Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Royston is driving to a popular amusement park with his family. Royston’s car had 1515 gallons of gas at the start of the trip. During the trip, he stopped at a gas station and refueled the car with 535 gallons. If the car consumed 1745 gallons of gas during the trip, there are still gallons of gas remaining in the tank. 100 points

The height of the rectangular pyramid tent's center pole = 5.5 feet.

Volume of rectangular pyramid = 1/3(length)(width)(height).

Given the following:

Substitute

88 = 1/3(8)(6)(height)

88 = 16(height)

88/16 = height

5.5 = height

Therefore, the height of the rectangular pyramid tent's center pole = 5.5 feet.

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The value of x is 20°

According to the question we have been given two parallel lines which is cut by a transversal line. There are total 8 angles and given is the measure of

∠4 = 5x + 35° and ∠7 = 45°.

We need to find the value of x.

Note that when two parallel lines are cut by a transversal then

i) corresponding angles are equal that is

                ∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8

ii) alternate interior angles are equal that is

                 ∠3 = ∠6, and ∠4 = ∠5

iii) alternate exterior angles are equal that is

                ∠1 = ∠8, and ∠2 = ∠7

iv) Consecutive interior angle sum is 180°

          ∠4 + ∠6 = 180°, and ∠3 + ∠5 = 180°.

Now using these rules we will solve this problem

Because of corresponding angles ,  ∠3 = ∠7 = 45°

Also ∠3 and ∠8 make a linear pair and sum of linear pair is 180°.

Therefore ,  ∠3 + ∠8 = 180°

                   45° + 5x + 35° = 180°

                     5x = 180° - 80°

                      x = 20°

Hence the value of x is 20°

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Answer:

x = -2.5

Step-by-step explanation:

The probability that a single card drawn from a standard deck of cards is either an 8 or a heart is 4/13.

Probability of an event E denoted by P(E) is defined as (number of favorable outcomes )/( total number of outcomes).

For example : the probability of getting Head in  single toss of an unbiased coin.  P(H)=1/2.

According to the given question

Total number of cards in a standard deck of cards is 52.

There are 4 suit in a deck each having 13 card each.

number of 8 card in a deck = 4

Number of hearts in a deck = 13-1=12      (-1 because 8 of heart is counted before.)

number of favorable cases of getting  either an 8 or a heart is 4+12=16.

The probability of getting either an 8 or a heart is [tex]\frac{16}{52} =\frac{4}{13}[/tex].

Therefore , the probability that a single card drawn from a standard deck of cards is either an 8 or a heart is 4/13.

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Answer: Absolute value equations are equations where the variable is within an absolute value operator, like |x-5|=9. The challenge is that the absolute value of a number depends on the number's sign: if it's positive, it's equal to the number: |9|=9. If the number is negative, then the absolute value is its opposite: |-9|=9.

Step-by-step explanation:

step by step explanation:

-4c+12d

1. Distribute:

11c+3(-5c+4d)

11c-15c+12d

2. Combine like terms:

11c-15c+12d

-4c+12d

The proof for the decimal expansion d₁d₂d₃d₄.... is evaluated.

A number's decimal expansion is its base-10 representation (i.e., in the decimal system).

Now, as per the given question;

We focus on non negative decimal expansions as well as nonnegative real numbers. Every nonnegative decimal expansion, in our opinion, is short form for the limit of a constrained increasing sequential manner of real numbers.

Assume we're given a decimal expansion K. d₁d₂d₃d₄.... where K is a non-negative integer and each value of dj belongs to {0,1,2,3,4,5,6,7,8,9}.

Then Sn is defined as the increasing sequential of real numbers and Sn is also restrained by (sn < k + 1) .

Using Theorem; converges to a real number, which we usually write as K. d₁d₂d₃d₄....

Like. 3.33333 can be written as;

[tex]\lim _{n \rightarrow \infty}\left(3+\frac{3}{10}+\frac{3}{10^2}+\cdots+\frac{3}{10^n}\right)[/tex]

We use the following geometric series fact to calculate this limit:

[tex]\lim _{n \rightarrow \infty} a\left(1+r+r^2+\cdots+r^n\right)=\frac{a}{1-r} \quad \text { for } \quad|r| < 1 .[/tex]

Where a =3 and r = 1/10.

Similarly, for 0.9999.....it can also be written as

[tex]\lim _{n \rightarrow \infty}\left(\frac{9}{10}+\frac{9}{10^2}+\cdots+\frac{9}{10^n}\right)=\frac{\frac{9}{10}}{1-\frac{1}{10}}=1 .[/tex]

Therefore, 0.9999... and 1.0000... are different decimal expansions for the same number.

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The correct question is-

For a decimal expansion K. d₁d₂d₃d₄....let (sn) be defined. Prove (sn < k + 1) for all n ∈ N. Hint:' [tex]\frac{9}{10}+\frac{9}{10^2}+\cdots+\frac{9}{10^n}=1-\frac{1}{10^n}[/tex]

We get the perimeter of the circle as 87.92 m and area of the circle as 615.44 m².

We are given the radius of the circle as:

Radius = r = 14 m

We are also given the value of π as:

π = 3.14

We need to find the perimeter and area of the circle.

Perimeter of the circle is given by:

Perimeter = 2 π r

Substituting the values in the formula, we get that:

P = 2 × (3.14) × (14) m

P = 87.92 m.

Area of the circle is given by:

Area = π r²

Substituting the values in the formula, we get that:

Area = (3.14) × (14)²

A = 615.44 m²

Therefore, we get the perimeter of the circle as 87.92 m and area of the circle as 615.44 m².

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Answer: The Answer would be -49/8d -1/10

Step-by-step explanation: I got it right on the test

have a good day

The answer for the given expression is -49d/8 - 1/10. Thus, the correct option is option A.

The expression can be solved by simple arithmetic operation.

(-3 1d/4 + 3/5) - (2 7d/8 + 7/10)

In the next step simplify the terms and open brackets.

-13d/4 + 3/5 -23d/8 - 7/10

Taking the like terms together.

-13d/4 - 23d/8 + 3/5 - 7/10

Solving the terms by taking L.C.M.

(-104d-92d/32) + (30-35/50)

-196d/32 - 5/50

Simplifying the terms.

-49d/8 - 1/10.

Thus, the value of the expression is -49d/8 - 1/10.

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where is the problem, how can I help you?

The coordinates of point Z is (-5/7, 16/7)

The formula for calculating a coordinate points using the points (-5, -2) and point P is located at (1, 4) in the ratio 2:5 is expressed as:

Z (x, y) = {(ax₁+bx₂)/a+b, (ay₁+by₂)/a+b}

Substitute the coordinates and ratios to have;

Z (x, y) = {(2(-5)+5(1))/2+5, (2(-2)+5(4))/2+5}

Z(x, y) = {-10+5/7, -4+20/7}

Z(x, y) = (-5/7, 16/7)

Hence the coordinates of point Z is (-5/7, 16/7)

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Answer:

0,5(3x+12+8x)

0,5(11x+12)

5,5x+6

Answer:

5.5x + 6

Step-by-step explanation:

0.5{3x + 4(3 + 2x)}

Apply the distributive property, multiply 4 by 3 and 4 by 2x.

0.5(3x + 12 + 8x)

Add 3x and 8x

0.5(11x + 12)

Apply the distribdistributive proproperty again and multiply 0.5 by 11x and 0.5 by 12.

The product would be 5.5x + 6.

Yes

We can tell if a triangle can exist based on the relationship between the side lengths.

Side Length Relationships

For a triangle to really exist, the sum of the smaller legs must be greater than the length of the longest leg. This can be expressed with the inequality a + b > c, where a and b are the shorter legs.

Now, we can plug the values we are given into this inequality.

Since the inequality is true, this triangle does exist.

Other Examples

One of the most important things to remember is that the sum of the shorter legs must be greater than, not equal to, the longest leg. So take the sides 4, 6, and 10.

This statement is not true. 10 is not greater than 10; they are equal. Thus, these sides cannot make a triangle.

Additionally, if the 3 numbers are Pythagorean triples, then it will be a right triangle. For example, the sides 5, 12, and 13 will create a right triangle.

The solution to the division of the polynomial equation is [tex]=-3x^2+17x -74 +\dfrac{289}{x+4}[/tex]

Polynomial long division is an extended form of the well-known arithmetic method of long division used in algebra to divide one polynomial with another polynomial of the same or lower degree. Addressing a difficult division issue and breaking it into manageable pieces makes it feasible to solve by using this method.

From the given information, we Divide:

[tex]=\dfrac{(-3x^3+5x^2-6x-7)}{(x+4)}[/tex]

[tex]=-3x^2+\dfrac{17x^2-6x-7}{x+4}[/tex]

Divide: [tex]\dfrac{17x^2-6x-7}{x+4}[/tex]

[tex]=-3x^2+17x + \dfrac{-74x-7}{x+4}[/tex]

Divide: [tex]=\dfrac{-74x-7}{x+4}[/tex]

[tex]=-3x^2+17x -74 +\dfrac{289}{x+4}[/tex]

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Answer:

Step-by-step explanation:

gnhbn

Answer:

20.36 is the answer

2.12x3=6.36

3.50x4=14

14+6.36=20.36

Answer:

20.36

Step-by-step explanation:

1)3*2.12=6.36

2)4*3.50=14

3)6.36+14=20.36

The slope is 4 and point on the line is origin (0,0).

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

Given:

The equation of the line is

y+4=4(x-2)

We have to find the slope and point on the line.

y+4=4(x-2)

y+4=4x-8

Substract 4 from both sides we get,

y=4x-12

Since the equation now is in y = mx + b form, we can identify the slope m=4 and the y-intercept b=-12 and point on the line origin (0,0).

Therefore, the slope is 4 and point on the line is origin (0,0).

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Answer:

3x - 1 = 6x - 7

x = 2

Explanation and Check part below

Hope this helps :)

Step-by-step explanation:

1. To solve it, first get the variable on same side.

3x - 1 = 6x - 7

- 3x - 3x

- 1 = 3x - 7

2. Isolate the variable by doing the inverse operation which is in this case addition (adding 7).

- 1 = 3x - 7

+ 7 + 7

6 = 3x

3. Isolate variable by doing the inverse operation which is in this case division (dividing by 3).

6 = 3x

3 3

2 = x

OR

x = 2

Check:

1. Substitute x with 2 and solve.

3(2) - 1 = 6(2) - 7

6 - 1 = 12 - 7

5 = 5

True statement.

Answer: C. 5/7

CALCULATOR

Answer:

As a biological stain, iodine is useful for studying plant cells because it stains starch blue-black and in animal tissue, it can help in the demonstration of nuclei and cell membranes

Answer: Iodine is also a useful stain. When studying plant cells, iodine is used. Because it is a starch indicator, it reacts with starch and turns blue-black. Iodine can also be used as a stain on animal cells, making the cell membrane and nucleus appear more visible

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

biweekly salary =

365/14=

23

then total salary

of her is =$1230.90

*23

=

Step-by-step explanation:

Applying the alternate exterior angles theorem, the value of x = 10.

According to the alternate exterior angles theorem, the following alternate interior angles are congruent to each other:

m<JPM = m<NQK

Given the following:

m<JPM = 125°

m<NQK = (13x - 5)°

Substitute

125 = 13x - 5

125 + 5 = 13x

130 = 13x

Divide both sides by 13

130/13 = 13x/13

10 = x

x = 10

Therefore, applying the alternate exterior angles theorem, the value of x = 10.

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Answer:

1.5 or 3/2

Step-by-step explanation:

The scale factor is the factor by which the side lengths of the original shape are multiplied by. In this case, the original shape had side lengths 17 and was multiplied by [tex]x[/tex] to get the scaled shape.

Now we get the equation [tex]17\cdot x=51/2[/tex]. Solving, we get x=1.5

The proof of the expression 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1 is evaluated for pqr = 1.

For the given expression;

pqr = 1. Then pq = 1/r; qr = 1/p; pr = 1/q.

OR, pq = r⁻¹ ; qr = p⁻¹ ; pr = q⁻¹ .

The given expression is;

1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1

Consider LHS part;

= 1/(1+p+pr) + 1/(1+q+pq) + 1/(1+r+qr)

Multiply and divide q in the first part;

=  q/(q+qp+qpr) + 1/(1+q+pq) + 1/(1+r+qr)

Put prq = 1 (given)

=  q/(q+qp+1) + 1/(1+q+pq) + 1/(1+r+qr)

Add 1st and 2nd part;

= (q+1)/(q+qp+1) + 1/(1+r+qr)

Multiply and divide r in the first part;

=  (q+1)r/(rq+rqp+r) + 1/(1+r+qr)

Put prq = 1 (given)

=  (qr+r)/(rq+1+r) + 1/(1+r+qr)

Add both

=  (qr+r+1)/(rq+1+r)

Both will be cancelled;

= 1 = RHS

Therefore, proof for 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1 is evaluated.

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The complete question is-

If pqr = 1, then prove that 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1

Answer:

pqr = 1

Step-by-step explanation:

Answer:

111/22 or 5 and 1/22

Step-by-step explanation:

9 and 7/22 equals 205/22

4 and 3/11 equals 47/11

multiply 47/11 times 2/2 to get common denominator

47/11 times 2/2 is 94/22

205/22 minus 94/22 is 111/22 which is also 5 and 1/22

Answer:

Step-by-step explanation:

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The number of homeowners in the neighborhood could be expected to have cable television is 128.

Given that, a survey showed that 8 out of 20 homeowners in a neighborhood had cable television.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Now, 8/20 × 320

= 8 × 16

= 128

Hence, the number of homeowners in the neighborhood could be expected to have cable television is 128.

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The probability of at least one person being vaccinated out of four people chosen at random is 0.30, or 30%, rounded to the nearest hundredths.

To find the probability that at least one of them has been vaccinated:

We use P(1) for only one person; the same reasoning should apply to other subscripts.

Adding all these probabilities given 0.3042802.

As a result, the probability of at least one person being vaccinated out of four people chosen at random is 0.30, or 30%, rounded to the nearest hundredths.

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Extreme values have little impact on the median and quantiles because they all come inside the middle half of the data.

Calculation:

Let’s assume the 24 students in the room range in age from 185, 185, 186, 186,.... 195, 195, 196, 196 months.

The total of x2 is 871252.

The sum of x is 4572.

The mean is 190.5 (4572/24).

The median, which lies between positions 12 and 13, is 190.5.

Standard deviation is (871252/24 -190.52)^0.5 = 3.45

Halfway between the( 18th and 19th)- (6th and 7th)interquartile range

= 6 (193.5 - 187.5).

Include his age of 716 months in the calculations as the teacher now.

Total x2 = 1383908

Total x = 5288

Mean (5288/25) = 211.52

Median (13th) = 191

Standard Deviation is (1383908/25 - 211.522)^0.5 = 103.03

Interquartile range (7th minus 19th) is 194 - 188 = 6

Therefore the mean has changed by 21.02 after the addition of a piece of data that is vastly different from the rest, yet the median has changed by only 0.5.

The interquartile range has remained constant, whereas the standard deviation has increased by over 100 and by a factor of approximately 30.

The result of adding together and dividing the total number of numbers or variables is the arithmetic mean, which is also known as the average or average value.

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Answer:

260 m2

Step-by-step explanation: