It took Todd 11 hours to travel over pack ice from one town in the Arctic to another town 330 miles away. During the return journey, it took him 15 hours.

Assume the pack ice was drifting at a constant rate, and that Todd’s snowmobile was traveling at a constant speed relative to the pack ice.

What was the speed of Todd's snowmobile?

Answer:

B and D I think.............

Answer:

B and D

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf 900}\)

Step-by-step explanation:

Sides of the figure = n = 7

(n - 2)×180

Where n is the number of sides in the polygon

So,

= (n - 2) × 180

= (7 - 2) × 180

= 5 × 180

= 900

\(\rule[225]{225}{2}\)

Answer: 720°

Step-by-step explanation:

- Assuming this is a regular hexagon, all the sides are equal and all the angles are equal

- One of the properties of a regular hexagon is that the sum of all the interior angles is 720°

- Since the sum of all the interior angles is 720°, this means each interior angle is 120°

hope this helps :)

Answer:

\(\sf \dfrac{2}{3} = \dfrac{32}{48} = \dfrac{30}{45}\)

\(\sf \rightarrow \dfrac{2}{x} = \dfrac{32}{48}\)

\(\sf \rightarrow 2(48)= {32x}\)

\(\sf \rightarrow 32x= 96\)

\(\sf \rightarrow x = 3\)

\(\rightarrow \sf \dfrac{32}{48} = \dfrac{30}{y}\)

\(\rightarrow \sf {32y} = 30(48)\)

\(\rightarrow \sf {32y} = 1440\)

\(\rightarrow \sf y = 45\)

Step-by-step explanation:

sin x= P/H

sin x = 0.96 = 96/100 = 24/25.

Let the ratio of the sides be x.

B²=H²-P²

B²=(25x)²-(24x)²

B²=625x²-576x²

B²=49x²

B=√49x²

B= 7x.

cos x = 7x/25x = 7/25.

therefore, tan x = sin x / cos x = (24/25)/(7/25) = 24/25×25/7 = 24/7 .

hope this helps you.

Therefore, P(K|J) is equal to 1/5 in its simplest form.

What is fraction?

A fraction is a mathematical expression that represents a part of a whole. It is written in the form of one integer (the numerator) divided by another integer (the denominator), separated by a horizontal line. For example, the fraction 2/5 represents two parts out of a total of five parts.

The numerator represents the number of parts we are interested in, while the denominator represents the total number of equal parts that make up the whole. Fractions can be proper (the numerator is less than the denominator), improper (the numerator is greater than or equal to the denominator), or mixed (a whole number and a fraction together). Fractions are used in a wide range of mathematical operations, such as addition, subtraction, multiplication, and division.

by the question.

We can use the formula P(B/A) = P(B∩A)/P(A) to calculate P(KJ), where A is the event that J occurs, and B is the event that K and J occur.

First, we need to find P(K|J∩N). We can use the formula P(JNK) = P(KJ∩N)/P(J) to find this value.

\(P(K|J∩N) = P(JNK) * P(J) = (1/5) * (3/7) = 3/35\)

Next, we need to find P(J) = 3/7.

Finally, we can use the formula P(K|J) = P(K|J∩N)/P(J) to find P(KJ):

\(P(K|J) = P(KJ∩N)/P(J) = (3/35) / (3/7) = (3/35) * (7/3) = 1/5\)

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Answer:

0.45 m, 0.63 m, 0.72 m

Step-by-step explanation:

Let the three parts of the line be 5x, 7x and 8x

Therefore,

5x + 7x + 8x = 1.8

20x = 1.8

x = 1.8/20

x = 0.09

5x = 5*0.09 = 0.45 m

7x = 7*0.09 = 0.63 m

8x = 8*0.09 = 0.72 m

Answer:

A 90% confidence interval for the mean weight is [21.78 ounces, 21.98 ounces].

Step-by-step explanation:

We are given the weights, in the ounces, of a sample of 12 boxes below;

Weights (X): 21.88, 21.76, 22.14, 21.63, 21.81, 22.12, 21.97, 21.57, 21.75, 21.96, 22.20, 21.80.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                         P.Q.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar X\) = sample mean weight = \(\frac{\sum X}{n}\) = 21.88 ounces

            s = sample standard deviation = \(\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }\)  = 0.201 ounces

            n = sample of boxes = 12

            \(\mu\) = population mean weight

Here for constructing a 90% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 90% confidence interval for the population mean, \(\mu\) is ;

P(-1.796 < \(t_1_1\) < 1.796) = 0.90  {As the critical value of t at 11 degrees of

                                                  freedom are -1.796 & 1.796 with P = 5%}  

P(-1.796 < \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\) < 1.796) = 0.90

P( \(-1.796 \times {\frac{s}{\sqrt{n} } }\) < \({\bar X-\mu}\) < \(1.796 \times {\frac{s}{\sqrt{n} } }\) ) = 0.90

P( \(\bar X-1.796 \times {\frac{s}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+1.796 \times {\frac{s}{\sqrt{n} } }\) ) = 0.90

90% confidence interval for \(\mu\) = [ \(\bar X-1.796 \times {\frac{s}{\sqrt{n} } }\) , \(\bar X+1.796 \times {\frac{s}{\sqrt{n} } }\) ]

                                        = [ \(21.88-1.796 \times {\frac{0.201}{\sqrt{12} } }\) , \(21.88+1.796 \times {\frac{0.201}{\sqrt{12} } }\) ]

                                        = [21.78, 21.98]

Therefore, a 90% confidence interval for the mean weight is [21.78 ounces, 21.98 ounces].

Answer:

6 = u

Step-by-step explanation:

54 / u = 9

We have to isolate "u" all by itself;

54 = 9*u

54 / 9 = u

6 = u

Hope this helps!

Answer:

6

Step-by-step explanation:

We need to find of u value such that , 54 divided by u = 9. Converting it into equation ,

Equation :-

→ 54/u = 9

→ 1/u = 9 × 1/54

→ 1/u = 1/6

→ u = 6

Answer:

y  ≥ 5x+ (-3)

Step-by-step explanation:

greater than or equal to ≥

The sum means add

y  ≥ 5x+ (-3)

Answer:

Option D, y ≥ 5x + (-3)

Step-by-step explanation:

Step 1:  Make an expression

The value of y is greater than or equal to the sum of five times the value of x  and negative three.

The value of y is greater than or equal to ← y ≥

The sum of five times the value of x  and negative three ← 5x + (-3)

y ≥ 5x + (-3)

Answer:  Option D, y ≥ 5x + (-3)

Answer:

-45.4545455

Step-by-step explanation:

you would do like you would do with a regular division problem accept you take the negative out and you don't put until last bcuz whatever answer you get is gonna be a negative number. You would also move the decimal place of .22 back by two times so that the decimal place would be behind the number altogether and it becomes 22 and you would also add 2 zeros behind the negative 10 and get 1000.

Now just divide 1000 by 22 and get your answer and put the negative sign back. I know the way I explained it is weird, but that's cuz I'm not used to having to explain.

Answer: 45

Step-by-step explanation:

\(f(-5)=2(-5)^{2} -5\)

\(f(-5)= 2(25) -5\)

\(f(-5) = 50-5\)

\(f(-5) = 45\)

Answer: B

Step-by-step explanation: Hope this helps:)

-6(1+7x)+7(1+6x)=-2​

This is False.

Use distributive property:

-6 -42x + 7 +42x = -2

Combine like terms to get:

1 = -2

Since 1 is not -2, it is false.

Answer:

like 10 i think

Step-by-step explanation:

the flat line is the time it spends stopped im pretty sure so that would be 10 seconds

Answer:

The answer is -4.

Step-by-step explanation:

It is -4 using the method of PEMDAS.  Subtract 4 and 2 together in the parentheses to get 2.  Multiply to the third root power to get 8.  Then, multiply -3 by 4 together to get -12.  Finally, subtract 12 from 8 to get -4 as your final answer.

Answer:

Step-by-step explanation:

area of trapezium ABCD

=(16.5+12)/2 \times 15

=(28.5)/2 \times 15

=213.75 cm^2

\(\frac{PQ}{DC} =\frac{8}{12} =\frac{2}{3}\)

Area of PQRS

=213.75 \times (\frac{2}{3} )^2\\=213.75 \times\frac{4}{9} \\=95 ~cm^2

area of green portion=213.75-95=118.75 cm²

Answer:

Step-by-step explanation:

option (d) 4hrs 40mins

Answer:

Check image

Step-by-step explanation:

The approximate 90% confidence interval for this situation is given as follows:

(70244, 70632).

The bounds of the confidence interval are given by the rule presented as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

From the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.645.

The parameters are given as follows:

\(\overline{x} = 70438, \sigma = 645.3, n = 30\)

The lower bound of the interval is given as follows:

\(70438 - 1.645 \times \frac{645.3}{\sqrt{30}} = 70244\)

The upper bound of the interval is given as follows:

\(70438 + 1.645 \times \frac{645.3}{\sqrt{30}} = 70632\)

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The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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10) Total revenue is 0.1x¹ + 4.3x³ - 34.2x² + 295.7x - 137.7. 11) Profit for this year minus profit for last year equals 0.3x⁴ - 7.8x³ + 66.6x² - 211.4x + 185.9.

Profit is the financial gain that is achieved when the revenue from sales or business activities exceeds the expenses, costs, and taxes associated with running the business or conducting those activities.

10) To find the polynomial that models the total profit for both last year and this year, we add the two given profit equations:

Last year's profit: -0.3x¹ + 843 - 70.3x² + 247.5x - 137.7

This year's anticipated profit: 0.243 - 3.7x² + 36.1x + 48.2

Total profit = Last year's profit + This year's anticipated profit:

Total profit = (-0.3x¹ + 843 - 70.3x² + 247.5x - 137.7) + (0.243 - 3.7x² + 36.1x + 48.2)

Simplifying and combining like terms, we get:

Total profit = -0.3x¹ + 36.1x - 74x² + 295.7

Therefore, the polynomial that models the total profit for both last year and this year is:

A. 0.1x¹ + 4.3x³ - 34.2x² + 295.7x - 137.7

11) To find the polynomial that models how much more profit Helena anticipates this year compared to what she made last year, we can subtract the equation for last year's profit from the equation for this year's anticipated profit:

This year's anticipated profit: 0.243 - 3.7x² + 36.1x + 48.2

Last year's profit: -0.3x + 843 - 70.3x² + 247.5x - 137.7

Difference in profit = This year's anticipated profit - Last year's profit:

Difference in profit = (0.243 - 3.7x² + 36.1x + 48.2) - (-0.3x¹ + 843 - 70.3x² + 247.5x - 137.7)

Simplifying and combining like terms, we get:

Difference in profit = 0.3x¹ - 3.7x² + 36.1x - 595.5

Therefore, the polynomial that models how much more profit Helena anticipates this year compared to what she made last year is:

D. 0.3x⁴ - 7.8x³ + 66.6x² - 211.4x + 185.9

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The coordinates of the y-intercept are (0, 3.5) and the coordinates of the x-intercepts are (-17.5, 0). Using these coordinates, the graph of the equation is shown below.

From the question, we are to graph the given linear equation.

To graph the equation,

We will determine the coordinates of the x-intercepts and y-intercepts.

When x = 0

y = 1/5x + 3.5

y = 1/5(0) + 3.5

y = 3.5

(0, 3.5)

When y = 0

y = 1/5x + 3.5

0 = 1/5x + 3.5

Multiply through by 5

0 = x + 17.5

x = -17.5

(-17.5, 0)

Using the coordinates of the x-axis and y-axis, the graph of the equation is shown below.

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Answer:

The range of values from one job is between $50 and $650.

Step-by-step explanation:

An electrician charges y amount to work x hours on a job. The electrician charges a $50 service fee and $30 per hour.

This means that his earnings in a job can be modeled by the following function:

\(y = 30x + 50\)

The electrician works maximum of 20 hours on any job. What is the range of values for one job?

Minimum, he works 0 hours, and earns:

\(y(0) = 30(0) + 50 = 50\)

Maximum, he works 20 hours, and earns:

\(y(20) = 30(20) + 50 = 650\)

The range of values from one job is between $50 and $650.

Answer:

answers are:

7 and 14

The factors of 7 is:  1, 7

The factors of 14 is:  1, 2, 7, 14

28 and 7

Factors of 28:  1, 2, 4, 7, 14, 28

Facotrs of 7:  1, 7

Step-by-step explanation:

others:  

21, 3 is GCF is 3

The factors of 3 are: 1, 3

The factors of 21 are: 1, 3, 7, 21

7, 1 is GCF is 1

The factors of 1 are: 1

The factors of 7 are: 1, 7

EXPLANATION:

The proportion states that he walks 1.93 kilometers at a constant speed in 23 minutes, so we can formulate the equation in the same way:

-First we must divide to find the constant or the proportion, then we divide 1.93 by 23; we represent the constant with the letter k:

With the constant found we can propose an equation that determines the constant speed at which Halona walks at any time.

Now we can formulate the following equation:

Multiplying any time with the constant will give us the constant speed.

IMPORTANT NOTE:

When we give different values ​​to time, it must be multiplied by the constant, which means that the speed remains stable.