if log 5 a= 3, then log 5 (a^3) =

a) The total interest that Charlie, who borrows $700 at a simple interest rate of 4% per annum, will pay after 4 years is $112.

b) The total repayment amount after 4 years, including interest, is $812.

The simple interest system is one that does not add interest to the principal before calculating subsequent years' interest.

The simple interest system is different from compound interest.

The simple interest formula is given as Principal x Time x Rate.

Principal loan = $700

Loan period = 4 years

Annual interest rate = 4%

Interest system = Simple Interest

Simple interest after 4 years = $112 ($700 x 4% x 4)

Amount to be repaid = Principal + Interest

= $812 ($700 + $112)

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The Average Acceleration of the car will be 14.67 ft/[tex]s^{2}[/tex].

What is Acceleration?

The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. Any procedure where the velocity varies is referred to as acceleration. There are only two ways to accelerate: changing your speed or changing your direction, or changing both. This is because velocity is both a speed and a direction.

Formula: a = (v(final) - v(initial))/t

In the given formula, it is given that:

v(initial) = 30mph = 44 ft/s

v(final) = 70mph = 102.67 ft/s

t(time) = 4s

Putting these values in our formula, we get:

a(acceleration) = (102.67 - 44)/4

a = 14.67 ft/[tex]s^{2}[/tex].

Therefore as per the given problem, the acceleration of the given car is 14.67 ft/[tex]s^{2}[/tex].

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The 95% confidence interval for the population mean is given as follows:

(3.64, 4.18).

It tells that we are 95% sure that the true population mean rating is between these two bounds.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 15 - 1 = 14 df, is t = 2.1448.

The remaining parameters for this problem are given as follows:

[tex]\overline{x} = 3.91, s = 0.48, n = 15[/tex]

Hence the lower bound of the interval is of:

[tex]3.91 - 2.1448\frac{0.48}{\sqrt{15}} = 3.64[/tex]

The upper bound of the interval is of:

[tex]3.91 + 2.1448\frac{0.48}{\sqrt{15}} = 4.18[/tex]

The sample is given as follows:

3.9

3.1

3.7

4.4

3.2

4.1

3.3

4.4

4.3​,

4.4

4.5

3.9

3.2​

4.2,

4.0

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Answer:

Step-by-step explanation:

Given ∠B=45,∠C=55

So, ∠A=180°−45°−55°

=80°

From △ABD,40°+45°+∠ADB=180°

⟹∠ADB=95°

From△ADC,40°+55°+∠ADC=180°

⟹∠ADC=85°.

Answer:

Yes

Step-by-step explanation:

328/8 = 41

Thus if 41 members are in each line, there should be no members left without a spot and it should be equal all across

Answer: 15

Step-by-step explanation:

The range is the set of all Y values, in this question -8 is the minimum and +7 is the maximum, therefore the range is (-8-7) = -15, but range is not negative so we get 15

Answer:

4.59 × 10^(5)

Step-by-step explanation:

Answer: 4.59 x 10^5

Step-by-step explanation:

If we move the decimal place over 5 times in the answer we get 459,000.

I hope this was able to help you :D

Answer:

  (b)  40

Step-by-step explanation:

You want the value of the "whole" corresponding to a "part" of 25 in the given table.

Based on the relationships in the 2nd and 3rd columns, it appears that the parts on the second line are 5/8 of the whole.

This means that 25 is 5/8 of B, or ...

  B = 8/5 × 25 = 40

The value of B in the table is (b) 40.

__

Additional comment

The parts on the first line will be 3/5 of the value of the parts on the second line. The sum of the two parts in each column is equal to the whole.

<95141404393>

A dataset's quartiles are critical summary statistics that split the data into four equal groups. The first quartile (q1), often known as the lower quartile, splits the data into the bottom 25% and the remainder.

The second quartile (q2), commonly known as the median, splits the data into the lowest and highest 50%. The third quartile (q3), often known as the upper quartile, divides the data into the lowest 75% and the highest 25%. These quartiles give useful information regarding the data distribution and value spread.

The quartiles may also be used to find outliers in the dataset. Understanding the quartiles is an important element of data analysis and may assist inform data-driven decision making.

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The required point-slope form for the given line is  y = 3x/2 + 14.

In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change. Draw a sloping triangle connecting the two spots you find on the line. ​

We have,

A line passes through the point (-6, 5) and has a slope of 3/2

Then the equation of line is;

y - 5 = 3/2(x - (-6))

y - 5 =  3/2 (x + 6)

2y - 10 = 3x + 18

2y = 3x + 28

y = 3x/2 + 14

Thus the point slope form of the line is y = 3x/2 + 14.

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Answer:

The distance between -19 and 12 is 31.

Step-by-step explanation:

The class width of each class is 17.

Class width is the distance between a class's upper and lower bounds (category). It may also refer to one of the following more precisely, depending on the author:

the difference between the upper and lower limits of two (nearby) consecutive classes, or the lowest and higher limits of two classes.

The width of each class in a frequency distribution table must be the same. Due to the fact that you are only working with a single width, this makes calculating the class width relatively simple (as opposed to varying ones).

To find the class width in this, we subtract the lower limits of two consecutive class. i.e.

47 - 30 = 17

64 - 47 = 17

81 - 64 = 17

98 - 81 = 17

So that, The class width of each class is 17.

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An equation which can represent a baby manatee's growth include the following: B. x + 4 ≤ 13.

The variable x represent the baby manatee's growth after birth.

In order to write and solve an inequality that represents a baby manatee's growth, we would take note of the following important information;

Now, we can write an inequality that represents the value of x for which a baby manatee's growth as follows;

x + 4 ≤ 13

By subtracting 4 from both sides of the inequality, we have the following:

x + 4 - 4 ≤ 13 - 4

x ≤ 11

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An exponential model has the formula A is A0(b)t/c, so, we get 1071371.

A = A0(b)t/c,

97532 ( 455277)1/ 41446 = 1071371.

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The number of members for counseling groups of children should generally be smaller as compared to counseling groups for adults. This is because children may feel overwhelmed in larger group settings and may not be able to adequately express themselves. Smaller groups also allow for more individualized attention and support.

The recommended number of members for counseling groups of children should generally be smaller than that of groups for adults. This is because children may feel overwhelmed in larger group settings and may not be able to adequately express themselves. This can lead to a lack of engagement and little benefit from the group counseling sessions. Smaller groups also allow for more individualized attention and support, which is important for young people to feel comfortable expressing their thoughts and feelings. Additionally, smaller groups can help create a more intimate environment for participants to safely share their experiences and feelings with one another. As such, reducing the size of the group for counseling sessions with children can help ensure a more successful therapeutic experience.

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Answer:

Step-by-step explanation:

The value of x for the given expression will be x = 0.1535.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is [tex]15^{5x}=8[/tex]. The expression will be solved as below,

[tex]15^{5x}=8[/tex]

Take log on both the sides and solve for the value of x.

5x = 3log₁₅(2)

x = (3/2)log₁₅(2)

x = 0.1535

Hence, the value of x will be 0.1535.

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A graph of each function is shown in the image attached below.

The number of commercials (x) is equal to 8 commercials while the number of movies (y) is equal to 4 movies.

In order to graphically solve the system of equations, we would write two (2) equations that models the situation by assigning variables to the number of commercials and number of movies respectively, and then translate the word problem into algebraic equation as follows:

Since Gianna would earn $50 every time one of her songs is played in a commercial and $100 every time one of her songs is played in a movie, an equation which models it is given by;

50x + 100y = 800

Additionally, Gianna's songs were played on twice as many commercials as movies;

x = 2y

Next, we would use an online graphing calculator to plot the above system of equations with a point of intersection at (8, 4) as shown in the image attached below.

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Answer:

9 x - 5

Step-by-step explanation:

Simplify the following:

6 x - 3 - (-3 x + 2)

-(-3 x + 2) = 3 x - 2:

6 x - 3 + (-2 + 3 x)

Grouping like terms, 6 x - 3 - 2 + 3 x = (6 x + 3 x) + (-3 - 2):

(6 x + 3 x) + (-3 - 2)

6 x + 3 x = 9 x:

9 x + (-3 - 2)

-3 - 2 = -(3 + 2):

9 x + (-(3 + 2))

3 + 2 = 5:

Answer: 9 x - 5

The percentage and decimal values of the given fraction are 26.67% and 0.267 respectively.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given a fraction number 4/15

To convert it into decimals we need to divide 4 by 15

Thus, the Decimal value = 0.2666...

the Decimal value = 0.267

To convert it into a percentage we need to multiply it with 100

So,

The percentage values of the given fraction = 4/15 * 100

The percentage values of the given fraction = 26.67%

Therefore, the percentage and decimal values of the given fraction are 26.67% and 0.267 respectively.

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The length of side x is given as follows:

[tex]x = \frac{11\sqrt{3}}{3}[/tex]

The three trigonometric ratios are defined as follows:

For this problem, we have that:

Applying the tangent, the length x is obtained as follows:

tan(60º) = 11/x

x = 11/tan(60)º

[tex]x = \frac{11}{\sqrt{3}}[/tex]

[tex]x = \frac{11\sqrt{3}}{3}[/tex]

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If the residual is negative, it means the observed number of wins is lower than the predicted number of wins, indicating that the team performed worse than expected based on their yards allowed.

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Answer:i think it is yes! this )--89+98

Step-by-step explanation:

a) E(e^(taY)) = m(at), then the moment-generating function of U is e^(tb)m(at).

b) µ is the mean of Y and σ^2 is the variance of Y.

c) the moment-generating function of X =e^((−3µ + 4)t + (9/2)σ^2t^2) and The distribution of X is normal.

a) If Y is a random variable with moment-generating function m(t), and U is given by U = aY + b, then the moment-generating function of U is e^(tb)m(at). This can be shown by using the definition of a moment-generating function:

E(e^(tU)) = E(e^(taY + tb)) = E(e^(taY)e^(tb)) = e^(tb)E(e^(taY))

Since E(e^(taY)) = m(at), then the moment-generating function of U is e^(tb)m(at).

b) To find the mean and variance of U using the moment-generating function, we can take the first and second derivatives of e^(tb)m(at) and set t = 0. The first derivative with respect to t evaluated at t = 0 is:

(d/dt)e^(tb)m(at) = be^(tb)m(at) + ae^(tb)m'(at)

Setting t = 0, we get the mean of U:

E(U) = be^(0)m(a0) + ae^(0)m'(a0) = b + a*(m'(0)) = b + a*µ

Where µ is the mean of Y.

The second derivative of e^(tb)m(at) is:

(d^2/dt^2)e^(tb)m(at) = b^2e^(tb)m(at) + 2abe^(tb)m'(at) + a^2e^(tb)m''(at)

Setting t = 0, we get the variance of U:

Var(U) = b^2e^(0)m(a0) + 2abe^(0)m'(a0) + a^2e^(0)m''(a0) = b^2 + 2ab*(m'(0)) + a^2*(m''(0)) = b^2 + 2abµ + a^2σ^2

Where µ is the mean of Y and σ^2 is the variance of Y.

c) If the moment-generating function of a normally distributed random variable Y with mean µ and variance σ^2 is m(t) = e^(µt + (1/2)t^2σ^2), then the moment-generating function of X = −3Y + 4 is e^((−3µ + 4)t + (1/2)(−3)^2σ^2t^2) = e^((−3µ + 4)t + (9/2)σ^2t^2)

The distribution of X is normal with mean (-3µ + 4) and variance (9/2)σ^2. This can be deduced by the fact that if Y is normally distributed, then a linear transformation of Y (such as X = aY + b) is also normally distributed with mean aµ + b and variance a^2σ^2.

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EASY just say THANK YOU!!!

Answer:

1. 3 ones

2. 3

3. 3 tens

4. 3

5. 3 hundreds

6. 3

7. 3 halves

8. 3 (not 3/2)

9. 3 fourths

10. 3

11. 3

12. 2

13. 1/2

14. 3

15. 5/2

16. 3/4

17. 3

18. 3/2

19. 3/4

20. 7/2

21. 2/3

22. 4/11

NOTE: Read the step-by-step explanation on how we arrive on these final answers. Don't just copy-paste it and try to understand the concept so that next time you already know how to solve this type of expressions.

Step-by-step explanation:

This is a simple mathematic problem which requires basic strategies to be solved. People should already know on how to calculate these simple mathematic tasks. Most especially to the first 7 items, we will just use division to get the final answer (numerator/denominator).

[tex]\frac{9}{3}[/tex] = 3 or

9 ÷ 3 = 3

Similar, with the rest of items that includes fractions. We will just reciprocate the denominator and multiply it to the numerator to get the final answer.

Example was the item 8:

= [tex]\frac{9}{2}[/tex] ÷ [tex]\frac{3}{2}[/tex]

= [tex]\frac{9}{2}[/tex] x [tex]\frac{2}{3}[/tex]

= [tex]\frac{18}{6}[/tex]

= 3

Answer:

Rise: 2

Run: 1

Slope: 2

At what point does the line intersect the y-axis? (0,-1)

According to the given vector, the component form of u is (−3.87, 1.048)

The term vector in math is known as a quantity or phenomenon that has two independent properties such as magnitude and direction

Here we have given that the value of the following are obtained through the given diagram.

θ = 165°

Then the value of |u| is calculated by using the formula,

=> ∣u∣ = 4θ

When we apply the value on it, then we get,

=> ∣​u​​​∣=4

Now, we have to calculate the value of

=> ∣​u​​​∣cos165° ​​​= −3.864

=> ∣​u​∣sin165° ​ ​= 1.035

Then the component form of the vertor u is written as,

=> ​u ​​= (∣​u​​​∣cos165°​​, ∣​u​​​∣sin165​°​​)

When we apply the values on it, then we get the resulting form as,

=> ​u ​= (−3.87, 1.048)

Complete question:

The vector u is shown below. Find the component form of u.

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Answer:

A resposta correta é 6. Esta sequência geométrica,  tem uma razão comum de r = 1/2.  O 10º prazo o da sequência pode ser encontrado usando a fórmula an = a1 * r-n1, em de n é o número do prazo. Assim, o 10º prazo é: ano = 384 * (1/2)9 = 384 * (1/512) = 6

The equation of the graph is g'(x) = -(x + 2)² - 1

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

g(x) = x²

From the graph, we can see that the graph is inverted

This means that

g'(x) = -x²

Next, the graph is shifted left by 2 units

This implies that

g'(x) = -(x + 2)²

Lastly, the graph is shifted down by 1 unit

So, we have

g'(x) = -(x + 2)² - 1

Hence, the equation is g'(x) = -(x + 2)² - 1

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Step-by-step explanation:

[tex] \alpha + \beta = \frac{ - b}{a} = 6 \\ \alpha \beta = \frac{c}{a} = 19 \\ p(x) = k( {x}^{2} - ( \alpha + \beta )x + ( \alpha \beta )) = 0\\ = k( {x}^{2} - 6x + 19) \\ polynomial \: = {x}^{2} - 6x + 19 = 0[/tex]

it takes so much tume to solve and type it here and its so hard so plzzz mark me as brainliest plz .