A new ramp is being built at the school. It will be two meters long and one meter high. What will the slope of the ramp be?

The confidence interval, expressed as a trilinear inequality, is 71.6%

What does a confidence interval mean?

The range of values we see in our sample and expect to find the value that most accurately represents the population are referred to as a confidence interval.

The lower bound is 71.6% - 8.2% = 63.4% and the upper bound is 71.6% + 8.2% = 79.8%.

Thus the confidence interval, expressed as a trilinear inequality, is 63.4% < p < 79.8%, where p= 71.6%.

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Answer:

Step-by-step explanation:

160/3

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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Answer:

156

Step-by-step explanation:

4x + 3 = 3(2x - 5)

4x + 3 = 6x - 15

3 = 2x - 15

2x = 18

x = 9

4(9) + 3

= 36 + 3

= 39

39 * 4 = 156

Hope it helps!

Answer: 156 inches

Step-by-step explanation:

So we know that all of the sides are equal to each other.

Now we need to know what x equals.

4x + 3 = 3(2x -5)

4x + 3 = 6x - 15

3 = 2x -15

18 = 2x

9 = x

Plug 9 into one of the equations.

4(9) + 3

36 + 3 = 39

39 * 4 = 156

Perimeter = 156 inches

Hope this helps!!! :)

Answer:

1 gallon of gas is $2.95

9.5 gallons of gas is $28.025

Step-by-step explanation:

[tex]\frac{12.2}{35.99} =\frac{1}{y}[/tex]

Cross Multiply.

12.2 · y = 1 · 35.99

12.2y = 35.99

12.2y ÷ 12.2 = 35.99 ÷ 12.2

y = 2.95

1 gallon of gas is $2.95.

[tex]\frac{1}{2.95} =\frac{9.5}{y}[/tex]

1 · y = 2.95 · 9.5

y = 28.025

9.5 gallons of gas is $28.025.

If she starts with £400 in her account, her balance for the next three years IS; $608.35

The general formula for exponential equation is;

y = a(b)ˣ

where;

a represents an initial value or amount

b is the constant multiplier, is a growth factor or factor of decay.

We are given;

Initial value; a = £400

constant multiplier; b = an increase of 15% yearly = 1.15

Thus, her balance for the next three years is;

y(3) = 400(1.15)³

y(3) = $608.35

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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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Nominal and ordinal categorical variables are the two different types.

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Answer:

O A. 3, 11, 23, 21

OB. 7, 17, 29

OC. 2, 3, 5

OD. 2, 5

Step-by-step explanation:

Answer: x+7=1+2x

Step-by-step explanation:

If x represents the number,The sum of a number and 7 is x + 7One more than twice the number is 1 + 2xThe IS in the middle of the sentence means =So, x + 7 = 1 + 2x  Solve this equation,If you need further assistance message me.

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.

The diagonal can be written as -

d = √{(L)² + (B)² + (H)²}

Given is a graph as shown in the figure.

Since the dimensions of a right rectangular prism are not given, assume the length, width and height to be [L], [W] and [H]. Then the diagonal can be written as -

d = √{(L)² + (B)² + (H)²}

Therefore, the diagonal can be written as -

d = √{(L)² + (B)² + (H)²}

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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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The equation of the line that is parallel to the line x + y + 2 = 0 and passing through (2, -2) will be x + y = 0.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as,

ax + by + d = 0

The equation of the line is given below.

y = - x - 2

x + y + 2 = 0

Then the equation of the line that is parallel to x + y + 2 = 0 is given as,

x + y + d = 0

The line is passing through (2, -2), then we have

2 + (-2) + d = 0

d = 0

The equation of the line that is parallel to the line x + y + 2 = 0 and passing through (2, -2) will be x + y = 0.

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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

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:

4

Step-by-step explanation:

n/2 + 7 = 9

n/2 + 7 - 7 = 9 - 7

n/2 = 2

n = 4

140 is the same as multiplying by 319 as an equation can be written as 140 = a x 319.

An equation is a mathematical expression that contains an equal symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculation.

Hence, the sentence as an equation for 140 is the same as multiplying by 319 is, 140 = a x 319.

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To express the given numbers in equation form it can be written as =

140 is the same as multiplying by 319 as an equation can be written as 140 = a x 319.

What is an equation?

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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

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:

Missing term [tex]\dfrac{1}{4}[/tex]

Factored term on RHS:   [tex]$(x+\dfrac{1}{2})^{2}$[/tex]

Step-by-step explanation:

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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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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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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Answer:

b

step by step explanation

Answer:

C.

19.5m2+11.7m

Step-by-step explanation:

hope this helps

Answer:

C.

19.5m2+11.7m

Step-by-step explanation:

what i got on the test

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.

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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