Look back at the plans these students used to solve the word problem below.
Who found a correct solution?
- STEP 4: LOOK BACK
According to soap box derby rules, a racer must weigh 250
pounds or less. The Math Club's car weighed in at 266
pounds on the day of the derby. How many pounds did the
Math Club need to remove from their soap box racer?
Dana added the weight limit to the Hector subtracted the weight limit
racer's weight. Since
from the racer's weight. Since
250 +266 = 516, the Math Club 266 - 250 = 16, the Math Club
needed to remove 516 pounds from needed to remove 16 pounds
the racer
from the racer
O A. Dana
B. Hector

The cost price of the shorts is K22.50.

To find the cost price of the shorts, we need to reverse calculate the original price before the markup and taxes were applied.

Let's assume the cost price of the shorts is represented by C.

The markup of 17% is applied to the cost price, which means the selling price (including the markup) is 117% of the cost price.

117% of the cost price C can be calculated as (117/100) * C.

GST (Goods and Services Tax) is also included in the selling price. GST is typically calculated as a percentage of the selling price. In this case, the selling price of the shorts including GST is K29.25.

Since the GST is included in the selling price, we can subtract it from the selling price to obtain the selling price before GST.

Let's assume the GST rate is R% (as a decimal), then the selling price before GST can be calculated as:

Selling price before GST = Selling price - (Selling price × R)

In this case, the selling price before GST is K29.25, and the GST rate is 17% (0.17 as a decimal). Substituting these values into the equation, we have:

K29.25 = Selling price - (Selling price × 0.17)

Simplifying the equation

K29.25 = Selling price × (1 - 0.17)

K29.25 = Selling price × 0.83

Selling price = K29.25 / 0.83

Now we can substitute the selling price in terms of the cost price:

K29.25 / 0.83 = (117/100) × C

Simplifying the equation:

C = (K29.25 / 0.83) × (100/117)

Calculating the cost price C:

C = K22.50

Therefore, the cost price of the shorts is K22.50.

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Based on the information we can infer that the equation shown in the image is 1.23 - 0.35 = 0.88 (option B).

To identify the correct equation we must look at the graph and identify the information it provides. In this case we have two squares divided into 100 squares each. Additionally, the square on the left has 88 squares painted in red and 12 squares with an X inside. In the case of the square on the right, it has 23 squares colored in red with an X inside.

In total we have 123 squares painted in red, which in decimal number is equivalent to 1.23. On the other hand, the number of squares painted red and with an X inside is 35, this value would be 0.35.

On the other hand, the squares painted only in red are 88, so the equivalent in decimal numbers would be 0.88. Therefore, the correct way to express this relationship through an equation would be:

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By definition of proportion, the value of x is,

⇒ x = 80

We have to given that;

In a triangle,

Perpendicular = 60

Now, By Pythagoras theorem we get;

60² = 36² + y²

3600 = 1296 + y²

y² = 3600 - 1296

y² = 2304

y = 48

Hence, By definition of proportion;

⇒ x / 48 = 60 / 36

⇒ x = 80

Thus, By definition of proportion, the value of x is,

⇒ x = 80

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\(f(x) = 4 {x}^{2} - 6x + 11\)

\(f(10 + h) = 4 ({10 + h})^{2} - 6(10 + h) + 11 \\ \)

\(f(10 + h) = 4(100 + 20h + {h}^{2}) - 60 - 6h + 11 \\ \)

\(f(10 + h) = 400 + 80h + 4 {h}^{2} - 60 - 6h + 11 \\ \)

\(f(10 + h) = 4{h}^{2} + 74h + 351\)

_____________________________________________

\(f(10) = 4 ({10})^{2} - 6(10) + 11\)

\(f(10) = 400 - 60 + 11\)

\(f(10) = 351\)

_____________________________________________

\( \frac{f(10 + h) - f(10)}{h} = \\ \)

\( \frac{4 {h}^{2} + 74h + 351 - (351)}{h} = \\ \)

\( \frac{4 {h}^{2} + 74h }{h} = \\ \)

\( \frac{4 {h}^{2} }{h} + \frac{74h}{h} = \\ \)

\(4h + 74\)

_____________________________________________

\(ah + b\)

\(4h + 74\)

So :

\(a = 4\)

\(b = 74\)

Answer:

D 60 degrees

Step-by-step explanation:

I took the test and got it right

Your welcome :)

Answer:

x = - \(\frac{3}{4}\) , x = 1

Step-by-step explanation:

4x² = x + 3 ← subtract x + 3 from both sides

4x² - x - 3 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 4 × - 3 = - 12 and sum = - 1

the factors are - 4 and + 3

use these factors to split the x- term

4x² - 4x + 3x - 3 = 0 ( factor the first/second and third/fourth terms )

4x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(4x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

4x + 3 = 0 ( subtract 3 from each side )

4x = - 3 ( divide both sides by 4 )

x = - \(\frac{3}{4}\)

x - 1 = 0 ( add 1 to both sides )

x = 1

solutions are x = - \(\frac{3}{4}\) , x = 1

Answer: "The pyramid and the cone have the same volume despite their different shapes."

Step-by-step explanation: If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:

"The pyramid and the cone have the same volume despite their different shapes."

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Answer:

C.

y = –3x + 9

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula  

y − y 1 = m ( x − x 1 )  to find the line parallel to  y = − 3 x .

y = − 3 x + 9

...................................................................................................................................................

Find the negative reciprocal of the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line perpendicular to  y = − 3 x .

y = 1 /3 x − 1

Answer: C) between 6 and 7 pounds

Step-by-step explanation: 50 divided by 8 = 6.25

Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

Answer:

\(\frac{4}{5}\)

0.8

Step-by-step explanation:

Happy to help:)

Answer:

1. ROUNDED 64.85 + 14.27 = 79.12

NOT ROUNDED 64.85 + 14.26 = 79.11

2. 143.50 + 9.32 = 152.82 not rounded

143.50 + 9.33 = 152.83 rounded

Step-by-step explanation:

1.

We need to find 22% of 64.85, and we do that by multiplying

64.85 x 0.22 = 14.267

Now we have 2 choices, if you round, the tip will be 14.27, but if you do not round, it will be 14.26. If you aren't sure, round the answer. 64.85 + 14.27 = 79.12  OR 64.85 + 14.26 = 79.11

2.

We will first solve for the total cost of the tickets before the sales tax

140.00 + 3.50 = 143.50

Then, we will calculate sales tax

143.50 x 0.065 = 9.32 not rounded

143.50 x 0.065 = 9.33 rounded

143.50 + 9.32 = 152.82 not rounded

143.50 + 9.33 = 152.83 rounded

The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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The six terms of the series 247 are 2, 2, 2, 2, 2, and 2.

To find the six terms of a series, we need to first understand what a series is. A series is defined as the sum of the terms of a sequence. A sequence is a set of numbers in a specific order.

Therefore, a series is a sum of terms from a sequence. There are different types of series, and they have different formulas for calculating their terms.In this case, we are required to find the six terms of the series 247. Since this is a finite series, we can use a formula to calculate the nth term of a finite series.

The formula is given as follows:Tn = a + (n - 1) dWhere Tn is the nth term of the series, a is the first term of the series, n is the number of terms in the series, and d is the common difference between the terms of the series.To find the six terms of the series 247, we need to know the value of a and d. In this case, we can see that the first term of the series is 2. Therefore, a = 2.

Since this is a constant series, we can see that the common difference between the terms is 0. Therefore, d = 0.Substituting these values in the formula, we get:T1 = a + (1 - 1) dT1 = 2 + 0T1 = 2T2 = a + (2 - 1) dT2 = 2 + 0T2 = 2T3 = a + (3 - 1) dT3 = 2 + 0T3 = 2T4 = a + (4 - 1) dT4 = 2 + 0T4 = 2T5 = a + (5 - 1) dT5 = 2 + 0T5 = 2T6 = a + (6 - 1) dT6 = 2 + 0T6 = 2.

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The probability that in a given week in September, it will rain on at most two days is 0.12.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The probability that it rains on any given day in September = 0.3.

P ( rains ) = 0.3

And,

The probability that it will not rain on any given day in September.

P (no rain) = 1 - 0.3

P(no rain) = 0.7

Now,

The probability is that in a given week in September, it will rain on at most two days.

= P (x ≤ 2)

= P(no rain) + P(rain) + P(rain)

= 0.7 + 0.3 + 0.3

= 0.12

Thus,

The probability that in a given week in September, it will rain on at most two days is 0.12.

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Answer:

a) -73°C, -15°C, -12°C, 0°C, 16°C, 37°C, 96°C

a) 96°C, 37°C, 16°C, 0°C, -12°C, -15°C, -73°C

b) -36°C, -15°C, -7°C, -1°C, 0°C, 20°C, 23°C

b) 23°C, 20°C, 0°C, -1°C, -7°C, -15°C, -36°C

Answer:

162 square feet

Step-by-step explanation:

Let the side lengths of the square be l feet each.

Then the diagonal together with any two sides forms an isosceles right triangle.

We can apply the Pythagoras Theorem, which says that, the sum of the squares of the two shorter legs equals the square of the hypotenuse ( the diagonal) in this case.

Divide both sides by

The area of the square garden is 162 ft²

The number of 1 foot by 1 foot square planter boxes that can fill this garden is

The area of the square garden will be 162 square feet.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.

Given that the length of the diagonal of the square is 18 feet. The area of the square will be calculated as,

Area = 1 / 2 x d₁ x d₂

Area = 1 / 2 x 18 x 18

Area = 9 x 18

Area  = 162 square feet

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Answer:

w=7a+4b

or,w-4b=7a

or,(w-4b)/7=a

\( \frac{w - 4b}{7} = a\)

Answer:

x = 27692903

Step-by-step explanation:

x - 2 + 3 = 27692904

x + 1 = 27692904         Combine like terms

x = 27692903        Subtract 1 from both sides

Hey there!

x - 2 + 3 = 27,692,904

COMBINE the LIKE TERMS

x + 1 = 27,692,904

SUBTRACT 1 to BOTH SIDES

x + 1 - 1 = 27,692,904 - 1

CANCEL out: 1 - 1 because it give you 1

KEEP: 27,692,904 - 1 because it gives you the x-value

NEW EQUATION: x = 27,692,904 - 1

SIMPLIFY IT!

x = 27,692,903

Therefore, your answer is:

x = 27,692,903

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Intersection of B'∩C = {k, y}

To find the intersection of B' and C, we need to first find the complement of set B (B') and then find the intersection between B' and C.

1. Complement of set B (B'):

The complement of set B (B') consists of all elements in the universal set U that are not in set B. From the given information, set B is defined as {k, s, y}', which means it contains all elements in U except for k, s, and y. Therefore, the complement of set B is {f, m, x, z}.

2. Intersection between B' and C:

Now, we need to find the intersection between B' (complement of B) and set C. From the given information, set C is defined as {s, z}. To find the intersection, we need to identify the common elements between B' and C.

The elements present in both B' and C are k and y. Therefore, the intersection of B' and C is {k, y}.

So, the answer to (b) is B'∩C = {k, y}.

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The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

The Answer is (0, 1)

Step-by-step explanation:

add 2 and 4 to the x and y

Answer:

(0, 1)

Step-by-step explanation:

2 units right -> -2 + 2 = 0

4 units up -> -3 + 4 = 1

Answer:

-6

Step-by-step explanation:

The answer to this question is -6

Answer:

+_ 6

Step-by-step explanation:

+6×-6=-36

Does that make any sense.

I hope this is what the question is asking

Answer:

6

Step-by-step explanation:

7 is in the ones place

6 is in the tenths place

Answer:

E.

Step-by-step explanation:

2x+4>10

Subtract 4 from both sides

2x>6

Divide both sides by 2

x>3

So, E represents this inequality as x is greater than 3 and it does not include 3 in it which is represented by an empty bubble.

Answer:

E

Step-by-step explanation:

The average rate of change for the interval from x =  7 to x =  8 is 35.  

To calculate the average rate of change for the interval from x =  7 to x =  8, we need to find the difference in y- values and divide it by the difference inx-values within that interval.

Let's calculate it step by step using the given table  

For the interval from x =  7 to x =  8  x1 =  7, y1 = -37  x2 =  8, y2 = -2   Difference in y- values Δy =  y2- y1 = -2-(- 37) =  35  

Difference inx-values Δx =  x2- x1 =  8- 7 =  1  

Average rate of change =  Δy/ Δx =  35/ 1 =  35  

Thus, the average rate of change for the interval from x =  7 to x =  8 is 35.   Note: It's important to mention that the values calculated then are grounded solely on the given data. Please  insure you  corroborate the  delicacy of the  handed data and  environment before using the answer in any important or critical  operations.

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The domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11. Option C

The domain of a function refers to the entire area for which the function returns a value. The function in this case is; f(x) = x^2 - 3x - 28/x + 4. The domain of the function will be real numbers except -4.

Hence, we can say that domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11.

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Answer:

The answer is C.

The vertex form of an equation is,

⇒ y = - 7 (x - 1)² + 2

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The equation is,

⇒ y = - 7x² + 14x - 5

Now, We can solve the equation for the vertex form as;

⇒ y = - 7x² + 14x - 5

⇒ y = - 7 (x² - 2x + 1) + 7 - 5

⇒ y = - 7 (x - 1)² + 2

Thus, The vertex form of an equation is,

⇒ y = - 7 (x - 1)² + 2

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