What is the average amount of trail mix in each bag?

(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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The point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0.

To graph the equation 2x + 3y = 6, we can rewrite it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Starting with the given equation, we isolate y to one side:

3y = -2x + 6

y = (-2/3)x + 2

Now, we have the equation in slope-intercept form, y = (-2/3)x + 2. The slope is -2/3, and the y-intercept is (0, 2).

To find the point where the graph intersects the x-axis, we need to determine the coordinates where y is equal to zero. This occurs when the line crosses the x-axis.

Setting y = 0 in the equation, we have:

0 = (-2/3)x + 2

(-2/3)x = -2

x = (-2)(-3/2) = 3

Therefore, the point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0, indicating the point of intersection with the x-axis on the graph.

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The class had cleaned x × A square miles before lunch.

Let's assume that the area of the park is A square miles, and the portion of the park cleaned by Mai's class before the lunch break is represented by x (a fraction or decimal between 0 and 1).

If the class had cleaned x portion of the park, then the area they had cleaned is x times the total area of the park:

Area cleaned before lunch = x × A

Since x represents a fraction or decimal, multiplying it by the total area A gives us the corresponding portion of the park that was cleaned.

Let's say the park has an area of A square miles, and the area that Mai's class cleaned up before lunch is denoted by the number x (a fraction or decimal between 0 and 1).

If the class had cleaned a certain percentage of the park, their cleaned area would be x times the park's overall area:

Before lunch, the area was cleaned = x A

We may calculate the proportion of the park that was cleaned by multiplying x by the entire area A because it indicates a fraction or decimal.

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Please don't spam the questions.

Step-by-step explanation:

The total centimeters that the plants grew in all was 200 centimeters or 2.00 centimeters when written as a decimal.

Centimetres (cm) is a unit of length in the metric system, equal to one-hundredth of a metre. It is commonly used in everyday life, for example when measuring the height of a person or the size of a room. Centimetres are also used in scientific and engineering measurements, such as the size of an object or the distance between two points. Centimetres are divided into millimetres, which are one-thousandth of a metre.

This can be written as a decimal as 2.00 centimeters.

To determine the total centimeters, we simply add the individual centimeter measurements of the two plants.

Daysha's plant grew 100 centimeters and India's plant grew 100 centimeters.

Therefore, the total centimeters that the plants grew in all was 200 centimeters, or 2.00 centimeters when written as a decimal.

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Answer:

2

Step-by-step explanation:

5 weeks divded by 15 chapters times 6 chapters = 2 weeks

Answer:

Micheal is 12.

Step-by-step explanation:

Michaels brother is 4 years older than him, correct?

If michael is 12, and his brother is 4 years older, you have to add 4 to 12, 12+4=16, And 12+16=28.

The slope of the line represented by the equation f(t)=2t−6 will be 2.

The slope of the function is nothing but the tangent of the angle of the graph at that point.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

In other terms, a function is a relationship between variables, and the type of relationship that exists between the variables defines the function, such as y = sinx and y = x +6.

Given that

f(t)=2t−6

Now slope = first derivative of the function

f'(t) = 2 hence, slope of the given function will be -2.

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An answer to the question is as follows:

a)

Generally, the equation for degrees of freedom is  mathematically given as

df= n-1

Therefore

df= 50-1

df= 49

b)

For the  critical value

Confidence interval= 95%

df= 49

Solving using a critical value  calculator we have

test critical value = 2.01

c)

In conclusion, The number of degrees of freedom for a collection of sample data is the number of sample values that are determined after certain restrictions have been imposed on all data values. Option D is correct

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The volume of a paraboloid is therefore 1/3 of the volume of a cylinder with the same height and base radius.

The volume of a paraboloid can be expressed as:

The formula for a paraboloid's volume is Vparaboloid = (π/3) x (r²) x h, where r is the base's radius and h is the object's height.

A cylinder's volume can be expressed as follows with the same height and base radius:

Vcylinder = π x (r²) x h.

A paraboloid's volume to a cylinder's volume with the same height and base radius is calculated as follows:

Vparaboloid / Vcylinder = (π/3) x (r²) x h / (π x (r²) x h) = (π/3) / π = 1/3.

The volume of a paraboloid is therefore 1/3 of the volume of a cylinder with the same height and base radius.

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Answer:

quadrant 2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Whole numbers are numbers without fractions or integers.

Answer:

The answer is Zack garden

Answer:       5.1 x 10⁻¹ kg

To find the mass of water in the bottle, we can multiply the mass of one molecule by the number of molecules.

By using dimensional analysis, or by cancelling out units, we can figure out what to multiply or divide. Dimensional analysis uses fractions written with units. Dividing the same unit cancels out units we don't need.

To solve:

We are looking for the mass of H₂O in the bottle.

The units we need in the answer are:      \(\displaystyle{ \frac{kg}{bottle} }\)

The question tells us:

Our equation puts the fractions in an equation, making them multiply to get the units we need.

\(\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}\ =\ \frac{kg}{bottle}\)

Why is this equation correct?

Remember that dividing the same unit will cancel them out. In the equation, we have H₂O in a numerator and H₂O in a denominator. So, H₂O will cancel out. In the end, we will only have kg in the numerator and bottle in the denominator.

Take the equation we wrote. Now that we know our equation gives us the right units, we only need the front part.

\(\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}\)

Cancel out H₂O:

\(=\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1} \ *\ \frac{(1.7*10^{28})}{1\ bottle}}\)

Simplify the equation:

\(=\displaystyle{ \frac{(3 * 10^{-29})*(1.7*10^{28})\ kg}{1\ bottle}\)

\(=\displaystyle{ \frac{3 * 10^{-29}*1.7*10^{28}\ kg}{1\ bottle}\)

Use exponent rules to multiply 10⁻²⁹ with 10²⁸:

\(=\displaystyle{ \frac{3 *1.7*10^{28-29}\ kg}{1\ bottle}\)

\(=\displaystyle{ \frac{3*1.7*10^{-1}\ kg}{1\ bottle}\)

Multiply within the numerator to simplify:

\(=\displaystyle{ \frac{5.1*10^{-1}\ kg}{1\ bottle}\)

∴ The mass of water in the bottle is 5.1 x 10⁻¹ kg.

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Answer:

the answer is 33

Step-by-step explanation:

9 + 2^2 x 8 - 2^3 = 33

Answer:

33

Step-by-step explanation:

9 + 2² * 8 -2^3

--> 9 + 4 * 8 - 8

--> 9 + 32 -8

--> 33

Rollaway Skates is cheaper when the number of people is less than or equal to 4. For example, the cost for 2 people at Rollaway Skates is $10, while the cost for 2 people at Wheelie's Skates and Stuff is $106.

Wheelie's Skates and Stuff is cheaper when the number of people is greater than or equal to 5. For example, the cost for 6 people at Rollaway Skates is $30, while the cost for 6 people at Wheelie's Skates and Stuff is $118.

I hope this helps! Do you have any other questions?

Answer:

130 degrees

Step-by-step explanation:

DE+DA=130

Answer:

1 adult ticket and 7 student tickets were purchased

Step-by-step explanation:

let a represent number of adult tickets purchased and s the number of student tickets purchased, then

a + s = 8 ( subtract s from both sides )

a = 8 - s → (1) ← based on total tickets purchased

10.5a + 7.25s = 61.25 → (2) ← based on cost of tickets

substitute a = 8 - s into (2)

10.5(8 - s) + 7.25s = 61.25

84 - 10.5s + 7.25s = 61.25

84 - 3.25s = 61.25 ( subtract 84 from both sides )

- 3.25s = - 22.75 ( divide both sides by - 3.25 )

s = 7

substitute s = 7 into (1)

a = 8 - 7 = 1

that is 1 adult ticket and 7 student tickets were purchased

Answer:

the answer is A

Step-by-step explanation:

if you multiple 6 to 4 you get 24. if you multiple 24 to 6 you get 144. if you multiple 144 to 6 you get 864.

The probability that at least 2 of the colors will be the same, the following is the best simulation is Option D Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.

Given, Sienna buys a mystery pack of sparkly modeling clay. The pack has 5 colors, and there are 7 possible colors that are all equally likely. We have to find the probability that at least 2 of the colors will be the same. There are 5 colors in the pack of clay, and 7 colors are possible in total.

So, the probability of picking any color at random is

P(picking a color) = 5/7 = 0.7143Let P(X = 2) be the probability that exactly 2 of the colors are the same.

Then, the probability that at least 2 of the colors are the same can be calculated by using the formula:

P(X ≥ 2) = 1 - P(X < 2).

The simulation method that can be used to find the probability of at least 2 of the colors will be the same in the mystery pack is option D.

Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.

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Answer:

x = 0

Step-by-step explanation:

8^x = 8^2^x

8^x = 8^2x

x = 2x

2x - x = 0

x = 0

The tip of the minute hand on a clock travels a distance of 4π inches in 15 minutes.

The distance traveled by the tip of a minute hand on a clock can be calculated using the circumference formula.

The circumference of a circle is given by the formula:

C = 2πr C is the circumference, π is pi (approximately 3.14159) and r is the radius.

The distance from the center of the clock to the tip of the minute hand is the radius is 8 centimeters.

The circumference of the circle traced by the tip of the minute hand is:

\(\text{C} = 2\pi \text{r}\)

\(= 2\pi (8)\)

\(= 16\pi \ \text{centimeters}\)

Since the minute hand travels the full circumference of the circle in 60 minutes, in 15 minutes it will cover 15/60 = 1/4 of the circumference.

The distance traveled by the tip of the minute hand in 15 minutes is:

\(\text{Distance} = \huge \text(\dfrac{1}{4}\huge \text) \times C\)

\(= \huge \text(\dfrac{1}{4}\huge \text) \times (16\pi)\)

\(= 4\pi \ \text{centimeters}\)

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Answer:

4π cm ≈ 12.6 cm

Step-by-step explanation:

The clock can be modelled as a circle, where the radius (r) is equal to the length of the minute hand:  r = 8 cm.

A clock face is divided into 12 equal sectors (numbered 1 to 12).

It takes 60 minutes for the minute hand to complete one revolution of the clock. Therefore, each sector represents the passing of 5 minutes.

This means that 15 minutes equals 3 sectors, which is a quarter of the circle.

To find the distance the tip of the minute hand travels in 15 minutes, we need to find a quarter of the circumference of a circle with radius 8 cm.

The formula for the circumference of the circle is C = 2πr, where r is the radius. Therefore, the equation to find the distance the tip of the minute hand travelled in 15 minutes is:

\(\sf Distance=\dfrac{2 \cdot \pi \cdot 8}{4}\)

Simplifying, we get:

\(\sf Distance=\dfrac{16 \cdot \pi}{4}\)

\(\sf Distance=4 \pi\)

Therefore, the minute hand will travel 4π cm or approximately 12.6 cm (to the nearest tenth) in 15 minutes.

Answer:

(-7, 3)

Step-by-step explanation:

what Since the endpoints of the interval are not included, use parentheses.

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer:

17

Step-by-step explanation:

step-by-step explanation

Answer:

this is hard

Step-by-step explanation:

is it trigonometry?

The Complete statements are shown below.

Given:

we have AB || CD

We have to prove that ABCD is a parallelogram so that

So, <CBD = <ABD { alternate Interior angle}

AB|| CD (given)

<CDB = <ABD { alternate Interior angle}

BD = BD (Common)

So,  ΔADB ≅ Δ CDB by ASA criteria

Then by CPCT

AB= DC and AD = BC and <BCD = <DAB

So, <CDA = <CDB+ <ADB and <ABC = <CDB+ <ADB by Add Angle postulate.

Then, by transitive property

<CDA = <ABC

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Answer:

7.81

Step-by-step explanation:

its a triangular shape

let x = 4 + 2 = 6

let y = 5

length between two points = h

h² = x² + y²

h² = 6² + 5²

h = sqrt of 61

h = 7.81

The dairy farmer should use 400 pounds of the 75% protein supplement and 800 pounds of the 30% protein ration to make 1200 pounds of a high-grade 45% protein ration.

To determine how many pounds of each protein supplement the dairy farmer should use, we can set up a system of equations based on the given information.

Let's denote the following:

x = pounds of the 75% protein supplement

y = pounds of the 30% protein ration

The total weight of the mixture is 1200 pounds, so we have the equation:

x + y = 1200

The protein content in the mixture should be 45% of the total weight, so we have the equation:

0.75x + 0.30y = 0.45 * 1200

Now we can solve this system of equations.

First, let's rewrite the second equation in decimal form:

0.75x + 0.30y = 540

To make it easier to work with, we can eliminate the decimals by multiplying both sides of the equation by 100:

75x + 30y = 54000

Now we have a system of equations:

x + y = 1200

75x + 30y = 54000

We can solve this system using any appropriate method, such as substitution or elimination. In this case, let's use the substitution method:

Solve the first equation for x:

x = 1200 - y

Substitute the value of x into the second equation:

75(1200 - y) + 30y = 54000

Simplify and solve for y:

90000 - 75y + 30y = 54000

-45y = -36000

y = 800

Now we can substitute the value of y back into the first equation to find x:

x + 800 = 1200

x = 1200 - 800

x = 400

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