EXERCISE
Based on what you've read, decide which of the four basic operations you need to use. Then, solve the problems.

On a trip to Florida, Santina drove 203 miles and Carole drove 189 miles. How many more miles did Santina drive than Carole?
A restaurant uses 80 pounds of potatoes per week. The restaurant owner buys the potatoes in 10-pound bags from a local farmer. How many bags will the owner need to buy this week?
Six-packs of cola were on sale at a grocery store. John bought the limit, which was 8 six-packs. How many individual cans of cola is this?
Lori is reading The Grapes of Wrath for her American literature class. She read 85 pages last weekend, 135 pages during the week, and 98 pages this weekend. What is the total number of pages she has read so far?
A football team scored 34 points in their first game, 21 points in their second game, 9 points in their third game, and 28 points in their fourth game. What is the team’s average score for the season so far?
Reuben chews four pieces of chewing gum a day. The gum is sold in packages containing seven pieces. How many packages of gum will he need to buy this week?
Apply the rules of order of operations to solve the following problems.
52 – 6 × 7 = ?
108 ÷ 9 × 5 = ?
(54 + 42) ÷ 12 =?
183 – [(12 + 7) × 4] = ?
Chan wants to buy a used car that costs $8,500. He took out a loan for the cost of the car, and his payments are $209 per month for four years. At the end of four years, how much more than the car’s original price will he have paid? (Remember, there are twelve months in one year.)
Linda commutes a total of 54 miles to and from work every day. She needs a new car, and good gas mileage is important to her. She’s considering two models. The first model averages 30 miles per gallon, and the second averages 27 miles per gallon. How many gallons of gas will she save in a five-day work week if she buys the first car instead of the second car?
A waitress earned the following tips during one hour: $4.50, $3.00, $5.00, and $3.75. She gave each of the two busboys working with her $2.50. In addition to tips, the restaurant pays her $4.25 per hour. How much did she earn during that one hour of work?
Juan went out to lunch with five friends. They decided to divide the bill evenly among them. Juan estimated that his lunch cost $5.25. The entire bill came to $37.20. Would Juan’s lunch have cost more or less if he paid for it separately? How much more or less?

Step-by-step explanation:

she has x money at the beginning.

(3/4)x = dictionary

the remainder is (1/4)x.

1/2 of that (1/4 × 1/2 = 1/8) is the calculator.

that means she has (1/4)x - (1/8)x = (1/8)x left.

the dictionary is $30 more than the calculator.

so,

(3/4)x = (1/8)x + 30

(6/8)x = (1/8)x + 30

(5/8)x = 30

5x = 240

x = 240/5 = $48

so, the dictionary cost

(3/4)x = (3/4)×48 = 3×12 = $36

The length that is οver οr cοmparable tο 40 albeit less than 45 is denοted by the expressiοn "40 ≤ y < 45". Similar tο the previοus example, "45 ≤ y < 50" indicates that nοw the length is greater than οr equal tο 45 albeit less than 50, and sο οn.

When describing an οrganism's size οr the distance between twο pοints, the wοrd "length" is οften emplοyed. Fοr instance, the table belοw reveals actual length οf a ruler.

The data must be divided intο intervals, and the frequency οf each interval must be cοunted in οrder tο build a frequency table again fοr prοvided data.

We οbtain the fοllοwing results using a 5-interval size:

40 ≤ y < 45: 1 value (42)

45 ≤ y < 50: 4 values (45, 47, 48, 50)

50 ≤ y < 55: 2 values (50, 55)

55 ≤ y < 60: 3 values (57, 59, 60)

Sο, the fοllοwing is the frequency chart fοr the prοvided data:

Length (cm)                    Frequency

40 ≤ y < 45                         1

45 ≤ y < 50                         4

50 ≤ y < 55                         2

55 ≤ y < 60                         3

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Answer:

To solve the equation 3x + 5y = 500 for x, we need to isolate x on one side of the equation. First, we can subtract 5y from both sides to get 3x = 500 - 5y. Then, we can divide both sides by 3 to get x = (500 - 5y) / 3.

It might be helpful to rewrite the equation in terms of one variable if we want to solve for one unknown quantity in terms of another. In this case, rewriting the equation in terms of x allows us to see how many child tickets the school needs to sell to raise exactly $500, given any number of adult tickets sold. This can be useful in planning and budgeting for the carnival.

Step-by-step explanation:

If the boxes are all stacked on top of each other, what is their combined height is 11/8

Height of large box = 7/8m

Height of medium box = 2/6m shorter than large box

Height of small box = 1/4m shorter than the medium box

Calculating the height of the medium and small boxes.

Medium box height x large box height

= 2/6 × 7/8

= 7/24

Since, the small box is 1/4 of a meter shorter than the medium box, therefore its height -

= 7/24 - 1/4

= 5/24

Calculating the height of three boxes -

7/8 + 7/24 + 5/24

= 21/24 + 7/24 + 5/24

= 33/24

= 11/8

Correct Question:

Lupe measured the height of three rectangular prisms she was using to pack up some clothing. The large box was 7/8 of a meter tall. The medium box was 2/6 shorter than the large box. The small box was 1/4 of a meter shorter than the medium box. If the boxes are all stacked on top of each other, what is their combined height?

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P(female or grade 11) = 31/34

Given that a classroom has 23 grade twelves (13 females and 10 males) and 11 grade elevens (7 females and 4 males). The teacher randomly chooses a student at random, what is the probability that it is a female or a grade eleven?The sample space is the total number of students which is given by23 + 11 = 34.There are 13 females in the grade 12 and 7 females in the grade 11. So the total number of female students is 13 + 7 = 20.There are 11 grade 11 students. So the total number of grade 11 students is 11.The total number of students that are female or in grade 11 is obtained by adding the two:20 + 11 = 31.So the probability of choosing a female or grade 11 student is:P(female or grade 11) = 31/34

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Answer:

x = 17

Step-by-step explanation:

We Know

(6x + 3) + (7x - 44) = 180°

Let's solve

6x + 3 + 7x - 44 = 180

13x - 41 = 180

13x = 221

x = 17°

So, x = 17°

Therefore , the solution of the given problem of expressions comes out to be Sebastian strolled his dog for 4/5 of the allotted time today.

Calculations like arbitrary division, joining, multiplication variable , and removal are required. If they were merged, they would produce the following: A mathematical formula, some data, and an equation. A declaration of veracity is made up of values, elements, formulae, and mathematical operations like additions, subtractions, errors, and segments. It is possible to assess and analyse words and sentences.

Here,

You can calculate how much of the allotted time Sebastian spent walking his dog today by dividing the time he spent walking him (20 minutes) by the time he was meant to walk him (25 minutes).

Therefore, the division formula that represents this portion is:

=> 20 ÷ 25

The short form of this phrase is:

=>  4/5

As a result, Sebastian strolled his dog for 4/5 of the allotted time today.

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A greater distance if it hits any other part of the bat.

When a ball hits the sweet spot of a bat, it will travel a greater distance than if it hits any other part of the bat. This is because the sweet spot is part of the bat where the energy transfer from the bat to the ball is most efficient, resulting in a more powerful hit and greater distance travelled by the ball.

This is because the sweet spot is part of the bat where the energy transfer from the bat to the ball is most efficient, resulting in a more powerful hit and greater distance travelled by the ball.

If the ball hits any other part of the bat, the energy transfer is less efficient, resulting in a less powerful hit and a shorter distance travelled by the ball.

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After solving the given numbers with (PEMDAS) 11 - 11 x 11 + 11 = we get the answer of -88.

To solve 11-11x11+11, we need to use the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is:

Parentheses

Exponents

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

Using this order of operations, we can simplify the expression as follows:

11 - 11 x 11 + 11

= 11 - 121 + 11 (since multiplication should be done before addition and subtraction)

= -99 + 11

= -88

Therefore, the value of 11-11x11+11 is -88.

In general, when simplifying expressions, it is important to follow the order of operations to ensure that you get the correct answer. Additionally, it is always a good idea to check your work by plugging the answer back into the original expression and making sure that it is correct.

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Answer:

Vol = 120 cm^3

Step-by-step explanation:

The volume of a prism is:

Vol = BaseArea×height

Here, the base is the triangle.

Area_triangle

= 1/2bh

= 1/2•6•4

= 12 cm^2

The height is 10cm (and we don't even need the 5cm measurement given)

Volume

= BaseArea × height

= 12 × 10

= 120 cm^3

Answer:

95ft²

Step-by-step explanation:

2πr = 11π

πr = 11π/2

r = 11/2 = 5.5ft

area = πr²

area = π(5.5)² = 95.0331... ≈ 95ft²

The expanded form that can be used to factor the function is 12x² - 18x + 10x - 15.

option C,

To factor 12x² - 8x - 15 by grouping, we need to split the middle term -8x into two terms whose sum is -8x and whose product is -180 (the product of 12 and -15).

We can do this by splitting -8x into -18x and +10x:

12x² - 18x + 10x - 15

Now, we can group the first two terms together and the last two terms together, and factor out the greatest common factor from each group:

6x(2x - 3) + 5(2x - 3)

Notice that we have a common factor of (2x - 3) in both groups, so we can factor it out:

(2x - 3)(6x + 5)

Therefore, the factored form of 12x² - 8x - 15 by grouping is (2x - 3)(6x + 5).

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According the given question the side οf the WY is 25.

Angle-Side-Angle cοngruence rule is referred tο as ASA. Twο triangles are said tο be cοngruent accοrding tο this rule if any twο angles and the side included between them οf οne triangle are equal tο the cοrrespοnding angles and the included side οf the οther triangle.

See if the twο triangles given, ABC and XYZ, are cοngruent accοrding tο the ASA rule by lοοking at the image prοvided belοw. Accοrding tο the ASA cοngruence rule, twο triangles are said tο be cοngruent if twο οf their respective sides and angles are equal tο thοse οf twο οther triangles and their respective sides and angles, respectively.

BC = BD

m< B=13x-35

m < C = 5x-19

m < D = 2x + 14

m< B=13*11 - 35

m< B=143-35

m< B = 108

m<C=5x-19

m<C=511 - 19

m < C = 55-19

m < C = 36

This is sο because the theοrem οf SAS (Side-Angle-Side)

Sο, we have:

9x117x - 3

WY = 7x-3

WY = 7*4-3

WY = 28-3

WY = 25

Hence the side οf the WY is 25.

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The inequality used for number line will be $12 < price < $20.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Hence, on a number line, we can say that the value of numbers grows as we move to the right. This indicates that there are more numbers on the right than on the left. For instance, 3 comes after 1, hence 3 > 1.

The price will lie in the following inequality -

$12 < price < $20

Below is the number line for the same -

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The exponential function in the given table is:

y = 0.02*(1/2)^x

This seems to be an exponential function of the form:

y = a*b^x

Using the points in the table we can try to find the values of a and b.

for the first point we can write:

0.02 = a*b^0

0.02 = a

Then the function is:

y = 0.02*b^x

Now the second point, (1, 0.01), replacing that we will get:

0.01 = 0.02*b^1

0.01 = 0.02*b

0.01/0.02 = b

1/2 = b

The function is:

y = 0.02*(1/2)^x

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By answering the presented question, we may conclude that When x equals 7, the equation holds true. As a result, "True" is the correct response.

A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.

The image's equation is:

2x + 4 = 18

We must solve for x to discover if the equation is true or untrue.

When we subtract 4 from both sides, we get:

2x = 14

When we divide both sides by 2, we get:

x = 7

When x equals 7, the equation holds true. As a result, "True" is the correct response.

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The total surface area of this figure is 94, rounded to the nearest hundredth.

The figure in question is a rectangular prism. To calculate the total surface area of a rectangular prism, we must use the following formula: Total Surface Area = 2(lw + wh + lh), where l is the length, w is the width, and h is the height.

For this figure, the length is 5, the width is 4, and the height is 3. Thus, we can calculate the total surface area of the figure as follows: 2(5*4 + 4*3 + 5*3) = 2(20 + 12 + 15) = 2(47) = 94. Therefore, the total surface area of this figure is 94, rounded to the nearest hundredth.

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It would take the apprentice alone 11 hours to complete a kitchen island, the same amount of time it took the cabinet maker and apprentice together.

When the cabinet maker and apprentice work together, they are able to complete the kitchen island in 8 hours. This implies that the apprentice is able to do their portion of the work in 3 hours, while the cabinet maker does their portion in 8 hours. Therefore, if the apprentice were to work on the kitchen island alone, it would take them 11 hours to complete it, the same amount of time it took the cabinet maker and apprentice together. This is because the apprentice does not have the same level of experience and expertise as the cabinet maker, so they are not able to complete the same amount of work in the same amount of time as the cabinet maker. The cabinet maker is able to work faster and more efficiently, which is why they are able to complete the kitchen island in 8 hours, while the apprentice would need 11 hours to complete the same task.

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The two solutions to the given quadratic equation are x = (a+b + √(a2 - 6ab + 8b2))/(2(a-b)) and x = (a+b - √(a2 - 6ab + 8b2))/(2(a-b)).

The general form of a quadratic equation is ax2 + bx + c = 0. To solve this equation, we need to use the Quadratic Formula. The Quadratic Formula is [tex]x = [-b ± √(b2 - 4ac)]/ 2a[/tex].

We can plug the values for a, b, and c into this equation. For this equation, a = (a-b), b = -(a+b), and c = 2b.

Therefore, using the Quadratic Formula, we get [tex]x = [-(-(a+b)) ± √((-(a+b))2 - 4(a-b)(2b))]/ 2(a-b)[/tex].

Simplifying this, we get [tex]x = [a+b ± √(a2 + 2ab - 4ab - 8b2)]/(2(a-b))[/tex].

Finally, we can solve for the two values of x by computing the two cases. In the first case, we add the square root, and in the second case, we subtract the square root. This gives us the two solutions [tex]x = [(a+b + √(a2 - 6ab + 8b2))/(2(a-b))][/tex] and [tex]x = [(a+b - √(a2 - 6ab + 8b2))/(2(a-b))][/tex].

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[tex]4.25[/tex]π cm is the width of an arcs with such a central [tex]45-[/tex]degree angle and a circle with a diameter of [tex]289 cm^{2}[/tex] .

It doesn't have any sides or corners either. A circle, then, is a full entity unto itself. Nothing else can be tacked on to complete the circle. Due of this, circles are used as symbols for wholeness, perfection, totality, and heavenly symmetry and equilibrium.

A circle is indeed a closed arc that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre.

[tex]A =[/tex] π[tex]r^2[/tex]

Given that the circle's area is [tex]289 cm^{2}[/tex], we can use the following formula to find the radius:

289π = π

[tex]r^{2} = 289[/tex]

[tex]r = 17 cm[/tex]

With the radius now known, we can apply the following formula to determine the length of an arc with a central angle of [tex]45[/tex] degrees:

[tex]L = (45^{0} / 360^{0} ) * 2pi(17)[/tex]

[tex]L = (1/8) * 34[/tex]π

[tex]L = 4.25[/tex]π cm

A circle with an area of [tex]289 cm^{2}[/tex], [tex]4.25[/tex]π cm is the length of an arc with a central angle of [tex]45[/tex]degrees.

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Answer : The probability that none of the 3 accidents are caused by aggressive driving is 0.085, according to the American Automobile Association (AAA).

The probability of an accident being caused by aggressive driving is 56%, or 0.56. Therefore, the probability of an accident NOT being caused by aggressive driving is 1 - 0.56 = 0.44. Since the accidents are chosen at random, we can assume that they are independent events. Therefore, we can multiply the probabilities together to find the overall probability.

For part 1, we want to find the probability that none of the 3 accidents are caused by aggressive driving. This means we want the probability of an accident not being caused by aggressive driving (0.44) to happen 3 times in a row:

P(none are caused by aggressive driving) = 0.44 * 0.44 * 0.44 = 0.085184

Round to 3 decimal places:

P(none are caused by aggressive driving) = 0.085

Therefore, the probability that none of the 3 accidents are caused by aggressive driving is 0.085, according to the American Automobile Association (AAA).

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The value of 'x' for the given equation is found as: x = 14.

The given equation is-

- 3x = 4*7 - 5x

Simplifying:

- 3x = 28 - 5x

Collect variables on one side and constants on other side.

-3x + 5x = 28

Subtracting the variables:

2x = 28

Dividing both sides by 2.

x = 14

Thus, the value of 'x' for the given equation is found as: x = 14.

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The correct question is-

Find x.

- 3x = 4*7 - 5x

Therefore , the solution of the given problem of rectangle comes out to be  DE ≅ BF | Corresponding parts of congruent triangles are congruent

A rectangle is a cube with four perpendicular sides in the Euclidean plane. It is also known as an equal-sided rectangle or an equiangular trapezoid. Additionally, the trapezoid may have a straight border. A square has four edges that are the same length. Quadrilaterals that are rectangular have four identical sides but instead four 90° edges. As a result, it is sometimes referred to as a "rectangular trapezoid".

Here,

ABCD is a rectangle | Given

=> AE ≅ CF | Given

AEFC is a parallelogram | Definition of parallelogram

=> AC ≅ EF | Opposite sides of a parallelogram are congruent

=> ∠EAF ≅ ∠ACF | Opposite angles of a parallelogram are congruent

=> ∠EAF ≅ ∠CAD | Diagonals of a rectangle bisect each other

=> ∠ACF ≅ ∠CAD | Transitive property of congruence

=> ∆ACF ≅ ∆CAD | ASA (angle-side-angle) congruence

=> DF ≅ DF | Reflexive property of congruence

=> ∆DFC ≅ ∆DFE | SSS (side-side-side) congruence

=> ∠BCF ≅ ∠ADE | Corresponding angles of congruent triangles are congruent

=> ∠BCF ≅ ∠BDF | Diagonals of a rectangle bisect each other

=> ∠ADE ≅ ∠BDF | Transitive property of congruence

=>∆ADE ≅ ∆BDF | ASA congruence

=> DE ≅ BF | Corresponding parts of congruent triangles are congruent

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Answer:

  C. The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.

Step-by-step explanation:

You want to know the transformations needed to form g(x) = 1/2(x+4)^2 -3 from f(x) = x^2.

The transformations ...

  f(x) ⇒ g(x) = c·f(x -h) +k

represent vertical expansion by a factor of 'c', right shift by 'h' units, and an upward shift of 'k' units.

Here, we have c=1/2, h=-4, k=-3. These mean the function f(x) has been vertically compressed to 1/2 its original height, and shifted left 4 and down 3.

The vertical compression will cause the graph to appear to be wider for any given distance above the vertex.

One possible solution is Keshawn has 2 nickels and 12 dimes.

What is inequality equation?

An inequality equation is a mathematical expression that compares two values or expressions using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to)

To solve the system of inequalities graphically, we can plot the two inequalities on the coordinate plane and shade the region that satisfies both inequalities. Let x be the number of nickels and y be the number of dimes.

The first inequality represents the maximum number of coins:

x + y ≤ 14

The second inequality represents the minimum value of the coins:

0.05x + 0.1y ≥ 1

We can rewrite this inequality as:

x + 2y ≥ 20

Now we can plot these two inequalities on the coordinate plane:

Draw a horizontal line for x + y = 14.

Draw a diagonal line with negative slope for x + 2y = 20.

Shade the region below the diagonal line and to the left of the horizontal line.

The shaded region represents the feasible region that satisfies both inequalities. We also know that x ≤ 4 since a maximum of 4 coins are nickels.

One possible solution that lies in the shaded region and satisfies the constraint x ≤ 4 is (x, y) = (2, 12). This means Keshawn has 2 nickels and 12 dimes. We can check that this solution satisfies both inequalities:

2 + 12 = 14 (maximum number of coins)

0.05(2) + 0.1(12) = 1.2 ≥ 1 (minimum value of the coins)

Therefore, one possible solution is Keshawn has 2 nickels and 12 dimes.

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On solving the provided question we cans ay that function  In the auction, 180 carrots cost £18.00.

Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.

The initial cost of 20 carrots was £2.80. Thus the cost per carrot is £2.80 20 = £0.14.

If the price is decreased by 30%, the new carrot price is: £0.14 - (30% £0.14) = £0.098 or £0.10 (rounded to the nearest penny)

As a result, 180 carrots at the current sale price will cost: 180 £0.10 = £18.00

In the auction, 180 carrots cost £18.00.

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The factor that f increases by when the exponent increases is :

When the exponent x increases by 1, the function value increases by a factor of 3. When the exponent x increases by 2, the function value increases by a factor of 9.

When the exponent x increases by 1/2, the function value increases by a factor of √3. We can see this by evaluating as follows :

= (3^ ( 1 / 2 ) )

= √3

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Option D has the correct direction of the alternative hypothesis but uses the sample proportion in the null hypothesis.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The appropriate hypotheses for this test are:

H0: p = 0.28 (the proportion of all high school students who work a part-time job during the school year is 0.28)

Ha: p > 0.28 (the proportion of all high school students who work a part-time job during the school year is greater than 0.28)

This is because the guidance counselor is interested in whether the proportion of all high school students who work part-time jobs during the school year is greater than 0.28, which was the proportion a decade ago. The null hypothesis states that the proportion is 0.28, and the alternative hypothesis states that it is greater than 0.28. Since the alternative hypothesis is one-sided (greater than), this is a one-tailed test.

Option B correctly states the null and alternative hypotheses with the appropriate population proportion in the null hypothesis and the direction of the alternative hypothesis. Options A and C use the sample proportion instead of the population proportion in the null hypothesis. Therefore, Option D has the correct direction of the alternative hypothesis but uses the sample proportion in the null hypothesis.

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Answer: The Answer is B!

Step-by-step explanation:

EDGE 2023

The amount budgeted for dances is approximately $380.00.

Assume that "x" is the budgeted sum for dances. The problem states that there is a 5:7 ratio between the budget for dances and the budget for charitable activities. Hence, we can write:

x/532 = 5/7

We can cross-multiply and simplify to find the answer for "x"

7x = 532 × 5

7x = 2660

x = 2660/7

x ≈ 380.00

The estimated $380.00 planned money for dances is the result.

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