4. Four years ago, Melody was one fourth as old as her sister was then, In six years, Melody will be half as old as het sister will be then. Find their ages now.
5. The sum of the digits of a two-digit number is 12 . The value of the number is 6 less than 5 times the units digit. Find the number.
6. Hannah likes to spend her free time hanging out at the airport. She likes to run on the walkways. While running with the walkway, she can cover 48 feet in 3 seconds. While running against the walkway, she can cover 24 feet in 2 seconds. Find Hannah's rate (in feet per second) if the walkway stopped moving.

Answer:

26π (This is the answer to the problem as it is posted.)

or

169π (This is the answer to the problem if you meant πr².)

Step-by-step explanation:

π = π; r = 13

πr × 2 = π × 13 × 2 = 26π

If you meant πr², then

πr² = π × 13² = 169π

Answer:

- 2 - 16i

Step-by-step explanation:

(5 - 6i) + (- 7- 10i ) ← remove parenthesis

= 5 - 6i - 7 - 10i ← collect like terms

= (5 - 7) + (- 6i - 10i)

= - 2 + (- 16i)

= - 2 - 16i

The exponential function f(x) = 3ˣ has a function table of values calculated below and a graph attached

A function table is a visual table with columns and rows that displays the function with regards to the input and output. Younger students will also know function tables as function machines. Every function has a rule that applies and represents the relationships between the input and output.

In the function given;

f(x) = 3ˣ

When x = -2

f(-2) = 1/9

When x = -1

f(-1) = 1/3

When x = 0

f(0) = 1

When x = 1

f(1) = 3

when x = 2

f(2) = 2

The function can be represented in a graph below;

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The opposite rational number of -3/2 is -2/3.

p/q where q is not equal to 0 is the form of a rational number, which is a sort of real number in mathematics. A rational number is any fraction with a non-zero denominator. 1/2, 1/5, 3/4, and other like numbers are a few examples of rational numbers. A rational number is one that can be stated mathematically as the quotient or fraction pq of two numbers, p and q, with p being the numerator and q being the denominator. Every integer, such as 5 = 51, is a rational number, as is the number 37.

Given,

Rational number:

-3/2

Reciprocating,

-2/3

The opposite rational number of -3/2 is -2/3.

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The percentage of the purchase price is 180%

In this question, the figures are given as

Amount bought = $55

Amount sold = $99

These figures can be represented as

Cost price = 55

Selling price = 99

The sales price as a percentage of the purchase price is then calculated as

Percentage = Selling price/Cost price

Substitute the known values in the above equation, so, we have the following representation

Percentage = 99/55

Evaluate

Percentage = 1.8

Express as percentage

Percentage = 180%

Hence, the percentage is 180%

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Answer:

Wrong

Step-by-step explanation:

Type the math problem correctly please.

The representation of the given equation 'v' as subject of the formula v = 6 ( T - 5 ).

Given,

T = v / 6 + 5

substract 5 on both the sides, we get

⇒ T - 5 = v / 6 + 5 - 5

⇒ v / 6 = T - 5

Now represent 'v' as a subject of the formula we get,

v = 6 ( T - 5)

Hence, v = 6 (T - 5 ) is the representation of the given equation 'v' as subject of the formula.

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Answer:

51 x 51 = 2601

Step-by-step explanation:

Answer:

2601

Step-by-step explanation:

hope it helps

The probabilities are given as follows:

a) Ann gets Introduction to Counting & Probability: 1/4 = 0.25 = 25%.

b) Ann gets Introduction to Counting & Probability and Beth does not get Introduction to Geometry: 1/6 = 0.167 = 16.7%.

c) Counting & Probability and Beth does not get Introduction to Geometry and Caleb gets Introduction to Algebra: 1/24 = 0.0417 = 4.17%.

A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.

In this problem, the total number of outcomes is the arrangements of 4 elements, hence:

Total = 4! = 24.

For item a, we want Ann to get one book, and the remaining 3 books are arranged, hence the probability is of:

p = 3!/4! = 1/4 = 0.25 = 25%.

For item b, we want for Ann to get one book, Beth can get 2 of them, and the remaining 2 are arranged, hence the probability is of:

p = 2 x 2!/4! = 4/24 = 1/6 = 0.167 = 16.7%.

For item c, we have a fixed book for each student, hence the probability is of:

p = 1/24 = 0.0417 = 4.17%.

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Employees are required to achieve short-term performance goals. Employees can better comprehend what is expected of them or their positions when goals are defined for them.

Additionally, it aids in the proper evaluation and direction of workers by employers.

A performance goal is a brief target connected to particular corporate objectives or work duties. Obtaining a new client or reaching a quarterly sales quota are two examples.

Establish a procedure for monitoring progress on important projects, including milestones and decision deadlines, in order to promote concentration on finishing a work. Share by February 10 with the management.

Report on weekly updates. To encourage leadership: "I believe you have a lot of promise as a leader."

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Answer:

A(1,2) -> A'(3,6)

B(3,1) -> B'(9,3)

Step-by-step explanation:

A(1,2) ×3 -> A'(3,6)

B(3,1) ×3 -> B'(9,3)

Answer:

a)  A = (1, 2),   A' = (3, 6)

b)  B' = (9, 3)

Step-by-step explanation:

From inspection of the given diagram:

   A = (1, 2)

   A' = (3, 6)

As the triangle has been enlarged by a scale factor of 3 and centre (0, 0), to find the coordinates of B' simply mulitply the coordinates of B by the scale factor:

   As B = (3, 1)

   ⇒ B' = (3 × 3, 1 × 3) = (9, 3)

Answer:

B and F

Step-by-step explanation:

B: f(x) = 2 lx+1l +3 vertex: (-1,3)

F: f(x) = lx+1l +3 vertex: (-1,3)

69200000 in scientific notation is  6.92 × 10⁷.

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.

Scientific Notation is a special way of writing numbers:

For example 800 is written as 8 × 10² in Scientific Notation.

Therefore, let's write the scientific notation of the number 69200000.

Hence,

69, 200, 000 = 6.92 × 10⁷

The logic is that we will count backwards until we meet the last number. Since we counted towards the left side, the exponent will be positive.

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There are 63 distinct color groupings to make with your paint.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are 6 tubes of paint.

Now,

Number of tubes = 6

So, The number of distinct color groupings to make with 6 paints is;

⇒ 2⁶ - 1

⇒ 64 - 1

⇒ 63

Thus, There are 63 distinct color groupings to make with your paint.

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Answer:

Step-by-step explanation:

A. 60 + 30 = 90

B. 690000

C. 90 x 2000 = 180000

Answer:

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

Steps should be self-explanatory. Happy to explain if anything is not clear.

Answer:

Step-by-step explanation:

1) 4v + 7 = 7, for v?

→ 4v + 7 = 7

→ 4v = 7 - 7

→ v = 0/4

→ [ v = 0 ]

2) 3(u + 4) = 27, for u?

→ 3(u + 4) = 27

→ 3u + 12 = 27

→ 3u = 27 - 12

→ u = 15/3

→ [ u = 5 ]

3) -20 = 10(h + 5), for h?

→ -20 = 10(h + 5)

→ 10h + 50 = -20

→ 10h = -20 - 50

→ h = -70/10

→ [ h = -7 ]

4) -10 = (n - 52)/5, for n?

→ -10 = (n - 52)/5

→ n - 52 = -10 × 5

→ n = -50 + 52

→ [ n = 2 ]

5) (48/x) - 3 = 3, for x?

→ (48/x) - 3 = 3

→ 48/x = 3 + 3

→ 6x = 48

→ x = 48/6

→ [ x = 8 ]

6) 8r = 2r + 42, for r?

→ 8r = 2r + 42

→ 8r - 2r = 42

→ r = 42/6

→ [ r = 7 ]

These are required values.

0.2456 = 24.56%  probability of the mean IQ score of people in the sample is less than 99.

What is the Normal Probability Distribution?

The Normal (or Gaussian) distribution is the most common continuous probability distribution. The function calculates the likelihood that an event will occur between any two real number limits as the curve gets closer to zero on either side of the mean. The area beneath the normal curve is always one.

Problems of normal distributions can be solved using the z-score formula.

In a set with mean  and standard deviation, the z-score of a measure X is:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

This is the P value of Z when X = 98.

[tex]z = \frac{x - \mu}{\sigma}[/tex]

z = (99 -100)/15

z = -0.066

z = -0.066 has a P value of 0.2456

Hence, 0.2456 = 24.56%  probability of the mean IQ score of people in the sample is less than 99.

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Answer:

[tex]r=12, y=12x[/tex]

Step-by-step explanation:

[tex]\frac{y}{x}=\frac{48}{4}=12 \\ \\ \therefore r=12 \implies y=12x[/tex]

According to the given confidence interval, the number of samples for this research is 1134.

Confidence interval

Confidence interval means the percentage of probability, or certainty, that the confidence interval would contain the true population parameter when you draw a random sample many times.

Given,

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.18.

Here we need to find the number of samples.

Here we know that the Confidence level=0.99,

So, the value of

=> 1−α=0.99,

Noe, the estimate of population proportion = 0.18,

So, the value of pˆ=0.19,

And the Allowable error = 0.03

Which is E=0.03

Now, the determined value of α is calculated as,

=> α = 1 − 0.99 = 0.18

Thus, the value of z will produce 99%confidence is,

=> zα / 2 = z 0.01/2

=> z0.005 = 2.575

=> (2.575)√(.18)(1-0.18)/√0.03

Therefore, the resulting value is 1134

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Answer:

no

Step-by-step explanation:

For a relation to be a function each input must have only one output.

If you look at the points (-4,-1) and (-4,-3) you can see that The input (-4) has more than one output (-1 and -3), so it is not a function.

The quartiles of the distribution are given as follows:

The sample size of the distribution is of:

n = 40.

The first quartile is the value that is greater than 25% of the distribution, hence it is the value at the position which is 25% of the sample size, hence:

The second quartile is the value that is greater than 50% of the  distribution, hence it is the value at the position which is 50% of the sample size, hence:

The third quartile is the value that is greater than 75% of the  distribution, hence it is the value at the position which is 75% of the sample size, hence:

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Answer:

See below

Step-by-step explanation:

From the graph , function 1 has a max value of   1 at  4,1

From the equation for function 2, its max occurs at x = - b/2a = - (2/(2*-1) = 1

   plugging in this value shows max value of   - 14     (1,-14)  

The interval that represents the middle 95% of his commute times is [45 , 55]

What is standard deviation ?

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

The empirical rule states that the 95% of the sampled observations will fall within two standard deviations of the mean for a normally distributed population.

Where:

68% is the first standard deviation

95% is the second standard deviation about the mean

99.7% is the 3rd standard deviation about the mean.

Therefore. the middle 95% interval is calculated as:

CI = µ + 2 σ

   =  50 ± 2 (2.5)

   = 50 ± 5

  = [45 , 55]

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The dimension outside the frame is 11 inches long and 9 inches wide.

In the given question we have to find the outside dimensions of the frame.

In the given question, a picture 10 inches long by 8 inches wide has a frame whose area is one half the area of the picture.

The dimension of a picture is 10 inches long by 8 inches wide.

The area of the frame is one half i.e(1/2=0.5)to the area of the picture.

So the length of the frame is

=10+0.5+0.5

=11 inches

The width of the frame is

=8+0.5+0.5

=9 inches

Hence, the dimension outside the frame is 11 inches long and 9 inches wide.

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Answer:

56 cm²

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{3.5 cm}\underline{Area of a rectangle}\\\\$A=w\;l$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\ \phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}[/tex]

The given composite figure is made of two rectangles joined together.

Area of rectangle 1

[tex]\begin{aligned}\implies A&=4 \cdot 8\\&=32\; \sf cm^2\end{aligned}[/tex]

Area of rectangle 2

[tex]\begin{aligned}\implies A&=(8-5)(12-4)\\&=3 \cdot 8\\&=24\; \sf cm^2\end{aligned}[/tex]

Therefore:

[tex]\implies \textsf{Total area}=32+24=56\; \sf cm^2[/tex]

Answer:

56 cm²

Step-by-step explanation:

We are interested in finding the area of the given shape which is made up of two rectangles .

(for figure refer to the attachment)

Step 1 : Find the area of two rectangles

[tex]\longrightarrow Area_{AGHE}= length \times breadth \\[/tex]

[tex]\longrightarrow Area_{AGHE}= 5cm (4cm)\\[/tex]

[tex]\longrightarrow Area_{AGHE}= 20cm^2 [/tex]

Again ,

[tex]\longrightarrow Area_{GBCD}= 3cm(12cm)\\[/tex]

[tex]\longrightarrow Area_{GBCD}=36cm^2[/tex]

Step 2: Add up the areas

[tex]\longrightarrow Area = 20cm^2+36cm^2\\[/tex]

[tex]\longrightarrow \underline{\underline{Area = 56cm^2}}[/tex]

The required value of x is  135° in the given polygon. which is the correct answer would be an option (A).

A polygon is given in the figure

According to the given question, the required solution would be as:

Number of sides = 8

The required value of x is the equal to measure of one Interior angle in the given polygon.

Interior angles of a polygon = (sides - 2) × 180°

In this case, the number of sides is 8

Sum of Interior angles = (8 - 2) × 180

Sum of Interior angles = (6) × 180

Sum of Interior angles = 1080°

the measure of one Interior angle = 180°/8

the measure of one Interior angle = 135°

Thus, the required value of x is  135°.

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The equivalent ratio according to the given ratios are 2 : 1 and 1 : 2, 7 : 2 and 7 : 2, 1 : 4 and 1 : 4, 1 : 10 and 2 : 10.

The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is. A ratio divides two quantities in order to compare them.

As per the given question,

The ratios are,

24 : 12 and 6:12 = 2 : 1 and 1 : 2

7 : 2 and 14 : 4 = 7 : 2 and 7 : 2

5 : 20 and 1 : 4 = 1 : 4 and 1 : 4

1 : 10 and 2 : 11 = 1 : 10 and 2 : 10

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The correct estimate is 2000. Thus, Lenore’s estimate is not reasonable

Estimation is a method used for calculating the approximate value of a quantity (just to get a 'rough answer')

In estimation 1, 2,3, and 4 are rounded down while 5, 6, 7, 8 and 9 are rounded up.

Given:  51 x 37

In order round each factor to the nearest ten to estimate the reduction

51 will be rounded down to 50 (because of the 1 after the 5 in 51)

37 will be rounded up to 40 (because of the 7 after the 3 in 37)

Thus, the estimate will be:

50 x 40 = 2000

Therefore, Lenore’s estimate is not reasonable because she rounded down 37 to 30

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The values of the expression are;

1. bd/a + c = 6

2.  ac/b - (a + d) = 14

3. d³/a² - (c + b) = 63/4

4. pr/n + m = - 48

5.  p²/m - (np + r) = 10

6. p³/r² - (m + np) = 16

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are,

a = - 2, b = 3, c = - 12 and d = - 4

m = - 32, n = 2, p = - 8 and r = 4

Now,

Find the values of the expressions as;

1. bd/a + c

Substitute all the values, we get;

bd/a + c = (3 x - 4)/(-2) + (-12)

             = - 12/- 2 - 12

             = 6 - 12

             = - 6

2. ac/b - (a + d)

Substitute all the values, we get;

⇒ ac/b - (a + d) = - 2 x - 12 /3 - (- 2 - 4)

                    = 8 + 6

                    = 14

3. d³/a² - (c + b)

Substitute all the values, we get;

d³/a² - (c + b) = 3³/(-2)² - (-12 + 3)

                    = 27/4 + 9

                    = 63/4

4. pr/n + m = - 8 x 4 /2 + (-32)

                 = - 16 - 32

                 = - 48

5. p²/m - (np + r) = (-8)²/- 32 - (2 x - 8 + 4)

                         = - 64/32 - (- 16 + 4)

                          = - 2 + 12

                          = 10

6. p³/r² - (m + np) = (-8)³/4² - (- 32 + 2 x - 8)

                           = - 32 - (- 32 - 16)

                           = - 32 + 48

                           = 16

Thus, The values of the expression are;

1. bd/a + c = 6

2.  ac/b - (a + d) = 14

3. d³/a² - (c + b) = 63/4

4. pr/n + m = - 48

5.  p²/m - (np + r) = 10

6. p³/r² - (m + np) = 16

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