lan's car can go 117 miles on 3 gallons of gas. During a drive last​ weekend, ian used 4
gallons of gas. How far did he ​drive? Use pencil and paper. Explain how the problem changes if you were given the distance iandrove last weekend instead of how much gas used.

There are five possibilities for whole numbers such that radical expression 4 ≤ √3 + √x ≤ 5: {6, 7, 8, 9, 10}

In this problem we have the case of a radical expression, from which we need to determine at least a whole number such that following inequality is fulfilled:

4 ≤ √3 + √x ≤ 5

This can be done by algebra properties. First, determine the limits of the inequality:

4 ≤ √3 + √x

4 - √3 ≤ √x

(4 - √3)² ≤ x

x ≥ (4 - √3)²

x ≥ 16 - 8√3 + 3

x ≥ 19 - 8√3

√3 + √x ≤ 5

√x ≤ 5 - √3

x ≤ (5 - √3)²

x ≤ 25 - 10√3 + 3

x ≤ 28 - 10√3

There are five possibilities for five whole numbers: 6, 7, 8, 9, 10

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i. ∃x ∈ Z, x² = 2x, ii. ∀y ∈ school buses, y is not purple and iii. ∀x ∈ R, if x is even, then x² is even.

i. The equivalent predicate statement for the first statement is:

∃x ∈ Z, x² = 2x

The symbol "∃" means "there exists", the symbol "∈" means "is an element of", and the symbol "Z" represents the set of integers.

ii. The equivalent predicate statement for the second statement is:

∀x, (x is a school bus) → (x is not purple)

The symbol "∀" means "for all", and the symbol "→" means "implies".

iii. The equivalent predicate statement for the third statement is:

∀x ∈ R, (x is even) → (x² is even)

The symbol "∈" means "is an element of", and the symbol "R" represents the set of real numbers.

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Answer: about 0.79

Step-by-step explanation:

First divide 8 by 9 --> (8/9) = about 0.8889

then square that value --> (0.8889)^2 = about 0.79.

PEMDAS is your friend!

Answer:

see below

Step-by-step explanation:

11: write 3 equiv ratio of 1:3, so it' could be 3:9, 2:6, 4:12

12.  20:15 = 4:3, 12:9, 8:6

Answer:

1,3,5,15

Step-by-step explanation:

A factor cannot be greater then the number itself so we can scratch 30 and 45. 15 is divisible by itself and 1, as every other number. 2 is not a factor of 15 because 15 is not even. Also not 9. But it does have factors 5 and 3 because 5×3=15.

Hope that helps, let me know if you have any further questions!

Answer:

57 = 33+24 = 3a+3c

Step-by-step explanation:

Let a= adults, c = children

total costs = 11a+8c

57 = 33+24 = 3a+3c

Answer: We can use the variables x and y to represent the number of adult tickets and children's tickets, respectively. The cost of adult tickets is $11 each and the cost of children's tickets is $8 each. So, we can use the following equation to represent the total cost for the movie tickets:

C = 11x + 8y

Where C is the total cost of the tickets, x is the number of adult tickets and y is the number of children's tickets

One combination of tickets that would total $57 is:

C = 11x + 8y = $57

x + y = 7 (number of tickets)

One way to satisfy this equation is to have 5 adult tickets and 2 children's tickets

x = 5

y = 2

C = 115 + 82 = $57

So, 5 adult tickets and 2 children's tickets is one combination that would total $57.

Step-by-step explanation:

Answer: AAS → Makes the most sense

- They give two angles and a side for both triangles

Step-by-step explanation:

The questionnaire given to patients about their quality of life before and after the surgery included in the research design does add risks to the overall study design. Hence, the given statement is false.

Even though the questionnaire itself may not cause any additional physical risks, it can still have an impact on the overall study design. The questionnaire can add additional burden to the participants, who may already be dealing with physical and emotional stress from the surgery. Also, the questionnaire results may not be accurate if participants are not fully honest or unable to understand the questions being asked. Therefore, the inclusion of such a questionnaire in the research design should be carefully considered after evaluating its potential impact on the overall study.

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The number of sides of a regular polygon with an interior angle that measures 150° is equal to 12 sides.

In Euclidean geometry, a regular polygon simply refers to a form of polygon which has all of its sides and interior angles being equal.

In Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:

Sum of interior angles = 180 × (n - 2)

Where:

n represents the number of sides of a regular polygon.

Similarly, the number of sides of a regular polygon with a given interior angle can be calculated by using this mathematical expression:

Interior angles = 180 × (n - 2)/n

150° = 180(n - 2)/n

150n = 180n - 360

180n - 150n = 360

30n = 360

n = 360/30

n = 12 sides.

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The figures in the triangle represent the coefficients of the terms on the right side of a binomial equation.

Binomial Theorem: The expansion grows complex and time-consuming to calculate as the power rises. The Binomial Theorem can be used to quickly calculate a binomial statement that has been raised to a very high power. Find out everything there is to know about the binomial theorem, including its definition, characteristics, and uses.

An expression that has been raised to any finite power can be expanded using the binomial theorem. A useful expansion technique with applications in probability, probability theory, and algebra is the binomial theorem.

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Answer:

angle 1 = 118 deg

angle 2 = 62 deg

Step-by-step explanation:

To find angle one you must know that angles 1 and 118 deg are alternate angles. Therefore since these lines are parallel, angles 1 and 118 are equal.

To find angle 2 to you must know that angle 1 + angle 2 = 180.

angles on a straight line always equal 180 deg

therefore:

180

118 -

62 deg

hope this helps :)

Answer:

m<1 = 118°

m<2 = 62°

Step-by-step explanation:

The horizontal lines are parallel.

Angles 1 and 118° are alternate interior angles of parallel lines cut by a transversal, so they are congruent.

m<1 = m<2 = 118°

Angles 1 and 2 are a linear pair, so they are supplementary. That means that their measures add to 180°.

m<1 + m<2 = 180°

118° + m<2 = 180°

m<2 = 62°

After setting f (x) = 0, solve for to determine the intercept(s) of. Set y = f(0) and then find to determine the intercept of. Choose test points to establish the sign of each interval on the axis after using the intercept(s) to divide it into intervals. Determine the test points.

The Use of Zeros When Graphing Polynomials

You may graph a polynomial function using the steps below.

To assess how the graph will behave at its finish, use the leading-term test.

Choose the x− capture(s) of f(x) by putting f(x)=0 and then figuring up a solution for x .

Choose the y− a snare in f(x) by putting y=f(0) and discovering y.

Use the x− dividing intercept(s) x−

Divide the axis into intervals and then select test points to ascertain the sign of f(x) per interval.

the test points on a map.

To identify the general form of the graph, locate additional points as necessary.

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Answer:

in order from top row to bottom row

Step-by-step explanation:

Answer: The answer is 7

Step-by-step explanation:

Answer: x = 7

Step-by-step explanation:

Subtract 7 on each side to isolate X

7 + x = 14

-7         -7

x = 7

Answer:

Step-by-step explanation:

a) The probability that a wash-down motor will have to be replaced free of charge - 1,904  

b) A percentage of wash-down motors can be expected to operate at 2,28 %

c)  The average hours of operation before failure would be 13500 h

Normal Distribution

μ₀  = 14000    hours   and        σ  =  1050    hours

a) Probability of X  (replacement of motor free of charge)

Z = ( X - μ₀ ) /  σ

Z  =  ( 12000- 14000) / 1050

Z  =  - 2000/1050

Z = - 1,904    

From z Table we get

for  z = -1.904       P [ X ≤ 12000 ]  = 0.0262

P [ X ≤ 12000 ]  = 0.0262      or      2.62 %

b) What % of motors can be expected to operate more than 16100 hours

z = ( 16100 - 14000) / 1050

z = 2100/1050     ⇒   2

From the z table, we find with z = 2 total number of f motors operating up to 16100 hours

From the z table, we find 0,9772

Then the probability of motors operating for more than 16100 hours is:

P [ X > 16100]  =  1  -  0.9772    =  0,0228

Then

P [ X > 16100]  = 0,0228    or   2,28 %

c) The average hours of operation before failures if only 1% of motors would be replaced free of charge is:

1%  = 0,01    Probability then z score is  z = 0,4960

0,4960  =  ( 14000 - X ) / 1050

0,4960 * 1050 = ( 14000 - X )

520,8 - 14000 =  - X

X = 13479,2 hours  as is not common such offer company could set up a guarantee for  13500 h

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Answer:

Step-by-step explanation:

The slope of the given line in the graph is "undefined".

Slope, usually referred to as rise over run, is the "steepness" of the line.

By dividing the difference in y values between two points by the difference in x values, we may determine slope.

Thus, as the line is passing through the y axis and parallel to the x axis, the slope of the given line is undefined.

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Answer:4.5

Step-by-step explanation:

Answer: ASA

Step-by-step explanation: Hello! You can use ASA to prove that the triangles ABC and ABD are congruent.  This is because you are given two angles of each triangle.  You know that your answer should be ASA or AAA, which are the only two triangle congruence postulates that involve two or more congruent angles.  Lastly, you can use the reflexive property.  An example of reflexive property is 3 = 3, which means anything is congruent to itself.  You know that both triangles share line segment AB, meaning that they have one side and two angles that are congruent.  Since you know that the two angles and the included side are congruent, ASA proves that both triangles ABC and ABD are congruent.  I hope this helps you!

The domain of the function graphed in this problem is given as follows:

{x | x ≥  -4}.

The domain of a function is the set composed by all the input values that the function accepts.

On the graph, the domain of the function is given by the values of x.

From the graph of the function, the function has a closed interval at x = -4, and is defined for all the values for the right of that, that is, greater than -4, hence the notation for the domain is given as follows:

{x | x ≥  -4}.

Meaning that the correct option is given by the second option.

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Time in GMT is 5:14:20 P.M (GMT)

Eastern Daylight Saving Time is four hours behind GMT (Greenwich Mean Time).

The time on the Earth's meridian, or zero-degree line of longitude, is known as Greenwich Mean Time (GMT). This passes via the Old Royal Observatory in the London district of Greenwich on its way from the North Pole to the South Pole.

This is,

Eastern Standard Time is equal to Greenwich Mean Time plus four.

Therefore,

1:14:20 p.m. EDT (Eastern Daylight) will be equivalent to;

1:14:20 p.m + 4 hours (GMT)

5:14:20 P.M (GMT)

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On solving the equations x + y = 104 and 0.05x + 0.25y = 22, the number of nickels and quarters Lenny has is 20 and 84 respectively.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The value of 1 nickel is = $0.05

The value of 1 quarter is = $0.25

The total amount of coins is = $22.0

The total number of coins is = 104

Let the number of nickel be = x

Let the number of quarter be = y

The equation for total number of coins =

x + y = 104 ....(1)

The equation for total amount of coins =

0.05x + 0.25y = 22 ...(2)

Multiply equation (1) by 0.05 -

0.05(x + y) = 104 × 0.05

0.05x + 0.05y = 5.2 ... (3)

Subtracting equation (3) from (2) -

0.05x + 0.25y - (0.05x + 0.05y) = 22 - 5.2

0.05x + 0.25y - 0.05x - 0.05y = 22 - 5.2

0.20y = 16.8

y = 84

Substitute the value of y in equation (1) -

x + 84 = 104

x = 104 - 84

x = 20

Therefore, the value for x and y is obtained as x = 20 and y = 84.

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Answer:

We can start solving the problem by using algebra. Let x be the number of points scored by each girl, and y be the number of points scored by each boy. Then, based on the information given in the problem, we have the following equations:

x + y = 27 (the total number of points scored by the team)

3x - 2y = 15 (the difference between the number of points scored by the 3 girls and the 2 boys)

To solve for x and y, we can use the second equation to eliminate one of the variables. Multiplying both sides of the second equation by 2, we get:

6x - 4y = 30

Now we can substitute this into the first equation:

6x - 4y + y = 27

6x = 27 + 4y

x = (27 + 4y)/6

Now we can substitute this back into the second equation:

3((27 + 4y)/6) - 2y = 15

27 + 2y - 2y = 15

27 = 15

This is a contradiction, so the given information is insufficient to find the number of points scored by each girl and each boy.

Step-by-step explanation:

To evaluate the expression 1+(-2/3)-(-m) where m = 9/2, we need to substitute the value of m into the expression and simplify it.

What is a mathematical expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

1+(-2/3)-(-m)

1+(-2/3)-(-9/2)

Here, we have to simplify the inner expressions first,

-9/2 can be simplified to -4.5

1+(-2/3)-(-4.5)

Next, we add and subtract the terms:

1-2/3+4.5

Now, we simplify -2/3 by multiplying both numerator and denominator by -1:

1+4/3+4.5

Now, we add the fractions,

1+4/3+4.5

7/3+4.5

Finally, we get the value of the expression as

7/3+4.5 = 4.5 + 7/3 = 25/3.

So the final value of the expression 1+(-2/3)-(-m) where m=9/2 is 25/3.

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The Area of the circle, A is 530.66 inch.

An area of a circle is the amount of two-dimensional space within the boundaries of the circle. It is the region enclosed by a circle's circumference. The area of a circle can be found by using the formula A = πr2, where A denotes the area of the circle, r represents its radius, and π is equal to 3.1416. The radius of a circle is the distance from its center to its circumference. It can also be found by dividing the circumference by 2π.

Given,

Diameter, d = 26 inch

Radius, r = d/2 = 26/2 = 13 inch

π = 3.14 or 22/7

We apply all these above values in the formula, we get area of circle:

A = πr²

A = 3.14 x (13)²

A = 530.66 inch

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2:1 is the  new ratio of the number of Mimi’s Eminem cd’s to Rita’s.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

let Rita has X CDs.

Then Mimi has x-18 CDs.

x-18/x=5/8

8(x-18)=5x

Apply distributive property

8x-144=5x

Subtract 5x+144 on both sides

3x=144

Divide both sides by 3

x=48

Now Rita has 48-22= 26 CDs .

Mimi has 30+22= 52 CDs.

Required Ratio = 52:26 = 2:1

Hence, 2:1 is the  new ratio of the number of Mimi’s Eminem cd’s to Rita’s.

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Answer: 20/3 / 1/6 is a division problem that can be simplified as follows:

20/3 divided by 1/6 = (20/3) * (6/1) = (206) / (31) = 120/3 = 40

The value of the division is 40. However, without knowing the context, it is impossible to know what the meaning of this value is. In particular, without knowing the units of 20/3 and 1/6, it is not possible to interpret the division as miles per gallon or any other unit.

It is important to note that 20/3 and 1/6 should be represented as mixed numbers (6 2/3 and 1/6) or as decimal numbers (6.66 and 0.16666) in order to be able to proceed with the division.

Step-by-step explanation:

Answer:

  9.  reduction, 1/2

  10.  enlargement, 3/2

  11.  enlargement, 3

  12.  reduction, 1/3

Step-by-step explanation:

You want to know whether the dilations shown are reduction or enlargement.

Dilation

If the image (figure B) is larger, the dilation is an enlargement. (10, 11)

If the image (figure B) is smaller, the dilation is a reduction. (9, 12)

The scale factor is the ratio of a length on the image to the corresponding length on the original figure. It will also be the ratio of distances from the center of dilation (the origin) of corresponding points.

The ratio of line lengths B/A is 3/6, a reduction by a factor of 1/2.

The ratio of distances from the origin on the x-axis is 3/2, an enlargement by a factor of 3/2.

The ratio of distances from the origin on the x-axis is 6/2, an enlargement by a factor of 3.

The ratio of distances from the origin on the x-axis is 2/6, a reduction by a factor of 1/3.

The distance that exists between star A and B is given as 29.87 light years

We can solve this by creating a triangle where Point a Is star a, point b is star b and the point c is earth

the angle is given as 60 degrees

AC = 22 light years

BC = 34 light years

ab² = ac² + bc² - 2 *ac * bc* cos60

we would have to put in the values

ab² = 22² + 34² - 2 * 34 * 22 * cos 60

ab² = 484 + 1156 - 748

ab² = 892

square both sides

ab = 29.87 light years

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