Write an
explicit formula for an, the nth term of the sequence 8, 40, 200, ....

Answer: 22

Step-by-step explanation:

[tex]f(f^{-1}(x))=f^{-1}(f(x))=x[/tex]

If I deposit $400 each month into an account earning 8% interest compounded monthly, I will have $6,517 in my account in 35 years. The total money that I will put into the account is $168,000. I will earn a total compound interest of $6,117.

Given information is as follows,

Principal, P = $400

Rate = 8%

Time, T = 35 years

n = 12 (Compounded monthly)

The amount for compound interest is given as,

A = [tex]P\frac{(1+\frac{R}{n} )^{nT} -1}{R/n}[/tex]

A = [tex]400\frac{(1+\frac{0.08}{12} )^{12.35} -1}{0.08/12}[/tex]

A = 6,517.02

A = $6,517 (to the nearest cents)

Since, $400 is deposited every month for 35 years,

Amount Put in 35 years for this compound interest =$400 × 12 × 35

= $168,000

A = P + CI

Thus, the compound interest is given by,

CI = A - P

CI = 6517 - 400

CI = $6,117

I will earn a total interest of $6,117

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Based on the dataset given, the first quartile is 38.75, and the third quartile is 45.25. This interquartile range is 6.5. The lower fence is 29 and the upper fence is 55.

Order the sets:

31, 38, 39, 40, 41, 45, 45, 45,46, 58

First quartile position:

= 1(10 + 1) / 4

= 2.75th position

= 38 + 0.75 x (39 - 38)

= 38.75

Third quartile:

= 3(10 + 1) / 4

= 8.25th position

= 45 + 0.25 x (46-45)

= 45.25

Interquartile range:

= 45.25 - 38.75

= 6.5

Upper fence:

= 45.25 + (1.5 x 6.5)

= 55

Lower fence:

= 38.75 - (1.5 x 6.5)

= 29

59 is an outlier.

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The coordinates of the edges of the mini-solar cooker are (x₁, y₁) = (0, - 60) and (x₂, y₂) = (0, 60).

The distance between the two edges is 120 centimeters.

The equation for the parabolic mirror is x + 32 = (2/225) · y².

Herein we must understand the geometry of the design of the mini-solar cooker to determine all needed information. The y-coordinates of the edges of the cooker are determined by Pythagorean theorem:

[tex]y = \pm \sqrt{(68\,cm)^{2}-(32\,cm)^{2}}[/tex]

y = ± 60

The coordinates of the edges of the mini-solar cooker are (x₁, y₁) = (0, - 60) and (x₂, y₂) = (0, 60). The distance between the two edges is 120 centimeters.

Lastly, the equation of the parabolic mirror can be determined based on the equation of the parabola in vertex form:

x - h = C · (y - k)²     (1)

Where:

h, k - Coordinates of the vertex

C - Vertex constant

If we know that (h, k) = (- 32, 0) and (x, y) = (0, 60), then the vertex constant of the equation of the parabola is:

0 + 32 = C · 60²

C = 2/225

Then, the equation for the parabolic mirror is x + 32 = (2/225) · y².

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$9.75

Given the information, we know that for the first 3 days, she spends a total of $7.25. On the fourth day, she deposits $10 before buying lunch for $3.

This means she had $20, but spent $10.25. $20-$10.25=$9.75 is the amount she has in her account.

The situation presented can be represented using the following letters CC, CP, PC, and PP.

The possible combinations are:

Based on this, the option that represents the situation is:

CC, CP, PC, and PP.

Note: This question is incomplete; here is the missing section:

What is the sample space of the event described above?

Answer choices:

a. CC, CP, PC, PP

b. CC, PP

c. CC, CP, PC

d. C, P

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The given vertex and Focus are of a vertical parabola having an opening downward as the focus is in downward direction as the vertex.

Focus of the parabola can be written as :

[tex]\qquad \sf  \dashrightarrow \: (h ,k+ a )[/tex]

where, h and k are coordinates of vertex

so,

So, the equation of parabola can be written as :

[tex]\qquad \sf  \dashrightarrow \: (x - h) {}^{2} = 4a(y - k)[/tex]

plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: (x - 1) {}^{2} = 4(- 1)(y + 1) {}^{} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (x - 1) {}^{2} = - 4(y + 1)[/tex]

Answer:

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

Step-by-step explanation:

Standard form of a parabola with a vertical axis of symmetry:

[tex](x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0[/tex]

Given:

Comparing with the formulas:

⇒ h = 1

⇒ k = -1

⇒ k + p = -2  ⇒ -1 + p = -2  ⇒ p = -1

Substituting the values into the formula:

[tex]\implies (x-1)^2=4(-1)(y-(-1))[/tex]

[tex]\implies (x-1)^2=-4(y+1)[/tex]

Answer: Answer C is correct, 50.9.

The number of tickets sold on Friday were 66 children tickets and 97 adult tickets.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of children and y represent the number of adult, hence:

5.2x + 9.9y = 1303.5     (1)

Also:

x + y = 163    (2)

From both equations:

x = 66, y = 97

The number of tickets sold on Friday were 66 children tickets and 97 adult tickets.

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Answer:

A.

Step-by-step explanation:

1) according to the given graph, the real roots are: -1 and 4, it means the given expression can be evaluated using (x+1)(x-4)=x²-3x-4.

2) if to divide the given expression by (x²-3x-4), then

x⁴-7x³+23x²-29x-60=(x²-3x-4)(x²-4x-15), where

3) x=-1;4 - real roots, and

[tex]x=2^+_-i\sqrt{11} \ -nonreal \ roots.[/tex]

There are 14 yellow blocks in the box

The given parameters are:

The number of yellow blocks is calculated as:

Yellow = (1 - P(Red) - P(Red and Yellow)) * n

So, we have:

Yellow = (1 - 1/3 - 1/12) * 24

Evaluate

Yellow = 14

Hence, there are 14 yellow blocks in the box

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Complete question

A box contains a group of 24 blocks. Some are red, some are yellow, and some are a mixture of the two colors. The probability of drawing a red block is 1/3. The probability of drawing a red and yellow block is 1/12. Determine the number of yellow blocks.

The unit measurement of the a volume in mm is mm³(millimetres cube.)

Volume is is defined as the space occupied within the boundaries. The objects are usually solid objects.

The volume of a 3 dimensional figure is the product of the base area and the height.

Therefore, the units of volume is measured in cubic units.

The volume of a prism with side lengths measured in millimetres is 20.

Therefore, the measurement can be represented as follows:

20 mm³

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The carbon dioxide that is produced from the vampire energy used by the office computer is 1042.8 kWh.

Based on the information given, the number of hours that the computer is plugged on a day will be:

= 20/7

= 2.857 hours

Therefore, the power consumption in a year will be:

= 2.857 × 365

= 1042.8 kWh

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Answer:

1/21

Step-by-Step Explanation:

Let's solve your equation step-by-step.

3(1−5x)=2(3x+1)

Step 1: Simplify both sides of the equation.

3(1−5x)=2(3x+1)

(3)(1)+(3)(−5x)=(2)(3x)+(2)(1)(Distribute)

3+−15x=6x+2

−15x+3=6x+2

Step 2: Subtract 6x from both sides.

−15x+3−6x=6x+2−6x

−21x+3=2

Step 3: Subtract 3 from both sides.

−21x+3−3=2−3

−21x=−1

Step 4: Divide both sides by -21.

-21x/-21=-1/-21

x=1/21

[tex]\boldsymbol{\sf{3(1-5x)=2(3x+1)}}[/tex]

Reorder terms

Distribute

Subtract 3x from both sides.

Simplify

Subtract 6x from both sides.

Simplify

Divide both sides by the same factor

Simplify

Answer: 1/5

Step-by-step explanation:

There are 10 numbers, out of 50, which have a 4 in their tens place: 40, 41, 42, 43, 44, 45, 46, 47, 48, and 49.

Therefore our desired probability is 10/50 or 1/5.

Answer:

x = ±√10i (i outside the radical), or approximately ±3.62i, or no solution depending on your class.

Step-by-step explanation:

x^2 + 10 = 0

x^2 = -10

x = ±√-10

x = ±√10i (i outside the radical), or approximately ±3.62i.

The solution is not real.

If you meant x^2 - 10 = 0 then x = ±√10 or approximately ±3.62. This solution is real.

Answer:

As x increases, y increases along the entire graph.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Assuming that your expression is:}[/tex]

[tex]\textsf{0.5x = 0}[/tex]

[tex]\huge\textbf{If so, let's solve for the given expression:}[/tex]

[tex]\textsf{0.5x = 0}[/tex]

[tex]\huge\textbf{Divide 0.5 to both of the sides you have:}[/tex]

[tex]\mathsf{\dfrac{0.5x}{0.5} = \dfrac{0}{0.5}}[/tex]

[tex]\huge\textbf{You have to simplify the equation above:}[/tex]

[tex]\mathsf{x = \dfrac{0}{0.5}}[/tex]

[tex]\mathsf{x = 0}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = }\frak{0}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The points that are a horizontal distance of 6 and a vertical distance of 2 from the origin are (6, 2), (-6, 2), (6, -2), (-6, -2)

Points are undefined terms in geometry, however they are used to represent the coordinate or location of items in a coordinate plane

The features of the point are given as:

Horizontal distance = 6

Vertical distance = 2

The above means that:

x = 6

y = 2

The points are then represented as:

(x, y) = ±(x. y)

So, we have

(x, y) = ±(6, 2)

When the above equation is expanded, we have

(x, y) = (6, 2), (-6, 2), (6, -2), (-6, -2)

Next, we plot the points on a coordinate plane

See attachment for the graph of the plane

Hence. the points that are a horizontal distance of 6 and a vertical distance of 2 from the origin are (6, 2), (-6, 2), (6, -2), (-6, -2)

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The fraction of those who were delivered by car will be 1/6.

It should be noted that from the information given, the students were questioned on how they got to schoo and half of the students said they walk, one-third said they take a taxi,and the rest claimed they drive.

Therefore, the fraction of those who were delivered by car will be:

= 1 - (1/2 + 1/3)

= 1/2 - 5/6

= 1/6

In conclusion, the fraction of those who were delivered by car will be 1/6.

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Answer:

It is the second answer.

Step-by-step explanation:

When numbers with the same base are multiplied, you add the bases.

1/2 + 3/4 is the same as

2/4 + 3/4 = 5/4

So now we have 2 ^5/4^2.  When we have a power raised to a power.  We multiply the powers.

5/4(2)

(5/4(2/1) = 10/4 = 5/2.  The second answer is the same way to describe

2^(5/2)

. sorry sorrysorrysorrysorrysorrysorrysorrysorrysorrysorrysorry

Answer:

52 and 3

Step-by-step explanation:

17x+1 + 1x =55

18x+1=55

18x=54

x=3

Hello,

What is 72 decreased by 32%

72 × (1 - 32%)

= 72 × (1 - 32/100)

= 72 × (1 - 0,32)

= 72 × 0,68

= 48,96

Answer:225

Step-by-step explanation:

Answer:

THE ANSWER for this IS d) 53

The t- score for a sampling distribution is 2

The t-score is the number of standard deviations from the mean in the t-distribution.

The upper and lower bounds of a confidence interval when the data are approximately normally distributed.

T-scores and confidence intervals

Confidence intervals use t-scores to calculate the upper and lower bounds of the prediction interval. The t-score used to generate the upper and lower bounds is also known as the critical t or t* value.

The t- distribution is given by

t=(x – μ) / (S / √n)

t = T – Distribution

x = sample mean

μ = population mean

S = standard deviation

n = Sample size

It is given that sampling distribution mean of 10.5, a standard deviation of 1.5, and a size of 36 drawn from a population that has a mean of 10.

We need to find the t-score for sampling distribution

t=(x – μ) / (S / √n)

Here, x= 10.5 , μ= 10, S=1.5, n=36

t = (10.5 - 10)/ (1.5 /√36)

t= 2

Hence the value of t-score is 2

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The cost given shows that the amount left is £12.

From the information given, it was stated that the person saved £60 and spent £42 on coat and £6 on scarf

The amount that the person has left will be:

= £60 - £42 - £6

= £12

In conclusion, the person has £12 left.

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Answer: Option C   [tex]\boldsymbol{7^6}[/tex]

Work Shown:

[tex]\frac{7^{13}}{7^{7}}\\\\\\7^{13-7}\\\\\\\boldsymbol{7^6}[/tex]

Subtract the exponents to get the answer. The rule is [tex]\frac{a^{b}}{a^{c}} = a^{b-c}[/tex]. This rule only works when the bases are the same.