Translate to an equation, then solve.The product of 2, and a number increased by 7, is – 36.

The probability that a randomly selected student is taking a math class or an English class is 0.88

And the probability that a randomly selected student is taking neither a math class nor an English class 0.12

In this question, we have been given in a large school, it was found that 80% of students are taking a math class, 75% of student are taking an English class, and 67% of students are taking both.

Let A represents math class, B represents English class

P(A) = 0.80

P(B) = 0.75

P(A ∩ B) = 0.67

We need to find the probability that a randomly selected student is taking a math class or an English class.

P(A U B) = P(A) + P(B) - P(A ∩ B)

P(A U B) = 0.80 + 0.75 - 0.67

P(A U B) = 0.88

Also, we need to find the probability that a randomly selected student is taking neither a math class nor an English class.

P(~(A U B) ) = 1 - P(A U B)

P(~(A U B) ) = 1 - 0.88

P(~(A U B) ) = 0.12

Therefore, the probability that a randomly selected student is taking a math class or an English class is 0.88

And the probability that a randomly selected student is taking neither a math class nor an English class 0.12

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To answer this question, we need to transform all the values into one type of measure. In this case, we can work with inches. Then, we have:

Then, we have that in two feet we have 24 inches. Then, we have:

Juan's dog: 24 inches + 3 inches ---> 27 inches tall.

Peter's dog: 9 inches tall.

Now, how much taller is Juan's dog than Peter's dog is:

Therefore, Juan's dog is 3 times taller than Peter's dog.

The first compound inequality 4x+3>15 or -6x≥12 matches the third graph, i.e x>3 or x≥-2.

The second compound inequality -8x>-24 and -10≤2x-6 matches the second graph, i.e x>3 or x≥-2.

The third compound inequality -29≤9x-2<16 matches the first graph, i.e -3≤x<2.

Given the expressions are:

a. 4x+3>15 or -6x≥12

simplify.

4x+3>15  or  -6x≥12

4x>15-3   or  x≥12/-6

4x>12      or     x≥-2

x>3          or     x≥-2

hence the graph is third.

b. -8x>-24 and -10≤2x-6

simplify.

-8x>-24 and -10≤2x-6

x>-24/-8  and  -10+6≤2x

x>3  and  -4≤2x

x>3  and  -4/2≤x

x>3  and  -2≤x

x>3 and x≥-2

hence the second graph matches.

c. -29≤9x-2<16

first take -29≤9x-2

simplify

-29+2≤9x

-27≤9x

-27/9≤x

-3≤x

now take 9x-2<16

simplify.

9x<16+2

9x<18

x<18/9

x<2

hence we get -3≤x<2

hence the first graph matches the given inequality.

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Use ''compound inequality'' in the main answer and ''graph'' in the explanation.

The solution to the equation would be 20/33 as a simplified fraction.

The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of that variable would give a true mathematical statement.

We have been given an equation as; −6.6x=−4

Thus we need to solve the equation to find the solution.

-6.6x = -4

Then Divide both sides by -6.6.

x = -4/(-6.6)

x = 40/66

x = 20/33

Hence, the solution to the equation would be 20/33 as a simplified fraction.

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x² + 7x + 12 = 0

Using the factorisation method

Find two numbers such that its product gives 12 and its sum gives 7

The two numbers are 3 and 4

Replace 7 in the equation by those two numbers and then factorise

That is;

x² + 3x + 4x + 12 = 0

x(x+3) + 4(x+3) = 0

(x+3)(x+4) = 0

Either x+3 = 0 or x+4 =0

Either x = -3 or x= -4

We need to know if the number given belongs to the set or no

0----- YES

-10------ NO

8 ------NO

-9 ----NO

9 ------NO

5 -----YES

The percentage increase or decrease can be calculated by :

7. New = 13, Orig = 10

% change = [(13 - 10)/10] x 100 = 30% (Increase)

8. New = 3, Orig = 5

% change = [(3 - 5)/5] x 100 = -40% or 40% (decrease)

Answer:

(a) 31 years

(b) 59 years

(c) 56 years

Step-by-step explanation:

In general, when reading a stem and leaf plot, we read firstly the number in the steam (middle) and then in the leaf.

Now, let's move on to the question:

(a) As we can see in the graph, the youngest actor has 31 years.

(b) The youngest actress is 21 years old and the oldest is 80.

So, the difference is 80 - 21 = 59 years.

(c) In this exercise, we have to look for actors who had the same age. That means, when evaluating the steam, we will have to find similar values in the leaf. The oldest age shared is 56 years.

We can solve the given expression for [tex]a=\frac{1}{3m}[/tex] by using the division method.

The given expression is [tex]12am=4[/tex].

We have to solve the given expression for [tex]a=\frac{1}{3m}[/tex].

Now we solving the expression.

[tex]12am=4[/tex]

We can easily solve the expression by seeing the value that we have to solve.

We using the division method to solve the given expression.

In the division method we divide the both side by same variable to find to value of particular variable.

For solving the expression for [tex]a[/tex] we eliminate [tex]12m[/tex].

We divide the given expression by [tex]12m[/tex] on both side

[tex]\frac{12am}{12m}=\frac{4}{12m}\\a=\frac{4}{3\times4m}\\a=\frac{1}{3m}[/tex]

Now we solve the given expression for [tex]a=\frac{1}{3m}[/tex].

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The formula for determining the length of an arc is expressed as

length of arc = #/360 * 2 * pi * radius

where

# represents the central angle

From the information given

length of arc = 36

We would convert from radians to degree

1 pi rad = 180 degrees

pi/2 rad = 180/2 = 90 degrees

Thus, # = 90 degrees

The equation becomes

36 = 90/360 * 2 * pi * radius

36 = 0.25 * 2 * 3.14 * radius

36 = 1.57 * radius

radius = 36/1.57

radius = 22.93 feet

Answer:

[tex]\frac{9}{10}[/tex]

Step-by-step explanation:

multiplies of 9, 18,27,36, and 45.  Every number has a change to be selected, but these 5.  There are 50 numbers

[tex]\frac{50-5}{50}[/tex]

[tex]\frac{45}{50\\}[/tex]

[tex]\frac{9}{10}[/tex]

Answer:

200.5

Step-by-step explanation:

reading of odometer at beginning = 187,198.9 km

reading of odometer after reaching home = 187,399.4

distance travelled = 187,399.4 - 187,198.9 = 200.5 km

When Fowler inc, just paid a dividend, the price in 15 years for the share is $72.36.

This will be illustrated as:

P0 = D1 / (Ke - g)

P0 = Current Price

D1 = Expected Dividend after 1 Year

Ke = COst of Equity

g = Growth Rate

Dividend for first year will be:

D1 = D0(1+g)

= $ 2.55 (1+0.039)

= $ 2.55(1.039)

= $ 2.6495

Current price will be:

P0 = D1 / (Ke - g)

= $ 2.6495 / (0.104-0.039)

= $ 2.6495 / 0.065

= $ 40.76

Price in 15 years will be

P15 = D16 / (Ke - g)

P15 = Price after 15 Years

D16 = Expected Div after 16 Years

Ke = COst of Equity

g = Growth Rate

D16 = D0(1+g)^16

= $ 2.55 (1+0.039)^16

= $ 2.55(1.039)^16

= $2.55 * 1.8444

= $ 4.7031

P15 = D16 / (Ke - g)

= $4.7031 / (0.104-0.039)

= $4.7031 / 0.065

= $72.36

The price is $72.36

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The margin error M.E. that corresponds to a sample of size 22 with a mean of 69.3 and a standard deviation of 8.6 at a confidence level of 95% is 0.04694

We would utilize the t distribution in the estimation of the margin of error because the population standard deviation is unknown (and the sample size is less than 30).

Error margin = t-critical * standard deviation/square root sample size

It is given in the above question that,

Standard deviation is given as = 8.6

And, the Sample size which is given is = 22

Also, the confidence level which given is = 95%

Then the alpha will be = 100% - 95%

= 5% = 0.05

Now, the critical value, t would be = alpha / 2

= 0.05 /2 = 0.025

Also, the sample we'll consider will be = given sample size - 1 = 22 -1 = 21

To find the margin error, we'll put all the values in the formula

Error margin = t-critical * standard deviation/square root sample size

=  [tex]\frac{0.025 * 8.6}{\sqrt{21} }[/tex]

= 0.215 / 4.58

= 0.04694

Hence, the margin error M.E. that corresponds to a sample of size 22 with a mean of 69.3 and a standard deviation of 8.6 at a confidence level of 95% is 0.04694

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The rule of the slope of a line has 2 points is

A = (1, -2), B = (3, 4), C = (-2, 6)

We will take the altitude from A to the opposite side of BC

Then we will find the slope of BC first

x1 = 3 and y1 = 4. point B

x2 = -2 and y2 = 6. point C

We will substitute them in the rule above

The slope of BC = -2/5

Since the product of the slopes of the perpendicular line is -1, then if the slope of one is m, then the slope of the other will be -1/m, we reciprocal it and change its sign, then the slope of the altitude of BC should be 5/2

The form of the equation in point-slope is

y - y1 = m(x - x1)

m = 5/2

Since point A is lying on the altitude from A to BC, then

x1 = 1 and y1 = -2 point A

Substitute m and coordinates of point A in the form of the equation above

y - (-2) = 5/2 (x - 1)

The equation of the altitude from A to BC is

y + 2 = 5/2 (x - 1)

Explanation

Step 1

we have the recursive formula

A recursive formula is a formula that defines each term of a sequence using the preceding term(s), we can see in the formula that the new term ( f(n)) equals the previous term minus 2

so

and so on,

Now for n=3

for n=4

so, the answer is

D) 17,15,13,11

I hope this helps you

The diagram which best represents the hiking track of the hiker is attached below.

As time increases, speed is constant, i.e., 214 miles per hour

So, the distance increases with an increase in time.

Speed = Distance/Time

Let, Distance = D and Time = T,

214 = D / T

D = 214T

Let, D = Y coordinate, Time = X coordinate

y = 214 x→→Equation of the line passing through the origin and slope 214.

For the given situation, the equation is a linear equation and the equation will be on the y-axis.

Hence, a diagram that represents this information is:  

Correct question :

A hiker began hiking from the 0-mile mark of a trail. The hiker walked at a steady rate of 214 miles per hour. Draw the diagram which best represents this information?

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Explanation:

A proportional relationship means that the two variables are related by a constant called constant of proportionality:

k is the constant of proportionality.

To find k we have to use the values of a and b from the table:

Answers:

• equation: ,a = 8/3 b

• constant of proportionality:, 8/3

We have the following:

now, for 500 miles

therefore about 11.11 gallons of gas is needed

Answer: roughly 12 gallons or exactly 11.11111111111111111 etc

Step-by-step explanation:

Answer:

$10,005

Step-by-step explanation:

We need to find the total cost of the plan and we already know that the client need to pay $150 for downpayment and 15 monthly payments of $657.

So all we need to find is the 15 monthly payments of $657. (Which we could found with multiplying $657 with 15)

$657×15 = $9,855

Now we just add it with the downpayment ($150) to find the total cost of the plan.

$9,855+$150 = $10,005

You could write the steps like this:

$150+($657×15)=$10 005

Answer

Options A, D and E are correct.

The two functions are increasing.

The function for plan II has a greater unit rate.

The function for plan I has a greater y-intercept.

Explanation

The slope and y-intercept form of the equation of a straight line is given as

y = mx + b

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

b = y-intercept of the line.

For the first plan, there's a one time investment of 15,000 dollars and subsequent monthly payments of 500 dollars.

y = 15,000 + 500x

y = 500x + 15,000

Slope = unit rate of increase = 500

y-intercept = 15,000

For the second plan, the function is just given as

y = 12,000 + 520x

y = 520x + 12,000

Slope = unit rate of increase = 520

y-intercept = 12,000

We can see that

The two functions are increasing.

The function for plan II has a greater unit rate.

The function for plan I has a greater y-intercept.

Hope this Helps!!!

The height of the sand dune after 13 years is 324 cm. The rate of change height of sand dunes is - 8t.

Given the equation is -

f(t)=1000-4t²

f(13) = 1000 - 4 (13)²

= 1000 - 676

= 324 cm

f'(t) = - 8t

f'(13) = - 8(13)

= -104cm

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Complete Question -

The height of a sand dune (in centimeters) is represented by f(t)=1000-4t2 cm, where t is measured in years since 1995. Find f(13) and f'(13), and determine what each means in terms of the sand dune. Give the values of f(13) and f'(13) below, including units.

Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient so equation of line d is y = -5x + c.

Substitute (2,-6) into the equation to find c.

-6 = -5(2) + c

c = 4

Hence equation of line d is y = -5x + 4.

Considering the definition of a line, the equation in slope-intercept of the line that passes through the point (1, 10) and has a slope of 1 is y=x+9.

A linear equation o line can be expressed in the form y = mx + b

where

In this case, you know:

Substituting the value of the slope m, the line has a form: y=1x + b or what is the same y=x +b.

Replacing the value of the point in the expression of a linear equation, the value of the ordinate to the origin b can be obtained:

10= 1×1 + b

10= 1 + b

10 -1 = b

9= b

Finally, the equation of the line is y=x +9.

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Answer:

• k=50/13

• y=69.231 (to the nearest 1000th)

Explanation:

If y varies directly as x, the equation of variation is:

When x=13 and y=50

Substituting k into the equation above, we have:

Therefore, when x=18