2) The solution interval to 5sin x ≥- 2cosx; [0, 2n) is [0, 2.532] U [3.751, 6. 283]. If true, justify why it is correct. If false, justify why. Show step by step process to receive full credit.

The 10th percentile of pit depths is 780μm. A certain pit with 780 μm deep is at the 10th percentile. The proportion of pits have depths between 800 and 830 μm is 7.33%.

A)

To find the 10th percentile of pit depths, we need to use the z-score table. Where x = μ + zσ, here we are looking for the z-score, for the given 10th percentile.

Using the standard normal distribution table, we get the value of -1.28 which corresponds to the 10th percentile.

Therefore,

x = 818 - 1.28 * 29x = 779.88 = 780μm.

So, 780μm is the 10th percentile of pit depths.

B)

We are given that the mean is 818 μm and standard deviation is 29 μm. A certain pit is 780 μm deep. To find the percentile for this, we need to find the z-score for this given pit.

x = 780 μm, μ = 818 μm, σ = 29 μm

Now, z-score can be found as,

z = (x - μ) / σ = (780 - 818) / 29 = -1.31

We can find the percentile using the standard normal distribution table.

Therefore, the given pit is at the 10th percentile.

C)

We are given that the mean is 818 μm and standard deviation is 29 μm. The proportion of pits with depths between 800 and 830 μm can be calculated as follows:

P(z < (X- x) / σ) - P(z < (830 - 818) / 29) - P(z < (800 - 818) / 29)

P(z < -0.41) - P(z < -0.62) = 0.3409 - 0.2676 = 0.0733

(rounded off to four decimal places)

Therefore, approximately 7.33% of pits have depths between 800 and 830 μm.

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 To find the measure of x and the unknown angles in a polygon, we can create an equation based on the sum of the interior angles, which is 540 degrees.final answer is 108°.

Let's assume the polygon has n sides. Each interior angle of a polygon can be calculated using the formula (n - 2) * 180° / n. In this case, we are given that the sum of the interior angles is 540 degrees.
So, we can set up the equation:
(n - 2) * 180° / n * n = 540°
Simplifying the equation:
(n - 2) * 180° = 540°
(n - 2) = 540° / 180°
(n - 2) = 3
Solving for n:
n = 3 + 2
n = 5
Now that we know the polygon has 5 sides, we can find the measure of x by substituting it back into the formula:
x = (5 - 2) * 180° / 5
x = 3 * 180° / 5
x = 540° / 5
x = 108°
In conclusion, the measure of x is 108 degrees, and each of the unknown angles in the polygon would also be 108 degrees since all angles in a regular polygon are equal.

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lambert's cylindrical projection preserves the relative size of geographic features. this type of projection is called equivalent.

cylindrical projection, in cartography, any of numerous map projections of the terrestrial sphere on the surface of a cylinder that is then unrolled as a plane.

Originally, this and other map projections were achieved by a systematic method of drawing the Earth's meridians and latitudes on the flat surface.

Mercator projection is defined as a map projection was found in 1569 by Flemish cartographer Gerardus Mercator.

The Mercator projection seems parallels around a cylindrical globe and meridians appears as straight lines, but there is distortion of scale near the poles which do not make it a practical world map.

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I Hope it is correct

Step-by-step explanation:

The total number of sodas in the fridge is:

6 + 4 + 5 + 9 + 7 + 3 + 6 = 40

The number of NuGrapes or ginger ales is:

7 (NuGrapes) + 6 (Canada Dry ginger ales) = 13

The probability of selecting a NuGrape or a ginger ale is the number of favorable outcomes (selecting a NuGrape or a ginger ale) divided by the total number of possible outcomes (selecting any soda):

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 13 / 40

Probability = 0.325

So, the probability of selecting a NuGrape or a ginger ale is 0.325 or 32.5%.

Answer:

26

Step-by-step explanation: I'm pretty sure its 26 because if k = 7 then 4 times 7 equals 28. Then you subtract 2. That's how I got 26.

Answer:

Step-by-step explanation:

\(4k-2\\k= 7\\\)

Substitute 7 for k into the given equation

\(4(7)-2\\\\=28-2\\\\=26\)

The probability of getting the color yellow when spinning a spinner with three equal sections colored red, white, and blue is 0%. Therefore, the correct answer is d) 0%.

Since the spinner has three equal sections colored red, white, and blue, and there is no section labeled yellow, it is not possible to obtain the color yellow when spinning the spinner. Each section has an equal chance of being landed on, but none of them represent the color yellow. Therefore, the probability of getting the color yellow is 0%. It's important to note that probability represents the likelihood of an event occurring, and in this case, the event of landing on the color yellow is not possible given the given information about the spinner. Therefore, the probability is 0%.

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The sample standard deviation is approximately 0.83.

Sample size \(($n$)\) = 36

Population mean \(($\mu$)\) = 50

Population standard deviation \(($\sigma$)\) = 5

The sample standard deviation, denoted as \($s$\) can be estimated using the formula:

\(\[ s = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}} \]\)

where:

\($x_i$\) represents the individual data points in the sample

\($\bar{x}$\) is the sample mean

In this case, since we don't have individual data points, we can use the population standard deviation as an estimate for the sample standard deviation when the sample size is relatively large (as in this case \($n = 36$\)). This approximation is known as the standard error of the mean.

Therefore, the sample standard deviation can be approximated as:

\(\[ s \approx \frac{\sigma}{\sqrt{n}} \]\)

Substituting the given values:

\(\[ s \approx \frac{5}{\sqrt{36}} = \frac{5}{6} \] = 0.83\)

Hence, the sample standard deviation is approximately 0.83.

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Answer:

6.25 hours

Step-by-step explanation:

pages per hour

pages/hour

90/2.5 = 36

36 pages per hour

225 / 36 = 6.25 hours

Answer:

6.25 hours

Step-by-step explanation:

2 and half hours = 2.5 hours

Proportions:

90 pages  ⇔  2.5 hours

225 pages  ⇔  E hours

E = 225*2.5/90

E = 6.25 hours

6.25 hours = 6 and 1 quarter hours

Answer:

15a⁴b²-20a³b³+30a²b⁴

Step-by-step explanation:

3a²-4ab+6b²

so for 5a²b²

(5a²b²)(3a²-4ab+6b²)

=15a⁴b²-20a³b³+30a²b⁴

By applying the distributive property, 5a²b² × (3a²- 4ab + 6b²)​ = 15a⁴b² - 20a³b³ + 30a²b⁴

Given the expression: 5a²b² × (3a²- 4ab + 6b²)​

We would apply the distributive property by multiplying every term inside the parentheses by 5a²b².

This can be done as shown below:

5a²b² × (3a²- 4ab + 6b²)​ = 5a²b²(3a²) - 5a²b²(4ab) + 5a²b²(6b²)​

5a²b² × (3a²- 4ab + 6b²)​ = 15a⁴b² - 20a³b³ + 30a²b⁴

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Answer:

The answer is x=4

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

"at least 50" includes 50 as a possibility, which means it would be \(p\geq 50\)

Answer:

a

Step-by-step explanation:

Here is the question used in answering this question :

Gio weighed five boxes before he shipped them. The weights were: 52,48,48,54, and 50. Which statement is true?

A) The mode is equal to the minimum

B)  The mode is greater than the mean

C)  The median and mode are equal

D) The mean is less than the medium

Mode is the number that occurs the most. that number is 48.

Mean = sum of numbers / n = 52 + 48 + 48 + 54 + 50  / 5 = 50.4

Median is the middle number

Arranging the numbers in ascending order : 48, 48. 50, 52, 54. The median is 50

the mode is 48 which is equal to the minimum

the mean is greater than the mode

the mode and median are different figures

A numerical measure computed from a sample, such as sample mean, is known as Sample statistic

What is Statistic?

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.

A sample statistic is a metric that is calculated from a sample, such as sample mean. A population parameter is a numerical measure derived from a population, such as a mean.

Any value calculated from your sample data is referred to as a sample statistic (or simply a statistic). The sample average, median, sample standard deviation, and percentiles are a few examples. Because a statistic is based on data gathered through random sampling, which is a random experiment, it is a random variable.

Hence, A numerical measure computed from a sample, such as sample mean, is known as Sample statistic

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The correct option for the given question is 1/3 distance from the fulcrum which is option B according to the balance rule.

On a balanced seesaw, the torques around the fulcrum calculated on one side and on another side must be equal. This means that the:\(W_1 d_1 = W_2 d_2\)

where we label the things here,

\(W_1\) is the weight of the boy

\(d_1\) is its distance from the fulcrum

\(W_2\) is the weight of his partner

\(d_2\) is the distance of the partner from the fulcrum

We know that the boy is three times heavier than his companion in this situation, so

\(W_1 = 3 W_2\)

If we plug this into the equation, we get:

\((3 W_2) d_1 = W_2 d_2\)

and by simplifying:

\(3 d_1 = d_2\\\\d_1 = \frac{1}{3}d_2\)

From the above equation, we get that the boy sits at 1/3 the distance from the fulcrum.

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Answer:

1.63253e+6

Step-by-step explanation:

Answer:

0.035745

Step-by-step explanation:

\(10^{4}=10,000\\\)

357.45 ÷ 10,000 = Moving the decimal towards three, four times.

00357.45

0035.745 (One)

003.745 (Two)

00.3745 (Three)

0.03745 (Four)

357.45 ÷ 10,000 = 0.035745

Car B will catch up with Car A at 4:45pm, after travelling for 2 5/8 hours (3 hours minus 1 hour minus 3/8 of an hour).

Car A leaves the Grand Canyon at noon and travels at 80 mph. At 3 pm, it stops for an hour. Car B leaves the Grand Canyon at 2 pm and travels at 90 mph without stopping.To calculate when Car B will catch up with Car A, we need to find the time difference between their departure times and the difference in their speeds.Car A leaves one hour before Car B, so we can subtract 1 hour from the total travel time. The difference in their speeds is 10 mph, which is equivalent to 1/8 of an hour for every hour of travel. Therefore, we can subtract 1/8 of an hour from the total travel time for every hour of travel.We can use these two deductions to calculate the total travel time: 3 hours - 1 hour - 3/8 of an hour = 2 5/8 hours. Therefore, Car B will catch up with Car A at 4:45pm.

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Ayana's sandcastle is 1/8 foot taller than her sister's.

Fractions in Math, represent a numerical value that expresses a part of a whole. The whole can be any number, specific value, or a thing.

Given,

Ayana's sandcastle was 1/2 of a foot tall

Her sister's was 3/8 of a foot tall.

Difference between the height of the both sandcastle

= 1/2 - 3/8

= (4 - 3)/8

= 1/8

Hence, Ayana's sandcastle is taller than her sister's by 1/8 foot.

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Answer:

The solution is (-2,-2)

Step-by-step explanation:

This is the point where the two graphs intersect.

The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

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Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

The stems are 0, 2, 3, 4, 5, 6, 8. Therefore option e, is the correct answer

Stem and leaf plot are used in statistics to organize data that are collected. Any number in a data is broken down into a stem and a leaf.

Stem displays data on the left while leaf displays data to the right

The data for the amounts of money (cents) in coins carried by 10 students in a statistics class: 50, 35, 0, 46, 86, 0, 5, 47, 23, 65 can be represented in the stem and leaf plot below:

2 I 3 ⇒ 2 on the stem and 3 on the leaf read as 23

3 I 5 ⇒ 3 on the stem and 5 on the leaf read as 35

4 I 6 ⇒ 4 on the stem and 6 on the leaf read as 46

4 I 7 ⇒ 4 on the stem and 7 on the leaf read as 47

5 I    ⇒ 5 on the stem as 5

5 I 0 ⇒ 5 on the stem and 0 on the leaf read as 50

6 I 5 ⇒ 6 on the stem and 5 on the leaf read as 65

8 I 6 ⇒ 8 on the stem and 6 on the leaf read as 86

Hence, stems are 0, 2, 3, 4, 5, 6, 8

Therefore, option e, is the correct answer

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Answer:

THAT QUESTION WILL BE ANSWERED THIS SUNDAY NIGHT!

Answer:

8 bars

Step-by-step explanation:

1,200÷150=8

Have a wonderful day!

Answer:

he can eat 8 granola bars in a day to stay within his goal.

Step-by-step explanation:

Answer:

It will equal 4.

Step-by-step explanation:

Because when you see the 2 above a 2 you multiply the 2 by 2 to get 4.

Have an amazing day!

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Buying bulk topsoil is less expensive than buying bags of topsoil in this case.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).

To find the volume of a simple object such as a cube, rectangular prism, or cylinder, you can use a formula that involves multiplying the length, width, and height of the object. For example, the formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

For more complex objects, such as irregular shapes or those with curved surfaces, you can use techniques such as integration or approximation to find the volume.

First, we need to determine how many cubic feet of topsoil Austin needs to cover his backyard with a 4 inch layer. We can start by calculating the volume of his backyard in cubic feet:

Volume = length x width x depth

Volume = 70 ft x 60 ft x (4 in / 12) ft

Volume = 1400 ft³

So Austin needs 1400 cubic feet of topsoil to cover his backyard with a 4 inch layer.

Option 1: Bags of Topsoil

Each bag of topsoil covers 3 cubic feet, so Austin needs 1400 / 3 = 466.67 bags of topsoil. Since he can only buy whole bags, he will need to buy 467 bags. Each bag costs $2.50, so the total cost of the topsoil would be:

Total cost = number of bags x cost per bag

Total cost = 467 x $2.50

Total cost = $1167.50

Since delivery is free, the total cost of the topsoil is $1167.50.

Option 2: Bulk Topsoil

Bulk topsoil costs $22.00 per cubic yard, and Austin needs 1400 / 27 = 51.85 cubic yards. Since he can only buy whole yards, he will need to buy 52 yards. The cost of the topsoil itself would be:

Cost of topsoil = volume of topsoil x cost per cubic yard

Cost of topsoil = 52 yd³ x $22.00/yd³

Cost of topsoil = $1144.00

There is also a $20 delivery fee, so the total cost of the topsoil would be:

Total cost = cost of topsoil + delivery fee

Total cost = $1144.00 + $20.00

Total cost = $1164.00

Therefore, buying bulk topsoil is less expensive than buying bags of topsoil in this case.

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Answer:

s

Step-by-step explanation:

Answer:

fourth option) 5/8 lb

The height of the tide in a small beach town is measured along a seawall. Water levels oscillate between 5 feet at low tide and 15 feet at high tide. On a particular day, low tide occurred at 6 am and high tide occurred at noon. Approximately every 12 hours, the cycle repeats.

To find an equation to model the water levels, we can use a sinusoidal equation. Let h(t) be the height of the water at time t (in hours). We know that h(6) = 5 and h(12) = 15. Using this information, we can find the equation:

h(t) = 10 sin (πt/6) + 10
To find an equation that models the water levels in a small beach town, given that the height of the tide is measured along a seawall, we need to use the following information:

Water levels oscillate between 5 feet at low tide and 15 feet at high tide. Low tide occurred at 6 am, and high tide occurred at noon. The cycle repeats approximately every 12 hours. Let the water level at low tide be represented by y = 5, and the water level at high tide be represented by y = 15. We can write these points as (0,5) and (12,15), respectively. Since the water levels oscillate every 12 hours, we can create a sine function that models this pattern. We can use the sine function y = a sin(bx + c) + d, where a is the amplitude (half the height of the wave), b is the frequency (number of waves per unit time), c is the phase shift (horizontal displacement of the wave), and d is the vertical displacement of the wave. Using the given information, we can determine the values of a, b, c, and d:a = (15 - 5)/2 = 5, since the amplitude is half the height of the wave. b = 2π/12 = π/6, since the wave repeats every 12 hours (or twice a day), and the period is 2π/b.c = -π/2, since the graph starts at high tide (the maximum point), not at the midpoint between low and high tide (the x-axis).d = (15 + 5)/2 = 10, since the midpoint between low and high tide is the vertical axis of the sine function. Therefore, the equation that models the water levels is: y = 5 sin(π/6 x - π/2) + 10.

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1. x-3y -3=0, 3x-9y-2=0 has no solution

2. 2x+y=5,3x+2y=8 has a unique solution

3. 3x-5y=20,6x-10y=40 has infinitely many solution

4.  x-3y-7 =0,3x-3y-15=0 has No solution

5. 8x+5y=9,3x+2y=4 has a unique solution

(i) To solve using substitution method, we can rearrange the first equation to x=3y+3 and substitute it into the second equation:

3(3y+3) - 9y - 2 = 0

9y + 9 - 9y - 2 = 0

7 = 0

This is a contradiction, so the pair of equations has no solution.

(ii) To solve using elimination method, we can multiply the first equation by 2 and subtract it from the second equation:

3x + 2y = 8

(4x + 2y = 10)

-x = -2

So, x = 2. Substituting this value into the first equation, we get:

2x + y = 5

2(2) + y = 5

y = 1

Therefore, the unique solution is (x,y) = (2,1).

(iii) To solve using elimination method, we can multiply the first equation by 2 and subtract it from the second equation:

6x - 10y = 40

(6x - 10y = 40)

0 = 0

This equation is true for any value of x and y, so the pair of equations has infinitely many solutions.

(iv) To solve using elimination method, we can subtract the first equation from the second equation:

3x - 3y - 15 - (x - 3y - 7) = 0

2x - 22 = 0

x = 11

Substituting this value into the first equation, we get:

11 - 3y - 7 = 0

-3y = -4

y = 4/3

Therefore, the unique solution is (x,y) = (11,4/3).

(v) To solve using elimination method, we can multiply the first equation by 2 and subtract it from the second equation:

3x + 2y = 4

(16x + 10y = 18)

-29x - 18y = -14

Solving for y, we get:

y = (29/18)x + (7/9)

Substituting this expression for y into the first equation, we get:

8x + 5((29/18)x + (7/9)) = 9

(143/18)x = 2/9

x = 2/13

Substituting this value into the expression for y, we get:

y = (29/18)(2/13) + (7/9) = 41/117

Therefore, the unique solution is (x,y) = (2/13,41/117).

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The answer is C. Ability to rust. This is because rusting is a chemical property of a substance, which is caused by environmental factors causing said substance to tarnish.

Answer:

\(\frac{11}{25}\)

Step-by-step explanation:

\(44\%=\frac{44}{100}=\frac{22}{50}=\frac{11}{25}\)