George spent $109.65 for a radio, which was 43% of his savings. How much did he have in savings before
he purchased the radio?
Enter your answer in number form only. Do not attach a label.

The solution set for the given graph is a null set or empty set.

Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form.

Given is a graph of parallel lines, as we know in the system of linear equations, equations having parallel lines yields no solutions, therefore, for this also, there is no solution,

Therefore, the set will be null set or empty set.

Hence, the solution set for the given graph is a null set or empty set.

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The number of different sequences of tosses could there have been, if the number of tosses was even 1/2

You should understand that the tosses involves a sequence which is an array of numbers in a particular order

The question reads thus How many different sequences of tosses could there have been, if the number of tosses was even.

Number of tosses = 12

The tosses are 1,2,3,4,5,6,7,8,9,10,11,12 = 12 Times

The even numbers are

2,4,6,8,10,12 = 6 times

The Probability of the toss is 6/12

Therefore the number of tosses equals 1/2

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The analysis of the distance to the Grand Canyon, and the distance traveled on an amount of gas are as follows;

1 a. The distance from the middle school to the Grand Canyon = 80 miles

2 a. The graph showing the correlation between the distance traveled to the number of gallons used, created with MS Excel is attached

b. The table of values based on the data used to create the graph, presented in a tabular form using MS Word is attached

c. The equation is; d = 10·g

d. The advantages are;

The graphical presentation is a pictorial representation of the distance

The table enables further analysis

The equation can be used to predict the distance the Hybrid can travel on an amount of gas

A correlation is an indication or measure of the degree of relationship between variables.

1 a. The data for the Camper and the SUV that both use only gas, and the Hybrid car are as follows;

                                              [tex]{}[/tex]   Camper                    SUV    Hybrid Car

Average Miles per Gallon [tex]{}[/tex]       4                                8           10

Gallons of gas consumed [tex]{}[/tex]       20                             10           8

Distance traveled = Number of gallons used × Miles traveled per gallon

The distance between the middle school and the Grand Canyon, using the data for the Camper, is therefore;

d = 20 gallons × 4 miles/gallon = 80 miles

2. Amount of gas in gallons = g

Distance car drives in miles = d

The model used = The Hybrid car

Miles traveled per gallon = 10 miles/gallon

Therefore, d/g for the Hybrid car = 10 miles/gallon

d = 10·g

a. Please find attached the graph of the driven distance to the amount of gas used, created with MS Excel

b. The table based on the distance covered using different amount of gas can be created using the data used for creating the graph as follows;

Amount of gas; 0     1  [tex]{}[/tex]    2     3      4        5      6      7     8      9     10        11

Distance;           0     10   20   30    40     50    60   70    80   90   100      110

c. The equation that represents the distance traveled in miles, d, with the Hybrid when a specified amount of gasoline is used, g, is presented as follows;

d. The advantage of each representation are as follows;

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So on solving the provided question we cans ay that trigonometry y =sec^2(y); y = 1/[tex]\sqrt{2}[/tex]

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

y´=sec^2(y)

here, y = 90

y = sec^2(90)

y = 1/[tex]\sqrt{2}[/tex]

​

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The smiley face is solved to get a value of 72

The solution to the value of the smiley face is solved by forming some equations

Using the third row that have only squares

8 square - 6 square + 3 square = 60

2 square + 3 square = 60

5 square = 60

dividing through by 5

square = 60 / 5 = 12

hence a square is 12

Using the second row

12 square + 5 star = 234

substituting a square = 12

12 * 12 + 5 star = 234

144 + 5 star = 234

5 star = 234 - 144

5 star = 90

dividing through by 5

star = 90 / 5 = 18

hence a star is 18

using the first row

square + 3 triangle + star = 57

substituting square = 12 and star = 18

12 + 3 triangle + 18 = 57

3 triangle + 30 = 57

3 triangle = 57 - 30

3 triangle = 27

dividing through by 3

triangle = 27 / 3 = 9

hence triangle = 9

solving for the smiley face

substituting the values of the figures

18 (9 + 18 - 12) + 12 (18 + 9 + 9) = smiley face

solving the parenthesis

smiley face = 18 (15) + 12 (36)

smiley face = 18 * 15 + 12 * 36

smiley face = 702

hence the smiley face is 702

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Answer: The soccer field is about 8.6 blocks away from Leah's home.

Step-by-step explanation:

The soccer field is about 8.6 blocks away from Leah's home.

Leah walks 6 blocks north and 4 blocks east. To find the total distance she walked, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The distance is the square root of (6 blocks)^2 + (4 blocks)^2 = 36 + 16 = 52 then square root of 52 = 7.21

The distance of the soccer field from Leah’s home is 7.21 blocks, but it can be rounded to nearest tenth which is 8.6

The two ratios are equivalent because if we multiply both of the numbers by 3, we will get the other ratio.

Here we want to explain why the two ratios:

5:6 and 15:18

Are equivalent, where equivalent means that these two ratios mean the same thing.

Now, if we take any ratio

a:b

and we multiply both numbers by the same real number k (except for zero) we will get the equivalent ratio.

k*a: k*b

Now, let's look to our ratios:

5:6

If we multiply these 2 numbers by 3, we will get.

3*5: 3:6

15: 18

So yes, these are equivalent.

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So on solving provided question we can say that the probability 20% of these coins are pre-1910, 15% are between 1910 and 1950, and the remaining 75% are post-1950.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

Emma has a collation of 240 coins.

Of these coins, 20% are dated before 1910,  15% are dated between 1910 and 1950 and  the remainder are dated after 1950.

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Answer:

2nd option

Step-by-step explanation:

[4    -7] * [a    b] *  = [1    0]

[-1    2]    [c    d]       [0    1]

4 * a + (-7) * c = 1

4 * b + (-7) * d = 0

-1 * a + 2 * c = 0

-1 * b + 2 * d = 1

4a - 7c = 1  ==> equation 1

4b - 7d = 0  ==> equation 2

-a + 2c = 0  ==> equation 3

-b + 2d = 1  ==> equation 4

(-b + 2d = 1) * 4  ==> make -b into -4b

   -4b + 8d = 4

+   (4b - 7d = 0)

-4b+4b + 8d-7d = 4+0  ==> add equations 2 and 4 to cancel the variable b

8d-7d = 4 ==> -4b+4b=0 and adding anything by 0 will result in itself: 0+3=3

d = 4

-b + 2d = 1

-b + 2(4) = 1  ==> substitute 4 for d

-b + 8 = 1   ==> simplify

-b = -7  ==> subtract 8 on both sides

b = 7  ==> simplify

Since we got the values of b and d, the matrix now looks like this:

[4    -7] * [a    7] *  = [1    0]

[-1    2]    [c    4]       [0    1]

Now solve for a and c using equations 1 and 3:

4a - 7c = 1  ==> equation 1

-a + 2c = 0  ==> equation 3

(-a + 2c = 0) * 4  ==> make -a into -4a

   -4a + 8c = 0

+   (4a - 7c = 1)

-4a+4a + 8c-7c = 0+1  ==> add equations 1 and 3 to cancel the variable b

8c-7c = 1 ==> -4a+4a=0 and adding anything by 0 will result in itself: 0+3=3

c = 1

-a + 2c = 0

-a + 2(1) = 0  ==> substitute 1 for c

-a + 2 = 0   ==> simplify

-a = -2  ==> subtract 2 on both sides

a = 2  ==> simplify

Since we got the values of a and c, the matrix now looks like this:

[4    -7] * [2    7] *  = [1    0]

[-1    2]    [1    4]       [0    1]

Hence, the answer is the 2nd option.

Answer: 12 passengers.

Step-by-step explanation:

55 x 0.40 = 22

22 + 2 = 24

24 ÷ 3 = 8

8 + 9 = 17

17 - 12 = 5

5 + 5 = 10

There are 36 fluid ounces in 4.5 cups

Keisha reads a label on a measuring cup

The reading shows that 16 fluid ounces is the same as two cups

Therefore the number of fluid ounces in 4.5 cups can be calculated as follows

16/2

= 8

8 × 4.5

= 36

Hence there are 36 fluid ounces in 4.5 cups

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The value of [tex]m \angle R Q S[/tex] is 40.

The opposite angles of a parallelogram are equal, therefore:

[tex]m \angle R=m \angle T \\[/tex]

so

[tex]m \angle R=75[/tex]

Opposite sides of a parallelogram are parallel and equal so:

[tex]Q T & =R S \\[/tex]

[tex]4 x & =12 \\[/tex]

[tex]x & =\frac{12}{4} \\[/tex]

[tex]x & =3[/tex]

[tex]$$$\angle \mathrm{TSQ}$[/tex] and [tex]$\angle \mathrm{RQS}$[/tex] are alternate interior angles, therefore:

[tex]m \angle R Q S=m \angle T S Q \\[/tex]

[tex]80: \\[/tex]

[tex]m \angle R Q S=40[/tex]

The complete question is,
Consider parallelogram QRST below. Use the information given in the figure to find m ZR, x, and m ZROS.

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Answer:

Part A:

To find the length of the ramp in yards, we need to first determine the horizontal distance covered by the ramp. The slope of the ramp is 1/12, meaning that for every 12 inches of horizontal distance, the height of the ramp increases by 1 inch. Since the height of the ramp when it connects to the house is 9 inches, we can use this information to determine the horizontal distance covered by the ramp.

9 inches / (1/12) = 108 inches

To convert inches to yards, we divide by 36, so

108 inches / 36 inches/yard = 3 yards

Part B:

To determine the length of the ramp, I used the information provided about the slope of the ramp and the height of the ramp when it connects to the house. I used the slope of the ramp (1/12) to calculate the horizontal distance covered by the ramp. Then I converted the horizontal distance from inches to yards by dividing by 36. Finally, I obtained 3 yards as the length of the ramp.

Answer:

Part A = 3 yards

Part B = 9 x 12 = 108 inches = 9 feet = 3 yards

Step-by-step explanation:

Part A

1 inch height - 12 inches length

9 inches height - 9 x 12 = 108 inches length

36 inches = 1 yard

108 inches = 108/36 = 3 yards

Part B

Shown above

The ramp is 9 inches tall, so the length of the ramp is 9 x 12 = 108 inches.

1 feet = 12 inches

108 inches = 108/12 feet = 9 feet

1 yard = 3 feet

9 feet = 3 yards.

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Answer:

Step-by-step explanation:

The terminal point of the vector a=⟨4,3⟩ based at P=(5,2) is the point (9,5). This can be calculated by adding the components of the vector to the corresponding components of the base point:

Terminal point = (x,y) = (Px + ax, Py + ay)

      = (5 + 4, 2 + 3)

      = (9,5)

Answer:

Step-by-step explanation:
✔️For determining terminal point of vector a=(4,3)  whose base is at the point P=(5,2).

✔️ Add to point P and that

✔️Point that the vector is pointing at to find the terminal point....

➖So we can say That

✔️Since the tail of the vector a=(4,1) a=(4,1) is a point P(2,3) then the tip of the vector, the terminal point woll be :-

(5,2)+(4,3)=(9,6)

your welcome !

Answer: There is no way 200 is the answer. it should be 103.055

Step-by-step explanation: See, 36 miles can stop in 53 feet. We want to know how many feet are there when 70 miles fast. We can write  that as 36/53 = 70/x. 36 corresponds to 70 and 53 corresponds to x. Do it and you get 103.055

The rate of change of function A is not same with the rate of change of function B.

The slope of a linear function is another name for its rate of change.

The slope and the function's starting value are both included in the slope-intercept form equation of a line. When the input of a linear function is 0, the output is the initial value, or y-intercept.

Function b is in slope intercept form as Y= 1/2X + 2 and here the slope is 1/2

calculation of slope pf function A

The slope, m of the linear function is calculated using the points (2 , 3) and (-1 , -3)

m = (y₀ - y₁) / (x₀ - x₁)

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

m = (6) / (3)

m = 2

The slopes are not the same

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Answer:  The merchant made a profit of Rs 35,000 by selling the potatoes.

Step-by-step explanation:

To find the profit or loss of the merchant, we first need to calculate the revenue he earned from selling the potatoes.

A quintal is a unit of weight equivalent to 100 kg, therefore, the merchant bought 100 kg of potatoes.

If the merchant sold all potatoes at Rs 390 per kg, the revenue would be 100 * 390 = Rs 39,000.

To find the profit or loss, we need to compare the revenue to the cost of the potatoes.

If the merchant bought a quintal of potatoes for Rs 4000, the cost is Rs 4000.

To calculate the profit or loss, we can use the following formula:

Profit or loss = Revenue - Cost

Using this formula, we can calculate the profit or loss as:

Profit or loss = 39,000 - 4,000 = Rs 35,000

So, the merchant made a profit of Rs 35,000 by selling the potatoes.

It is important to note that when calculating the profit or loss, we need to make sure that the units of measure for cost and revenue are the same.

Using the given conditions in the question,the probability that the first gift chosen is gift #3 and the second is gift #9 is (1/10) * (1/9) = 1/90.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain. Events with a probability of 0.5 or greater are considered likely, while those with a probability less than 0.5 are considered unlikely. The probability of all possible events in a given situation must add up to 1. In mathematical terms, probability is the ratio of the number of favorable outcomes to the total number of possible outcomes.

The chance of something happening can be measured by probability. It's a number between 0 and 1, where 0 means it's impossible for the event to happen and 1 means it's certain to happen. The closer the number is to 1, the more likely the event is to happen.

The probability that the first gift chosen is gift #3 and the second is gift #9 is (1/10) * (1/9) = 1/90. This is because the probability of choosing any specific gift on the first turn is 1/10, and the probability of choosing any specific gift on the second turn, given that there are now 9 gifts left in the pile, is 1/9. Multiplying these probabilities together gives the overall probability of the first gift being #3 and the second gift being #9.

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Answer:

x = 9

Step-by-step explanation:

[tex] - 1 + 14x = 12x + 17 \\ 2x = 18 \\ x = 9[/tex]

The average rate of change of g(x) =5x^3+4/x^2 on the interval [-1,2] is -2

A function can be defined as a law, rule or expression explaining the relationship between two variables.

These variables are called;

From the information given, we have the function;

g(x) =5x^3+4/x^2

For the interval, {1, -2}

Let's substitute the value of x as 1

g(1) = 5(1)³ + 4/(1)²

find the values

g(1) = 5 + 4/1

g(1) = 9/1 = 9

For x = -2

g(-2) = 5(-2)³ + 4/(-2)²

find the values and substitute

g(-2) =5(-8) + 4/ -8

g(-2) = -40 + 4/-8

add the numerators

g(-2) = -36/8

divide the values

g(-2) = -9/2

The average change = 9 ÷ -9/2 = 9 × 2/-9 = -2

Hence, the value is -2

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The answer to this question is 0.583

Answer:

improper fraction

Step-by-step explanation:

A mixed number has a whole number and a fraction.

An improper fraction is a fraction with a numerator bigger than the denominator.

Since 17 > 4 and there is no whole number,  this is an improper fraction.

It can be changed to a mixed number by dividing the numerator by the denominator

17 ÷4 = 4 and there is a remainder of 1.  The remainder goes over the denominator

4  1/4

Answer: It's an improper fraction

Step-by-step explanation: It's an improper fraction because an improper fraction is a fraction where the numerator is greater than the denominator, whereas a proper fraction is the opposite. A mixed number is when there is a whole number and then a regular (proper) fraction beside it. Here's an example:

[tex]5\frac{1}{7}[/tex]

Since 17 is greater than 4, 17/4 is an improper fraction. Now, if you wanted to find 17/4 as a fraction, you would divide the 17 by the 4, so the  whole number (4 in this case) would be the whole number, and the faction would be 1/4

So, [tex]\frac{17}{4}[/tex]= [tex]4\frac{1}{4}[/tex]

To check, you can multiply the 4 by the 4, which is 16, and add the numerator (1) to it, which would be 17/4. I hope this helps.

The plane weights 1988 pounds when it has 16 gallons of fuel on board. It is 2175 pounds heavier when carrying 50 gallons of fuel. w= 2500 .

The following correlation is true if the relationship between weight and fuel consumption is linear:

[tex]$\frac{2175 \text { pounds }-1988 \text { pounds }}{50 \text { gallons-16gallons }}=\frac{W-1988 \text { pounds }}{64 \text { gallons-16galons }}$[/tex]

We resolve this equation:

w = 2500.

Assume that the weight of an airplane, measured in pounds, is a linear function of the fuel tank's capacity, measured in gallons. The aircraft weighs 2030 pounds while carrying 20 gallons of fuel. It weighs 2225 pounds while carrying 50 gallons of fuel. It weighs 2338 pounds while carrying 52 gallons of fuel. Weight (in pounds) of an airplane fuel consumption (in gallons) Per gallon, Jet-A Prist is 6.75 pounds. A 100LL gallon weighs 6.0 pounds. 6.0 pounds per gallon for extras.

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Probability is a metric used to express the possibility or chance that a particular event will occur. Two eighths of a vowel will be drawn at random. Option A is correct.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The formula for calculating probability is expressed as:

Probability = expected/total outcome

If the given a set of cards laying face down that spell P, E, R, C, E, N, T, S, then the total outcome is:

n(S) =8

If a vowel is selected randomly, hence the expected outcome is;

E = {E, E}

n(E) = 2

P(vowel) = 2/8

Hence the probability of randomly drawing a vowel is two eighths

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Answer: A: 2/8 (Two Eighths)

Step-by-step explanation:

To maximize the volume we need to cut squares with a side length of 20cm.

Suppose that the length of the sides of the squares that we cut is X, that will be the height of the box, then its volume will be:

V = (60 - X)*(60 - X)*X

Now we just need to maximize that cubic equation.

V = X*( X^2 - 120*X + 3600)

V = X^3 - 120X^2 + 3600X

To maximize this we need to differentiate it and find the value of X that makes it equal to zero, we will get:

V' = 3*X^2 - 2*120*X + 3600

V' = 3*X^2 - 240*X + 3600

Now we make this equal to zero:

3*X^2 - 240*X + 3600 = 0

The solutions are given by the quadratic formula:

[tex]X = \frac{240 \pm \sqrt{240^2 - 4*3600*3} }{2*3} \\\\\\X = \frac{240 \pm 120 }{6}[/tex]

We will take the smaller solution:

X = (240 - 120)/6  = 20

Because the other solution makes the volume equal to zero.

This means that we need to cut squares with a side length of 20 cm.

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Answer: yes, it is

Step-by-step explanation:

Answer:4

Step-by-step explanation:

Answer:

108

Step-by-step explanation:

average of first two multiples = 28

sum of first two multiples = 28 * 2 = 56

average of last two multiples = 44

sum of last two multiples = 44 * 2 = 88

average of all four multiples = ( 56 + 88 ) / 4 = 36

value of greater multiple = (88 + 56) - 36 = 108

Answer:

Step-by-step explanation:

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Answer:

24 gift bags

Step-by-step explanation:

Well first the question says to find the GCF and you find that by finding prime factors in each number. Then you would want to subtract 96-72 and get the answer of 24 so you would be able to make 24 gift bags. Hope this helps!!

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