3. Given the function f(x) shown graphed below, what is its average rate of change from } x=1 to x=7 ?

(1) -1
(2) -4/3
(3) 8
(4) 3/5

4. A function h(x) has an average rate of change equal to 7 on the interval 5 ≤ x≤ 9. If h(5)=12, then which of the following must be the value of h(9) ?

ŷ= 6.45x + 31.5 is the equation of the regression line for the given data

Construct the table of the data as follows:

x    >>>>     y  >>>>  x²  >>>>  y²  >>>>   xy

1                39            1            1521         39

2               45            4           2025       90

3               52             9          2704       156

4               49            16          2401        196

5               61             25         4096       305

5               72            25          5184        360

................................................................................................

20             318           80          17931       1146

.................................................................................................

∑x = 20,  ∑y = 318, ∑x²= 80, ∑xy = 1146,  n = 6 (number data points)

The linear regression equation is of the form:

ŷ = ax + b

where a and b are the slope and y-intercept respectively

a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )

a = (6×1146 - 20×318) / ( 6×80-20² )

a = 6876-6360 / 480-400

a = 516 / 80

a = 6.45

x' =  ∑x/n

x' = 20/6 = 10/3

y' = ∑y/n

y' = 318/6 = 53

b = y' - ax'

b = 53 - 6.45×(10/3)

b = 53 - 21.5

b = 31.5

ŷ = ax + b

ŷ= 6.45x + 31.5

Thus,  the equation of the regression line for the given data is ŷ= 6.45x + 31.5. (The scatter plot of the data is shown in the attached image)

(a) x=3 hours

ŷ= 6.45(3) + 31.5 = 50.85

(b) x=4.5 hours

ŷ= 6.45(4.5) + 31.5 = 60.525

(c) x=13 hours

ŷ= 6.45(13) + 31.5 = 115.35

(d) x=1.5 hours

ŷ= 6.45(1.5) + 31.5 = 41.175

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Answer:

p=24/528

Step-by-step explanation:

4+2p=10(53p-2)

4+2p=530p-20

24+2p=530p

24=528p

24/528=p

Answer:

Step-by-step explanation:

The formula you want is: fv=p(1+int/c)^(nc)

future value

principal

int

compound

years

fv=4000(1.04/4)^(16)=$4690.31

The simplification of complex fraction -⅔/⅚ is - 4/5

A complex fraction is a rational expression that has a fraction in its numerator, denominator or both. In other words, there is at least one small fraction within the overall fraction.

In fraction when the numerator is bigger than the denominator , then it is called improper fraction, when a fraction consist of whole number and proper fraction is called mixed fraction

-2/3 ÷ 5/6

= -2/3×6/5

= -4/5

Therefore -⅔/⅚ can be simplified to -⅘

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a) The probability that both are girls is of: 21/150.

b) The probability that both are from the same school is of: 0.7333 = 73.33%.

The probabilities are obtained as the division of the number of desired outcomes by the number of total outcomes.

For item a, the outcomes are given as follows:

Hence the probability that both are girls is of:

p = 7/15 x 3/10 = 21/150.

The probability that the two boys are from the same school can be given by these two cases:

Then the probability is of:

p = 8/15 x 7/14 + 7/10 x 6/9 = 0.7333 = 73.33%.

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The missing sides of triangle ABC, If M is the centroid of triangle ABC, AM = 44, CE =54, and DM = 23, are FM = 22, AM = 44.

Three medians of a triangle intersect to produce the centroid of the triangle. It is one of a triangle's four points of concurrency. When the midpoints of the triangle's opposite sides are linked, the triangle's vertices become the triangle's medians.

Given:

The [tex]M[/tex] is centroid of triangle ABC, AM = 44, CE = 54, and DM = 23,

The centroid of a triangle divides the median in the ratio [tex]2 : 1[/tex]

Therefore, [tex]AM : FM = 2 : 1[/tex]

Let AM = 2x and FM = x

Since, AM = 44

Hence, 2x = 44

x = 44 / 2

x = 22

FM = 22

Therefore, the missing sides are FM = 22 and AM = 44.

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The missing figure is attached below.

Answer:

b

step by step explanation

By using fraction, it can be calculated that

30 boards are required to cover a floor of width 205 inches wide

What is fraction?

Suppose there is a collection and a part of collection has to be taken.

The part which is taken is called fraction. In other words part of a whole is called fraction.

The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

This is a word problem on fraction

Width of each board = [tex]6\frac{5}{6}[/tex] inches = [tex]\frac{41}{6}[/tex] inches.

Total width of floor = 205 inches.

Number of boards required = [tex]205 \div \frac{41}{6}[/tex] = [tex]205 \times \frac{6}{41}[/tex] = 30

30 boards are required

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Answer:

  a) 4(8019) +3s ≥ 70000

  b) yes

Step-by-step explanation:

Diego has walked an average of 8019 steps per day for 4 days and wants to walk 70000 steps in a week. You want an inequality for the average number of steps per day that Diego must walk for the last 3 days of the week, and you want to know if 12642 is a solution.

The inequality will express the relationship between the steps walked and the goal. Let s represent the average number of steps walked each day for the last 3 days of the week.

The total number of steps walked in the first 4 days is the average per day times the number of days: 4(8019). The total number of steps walked in the last 3 days is the average per day times the number of days: 3s.

The total for the week is the sum of these. We want that to exceed 70000:

  4(8019) +3s ≥ 70000 . . . . . . . the desired inequality

Solving for s, we find ...

  3s ≥ 7000 -4(8019)

  3s ≥ 37924 . . . . . . . . . subtract 32076

  s ≥ 12641 1/3 . . . . . . . . divide by 3

The offered number, 12642, is greater than 12641 1/3, so is a solution.

Diego will meet his goal if he averages 12642 steps per day for the last 3 days of the week.

__

Additional comment

If Diego's 3-day average is 12462, he will have walked 70002 steps for the week, a number that is more than 70000.

Answer:

4

Step-by-step explanation:

20% = 40

10% = 20

100% = 200

200 * .02 = 4

The value of 2% of that number is,

⇒ 4

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

20% of a number is 40.

Let the number = x

Hence, We get;

⇒ 20% of x = 40

⇒ 20/100 × x = 40

⇒ 1/5 × x = 40

⇒ x = 200

Thus, The value of 2% of that number is,

⇒ 2% of 200

⇒ 2/100 x 200

⇒ 4

Thus, The value of 2% of that number is,

⇒ 4

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The answer is the Theoretical probability is higher than the Experimental probability.      

Experimental probability:

The basis for experimental probability is what actually happens. It is dependent on the outcomes of several tests or experiments.

It is calculated by repeatedly recreating the event, recording the outcomes, and then converting the outcomes into a ratio or decimals.

Experimental probability =  No of times event occurs/ No of trials

Theoretical Probability:

Theoretical probability is derived from a theory or what is predicted to occur. It is based on information and math.

It is determined by dividing the total number of outcomes by the proportion of favorable results. Either convert it to decimal form or leave it as a ratio or fraction.

Theoretical probability = No of favorable outcomes/ No of outcomes

Here we have

Tami rolled a die 20 times

14 times it landed on an even number;

6 times it landed on an odd number.  

The die rolled for an odd number

As we a die will have 6 faces

Number of odd numbers = 3       [i.e 1, 3, 5 ]                    

Number of even numbers = 3    [ i.e 2, 4, 6 ]

⇒ Theoretical probability = 3/ 6 × 100 = 50%

The die is rolled 20 times, 6 times it landed on an odd number.

⇒ Experimental probability =  6 / 20 = 30%

As we can see,

The theoretical probability is higher than the Experimental probability.

Therefore,

The answer is the Theoretical probability is higher than the Experimental probability.  

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You will find 5 rare trading cards if you bought 110 packs of trading cards

Given that:

The chances of finding a rare card in a pack of trading cards can be represented with the equation y equals one twenty-second times x.

Thus, we can the equation as:

y = (1/22)x

To determine the number of rare trading cards if you bought 110 packs of trading cards, substitute x = 110 into the equation:

y = 1/22 × 110

y = 5

Therefore, you will find 5 rare trading cards if you bought 110 packs of trading cards

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Answer:

Step-by-step explanation:

y = the number of rare trading cards found

x = the number of packs of trading cards

1/22 = the probability of finding a rare card per pack

Equation

y = 1/22(x)

y = 1/22(110)

y = 110/22

y = 5

There is a chance of finding 5 rare cards in 110 packs of trading cards.

Answer:

4

Step-by-step explanation:

n/2 + 7 = 9

n/2 + 7 - 7 = 9 - 7

n/2 = 2

n = 4

The probability that the card is between four and eight (inclusive) or is a club is 4/13.

Probability helps us to know the chances of an event occurring.

The number of cards can be written as,

The number of cards between 4 and 8 is 3 {4,5,6,7,8}.

   Number of club cards = 13

   Number of cards between 4 and 8 from heart, spades, and diamonds = 15

Now, the probability that the card is between four and eight (inclusive) or is a club is,

Probability = desired outcomes / total number of outcomes possible

= (Number of club cards+ Number of cards between 4 and 8)/(Total number of cards)

= (13+15)/(52)

= 28/52

= 4/13

Hence, the probability that the card is between four and eight (inclusive) or is a club is 4/13.

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Answer:

27.7 min

Step-by-step explanation:

In 6 minutes the truck will be 6 miles ahead of the car....

   the car is going 13 mph faster and will cover this 6 miles in

     6 mi / 13 mi/hr = .4615 hr =27.7 min

Tan A + Cot A = 2 Cosec 2A.

It is a simple TRIGNOMETRY question, which is directly based on their formulas.

In this question we have one side of formula either LHS or RHS and we have to find other,

Tan A + Cot A

we know Tan A = sin A /Cos A  and Cot A = cos A / sin A

So by putting this in place of  Tan A + Cot A we get,

⇒ (sin A / cos A) + (cos A / sin A)

⇒ (sin∧2 A + cos∧2 A) / cos A sin A

⇒1/ cos A sin A

⇒2/2cos A sin A

⇒ 2/Sin 2A

⇒ 2 Cosec 2A

Hence, the question is simplified.

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The probability that an eligible voter selected at random did not have a college degree and did not vote in the last presidential election is  49.5%.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

The no. of people who don't have a college degree is (1000 - 100) = 900.

45% of the people who did not have a college degree voted in the last presidential election hence (100 - 45) = 55% of the people who did not have a college and did not vote in the last presidential election.

∴ (55/100)×900.

= 495 people.

∴ The probability that an eligible voter selected at random did not have a college degree and did not vote in the last presidential election is,

= 495/1000.

= 0.495.

= 49.5%.

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Answer:

11(12w+5)

Step-by-step explanation:

common factors of 132 and 55 is 11

So we can take it out by dividing both terms by 11

11(12w+5)

Hopes this helps

Answer:I hope this is helps

good luck

Step-by-step explanation:

132w+55

Factor out from the expression
11(12w+5) this is the distributive Property

Answer:

O A. 3, 11, 23, 21

OB. 7, 17, 29

OC. 2, 3, 5

OD. 2, 5

Step-by-step explanation:

It is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.

If a contradiction is rational, then log3(7) = a/b for some a,b∈R .

In which, b≠0 will be true.

As a result, 7 = 3ᵃ/ᵇ according to the definition of logarithms.

7 = 1*7 is unique according to the unique factorization theorem.

Thus, it is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.

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-First question:

To calculate the number of liters, the number of roofs must be multiplied by the amount of waterproofing used for each roof.

To multiply the fractions, transform the mixed fractions to improper:

[tex]\begin{gathered} \sf1 \frac{1}{4} \times 4 = \\ \\ \sf \frac{4 \times 1 + 1}{4} \times \frac{4}{1} = \\ \\ \sf \frac{4 + 1}{4} \times \frac{4}{1} = \\ \\ \sf\frac{5}{4} \times \frac{4}{1} = \\ \\ \sf \frac {5 \times 4}{4 \times 1} = \\ \\ \boxed{ \sf \frac{ \red{20}}{ \red4}} = \sf \blue5\end{gathered}[/tex]

So you need five liters of waterproofing to get the job done.

-Second question:

To calculate the number of liters; It must be subtracted from the number of liters you need in total, which you already had or had:

[tex]\begin{gathered} \sf5 - 2 \frac{1}{4} = \\ \\ \sf \frac{5}{1} - \frac{4 \times 2 + 1}{4} = \\ \\ \sf\frac {5}{1} - \frac{8 + 1}{4} = \\ \\ \sf \frac{5}{1} - \frac{9}{4} = \\ \\ \sf\frac{4 \div 1 \times 5 - 4 \div 4 \times 9}{4} = \\ \\ \sf \frac{20 - 9}{4} = \\ \\ \boxed{ \sf \frac{11}{4}} = \boxed{ \sf \blue2 \: \: \blue{\sf\frac{3 }{4} }}\end{gathered}[/tex]

So, you need two whole and three quarter liters of waterproofing.

After using the trigonometry method the answer is sin 2 (pi/7)/2

What principle underlies trigonometry?

The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the branch of mathematics known as "trigonometry." Therefore, using trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle.

What distinguishes geometry from trigonometry?

The study of triangle properties, particularly those of right triangles, is known as trigonometry. But the study of geometry focuses on the characteristics of all geometrical figures.

Given that:

sinπ/7·cosπ/7

if we can divide and multiply 2 so it can be converted to sin 2 theta

sin 2 (pi/7)/2

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Answer: r > 30

Step-by-step explanation:

If the length of the side PR is 7 feet. Then the perimeter of the triangle ΔPQR will be 17 feet.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The perimeter of the triangle is determined by adding together all of its sides.

The triangles ΔPQR and ΔSTU are congruent triangles. Then we have

PR = SU

3y - 2 = y + 4

3y - y = 2 + 4

2y = 6

y = 3

Then the value of the side PR is given as,

PR = 3(3) - 2

PR = 9 - 2

PR = 7 feet

Then the perimeter of the triangle ΔPQR is calculated as,

P = 4 + 6 + 7

P = 17 feet

If the length of the side PR is 7 feet. Then the perimeter of the triangle ΔPQR will be 17 feet.

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Answer:

  (a)  √8

Step-by-step explanation:

You want to know the radical equivalent to 2^(3/2).

The relationship of indices to radicals is ...

  [tex]\large{\sqrt[n]{a^m}}={a^{\frac{m}{n}}[/tex]

The given expression can be rewritten as ...

  [tex]2^{\frac{3}{2}}=\sqrt[2]{2^3}=\boxed{\sqrt[2]{8}}[/tex]

__

Additional comment

When the index of the radical is 2, it is usually left off. The radical can be simplified by removing the perfect square factor.

  [tex]\sqrt[2]{8}=\sqrt{8}=2\sqrt{2}[/tex]

Nominal and ordinal categorical variables are the two different types.

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The explicit formula for the geometric sequence would be [tex]a_n =10000.87\times (0.95)^{n-1}[/tex].

What is a geometric sequence?

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Given:

         [tex]a_4=8573.75\\\\a_6=7731.81[/tex]

Now by using the formula for the nth term of a GP, we get

           [tex]a_n = ar^{n-1}\\\\a_4=ar{4-1}\\\\8573.75=ar^3[/tex]

Now for n = 6, we get

           [tex]a_n = ar^{n-1}\\\\a_6=ar{6-1}\\\\7737.81=ar^5[/tex]

Now divide we get

[tex]\frac{ar^5}{ar^3} =\frac{7737.81}{8573.35} \\\\r^2=0.9025\\\\r=0.95[/tex]

Now we can get the value of a,

        [tex]8573.75=ar^3\\\\a = \frac{8573.75}{(0.95)^3}\\\\a = \frac{8573}{0.8573}\\\\a = 10000.87[/tex]

So we can prepare the explicit formula as

            [tex]a_n =10000.87\times (0.95)^{n-1}[/tex]

Hence, the explicit formula for the geometric sequence would be [tex]a_n =10000.87\times (0.95)^{n-1}[/tex].

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