Albert invests money in an account that earns a yearly dividend. The amount, A, in his account at the end of t years is given by the equation Which statement is correct?​

The expression to represent the phrase "6 times a number plus 3" is:

"6n + 3".

"n" represents an unknown number, and "6" and "3" are constants. The expression means that 6 is being multiplied by "n" to get an intermediate result, and then 3 is being added to that result to get the final answer.

For example, if n = 2, then the expression would evaluate to 6 * 2 + 3 = 12 + 3 = 15. So, the expression "6n + 3" represents the mathematical relationship between the unknown number "n" and the final result.

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The population of bacteria after h hours is 0.075.

Bacterial growth is proliferation of bacterium into two daughter cells, in a process called binary fission. Providing no event occurs, the resulting daughter cells are genetically identical to the original cell. Hence, bacterial growth occurs. Both daughter cells from the division do not necessarily survive. However, if the surviving number exceeds unity on average, the bacterial population undergoes exponential growth.

The equation that models the population of bacteria h-hours after the original 275 bacteria were measured is given by:

P(h) = 275 × [tex](1 + 0.075)^h[/tex]

p(h)=0.075

where P(h) is the population of bacteria after h hours and 0.075 is the growth rate of 7.5% per hour.

Therefore, the population of bacteria after h hours is 0.075.

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In a right triangle, the Pythagorean theorem states that the sum of the legs squared is equal to the hypotenuse squared.

Or that a² + b² = c²

Where and and b are the legs and c is the hypotenuse

(Note that the hypotenuse is the longest side and the legs are the two shorter sides)

Here, we are given the length of the hypotenuse as well as the length of one of the legs. Given this we are asked to find the other leg UT.

We can find the length of UT by plugging in the given values into the Pythagorean Theorem and then solving for the missing variable.

Because the given hypotenuse is 17 we can say that c = 17 and since a leg is given we can say that a = 8

Plugging this into the formula we acquire (b is UT or the other leg)

8² + b² = 17²

==> evaluate the exponents

64 + b² = 289

==> subtract 65 from both sides

b² = 225

==> take the square root of both sides

b = 15

The length of UT is 15

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The other side lengths of the triangle will be 24 and 26 units.

How to calculate the side?

The shortest side of a triangle similar to triangle XYZ is 20 units long and the shortest side on the other. triangle is 10. This means the proportion is [tex]\frac{20}{10}[/tex]=2

The other sides will be:

⇒12 × 2 = 24

⇒13 × 2 = 26

Therefore, the sides are 24 and 26 respectively.

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The inverse tangent function [tex]tan^{-1}[/tex] can be used to find the values of x for which tan x = 0.8645 in the interval 0 degrees < x < 360 degrees. The inverse tangent function gives us the angle that has a tangent equal to the input value.

The function can be expressed as:

[tex]x = tan^{-1 (0.8645)}[/tex]

Using a scientific calculator or trigonometry tables, we can find that the value of [tex]tan^{-1 (0.8645)}[/tex] is approximately 47.5 degrees.

So, in the interval 0 degrees < x < 360 degrees, there is one value of x that satisfies the equation tan x = 0.8645, and it is approximately 47.5 degrees. It's important to remember that the inverse tangent function is a one-to-one function and its range is restricted to the interval -90° < x < 90°, so the value found represents the smallest angle in the interval 0° < x < 360° that has a tangent equal to 0.8645.

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The equation that represents the number of books will be 6x - 8 = 58. And the number of books will be 11.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Melissa bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6.

Let 'x' be the number of books. Then the equation is given as,

6x - 8 = 58

Simplify the equation, then we have

6x - 8 = 58

6x = 66

x = 11

The equation that represents the number of books will be 6x - 8 = 58. And the number of books will be 11.

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Answer:

10.8s

Step-by-step explanation:

120÷11.1= 10.8s (to 3 s.f.)

Answer:

306

Step-by-step explanation:

Let's call the number of fiction books "f" and the number of non-fiction books "n". From the given information, we know that the ratio of fiction books to non-fiction books is 5:2 and the total number of books is 1421, so we can write the following equation:

f + n = 1421

Since the ratio of fiction books to non-fiction books is 5:2, we can write:

f/n = 5/2

We can cross-multiply to solve for f:

f = (5/2) * n

Substituting this expression for f into the first equation:

(5/2) * n + n = 1421

Expanding the left side:

(5/2 + 2/2) * n = 1421

Simplifying the left side:

(5 + 2)/2 * n = 1421

(7/2) * n = 1421

Dividing both sides by (7/2):

n = 1421 * 2/7

n = 204

So there are 204 non-fiction books and 5/2 * 204 = 204 * 5/2 = 102 * 5 = 510 fiction books.

The difference between the number of fiction books and non-fiction books is 510 - 204 = 306. So there are 306 more fiction books than non-fiction books in the library.

Step-by-step explanation:

If the ratio of fiction and non-fiction books are 5:2. Therefore that means that the total books were divided into 7 parts and the fiction books took 5 parts while the non-fiction books took two parts.

To get the number of fiction and non-fiction books we first add the ratio

[tex]5 + 2 = 7[/tex]

So that means that 7 = 1421

After adding the ratio we now take

The total parts that the books took as the numerator and the total of the ratio as the denominator, and multiply the fraction by the total number of books which is 1421

[tex] \frac{5}{7} \times 1421 = number \: of \: fiction \: books[/tex]

[tex] \frac{2}{7} \times 1421 = number \: of \: non - fiction \: books[/tex]

let's work out each fraction separately

[tex] \frac{5}{7} \times 1421 = \frac{7105}{7} [/tex]

[tex] \frac{7105}{7} = 1015[/tex]

[tex] \frac{2}{7} \times 1421 = \frac{2842}{7} [/tex]

[tex] \frac{2842}{7} = 406[/tex]

To get the answer to the question we subtract the number of non-fiction books from the number of fiction books

[tex]1015 - 406 = 609[/tex]

The standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point is 1/36(x +4)² - 1.

Equation of a quadratic function in the vertex form is given by;

f(x) = a(x - h)² + k

Here, (h, k) is the vertex of the parabola representing the quadratic function;

Given;

Vertex of the quadratic function (−4, −1);

Parabola passes through a point  (−2, 4);

Substitute the vertex in the quadratic function;

f(x) = a(x +4)² - 1

Because, this parabola passes through a point (7, 0),

0 = a(-2- 4)² - 1

0 = 36a - 1

a = 1/36

Equation of the quadratic function will be;

f(x) = 1/36(x +4)² - 1

Therefore, equation of the quadratic function will be f(x) = 1/36(x +4)² - 1;

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Answer:

Your answer should be: TRUE FALSE TRUE FALSE

The quadratic equation that we need to solve is:

96 = 208 - 16t^2

And the solution is t = √7

We know that the height equation is the quadratic equation below:

h = h0 - 16t^2

If the initial height is 208, then we can write:

h = 208 - 16t^2

Now we can find how long takes to reach a height of 96 feet, then we can write:

96 = 208 - 16t^2

That is the equation we need to solve.

Solving that for t we will get:

96= 208 - 16t^2

16t^2 = 208 - 96

16t^2 = 112

t^2 =112/167

t = √7

The correct option is the last one.

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The discount amount based on 35% discount offered on $89.95 is $31.5.

The discount amount can be calculated by the formula -

Final amount = original price - discount percentage × original price

The method of solving this formula will be to first multiply followed by subtraction according to PEMDAS rule.

Now, keep the values in formula

Final amount = 89.95 - 35/100 × 89.95

Performing multiplication and division on Right Hand Side of the equation

Final amount = 89.95 - 31.48

Now performing subtraction on Right Hand Side of the equation

Final amount = $58.47

Here we see that that the discount amount is $31.48

Round to nearest penny = $31.5

Thus, the discount amount is $31.5.

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The cumulative frequency and relative cumulative frequency for students who earned a score of 20 or lower on the quiz is 29; 58%. (option d)

Cumulative frequency refers to the running total of frequencies, or the sum of frequencies up to a certain point. In this case, the cumulative frequency is the number of students who scored 20 or lower on the quiz.

Relative cumulative frequency, on the other hand, expresses the cumulative frequency as a percentage of the total number of students in the sample. To find the relative cumulative frequency, we divide the cumulative frequency by the total number of students and multiply by 100.

Therefore, for students who scored 20 or lower on the quiz, the cumulative frequency is 29 and the relative cumulative frequency is 58% (29/50 * 100).

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Answer: 38, 76%

Step-by-step explanation:

Recall that for cumulative frequency we add up all the values that fall above or below a given bin of data. So, if we want all scores less than 20 it should be the first four bins with a total of:

8 plus 8 plus 13 plus 9 equals 38

To get the relative frequency we take the total in the bins for scores of 20 and lower divided by the total of all bins:

38 over 50 equals 0.76 equals 76 percent sign

The greatest possible speed that Oleg could have bicycled that day is 13 miles per hour.

Let's call the total distance that Oleg jogged z. Then z = 2x.

The total distance that Oleg bicycled was 30 - z - 2. Let's call this distance w. Then w = 30 - 2x - 2.

Since Oleg bicycled for 2 hours, the speed that he bicycled was w / 2. So, w / 2 = y.

Substituting the expressions for z and w, we have:

y = (30 - 2x - 2) / 2.

Since y must be the greatest possible speed that Oleg could have bicycled that day, x must be the smallest possible value.

Since Oleg jogged for 2 hours, the minimum value of x is 2 / 2 = 1.

Substituting x = 1 into the expression for y, we have:

y = (30 - 2 * 1 - 2) / 2 = (26) / 2 = 13.

So, the greatest possible speed that Oleg could have bicycled that day is 13 miles per hour.

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In a coin flip experiment, you would see a pattern of 50/50 heads and tails if every student in the class skewed their findings to show 5 heads and 5 tails.

This is due to the fact that each participant purposefully altered their results to display an equal number of heads and tails.

It is crucial to remember that this pattern does not accurately reflect the chances of either getting heads or tails in a fair coin flip. The results cannot be taken as a representative sample of a fair coin flip because everyone purposefully slanted their findings. It is crucial to conduct experiments with appropriate controls and prevent results bias in order to acquire reliable findings.

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The table should be completed as follows;

Coordinate   Key feature    Does the coordinate        Justification

                                                  make sense  ___________________

(-7.565, 0)   it is a key feature          yes                     it is a zero (root).

(0, 37)          it is a key feature          yes                     it is the y-intercept.

(6, 46)          it is a key feature          yes                     it is the vertex.

A reasonable constraint for the context in set builder notation is {y|y ∈ R ≤ 46}.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two or more variable on a graph, with a maximum exponent of two (2).

In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this scenario, the y-intercept of this quadratic function can be calculated as follows;

G(x) = -1/4(x²) + 3x + 37

G(0) = -1/4(0²) + 3(0) + 37

G(0) = 37.

In conclusion, the vertex (maximum point) of this quadratic function is given by the ordered pair (6, 46).

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The equation represents a direct proportion

The proportionality constant is 1.2

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

a=1.2b

The above equation is a proportional linear equation

A proportional linear equation is represented as

y = kx

Where

The constant of proportionality is k

Using the above as a guide, we have the following:

The equation a=1.2b is a direct proportion and the proportionality constant is 1.2

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4500(1+0.055)^24

4500(1.055)^24

= 16,265.65456755

The value of the other side is 9. 7 m

Using the Pythagorean theorem stating that the square of the hypotenuse side is equal or equivalent to the sum of the squares of the other two sides.

From the information given, we have that;

This is represented as;

12² = 7² + x²

Find the value of the squares, we get;

144 = 49 + x²

collect like terms. we get;

x² = 144 - 49

subtract the values, we have;

x² = 95

Find the square root of both sides

x = 9. 7 m

Hence, the value is 9. 7 m

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The first term is 2, the common difference is 2 and the sum of the first ten terms is 110

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

An arithmetic term is given as:

[tex]a_n=a+(n-1)d[/tex]

where a is the first term and d is the common difference.

The 5th term and 8th term of an AP are 10 and 16. Hence:

a + 4d = 10    (1)

and:

a + 7d = 16     (2)

subtract equation 1 from 2 to get d:

3d = 6

d = 2

Common difference is 2

a + 4d = 10

a + 4(2) = 10

a = 2

First term is 2

The sum of first ten terms is:

[tex]S_{10}=\frac{n}{2} (2a+(n-1)d)=\frac{10}{2}(2(2)+(10-1)2) = 110[/tex]

The sum is 110

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Answer:

Step-by-step explanation:

I gotchu.

sinP = 5/14

       = 0.36

P = sin^-1(5/14)

P = 20.92

Answer:

y-intercept: 5

slope: -1

equation: y = -x + 5

Step-by-step explanation:

The y-intercept is when x is 0, and it is shown on the table as 5.

The slope can be found by doing [tex]y_1-y_2/x_1-x_2[/tex], which is 6-5/-1-0 = 1/-1 = -1.

The equation is y = mx + b, so we can write it as y = -x + 5

Step-by-step explanation:

Step One→ Solve one equation for either x or y.

Step Two→ Substitute the expression from step one into the 2nd equation.

Step Three→ Solve the second equation for the given variable.

Step Four→ Plug you solution back into the first equation.

Step Five→ Write your solution as a point.

The time it will take both of them to pick enough apples is 7.27 minutes.

The time it will take both of them to pick enough apples is calculated as follows;

Let the time = t ( minutes )

3t  + (5/2)t = 40

3t + ( 5t / 2 ) = 40

multiply through by 2

6t + 5t = 80

11t = 80

divide through by 11

t = 80 / 11

t = 7.27 minutes

Thus, the time to pick enough apples depends on the rate at which they are picking the apples.

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Answer: The savings per movie with the pass is $3.50 - $1.00 = $2.50. For the pass to benefit Seth's father, Seth must attend enough movies such that the total savings is equal to or greater than $40.

Let's call x the number of times Seth must attend for the pass to benefit his father. Then:

$2.50x >= $40

Solving for x:

$2.50x/$2.50 >= $40/$2.50

x >= 16

So Seth must attend at least 16 movies in order for the pass to benefit his father.

The equation involving an integral expression that can be used to find the value of k is π integration [(k - x²)² - (k - 4)²] dx.

We need to perform integration to find the value of k which will have same volume. Thus, tos over the question the clarity of concepts of volume of any area and integration is required.

The graph representing the mentioned situation is attached in the picture. So, now, writing the expression -

π integration [(k - x²)² - (k - 4)²] dx

Remember tha the integration limit in the mentioned equation will be -2 to 2.

On solving we will get the volume 256π/5.

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The comp question is -

The shaded region, R, is bounded by the graph of y = x² and the line y = 4, as

shown in the figure.

There exists a number k, k 4 , such that when R is revolved about the line y = k , the resulting solid has the same volume as the solid in part (b).

Write, but do not solve, an equation involving an integral expression that can be used to find the value of k.

option B is correct, the equation or function of the graph is y≥3/4x-3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The line passing through points (4,0) and (0,3)

Slope=3/-4=-3/4

Now let us find y intercept

0=-3/4(4)+b

0=-3+b

b=3

Hence, option B is correct, the equation or function of the graph is y≥3/4x-3.

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Answer/Solution:

15a^5b^15

Explanation:

First, multiply the numbers, then combine the exponents until you get the answer.

Answer:

7a - 4ab + 3b

Step-by-step explanation:

5a - 3ab + 6b - (ab - 2a + 3b)

=5a - 3ab + 6b - ab + 2a - 3b

=7a - 4ab + 3b