What would the new coordinate l' be if you translated the image +5 units on the x-axis and +4 units on the y-axis?

Answer:

8 footballs

18 basketballs

36 baseballs

24 softballs

Step-by-step explanation:

Let f = footballs

f = 8

Let b = basketballs

b = 2+2f = 2 +2(8) = 2 +16 = 18

Let B = baseballs

B = 5f -4 = 5(8) -4 = 40-4 = 36

Let s = softballs

s = 6+1/2B = 6+1/2(36) = 6+18 = 24

The total is 86

f+b+B +s = 86

8+18+36+24 = 86

86=86

There are 8 footballs.

Two more than twice the number of footballs are basketballs:

2f + 2 = b

f = number of footballs

b = number of basketballs

In the first statement, there are 8 footballs. So, f = 8

2(8) + 2 = b

16 + 2 = b

18 = b

Therefore, there are 18 basketballs.

Four less than 5 times the number of footballs are baseballs:

5f - 4 = a

f = number of footballs

a = number of baseballs

In the first statement, there are 8 footballs. So, f = 8

5(8) - 4 = a

40 - 4 = a

36 = a

Therefore, there are 36 baseballs.

Six more than half of the baseballs are softballs:

a/2 + 6 = s

a = number of baseballs

s = number of softballs

In the third statement, there are 36 baseballs. So, a = 36

(36)/2 + 6 = s

18 + 6 = s

24 = s

Therefore, there are 24 softballs.

Best of Luck!

Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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Answer:sbutaraction property of equality

Step-by-step explanation:

Answer:

subtraction property of equality

Step-by-step explanation:

Lily’s process of solving the equation is correct until step 3.

Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

3.1 Activity: Procedural and Conceptual Understanding in Action

Content Area: Fractions

Problem: Comparing Fractions

Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.

Activity Steps:

Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).

Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.

After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:

What does it mean for one fraction to be greater than or less than another?

Can you explain why we need a common denominator when comparing fractions?

How can you visually represent and compare fractions to better understand their relative sizes?

Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.

Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.

Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.

Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.

By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.

3.2 Example: Conceptual Knowledge vs. Procedural Knowledge

Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.

Example: Division of Fractions

Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.

Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.

In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

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Answer:

x=-3  y=-1

(-3,-1)

Step-by-step explanation:

-1(2x-7y=1)

-7x-7y=28

-2x+7y=-1

-9x=27

x=-3

-2*-3-7y=1

y=-1

The length of the guy wire to the nearest foot would be = 10 ft.

The relationship between the tower, guy wire and pole forms the shape of a right angle triangle.

The distance from the stake to the pole (opposite) =a = 5 ft

The distance from the pole to the tower (adjacent) =b= 9ft

The length of the guy wire= c = X

Using the Pythagorean formula:

c² = a² + b²

c² = 5² + 9²

c² = 25+81

c² = 106

C = √106

C= 10 ft ( to the nearest foot)

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Complete question:

A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophie places a 7 ft tall pole to support the guy wire. After placing the pole, Sophie measures the distance from the stake to the pole to be 5 ft. She then measures the distance from the pole to the tower to be 9 ft. Find the length of the guy wire, to the nearest foot.

Step-by-step explanation:

Step 1:  List out all of the formulas for the trigonometric functions

sin(x) = opposite/hypotenuse

cos(x) = adjacent/hypotenuse

tan(x) = opposite/adjacent

Step 2:  Find the following expression that has a value of 2/5

sin(B) = opposite/hypotenuse = ?/5 is FALSE

cos(B) = adjacent/hypotenuse = 2/5 is TRUE

tan(B) = opposite/adjacent = ?/2 is FALSE

Answer:  The correction expression that has a value of 2/5 is option B

Answer:

B is the correct option

Step-by-step explanation:

Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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Answer:

Remember that if we have a proposition P, ¬P is the negation of that proposition.

We have:

W = car is white

¬W = car is not white

N = car is new

¬N = car is not new

M = the car is mine

¬M = the car is not mine.

Now, whit that defined, let's analyze the statements:

a: " If the car is not white and new, then it is mine."

We can write this as:

"Not W and N, then M"

using only symbols this is:

(¬W ∧ N) ⇒ M

where the symbol ∧ means "and"

and the symbol ⇒ means "then"

b " The car being white or new is a sufficient condition for it being not mine."

We can rewrite this in a simpler way:

"if the car is white or new, then is not mine"

We can write this as:

W or N, then, not M

using the symbols, we get:

(W ∨ N) ⇒ ¬M

Where the symbol ∨ means "or"

c " The car is mine if and only if it is new and not white."

This can be rewritten as:

"M if and only if N and not W"

Using only symbols, we get:

M ⇔ (N ∧ ¬W)

Where "⇔" means "if and only if"

Step-by-step explanation:

∠6 = 10x

∠7 = 5x

∠6 = ∠8

∠7 = ∠5

Find value of x

∠5 + ∠6 + ∠7 + ∠8 = 360

5x + 10x + 5x + 10x = 360

30x = 360

x = 360/30

x = 12°

The measure of distance x, that is, the distance between a point P and the point of horizon, is equal to 284.372 miles.

In this problem we must determine the distance between a point P located about earth's circumference and the point of horizon, located on earth's circumference. Since the line between these two points is tangent to earth, then, distance x can be found by Pythagorean theorem:

x = √[(3959 mi + 10.2 mi)² - (3959 mi)²]

x = 284.372 mi

The distance x is equal to 284.372 miles.

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Answer:

0.0482

Step-by-step explanation:

Given the following :

Probability of success : p(success) = 0.25

Number of trials = 800

X = number of successes

Calculate P(X > 220)

The problem above can be solved using the binomial probability formula:

P(X > 220) = P(X = 221) + P(X =222)... + P(X =800)

To save computation time, we coild use the online binomial probability calculator :

P(X > 220) = 0.0482

The binomcdf function of a graphing calcukatur can also be used :

1 - binomcdf(800, 0.25, 220)

1 - (0.95177363855) = 0.04822

Answer:

A

Step-by-step explanation:

The answer is option (A) 8560. This combination cannot be the correct combination for your brother's lock because it contains the digit '6' in the same position as the correct combination (6348), but the other digits do not match.

The nominal return on an investment doesn’t consider the effect of inflation on purchasing power. If the inflation rate is positive, the real return will be less than the nominal return on an investment.

What is inflation?

In simple words continuing to rise in general price is regarded as inflation. There is a different kind of inflation, for example; The increase in price due to an increase in the aggregate of goods and services compared to aggregate supply is called demand-pull inflation.

If the inflation rate is positive, the actual return will be less than the nominal return on investment.

Therefore, In order to complete the statement, The nominal return on an investment doesn’t consider the effect of inflation on purchasing power. If the inflation rate is positive, the real return will be less than the nominal return on an investment.

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Answer:

The REAL RETURN on an investment considers the effect of inflation on purchasing power. If the inflation rate is positive, the nominal return will be

GREATER THAN the real return on an investment.

Step-by-step explanation:

Using the information in the given diagram, the value of the missing angle is: m∠1 = 75°

The transverse line theorem states that If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Now, when we draw a horizontal line parallel to lines a and b and directly cutting across the vertex of angle 1, we can see that angle 1 will be composed of two angles.

Now, for the transverse line theorem we can say that:

Angle 1 will be composed of two angles namely:

48 degrees and (180 - 153) degrees.

Thus:

m∠1 = 48° + 27°

m∠1 = 75°

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Answer:

Step-by-step explanation:

\((-3,-1) = (x_1, y_1) \\ m = 4\)

Substitute values into point slope form

\(y-y_1 = m(x-x_1) \\ y - ( - 1) = 4(x - ( - 3)) \\ y + 1 = 4(x + 3) \\ y + 1 = 4x + 12\)

Collect like terms and simplify

\(y = 4x + 12 - 1 \\ y = 4x + 11\)

Answer:

y=4x + 11

Step-by-step explanation:

y = mx + b

y = 4x + b

-1= 4(-3) + b

b= 11

y= 4x + 11

The last row of the table will show the total interest paid, which is approximately $243.11.

The correct option is C.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

To calculate the total interest paid,

we need to first find out how many months it will take to pay off the entire balance.

We can use the following formula to calculate the number of months:

N = -log(1-(r×b/p))/log(1+r)

where N is the number of months, r is the monthly interest rate (which is the annual percentage rate divided by 12), b is the balance, and p is the payment.

In this case,

r = 0.1799/12 = 0.01499 (monthly interest rate), b = $1,800, and p = $125.

Plugging these values into the formula, we get:

N = -log(1-(0.01499 × 1800/125))/log(1+0.01499) ≈ 16.24

So it will take about 16.24 months to pay off the entire balance.

Using a spreadsheet, we can create a table with the following columns:

Month: 1 to 16

Balance: starting with $1,800 and decreasing by $125 each month

Interest: calculated as the monthly interest rate times the balance

Payment: $125

Total Interest: calculated as the sum of the interest for all previous months

The last row of the table will show the total interest paid, which is approximately $243.11.

Therefore, the value is (C) $243.11.

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Answer: Option C is correct $243.11

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

Let us define probability.

Probability is a mathematical tool used to study randomness. It deals with the chance or the likelihood of an event, E occurring from a sample space, S. This can be represented mathemaically as shown below

From the given question, the sample space has the following elements

The elements of the events that the spinner would stop at an even number or a multiple of 3 would be

Therefore, the probability that the spinner will stop on an even number or a multiple of 3 would be

Hence, the probability that the spinner will stop on an even number or a multiple of 3

Answer:

98/115

Step-by-step explanation:

2 4/5 / 3 2/7

14/5x23/7

14/5x7/23

98/115

Answer:

it is 98/115 but I dont know what the simplified part of it is

Step-by-step explanation:

2 and 4/5 turns into 14/5.  3 and 2/7 turns into 23/7.  keep 14/5 the same but flip 23/7 over to be 7/23.  then multiply it and you get 98/115

Answer:

x > 22

Step-by-step explanation:

Hey there!

Well to solve,

52 - 3x < -14

we need to single out  x

52 - 3x < -14

-52 to both sides

-3x < -66

Divide both sides by -3

x > 22

The < changes to > because the variable number is a - being divided.

Hope this helps :)

Answer:

x > 22

Step-by-step explanation:

First, rearrange the equation

Then, pull out the like terms:

Next, apply algebra to the equation by dividing each side by -3. It should now look like this: x > 22.

Therefore, the solution set of the inequality would be x > 22.

Answer:

A. \(n=100\)
B. \(k=0\)

Step-by-step explanation:

A. The equation "110% n = 11" can be solved as follows:

110% n = 11

To solve for n, we need to get rid of the percentage sign (%). We can do this by dividing both sides of the equation by 110%, or 0.110 (since 110% is equivalent to 1.1 in decimal form).

(110% n) / 110% = 11 / 110%

n = 11 / 0.110

n = 100

So, the solution for n in the equation "110% n = 11" is n = 100.

B. The given equation is:

(328 x 128) x k = 328 x (82 x 128) x k

To solve for k, we can simplify the equation using the properties of multiplication.

Step 1: Perform the multiplications inside the parentheses:

41984 x k = 328 x 10576 x k

Step 2: Rearrange the equation by applying the associative property of multiplication:

41984 x k = 328 x (10576 x k)

Step 3: Divide both sides of the equation by 328:

(41984 x k) / 328 = 10576 x k

Step 4: Cancel out the common factor of k on the left-hand side:

(41984 / 328) x k = 10576 x k

Step 5: Simplify the left-hand side:

128 x k = 10576 x k

Step 6: Subtract 10576 x k from both sides of the equation to isolate k:

128 x k - 10576 x k = 0

Step 7: Factor out k on the left-hand side:

k x (128 - 10576) = 0

Step 8: Simplify further:

k x (-10448) = 0

Step 9: Divide both sides of the equation by (-10448):

k = 0

So, the solution for k in the equation "(328 x 128) x k = 328 x (82 x 128) x k" is k = 0.

Answer: $9.25 an hour

Step-by-step explanation:

Answer:

\(\boxed{\frac{3}{5}}\)

Step-by-step explanation:

The trigonometric functions are described as follows:

\(sin = \frac{opposite}{hypotenuse}\\\\cos = \frac{adjacent}{hypotenuse}\\\\tan = \frac{opposite}{adjacent}\)

Using reference angle ∠A, use the sin trigonometric function. This will be the side opposite (cannot be the hypotenuse) of ∠A over the side adjacent (cannot be the hypotenuse).

The side opposite of ∠A is 3. The hypotenuse of the triangle is 5.

\(\boxed{\frac{3}{5}}\)  is the final answer!

Answer:

Step-by-step explanation:

i hope this is good enough

Answer:

Substitute 0 for the value of x and y.

5x - 6y = 30

5x - 6(0) = 30

5x = 30

The x-intercept is 6.

x = 6

(6, 0)

5x - 6y = 30

5(0) - 6y = 30

-6y = 30

y = -5

The y-intercept is -5.

(0, -5)

(The graph is in the picture)

The graph of the given function is shown below

From the question, we are to graph the given function

The given function is f(x) = (3/2)2^x

That is

f(x) = (3/2)2ˣ

To graph the function, we determine some of the points on the line

Find f(-2)

f(x) = (3/2)2ˣ

f(-1) = (3/2)2⁻²

f(-1) = (3/2) × 1/2²

f(-1) = (3/2) × 1/4

f(-1) = 3/8

f(-1) = 0.375

Find f(-1)

f(x) = (3/2)2ˣ

f(-1) = (3/2)2⁻¹

f(-1) = (3/2) × 1/2

f(-1) = 3/4

f(-1) = 0.75

Find f(0)

f(x) = (3/2)2ˣ

f(0) = (3/2)2⁰

f(0) = (3/2)1

f(0) = 3/2

f(0) = 1.5

Find f(1)

f(x) = (3/2)2ˣ

f(1) = (3/2)2¹

f(1) = (3/2)2

f(1) = 3

Find f(2)

f(x) = (3/2)2ˣ

f(1) = (3/2)2²

f(1) = (3/2)4

f(1) = 6

Using the points calculated above, the graph of the given function is shown below

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Answer: it is NOT proportional

Step-by-step explanation: it doesn’t stick to 1 number going up if that makes sense, it’s adding 1 each time it goes up but it has to stick to one number going up making this NOT proportional

Answer:

2/3

Step-by-step explanation:

x adds by 2's: 0 2 4 6...

y adds by 3's: 0 3 6 9...

Answer:

\(a - \: \: 42 + 14\pi\)

Step-by-step explanation:

There are 6 sides that are 7 in length.

\(7 \times 6 = 42\)

There are 4 quater circles which equals the perimeter of one circle

\(circles \: perimeter - 2\pi \: r\)

\(2\pi \: r = 2 \times\pi \times 7\)

\( = 14\pi\)

therefore final expression is

\( = 42 + 14\pi\)