Tom bought a new mirror for his house. One side of the mirror is 38 inches and the other side is 30 inches. What is the length of the diagonal of the mirror? a. 68 inches b. 23 inches c. 34 inches d. 48 inches

Answer:

Step-by-step explanation:

From the first question:

We are to find PV of the annuity.

Using the formula:

Present value of Annuity  = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)

Where , Annuity Amount = $4,000            

n = No. of periods = 7 years × 4 quarters per year = 28 periods but since the first payment is at beginning of the quarter, Then, n = 27 when considered for PVAF

r  = 6.2% / 4 quarters = 1.55%,

PVAF(n0,r) when first payment is at beginning of n i.e. n0 = 1 + { [1-(1+r)^ -n0 ]/r }

= 1 + { [1-(1+0.0155)^ {-27}]/0.0155 }

= 1 + [ (1 - 0.66015 ) ] / 0.0155]

= 1 + 21.926

= 22.926

PVAF(28,1.55%) = 22.926

Thus , Present Value of Annuity = $4,000 × 22.926  = $91704.00

2. Present value of Annuity due = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)

Present Value of Annuity  = $90,000

n = No. of periods = 7.5 years × 4 quarters per year = 30 periods

r  = 5.4% / 4 quarters = 1.35%,

PVAF(n,r) = [1-(1+r)^-n]/r

PVAF(n,r) = [1-(1+0.0135)^ -30]/0.0135

PVAF(30,1.35%) = (1 - 0.6688)/0.0135

PVAF(30,1.35%) = 0.3312/0.0135

PVAF(30,1.35%) = 24.53

Hence ;

$90,000 = Annuity Amount × 24.53

Annuity amount = $90,000/24.53 = $3,668.48

Answers:

1. Adding decimals is very similar to adding whole numbers.

2. Line up the number vertically so that all the decimal points are aligned.

3. Add extra zeros to the right of he number so that each number has the same number of digits the right of the decimal point.

4. Place the decimal point of the result in line with the other decimal points.

I hope this helped you. If it is please click the thanks button. Thank You, Bye! ;-D

1. Adding decimals is very similar to adding whole numbers.

2. Line up the number vertically so that all the decimal points are aligned.

3. Add extra zeros to the right of the number so that each number has the same number of digits to the right of the decimal point.

4. Place the decimal point of the result in line with the other decimal points.

While adding two decimals.

Learn more about decimal form here:

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Learn more about decimal addition here:

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Answer: The Answer is 0

Step-by-step explanation:

The key here is combining like terms. Here:

1) 5x-7=2x+1+3x

2) 5x-7=5x+1

Then you add 7 to both sides anywhere that there is no variable. You also subtract 5x to the other 5x

3) 0x=8

When you divide by zero on both sides, your answer should be 0

Answer:

168 milliliters

Step-by-step explanation:

Since roses need 14 times as much water as irises and we are given the water irises need, you multiply them together.

Answer:

27

Step-by-step explanation:

Answer:

Yes, by 27 times

Step-by-step explanation:

I hope it helps you

Answer:

b = − 3

m = 5 ( 39 + 2 m ) /23

Answer:

Step-by-step explanation:

P(-a<z<a)=0.60, from the symmetry of normal distribution, P(z<a) = 0.60+ (1-0.60)/2 =

0.60+0.4/2

0.60+0.2

= 0.8

Considering the standard normal distribution table, we have a = 0.80, thus

z =(x-m)/std = 0.80

the maximum x = m + 0.80×std =

Where m = 246300

Std = 15000

246300+0.80×15000

= 246300+12000

= 258300

For the minimum x

x = m - 0.80×std

x = 246300-0.80×15000

246300-12000

= 234300

Answer:

This relation IS a function

Answer:

This is a function

Step-by-step explanation:

Down below none of them overlap

There is no two points in the lines.

its not greater than 50 grams. and the answer rounder to the four decimal places is 32.6106

Answer:

$654.06

Step-by-step explanation:

ジオメトリヘルプミープリーズは、速くて正しい場合に最も頭が良くなります

関係のドメインは？ 1）関係の出力（y）値2）関係の入力（x）値3）入力値をペアにするポイントのセット…

f（x）= 16 – x ^ 2、g（x）= 4 –xとします。 （fg）（x）とその定義域を見つけます。

助けてくださいお願いします

助けてください

Answer: the answer would be 79.06

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

5 divided by 25 multiplied by 100 will give you 20%.

I hope you understand

Answer:

Distributive Property

Step-by-step explanation:

[tex]x(8x+3y)\\We\ multiply\ the\ term\ outside\ brackets\ with\ terms\ inside\ the\ bracket\ equally,\\through\ the\ distributive\ property\ method\ .\\\\Hence,\\x(8x+3y)\\=8x*x+3y*x\\=8x^2+3xy[/tex]

Answer: 306 inches or 25.5 feet or 8.5 yards.

Step-by-step explanation:

Given: Carol has 90 inches of ribbon, Tino has 7.5 feet of ribbon, and Baxter has 3.5 yards of ribbon.

1 feet = 12 inches

length of ribbon Tino has = 12 x 7.5 = 90 inches

1 yard = 36 inches

length of ribbon Baxter has = 3.5 x 36 = 126 inches

Total ribbon they have = (length of ribbon Carol has) + (length of ribbon Tino has) + (length of ribbon Baxter has)

= (90+90+126) inches

= 306 inches

In feet , Total ribbon = [tex]\dfrac{306}{12}\text{ feet}[/tex]   [tex][\text{ 1 inch}=\dfrac{1}{12}\text{ feet}][/tex]

[tex]=\text{25.5 feet}[/tex]

In yards, Total ribbon =[tex]\dfrac{25.5}{3}\text{ yards}[/tex]    [tex][\text{1 feet}=\dfrac{1}{3}\text{ yard}][/tex]

[tex]=\text{ 8.5 yards}[/tex]

Hence, the total length of ribbon the three friends have is 306 inches or 25.5 feet or 8.5 yards.

Answer:

x = -4

Step-by-step explanation:

Answer:-4

Step-by-step explanation:

Answer:

4 inches because March was 4 so april has to be 4 too

Step-by-step explanation:

Answer:

<DBC=31

Step-by-step explanation:

<ABC=<ABD+<DBC

125=94+<DBC

125-94=<DBC

31=<DBC

The answer is the second one

Explanation above

Answer:

The correct answer is "y = 3/4x"

Step-by-step explanation:

Slope-intercept form is y2-y1/x2-x1. If you place the points into slope-intercept form you get 6-3/8-4.  After reducing the fractions you will get 3/4. So the equation is y = 3/4x.

Answer:

At least 401 chosen guests

Step-by-step explanation:

Represent those with same birth day with Same

So:

[tex]P(Same) > \frac{2}{3}[/tex]

Represent number of people with n

There are 365 days in a year and 364 days out of these days is not your birthday.

So, there the probability that n people do not share your birthday is [tex](\frac{364}{365})^n[/tex]

i.e.

[tex]P(none) = (\frac{364}{365})^n[/tex]

Solving further, we have that:

[tex]P(same) + P(none) = 1[/tex]

[tex]P(same) + (\frac{364}{365})^n = 1[/tex]

[tex]P(same) = 1 - (\frac{364}{365})^n[/tex]

We're calculating the probability that [tex]P(Same) > \frac{2}{3}[/tex].

So, we have:

[tex]1 - (\frac{364}{365})^n > \frac{2}{3}[/tex]

Collect Like Terms

[tex]1 - \frac{2}{3}> (\frac{364}{365})^n[/tex]

[tex]\frac{3-2}{3}> (\frac{364}{365})^n[/tex]

[tex]\frac{1}{3}> (\frac{364}{365})^n[/tex]

[tex]3^{-1} > (\frac{364}{365})^n[/tex]

Take natural logarithm (ln) of both sides

[tex]ln(3^{-1}) > ln((\frac{364}{365})^n)[/tex]

[tex]-ln\ 3 > n\ ln\ (\frac{364}{365})[/tex]

Apply laws of logarithm

[tex]-ln\ 3 > n\ (ln(364) - ln(365))[/tex]

Multiply through by -1

[tex]ln\ 3 < n\ (ln(365) - ln(364))[/tex]

Solve for n

[tex]\frac{ln\ 3}{(ln(365) - ln(364))} < n[/tex]

Reorder

[tex]n > \frac{ln\ 3}{(ln(365) - ln(364))}[/tex]

[tex]n > \frac{1.09861228867}{(5.89989735358 - 5.89715386764)}[/tex]

[tex]n> \frac{1.09861228867}{0.00274348594}[/tex]

[tex]n > 400.443928891[/tex]

[tex]n > 400[/tex] (approximated)

This implies that n = 401, 402, 403 .....

i.e

[tex]n \geq 401[/tex]

So, at least 401 people has to be invited

Answer:

She typed 32 words in her letter

Step-by-step explanation:

Assume that the letter has x words

∵ She typed x words in her letter

∵ She misspelled 8 words

∵ She misspelled 25% of the words she typed

∴ She misspelled 25% of x

→ That means 8 is equivalent to 25% of x

∴ 25% of x = 8

∴ 25% × x = 8

→ Change 25% to decimal by divide it by 100

∵ 25% = 25 ÷ 100 = 0.25

∴ 0.25 × x = 8

∴ 0.25x = 8

→ Divide both sides by 0.25

∵ [tex]\frac{0.25x}{0.25}[/tex] = [tex]\frac{8}{0.25}[/tex]

∴ x = 32

∵ x represents the number of words that she typed in the letter

∴ She typed 32 words in her letter

Answer:

A. 8.5 N

Step-by-step explanation: F = 8.5 N

Answer:

the addition property of equality and then the division property of equality

Answer:

A

Step-by-step explanation:

[tex]f(x) = (x + 2)^2(x-4)(x + 1)^3[/tex]

x+2=0

x+2-2=0-2

x=-2.....(x+2) was squared...exponent of 2...multiplicity of 2

x-4=0

x-4+4=0+4

x=4....(x-4) has no visible exponent which means it is essentially to the power of 1...multiplicity of 1

x+1=0

x+1-1=0-1

x=-1....(x+1) was cubed...exponent was 3...multiplicity of 3

The roots and their respective multiplicity are –2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3 thus option (A) is correct.

The roots of an equation are the solution of that equation, since an equation consists of hidden values of the variable so to determine them by different processes and then the resultant is called roots.

For example root of x -4 = 0 is x = 4 so 4 will be the only root of this linear equation.

As per the given function,

f(x) = (x + 2)²(x - 4)(x + 1)³

The roots are the points at which the value of the function is zero.

f(x) = 0

(x + 2)²(x - 4)(x + 1)³ = 0

(x + 2)² = 0

x = -2 (with a multiplicity of 2)

(x - 4) = 0

x = 4  (with a multiplicity of 1)

(x + 1)³ = 0

x = -1  (with a multiplicity of 3)

Hence "The roots and their respective multiplicity are –2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3 thus option (A) is correct".

To learn more about the roots of equations,

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Answer:

The parenthesis go around the 12 and 6, just like this. (12 - 6)

Answer- 2 + 36 ÷ (12-6)

Answer:

[tex]x = 44^\circ[/tex]

Step-by-step explanation:

Triangle Congruence

Given triangle ABC is congruent to triangle DEC, then it's true that angle ABC is congruent to angle DEC.

The figure shows that:

[tex]m\angle B = 48^\circ[/tex]

[tex]m\angle E = x + 4^\circ[/tex]

Those angles are congruent, or have the same measure, thus:

[tex]x + 4^\circ = 48^\circ[/tex]

Subtracting 4°:

[tex]x = 48^\circ - 4^\circ[/tex]

[tex]\mathbf{x = 44^\circ}[/tex]

Answer: 7.20$

Step-by-step explanation:

Since there are five people over all, and three of them bought shoes for 2$, you would take 2$ Times that by 3 = 6$, now take that 6$ and subtract that by the 42$, leaving you with 36$ left. Take that 36$ and divide it among the 5 people and you get 7.20$ for a lane

Answer:

Sub the values in the brackets of each question into the equation

Step-by-step explanation:

eg. c. f(0) = 2(0)^2 + 1 = 1

Complete question :

A study was done to investigate the population of bald eagle breeding pairs over time. The correlating regression model is shown

below, wiere x represents the number of years after 1986, and y represents the number of bald eagle breeding pairs. Interpret the y-

intercept

y = 1.772 +334x

Answer:

B. There were approximately 1.772 eagle breeding pairs in 1986

Step-by-step explanation:

Given the regression equation : y = 1.772 +334x

Recall the general form of a linear regression equation :

y = mx + c

y = predicted variable ; x = predictor Variable ; c = intercept ; m = slope

x = number of years after 1986 ; y = number of bald eagle pairs.

The intercept is a constant value at time t = 0

For x to be 0, on a graph, this this the value on the y axis where the regression line crosses the y - axis. That is in 1986; the number of y when in 1986 when x = 0 is 1.772