✨[ALGEBRA]✨
A plumbing company charges $75 per hour with a $100 inspection fee. A sales tax of 8.25% is then calculated based on the charges (subtotal). Write a function for the charges c(h) for the number of hours worked, h. Then write a function for the sales tax, s(c) collected on the charges. Finally, write a function for the total, t(h), using c(h) and the composite of s(h) and c(h).
Help me please someone.​

Answer:

60 degrees

Step-by-step explanation:

180-90-30 = 60 degrees

The equation that shows the miles Andrea drove is $104 = $50 + $3x.

The total cost of renting the moving truck is a function of the cost to rent per day and the total miles driven. The cost to rent the truck per day is the fixed cost while the cost per mile is the variable cost.

Total cost = cost to rent per day + (cost per mile x total mile driven)

$104 = $50 + $3x

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Using it's concept, considering the number of desired and total outcomes, it is found that the probabilities are given by:

a. 0.6 = 60%.

b. 0.4 = 40%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In an experimental probability, these numbers of outcomes are taken from previous trials.

Researching the problem on the internet, it is found that there is a total of 127 + 44 + 95 + 104 = 370 customers.

Item a:

127 + 95 = 222 customers prefer either baked potato or asparagus, hence the probability is given by:

p = 222/370 = 0.6 = 60%.

Item b:

44 + 104 = 148 customers prefer either steamed broccoli or sweet potato, hence the probability is given by:

p = 148/370 = 0.4 = 40%.

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Answer:

35 failed and 140 passed

Step-by-step explanation:

Let  p = number who passed

f = number who failed

p+f = 175

4 times the number of students passed as failed, so we need to balance this to set it equal

4f = p

Substitute this into the first equation

4r+f = 175

5f = 175

5f/5 =175/5

f = 35

Now find the number who passed

p = 4f

p = 4*35

p =140

Answer: 22 minutes

Step-by-step explanation: m + 2m + m + 7 = 4m + 7

4m + 7 = 50

4m = 44

m = 11

2m = 11 x 2 = 22 minutes

Answer:

K/q = p if you're taking about the inverse proportions

a) A function that gives the area of the playground (in square meters) in terms of x is A(x) = 60x - x².

b) The side length that gives the maximum area that the playground can have is x = 30 m.

c) The maximum area that the playground can have is 900 m².

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

120 = 2(x + W)

60 = x + W

W = 60 - x

Therefore, the area of the rectangular playground (in terms of x) is given by this function;

A = LW

A(x) = x(60 - x)

A(x) = 60x - x²

Part b.

For the side length, we would take the first derivative of the area:

A(x) = 60x - x²

A'(x) = dA/dx

A'(x) = 60 - 2x

60 - 2x = 0

x = 60/2

x = 30 m

Part c.

W = 60 - x

W = 60 - 30

W = 30 m.

Therefore, the maximum area is given by;

A = 30 × 30

A = 900 m².

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Answer:

2/3 pounds of lima beans

Step-by-step explanation:

2 divided by 3 = 2/3 = 2/3

Hope this helps!

Answer:

2/3 pounds (Option B)

Step-by-step explanation:

Using unitary method ,

3 families will receive = 2 pounds of lima beans.

(Dividing both the sides by 3)

⇒ \(\frac{3}{3}\)  family will receive = \(\frac{2}{3}\) pounds of lima beans

⇒ 1 family will receive = \(\frac{2}{3}\) pounds of lima beans.

∴ Each family will receive 2/3 pounds of lima beans.

hope you understand from the image...

:-)

The linear function parallel to the line represented by y = 3x/4 - 1/2 is given as follows:

y = 3x/4 + 1/2.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

When two lines are parallel, they have the same slope.

The slope of the line y = 3x/4 - 1/2 is given as follows:

m = 3/4.

Hence the equation of the parallel line is given as follows:

y = 3x/4 + 1/2.

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\(QUESTION:\)

How to convert mixed numbers into improper fractions?

\(ANSWER:\)

Here we have a mixed number:

\(3\frac{1}{7}\)

What we must do:

1. Multiply 3 by 7.

2. Add 1 (the numerator)

Here's what we have:

\(\frac{22}{7}\)

Hope it helps!

\(************************************\)

\(QUESTION:\)

How to convert improper fractions into mixed numbers?

\(ANSWER:\)

Here we have an improper fraction:

\(\frac{12}{5}\)

What we must do:

1. Divide the numerator by the denominator.

No decimals.

\(2\frac{x}{y}\)

The denominator stays the same:

\(2\frac{x}{5}\)

And now, \(x\) is our numerator.

If we multiply 2 by 5, we won't get 12. We'll get 10. 12-10=2 and 2 is the new numerator.

\(2\frac{2}{5}\)

Hope it helps! :)

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The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Answer:

5/6 is the probability

Step-by-step explanation:

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and rolling a 6-sided die you can get 1, 2, 3, 4, 5, 6 so 5 is the only thing you can roll that isn't a factor of 24 so

The quantity of water left in the barrel is 5.175 gallons. The correct option is the second option 5.175 gallons

From the question, we are to determine how much water is left in the barrel

From the given information,

"The barrel is filled with 18 gallons of water"

and

"Ryan used 9.7 gallons to water his garden in June"

After this time,

The quantity of water that would be left in the barrel will be 18 gallons - 9.7 gallons

= 8.3 gallons

Then,

3 and one eighth gallons in July

3 and one eighth = 3 1/8 = 3.125 gallons

The quantity of water that would be left is 8.3 gallons - 3.125 gallons

= 5.175 gallons

Hence, the quantity of water left in the barrel is 5.175 gallons. The correct option is the second option 5.175 gallons

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Answer:

b

Step-by-step explanation:

These pairs of sets of numbers: (a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1} b) {{1}},{1,{1}} ) ∅,{∅}  are  equal, not equal and not equal respectively

The given pairs of sets of numbers are

a) (1, 3, 3, 3, 5, 5, 5, 5, 5}, {5, 3, 1} b) {{1}}, {1, {1}} c) Ø, {0}​

To determine the reasons for the answers we have

(a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1}

All the number are distinct elements without any repetition is the same in both sets.

This implies that the sets are equal

b) {{1}},{1,{1}}

From the second set of numbers, the number of elements is not the same in both sets. The number of elements in the two sets are 1 and 2.

This therefore means that the pair of numbers are not equal

c) ∅,{∅}

In the third set of numbers, the number of elements is not the same in both sets.

The number of elements in the pairs are 0 and 1 in each of the sets . This implies that the pair of sets of numbers are not equal

In conclusion these pairs of sets of numbers: (a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1} b) {{1}},{1,{1}} ) ∅,{∅}  are  equal, not equal and not equal respectively

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Answer:

Given equations are,

5x+2y=−2        (1)

3x−5y=17.4      (2)

Multiply equation (1) by 5 and equation (2) by 2, we get,

5(5x+2y)=5×−2

∴25x+10y=−10          (3)

2(3x−5y)=2×17.4

∴6x−10y=34.8          (4)

Adding equations (3) and (4), we get,

31x=24.8

∴x=

31

24.8

​

Put this value in equation (1), we get,

5(

31

24.8

​

)+2y=−2

∴

31

124

​

+2y=−2

∴2y=−2−

31

124

​

∴2y=

31

−186

​

∴y=

31

−93

​

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sales Revenue:  $800.00

Cost of good sold:  $350,000.00

Subtract:                   $450,000.00

Sales Revenue:         $795,000.00

Cost of good sold:     $600,000.00

Subtract Sales             $195,000.00

Revenue from Cost

of goods sold.

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Answer:

C) -2/9

Step-by-step explanation:

\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

The simplified form of expression \(\frac{(5m^3n^3)^2}{n}\) is \(25m^6n^5\)

Consider the expression \(\frac{(5m^3n^3)^2}{n}\)

We know that the exponent rule that \((a\times b)^m=a^m \times b^m\)

and \((a^m)^n=a^{m\times n}\)

where a, b, m and n real numbers.

Consider the numerator of above expression.

\((5m^3n^3)^2\)

Using the rule  \((a\times b)^m=a^m \times b^m\) ,

\((5\times m^3\times n^3)^2\\\\= 5^2\times (m^3)^2\times (n^3)^2\\\)

We know that the square of 5 is 25

so, 5² = 25

Now we use the rule \((a^m)^n=a^{m\times n}\)

so, above expression becomes,

\(5^2\times (m^3)^2\times (n^3)^2\\\\=25\times m^{3\times 2}\times n^{3\times 2}\\\\=25\times m^6 \times n^6\)

Also, we know that inverse of any value can be written as \(\frac{1}{a} =a^{-1}\)

So, using this rule of exponent the value of 1/n would be \(n^{-1}\)

So, the expression \(\frac{(5m^3n^3)^2}{n}\) becomes,

\(\frac{(5m^3n^3)^2}{n}\\\\=\frac{25\times m^6 \times n^6}{n}\\\\=(25\times m^6 \times n^6)\times n^{-1}\\\\=25\times m^6 \times n^6\times n^{-1}\)

We know that if the base of exponents are same then we add the powers of exponents.

So, our expression becomes,

\(=25\times m^6\times n^{6-1}\\\\=25\times m^6\times n^5\)

This is the required expression.

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Answer:

Yes, the confidence interval contradict this statement.

Step-by-step explanation:

The complete question is attached below.

The data provided is:

\(n_{1}=318\\n_{2}=297\\\bar x_{1}=25\\\bar x_{2}=24.1\\s_{1}=3.6\\s_{2}=3.8\)

Since the population standard deviations are not provided, we will use the t-confidence interval,

\(CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\cdot s_{p}\cdot\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}\)

Compute the pooled standard deviation as follows:

\(s_{p}=\sqrt{\frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2}}=\sqrt{\frac{(318-1)(3.6)^{2}+(297-1)(3.8)^{2}}{318+297-2}}=2.9723\)

The critical value is:

\(t_{\alpha/2, (n_{1}+n_{2}-2)}=t_{0.05/2, (318+297-2)}=t_{0.025, 613}=1.962\)

*Use a t-table.

The 95% confidence interval is:

\(CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\cdot s_{p}\cdot\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}\)

     \(=(25-24.1)\pm 1.962\times 2.9723\times \sqrt{\frac{1}{318}+\frac{1}{297}}\\\\=0.90\pm 0.471\\\\=(0.429, 1.371)\\\\\approx (0.43, 1.37)\)

The 95% confidence interval for the difference between the mean weights is (0.43, 1.37).

To test the magazine's claim the hypothesis can be defined as follows:

H₀: There is no difference between the mean weight of 1-year old boys and girls, i.e. \(\mu_{1}-\mu_{2}=0\).

Hₐ: There is a significant difference between the mean weight of 1-year old boys and girls, i.e. \(\mu_{1}-\mu_{2}\neq 0\).

Decision rule:

If the confidence interval does not consists of the null value, i.e. 0, the null hypothesis will be rejected.

The 95% confidence interval for the difference between the mean weights does not consists the value 0.

Thus, the null hypothesis will be rejected.

Conclusion:

There is a significant difference between the mean weight of 1-year old boys and 1-year old girls.

Answer:

\(\\c=85mi\\\)

Step-by-step explanation:

\(77mi^{2} +36mi^{2} =7,225mi\\\\7225mi=c^{2}\)

\(\sqrt{7225} =85\)

The set of side measurements that could be used to form a right triangle is

The problem is solved using the Pythagoras theorem is applicable to right triangle.  

the formula of the theorem is

hypotenuse² = opposite² + adjacent²

the set of sides that adheres to this theorem can form a right triangle

plugging the values as in the problem  6, 8, 10

say side 10 = x

x² = 6² + 8²

x² = 36 + 64

x² = 100

x = √100

x = 10

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Answer:

D.

Step-by-step explanation:

Answer it is educational

Step-by-step explanation:

Answer:

x=30,F=1260,y=6

Step-by-step explanation:

is what your looking for

Answer:

2.5 x 4 = 10 not 8

so step 2

Answer:

B, Step 2

Step-by-step explanation:

Gary did, in fact, made a mistake. In step 2, 2.5*4 does not equal 8. In fact, 2.5*4 = 10

Answer:

Step-by-step explanation:

The area between the concentric circles:

If we tale π ≈ 3, we know R = 5 cm, we see r = R - 2 =  5 - 2 = 3 cm, then

Correct choice is B