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Using it's concepts, the domain of the composite functions are given as follows:

In a graph, the domain and the range are found as follows:

For the composite functions in this graph, we have that:

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Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

the two numbers' primary factors are as follows:

-25\(b^{2}\) + 15b

Common prime factors can be multiplied to determine the GCF:

=> -25\(b^{2}\)  = -(5)(5) * \(b^{2}\)

=> 15b = (5)(3)b

The expression can be factored in the following fashion because the GCF is 5b:

=> -(5)(5) * \(b^{2}\) +  (5)(3)b

=> (5b)(-5b+3)

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

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Answer:

x = 17

Step-by-step explanation:

The sum of the interior angles of a triangle is 180

x + 17 + 4x - 34 + 6x + 10 = 180  Combine like terms

11x -7 = 180  Add 7 to both sides

11x - 7 + 7 = 180 + 7

11x = 187  Divide both sides by 11

\(\frac{11x}{11}\) = \(\frac{187}{11}\)

x = 17

Answer:

the answer is x=17 because the triangle is isosceles

The volume of the composite figure in this problem is given as follows:

76 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

2 x 6 x 3 + 2 x 4 x 5 = 76 ft³.

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From the table , the insurance cost for the second year based on the prescription given is : $1329

Using the prescription table, the six cylinder compact , second year car with a mileage of 14000 falls in the mid table category with the 13000 mileage label .

The operating cost in insurance for the second year is therefore $1329.

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Answer:

\(t=\frac{74.1-72}{\frac{13.3}{\sqrt{50}}}=1.116\)    

The degrees of freedom are given by:

\(df=n-1=50-1=49\)  

Now we can calculate the p value with the following probability:

\(p_v =P(t_{(49)}>1.116)=0.135\)  

Since the p value is higher than the significance level provided of 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly higher than 72 per hour.

Step-by-step explanation:

Information provided

\(\bar X=74.1\) represent the sample mean

\(s=13.1\) represent the sample standard deviation

\(n=50\) sample size  

\(\mu_o =72\) represent the value that we want to test

\(\alpha=0.1\) represent the significance level

t would represent the statistic

\(p_v\) represent the p value

Hypothesis to test

We want to analyze if the true mean for this case is higher than 72, the system of hypothesis would be:  

Null hypothesis:\(\mu \leq 72\)  

Alternative hypothesis:\(\mu > 72\)  

The statistic is given by:

\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\)  (1)  

Replacing the info we got:

\(t=\frac{74.1-72}{\frac{13.3}{\sqrt{50}}}=1.116\)    

The degrees of freedom are given by:

\(df=n-1=50-1=49\)  

Now we can calculate the p value with the following probability:

\(p_v =P(t_{(49)}>1.116)=0.135\)  

Since the p value is higher than the significance level provided of 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly higher than 72 per hour.

The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

The volume of a rectangular prism can be calculated using the formula:

V = l x b x h..........(i)

where,

V ⇒ Volume

l  ⇒ length

b ⇒ width

h ⇒ height

From the question, we are given the values,

l = 8 inches

b = 4 inches

h = 9 inches

Putting these values in equation (i), we get,

V = 8 x 4 x 9

⇒ V = 288 in³

Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

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Answer:

Step-by-step explanation:

9. 31 + 5 = 36

10. 16 - 4 = 12

11. 28 - 1 = 27

12. 9

13. 34 + 44 = 78

14. 101 - 1 = 100

Answer:

F(1)=-6(1)+16=10

F(5)=(5+6)(5-3)/(5-2)=11*2/3=22/3=7.33

F(2)=3*2+2=8

Which of the following is a true statement? 0.63>13/20

0.63<13/20

68%<13/20

84%>0.91​

Verify each statement

1) 0.63>13/20

we have that

0.63=6.3/10=12.6/20

the statement is false

2) 0.63<13/20

is true

3) 68%<13/20

68%=68/100

The number of ways it can be done if order of the choices is taken into consideration is 15,444 ways

Permutation has to do with arrangement and combination has to do with selection.

If we are choosing 5 objects, without replacement, from 15 distinct objects, this has to do with permutation if the order of the choices is taken into consideration

15P5 = 15!/(15-5)!5!
15P5 = 15!/10!5!
15P5 = 15*14*13*12*11/5*4*3*2

15P5 = 15,444 ways

Hence the number of ways it can be done if order of the choices is taken into consideration is 15,444 ways

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Complete question

Suppose we want to choose 5 objects, without replacement, from 15 distinct objects. How many ways can this be done, if the order of the choices is taken into consideration?

Answer:

-2<=y<=-7

Step-by-step explanation:

Answer:

Explanatory variable : web page design

Response variables : Visitor's rating and amount of time visiting the site.

Kindly check explanation for the rest.

Step-by-step explanation:

The explanatory variable simply means the independent or predictor variable which is used to bring about a change in the dependent or predicted variable. The explanatory variable in the scenario above is the web page design which is used to measure the behavior and changes in the response variable which are the rating given by visitors and the number of visits on each of the two different web page designs available (explanatory variable).

The confounding factor which may affect the study is the different area assigned to test the effectiveness of each page ; designating one page for the Oakland area and the other for Miami. User preferences for each area may itself mask the actual outcome of the experiment.

Answer:

when Riley starts selling her $h1t

Answer:

f(3) = g(6)

Step-by-step explanation:

Step-by-step explanation:

To work out the height of the cuboid, we need to use the formula:

Volume = Length x Width x Height

We have been given the volume and the length, so we can substitute those values into the formula:

540 = 6 x Width x Height

Now we need to convert the width from millimeters to centimeters, so we divide it by 10:

150mm ÷ 10 = 15cm

Substituting this value into the formula:

540 = 6 x 15 x Height

Simplifying:

540 = 90 x Height

Dividing both sides by 90:

6 = Height

Therefore, the height of the cuboid is 6cm.

Answer: 2808 ft.

Explanation: 78*36 is 2808

The probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

Since the probability density function is uniform, the probability of the friend being between 10 and 30 minutes late is equal to the area of the rectangle that lies between x = 10 and x = 30, and below the curve of the probability density function.

The height of the rectangle is equal to the maximum value of the probability density function, which is 1/30 since the interval of possible values for x is [0, 30] minutes.

The width of the rectangle is equal to the difference between the upper and lower limits of the interval, which is 30 - 10 = 20 minutes.

Therefore, the probability of the friend being between 10 and 30 minutes late is:

P(10 < x < 30) = (height of rectangle) x (width of rectangle)

= (1/30) x 20

= 2/3

≈ 0.6667

So the probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

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Answer:

1. b = 36 2. b = 42

Step-by-step explanation:

In diagram one, there is a right angle

90 - 54 = 36

b = 36

In diagram two, you can discern an angle of 180 degrees

180 - 138 = 42

b = 42

The algebraic expression for the given word problem is 12/y + 7

From the question, we are to write the algebraic expression for the given word problem

The given word problem is

"the quotient of 12 and a number y increased by 7"

First,

"the quotient of 12 and a number y" can be expressed as

12/y

Then,

"the quotient of 12 and a number y increased by 7" becomes

12/y + 7

Hence, the algebraic expression for the given word problem is 12/y + 7

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Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

numbers are 20 and 30 or 30 and 20.

A statement that represents the equality between two mathematical expressions. An equation can have one variable or two variables.

sum of two numbers = 50

sum of their reciprocal = 1/12

what is the 2 numbers.

let, one number is X and the other number is Y

as per the given condition, sum of X and Y is 50

X + Y =50 ...... equation 1

again, sum of the reciprocal of X and Y = 1/12

1/ X + 1/ Y = 1/12 ..... equation 2

 (X + Y)/ XY = 1 /12

(X + Y)12 = XY...  equation 3

from equation 1, we can write, Y = 50 - X

putting this value of Y in the equation 3

12X + 12(50 - X) = X(50 -X)

12X + 600 - 12X = 50X - X²

X² - 50X+600= 0

from the formula for quadratic equation, X = [50 ±√ (50² - 4×600)] / 2×1

                                                         X = (50±10) / 2

                                    X = 30, 20

          Y = 50 -30 = 20

      Y = 50- 20 = 30

hence, the 2 numbers are 20 and 30.

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Answer:

let the amount of time needed to sew 49 pair of trousers be x

If 1 pair of trousers = 57 minutes

49 pairs of trousers = 49 × 57/1

= 2793 minutes

Hope this helps.

Answer:

46 hours and 55 minutes

Step-by-step explanation:

If 57 minutes is required for 1 pair, to find how much time it will take to sew 49 pairs we simply multiply 57 by 49

After you do that you will be left with 2,793 minutes.

Since 60 minutes make an hour we divide the answer by 60.

2,793 ÷ 60 = 46 hours and 55 minutes.

I really hope this helps.

Step-by-step explanation:

1/4 in percentage

= 1/4 * 100%

= 25%

Answer:

4/4=100%

1/4=100÷4

   = 25%

The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)

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

35/100,5/10,65/100

In the above sequence, we can see that 15/100 is added to the previous term to get the new term

This means that

First term, a = 35/100

Common difference, d = 15/100

The nth term is then represented as

f(n) = a + (n - 1) * d

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

f(n) = 35/100 + 15/100(n - 1)

So, we have

f(n) = 7/20 + 3/20(n - 1)

Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)

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Answer:

attached below is the detailed solution

i) equilibrium solution : y = 0 , y^2 = 1 , y = -1 , +1

ii) attached below

iii) attached below

iv) attached below

v) attached below

Step-by-step explanation:

v) For the sketch of curve attached

red curve ( y(0) ) = -3/2

blue curve ( y(0) ) = 1/2

green solution curve ( y(0) ) = 3/2

Answer:

The answer to this question should be D. 0.67

Hope this helped.

Answer:

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

Use area formula for circle:

Substitute 22/7 for π and 70 for r:

The area is 15400 m².

Answer:

15400 m²

Step-by-step explanation:

The formula to find the area of the circle is:

\(\sf A=\pi r^2\)

Given that,

r = 70 m

Let us find the area of the circle

\(\sf A=\pi r^2\\\\\sf A=\dfrac{22}{7}*70*70\\\\\sf A =15400 \:m^2\)

Answer:

5.5227%

Step-by-step explanation:

Z score formula = (x-μ)/σ

where x is the raw score = < 18.5

μ is the population mean = 26.8

σ is the population standard deviation = 5.2

For x < 18.5

z = 18.5 - 26.8/5.2

z = -1.59615

Probability value from Z-Table:

P(x<18.5) = 0.055227

Converting to percentage

= 0.055227 × 100

= 5.5227%

Therefore, the percentage of young women that are underweight by this criterion is 5.5227%