Here are two students' answers for each question. Do you agree with either of them? Explain or show your reasoning.

How many feet are traveled by a person riding once around the merry-go-round?

⚫ Clare says, "The radius of the merry-go-round is about 4 feet, so the distance around the edge is about 8π feet."
⚫ Andre says, "The diameter of the merry-go-round is about 4 feet, so the distance around the edge is about 4π feet."

Answer:

https://cdn.flvs.net/assessment_images/educator_algebra2_v19/02_07_14_flvs.gif

Step-by-step explanation:

the correct answer is: ( x ) equals negative 1 plus or minus 2 I square root of 2

To solve the equation [tex]\( x^2 + 2x + 9 = 0 \)[/tex], you can use the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

In this case, [tex]\( a = 1 \), \( b = 2 \), and \( c = 9 \)[/tex]. Substituting these values into the formula:

[tex]\[ x = \frac{-2 \pm \sqrt{(2)^2 - 4(1)(9)}}{2(1)} \]\[ x = \frac{-2 \pm \sqrt{4 - 36}}{2} \]\[ x = \frac{-2 \pm \sqrt{-32}}{2} \]\[ x = \frac{-2 \pm 4i\sqrt{2}}{2} \]\[ x = -1 \pm 2i\sqrt{2} \][/tex]

So, the correct answer is: ( x ) equals negative 1 plus or minus 2 I square root of 2.

Answer:

We can conclude that Δ ABC ≅ Δ DEF by AAS postulate.

Step-by-step explanation:

Δ ABC and Δ DEF are congruents because:

1. Their non-included sides BC and EF are equal (7 units = 7 units)

2. Their angles ∠A and ∠D are equal (39° = 39°)

3. Their angles ∠C and ∠F are equal  (64° = 64°)

Now, we can conclude that Δ ABC ≅ Δ DEF by AAS postulate.

Answer:

[tex]\frac{32xy}{3}[/tex]

Step-by-step explanation:

Answer: 210

Step-by-step explanation: because 9 times 15 =135

and then you add 75

and then add them together and get 210 for the long distance phone call

Answer:

The cost of the 20 fruit cup is $ 60  .

Step-by-step explanation:

Given as :

The total students for fruit cup party = 18

The total teachers for fruit cup party = 2

The cost of each fruit cup =$ 3

The delivery charge = $ 10

So, The total number of people for party = Total number of student + Total number of teachers

Or , The total number of people for party = 18 + 2 = 20

∵ each fruit cup cost $ 3

∴ The cost of 20 fruit cup = $ 3 × 20

I.e The cost of 20 fruit cup = $ 60

Hence The cost of the 20 fruit cup is $ 60  . Answer

The range of the function for the fruit-cup party is $10 to $70, including the delivery charge and the cost of the fruit cups.

To find the range of the function for the fruit-cup party, we need to consider the total cost of the fruit cups and the delivery charge. The delivery charge is a fixed cost of $10. The cost of each fruit cup is $3. So, the total cost of the fruit cups for the 18 students and 2 teachers is (18 + 2) × $3 = $60. Therefore, the range of the function is $10 to $70, which includes the delivery charge and the total cost of the fruit cups.

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Answer:

c

Step-by-step explanation:

Answer:

its 31 when you round to 2 decimal points.

Answer:

A.10000

B.25 more trees must be planted

Step-by-step explanation:

⇒Given:

A.

⇒If the total trees per acre is doubled , which means :

total number of trees per acre [tex]t_{f}[/tex] = [tex]2*t_{i}[/tex] = 200

the yield will decrease by : [tex]t_{f}[/tex] - [tex]y_{i}[/tex]

[tex]y_{f}= 150-100= 50[/tex]

⇒total yield = [tex]50*200=10000[/tex]

B.

⇒to maximize the yield ,

let's take the number of trees per acre to be 100+y ;

and thus the average yield per acre = 150 - y;

total yield = [tex](100+y)*(150-y)\\=15000+50y-y^{2} \\[/tex]

this is a quadratic equation. this can be rewritten as ,

     ⇒   [tex]=15000+50y-y^{2}\\=15000+625 - (625 - 50y +y^{2})\\=15625 - (y-25)^{2}[/tex]

In this equation , the total yield becomes maximum when y=25;

⇒Thus the total number of trees per acre = 100+25 =125;

Answer:

The given description is equivalent to the algebraic expression,

[tex](\frac {11}{k})^{2}[/tex]

Step-by-step explanation:

The given description is ,

'The square of the ratio of 11 and k'

which is equivalent to the algebraic expression,

[tex](\frac {11}{k})^{2}[/tex]

Answer:

$15

Step-by-step explanation:

120/8=15

Answer:

Step-by-step explanation:

Total Cost of 8 copies of same CD =$120

Because the copies of the CD is same, the cost of each one should be same

Cost of one CD should be $120/8=$15

Answer:

14.6%

Step-by-step explanation:

Use binomial probability:

P = nCr pʳ (1−p)ⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

and p is the probability of success.

Here, n = 10, r = 4, and p = 1/4.

P = ₁₀C₄ (1/4)⁴ (1−1/4)¹⁰⁻⁴

P = 210 (1/4)⁴ (3/4)⁶

P ≈ 0.146

There is an approximate 14.6% probability that exactly 4 of the 10 adults are on a diet.

Answer:

Yes

Step-by-step explanation:

It is a Pythagorean Triple. A Pythagorean Triple is the sides of a triangle that fit perfectly into the Pythagorean Theorem, which is:

a²+b²=c²

12, 13, and 15 are numbers that you should know off the top of your head so if you see a triangle with 2 of those numbers, you instantly know the 3rd number.

~Stay golden~ :)

Answer: Yes

Step-by-step explanation: To determine if these side lengths can form a triangle, I attached a rule in the image provided which is very helpful to look at especially when you're new at this.

If a triangle has sides with lengths of 12, 15, and 13, notice that 12 + 15 or 27 is greater than 13.

So the sum of the lengths of two sides of the triangle is greater than the length of the third side.

This means that the triangle with sides of lengths of 12, 15, and 13, is possible.

The expression -y + 9z - 16y - 25z + 4 simplifies to -17y - 16z + 4 by combining like terms, which are the y terms and the z terms separately.

The task is to simplify the expression -y + 9z - 16y - 25z + 4. To do this, we will combine like terms.

First, combine the terms that contain y:

-y - 16y = -17y

Then, combine the terms that contain z:

9z - 25z = -16z

The number without a variable, which is 4 in this case, remains the same since it does not have any like terms to combine with.

Now, we put the simplified terms together:

-17y - 16z + 4

The expression is now simplified to its least terms.

Answer:

I'm pretty sure that you would try to find the least common multiple.

Step-by-step explanation:

Final answer:

When adding fractions, you need to find a common denominator using the least common multiple (LCM) of the denominators. In this case, the LCM of 5 and 6 is 30, so you multiply each fraction by a factor to make the denominators the same. Then, you can add the numerators together.

Explanation:

When adding fractions, you need to use the least common multiple (LCM) of the denominators to find a common denominator. In this example, the denominators are 5 and 6. The LCM of 5 and 6 is 30, so you need to find equivalent fractions with a denominator of 30.

To do this, multiply the numerator and denominator of each fraction by a factor that will result in a denominator of 30. For the first fraction, multiply both the numerator and denominator by 6 to get 24/30. For the second fraction, multiply both the numerator and denominator by 5 to get 25/30.

Finally, you can add the numerators together (24 + 25 = 49) and keep the common denominator of 30, giving you the final fraction of 49/30.

Answer:

[tex]f(x)=0.5(0.2)^x[/tex]

Step-by-step explanation:

Exponential function can be in this form : [tex]f(x)=ab^x[/tex]

To find a and b we can use any two pairs from the table.

We can use (0, 0.5) and (1,0.1)

[tex]0.5=a*b^0\\a=0.5[/tex]

let's find b

[tex]0.1=0.5b^1\\b=0.2[/tex]

The exponential function represented by the table is [tex]\( f(x) = 3.125 \times (0.5)^x \)[/tex], where x can take values -2, -1, 0, 1, or 2, and f(x) corresponds to the values given in the table.

1. Examine the given table with two columns: x and f(x), where x takes values -2, -1, 0, 1, and 2, and f(x) takes corresponding values 12.5, 2.5, 0.5, 0.1, and 0.02.

2. Notice that as x increases by 1, f(x) decreases by a factor of 5 (12.5 / 2.5 = 5, 2.5 / 0.5 = 5, etc.), indicating an exponential decay pattern.

3. Write the general form of an exponential decay function:

 [tex]\[ f(x) = a \times b^x \][/tex]

  where a is the initial value and b is the decay factor.

4. Use the first row of the table (x = -2, f(x) = 12.5) to find the initial value, a:

  [tex]\[ 12.5 = a \times (0.5)^{-2} \] \[ 12.5 = a \times 4 \] \[ a = \frac{12.5}{4} = 3.125 \][/tex]

5. Substitute the initial value, a, into the exponential function:

  [tex]\[ f(x) = 3.125 \times (0.5)^x \][/tex]

Therefore, the exponential function represented by the table is [tex]\( f(x) = 3.125 \times (0.5)^x \)[/tex], where x can take values -2, -1, 0, 1, or 2, and f(x) corresponds to the values given in the table.

Answer:

32

Step-by-step explanation:

4 x 8 = 32

Answer:

32 quarters

Step-by-step explanation:

if there are 4 stack with 8 quarters in each stack, then we know that all we have to do is multiply 4 x 8 which equals 32

Answer:

The answer is 52%

Step-by-step explanation:

The above data shows that (0.32) 32% of residents support Zhang and live in Cherry Hill.

Since the question asked is to know the percentage of the Cherry Hill residents polled that supported Zhang

We focus on Cherry Hill residents only.

(0.62) 62% of residents surveyed live in Cherry Hill

So you would divide 32% by 62% and that would be approximately 0.52  

Convert 0.52 to percentage

0.52 x 100 = 52%

Answer:

About 52%

Step-by-step explanation:

Answer:

BC = 28

Step-by-step explanation:

Since the triangle is equilateral then all 3 sides are congruent.

Equate AB and AC and solve for x, that is

12x + 4 = 8x + 12 ( subtract 8x from both sides )

4x + 4 = 12 ( subtract 4 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2, thus

AC = 8x + 12 = (8 × 2) + 12 = 16 + 12 = 28

Since the 3 sides are congruent then BC = 28

For this case we must simplify the following expression:

[tex]8- \frac {4} {5} x-14-2x =[/tex]

We add similar terms:

[tex]8-14- \frac {4} {5} x-2x =[/tex]

We take into account that:

Equal signs are added and the same sign is placed.

Different signs are subtracted and the major sign is placed.

[tex]-6+ (\frac {-4-10} {5} x) =\\-6+ (\frac {-14} {5} x) =\\-6- \frac {14} {5} x[/tex]

Finally, the simplified expression is:

[tex]-6- \frac {14} {5} x[/tex]

ANswer:

[tex]-6- \frac {14} {5} x[/tex]

Answer:

See explanation

Step-by-step explanation:

        Statements                         Reasons

1. [tex]\overline{AD}\parallel \overline{BC}[/tex]                                        Given

2. [tex]\angle ADB\cong \angle CBD[/tex]      As alternate interior angles when parallel lines AD and BC intersect by ltransversal BD

3. [tex]\overline{AD}\cong \overline{BC}[/tex]                                     Given

4. [tex]\overline{BD}\cong \overline{DB}[/tex]                     Reflexive property

5. [tex]\triangle ADB\cong \triangle CBD[/tex]                  SAS postulate

6.  [tex]\angle ABD\cong \angle CDB[/tex]              Corresponding parts of congruent triangles are congruent

7. [tex]\overline{AB}\parallel \overline{CD}[/tex]            Inverse alternate interior angles theorem

Answer:

The answer to your question is A.35

The perimeter of quadrilateral ACRM is 30. The closest option is 32 (Option 2).

Since M, R, and T are midpoints of the sides of ABC, they divide each side into two equal parts. Therefore, AM = MB, BR = RC, and CT = TA.

Now, let's find the lengths of AM, BR, and CT.

1. **Length of AM:**

[tex]\[ AM = \frac{1}{2} \cdot AB = \frac{1}{2} \cdot 18 = 9 \][/tex]

2. **Length of BR:**

 [tex]\[ BR = \frac{1}{2} \cdot BC = \frac{1}{2} \cdot 10 = 5 \][/tex]

3. **Length of CT:**

[tex]\[ CT = \frac{1}{2} \cdot AC = \frac{1}{2} \cdot 14 = 7 \][/tex]

Now, we need to find the perimeter of quadrilateral ACRM:

[tex]\[ \text{Perimeter} = AM + BR + RC + CT \][/tex]

[tex]\[ \text{Perimeter} = 9 + 5 + 7 + 9 = 30 \][/tex]

So, the perimeter of quadrilateral ACRM is 30. The closest option is 32 (Option 2). Please double-check the answer choices, as the calculated perimeter is not exactly matching any of the provided options.

Answer:

Part i) -14

Part ii) 11

Part iii) 4

Step-by-step explanation:

we know that

The average rate of change or slope using the difference quotient formula is equal to

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Part i) x= -3 and x= -1

In this problem we have

[tex]a=--3[/tex]

[tex]b=-1[/tex]

[tex]f(a)=f(-3)=3(-3)^{2} -2(-3)+5=38[/tex]  

[tex]f(b)=f(-1)=3(-1)^{2} -2(-1)+5=10[/tex]

Substitute

[tex]\frac{10-38}{-1+3}[/tex]

[tex]\frac{-28}{2}[/tex]

[tex]-14[/tex]

Part ii) x= -3 and x= 0

In this problem we have

[tex]a=--3[/tex]

[tex]b=0[/tex]

[tex]f(a)=f(-3)=3(-3)^{2} -2(-3)+5=38[/tex]  

[tex]f(b)=f(0)=3(0)^{2} -2(0)+5=5[/tex]

Substitute

[tex]\frac{5-38}{0+3}[/tex]

[tex]\frac{-33}{3}[/tex]

[tex]-11[/tex]

Part iii) x= (1-h) and x=(1+h)

In this problem we have

[tex]a=-(1-h)[/tex]

[tex]b=(1+h)[/tex]

[tex]f(a)=f(1-h)=3(1-h)^{2} -2(1-h)+5=3(1-2h+h^2)-2+2h+5=3-6h+3h^2+2h+3=3h^2-4h+6[/tex]  

[tex]f(b)=f(1+h)=3(1+h)^{2} -2(1+h)+5=3(1+2h+h^2)-2-2h+5=3+6h+3h^2-2h+3=3h^2+4h+6[/tex]  

Substitute

[tex]\frac{(3h^2+4h+6)-(3h^2-4h+6)}{1+h-(1-h)}[/tex]

[tex]\frac{8h}{2h}[/tex]

[tex]4[/tex]

Answer:

The correct option is 4) 0.72.

Step-by-step explanation:

Consider the provided information.

Let us consider that there are 100 members.

(Note: you can take any number the answer will remain the same.)

90% of its members drank protein shakes and of the members who drank  protein shakes.

90% of 100 is 90.

Thus, 90 members drank protein shake.

Of the members who drank   protein shakes, 30% took weight-loss medication.

30% of 90 is 27.

That means 27 out of 90 took weight loss medication.

Out of 100 members 90 drank protein shakes that means 10 members does not take protein shakes.

Only 10% of members  who did not drink protein shakes took weight-loss medication.

10% of 10 is 1, that means 1 member out of 10 took weight loss medication.

Thus the required table is:

                                        Medication   Not Medication      Total

Drank shakes                       27                   63                      90

Doesn't Drank shakes          1                      9                        10

Total                                      28                   72                     100

Now we need to find the probability that a gym member does not take weight-loss medication.

72 out of 100 members does not take weight-loss medication.

Therefore, the required probability is: [tex]\frac{72}{100}=0.72[/tex]

Hence, the correct option is 4) 0.72.

Answer:

x > - 2

Step-by-step explanation:

Given

7 + x > 5 ( subtract 7 from both sides )

x > - 2

Answer: 55/7π

Step-by-step explanation:

circumference = 2πr

2πr = 55/7

r = 55/14π

d = 2r

d = 55/7π

Answer:

b. y=10x

Step-by-step explanation:

                                                             1

                                                            1.5

                                                             2

                                                            2.5

y represents distance (miles): 5

                                                 10

                                                 15

                                                 20

                                                 25

let the 2 points be:  (1,10) and (2,20) [from the given information]

then the equation of it can be given as :

[tex]y-B=(\frac{D-B}{C-A} )*(x-A)[/tex]

[tex]y-10=(\frac{20-10}{2-1} )*(x-1)\\[/tex]

this is also equal to, [tex]y-10=10*(x-1)\\y-10=10x-10\\y     =10x-10+10\\y=10x[/tex]

Answer:

cot(∅) = [tex]\frac{10\sqrt{15} }{15}[/tex]

Step-by-step explanation:

tan ∅ and cot ∅ are inverse functions

therefore the inverse of

tan ∅ = √15 / 10

is equal to

cot ∅ = 10 / √15

Rationalizing the denominator

[tex]\frac{10}{\sqrt{15} }[/tex] * [tex]\frac{\sqrt{15} }{\sqrt{15} }[/tex]

cot ∅ = [tex]\frac{10\sqrt{15} }{15}[/tex]

Answer:(2\sqrt(15))/(3)

Step-by-step explanation:

Answer:

$18

Step-by-step explanation:

The initial price is $25

When the first 10% is off, the new amount is (100 - 10)% x 25

= 0.9 x 25

= 22.5

With an additional 20%

the new amount is (100 - 20)% x 22.5

= 0.8 x 22.5

= $18

The final price of the shirt is $18.00.

To find the final price of the shirt, we need to apply the discounts consecutively to the original price.

 First, we calculate the discount from two weeks ago, which was 10% off the original price of $25.00. A 10% discount is the same as multiplying the price by 0.9 (since 100% - 10% = 90%, or 0.9 in decimal form).

 So, after the first discount, the price of the shirt is:

[tex]\[ \text{Price after first discount} = 25 \times 0.9 = 22.50 \][/tex]

 Next, we apply the additional 20% discount to the original price, not to the already discounted price.

This means we calculate 20% of $25.00 and subtract that from the original price. A 20% discount is the same as multiplying the price by 0.8 (since 100% - 20% = 80%, or 0.8 in decimal form).

 So, after the second discount, the price of the shirt is:

[tex]\[ \text{Price after second discount} = 25 \times 0.8 = 20.00 \][/tex]

However, since the second discount is additional, we need to apply it to the already discounted price of $22.50.

Therefore, we calculate 20% of $22.50 and subtract that from $22.50.

[tex]\[ \text{Additional discount amount} = 22.50 \times 0.2 = 4.50 \][/tex]

[tex]\[ \text{Price after additional discount} = 22.50 - 4.50 = 18.00 \][/tex]

 Thus, the final price of the shirt after both discounts is $18.00.

Answer:

16

Step-by-step explanation:

All of the lengths of the rectangle are 4 making the area 4*4=16

Answer:

20 liters of 60% acid solution and 60 liters of 80% acid solution

Step-by-step explanation:

Let the amount of 60% solution needed be "x", and

amount of 80% solution needed be "y"

Since we are making 80 liters of total solution, we can say:

x + y = 80

Now, from the original problem, we can write:

60% of x + 80% of y = 75% of 80

Converting percentages to decimals by dividing by 100 and writing the equation algebraically, we have:

0.6x + 0.8y = 0.75(80)

0.6x + 0.8y = 60

We can write 1st equation as:

x = 80 - y

Now we substitute this into 2nd equation and solve for y:

0.6x + 0.8y = 60

0.6(80 - y) + 0.8y = 60

48 - 0.6y + 0.8y = 60

0.2y = 12

y = 12/0.2

y = 60

Also, x is:

x = 80 - y

x = 80 - 60

x = 20

Thus, we need

20 liters of 60% acid solution and 60 liters of 80% acid solution