Find the volume of this square
based pyramid.
10 in
12 in
[? ]in3

a) The longest time a borrower can take to pay off the new car loan of 2 - 6 years is 6 years.

b) Based on the above, the best interest rate the borrower could get is 8%.

Many factors are considered in determining the interest rate for a loan.

Some of the factors include:

We know that the longer the term of a loan, the higher the interest rate charged.  This higher rate is meant to compensate the lender for the time value of money, made variable by inflation and credit risks.

Thus, if a loan term varies between two and six years, the longest time to pay off the loan is 6 years while the best interest rate the borrower can be granted is 8%.

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The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The table represents a quadratic function C(t).

 t          C(t)

−2           1

−1           4

0           5

 1           4

2            1

From the table, the coordinate of the vertex will be at (0, 5). Then the equation is given as,

C(t) = a(t - 0)² + 5

C(t) = at² + 5

The equation is passing through the point (1, 4), then we have

4 = a (1²) + 5

4 = a + 5

a = - 1

The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.

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Answer:

B) 20%

Step-by-step explanation:

Exponential equation:

An exponential equation is given by:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which A(0) is the initial amount and r is the growth rate, as a decimal.

In this question:

[tex]P(t) = 85(1.2)^t[/tex]

Growth rate:

We want to find r, so:

[tex]1 + r = 1.2[/tex]

[tex]r = 1.2 - 1 = 0.2[/tex]

The growth rate is of 0.2 = 2%, and the correct answer is given by option B.

Answer:

Given that Figure A and Figure B are similar polygons, the scale factor of Figure A to Figure B = 5/2.

Recall:

Similar Polygons have corresponding side lengths whose ratio are equal. That is, their pairs of corresponding sides are proportional.

The ratio of any of their corresponding side length = scale factor

Given the two pairs of similar polygons, the scale factor of figure A to figure B will be calculated as follows:

A side length of Figure A = 10

Corresponding side length of Figure B = 4

Scale factor of Figure A to Figure B = 10/4 = 5/2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

The p-value of the test is 0.1738, which means that for a level of significance above this, there is evidence of a change from the status quo.

Step-by-step explanation:

A high school has found over the years that out of all the students who are offered admission, the proportion who accept is 70%. Test if there is a change from status quo.

At the null hypothesis, we test if the proportion is 70%, that is:

[tex]H_0: p = 0.7[/tex]

At the alternate hypothesis, we test if there is a change from status quo, that is, the proportion is different from 70%. So

[tex]H_a: p \neq 0.7[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

70% is tested at the null hypothesis:

This means that [tex]\mu = 0.7, \sigma = \sqrt{0.7*0.3}[/tex]

Suppose they offer admission to 210 students and 156 accept.

This means that [tex]n = 210, X = \frac{156}{210} = 0.7429[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.7429 - 0.7}{\frac{\sqrt{0.7*0.3}}{\sqrt{210}}}[/tex]

[tex]z = 1.36[/tex]

P-value of the test and decision:

The p-value of the test is the probability that the sample proportion differs from 0.7 by at least 0.7429 - 0.7 = 0.0429, which is P(|z| > 1.36), which is 2 multiplied by the p-value of z = -1.36.

Looking at the z-table, z = -1.36 has a p-value of 0.0869

2*0.0869 = 0.1738

The p-value of the test is 0.1738, which means that for a level of significance above this, there is evidence of a change from the status quo.

The perimeter and the area of the fountain is calculated to be

94.25 feet and 625.32 square feet respectively

The perimeter of the fountain consisting of two semicircles and a quarter circle is

= perimeter of semicircle * 2 + perimeter of circle * 1/4

= π d + 2 π r * 1/4

for semicircle, diameter, d = 20 ft

for circle, radius r, = 20 ft

substituting the values

= 20π + 2 * π * 20 * 1/4

= 20π + 10π

= 30π

= 94.25 feet

Area of the fountain

= area of semicircle * 2 + area of circle * 1/4

area of semicircle * 2 = area of circle of radius 10 ft

for semicircle, radius, r = 10 ft

for circle, radius r, = 20 ft

= π 10² + π 20² * 1/4

= 100π + 100π

= 200π

= 625.32 square feet

The area of the fountain is 625.32 square feet

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Answer:

BD = 2

Step-by-step explanation:

here's your solution

==> in ∆ABC and ∆ ABD

==> angle C = angle D. [ = to 90° ]

==> AB is common side

==> angle BAC = angle BAD. [ BA is angle bisector]

==> hence both traingle are congruent

==> so, BD = BC. [ by C.P.C.T ]

==> BC = 2. [ Given ]

==> BD = 2

hope it helps

Answer:

C. Expression A is 4 times as great as expression B.

Step-by-step explanation:

Without doing any calculations, compare Expression A to Expression B.

A. (34+25) ÷ 1/4

B. 34+25

Which statement is true?

A. Expression A is 2 times as great as expression B.

B.Expression B is 4 times as great as expression A.

C.Expression A is 4 times as great as expression B.

D. The two expressions are equal to each othe

7 long roms of plants

Without doing any calculation,

Expression A = (34+25) ÷ 1/4

= (34 + 25) × 4/1

= 4(34 + 25)

Expression A = 4(34 + 25)

Expression B = 34 + 25

Therefore,

C.Expression A is 4 times as great as expression B.

Answer:

option d is correct answer

Step-by-step explanation:

equation y=-7 and slope zero

as equation of staight line y= MX+c

The we can say that the slope of the line is undefined and the {y} - intercept is -7.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is that Zoran graphed the line shown in the image.

The line is parallel to the {x} axis. So, it has no slope. Or, we can say that the slope of the line is undefined. It intersects the line at y = -7, at the {y} - axis. So, the {y} - intercept will be {y} = -7.

Therefore, the we can say that the slope of the line is undefined and the {y} - intercept is -7.

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9514 1404 393

Answer:

  about 145.3 mg

Step-by-step explanation:

If half breaks down in the hour, then half remains. That is, each hour the amount remaining is multiplied by 1/2. The remainder after 6 hours is ...

  (9300 mg)(1/2)^6 = 145.3125 gm

About 145.3 mg will be left after 6 hours.

3x + 120° + x + 120° = 360°

4x + 240° = 360°

4x = 120°

x = 30°

y = 1/2 (3x - x)

y = 1/2 (90° - 30°)

y = 1/2 × 60°

y = 30°

Answer:

6 hours

Step-by-step explanation:

70miles divided by 4 hours equals 17.5mph

106miles divided by 17.5 mph = 6 hours

Answer:

6 hours

Step-by-step explanation:

105miles ÷ 70miles=1.5

4×1.5= 6

Answer:

1 [tex]\frac{1}{4}[/tex] miles

Step-by-step explanation:

the routes from Lexington to Somerville are

Lexington → Brookfield → Somerville with distance

[tex]\frac{3}{8}[/tex] + [tex]\frac{7}{8}[/tex] = [tex]\frac{3+7}{8}[/tex] = [tex]\frac{10}{8}[/tex] = 1 [tex]\frac{2}{8}[/tex] = 1 [tex]\frac{1}{4}[/tex] miles

the other route is

Lexington → Brookfield → Yardley → Somerville with distance

[tex]\frac{3}{8}[/tex] + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{3+4+4}{8}[/tex] = [tex]\frac{11}{8}[/tex] = 1 [tex]\frac{3}{8}[/tex] miles

the shortest distance is

Lexington → Brookfield → Somerville , a distance of 1 [tex]\frac{1}{4}[/tex] miles

Answer:

the bottom right could NOT

the fourth option is the answer (. ^ ᴗ ^.)

Answer: it D :)

Step-by-step explanation:

Probability that the length of the life of an instrument is greater than 12 months is 0.5 or 50%

If the length of the life of an instrument produced by the machine has a normal distribution with a mean of 12 months and a standard deviation of 2 months, then the random variable X representing the length of the life of the instrument is also normally distributed.

To find the probability that X assumes a value greater than 12 months, we need to use the cumulative distribution function (CDF) of the normal distribution. The CDF is given by the formula:

F(x) = (1/2) * [1 + erf((x - μ) / (σ * sqrt(2)))]

where μ is the mean, σ is the standard deviation, and erf(z) is the error function.

Plugging in the given values, we get:

F(12) = (1/2) * [1 + erf((12 - 12) / (2 * sqrt(2)))] = (1/2) * [1 + erf(0)] = (1/2) * [1 + 0] = 1/2

Since the CDF gives us the probability that X assumes a value less or equal than x, we need to subtract F(12) from 1:

P(X > 12) = 1 - F(12) = 1 - 1/2 = 0.5

So the probability that the length of the life of an instrument is greater than 12 months is 0.5 or 50%.

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The slope of the lines that passes trough the points (-2,-1) and (-4,-7) is m = 3 , (2,-3) and (6,-13) is m = -2.5 , (-3,4) and (-3,-8) is m = undefined , (-5,7) and (3,-1) is m = -1 .

What is slope ?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b).

           m=Δy/Δx

           m=(y2−y1)/(x2−x1)

           m=(−7−−1)/(−4−−2)

           m=−6/−2

           m = 3

          m=Δy/Δx

          m=(y2−y1)/(x2−x1)

          m=(−13−−3)/(6−2)

          m=−10/4

          m=−5/2

          m = -2.5

           m=Δy/Δx

           m=(y2−y1)/(x2−x1)

           m=(−8−4)/(−3−−3)

           m=−12/0

          m is undefined

            m=Δy/Δx

            m=(y2−y1)/(x2−x1)

            m=(−1−7)/(3−−5)

            m=−8/8

            m = -1

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Answer:

your answer would be A

Step-by-step explanation:

it is kinda confusing but if you are reflecting off the x axis, you change the y, and if you are reflecting off the y axis, you would change the x

hope this helps and have a nice day!

Answer:

x=0, y=1

Step-by-step explanation:

Answer:

[tex]\dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]

Step-by-step explanation:

Given expression:

[tex](a^{10}b^{0}cde^{3})^{-2}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{1}{(a^{10}b^{0}cde^{3})^{2}}[/tex]

[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \dfrac{1}{a^{(10 \times 2)}b^{(0 \times 2)}c^2d^2e^{(3 \times 2)}}[/tex]

Simplify:

[tex]\implies \dfrac{1}{a^{20}b^{0}c^2d^2e^{6}}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^0=1:[/tex]

[tex]\implies \dfrac{1}{a^{20}(1)c^2d^2e^{6}}[/tex]

[tex]\implies \dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]

Answer:

Its always ily, but never stwywimc

Step-by-step explanation:

Answer:

x=2/3

Step-by-step explanation:

when the three turned into a 2 it removed one third, so we need to remove one third from 1, which gives us 2/3.

Basically, if a rectangle side goes from x to y, we figure out the percent decrease, and subtract that percent from the other side to find the variable we need to find on the other rectangle

The point (5,5/3) also lies on the line.

A point (x, y) is located on a line with slope m if and only if it satisfies the equation:

y = mx + b

where b is the y-intercept of the line. In this case, we know that the point (3, 1) is located on the line, so we can use the information to find the value of b and then write the equation of the line in slope-intercept form.

The y-coordinate of the point (3, 1) is 1, so we can substitute this into the equation and solve for b:

1 = (1/3) * 3 + b

This simplifies to:

1 = 1 + b

so, b = 0

So, the equation of the line is

y = 1/3 * x +0

Now we can use this equation to find the coordinates of any point that lies on the line. So any point (x, y) that satisfies this equation could also be located on the line.

For example, we can pick any x, calculate corresponding y.

x=5, y=5/3

So point (5,5/3) also lies on the line.

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Answer:

Its between A and B

Step-by-step explanation:

I think its B Tho

Answer:

Subtraction property of equality

Step-by-step explanation: