A new alloy is made by mixing 72 grams of iron with 9 grams of zinc. How many grams of iron are required to make the alloy when combined with 144 grams of zinc?

A) 992 grams
B) 1,152 grams
C) 1,226 grams
D) 1,445 grams

Answer:

3

Step-by-step explanation:

12 divided by 4 is 3, 3 times 3 is 9 bam

Answer:

36

Step-by-step explanation:

12 = 2 * 2 * 3 = 2^2 * 3

4 = 2 * 2 = 2^2

9 = 3 * 3 = 3^2

For the least common multiple, use common and not common factors with the largest exponent.

Use 2^2 and 3^2

LCM = 2^2 * 3^2 = 4 * 9 = 36

Answer:

t ≤ 33°F

Step-by-step explanation:

Answer:

t ≤ 33° F

Step-by-step explanation:

Answer:

540°

Step-by-step explanation:

To find the acceleration of an object with a force of 7.92 N and mass of 3.6 kg, use the formula F = ma to calculate the acceleration as 2.2 m/s².

The force acting on the object can be calculated using the formula F = ma, where F is the force, m is the mass, and a is the acceleration.

Given F = 7.92 N and m = 3.6 kg, plug these values into the formula: F = 7.92 N, m = 3.6 kg.

Calculate the acceleration using the formula: a = F/m = 7.92 N / 3.6 kg = 2.2 m/s².

Therefore, the acceleration of the object with a force of 7.92 N and mass of 3.6 kg is 2.2 m/s².

Answer:

  B.  4 miles

Step-by-step explanation:

Jim ran a total of ...

  6.5 +5 +3 +2 +3.5 +4 = 24 . . . . miles

Then his average was ...

  (24 miles)/(6 days) = 4 miles/day

Answer:

step 1

Step-by-step explanation:

Alanna divided one side of the equation by 4 but multiplied the other side by 444. Alanna should have divided both sides of the equation by 4 to isolate c.

Alanna's mistake was dividing the equation by 12.4 instead of dividing both sides by 4.

Alanna made a mistake in the second step of solving the equation. The correct step should be as follows:

Step 1: 4c = 12

Step 2: Divide both sides by 4, not 4.4: (4c) / 4 = 12 / 4

Step 3: c = 3

So, the correct solution is c = 3, not c = 48 as Alanna calculated.

Alanna's mistake in solving the equation 4c = 12 occurred during the second step of the process. When attempting to isolate the variable "c," she divided both sides of the equation by 4, but her error lies in the value she used for this division. Instead of correctly dividing by 4, she mistakenly divided by 4.4.

The correct approach in this situation is to perform the same mathematical operation on both sides of the equation to maintain its balance. Dividing both sides by 4 allows us to isolate "c" and find its value. When we divide 12 by 4, we get 3, which is the correct solution to the equation.

In contrast, Alanna's incorrect division by 4.4 led her to the erroneous result of c = 48. This error likely arose from a simple calculation mistake. It's crucial to pay attention to each step of solving equations to avoid such errors, as they can significantly affect the final solution and lead to incorrect conclusions.

In summary, Alanna's mistake was dividing both sides of the equation by 4.4 instead of 4, resulting in the incorrect solution c = 48, when the correct solution is c = 3.

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Answer:D.27

They already won 12 games (80% of 15%) and need or win 15 more.

Check: 15+12 =27 =90%

30 30

Answer:

C

Step-by-step explanation:

First, find out how many games they won:

x/15 = 80/100

Cross multiply

x × 100 = 15 × 80

100x = 1200

x = 12

They won 12 out of 15 games

Second, find out how many wins out of 30 games are needed to have a 90% winning percentage

x/30 = 90/100

Cross multiply

x × 100 = 30 × 90

100x = 2700

x = 27

27 game wins are needed to have a 90% winning percentage

Lastly, find the difference between 27 wins (total needed) and 12 wins (total number of wins they currently have)

27 - 12 = 15

They need to win 15 more games to have a 90% winning percentage

Answer:

1 customer per 2 minutes or 1/2 of a customer per 1 minute(I would go with the 1st one since you can't have 1/2 of a customer.)

Step-by-step explanation:

The customers were entering at the rate of 1 customer in 2 minutes.

A unit rate means a rate for one of something.

Given that, 8 customers entered a store over the course of 16 minutes.

8 customers in 16 minutes

1 customer = 16/8 = 2 minutes.

Hence, The customers were entering at the rate of 1 customer in 2 minutes.

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Answer:

Option "B" is the correct answer to the following question.

Step-by-step explanation:

Given:

Rate of annual interest = 0.85%

Find

Value of 0.85% in decimal

Computation:

To convert any percent number into a decimal, we have to divide that number by 100.

So,

Value of 0.85% in decimal = [tex]\frac{0.85}{100}[/tex]

Value of 0.85% in decimal = 0.0085

Note: We have to eliminate the percent symbol from the given number.

Answer:

286 in³

Step-by-step explanation:

7×5 = 35

35×2 = 70in

9×5 = 45

45×2 = 90in

9×7 = 63

63×2 = 126in

70+90+126

=286in³

Answer:

C

Step-by-step explanation:

Using the formula for the area of a circle (A = πr²), with a radius of 15 mm and π approximated as 3.14, the area of the compass is found to be 706.5 mm². Option C is the correct answer.

To find the area of the compass, which is circle-shaped, we can use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius. Given the radius of the compass is 15 millimeters, we substitute 15 mm for r in the formula:

A = π(15 mm)²

A = 3.14(225 mm²)

A = 706.5 mm²

Therefore, the approximate area of the compass is 706.5 mm², which corresponds to option C.

Answer:

0.00037037037 m3 / kg

Step-by-step explanation:

Answer:

D 18

Step-by-step explanation:

3z + 6

Let z=4

3*4 +6

Multiply first

12+6

Then add

18

Known :

z = 4

Asked :

3z + 6 = ...?

Answer :

3z + 6

= 3(4) + 6

= 12 + 6

= 18

So, the value of 3z + 6 is 18 (D)

Hope it helpful and useful :)

Answer:

10% probability that each sample of size 3 is selected

Step-by-step explanation:

Each sample has the same probability of being selected.

There are 10 samples.

This means that the probability of each sample being selected is:

1/10 = 0.1

10% probability that each sample of size 3 is selected

The probability of each possible sample that can be drawn from a finite population of size N can be calculated using the hypergeometric distribution.

The formula for calculating the probability of getting k successes (in this case, a successful sample of size 3) in a sample of size n, drawn without replacement from a population of size N, is:

P(k) = (C(k, K) * C(n - k, N - K)) / C(n, N)

where C(k, K) is the number of ways to choose k items from a set of K items, and C(n - k, N - K) is the number of ways to choose n - k items from a set of N - K items.

For part (a), N = 4, n = 3, and K = 3. Therefore, there is only one possible successful sample of size 3, and the probability of getting that sample is:

P(3) = (C(3, 3) * C(0, 1)) / C(3, 4) = 1/4

For part (b), N = 6, n = 3, and K = 3. Therefore, there is only one possible successful sample of size 3, and the probability of getting that sample is:

P(3) = (C(3, 3) * C(0, 3)) / C(3, 6) = 1/20

For part (c), N = 12, n = 3, and K = 3. Therefore, there are C(3, 12) = 220 possible successful samples of size 3, and the probability of getting any one of them is:

P(3) = (C(3, 3) * C(0, 9)) / C(3, 12) = 1/220

For part (d), N = 18, n = 3, and K = 3. Therefore, there are C(3, 18) = 816 possible successful samples of size 3, and the probability of getting any one of them is:

P(3) = (C(3, 3) * C(0, 15)) / C(3, 18) = 1/816

Therefore, the probabilities of each possible sample of size 3 that can be drawn from the given populations are:

(a) 1/4

(b) 1/20

(c) 1/220

(d) 1/816

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Answer:

(A)3,500 + 0.06x > 4,000 + 0.04x

Step-by-step explanation:

Jose's Earnings

Monthly Salary = $3,500

6% commission on his sales, x =0.06x

Total = 3500+0.06x

Maris' Earnings

Monthly Salary = $4,000

4% commission on her sales, x =0.04x

Total = 4000+0.04x

If Jose's earnings be greater than Maris' earnings, then:

3500+0.06x > 4000+0.04x

Answer:

Maureen's null hypothesis is, H₀: p₁ ≥ p₂.

Step-by-step explanation:

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies wants test whether her goal of shipping 100% orders within 24 hours is achieved or not.

After reviewing the order filling operations at her warehouses she determines that neither the East coast nor the West coast warehouse has achieved the goal. But the East Coast warehouse has consistently out-performed the West Coast warehouse.

To check whether this determination is correct or not Maureen's staff randomly selected 200 orders from the West Coast warehouse (population 1) and 400 orders from the East Coast warehouse (population 2).

Of the 200 orders from the West Coast warehouse, 190 were shipped within 24 hours. And of the 400 orders from the East Coast warehouse, 372  were shipped within 24 hours.

The hypothesis can be defined as follows:

H₀: The proportion of orders that were shipped within 24 hours is not more for East Coast warehouse than for West Coast warehouse, i.e. p₁ ≥ p₂.

Hₐ: The proportion of orders that were shipped within 24 hours is more for East Coast warehouse than for West Coast warehouse, i.e. p₁ < p₂.

Thus, Maureen's null hypothesis is, H₀: p₁ ≥ p₂.

Maureen McIlvoy's null hypothesis would likely be that there is no significant difference in the shipment times of the East Coast and West Coast warehouses. Despite the initial data suggesting better performance at the West Coast, more statistical analysis such as a z-test or t-test would be required to confirm if there is a significant difference.

In this context, Maureen McIlvoy, who is the owner and CEO of a mail order business for wind surfing equipment, is evaluating the efficiency of order fulfilment at her warehouses. Given her goal is to ship 100% of her orders within 24 hours, she is interested in comparing the performance of the East Coast warehouse to the West Coast warehouse.

When conducting such an analysis, a null hypothesis serves as the baseline or default expectation. In this case, Maureen's null hypothesis could possibly be that there's no difference in the performance between the two warehouses in terms of orders shipped within 24 hours, despite the past performance.

With the given data of 190 out of 200 orders shipped on time at the West Coast, and 372 out of 400 orders shipped on time at the East Coast, we can further analyze the percentages of timely shipping - 95% and 93% respectively. Though the West coast performed better in the examined sample, this is not sufficient to reject the null hypothesis that the performances are identical without further statistical testing such as a z-test or t-test.

On the other hand, her alternative hypothesis could state that there is a significant difference in the efficiency of the two warehouses in achieving the 24-hour shipping target.

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Answer:

-1/6

Step-by-step explanation:

When dividing 2 by -12 you would use 2 as the numerator and -12 as the denominator and then simplify it by dividing both by two to end up with -1/6

Answer:

figure to out

Step-by-step explanation:

A sequence [tex]\{a_n\}[/tex] is arithmetic if the difference between consecutive terms is some fixed number, regardless of which pair of consecutive terms you pick out of the sequence.

For example, the following sequences are arithmetic:

1, 2, 3, 4, 5, 6, ... (difference = 1)

-25, -20, -15, -10, -5, ... (difference = 5)

2. Carla's sequence is not arithmetic, because the differences between consecutive terms are all different:

13 - 11 = 2

17 - 13 = 4

25 - 17 = 8

She can adjust the sequence by changing the last two numbers to 15 and 17, since this makes the difference fixed:

13 - 11 = 2

15 - 13 = 2

17 - 15 = 2

and so on.

3. The sequence

45, 48, 51, 54, ...

is arithmetic with difference 3 between terms. Recursively, we can write the [tex]n[/tex]th term, [tex]a_n[/tex], in terms of the previous, [tex](n-1)[/tex]th term, [tex]a_{n-1}[/tex]:

[tex]a_n=a_{n-1}+3[/tex]

By this definition, we can just as easily write the [tex](n-1)[/tex]th term in terms of the [tex](n-2)[/tex]th term:

[tex]a_{n-1}=a_{n-2}+3[/tex]

Then, substituting this into the previous equation, we have

[tex]a_n=(a_{n-2}+3)+3=a_{n-2}+2\cdot3[/tex]

We can continue this process to write [tex]a_n[/tex] in terms of [tex]a_1[/tex]:

[tex]a_{n-2}=a_{n-3}+3\implies a_n=a_{n-3}+3\cdot3[/tex]

[tex]a_{n-3}=a_{n-4}+3\implies a_n=a_{n-4}+4\cdot3[/tex]

and so on. (You might notice that the subscript of the term on the right side, and the number of 3s being added, together sum to [tex]n[/tex].) The pattern continues down to

[tex]a_n=a_1+(n-1)\cdot3[/tex]

The first term in this sequence is [tex]a_1=45[/tex], so we have

a. [tex]a_n=45+3(n-1)=42+3n[/tex]

where [tex]n=1,2,3,\ldots[/tex].

b. You can fill in the blanks by just adding 3 to the previous term:

45, 48, 51, 54, 57, 60, 63, 66, 69, ...

Then, using the formula found in (a), the 15th term of the sequence is

[tex]a_{15}=42+3\cdot15=87[/tex]

To find the volume of air in a beach ball with a 12-inch diameter, one must calculate the volume of a sphere using the formula V = 4/3 π r^3, with the radius being half the diameter, resulting in approximately 904.78 cubic inches.

The question you're asking pertains to the calculation of the volume of a sphere, as the beach ball is essentially a spherical object. When you have a diameter, the radius (which is half of the diameter) is necessary for the volume calculation. The formula for the volume of a sphere is given by V = 4/3 π r^3, where V is the volume, π (pi) is approximately 3.14159, and r is the radius of the sphere.

First, we convert the diameter into the radius by dividing by 2: 12 inches / 2 = 6 inches. Then, we use the formula to calculate the volume: V = 4/3 π • (6 inches)^3.

Therefore, the volume is: V = 4/3 π • 216 inches^3. After calculating this, we find that the volume of air inside the beach ball is approximately 904.78 cubic inches, assuming no other factors are affecting the volume, such as the thickness of the ball's material.

Answer:

The repair person did 5 hours of work.

Step-by-step explanation:

155 = 25x + 30

125 = 25x

5 = x

Answer:

5 hours

Step-by-step explanation:

155 less 30 initial = 125 divided by 25 an hour = 5

Answer:

The values  [tex]x=-6[/tex] and [tex]x=-4[/tex] satisfy this inequality

Step-by-step explanation:

Let us look at each individual value of the set  {−6, −4, −3, −1, 0, 2} with regards to the inequality

[tex]x=-6\\\\\frac{-1}{2}(-6)+3\geq 5\\3+3\geq 5\\\\6\geq 5[/tex]

As this inequality is true, [tex]x=-6[/tex] satisfies this inequality

[tex]x=-4\\\\\frac{-1}{2}(-4)+3\geq 5\\\\2+3\geq 5\\\\5\geq 5[/tex]

As this inequality is true, [tex]x=-4[/tex] satisfies this inequality

[tex]x=-3\\\\\frac{-1}{2}(-3)+3\geq 5\\\\\frac{3}{2} +3\geq 5\\\\\frac{9}{2} \geq 5[/tex]

As this inequality is false, [tex]x=-3[/tex] does not satisfy the inequality

[tex]x=-1\\\\\frac{-1}{2}(-1)+3\geq 5\\\\\frac{1}{2} +3\geq 5\\\\\frac{7}{2} \geq 5[/tex]

As this inequality is false, [tex]x=-1[/tex] does not satisfy the inequality

[tex]x=-0\\\\\frac{-1}{2}(0)+3\geq 5\\\\3\geq 5[/tex]

As this inequality is false, [tex]x=0[/tex] does not satisfy the inequality

[tex]x=2\\\\\frac{-1}{2}(2)+3\geq 5\\\\-1+3\geq 5\\\\2\geq 5[/tex]

As this inequality is false, [tex]x=2[/tex] does not satisfy the inequality

The values from the set less than -4 is -6

Given the inequality expression

Subtract 3 from both sides

−1/2x + 3 - 3 ≥ 5 - 3

-1/2x ≥ 5 - 3

-x ≥ 2 * 2

- x ≥ 4

x ≤  -4

This shows that the value of x must be less than -4. The values from the set less than -4 is -6

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Answer: 4/3

Step-by-step explanation:

The method of SOH CAH TOA helps tremendously in this equation.

TOA is the one necessary for this problem as it means tangent = opposite side/adjacent side.

Opposite side = 4

Adjacent side = 3

Opposite side/adjacent side = 4/3

Answer:

Step-by-step explanation:

Let w represent the width of the rectangle. Then the length is w+6, and the perimeter is ...

  P = 2(L +W)

  60 = 2((w+6) +w) . . . substitute known values

  30 = 2w +6 . . . . . . . .divide by 2, collect terms

  15 = w +3 . . . . . . . . . divide by 2 again

  12 = w

  w+6 = 18

The length is 18 units; the width is 12 units.

Answer:

suee has 18-x-5

tony has 18+x-((18+x)/2)

Step-by-step explanation:

Can i get brainliest plz

Answer:

s(18 - x)-5 t(18x/2) is initial

they now have;

t( 9x) s(13-x)

Step-by-step explanation:

Answer:

2.326

Step-by-step explanation:

They are only asking which z-score should you use. To determine find the confidence interval which is 98% or .98.

Subtract this number by 1 and divide by 2.

1-.98=.02/2=.01

Find the correlating z-score for z.01 on the z-score chart which is 2.326

The z-value for a 98% confidence level in statistics, used in constructing confidence intervals, is approximately 2.33 standard deviations away from the mean.

The question falls under the area of statistics, specifically, confidence intervals. In order to find the z-value for a 98% confidence level, we turn to the z-table or use a z-score calculator. The z-value for a 98% confidence level is approximately 2.33. This value represents the number of standard deviations away from the mean that your confidence interval is.

The idea here is that for us to be 98% confident that our interval contains the true population mean or proportion, our interval must extend 2.33 standard deviations on either side of our sample mean or proportion. Thus, in the context of your survey of office managers working overtime, this z-value would be used to calculate your confidence interval for the proportion of all office managers who work overtime.

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Answer:

1 Litre

Step-by-step explanation:

Convert to similar units. 1.2L = 1,200 ml

1200 - 200 = 1000 or 1L

1 litre of water is left in his water bottle

Answer:

B

Step-by-step explanation:

The solution of the equation are,

⇒ 5x = 10²

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The expression is,

⇒ log 5x³ - log x² = 2

Now, We can simplify by the definition of logarithmic we get;

⇒ log (5x³ / x²) = 2

⇒ log (5x) = 2

⇒ 5x = 10²

Thus, The solution of the equation are,

⇒ 5x = 10²

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