A leaf blower runs on a mixture of gas and oil. The ratio of ounces of gas to ounces of oil is 40 to 1. How many ounces of gas does the leaf blower need for 3 ounces of oil?

Answer and Step-by-step explanation:

You are correct in that we need to use the Law of Sines: [tex]\frac{c}{sinC} =\frac{b}{sinB}=\frac{a}{sinA}[/tex].

Here, when we use the Law of Sines, we have: [tex]\frac{28}{sin(63)}=\frac{29}{sinB}[/tex].

Cross multiply:

(sinB) * 28 = (sin63) * 29

28sinB ≈ 25.839

sinB ≈ 0.9228

Now, in order to solve for B, we need to use inverse sin ([tex]sin^{-1}[/tex]):

[tex]sin^{-1}(sinB)=sin^{-1}(0.9228)[/tex]

The sines on the left cancel out, and we're left with:

B ≈ 67.3 degrees

Now, one thing to keep in mind when doing Law of Sines is that there is potentially more than one answer possible for the degree measure. The other degree measure can be found by subtracting this one from 180:

180 - 67.3 = 112.7 degrees.

Hope this helps!

Answer:

67.3° , 112.7°

Step-by-step explanation:

sinx = 0.9228

Take inverse of sin, you get:

x = 67.3389176683

Since sin is positive in first two quadrants, second angle is:

180 - 67.3389176683

= 112.6610823317

Answer: if you’re talking about the one on edge it’s:

3.1

4.2

5.2

42

Step-by-step explanation:

The cones are congruent so just copy the other cone and find the radius (dividing the diameter by 2)

Answers and Step-by-step explanations:

9. Subtract root x from both sides: [tex]\sqrt{x+12} =6-\sqrt{x}[/tex]

Square both sides: x + 12 = 36 - 12[tex]\sqrt{x}[/tex] + x

Subtract x and 36 from both sides: -24 = -12[tex]\sqrt{x}[/tex]

Divide both sides by -12: 2 = [tex]\sqrt{x}[/tex]

Square both sides again: x = 4

10. Switch the places of the two root expressions: [tex]\sqrt{4x-1} =1-2\sqrt{x}[/tex]

Square both sides: 4x - 1 = 1 - 4[tex]\sqrt{x}[/tex] + 4x

Subtract 4x and 1 from both sides: -2 = -4[tex]\sqrt{x}[/tex]

Divide by -4 from both sides: 1/2 = [tex]\sqrt{x}[/tex]

Square both sides again: x = 1/4

11. Square both sides: 4x^2 = 4x - 1

Move all the terms to one side: 4x^2 - 4x + 1 = 0

Factorize: (2x - 1)(2x - 1) = 0  ⇒  x = 1/2

12. Square both sides: 4x - 1 = 4 - 8x + 4x^2

Move all the terms to one side: 4x^2 - 12x + 5 = 0

(2x - 5)(2x - 1) = 0  ⇒  x = 5/2 or x = 1/2

Hope this helps!

Answer:

9. x = 4

10. x = ¼

11. x = ½

12. x = ½

Step-by-step explanation:

9. sqrt(x + 12) = 6 - sqrt(x)

Square both sides

x + 12 = 36 - 12sqrt(x) + x

12sqrt(x) = 24

sqrt(x) = 2

x = 4

10. 2sqrt(x) = 1 - sqrt(4x - 1)

Square both sides

4x = 1 - 2sqrt(4x - 1) + 4x - 1

-2sqrt(4x - 1) = 0

sqrt(4x - 1) = 0

4x - 1 = 0

x = ¼

11. 2x = sqrt(4x - 1)

4x² = 4x - 1

4x² - 4x + 1 = 0

4x² - 2x - 2x + 1 = 0

2x(2x - 1) - (2x - 1) = 0

(2x - 1)(2x - 1) = 0

x = ½

12. sqrt(4x - 1) = 2 - 2x

4x - 1 = (2 - 2x)²

4x - 1 = 4 - 8x + 4x²

4x² - 12x + 5 = 0

4x² - 2x - 10x + 5 = 0

2x(2x - 1) - 5(2x + 1) = 0

(2x - 1)(2x - 5) = 0

x = ½ , 5/2

x = 2.5 is rejected because it doesn't satisfy the equation

* when solving equations involving radicals, make sure to verify your answers by plugging in the values in the initial equation

Step-by-step explanation:

-6 + 7 = 2x

1 =2x

If you have to find the value of x then

1/2 = x

Answer:

f(x)=6

Step-by-step explanation:

By Substitution

f(x or coefficient of x)

=6 since X doesn't exist in question above

Final answer:

The value of f(x) is 6, indicating a constant function where the output is the same irrespective of the input. For constant functions, the total differential is zero as there is no change in the function value with varying x.

Explanation:

The question is asking for the value of f(x) when f(x) is equal to 6. This is a type of question that involves understanding how functions work. In this particular case, the question seems to be abstract, suggesting that f(x) = 6 for all x, indicating a constant function. A constant function is one where the output value is the same no matter what the input value is.

Considering this, without additional context or a specific function definition besides f(x) = 6, we presume that the student is being asked to recognize this as a constant function. Therefore, the value of f(x) is always 6, regardless of the value of x.

However, if we are considering a function that changes with respect to x, the total differential would be involved to find infinitesimal changes in f(x) as x changes. For a constant function like this one, the differential would be zero since the function's value does not change as x changes.

Approximately 140 months have passed since Laura retired.

To find the number of months that have passed since Laura retired, we need to calculate the total number of months Laura's retirement savings can cover her living expenses, and then subtract that from the balance in her account.

First, we calculate the number of months Laura's retirement savings can cover her living expenses by dividing her total savings by the monthly withdrawal amount: $414,731.00 ÷ $2,224.00 = 186.41 months.

Then, we subtract the number of months from the balance in Laura's account to find the number of months that have passed since Laura retired: 186.41 - X = $381,371.00, where X is the number of months. So, X = 186.41 - $381,371.00 = 140.41.

Therefore, approximately 140 months have passed since Laura retired.

Answer:

i believe it to be 16. Im not sure though

Step-by-step explanation:

Answer:

The GCF for 84 and 90 is 6.

Step-by-step explanation:

The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Then the greatest common factor is 6.

Answer:

GCF=6

Step-by-step explanation:

In order to find the GCF of 84 and 90 you must find the prime factors of each term.

The total surface area will be 1360.2 square centimeters.

To find the amount of gift wrap needed to cover Jenny's gift box shaped like a triangular prism, we first need to calculate the surface area of the prism.

The box has two triangular bases and three rectangular sides.

Therefore,

Calculate the total surface area of the triangular prism: 2(base area) + (base perimeter * prism height)

Substitute the values:

= 2(1/2 * base side * base height) + (base side * 3base side + prism height)

Solve to find the total surface area:

= 2(1/2 * 12 cm * 10.4 cm) + (12 cm * 3 * 12 cm + 68 cm)

= 1360.2

After calculations, the total surface area will be 1360.2 square centimeters.

The amount of gift wrap needed to cover the box is 4,958.4 cm² or approximately 4.96 square meters.

To find the amount of gift wrap needed to cover a triangular prism, we need to calculate the total surface area of the prism.

Given information:

- Each side of the base is 12 cm.

- The triangular base has a height of 10.4 cm.

- The prism is 68 cm tall.

Calculate the area of the triangular base.

Area of a triangle = (1/2) × base × height

Area of the triangular base = (1/2) × 12 cm × 10.4 cm

Area of the triangular base = 62.4 cm²

Calculate the perimeter of the triangular base.

Perimeter of a triangle = sum of all sides

Perimeter of the triangular base = 12 cm + 12 cm + 12 cm = 36 cm

Calculate the area of the rectangular faces.

Area of a rectangle = length × width

Area of each rectangular face = 36 cm × 68 cm = 2,448 cm²

Total area of the rectangular faces = 2 × 2,448 cm² = 4,896 cm²

Calculate the total surface area of the triangular prism.

Total surface area = Area of the triangular base + Area of the rectangular faces

Total surface area = 62.4 cm² + 4,896 cm²

Total surface area = 4,958.4 cm²

Therefore, the amount of gift wrap needed to cover the box is 4,958.4 cm² or approximately 4.96 square meters.

The point estimate of the population mean is $20 per week. The 95% confidence interval, using a z-score of 1.96, ranges from $18.20 to $21.80.

The subject of this question deals with the statistical concept of confidence intervals. The point estimate of the population mean is simply the sample mean, which is $20 per week. To calculate the confidence interval for the population mean (μ), we first need to understand that for a 95% level of confidence, the z-score (standard score) is 1.96. This is derived from statistical tables or a z-distribution.

The confidence interval is then calculated with the formula:
(sample mean - (z-score * (standard deviation/√sample size)), sample mean + (z-score * (standard deviation/√sample size))
Substituting the known values in, the 95% confidence interval for μ is ($18.20, $21.80).

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The point estimate of the population mean is the sample mean of $20 per week. Using the given standard deviation and applying the formula for a 95% confidence interval, we determine the confidence interval for the population mean to be ($18.6, $21.4).

The point estimate of the population mean ( μ) is the sample mean which is $20 per week. To calculate the confidence interval, we can use the formula for a 95% confidence interval when the population standard deviation ( σ) is known:

CI = Y ± Z*( σ/ √n)

Given that σ = $5, n = 49, Z for a 95% confidence level is approximately 1.96. Plugging these values into the formula, we get the confidence interval:

CI = 20 ± 1.96*(5/√49)

CI = 20 ± 1.96*(5/7)

CI = 20 ± 1.96*(0.714)

CI = 20 ± 1.4

CI = (18.6, 21.4)

Therefore, the 95% confidence interval for the population mean ( μ) is ($18.6, $21.4).

Answer:

Diameter of circle is 9 units.

Answer:

2 x radius

Step-by-step explanation:

Answer:

probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG = 0.8668

Step-by-step explanation:

mean, μ = 80 mg/mi

Standard deviation, [tex]\sigma = 4 mg/mi[/tex]

probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG

[tex]P(X > x ) = P(z > \frac{x - \mu}{\sigma})[/tex]

[tex]P(X > x ) =1 - P(z < \frac{x - \mu}{\sigma})[/tex]

[tex]P(X > 86 ) =1 - P(z < \frac{86 - 80}{4})[/tex]

P(X > 86) = 1 - P(z < 1.5)

From the standard normal table, P(z < 1.5) = 0.9332

P(X > 86) = 1 - 0.9332

P(X > 86) = 0.0668

Complete Question: Check the file attached to this document to see the complete question

Answer:

P(X < 7) = 0.76

Step-by-step explanation:

Counting properly from the diagram attached to the question,

number of trials it took her to make less than 7 shots(i.e. 0 to 6 shots) = 38

The total number of trials she made = 50

Probability that it takes fewer than 7 shots to get her first successful shot, P(X < 7) = (number of trials it took to make less than 7 shots)/(Total number of trials)

P(X < 7) = 38/50

P(X < 7) = 0.76

Answer:

0.76

Step-by-step explanation:

Answer:

24 cracks will be filled

Step-by-step explanation:

Here, the first question asks how to convert 3 pounds to ounces.

we can do this using a mathematical approach. To convert pounds to ounces, we need to know that there are 16 ounces in a pound. so to convert pounds to ounces, we just need to multiply the number of pounds we have by 16 to get the equivalent number of ounces.

The second question asks to give the number of cracks that be repaired.

From the question, we were made to know that each of the cracks would eat up 2 pounds of cement to be filled.

Let’s calculate the amount of cement we have. That would be 3 * 16 = 48 ounces of cement.

The amount of cracks to be filled is thus 48 ounces/2 ounces = 24 cracks

The total possible outcomes of a serving would be 16.

Step-by-step explanation:

Given that,

The total number of beverages = b = 4 ( water, milk, juice,

or tea)

Ice options = i = 2 (with or without ice)

Serving options = s = 2 (glass or plastic cup)

We have to find the total possible outcome x, that can be calculated using

x = b x i x s

Putting the values in the equation, we get

x = 4 x 2 x 2

x = 16

Hence, the total possible outcomes of a serving would be 16.

Step-by-step explanation:

volume =π r*2 h

sub r=7, h =16,

volume = 49(16)π

=784π

Answer:

the answer to this is -7/6

Answer:

8.54

Step-by-step explanation:

3*3=9

8*8=64

9+64=73

Square root of 73= 8.54

Answer:

c 5%

Step-by-step explanation:

8000 + 410.7 = 8000 e^(r)

e^r = 1.05127125

r lne = ln1.05127125

r = 0.05006316309 × 100

5%

Answer:

C 5%

Step-by-step explanation:

I hope this is what you need

Answer:

  -142

Step-by-step explanation:

You seem to have an arithmetic sequence with first term -66 and common difference (-68-(-66)) = -2. The general term of such a sequence is given by ...

  an = a1 +d(n -1) . . . . . for first term a1 and common difference d

We want to evaluate this equation for a1 = -66, d = -2, n = 39:

  a39 = -66 -2(39 -1) = -66 -76 = -142

The 39th term is -142.

Answer:

x = -22

Step-by-step explanation:

2(5– x)3 – 11 = 151

(10 - 2x)3 - 11 = 151

30 - 6x = 162

-6x = 132

x = -22

Answer:

120 ways

Step-by-step explanation:

Answer:

2313

Step-by-step explanation:

Answer:

The population of Lasvegas = 1202000.

Population of Sacramento = 1479000

Step-by-step explanation:

Let the population of each be

 Las​ Vegas Nevada = L

and​

Sacramento, California = S

Initially L + S = 2681 000 people

Sacramento had 277 thousand more residents than Las Vegas

This mean that:

L = Population of Las Vegas

L+ 277,000 = population of Sacramento

2,681,000=L+(L+277,000)

2,681,000=2L + 277,000

2,681,000-277,000=2L

2,404,000=2L

2,404,000/2=L

1,202,000=L

The population of Lasvegas = 1202000.

1,202,000+277,000=1,479,000

Population of Sacramento = 1479000

Check base on the question.

2,681,000=1,202,000+1,479,000

2,681,000=2,681,000

Final answer:

To solve the problem, we used algebra to define variables for the population of Las Vegas and Sacramento, set up an equation based on the given information, and solved for the populations of both metropolitan areas.

Explanation:

The question involves solving a basic algebra problem to find the population of Las Vegas and Sacramento metropolitan areas when given the total combined population and the difference in populations between the two areas.

Let x represent the population of Las Vegas. Then, Sacramento's population would be x + 277277 thousand.

Solving the equation x + (x + 277277) = 26812681 will give us the populations of both areas.

Combine like terms to get 2x + 277277 = 26812681.

Subtract 277277 from both sides to get 2x = 26535404.

Divide both sides by 2 to find the population of Las Vegas, x = 13267702 thousand.

To find Sacramento's population, add 277277 to Las Vegas' population to get 13544979 thousand.

Therefore, the population of the Las Vegas metropolitan area was 13267702 thousand, and Sacramento's metropolitan area had a population of 13544979 thousand.

Answer:

The number of correct answers most likely is 3

Step-by-step explanation:

A Dot Plot is a histogram form of chart used to represent small amount of data  in which the values are small discrete countable variables. It is a graphical display of data using dots and graph like scales to show count (relationships) within a group or a category.

Here from the box plot, we have that the number with the highest frequency is 3. Therefore, the number of correct answers most likely is 3.

Answer:

4000

Step-by-step explanation:

this can be found by using the equation

1600/x = 40/100

cross multiply

40x = 160000

simplify

x= 4000

To find the total number of visitors the art museum had in the month, divide 1,600 by 0.4.

To find the total number of visitors the art museum had in the month, we can use the given information. We know that 1,600 visitors represents 40% of the total number of visitors for the month. To find the total number of visitors, we can set up the following equation:

1,600 = 0.4 * total number of visitors

To solve for the total number of visitors, we divide both sides of the equation by 0.4:

total number of visitors = 1,600 / 0.4 = 4,000

Therefore, the art museum had a total of 4,000 visitors that month.

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Answer:

392

Step-by-step explanation:

round 0.499 up to 0.5, then divide 196 by 0.5 and your answer is 392.

Answer: A

Step-by-step explanation:

Took quiz

Answer:

The correct answer is A on edg

Step-by-step explanation: