

Which inequality is equivalent to this one?

y minus 8 less-than-or-equal-to negative 2

y minus 8 + 8 greater-than-or-equal-to negative 2 + 8

y minus 8 + 8 less-than negative 2 + 8

y minus 8 + 2 less-than-or-equal-to negative 2 + 8

y minus 8 + 2 less-than-or-equal-to negative 2 + 2

Take the last option:

y minus 8 + 2 less-than-or-equal-to negative 2 + 2

remove the +2 on each side to get

y minus 8 less-than-or-equal-to negative 2

Answer:

\(\boxed{y - 8 + 2\leq - 2 + 2}\)

Step-by-step explanation:

Which inequality is equivalent to this one:

\(y - 8 \leq - 2\)

\(y - 8 + 8\geq - 2 + 8\)

\(y - 8 + 8< - 2 + 8\)

\(y - 8 + 2 \leq - 2 + 8\)

\(y - 8 + 2\leq - 2 + 2\)

Let’s take the last inequality.

\(y - 8 + 2\leq - 2 + 2\)

Subtract 2 on both sides.

\(y - 8 + 2-2\leq - 2 + 2-2\)

\(y - 8 \leq - 2\)

The inequality is equivalent.

The three statistical questions are: A. How many hours of sleep per night do students usually get when they have school the next day? B and E.

A statistical question is one that may be resolved via the collection and examination of data. The question frequently incorporates a variable that might differ from person to person or scenario to situation, and the solution is not always the same. The words "how many," "what is the average," "what is the range," "what is the distribution," etc. are frequently used in statistical queries.

The three statistical questions are:

How many hours of sleep per night do students usually get when they have school the next day?

What are the heart rates of the students in Mr. Peterson's physical education class?

How many runs did the New York Yankees score in their last game?

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Answer:

f inverse of x is equal to 3 to the power of the quantity x plus 6 end quantity minus 5 all over 4

Step-by-step explanation:

The function \(f(x)=\log_3 (4x+5)-6\) can be thought of as a series of steps, one operation at a time:

Start with x

Multiply by 4

Add 5

Take the \(\log_3\)

Subtract 6

That gives you a function value \(f(x)\).

To get the inverse function, read that list from the bottom up (in reverse order, using inverse operations at each step).

Start with x  (a bit confusing, because this  x  represents the function value you get at the end of the above list).

Add 6   (add is the inverse operation of subtract)

Raise 3 to the ...    \(3^{\text{result of previous step}\)

Subtract 5

Divide by 4

\(f^{-1}(x) = \frac{3^{x+6}-5}{4}\)

Let's test this out.  Find f(1).

\(f(1)=\log_3(4 \cdot 1 + 5)-6 =\log_3(9)-6=2-6=-4\)

Now put -4 into the inverse function.

\(f^{-1}(-4)=\frac{3^{-4+6}-5}{4}=\frac{3^2-5}{4}=\frac{9-5}{4}=\frac{4}{4} =1\)

The final result is the number we started with when we put 1 into f(x).

Finding an inverse is reversing the action of the function  f  by doing inverse operations in "backwards" order.

A lot of authors have you do this by switching  x  and  y  in the formula for a function, then solving for  x.

\(y = \log_3(4x+5)-6\text{ switch x and y}\\\\x = \log_3(4y+5)-6\\\\x+6 = \log_3(4y+5)\\\\3^{x+6}=4y+5\\\\3^{x+6}-5=4y\\\\\frac{3^{x+6}-5}{4}=y\)

Answer:

B-

Step-by-step explanation:

I took the test

Answer:

C) <BAC ≈ <QPR and BC ≈ QR

Step-by-step explanation:

C) <BAC ≈ <QPR and BC ≈ QR

The transformations of a parent function, Horizontal translation (shift) and Horizontal and vertical stretch and shrink are illustrated below.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over the x-axis, (x, -y).

Suppose we have a parent function f(x) = x².

Now, A horizontal 'a' transformation would be f(x ± a) = (x ± a)².

A horizontal and vertical stretch and shrink to f(x) = x² would be,

± bf( ± ax) = ± b( ± ax)².

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Answer:

the first one is 48 i will have to do more solving for it but when i do i will edit my answer

Step-by-step explanation:

Answer:

second answer would be 11.9716

Step-by-step explanation:

Using a system of equation to represent the scenario described, the cost is purchase made is $12.70

Cost of 5 bags of chips and 7 bottles of soda :

5(1.35) + 7(0.85) = $12.70

The cost of x bags of Chips and x bottles of soda can be expressed thus :

Therefore, the cost of x and y bags of Chips and soda respectively is 1.35x + 0.85y

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Answer:

15

Step-by-step explanation:

Anything above 5 you round up, below 5 you round down

15.26 round the 6 up

15.3 round the 3 down

15