Find the term t of each continuously compounded account below rounded to the nearest tenth of a year. In the chart, B is the
ending balance, P is the principal, and r is the interest rate expressed as a percent.

Suppose that quiz scores in a beginning statistics class have a mean of 7.1 with a standard deviation of 0.4, the range in which at least 75% of the data will reside is from 6.3 to 7.9.

Chebyshev's Theorem is a statistical tool that provides a range for how much data is likely to fall within a certain number of standard deviations from the mean.

Specifically, it tells us that, for any set of data, no matter how it is distributed, at least 1 - (1/k^2) of the data will fall within k standard deviations from the mean, where k is any positive number greater than 1.

In this case, we want to find the range in which at least 75% of the data will reside. We can use Chebyshev's Theorem to determine the minimum value of k that will give us this range. We know that at least 75% of the data should fall within two standard deviations from the mean, so we can set k = 2.

Using Chebyshev's Theorem, we can say that at least 1 - (1/2^2) = 75% of the data will fall within 2 standard deviations from the mean. The standard deviation is 0.4, so two standard deviations would be 2 * 0.4 = 0.8.

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to get the equation of any straight line, we simply need two points off of it, let's use the points in the picture below.

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-10}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{-10 +4}{6 +3} \implies \cfrac{ -6 }{ 9 } \implies - \cfrac{2 }{ 3 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- \cfrac{2 }{ 3 }}(x-\stackrel{x_1}{(-3)}) \implies y +4 = - \cfrac{2 }{ 3 } ( x +3) \\\\\\ y+4=- \cfrac{2 }{ 3 }x-2\implies {\Large \begin{array}{llll} y=- \cfrac{2 }{ 3 }x-6 \end{array}}\)

Answer:

8*4*3=96 boxes in total

Step-by-step explanation:

I think. I just multiplies the 3 numbers. Hope this helps (:

Answer:

8*4*3=96 boxes in total

Step-by-step explanation:

I just multiplies the 3 numbers.

Answer:

A.

Step-by-step explanation:

Recall that circumference is given by:

\(C=2\pi r\)

We know that the circumference is 8π inches. Thus, we can substitute 8π for C:

\(8\pi =2\pi r\)

To solve for r, the radius, we can divide both sides by 2π. Hence:

\(\displaystyle r = \frac{8\pi}{2\pi}=4\)

Therefore, the radius is four inches.

Our answer is A.

Result:

It will take Austin approximately 5.13 years to grow his investment to $4179, assuming no withdrawals are made.

We shall use the formula for compound interest to solve the problem

Using the formula for compound interest:

A = \(P(1 + r/n)^{nt}\)

Where:

A = the future value (in this case, $4179)

P = the principal amount (in this case, $3000)

r = the annual interest rate (in this case, 4.6% or 0.046 as a decimal)

n = the number of times interest is compounded per year (in this case, quarterly, so n = 4)

t = the number of years

We have:

4179 = 3000\((1 + 0.046/4)^{4t}\)

Let's solve for t by isolating it on one side of the equation:

\((1 + 0.046/4)^{4t}\) = 4179/3000

Then, we take the natural logarithm of both sides to eliminate the exponent:

ln(\((1 + 0.046/4)^{4t}\)) = ln(4179/3000)

Using the property of logarithms that states ln(\(a^{b}\)) = b*ln(a):

4t * ln(1 + 0.046/4) = ln(4179/3000)

We can now divide both sides by 4 * ln(1 + 0.046/4) to solve for t:

t = ln(4179/3000) / (4 * ln(1 + 0.046/4))

We can use a calculator to find that t = ≈ 5.13 years (rounded to two decimal places).

Therefore, it will take approximately 5.13 years for Austin's investment to grow to $4179, if there are no withdrawals and the interest is compounded quarterly.

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The vertex is at (0, 4), then we conclude that the turning point is at(0, 4), thus the correct option is the first one.

We define the turning point on a graph as the point where the graph changes its behavior (it changes from decreasing to increasing, or from increasing to decreasing).

For the case of absolute value functions, the turning point is always on the vertex, and remember that for the general absolute value function:

f(x) = |x + a| + b

The vertex is at (-a, b).

Then in this case:

f(x) = |x| + 4

The vertex is at (0, 4), then we conclude that the turning point is at(0, 4), thus the correct option is the first one.

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Answer: 0.147

Step-by-step explanation:

Liam / total

total = 10 + 3 + 11 + 44 = 68

10 / 68 = 5 / 34

0.1470588 = 0.147

The measures of the angles are a = 38, b = 52, c = 104 and d = 90 degrees

From the question, we have the following parameters that can be used in our computation:

The circle and its properties

The angle in a semicircle is 90 degrees

So, we have

d = 90

Using the properties of angles, we have

a = 1/2 * 76

a = 38

Also, we have

a + b + d = 180 --- sum of angles in a triangle

So, we have

38 + b + 90 = 180

This gives

b = 52

Using the properties of angles, we have

b = 1/2 * c

52 =  1/2 * c

c = 104

Hence, the measures of the angles are a = 38, b = 52, c = 104 and d = 90 degrees

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Answer:

x = -15

Step-by-step explanation:

In fractional equations we cross multiply the expressions:

In cross multiplying the denominator of the first fraction is multiplied with the numerator of the second fraction and vice versa:

-2x = 30 divide both sides by -2

x = -15

Answer:

I wish I can read all the text

Answer:

The correct answer is C = 16 兀

explanation:

In this problem, C represents the cost and r represents the rate. The formula for calculating the cost is C = 2 * r, where C is the cost in 兀 and r is the rate in 兀/unit.

When r is 8 兀/unit, the cost is C = 2 * 8 = 16 兀.

Answer:

C = 16 π

Step-by-step explanation:

If C = 2 π r, and r = 8:

C = 2 π (8)

Simplify (multiply 2x8):

C = 16 π

The missing value 'x' in the two-way relative frequency table is 0.36.

To convert the two-way table to a two-way relative frequency table, we need to calculate the relative frequencies for each category. Relative frequency is calculated by dividing the frequency of a particular category by the total count in that row or column.

Let's denote the missing value as 'x'. To find the value of 'x', we need to ensure that the sum of the relative frequencies in each row and each column adds up to 1.

First, let's calculate the relative frequencies for each category:

Likes hockey: The total count in this row is 12 + 18 = 30.

Relative frequency of "Likes hockey" = 12/30 = 0.4

Relative frequency of "Doesn't like hockey" = 18/30 = 0.6

Likes baseball: The total count in this column is 12 + 14 = 26.

Relative frequency of "Likes baseball" = 12/26 ≈ 0.4615

Relative frequency of "Doesn't like baseball" = 14/26 ≈ 0.5385

To ensure that the relative frequencies add up to 1, we can set up the following equations:

0.4 + x = 1 (sum of relative frequencies in the "Likes hockey" row)

0.4615 + 0.5385 + x = 1 (sum of relative frequencies in the "Likes baseball" column)

Simplifying the equations, we have:

x = 0.6 (1 - 0.4) = 0.6 * 0.6 = 0.36

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The solution of the given expression is 9*\(x^{4}\)/100.

GIven an expression equal to 27\(x^{12}\)/300\(x^{8}\).

We have to simplify the expression in which variable comes only once.

Expression is combination of numbers ,symbols, fraction, coefficients, indeterminants,determinants, etc. It is mostly not found in equal to form. It expresses a relationship between variables.

The given fraction is 27\(x^{12}\)/300\(x^{8}\).

When we observe we find that in numerator x has large power and denominator x has small power as compared to power in numerator. So we will deduct the powers so that they will give only one power to us.

=27\(x^{4}\)/300

Now divide numerator an denominator by 3.

=9\(x^{4}\)/300

Hence the expression 27\(x^{12} /300x^{8}\) will look like \(9x^{4} /100\) after simplifying.

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Answer:

\(Simplify:\sqrt\frac{27x^{12} }{300x^{8} }\)

\(O \frac{9}{100}x^{4}\)

✔ \(\frac{3}{10} x^{2}\)

\(O \frac{27}{300} x^{4}\)

\(O\frac{9}{10} x^{2}\)

Answer:

Well, I can't say which of the following combinations, because I can't see what you see. But I will list some equivalent ratios & hope one fits. If it doesn't, maybe type in the comments what the choices are & I can help more.

Step-by-step explanation:

2:5

4:10

6:15

8:20

10:25

12:30

14:35

Answer:

≈ -0.0005

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

You are asking a question trying to suggest whether it can be done later

The linear function that relates y to x is given as follows:

y = -0.5x + 57.

The slope indicates that the height decays 0.5 feet per minute. The y-intercept indicates that the descent starts at a cruising altitude of 57 feet.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

From the table, when x = 0, y = 57, hence the intercept b is given as follows:

b = 57.

When x increases by 10, y decays by 5, hence the slope m is given as follows:

m = -5/10

m = -0.5.

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Answer:

The sum will be close to 1/4

Step-by-step explanation:

1/8+1/6 is 7/24, and 1/4th of that is 6/24, so it is very close.

Answer: The sum will be close to 1/4

Step-by-step explanation:

You can start by making the fractions have the same denominator, (8*6) which gets you 48

You then want to use the butterfly method, so 1/8 becomes 6/48 and 1/6 becomes 8/48. You then add these up to 14/48.

12/48 is 1/4, and 14/48 is close to 12/48, thus making the answer the first option.

The width cannot be negative, the width of the walkway is 6 feet. The total area of the garden and the walkway is given as 648 square feet. We know the area of the garden is length multiplied by width, which in this case is 12 feet by 15 feet, so the garden area is\(12 \times 15 = 180\) square feet.

To find the area of the walkway, we subtract the garden area from the total area. Therefore, the area of the walkway is 648 - 180 = 468 square feet.

The walkway surrounds the garden on all sides, so its length and width will be greater than the corresponding dimensions of the garden.

To calculate the width of the walkway, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, the length is 12 + 2x (twice the width of the walkway) and the width is 15 + 2x.

So, we have the equation\((12 + 2x) \times (15 + 2x) = 468\).

Expanding and rearranging the equation, we get\(4x^2 + 54x - 228 = 0.\)

Solving this quadratic equation using factoring, completing the square, or the quadratic formula, we find that x = 6 or x = -9/2.

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Complete question is;

​In a sample of 800 U.S.​ adults, 199 think that most celebrities are good role models. Two Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.​adults, complete parts​ (a) through​ (c).

(a) Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is ________?(Round to three decimal places as​ needed.)

​(b) Find the probability that neither adult thinks most celebrities are good role models. The probability that neither adult thinks most celebrities are good role models is _______?(Round to three decimal places as​ needed.) ​

(c) Find the probability that at least one of the two adults thinks most celebrities are good role models. The probability that at least one of the two adults thinks most celebrities are good role models ______? (Round to three decimal places as​ needed.)

Answer:

A) 0.062

B)0.564

C)0.436

Step-by-step explanation:

There are 800 US adults sampled and 199 think that most celebrities are good role models.

Now, two are selected without replacement.

Thus;

A) Probability that both adults think most celebrities are good role models would be = (199/800) × (198/799) = 39402/639200 = 0.062

B) we want to find probability that neither adult thinks most celebrities are good role models.

Now, since 199 out of 800 think that most celebrities are good role models..

Thus, number that doesn't think most celebrities are good role models = 800 - 199 = 601

probability that neither adult thinks most celebrities are good role models. would be = (601/800) × (600/799)= 180300/319600 = 0.564

C) We want to find the probability that at least one of the two adults thinks most celebrities are good role models.

Now, since we already have the probability that neither of them thinks most celebrities are good role models, we will just subtract that probability from 1.

Thus;

probability that at least one of the two adults thinks most celebrities are good role models = 1 - 0.564 = 0.436

Answer:

x=1 y=2

Step-by-step explanation:

satisfy both equations 2x=x+1 then solve for

Answer:

0.38

Step-by-step explanation:

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

Answer:

A

Step-by-step explanation:

5 feet 9 in inches=69

86-69=17

Answer:  602 miles

=====================================================

Work Shown:

x = number of extra miles (past the 150 mark)

0.25x = cost for those extra miles

0.25x+180 = total cost

0.25x+180 = 293

0.25x = 293-180

0.25x = 113

x = 113/(0.25)

x = 452

So you drove the original 150 miles, plus an additional 452 miles.

The total is 150+452 = 602 miles

Answer: (x^2-5x+13)+(x^2+3x-6)

Step-by-step explanation:

Option (D) She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1 is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

Patti is using mental math to evaluate the expression (70 + 12.8 + 30) + 6.1.

The number expression is:

= (70 + 12.8 + 30) + 6.1

As we know from the commutative property

a +  b = b + a

Applying commutative property in the number expression:

= (70 + 30+ 12.8) + 6.1

She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1.

Thus, option (D) She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1 is correct.

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Answer:

B . Yes

Step-by-step explanation:

Recall: a tangent of a circle is perpendicular to the radius of a circle, forming a right angle at the point of tangency.

Therefore, if segment ST is tangent to circle P, it means that m<T = 90°, and ∆PST is a right triangle.

To know if ∆PST is a right triangle, the side lengths should satisfy the Pythagorean triple rule, which is:

c² = a² + b², where,

c = longest side (hypotenuse) = 37

a = 12

b = 35

Plug in the value

37² = 12² + 35²

1,369 = 1,369 (true)

Therefore we can conclude that ∆PST is a right triangle, this implies that m<T = 90°.

Thus, segment ST is a tangent to circle P.