which expressions below equal a rational number? select all that apply.

Answer: x=0.5, y=1

Step-by-step explanation:

-4x+3y=1

6x-y=2

6x-2=y

-4x+3(6x-2)=1

-4x+18x-6=1

-4x+18x=7

14x=7

x=0.5

6x-y=2

6(0.5)-y=2

3-y=2

y=1

Let's change the equation,

→ 6x - y = 2

→ y = 6x - 2

Then the value of x will be,

→ -4x + 3y = 1

→ -4x + 3(6x - 2) = 1

→ -4x + 18x - 6 = 1

→ 14x = 1 + 6

→ x = 7/14

→ [ x = 1/2 ]

Hence, the value of x is 1/2 (or) 0.5.

Now the value of y will be,

→ y = 6x - 2

→ y = 6(1/2) - 2

→ y = 3 - 2

→ [ y = 1 ]

Hence, the value of y is 1.

Working together will take them 2 hours and 46 minutes which is 166 minutes.

So,

The work equation is now:

[tex]\begin{aligned}&\frac{1}{4} t+\frac{1}{9} t=1 \\&\frac{9}{36} t+\frac{4}{36} t=1 \\&\frac{13}{36} t=1\end{aligned}\\\frac{36}{13} \cdot \frac{13}{36} t=\frac{36}{13} \cdot 1\\t=\frac{36}{13} \mathrm{hrs}\\\frac{36}{13} \cdot 60 \approx 166 \min[/tex]

Therefore, working together will take them 2 hours and 46 minutes which is 166 minutes.

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Proportion of females who have less than 3 close friend working note

What is the statistical median?

(a) Mean =1.04

Median=1

assuming the number of close friends as a whole value, our mean is also 1.

the distribution is roughly symmetric. because mean is approximately equal to median.

The explanation is provided in the image attached above;

Answer (b)Median number of a close friend for females is 1.

The calculation for median is provided in the image.

Answer(c) According to the shape of the distribution as we have observed from the data we can say that the median calculated for close friends of females is the same as the mean number of close friends for men.

Here we are not assuming the number of close friends in decimal(because it is not a continous variable).

Answer (d) P(less than 3)  = P(0)  +  P(1)  + P(2)

= 0.353+0.368+0.191=0.912

Proportion of females who have less than 3 close friend

working note:

m= mean =1.04

probability = ( e-m  x  mr)  /   r

P(0)   =  (e-1.04  x  1.040 )   /  0  = 0.353

P(1)   =  (e-1.04  x  1.041 )  /  1  = 0.368

P(2)   = (e-1.04  x  1.042 )  /  2  =  0.191

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The complete question is -

The following table reports counts of the number of "close friends" reported by a sample of men and a sample of women. Number of close friends 0 1 2. 3 4 Total Number of male respondents 20 12 10 5 N 49 Number of female respondents 25 13 9 6 2 2 55 a. Is the distribution corresponding to the number of female respondents roughly symmetric, skewed to the right, skewed to the left? Explain. b. Calculate the median number of close friends for females. Round your answer to two decimal places c. Based on the shape of the distribution (and only accounting for the number of close friends for females), do you expect the median calculated in part b. to be greater than the mean, smaller than the mean, or about the same as the mean number of close friends for men? Do not calculate the mean. d. What is the proportion of females who say they have less than 3 close friends? Give an exact answer.

Answer: 1 and 26

Step-by-step explanation:

Answer: 0.1, 1.5, 7/4, 2, 4

Step-by-step explanation:

Answer:

0.8r

Step-by-step explanation:

r - 0.2r = 1r - 0.2r = (1 - 0.2)r = 0.8r

Answer:

0.8r

Step-by-step ex

took test

The correct option is 6.82; the value of C on the number line is 6.82.

A number line is a straight line to numbers positioned at equal intervals or sections along its length in mathematics.

For, the given number line in the question;

As, the point C is situated between the points 6.8 and 6.9; thus the value of point C must lie in between these two values.

Thus, the only option which shows this condition is 6.82.

Therefore, the value point C on the number line is 6.82.

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The location of the point A' after dilation is; A'(-10, 15)

We are given that the Quadrilateral BASE is located at the following coordinates;

B(3, 4), A(-2, 3), S(4, 0), and E(-2, 5).

Now, if it is dilated by a scale factor of, it means that each of the coordinates values would be multiplied by 5 to get the new coordinates as;

B'(15, 20), A'(-10, 15), S'(20, 0), and E'(-10, 25).

Thus, we can conclude that the location of the point A' after dilation is; A'(-10, 15)

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I will use the example that they gave to describe the method

First, you need to find the difference between the new amount and the original amount. The new one is 30, while the original one is 24, so the original amount incrased by 6.

Now, you take the difference that you got, and divide it by the original amount. 6 : 24 = 1/4, or 25%. So, the percentage increase is 25%

Applying the same for the others :

32 -> 56 (increased by 24, 24:32 = 3/4 -> 75%)
15  -> 18  (increased by 3, 3:15 = 1/5 -> 20%)
30 -> 33 (increased by 3, 3:30 = 1/10 -> 10%)
150 -> 153 (increased by 3, 3:150 = 1/50 -> 2%)
120 -> 126 (increased by 6, 6:120 = 1/20 -> 5%)
200 -> 202 (increased by 2, 2:200 = 1/100 -> 1%)

Answer:

x= 12

Step-by-step explanation:

6x = 72 (÷6)

6x/6 = 72/6

x = 12

Answer:

50

Step-by-step explanation:

2(9)+10

3(9)-5

18+10=28

27-5 =22

28+22=50

Answer:

1 and 1/6 or 7/6

Step-by-step explanation:

Answer:

7/6

Step-by-step explanation:

=5/6+2/6

=5/6+1/3

7/6

Answer:

Q=-8

Step-by-step explanation:

Q-2-6

The difference between the square of the numbers 'r' and 15 is the same as the sum of the numbers 't' and 19.

The act of converting mathematical equations into a specified statement is known as equation to sentence transformation.

The mathematical equation is given below.

r² - 15 = t + 19

In the above equation, there are two variables that are 'r' and 't'. Then the mathematical equation can be converted into a sentence as,

The difference between the square of the numbers 'r' and 15 is the same as the sum of the numbers 't' and 19.

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The required expression is written into sentence as Fifteen less than the square of r equals the sum of t and nineteen.

A mathematical sentence makes a statement about two expressions. The two expressions either use numbers, variables, or a combination of both. A mathematical sentence can also use symbols or words like equals, greater than, or less than.

Given:

The given equation is

[tex]r^{2}[/tex]-15 = t+19

According to given question we have

The expression is written into sentence as Fifteen less than the square of r equals the sum of t and nineteen.

Therefore, the required expression is written into sentence as Fifteen less than the square of r equals the sum of t and nineteen.

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The cost of building a storage house is $89,600.

Area of rectangle:

Area of the rectangle is defined as the amount of space covered by a flat surface of a particular shape.

The formula for the area of the rectangle is,

Area of a Rectangle = (Length × Breadth) square units

Given,

The cost of building a storage house is $70 per square foot flooring.

Length = 10 feet

Width = 12 feet

Height = 8 feet.

Here we need to find the cost to build a storage house.

To find the cost of the storage,

First, we have to find the area of the storage house,

Apply the values on the formula, to find the area of the storage house,

=> A = 10 x 12

=> A = 120 square foot.

So, the cost of building the storage house is,

=> 120 x 70

=> 89600.

Therefore, the cost for building the storage is $89,600.

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Perimeter of the equilateral triangle KLM with vertices K(-2 ,1) and M (10,6) is equal to 39 units.

As given in the question,

Coordinates of vertices K(-2,1) and M(10,6)

KM = [tex]\sqrt{ (10-(-2)^{2} +(6-1)^{2} }[/tex]

      = [tex]\sqrt{12^{2}+5^{2} }[/tex]

      = 13units

In equilateral triangle  KL = LM = KM = 13 units

Perimeter of equilateral triangle KLM = 13 +13 +13

                                                           = 39 units

Therefore, perimeter of the equilateral triangle KLM with vertices K(-2 ,1) and M (10,6) is equal to 39 units.

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The probability that neither you nor the dealer is dealt a blackjack will be 1/26.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Suppose that you are playing blackjack against a dealer. In a freshly shuffled deck.

Then the total number of the event will be

Total events = 52

Then the probability that neither you nor the dealer is dealt a blackjack will be

Favorable event = 2 {Spade of Jack and Club of Jack}

Then the probability of that events will be

P = 2 / 52

P = 1 / 26

The probability that neither you nor the dealer is dealt a blackjack will be 1/26.

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Using translation concepts, we have that:

a) The parent function is f(x) = |x|.

b) The transformations were a reflection over the x-axis, vertical stretch by a factor of 2 and a shift down of 3 units.

c) The graph is given at the end of the answer.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the parent function is given by:

f(x) = |x|.

The transformations are given as follows:

The graph of the two functions, the parent(red) and the translated(blue), is given at the end of the answer.

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What is an associative property?

Given expressions with rearrangement as per associative property are:

(a) 7x+3+6x+11

  =(7x+6x)+(3+11)

(b) 12x+10+3+8x

  =(12x+8x)+10+3

(c) 10y+12-7y-8-3y

 =(10y-7y-3y)-(-12+8)

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Answer: 450 is divisible by 2, 3, 5, 6, and 9

Step-by-step explanation: 450 is divisible by 2 because the last digit (0) is an even number.

Divisible by three because the sum of all the digits in 450 is a multiple of three: 4+5+0 = 9 which is 3*3.

Divisible by 5 because it ends with a 0 (could also end in 5)

Divisible by 6 because it is divisible by both 2 and 3 (2*3=6)

Divisible by 9 because 45 is divisible by 9.

The correct option is C. Quantitative Continuous

The type of variable would their response be considered is Quantitative Continuous Variable.

Quantitative variables describe some aspect of the individual and are frequently measured (for example, body mass is evaluated with a scale) or counted (for example, the number of needle punctures necessary to receive the biopsy specimen has been counted).

A quantitative variable could be discrete or continuous. A continuous variable can theoretically take on any value under an interval.

Some key features regarding the Quantitative Continuous Variable are-

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The complete question is-

The following five questions are focused around a startup company. Management is trying to gain insight on current employees and have sent out a short anonymous survey to them. Read each prompt carefully and determine the variable type for each question.

Employees were asked to report their typical daily commute time, in minutes. What type of variable would their response be considered?

A. Categorical Nominal

B. Categorical Ordinal

C. Quantitative Continuous

D. Quantitative Discrete

Answer:

5 units

Step-by-step explanation:

The graph, the coordinates of point D is (-7, -5).

The given coordinates of the rectangle ABCD are A(−7, -2), B(3, -2) and C(3, −5).

We need to find the coordinates of point D.

A cartesian plane can be defined as a plane formed by the intersection of two coordinate axes that are perpendicular to each other. The horizontal axis is called the x-axis and the vertical one is the y-axis. These axes intersect with each other at the origin whose location is given as (0, 0). Any point on the cartesian plane is represented in the form of (x, y). Here, x is the distance of the point from the y-axis and y is the distance from the x-axis.

Now, plot A(−7, -2), B(3, -2) and C(3, −5) on cartesian plane.

The coordinates are plotted on the graph, shown below.

From the graph, the coordinates of point D is (-7, -5).

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The required probability that they differ in length by more than 10 cm is 1.

Given that,
A hardware store sells planks of wood. the lengths, in centimeters, of the planks are normally distributed with a mean of 210 and a standard deviation of 7. two planks are selected at random. find the probability that they differ in length by more than 10 cm is to be determined.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,

The
P(x > 10) = p(z = (x - μ)/σ)
P(x > 10) = p(z = (10 - 210)/7)
P(x > 10) = p(z = -28.57143)
P(x > 10) = 1

Thus, the required probability that they differ in length by more than 10 cm is 1.

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Answer:

1/2

Step-by-step explanation:

0.5 is half of 1 so 1/2 is 0.5 as a fraction

Answer:

35 x 30 X 27 x 30 is equal to your answer

Solution:

[tex]x=3.1[/tex]

Hope this helps!

Answer:

x = 3.1

Step-by-step explanation:

3x + 2.3 = 11.6

3x = 11.6 - 2.3

3x = 9.3

x = 9.3/3

x = 3.1

Check:

3*3.1 + 2.3 = 11.6

9.3 + 2.3 = 11.6

The amount in Jay's account after 6 years is $357.20.

Given that, the principal=$285, time period=6 years and rate of interest =1.9%.

We need to find the amount in Jay's account after 6 years.

Compound interest, or 'interest on interest', is calculated using the compound interest formula. The formula for compound interest is  [tex]A=P(1+\frac{r}{100} )^{nt}[/tex], where P is the principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods.

Now, [tex]A=285(1+\frac{1.9}{100} )^{6}=285(1.019)^{6}[/tex]

=285×1.1195=$357.20

Therefore, the amount in Jay's account after 6 years is $357.20.

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Step-by-step explanation:

In this equation, given

f(x) = 3x + 9 and g(x) = 5x -1

So the question is what is the value of f if we put the value of g(x) in f(x)

So to solve the equation we need to replace the value of x in f(x) with g(x)

So it was obtained as below

f(g(x)) = 3(5x-1) + 9

= (15 x - 3) + 9

= 15 x + 6

The process of measuring, analyzing, enhancing, and then controlling processes once they have been brought within the narrow Six Sigma quality tolerances or standards is referred to as the

Six Sigma process

The phrase "Six Sigma" refers to a collection of quality-control methods that organisations can utilise to get rid of flaws and enhance operations so as to increase productivity and revenues. A scientist created it in the 1980s while he was employed by Motorola.

A statistical and data-driven technique called Six Sigma examines small errors or flaws. It places a focus on cycle-time gains while lowering manufacturing faults to no more than 3.4 incidents per million units or events. The fact that only 3.4 out of a million events along a bell curve will deviate by more than six standard deviations indicates that an error usually occurs with an event that deviates by six standard deviations from the mean.

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