(2^-3x divided by 2^-2)^2=2^10

Answer:

Step-by-step explanation:

The answer is C. 5x + 15 because the 5 outside the parentheses () is supposed to multiply by what's inside the parentheses. So multiply 5 and x and 5 and 3 (5 * X = 5x) (5 * 3 = 15).

The amount of money Ryan will have in his account in 6 years is $3668.71.

Compound interest is calculated using the exponential formula y = P(1+r)ⁿ. P is for "Present" or Principal value; r stands for interest rate; n stands for time (in years), and y stands for future value after the amount compounds annually

Given:

Principal Amount = $2500

Rate of interest = 6.25%

Time = 6 years

The exponential equation can be given as:

y = P(1+r)ⁿ where n is the number of years.

y = 2500(1 + 0.0625)ⁿ

The money Ryan will have in his account in 6 years can be calculated as by putting n's value as 6 years.

y = 2500(1 + 0.0625)⁶

y = $3668.71

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Answer:

the ratio of n to m is 5 : 7

5m = 7 n

n : m = 5 : 7

$45.38 and $46.42 is the  interval can the branch manager be 95% certain that the sample mean will fall within

Using the Central Limit Theorem, the branch manager can be 95% certain that the sample mean will fall within $1.034 of the mean.

What does the Central Limit Theorem state?

It states that the sampling distribution of sample means of size n has standard deviation .

By the Empirical Rule, 95% of the sample means fall within 2 standard errors of the mean.

In this problem, we have that the standard deviation and the sample size are given as follows:

Hence the standard error is given by:

[tex]s = \frac{10.34}{\sqrt{400}} = 0.517.

Two standard errors is represented by:

2 x 0.517 = $1.034.

Hence, the branch manager can be 95% certain that the sample mean will fall within $1.034 of the mean.

$45.38 and $46.42 is the  interval can the branch manager be 95% certain that the sample mean will fall within

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The third side of the right angle triangle is x = 15 ft.

What is right angle triangle?

A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.

We have to find the measure of third side of given right triangle.

The two sides of right triangle are 9 ft and 12 ft.

Let the side of third side is x.

By using the Pythagoras theorem,

(9)^2 + (12)^2 = x^2

       81 + 144 = x^2

             225 = x^2

                  x = 15

Hence, the third side of the right angle triangle is x = 15 ft.

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The vertex and range of y = |x + 2| - 6 are: A. (-2, -6); -6 ≤ y < ∞.

Generally speaking, the vertex points of an absolute value function occurs when the absolute values are equal to zeros. Therefore, we would equate the x-values of this absolute value function to zero as follows;

y = |x + 2| - 6

|x + 2| = 0

x + 2 = 0

x = -2

When x = -2, the value of y for this absolute value function is given by;

y = |x + 2| - 6

y = |-2 + 2| - 6

y = 0 - 6

y = -6

Therefore, the vertex is (-2, -6).

Since |x + 2| ≥ 0, we would add -6 to both sides of the inequality in order determine the range as follows;

|x + 2| - 6 ≥ -6

y = f(x) ≥ -6

Therefore, the range of this absolute value function is defined for all real numbers that are greater than or equal to -6 i.e -6 ≤ y < ∞.

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Complete Question:

What are the vertex and range of y = |x + 2| - 6?

An equation that Elena can use to find the height 'h' is h = 24/b.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the area of a triangle is (1/2)×base×height.

Given, Elena is designing a logo in the shape of a triangle having an area of 12 square inches.

Therefore,

(1/2)×base×height = 12.

b×h = 12×2.

b×h = 24.

So, Elena can use the following equation to get the height 'h',

h = 24/b.

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The value of c is 72.

What is a quadratic equation?

A quadratic equation is a type of polynomial equation that has the form of ax^2 + bx + c = 0, where x is the variable, and a, b, and c are coefficients. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are constants. The solutions of a quadratic equation are given by the quadratic formula: x = (-b ± √(b^2-4ac)) / 2a

The equation x^2-17x+c=0 is a quadratic equation where a=1, b=-17 and c=c

To find c, we can use the difference of the two solutions of the equation, which is 1.

The two solutions of the equation are given by the quadratic formula

x = (-b ± √(b^2-4ac)) / 2a

x = (-(-17) ± √((-17)^2-41c)) / 2*1

x = (17 ± √(289-4c)) / 2

The difference of the two solutions is (17 + √(289-4c))/2 - (17 - √(289-4c))/2 = 1

we can solve for c:

(17 + √(289-4c))/2 - (17 - √(289-4c))/2 = 1

√(289-4c) = 1

289-4c = 1

4c = 288

c = 72

Hence, the value of c is 72.

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The unit price for the apples is $1.5 per pound. The statement is true.

Now, According to the question:

How to calculate the Unit rate of the cost per pound?

8 pounds of Apple costs $12

The unit rate is

8= 12

1= x

We can write, by cross - multiply

8x = 12

x= 12/8

x= 1.5

Hence, the unit rate of the cost per pound is $1.5

And,  5 pounds of apples cost $7.50

cross multiply,

5× 12/8

60/8 = 7.50

5 pounds of apples = 7.50

Hence, The unit price for the apples is $1.5 per pound. The statement is true.

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The numbers that can be formed using the  condition is [tex]20^n[/tex]

When a positive integer has n digits and the first digit is 2, all of the digits are prime, the probability that any two successive digits added together are prime is. Numbers from the set {1,3,5,7,9} must be used in the n odd locations, and numbers from the set {2,4,6,8} must be used in the n even spots.

We cannot include 0 in even positive integers because it is neither positive nor negative.

Order matters and repetitions are permitted.

So, here we are

possibilities are

[tex]5^n \times 4^n =20^n[/tex]

where n is the integral value

Therefore, the number of positive integers with digits and the specified restriction is [tex]20^n[/tex]

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The numbers are 4.5 and 13.5.

The ratio of two numbers = 1:3

Let the numbers be x and 3x.

After increasing each number by 9, the numbers will be x + 9 and 3x + 9.

Now, According to the question, after increasing each number by 9 the ratio becomes 3:5

Hence,         [tex]\frac{x + 9}{3x + 9}[/tex]  = [tex]\frac{3}{5}[/tex]

                  5x + 45 = 9x + 27

                  9x - 5x =  45 - 27

                     4x     = 18

                       x     = 18 / 4

                              = 4.5

if x = 4.5, then 3x = 4.5 * 3 = 13.5

So, the numbers are 4.5 and 13.5.

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It is plausible to assume that the die is fair because there is a 3% possibility that a loaded die might randomly yield the outcomes that we saw.

The appropriate conclusion is that there is a 3% chance that a loaded die could randomly produce the results we observed. We tested this hypothesis by rolling the die 200 times and our p-value turned out to be 0.03. This means that there is only a 3% chance that the results we observed could have been produced randomly by a loaded die, so it is reasonable to conclude that the die is fair. This is because a p-value of 0.03 is considered to be statistically significant, which indicates that the results we observed are unlikely to have been due to chance. Therefore, we can conclude that the seller's claim that the die will favor the outcome 6 is likely false.

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Answer:

4ft by 7 ft

Step-by-step explanation:

4*7=28 and 7-4=3 so the dimensions are 4ft by 7ft

The dimensions of the rectangle are 7 ft by 4 ft.

What is the area of the rectangle?

The area of a rectangle is defined as the product of the length and width.

Let x be the length of the rectangle.

The width of the rectangle is 3 less than the length, so the width can be represented as x-3.

The area of a rectangle is the length multiplied by the width, so:

Area = Length * Width

Area = x × (x-3)

Area = x² - 3x

We know that the area of the rectangle is 28 ft², so we can set the equation equal to 28 and solve for x:

x² - 3x = 28

x² - 3x - 28 = 0

Now we can use the quadratic formula or factoring method to find the solutions of x:

x = (3 ± √(3² - 41-28))/(2*1)

x = (3 ± √(9+112))/2

x = (3 ± √121)/2

x = (3 ± 11)/2

x = -4 or 7/2

The dimensions of the rectangle can't be negative, so the only valid solution is x = 7/2, which means the length of the rectangle is 7/2 ft and the width is (7/2 - 3) ft = -1/2 ft.

The width can't be negative, this answer is incorrect. So we have to check the other solution x = 7.

Therefore, the dimensions of the rectangle are 7 ft by 4 ft.

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3:7 are the odds in favor of choosing a book of poetry

given that

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. [note 1] [1] [2] The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half

the probability of randomly picking out a book of poetry from a bookshelf is 3/10

now, we need to find what are the odds in favor of choosing a book of poetry

P(poerty) = 3/10

P(non-poerty) = 1 - 3/10 = 7/10

number of odds = P(poerty) /P(non-poerty)

                          = 3/10/7/10

                          = 3/7

                          = 3:7

3:7 are the odds in favor of choosing a book of poetry

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The minimum number of 1 point foul shots that your team must make to win the game is given as follows:

20.

The expression for this problem is defined as follows:

3p + 2f + s.

In which the variables are given as follows:

The opponent made these following shots:

Hence the number of points of the opponent is given as follows:

8 x 3 + 12 x 2 + 11 = 59.

Your team made these following shots:

Hence the number of points of your team is given as follows:

10 x 3 + 8 x 2 + x = 40 + x.

The team wins when:

40 + x > 59

x > 19

Hence the minimum number is of 20, as the number of one point shots is a discrete amount.

Your basketball team made 10 three-pointers, 8 two-point field goals, and x one-point foul shots.

Your opponents made 8 three-pointers, 12 two-point field goals, 11 one-point foul shots.

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The number of pencils that he bought will be 21 pencils.

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

Karani bought 4 pencils and 6 biro pens for $66 and Mary bought 2 pencils and 5 biro pens for $51.

Let 'x' be the cost of pencils and 'y' be the cost of biro pens. Then the equations are given as,

4x + 6y = 66         ...1

2x + 5y = 51

4y + 10y = 102      ...2

From equations 1 and 2, then we have

10y - 6y = 102 - 66

4y = 36

y = 9

Then the value of 'x' is given as,

2x + 5(9) = 51

2x + 45 = 51

2x = 6

x = 3

Ondieki spent $228 to buy the same type of pencils and biro pens. If the number of biro pens he bought was 4 more than the number of pencils.

Let 'm' and 'n' be the number of pencils and biro pens, respectively.

3m + 9n = 288          ...3

n = m + 4                   ...4

From equations 3 and 4, then we have

3m + 9(m + 4) = 288

12m + 36 = 288

12m = 252

m = 21

Then the value of 'n' is given as,

n = 21 + 4

n = 25

The number of pencils that he bought will be 21 pencils.

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Answer: y=-33.25 or -33.3

Step-by-step explanation:

2x=88

x=44

the triangle has 180 total angle

4y+(5x+5)+2x=180

substituting the numbers

4y+(5(44)+5)+2(44)=180

4y+(220+5)+88=180

4y+225+88=180

4y+313=180

(-313)

4y=-133

(divide by 4)

y=-33.25 or -33.3

The first 12 numbers between 01 and 99 in the sample are: 99, 25, 68, 17, 9, 89, 56, 97, 43, 28, 3, 66.

The formula to generate random numbers between 01 and 99 is (number*99/max_number)+1.

For the first number in the row, 78038, the calculation would be (78038*99/78038)+1 = 99.

For the second number in the row, 18022, the calculation would be (18022*99/78038)+1 = 25.

For the third number in the row, 84755, the calculation would be (84755*99/78038)+1 = 68.

For the fourth number in the row, 23146, the calculation would be (23146*99/78038)+1 = 17.

For the fifth number in the row, 12720, the calculation would be (12720*99/78038)+1 = 9.

For the sixth number in the row, 70910, the calculation would be (70910*99/78038)+1 = 89.

For the seventh number in the row, 49732, the calculation would be (49732*99/78038)+1 = 56.

For the eighth number in the row, 79606, the calculation would be (79606*99/78038)+1 = 97.

The first 12 numbers between 01 and 99 in the sample are: 99, 25, 68, 17, 9, 89, 56, 97, 43, 28, 3, 66.

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the ratio of the line segment joining the points (-3, 1) and (-8, 9) is 5:4. The ratio of the line segment joining the points (-3, 1) and (-8, 9) is calculated by subtracting the x-coordinates and y-coordinates of the two points.

5:4

Given two points, (x1, y1) and (x2, y2)

The ratio of the line segment joining the points is:

(x2 - x1) : (y2 - y1)

Therefore, the ratio of the line segment joining the points (-3, 1) and (-8, 9)

The ratio of the line segment joining the points (-3, 1) and (-8, 9) is calculated by subtracting the x-coordinates and y-coordinates of the two points. Specifically, the ratio is given by the expression (x2 - x1) : (y2 - y1). In this case, the x-coordinates are -3 and -8, and the y-coordinates are 1 and 9. By substituting these values into the expression, we get ( -8 - (-3)) : (9 - 1) which simplifies to ( -5 ) : ( 8 ). Therefore, the ratio of the line segment joining the points (-3, 1) and (-8, 9) is 5:4.

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A system of 3 linear equations can have 0, 1, or an infinite number of solutions.

A system of linear equations is a group of equations with multiple variables. The number of solutions to the system of equations depends on how many equations and how many variables are in the system. A system of 3 linear equations can have 0, 1, or an infinite number of solutions.

If the number of equations is greater than the number of variables, the system is said to be overdetermined and has no solutions.

If the number of equations is equal to the number of variables, the system is said to be determined and has either one or an infinite number of solutions, depending on if the equations are dependent or independent.

If the number of equations is less than the number of variables, the system is said to be underdetermined and has an infinite number of solutions.

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Carolyn made an error in her calculation. She failed to take into account the cost of labor and overhead in her equation.

Her equation only accounted for the cost of materials, not the cost of labor and overhead. The equation should have been: 12(X-3.20) + Cost of Labour and Overhead = 54. This would have given her a more accurate calculation of the profit per necklace.

In addition, Carolyn did not account for other factors such as marketing, shipping, and taxes, which could also affect the total profit. If she had taken into account these other costs, she would have been able to better calculate her profit margin on each necklace. By not accounting for these costs, Carolyn could have underestimated her profit margin, leading to an inaccurate calculation.

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Answer:

  see attached

Step-by-step explanation:

You want to fill in the blanks to complete the description of writing a number in scientific notation.

A number written in scientific notation can be described as a coefficient times a power of ten (2nd attachment). Different terminology is used by different authors to describe these parts.

Sometimes the entire coefficient is also called the "mantissa." Sometimes, the term "mantissa" is used to refer to the fractional part of the coefficient, the digits to the right of the decimal point. Your curriculum calls the coefficient the "first factor."

The power of ten is chosen so that the first factor is always a number greater than or equal to 1, but less than 10.

The power of 10 has an exponent, also called the "characteristic". Your curriculum calls the combination of base (10) and exponent the "second factor." The exponent is equal to the exponent of the place value multiplier of the most-significant digit when the number is written in standard form (3rd attachment).

The filled-in description is shown in the first attachment. You will notice that its wording helps you fill in the blanks. It asks you how many parts there are to the number, then refers to them as the "first part" and the "second part." It asks you what the parts are called, then refers to the first one as the "first factor."

The given example in scientific notation is ...

  [tex]2.54\times10^6[/tex]

The exponent of 6 corresponds to the 6 little left-arrows in the figure in your problem statement. It is the power of 10 that represents "millions," the place-value multiplier of the most-significant digit of the number two million five hundred forty thousand.

So, the coordinates of the images S', R', T' under the translation are (11,9), (-4,-6) and T'(h+4,k-5) respectively.

a) For the point S(7,14), we are given the translation defined by (x,y) -> (x+4, y-5). This means that for any point (x,y), we add 4 to the x-coordinate and subtract 5 from the y-coordinate to find the image of that point. Applying this transformation to the point S(7,14) gives us the image point S'(7+4, 14-5) = S'(11,9). So the coordinates of the image S' is (11,9)

b) For the point R(-8,-1), we are given the same translation defined by (x,y) -> (x+4, y-5). Applying this transformation to the point R(-8,-1) gives us the image point R'(-8+4,-1-5) = R'(-4,-6). So the coordinates of the image R' is (-4,-6)

c) For the point T(h,k), we are given the same translation defined by (x,y) -> (x+4, y-5). Applying this transformation to the point T(h,k) gives us the image point T'(h+4,k-5).

Here h and k are variables and we can't say the coordinates of image point T' without specific values of h and k. But we can say the transformation of point T as T'(h+4,k-5)

So, we have found the coordinates of the images S', R', T' under the translation defined by (x,y) -> (x+4, y-5) as (11,9), (-4,-6) and T'(h+4,k-5) respectively.

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Solving the provide question, we can say that frequency distribution 70 years or older is 0.1333, 4/30, or 13.3% younger than 40 years old is 8/30, 0.2666, or 0.4000. (there are 12 under 50 out of 30 altogether).

In order to make the information easier to understand, frequencies are organized into frequency distributions, which are visual displays. The frequencies displayed in a frequency distribution can be absolute or relative, like ratios or percentages. Both a graph and a table of frequencies can be used to represent a frequency distribution. Both the exact number of observations and the proportion of observations falling within each range can be displayed in a frequency distribution.

Here,

A relative frequency distribution is the name given to the distribution in the latter scenario. The frequency of an observation is the frequency with which it appears in the data.

The frequency of the number 9 in the following list of numbers, for instance, is 5. (because it occurs 5 times). 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9,

70 years or older is 0.1333, 4/30, or 13.3% younger than 40 years old is 8/30, 0.2666, or 0.4000. (there are 12 under 50 out of 30 altogether).

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The complete question is "The following data represents the age of 30 lottery winners .Given the frequency distribution for the data,

Each column (left to right) is as follows: Age, Frequency, Relative Frequency, Cumulative Relative Frequency

[20,29] 1 0.0333 0.0333

[30,39] 7 0.2333 0.2666

[40,49] 4 0.1333 0.3999

[50,59] 5 0.1667 0.5666

[60,69] 9 0.3 0.8666

[70,79] 3 0.1 0.9666

[80,89] 1 0.0333 0.9999

What is the frequency of lottery winners of age between 19 and 40?

"

As per the unitary method, the amount of white beans are there than kidney beans are 30.

The term unitary method is known as a technique for solving a problem by first finding the value of a single unit and then finding the necessary value by multiplying the single unit value.

Here we have given that in a jar containing dry beans, the ratio of white beans to kidney beans is 5:4.

And we also know that if 30 white beans were replaced with 30 kidney beans, the ratio would be 1:1.

Here we have consider that let the number of pinto beans be x and that is the number of white beans will be x + 30

In which means the total number of beans in the jar will be written as,

=> x + x + 30 = 2x + 30

Here we know that the Total ratio is calculated as,

=> 5 + 4  = 9

In order to find the number of pinto beans then it can be calculated as,

=> ratio of pinto beans / Total ratio  X Total number of beans

Which can be written as.

=>  (2x + 30) = x

When we simplify this one then we get the value of x as,

=> x = 30.

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Answer:

(6x + 15y) / x

Step-by-step explanation:

(2x + 5y) * 3/x =

3 * (2x + 5y) / x =

(3 * 2x + 3 * 5y) / x  ==> distribute 3 to 2x and 5y

(6x + 15y) / x ==> simplify

The equation of the least square regression line mated closely with the given data: y = 5.5x + 52.

For the given data:

Option:  y = 5.5x + 52.

Put x = 2,

y = 5.5(2) + 52

y = 63

Put x = 4,

y = 5.5(4) + 52

y = 74

Thus, the equation of the least square regression line mated closely with the given data: y = 5.5x + 52.

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If two sides of a triangle have lengths 13.2 and 21.5, then the third side length be less than 34.7.

When a triangle's two sides are given lengths of 13.2 and 21.5, we must determine what the third side's length should be.

The sum of the lengths of any two sides of a triangle can always be more than the length of the third side.

The length difference between any two triangle sides will never be greater than the length of the triangle's third side.

13.2 and 21.5 add up to 34.7, and their difference equals 8.3.

The above condition must not be violated, and the length of the third side must be greater than 8.3 and less than 34.7.

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