Suppose y varies inversely with x, and y = 36 when x=112
What inverse variation equation relates x and y ?

Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

Answer:

(1,3)

Step-by-step explanation:

hope it's help ful

According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

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We can add 10 pounds of mixed nuts that contain 20% peanuts by solving equations.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

So, the quantity of mixed nuts we need is x pounds.

There are 0.70 pounds of peanuts in this mixture.

3 pounds of peanuts make up the 20% mix, or 0.20*15.

We got the equation:

0.70 x + 3 = 0.40(x + 15)

Now, solve this equation as follows:

0.70 x + 3 = 0.40(x + 15)

0.70 x + 3 = 0.40(x + 15)

0.70x + 3 = 0.40x + 6

0.70x - 0.40x = 6 - 3

0.30x = 3

x = 10 pounds

Therefore, we can add 10 pounds of mixed nuts that contain 20% peanuts by solving equations.

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The volume of the prism is 1323 feet³ (cubic feet).

Length= 21 feet.

Width= 9 feet.

Height= 7 feet.

The formula to calculate the volume of rectangular prisms is the following:

\(\sf V_{RP} =l*w*h\); where "l" is the length; "w" is the width, and "h" is the height of the prism.

Check the attached image to see where these values are measured from.

Substitute the variables in the formula by the values on step 1.

\(\sf V_{RP} =l*w*h=(21\ feet)*(9\ feet)*(7\ feet)=\boxed{\sf1323\ feet}.\)

The volume of the prism is 1323 feet³ (cubic feet).

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Answer:

The volume of the rectangular prism is 1323 cubic feet.

Step-by-step explanation:

Step 1: Write down the formula for the volume of a rectangular prism:

\(\qquad\Large\boxed{\rm{\:\:\:V = l \times w \times h\:\:\:}}\)

Step 2: Substitute the given values for the length, width, and height:

\(\qquad\Large\rm{V = 21\: ft \times 9\: ft \times 7\: ft}\)

Step 3: Multiply the numbers together:

\(\qquad\Large\rm\implies{V = 1323\: ft^3}\)

Step 4: Write the final answer with the appropriate units:

The volume of the rectangular prism is 1323 cubic feet.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Answer:

Step-by-step explanation:

| − | = | + 9I

THERE ARE TWO POSSIBILITIES

2x-1=4x+9                          and              2x-1=-4x-9

2x-4x=9+1                            and           2x+4x=-9+1

-2x=10                                   and            6x=-8

x=-5                                and                  x=-8/6

x=-5                               and                     x=-4/3

SOLUTION SET ={-5,-4/3}

\(\frac{2x-1}{3}-\frac{3x}{4}=\frac{5}{6}\\ taking LCM\\\frac{8x-4-9x}{12}=\frac{5}{6}\\\frac{-1x-24}{12}=\frac{5}{6}\\ by cross multiplication\\6(-1x-4)=12*5\\-6x-24=60\\-6x=60+24\\-6x=84\\\\x=-14\\soltion set {-14}\)

\(10+\sqrt{10m-1}=13\\\sqrt{10m-1}=13-10\\\\\sqrt{10m-1}=3\\ taking square on both sides\\10m-1=3^2\\10m-1=9\\10m=9+1\\10m=10\\m=1\)  

the number of solution to a linear equation is 1

2(x - 4) = 6 then x is ----7

Solution of | + | = − is ---------13/3,5/3

Answer:

≈4,365%.

Step-by-step explanation:

1) для нахождения требуемой вероятности необходимо найти вероятность каждого из пяти выниманий, а затем перемножить их;

2) при каждом вынимании вероятности:

\(P_1=\frac{C^1_{10}*C^1_{10}}{C^2_{10}}=\frac{10}{19};\\P_2=\frac{C^1_9*C_9^1}{C^2_{18}}=\frac{9}{17};\\P_3=\frac{C^1_8*C_8^1}{C^2_{16}}=\frac{8}{15};\\P_4=\frac{C^1_7*C^1_7}{C^2_{14}}=\frac{7}{13};\\P_5=\frac{C^1_6*C^1_6}{C^2_{12}}=\frac{6}{11};\)

3) требуемая вероятность:

P=P₁*P₂*P₃*P₄*P₅≈0,04365.

The x-coordinates where the graphs of the equations intersect are x = -1 and x = 3

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = x² - 3

The x-coordinates where the graphs of the equations intersect is when both equations are equal

So, we have

x² - 3 = 2x

Rewrite the equation as

x² - 2x - 3 = 0

When the equation is factored, we have

(x + 1)(x - 3) = 0

So, we have

x = -1 and x = 3

Hence, the x-coordinates are x = -1 and x = 3

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Question

From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.

y = 2x

y = x² - 3

Answer:

Here are the steps for conducting a survey in your school to find out which mode of transportation students prefer the most, arranged in order from start to finish:

1) Define the objective: Clearly define the objective of the survey, which is to determine the preferred mode of transportation among students in your school.

2) Determine the sample size: Decide on the number of students you want to include in your survey. This will depend on factors such as the size of your school and the resources available for conducting the survey.

3) Design the survey questionnaire: Create a well-designed survey questionnaire that includes relevant questions about different modes of transportation. Ensure that the questions are clear, unbiased, and cover all the necessary aspects.

4) Seek necessary permissions: If required, seek permission from school authorities or relevant individuals to conduct the survey on school premises and to involve students.

5) Pre-test the survey: Before distributing the survey to the entire student population, pre-test the questionnaire on a small group of students to identify any potential issues or areas for improvement.

6) Distribute the survey: Once the questionnaire has been finalized and pre-tested, distribute it to the selected sample of students. Ensure that the survey is distributed in a fair and unbiased manner, taking into account the diversity of the student population.

7) Collect the survey responses: Set a specific timeframe for students to complete the survey and collect the responses. Consider using a combination of online platforms and physical collection methods to maximize participation.

8) Analyze the data: Once you have collected all the survey responses, analyze the data to determine the preferred mode of transportation among students. Use appropriate statistical tools and techniques to interpret the results accurately.

9) Present the findings: Prepare a report or presentation summarizing the survey findings. Include key insights, trends, and any significant findings related to the preferred mode of transportation among students.

10) Share the results: Share the survey results with the school community, including students, teachers, and administrators. This can be done through presentations, newsletters, or other suitable communication channels.

By following these steps, you will be able to conduct a comprehensive survey to determine the preferred mode of transportation among students in your school.

Hope this helps!

I can not do it for you but I can give you what you should do

Explanation: take a survey

Answer:

1. (a)  [-1, ∞)

   (b)  (-∞, -1) ∪ (1, ∞)

2. (a)  (1, 3)

    (b)  (-∞, 1) ∪ (3, ∞)

3. (a)  9.6 m and 0.4 m

   (b)  03:08 and 15:42

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

Part (a)

When x < 0, the function is f(x) = x².

Since the square of any non-zero real number is always positive, the range of the function f(x) for x < 0 is (0, ∞).

When x ≥ 0, the function is f(x) = sin(x).

The minimum value of the sine function is -1 and the maximum value of the sine function is 1.  As the sine function is periodic, the function oscillates between these values.  Therefore, the range of function f(x) for x ≥ 0 is [-1, 1].

The range of function f(x) is the union of the ranges of the two separate parts of the function.  Therefore, the range of f(x) is [-1, ∞).

Part (b)

The domain of the function g(x) = ln(x² - 1) is the set of all real numbers x for which (x² - 1) is positive, since the natural logarithm function (ln) is only defined for positive input values.

Find the values of x:

\(\implies x^2-1 > 0\)

\(\implies x^2 > 1\)

\(\implies x < -1, \;\;x > 1\)

Therefore, the domain of function g(x) is (-∞, -1) ∪ (1, ∞).

Part (a)

To determine the interval where f(x) < 0, we need to find the values of x for which the quadratic is less than zero.

First, set the function equal to zero and solve for x:

\(\begin{aligned} x^2-4x+3&=0\\x^2-3x-x+3&=0\\x(x-3)-1(x-3)&=0\\(x-1)(x-3)&=0\\ \implies x&=1,\;3\end{aligned}\)

Therefore, the function is equal to zero at x = 1 and x = 3 and so the parabola crosses the x-axis at x = 1 and x = 3.

As the leading coefficient of the quadratic is positive, the parabola opens upwards. Therefore, the values of x that make the function negative are between the zeros.  So the interval where f(x) < 0 is 1 < x < 3 = (1, 3).

Part (b)
Since the square root of a negative number cannot be taken, and dividing a number by zero is undefined, function f(x) has to be positive and not equal to zero:  f(x) > 0.

As the parabola opens upwards, the values of x that make the function positive are less than the zero at x = 1 and more than the zero at x = 3.

Therefore the domain of g(x) is (-∞, 1) ∪ (3, ∞).

Part (a)

The range of a sine function is [-1, 1]. Therefore, to calculate the maximal and minimal possible water depths of the bay, substitute the maximum and minimum values of sin(t/2) into the equation:

\(\textsf{Maximum}: \quad 5+4.6(1)=9.6\; \sf m\)

\(\textsf{Maximum}: \quad 5+4.6(-1)=0.4\; \sf m\)

Part (b)

To find the times when the depth is maximal, set sin(t/2) to 1 and solve for t:

\(\implies \sin \left(\dfrac{t}{2}\right)=1\)

\(\implies \dfrac{t}{2}=\dfrac{\pi}{2}+2\pi n\)

\(\implies t=\pi+4\pi n\)

Therefore, the values of t in the interval 0 ≤ t ≤ 24 are:

Convert these values to times:

The simplified value of (2x - 4)² is 4x² - 16x + 16.

First, let us understand the algebraic identities;

Algebraic identities are equations in which the left hand side of the equation is identically equal to the right hand side of the equation.

Some of the identities are:

We are given (2x - 4)².

Use the identity (a - b)² = a² - 2ab + b² to expand to the given expression.

So, a = 2x and b = 4.

Put it into the identity, we will get;

Therefore,

(2x - 4)² = (2x)² - 2 * 2x * 4 + (4)² = 4x² - 16x + 16

Thus, the simplified value of (2x - 4)² is 4x² - 16x + 16.

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Answer: tan(pi+theta)=-9.9

Tan(2pi+theta)=-9.9

Step-by-step explanation:

By trigonometric expressions we conclude that the values of the tangent functions of the angles π + θ and 2π + θ radians are both equal to - 9.9.

A unit circle is a circle with a radius of a unit used to calculate the value of trigonometric functions associated to a right triangle. In this case, the tangent function for a point (x, y) is:

tan θ = y/x     (1)

The trigonometric expression for the tangent of the sum of two angles:

\(\tan (\alpha + \theta) = \frac{\tan \alpha + \tan \theta}{1 - \tan \alpha \cdot \tan \theta}\)     (2)

Now we proceed to calculate the trigonometric expressions:

\(\tan (\pi + \theta) = \frac{\frac{-0.99}{0.1}+0}{1-\left(\frac{-0.99}{0.1}\right)\cdot (0)}\)

\(\tan (\pi + \theta) = -9.9\)

\(\tan (2\pi + \theta) = \frac{\frac{-0.99}{0.1}+0}{1-\left(\frac{-0.99}{0.1}\right)\cdot (0)}\)

\(\tan (2\pi + \theta) = -9.9\)

By trigonometric expressions we conclude that the values of the tangent functions of the angles π + θ and 2π + θ radians are both equal to - 9.9.

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The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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Answer:

It's 16, i did the unit test already.

Step-by-step explanation:

Answer: 80%

Step-by-step explanation:

divide 120 by 150 and you get .8 then you move the decimal over 2

For the expression (3w²)/(w⁴) the simplified-value is 3/w², the correct option is (c).

The "Simplified-Expression" refers to an algebraic expression that has been reduced to its most basic and concise form, without changing the value of the expression.

The simplified expression is the most reduced-form, and it has the same value as the original expression.

We have to simplify the expression (3w²)/(w⁴),

We can rewrite w⁴ as (w²)², which means that we can cancel one of the w² terms in the numerator and denominator.

This gives us : (3w²)/(w⁴) = (3/1) × (w²/(w²)²) = 3/w²

Therefore, the simplified value of is (c) 3/w².

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Answer:

a) 95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.

b) Margin of error  = 0.0270.

Step-by-step explanation:

a)

\(\hat{p}\) = point estimate of p \(= 268/1020 =0.2627\)

\(\hat{q}= 1 - 0.2627 = 0.7373\)

\(SE = \sqrt{\hat{p}\hat{q}/n}\\\\=\sqrt{0.2627\times 0.7373/1020}=0.0138\\\alpha = 0.05\)

From Table, critical values of \(Z= \pm1.96\) ,

Lower limit

                  \(= \hat{p} - Z SE\\ = 0.2627 - (1.96 X 0.0138) \\ = 0.2627 - 0.0276 \\ = 0.236\)

upper limit = 0.2627 + 0.0276

                 = 0.2903

Correct option:

95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.

b) Margin of error =Z SE

                              = 1.96 X 0.0141

                              = 0.0270.

Answer:

Step-by-step explanation:

35 = x% of 70

35 = 1/2 of 70

x% = 50%

x = 50

Ok, so

We got these two functions:

We're going to find the composition (f o g)(x).

This composition is the same that evaluate the function f(x) in g(x).

This is, f (g(x)):

Simplifying:

As these two functions are polynomials, then, the domain of (fog)(x), will be:

Answer:

35 i think

Step-by-step explanation:

Angle QPS and angle RTS are congruent, both measuring 136°. Additionally, since OQ and RT are parallel, angle PSQ and angle RTS are alternate interior angles and are also congruent.

If OQ and RT are parallel lines and m QPS = 136°, we can use the property that when a transversal intersects two parallel lines, the corresponding angles are congruent.

Therefore, angle QPS and angle RTS are congruent, both measuring 136°. Additionally, since OQ and RT are parallel, angle PSQ and angle RTS are alternate interior angles and are also congruent.

Hence, angle PSQ measures 136° as well. In summary, angles QPS, PSQ, and RTS all have a measure of 136°.

This is because when two lines are parallel and intersected by a transversal, the corresponding angles and alternate interior angles are congruent.

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The complete question is given below:

If OQ and RT are parallel lines and m QPS = 136°

Answer:

C, 5x + 10y = 85

Step-by-step explanation:

There are 5 cents in a nickel, so that will be 5x because x will be the number of nickels as said earlier and 5 will be the nickel.

There is 10 cents in a dime, so that will be 10y because y will be the number of dimes used as mentioned, and 10 will be the dime.

Both of those added, (5x + 10) will have a result of 85.

That's why 5x + 10y = 85 would best be the appropriate equation to use here.

Answer:

y = -x + 7

Step-by-step explanation:

The slope formula is as follows:

y = mx + b

So, in order to get x + y = 7 into slope intercept form we have to do the following things:

If you do this step then your equation should look like this:

y = -x + 7

Hope this helps!!

- Kay

Answer:

y = -x + 7

Step-by-step explanation:

x + y = 7

x + y = 7

-x           -x

y = -x + 7

The solution is the point (0, 1/6) y = 1/6

Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.

In this case, the equation is in slope-intercept form (y = mx + b),

where m represents the slope (-3/4) and b represents the y-intercept (1/6).

The slope-intercept form allows us to determine various properties of the equation.

Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.

Each pair of x and y values that satisfy the equation represents a solution.

For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:

y = (-3/4)(0) + 1/6

y = 1/6

Therefore, the solution is the point (0, 1/6).

In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.

Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.

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Answer: 2,111 soccer balls

Step-by-step explanation:

         We will divide the total amount of money by the price per ball to find how many balls the league can buy.

        $6,333 / $3 = 2,111

        The league can buy 2,111 soccer balls.

The probability that a rivet is defective is 0.0247, and in ensuring that only 5% of all seams need reworking then the probability of a defective rivet is 0.0059.

Let p be the probability of a rivet being defective. The probability of a seam being defective is given by the binomial distribution:

P(defective) = 29Cx × p^x × (1-p)^(29-x)

where x is the number of defective rivets.

We know that 17% of seams are defective, so:

0.17 = ∑_{x=1}^{29} 29Cx × p^x × (1-p)^(29-x)

Solving for p, we have:

p = 0.0247

If only 5% of all seams need reworking, then:

0.05 = ∑_{x=1}^{29} 29Cx × p^x × (1-p)^(29-x)

Solving for p, we have:

p = 0.0059

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Answer:

694

Step-by-stp explanation:

Answer:

z(min)  = 1400

x = 3

y = 2

Step-by-step explanation:

Formulation:

Let´s call

x number of running hours of process 1

y number of running hours of process 2

Then Objective Function to minimize is:

z  =  400*x  + 100*y

Constrains:

Subject to

Demand constraint ( by type of brews)

300*x  + 100y ≥ 1000

100*x + 100*y ≥ 500

100*x ≥ 300

General constraint

y≥0     Note that we already have  x≥= (in the third constraint)

By using the on-line slver we find:

z (min) = 1400 $

x = 3

y = 2

Answers:

==========================================

Explanation: