Which equation is equivalent 2^4x=8^x-3

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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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:

the bottom right could NOT

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

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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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.

Answer:

x=0, y=1

Step-by-step explanation:

Answer: it D :)

Step-by-step explanation:

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:

-------------------------------

The height h of the tree is opposite to 49° angle of a right triangle with the other leg:

Use tangent to find the value of h:

The height of the tree is 40 feet to the nearest foot.

How can the height of the tree be found?

It can be found using similar triangles.

Let's call the height of the tree "x".

Since the angle of elevation to the sun is 49°, we have two similar triangles:

Triangle 1: Sun - Naomi - Ground (illustration attached)

Triangle 2: Sun - Tree - Ground

The height of Naomi, 5 feet, is one of the corresponding sides in the two triangles, and the height of the tree, x feet, is the other. We know the ratio of their heights is 8:1, so:

x ÷ 5 = 8

Solving for x, we find that:

x = 40

So the height of the tree is 40 feet to the nearest foot.

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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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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:

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:

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.

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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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.

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:

Subtraction property of equality

Step-by-step explanation:

Answer:

Kindly check explanation

Step-by-step explanation:

New Method : 81 80 79 81 76

Standard Method Score: 69 68 71 68 73 72

H0 : μn = μa

H0 : μn < μa

New Method :

Using a calculator :

Sample size, n1 = 5

Mean, x1 = 79.40

Standard deviation, s1 = 2.07

Standard Method :

Using a calculator :

Mean, x2 = 70.17

Sample size, n2 = 6

Standard deviation, s2 = 2.14

T = (x1 - x2) / √(s1²/n1 + s2²/n)

(x1 - x1) = (79.40 - 70.17) =79.40 -= 9.23

√(s1²/n1 + s2²/n2) = √(2.07²/5) + 2.14²/6) = 1.2729

T = (x1 - x2) / √(s1²/n1 + s2²/n)

T = 9.23 / 1.2729

Test statistic = 7.25

The Pvalue from Tscore at, smaller n - 1 = 5 - 1 = 4

Pvalue = 0.000961

Decision region :

If Pvalue < α ; Reject H0 ; otherwise fail to reject H0

α = 0.01

Since, Pvalue < α ; We reject H0 ; and conclude that new method is worse rhn the old.

`

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

y2-y1/x2-x1

= (-1-3)/(5+1)

= -4/6

= -2/3

y = -(2/3)x + c

3 = (2/3) + c

c = -2/3 + 3

c = -2/3 + 9/3

c = -7/3

y = (2/3)x + (7/3)

Answer:

C)

Step-by-step explanation:

5 x 3 = 15

15 + 6 = 21

Your answear is C

Answer:

C,D, and F should be the correct answers.

Step-by-step explanation:

C. 5(3)= 15+6=21

D. 7(3)= 21-2=19

F. 5(3)=15

Answer:

1100 square inches

Step-by-step explanation:

The faces are all rectangles (area = length x width)

Area of bottom:  20 x 10 = 200

Area of front: 20 x 15 = 300

Area of back (same as front) = 300

Area of right side: 10 x 15 = 150

Area of left side (same as right side) = 150

Total of all the sides: 1100

Answer:

[tex]w=\frac{s-2lh}{2(h+l)}[/tex]

Step-by-step explanation:

Given the equation, [tex]S=2(lw+lh+wh)[/tex], solve for w.

[tex]S=2(lw+lh+wh)[/tex], distribute the 2.

=> [tex]S=2lw+2lh+2wh[/tex], subtract [tex]2lh[/tex] from both sides.

=> [tex]S-2lh=2lw+2wh[/tex], factor out a [tex]w[/tex] from the right-hand-side.

=> [tex]S-2lh=w(2l+2h)[/tex], now divide [tex](2l+2h)[/tex] from each side.

=>[tex]\frac{S-2lh}{2l+2h}=w[/tex]

Final answer: [tex]w=\frac{s-2lh}{2(h+l)}[/tex]

Answer:

Its always ily, but never stwywimc

Step-by-step explanation:

Answer:

They are in A. P so the sum will be 2380

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