Solve the system of equations by using SUBSTITUTION.
y = 3x
x+y= -32
A) (8, 24)
B) (-8, -24)
C (-16, -48)
D (16, 48)
Plz give a explanation

Answer:

-8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ratio is 640 grams butter to x grams of flour =2/3.  2/3=640/x  

Cross multiply.  2x=3*640      2x=1920     x=960

Proof:  640/960 = 2/3

Answer:

Step-by-step explanation:

Answer:

\( \frac{5}{10} \times \frac{2}{1} = \frac{10}{10} = 1\)

\( \frac{1}{10} \times \frac{8}{3} = \frac{8}{30} = \frac{4}{15} \)

\( \frac{2}{6} \times \frac{12}{6} = \frac{24}{36} = \frac{2}{3} \)

\( \frac{1}{4} \times \frac{1}{3} = \frac{1}{12} \)

\( \frac{1}{5} \times \frac{1}{1} = \frac{1}{5} \)

We can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

A 95% confidence interval for the population mean can be constructed using the t-distribution when the sample size is small (<30) or the population standard deviation is unknown.

In this case, we have a random sample of 46 people with a mean body mass index (BMI) of 27.2 and a standard deviation of 6.0.

Thus, we need to use the t-distribution to construct the confidence interval.

The formula for the confidence interval is as follows:

Upper limit of the confidence interval:27.2 + (2.013) (6.0/√46) = 29.032Lower limit of the confidence interval:27.2 - (2.013) (6.0/√46) = 25.368

Therefore, the 95% confidence interval for the population mean BMI is (25.368, 29.032).

This means that we can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

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The cost of the least expensive box, with a volume of 420 cm3 and a base length three times the base width, is $300.

Let x be the width of the base. Then the length of the base is 3x. The height of the box is \(420/(3x^2) = 42/x^2.\)

The cost of the top and bottom is \(2(0.04)(42/x^2) = 8.4/x^2.\)

The cost of the sides is \(2(3x)(42/x^2) = 252/x.\)

The total cost is\(8.4/x^2 + 252/x.\)

To minimize the cost, we need to minimize \(8.4/x^2 + 252/x.\)

We can factor the expression as follows:

\(8.4/x^2 + 252/x = (8.4 + 252x)/(x^2)\)

We can see that the expression is minimized when x is as large as possible. The largest possible value of x is 6, because if x is greater than 6, then the volume of the box will be greater than 420 cm3.

When x = 6, the cost of the box is \((8.4 + 252*6)/(6^2) = 300\).

Therefore, the least expensive box costs $300.

Here is a table of the cost of the box for different values of x:

x | Cost

1 | 606

2 | 450

3 | 360

4 | 300

5 | 264

6 | 252

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Answer:

x = 138° because they are alternate interior angles. Alternate interior angles are congruent.

Step-by-step explanation:

The square root function contains a variable under the square root sign. The cube root function contains a variable under the cube root sign.

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between varying quantities and other variables.

A variable under the square root sign is present in a square root function, and a variable under the cube root sign is present in a cube root function.

Zero has a square root of zero, and one has a square root of one. Keep in mind that the graph only contains points where x and y are positive. For instance, using the imaginary number i is necessary when taking the square root of a negative number.

The square root function is f(x) = √x

For positive values, the graph resembles the square root graph, but cube roots can also be negative, making this equation infinite for all real numbers. Recall that a negative number will result from being multiplied an odd number of times.

The cube root function is f(x) = ³√x

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Answer:

1) 3/5

2) 20

3) 60%

Step-by-step explanation:

1) If 3 out of the 5 cats are ginger, that is your fraction with the total cats being the denominator.

2) You will then find out what number makes 100 when multiplied by 5. That number being 20.

3) With the denominator being 100, you would also multiply the numerator, and 3 × 20 is 60, so it would be 60/100, or 60%

Answer:

Step-by-step explanation:

Given that Zahra has 5 cats. 3 of those cats are ginger. We could also express that statement as, "3 out of 5 cats are ginger."  

Note: 3/5 = 60/100 = 0.60 = 60%

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Answer:

Yh

Step-by-step explanation:gg

Answer:

the answer is that i truly am gay and  that i will always be gay.

Step-by-step explanation:

a) To find the z-score for the number of sags (8998) for this transformer, we can use the formula:

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation. In this case, x = 8998, μ = 339 (mean number of sags per week), and σ = 30 (standard deviation of the sag distribution). Plugging in these values, we can calculate the z-score:

z = (8998 - 339) / 30 = 8.53

Therefore, the z-score for the number of sags of 8998 for this transformer is approximately 8.53.

b) To find the z-score for the number of swells for this transformer, we can use the same formula as above. In this case, x = 70 (number of swells observed), μ = 198 (mean number of swells per week), and σ = 25 (standard deviation of the swell distribution). Plugging in these values, we can calculate the z-score:

z = (70 - 198) / 25 = -5.12

The z-score for the number of swells of 70 for this transformer is approximately -5.12.

The z-score represents the number of standard deviations an observation is away from the mean. A positive z-score indicates that the observation is above the mean, while a negative z-score indicates that it is below the mean. In the case of the number of sags for this transformer, the z-score of 8.53 suggests that the observed value of 8998 is significantly higher than the mean. On the other hand, for the number of swells, the z-score of -5.12 indicates that the observed value of 70 is significantly lower than the mean.

In summary, the transformer's number of sags (8998) is considerably higher than the average for the sample, while its number of swells (70) is significantly lower than the average. These z-scores provide a standardized measure of deviation from the mean, allowing for meaningful comparisons across different distributions.

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The correct statement for a monopolistic competitor in long-run equilibrium is: p = ATC = MC = MR. The correct answer is B.

In long-run equilibrium, a monopolistic competitor maximizes its profit by setting its marginal cost (MC) equal to its marginal revenue (MR) and producing the quantity where MC = MR. At this quantity, the firm charges a price (p) equal to the average total cost (ATC) to cover all its costs.

By setting the price equal to the average total cost and producing where marginal cost equals marginal revenue, the monopolistic competitor achieves a balance between maximizing profits and covering costs. This equilibrium condition ensures that the firm does not have the incentive to enter or exit the market in the long run, as it is earning normal profits.

Therefore, The correct answer is B. p = ATC = MC = MR.

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Answer:

y-1=\(\frac{5}{6}\)(x+8)

Step-by-step explanation:

1. y-y1=m(x-x1) (point slope form)

2. y1 is the y of your given point and x1 is the x of your given point

3. m is the slope

Answer:

The answer is 13 1/8ft3

Explanation:

Substitute into the formula:

Volume = 3 1/2 x 2 1/2 x 1 1/2

= 7/2 x 5/2 x 3/2

= 105/8

= 13 1/8 ft3

Answer:

\(\dfrac{8}{3}\ \text{inches}\) or \(2.67\ \text{inches}\)

Step-by-step explanation:

The photo has length 6 inches and width 4 inches.

The ratio of length to breadth is

\(\dfrac{l}{w}=\dfrac{6}{4}=\dfrac{3}{2}\)

Now the reduced length of the photo is 4 inches.

Let \(x\) be the reduced width of the photo

\(\dfrac{3}{2}=\dfrac{4}{x}\\\Rightarrow x=\dfrac{4}{3}\times2\\\Rightarrow x=\dfrac{8}{3}\ \text{inches}=2.67\ \text{inches}\)

The width of the reduced photo is \(\dfrac{8}{3}\ \text{inches}\) or \(2.67\ \text{inches}\).

Answer:

A. And E.

Step-by-step explanation:

This is Simple, Just replace X With 2. Then Add :)

A = 2 + 3= 5

E: 2 - 7 = -5 ( Since your Subtracting a Bigger number From a Smaller number, Count Backwards 7 times from 2 on the number line )

Hope this helps

Answer:

The answer is 10.9

Step-by-step explanation:

hope this helps

336.752÷31= 10.86296774

And round it to the nearest ten which is 10.9

To rewrite the expression $3x^2 + 14x + 8$ in the form $(3x + a)(x + b)$, we need to find integers $a$ and $b$ such that the product of these two terms gives the original expression.

First, we need to find the factors of $3 \times 8 = 24$. The pairs of factors are: $(1, 24), (2, 12), (3, 8), (4, 6)$. We need a pair that has a sum of $14$ (the coefficient of the middle term). The pair $(2, 12)$ meets this requirement.

Now we can write the expression as:

$(3x^2 + 2x) + (12x + 8) = (3x + 2)(x + 4)$

So, $a = 2$ and $b = 4$. The value of $a - b$ is $2 - 4 = -2$.

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Answer:

See graph below

Step-by-step explanation:

The domain is (-∞,∞) and the range is [1,∞)

The Egyptian fraction representation for 7/9 using Fibonacci's Greedy Algorithm is 1/8 + 1/5 + 1/3 + 1/1080 = 711/1080.

Let's find the Egyptian fraction representation for the fraction 7/9.

1. Begin by representing the fraction 7/9 visually with a rectangle. Divide the rectangle into 9 equal parts horizontally and mark 7 parts.

```

---------------

| | | | | | | |

---------------

```

2. Now, let's use Fibonacci's Greedy Algorithm to find the Egyptian fraction representation for 7/9.

  a. Start with the largest Fibonacci number less than or equal to the denominator, which in this case is 8 (Fibonacci sequence: 1, 1, 2, 3, 5, 8).

  b. Take one unit of this Fibonacci number and mark it as a fraction on the rectangle.

```

---------------

| | | | | | | |

----|----------

```

  c. Subtract this fraction (1/8) from the original fraction (7/9) to get 7/9 - 1/8 = 41/72.

  d. Repeat steps a-c with the remaining fraction (41/72) until the numerator becomes 1.

  e. The sum of the fractions obtained in step b will be the Egyptian fraction representation of 7/9.

3. Applying the algorithm further:

  a. The largest Fibonacci number less than or equal to the remaining fraction (41/72) is 5.

  b. Take one unit of this Fibonacci number and mark it as a fraction on the rectangle.

```

---------------

| | | | | | | |

----|----|-----

```

  c. Subtract this fraction (1/5) from the remaining fraction (41/72) to get 41/72 - 1/5 = 7/360.

  d. Since the numerator is still greater than 1, we need to repeat steps a-c.

  e. The largest Fibonacci number less than or equal to 7/360 is 3.

  f. Take one unit of this Fibonacci number and mark it as a fraction on the rectangle.

```

---------------

| | | | | | | |

----|----|-----

      |

```

  g. Subtract this fraction (1/3) from the remaining fraction (7/360) to get 7/360 - 1/3 = 1/1080.

  h. Since the numerator is now 1, we stop the algorithm.

4. The sum of the fractions obtained in step b is the Egyptian fraction representation of 7/9:

  1/8 + 1/5 + 1/3 + 1/1080 = 135 + 216 + 360 + 1/1080 = 711/1080.

Therefore, the Egyptian fraction representation for 7/9 using Fibonacci's Greedy Algorithm is 1/8 + 1/5 + 1/3 + 1/1080 = 711/1080.

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Answer:

x=1

Step-by-step explanation:

3*1=3  3*3=9

  3+9=12

0.0910, I think.

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My dyslexia did not like theese numbers

The line of best fit before the transformation is y = 0.6366x + 2.3220 and after the transformation is y = 0.0411x + 0.5134

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

\(\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}\)

We have data as shown in the table.

Let's suppose the line of best fit is:

y = mx + c

Before the transformation, we can calculate the line of best fit.

m = 0.6366

c = 2.3220

y = 0.6366x + 2.3220

After transformation:

Line of best fit after transformation:

y = Mx + C

M = 0.0411

C = 0.5134

Line of best after transformation

\(\rm Transformation = \ log_1_0(y \ value)\)

y = 0.0411x + 0.5134

Thus, the line of best fit before the transformation is y = 0.6366x + 2.3220 and after the transformation is y = 0.0411x + 0.5134

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Answer:

4

Step-by-step explanation:

The total utility of 4 units is 50 and the marginal utility is 5

Total utility is the sum of satisfaction that is derived from the consumption of units of a good or service.

Total utility can be determined by adding the marginal utility of each unit that is consumed.

Total utility of consuming 4 units = marginal utility of the first unit + marginal utility of the second unit + marginal utility of the third unit + marginal utility of the fourth unit  

20 + 15 + 10 + 5 = 50

Marginal utility is the change in total utility when consumption increases by unit. Marginal utility is 5

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On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.

To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.

Given:

9 staff members taking calls.

On average, one call arrives every 5 minutes (standard deviation of 5 minutes).

Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).

To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:

"M" stands for Markovian or memoryless arrival and service times.

"c" represents the number of servers.

In our case, we have an M/M/9 queuing model since we have 9 staff members.

The average waiting time for a customer on hold is given by the following formula:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

Where:

c = number of servers (staff members) = 9

μ = average service rate (1 / average service time)

λ = average arrival rate (1 / average interarrival time)

ρ = λ / (c * μ)

First, let's calculate the average arrival rate (λ):

λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute

Next, calculate the average service rate (μ):

μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute

Now, calculate ρ:

ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407

Finally, calculate the waiting time:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))

≈ 1.16 minutes

Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.

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Answer:

...

Step-by-step explanation:

y=mx+b

y= -7/5x-3

Answer:

y=-7/5x-3

Step-by-step explanation:

Answer:23 mm

Step-by-step explanation:

add both 15 and 8 because they are as long as the one on the bottom

Answer:

70

Step-by-step explanation:

find the small unknown side by subtracting the two sides across from it. 12-7=5. add the 15 and 8 for the big unknown side. 15+8=23. add all the sides. 12+15+7+8+5+23=70