{f(x)=2x+1 g(x)=x2+2x−8

Answer:

A.

Step-by-step explanation:

so, the equation is

h(t) = -t² + 7t

so, we need to find the solutions for t (the time when the ball is exactly 10 ft in the air). there had to be 2 solutions, as the ball first goes up passing the 10 ft height, and then comes back down again, passing the 10 ft mark a second time. and between these 2 times the ball is higher (but not equal, so, we can only use < or > as inequality signs) than 10 ft.

10 = -t² + 7t

-t² + 7t - 10 = 0

the generation solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = t

a = -1

b = 7

c = -10

t = (-7 ± sqrt(7² - 4×-1×-10))/(2×-1) =

= (-7 ± sqrt(49 - 40))/-2 = (-7 ± sqrt(9))/-2

t1 = (-7 + 3)/-2 = -4/-2 = 2 seconds

t2 = (-7 - 3)/-2 = -10/-2 = 5 seconds

so, between 2 and 5 seconds airtime the ball is higher than 10 ft.

and remember : HIGHER THAN.

so, we cannot use any equality (like <= or >=).

t must be higher than 2 and lower than 5 :

2 < t < 5

The length of the base of the triangle is 12m

The formula for calculating the area of a triangle is expressed as:

A = 0.5 * base * height

If the height of a triangle is 4 m less than its base, then;

h = b - 4

Substitute

A = 0.5(b)(b-4)

48 = 0.5b²-2b

b²-4b - 96 = 0

Factorise

b² - 12b + 8b - 96 = 0

b(b-12)+8()b-12) = 0
b - 12 = 0

b = 12

Hence the length of the base of the triangle is 12m

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Answer:

Yes, because the p-value of the independent variable is less than 0.05

Step-by-step explanation:

The relationship between Red Sox away games and average daily revenues significant at the 95% confidence level because the p-value ( X) < 0.05 , Option C is the correct answer.

Probability is the study of chances of an event to happen.

It has a range form 0 to 1 , where 0 indicates uncertainty while 1 indicates certainty.

The data is given and on the basis of it

It can be seen that for 95 % confidence Level

P value =0.0005

So , the relationship between Red Sox away games and average daily revenues significant at the 95% confidence level because the p-value of the independent variable is less than 0.05.

Therefore Option C is the correct answer.

The complete question is

Is the relationship between Red Sox away games and average daily revenues significant at the 95% confidence level? Choose the correct answer with the corresponding correct reasoning.

No, because R Square is less than 50%

Yes, because the slope is positive.

Yes, because the p-value of the intercept is less than 0.05

Yes, because the p-value of the intercept is less than 0.95

Yes, because the p-value of the independent variable is less than 0.05

Yes, because the p-value of the independent variable is less than 0.95

The data table is attached with the answer.

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Answer:

x = 36°

y = 66°

z = 78°

Step-by-step explanation:

Setup equations:

Allowing the first angle to be x, the second to be y, and the third to be z, the three sentences describing the relationships between angle measures are given below:

Substituting equation 3, into equations 1 and 2

Eq1:  x + y + z = 180°

x + y + (y+12°) = 180°

x + 2y + 12° = 180°

x + 2y = 168°

x = 168° - 2y

Eq2:  y + z = 4x

substituting the result from equation 1, and Equation 3...

y + (y+12°) = 4*(168° - 2y)

2y + 12° = 672° - 8y

10y = 660°

y = 66°

Substituting back into Equation 3...

Eq3:  z = y + 12°

z = (66°) + 12°

z = 78°

Substituting both y, and z into Equation 1...

x + y + z = 180°

x + (66°) + (78°) = 180°

x + 144° = 180°

x = 36°

So, the three angle measures are:

x = 36°

y = 66°

z = 78°

"The sum of the measures of the angles of a triangle is 180."

x + y + z = 180°

36° + 66° + 78° = 180°

True

"The sum of the measures of the second and third angles is four times the measure of the first angle"

y + z = 4x

66° + 78° = 4*(36°)

144° = 144°

True

"The third angle is 12 more than the second"

z = y + 12°

78° = 66° + 12°

True

The required confidence interval for μ is (-12.07, 19.27 )

Annual returns (in percent) for a mutual fund as: 13, −2, 3, 18, and −14
95% Confidence interval

The statistic is the study of mathematics which deal with relations between comprehensive data.

Mean(x) = 13-2+3+18-14/5
x = 3.6

Standard deviation = [tex]\sqrt{\frac{\sum(x_i- x)^2}{n-1} }[/tex]
S = 12.6214

Point estimate  of (μ) = 3.6

Confidence interval = mean (+,-) Tc x S/√5
                              = 3.6 (+,-) 2.7764 x 12.62/√5
                              =3.6 (+,-) 15.671
                              = (-12.07, 19.27)

Thus, the required confidence interval for μ is (-12.07, 19.27 ).

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Answer:Given

a can do a piece of work = 40 days

so, A's 1 day work =1/4

so, A's 8 day's work =8/40=1/5

remaining work = 1- 1/5= 4/5

Now, B can do  4/5  piece of work in =16 days

So, B’s 1 day's work = (4/5) /16= 4/ 5x6=1/20

Therefore, (A+B)’s 1 day's work = 1/40+1/20 =

1+2/40=3/40

∴   Both (A+B) can do a piece of work in =

1/days (3/40) = 40/3 days

= 13 1/3 days

The value of the function h(-4) is (a) -2

The function is given as

h(x) = -2x - 10

When x = -4, we have:

h(-4) = -2 * -4 - 10

Evaluate the product

h(-4) = 8 - 10

Evaluate the difference

h(-4) = -2

Hence, the value of the function h(-4) is (a) -2

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Answer:

======================

Since the given is the GP, find the common ratio in terms of given values:

Equate the two values and solve for x to find the missing term:

x + 3x + 5x ( the variables are same you can add them immediately )

9x ( the answer is 9x for adding terms with the same variable just add the numbers and write the variable as itself)

HOPE IT HELPS

Answer: 9x

Step-by-step explanation:

As the variables are of same power (1) we can add it

x+3x+5x=9x

Answer:

/.............................../././///////////////////////////////////////

Step-by-step explanation:

.

The equivalent equation of 4y – 1 = 15 is 20x - 13 = 15

The equations are given as:

4y – 1 = 15 and y = 5x – 3.

Substitute y = 5x – 3. in 4y – 1 = 15

4(5x – 3) – 1 = 15

Expand

20x- 12 - 1 = 15

Evaluate the like terms

20x - 13 = 15

Hence, the equivalent equation of 4y – 1 = 15 is 20x - 13 = 15

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The most effective in controlling the confounding variables is matched pairs design.

A matched pairs design is when participants are matched based on shared characteristics that is of importance to the experiment. One member of the pair is put in the control group while the other is put in the experimental group.

Here are the options:

A completely randomized design experiment

A longitudinal observational study

A retrospective observational study

A matched-pair design experiment

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Answer:

There are 8 black marbles.

Step-by-step explanation:

First, set up your equation. You have black (b) and white (w) marbles, total of 30, so those will be your variables to set in your equation.

w + b = 30

You mentioned that there are 14 more white marbles then black. Therefore, white marbles will have b many marbles + 14, creating the equation:

w= b + 14

If w = b + 14 and w can be easily substituted in the first equation, substitute w for b + 14. This will result in having the equation of:

(b +14) + b= 30

Simplify this equation, combine like terms to break down the equation, making it easier for you to solve for b.

-Subtract 14 from both sides.

-Add b + b = 2b

Then, you will have your resulting equation in which you divided 2 from both sides to get b by itself.

2b = 16

b=8

There are 8 black marbles.

Answer:

answer is the second option  m<-2 7/12

Step-by-step explanation:

process:

convert -2 1/4 into an improper fraction

m+1/3 < -9/4

m <-9/4 -1/3

calculate the difference

m<-31/12

turn into a mixed fraction

The amount further by which Kate can see across the horizon than Paul is; 3.33 times farther

Formula for volume of a cone is;

V = ¹/₃πr²h

For Kate:

Height (h) = 50 m

Radius (r) = 6,371,000 m

Thus;

V = ¹/₃ * π * (6,371,000)² * 50

V = 2.12526863 × 10¹⁵ m³

To determine how much further can kate see across the horizon than Paul, we have:

⇒ (2.12526863 × 10¹⁵ m³)/6.3758059 × 10¹⁴ m³

= 3.33 times further.

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Considering the given graph, the profit during the period was of -2 dollars.

We add all the negative numbers, all the positive numbers, then keep the signal of the higher absolute value, and subtract the values.

From the graph, we have that:

8 > 6, hence the profit is negative given by:

-(8 - 6) = -2 dollars.

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Answer:

Let the greater number be x and the smaller number be y

A.T.Q,

x+y=32 ...(1)

x=3y ...(2)

putting the value of x from (2) in (1)

(3y)+y=32

4y=32

y= 32/4=8

x=3y

x=3(8)=24

x=24 , y=8

Hello,

Answer:

The next number is 35 585

Step-by-step explanation:

3 × 5 - 3 = 12

5 × 12 - 5 = 55

12 × 55 -12 = 648

55 × 648 - 12 = 35 585

The next number for the given series is 35,585.

A number series is a number-based sequence. In the number series questions, we must identify the rules that lead to the formation of a number series. These series vary in nature, as do the questions that may arise from them.

Given that the series is 3,5,12,55,648. The next number will be calculated by decoding the series as below,

3 × 5 - 3 = 12

5 × 12 - 5 = 55

12 × 55 -12 = 648

55 × 648 - 12 = 35,585

Therefore, the value of the next number for the series is 35,585.

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The number of the blue marbles are in the box will be 102.

The solution of the equation means the value of the unknown or variable.

A box contains 162 marbles which are either red (r) or blue (b).

r + b = 162 ...1

There are 42 more blue marbles than red marbles.

b = r + 42 ...2

Then from equation 1 and 2, we have

r + r + 42 = 162

           2r = 120

             r = 60

Then the number of blue marble will be

b = 60 + 42

b = 102

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Answer:

-3

Step-by-step explanation:

Equation: (x + 6) - 5 = -2

we want to isolate x

(x + 6) - 5 = -2              

          + 5    + 5      (add 5 to start getting x on its own)

x + 6 = 3                

  - 6      - 6                 (subtract 6 to isolate x)

x = -3

so, this answer was not provided, but is the correct answer.

The solution to this equation is -3,

so, the correct answer is: -3.

Here, we have,

given that,

Equation is:

(x + 6) - 5 = -2

we want to isolate x

(add 5 to start getting x on its own)

(x + 6) - 5+ 5 = -2 + 5                          

(subtract 6 to isolate x)

x + 6 - 6 = 3   - 6              

so, we get,                  

x = -3

so, the solution to this equation is -3,

so, the correct answer is: -3.

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An equation is formed when two equal expressions. The cost per pound of wheat flour is $0.55 and the cost of per pound of rye flour is $0.55.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the cost of a pound of wheat flour be x and the cost of a pound of rye flour be y.

A baker purchased 13 lb of wheat flour and 14 lb of rye flour for a total cost of $14.85.

13x + 14y = $14.85

x = (14.85-14y)/13

A second purchase, at the same prices, included 15 lb of wheat flour and 12 lb of rye flour.

15x + 12y = $14.85

Substitute the value of x from the above equation and solve for y,

[tex]\dfrac{15(14.85-14y)}{13} + 12y = 14.85\\\\222.75-210y+156y = 193.05\\\\y = 0.55[/tex]

Substitute the value of y in any one of the equations formed,

13x + 14(0.55) = 14.85

13x = 7.15

x = 0.55

Hence, the cost per pound of wheat flour is $0.55 and the cost of per pound of rye flour is $0.55.

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Final answer:

Since absolute values determine the distance between the number and the value whether the value is positive or negative. As distance is always positive.

Thus, |a| is always nonnegative, even though |a|=-a for negative values of a.

Step-by-step explanation:

Step 1

It is said that |a| is always nonnegative even though even though |a|=-a for negative values of a.

Step 2

This is because by the definition of an absolute value, any real number inside an absolute value symbol || will always be positive.

Considering the given stem-and-leaf plot, the quartiles are given as follows:

There is an even number of elements(26), hence the median is the mean of the 13th and 14th elements, which are 83 and 86, hence:

Me = (83 + 86)/2 = 84.5.

The first half has 12 elements, hence the first quartile is the mean of the 6th and 7th elements, which are 67 and 68, hence:

Q1 = (67 + 68)/2 = 67.5.

The third half also has 12 elements, starting at the second 86, hence the third quartile is the mean of the 6th and 7th elements of this half, hence:

Q3 = (91 + 92)/2 = 91.5.

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The equation of line which would intersect be

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Given:

y = 12 x + 2

and, a line passes through (-4, 0) and (0, 2)

Equation of line

y = -1/2 (x+ 4)

y= -x/2 - 2

The equations which would intersect the line will be

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Answer:

here

Step-by-step explanation: