A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour. At 2 p.m., the amount of oil left in
the lantern is 63 ounces. At 5 p.m., the amount of oil left in the lantern is 61 ounces.
Based on the average rate of oil burning per hour, how much oil, in ounces, was in the
lantern at 12 noon?

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Answer:

∠PQT = 97°

∠SQR = 83°

Step-by-step explanation:

Supplementary angles sum to 180°

⇒ ∠PQT + ∠SQR = 180°

Given:

Therefore:

⇒ (3x + 43) + (6x - 25) = 180

⇒ 3x + 6x + 43 - 25 = 180

⇒ 9x + 18 = 180

⇒ 9x = 162

⇒ x = 18

Substitute the found value of x into the expression for each angle:

⇒ ∠PQT = (3x + 43)°

⇒ ∠PQT = (3(18) + 43)°

⇒ ∠PQT = 97°

⇒ ∠SQR = (6x - 25)°

⇒ ∠SQR = (6(18) - 25)°

⇒ ∠SQR = 83°

Check

⇒ ∠PQT + ∠SQR = 97° + 83° = 180°

Answer:

17

Step-by-step explanation:

→ Substitute 7 f(x) into the function

7 + 10

→ Solve

17

Answer:

f(7) = 17

Step-by-step explanation:

To find f(7), substitute x = 7 in the function. Thus, you will receive:

[tex]\displaystyle{f(7)=7+10}\\\\\displaystyle{f(7)=17}[/tex]

Henceforth, the value of f(7) is 17.

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Answer:

1 HR ---> 42 km

? .----> 119 km

119 * 1/42

2.833

Answer:

[tex]\boxed {2 \frac{5}{6}}[/tex]

Step-by-step explanation:

Formula used :

[tex]\boxed {Time = \frac{Distance}{Speed}}[/tex]

Solving :

Time = 119/42

Time = 17/6

Time = 2 5/6 hours

Answer:

x = 7

Step-by-step explanation:

3(x - 4) - 5 = x - 3

3x - 12 - 5 = x - 3

2x = -3 + 12 + 5

2x = 14

x = 7

The hypothesis test shows that we reject the null hypothesis and there is sufficient evidence to support the claim that the return rate is less than 20%

The claim that the return rate is less than 20% is p < 0.2. From the given information, we can compute our null hypothesis and alternative hypothesis as:

[tex]\mathbf{H_o :p =0.2}[/tex]

[tex]\mathbf{H_i:p < 0.2}[/tex]

Given that:
Sample size (n) = 6965

Sample proportion [tex]\mathbf{\hat p = \dfrac{x}{n} = \dfrac{1302}{6965} \sim0.1869}[/tex]

The test statistics for this data can be computed as:

[tex]\mathbf{z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}}}[/tex]

[tex]\mathbf{z = \dfrac{0.1869 -0.2}{\sqrt{\dfrac{0.2(1-0.2)}{6965}}}}[/tex]

[tex]\mathbf{z = \dfrac{-0.0131}{0.0047929}}[/tex]

z = -2.73

From the hypothesis testing, since the p < alternative hypothesis, then our test is a left-tailed test(one-tailed.

Hence, the p-value for the test statistics can be computed as:

P-value = P(Z ≤ z)

P-value = P(Z ≤ - 2.73)

By using the Excel function =NORMDIST (-2.73)

P-value = 0.00317

P-value ≅ 0.003

Therefore, we can conclude that since P-value is less than the significance level at ∝ = 0.01, we reject the null hypothesis and there is sufficient evidence to support the claim that the return rate is less than 20%

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Answer:  [tex]\textsf{Option D, y = 2x - 3}[/tex]

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

Given: [tex]\textsf{The graph}[/tex]

Find: [tex]\textsf{The equation in slope intercept form}[/tex]

Solution: Looking at the graph, we can see that the line intersects the y-axis at -3 therefore that is the y-intercept.  All we need to do now is find a second point so we can determine the slope.  The line crosses at (1, -1) so we will use that as the second point.  Then we just plug all of the values into the slope intercept form.

Determine the slope

Plug in the values

Therefore, the option that would best fit the graph that was provided would be option D, y = 2x - 3.

By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].

In this question we must separate each variable on each side of the equivalence, integrate each side of the expression and find an explicit expression (y = f(x)) if possible.

[tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex]

[tex](\ln y)^{2}\,dy = -y \cdot \sqrt{x}\, dx[/tex]

[tex]-\frac{(\ln y)^{2}}{y}\, dy = \sqrt{x} \,dx[/tex]

[tex]-\int {\frac{(\ln y)^{2}}{y} } \, dy = \int {\sqrt{x}} \, dx[/tex]

If u = ㏑ y and du = dy/y, then:

[tex]-\int {u^{2}\,du } = \int {x^{\frac{1}{2} }} \, dx[/tex]

[tex]-\frac{1}{3}\cdot u^{3} = \frac{2\cdot x^{\frac{3}{2} }}{3} + C[/tex]

[tex]u^{3} = -2\cdot x^{\frac{3}{2} } + C[/tex]

[tex](\ln y)^{3} = - 2\cdot x^{\frac{3}{2} } + C[/tex]

[tex]C = (\ln e)^{3}[/tex]

[tex]C = 1[/tex]

And finally we get the explicit expression:

[tex]\ln y = \sqrt [3]{-2\cdot x^{\frac{3}{2} }+ 1}[/tex]

[tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex]

By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].

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Answer:

f(x) = square root of x

g(x) = 4x - 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remark. Since 6 has a decimal after it, I take it that is the question number.

y = 16x is the basic formula. x starts at 0. Then you add 16 to each number to get the next number in the sequence. Or you could do it the way I propose it.

x      0     1      2     3     4     5     6     7

y      0     16   32   48   64   80  96  112

Answer:

The answer will be 30.625 m

Answer:

Step-by-step explanation:

The domain includes all x values, and here, it is [-2, 4].

Answer:

x² + 4x + 3

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

       2

---- => fraction line

244x3+1474x2+63x/

x+6

A set is a mathematical model for a collection of items. The set of W' is {5, 20, 30}.

A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.

The complete question is given below.

Q13.

T ∪ V = Data points that are in T or V or both.

T ∪ V = {5, 10, 20, 30}

Q14.

T ∩ W = Data points that are in T and W both.

T ∩ W = {10}

Q15.

W' = Data points that are not in W.

W' = {5, 20, 30}

Hence, the set of W' is {5, 20, 30}.

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Answer:

the dependent variable is the data because it's the one that changes

The average rate of change = 109%

Rate of Change is the measure of the increase or decrease in the value with respect to the initial value.

It is given that

No of clown sold in 2010 = 11

No of clown sold in 2015 = 23

The average rate of change  = ((23-11)/11 ) *100 %

The average rate of change = 109%

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Answer:

-2

Step-by-step explanation:

-9/3=-3

-3+b=-1

b=-1+3

b=-2

The graphed trigonometric function is the one in option a.

The key parts that we can see on the graph are:

From this we know that the correct option is either a or b.

Now we can evaluate options a and b in x = 0 and see which one is equal to zero.

for a:

y = sin(0 - pi/2) + 1 = sin(-pi/2) + 1 = -1 + 1 = 0

for b:

y = cos(0 + pi/2) + 1 = 0 + 1 =  1

Then we can see that option a is the correct option.

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Answer:

1. santina drove 14 more miles than carole

2. the owner will need to buy 8 bags this week

Step-by-step explanation:

1. 203-189= 14

2. if they use 80 pounds a week and can only buy 10 pounds in one bag, they'll need 8 bags to equal 80 pounds since each bag is 10 pounds

1. 14

2. 8

3. 48

4. 318

5. 23

6. 4

7. a) 10 b) 60 c) 8 d) 107

8. $1,532

9. 1

10. $15.50

11. .95

Step-by-step explanation:

[tex]1) \text{ } 2^{1/2}=\sqrt{2}\\\\2) \text{ } 2^{2/3}=\sqrt[3]{2^{2}}\\\\3) \text{ } 3^{3/2}=\sqrt{3^{3}}\\\\4) \text{ } 3^{1/3}=\sqrt[3]{3}[/tex]

Answer: correct radical forms are:

[tex]2^\frac{1}{2} = \sqrt{2}[/tex]

[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]

[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]

[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]

Step-by-step explanation:

Radical form : If n is a positive integer that is greater than 1 and a is a real number then, [tex]\sqrt[n]{a} =a^\frac{1}{n}[/tex] where n is called the index, a is called the radicand, and the symbol √ is called the radical.

therefore,  

radical form of given values are :

[tex]2^\frac{1}{2} = \sqrt{2}[/tex]

[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]

[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]

[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]

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Answer:

all over the world

Step-by-step explanation:

use g00g!e maps

Answer:

Not in Russia

Step-by-step explanation:

McDonald's left Russia following the violations of human rights

Answer: 6x+12

Step-by-step explanation: Both denominators can be multiplied to create 6x + 12.

2x + 4

2x(3) + 4(3)

6x+12

3x + 6

3x(2) + 6(2)

6x+12

I hope this helps!

The function (fog)(x) would be (x^4 + 10x² + 27). Also, the domain of (fog)(x) is all the real numbers.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

f(x) = x² + 2

g(x) =  x² + 5

so, to take the composition of f and g (fog) replace the x in f(x)  with g(x);

(fog)(x) = (x² + 5)² + 2

(fog)(x) = (x^4 + 25 + 10x² )+ 2

(fog)(x) = (x^4 + 10x² + 27)

Also, the domain of (fog)(x) is all the real numbers.

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Answer:

The answer is 5/21 water left in the jug after 2 days.

Step-by-step explanation:

First convert 1 2/3 into a improper fraction. This will turn it into 5/3. After this, find a common denominator between 5/7 and 5/3. This common denominator is 21. Now, convert both fractions into a fraction with 21 as the denominator. This will transform 5/7 into 15/21, and 5/3 into 35/21. So we know from the equation that 15/21 is drank every day. So we multiply 15/21 by 2, which will make it 30/21. 35/21 will stay the same. Now we do 35/21 - 30/21, which gives you the final answer of 5/21 water left in the jug after 2 days.

Hope this helps!

Answer: Rectangles

Step-by-step explanation:

Whenever rectangles are rotated about an axis, a cylinder is formed.

The preparation of the journal entry to record the accounting transaction can be seen in the table below.

Initially, when preparing a journal, you have to read the transaction carefully and comprehend it. Discover which accounts need to be credited and debited before entering a journal entry.

From the given information:

The common stock par value = no of shares × par value of shares

The common stock par value = 4000 shares × $5/ share

The common stock par value = $20000

However, the amount paid in capital excess of the par value for the common stock is:

= $35000 - $20000

= $15000

Therefore, the Journal entry can be computed as follows:

Date        Account Title                          Post Ref     Debit ($)    Credit ($)

             Cash                                                            35,000

        Paid-in capital in excess of par

       value, common stock                                                         20,000

       (To record the insurance of common stock)    

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Answer:

circumference: 5.65 m

area: 2.54 m

Step-by-step explanation:

here are some relationships between measurements of a circle:

C  = π d

(Circumference = pi · diameter)

A = π r²

(Area = pi · radius²)

[π / pi is the ratio of a circle's circumference to its diameter. this ratio is actually a constant across all circles, which is where we derive our circumference and area formula from. π ≈ 3.14159]

so, let's work on finding the circumference first.

C  = π d

we know the diameter = 1.8,    and we know that π ≈ 3.14159

so, if we multiply these two numbers together, we will get the circumference

[this equation makes sense if you read my explanation of pi]

1.8 × 3.14159 = 5.654862

We can round this number to 5.65

So, the circumference of our circle = 5.65 m

now, let's find the area

A = π r²

we know that π ≈ 3.14159, but we still haven't found "r"

r, or radius, is the measurement from the center of a circle to any point of the circle. Because the diameter is the measurement from one side of a circle to the opposite side, diameter = twice the radius

this means we can take our diameter, 1.8, and divide it by 2 to find our radius.

1.8 / 2 = 0.9

now, we can solve for area.

π ≈ 3.14159 , r = 0.9

A = π r²

A = π (0.9)²

A = (3.14159) (0.81)

A = 2.5446879

we can round this area to 2.54

so, the area of our circle = 2.54 m