Given point M and plane α such that M ∉ α. MO is perpendicular to plane α. MP and MQ are inclined to α which make 30° and 60° with plane α, respectively. Find the length of PQ in terms of

MO if ∠POQ = 120°

If 12 out of every 15 people prefer eating at a restaurant, then 12/15 of the people who took the survey chose that option. We know that 12/15 of the total number of people who took the survey is equal to 400 people, so we can set up the equation:

(12/15)x = 400

To find the total number of people who took the survey, we can solve for x by multiplying both sides of the equation by 15/12:

x = (400)(15/12)

x = 500

So, 500 people took the survey.

The distance travelled by the car during this time  by using single  appropriate trapezium is  26.25 and the answer provided is an underestimate

A) Using a single appropriate trapezium, the estimated distance travelled by the car during the 30 seconds is approximately 55 metres.

This is calculated by taking the area of the trapezium formed by the two points of the speed graph: 8m/s and 6m/s.

The area is calculated by taking the average of the two points, multiplied by the time duration:

Area = (8+6/2) * 30

Area = 7*30

Area = 210

The area of the trapezium is then divided by the speed of the car at the start of the journey (8m/s) to get the estimated distance travelled:

Distance = 210/8

Distance = 26.25

This is rounded up to give an estimated distance travelled of 55 metres.

B) The answer of 55 metres is an underestimate of the actual distance travelled by the car. This is because the trapezium method only takes into account the start and end points of the graph, and not any of the other points in between. The actual distance travelled by the car is likely to be higher as the speed of the car is likely to have been greater at points in between the start and end points.

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The area of square = 72.0 in The surface area of a shape is measured using the area.use square units for area when you can multiply the length to determine the area .

Option B is correct.

The quantity of square units required to completely fill a square is known as the area of a square. The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. The measurement is made using square units, with square metres serving as the standard unit (m²).

Area of square = Side ²

side=6√2

Area=?

Area of square = ( 6√2)²

                            72 .0 inches.

This is because the sum of two lengths is used to calculate an area. If those are, for instance, measured in meters, you would multiply some meters by others. Consequently, the expression for the area in square meters. Similar to volume: You divide three lengths by.

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Answer:

4.34

Step-by-step explanation:

proportional: 2.8/2.5 =1.12

body + tail = body + 1.12 body = 2.12 body = 9.2.

so body = 9.2/2.12 = 4.34

Answer:

So there are 11 mg of calcium in apples.

38 mg of calcium in oranges.

And 6 mg of calcium in bananas.

So if he ate 7 apples, that adds up to:

7 * 11 = 77 mg of calcium.

4 oranges adds up to:

4 * 38 = 152 mg of calcium

2 bananas adds up to:

2 * 6 = 12 mg of calcium.

In total:

77 + 152 + 12 = 241

Alen ate 241 mg of potassium

Step-by-step explanation:

Hope it helps! =D

The total number of quarters James and his brother will be 5x

Addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

James has x quarters while his brother has 4 times as many quarters as James.

So, for determining the value of the total number of quarters James's brother have we will multiply the value of the total number of quarter James have by 4.

So, the value of the total quarter James's brother has = 4*x = 4x

Now for determining the total number of quarters of James and his brother we will add both values.

The total number of quarters James and his brother will be= x+4x = 5x

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Answer: 1/3 per friend.

Step-by-step explanation:1/3 1/6*4= 3/3 or 1 whole bag. to find the 1/6, 2/3 multiply by 1/4= 2/12 or 1/6 of popcorn per friend

Answer:

Since Marshall gives away 13 buttons out of b buttons, it means that b is an expression of a number which is greater than 13. Therefore,the answer is b - 13.

Figure ABCDE has vertices A(−3, 3), B(2, 3), C(5, −2), D(0, −3), and E(−3, −2) So the Area of figure = 36.5 sq units

To Find: Plot the points  

Decompose Figure ABCDE into rectangles and triangles.

lengths of Sides AB and AE.

area of Figure ABCDE

Plot ( x , y) ( x , y)

If x is positive, start right away from the origin. If it's negative, turn left.

If +ve, move y upward; if -ve, move y downward.

Plotted and labeled points

A(−3, 3), B(2, 3), (2, 3),

AB's length is five.

A(−3, 3) E(−3, −2).

AE length is 5

two triangles and one rectangle

area of a rectangle equal 5 * 5, or 25 square units.

The right angle triangle's area is equal to (1/2) * 5 * 3 = 7.5 square units.

another triangle's area is equal to (1/2) * 8 * 1 square units.

Figure's surface area is 25 + 7.5 + 4 = 36.5 sq units.

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The amount of money in Davinder's account after five years is equal to £236.

Mathematically, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have;

S.I = 200 × 4.5/100 × 5

S.I = 200 × 0.045 × 4

S.I = £36.

Next, we would calculate the future value as follows;

Future value, A = S.I + P

Future value, A = £36 + £200

Future value, A = £236.

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The function g(x) with a graph that is the reflection of the graph of f(x) = - square root 14x across the x-axis is given as follows:

[tex]g(x) = \sqrt{14x}[/tex]

The parent function f(x) is defined as follows:

[tex]f(x) = -\sqrt{14x}[/tex]

The rule for a reflection over the x-axis is given as follows:

g(x) = -f(x).

Meaning that only the signal of the function is changed.

Removing the negative signal, the function g(x) is then defined as follows:

[tex]g(x) = \sqrt{14x}[/tex]

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Answer:

0.82

Step-by-step explanation:

A： area =2( 0.8*0.6*+0.6*1+0.8*1) =2(0.48+0.6+0.8)=2*1.88 =3.76

B：area = 2(1.4*0.5+0.5*1.2+1.4+1.2) =2(0.7+0.6+1.68)=2*2.98=5.96

total 9.72

cost = $6.79* 9.72/80 =$0.82

deci nu știi să faci matematică?

The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) is g(f(x)) is x.

Write the function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.

steps for determining a function's inverse.

In the equation expressing the function, swap out f(x) with y.

Swap out x and y. To put it another way, swap out every x for a y and vice versa.

Solve for y.

Change y to f-1 (x).

The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x.

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The required two positive numbers are 11 and 14 which product is 154 and the sum is a minimum.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.

The product is 154 and the sum is a minimum.

As per the question, the required solution would be as:

product           sum  

1 x 154         1 + 154 = 155

2 x 77          2 + 77 = 79

11 x 14          11 + 14 = 25

7 x 22         7 + 22 = 29

Here, we can arrange these numbers as:

25 < 29 < 79 < 155

This means the sum (11 + 14 = 25) is a minimum.

So the minimum value = 11

And the maximum value = 14

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Range, because it measures the distinction between the highest and lowest values in a dataset, providing a clear estimate of variability for both sets of data. It is unaffected by skewness or symmetry, making it a useful measure of variability for comparing the temperature consistency of Desert Landing and Flower Town.

A histogram is a rough illustration of how numerical values are distributed. Karl Pearson coined the phrase at the beginning.

A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width. The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most typical type of histogram.

A common tool for graphing is the histogram. It is employed to summarise continuous or discrete data that is measured on an interval scale. It is frequently used to provide a convenient manner of illustration for the main characteristics of the data distribution.

Therefore, the correct answer is both option c) and d) Range, because Flower Town is skewed and symmetric.

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Answer:

The correct answer is:

Range, because Flower Town is symmetric

The slope intercept form of the expressions are 0 ≤ x, y > 4 and 5 ≥ x

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

The slope intercept form of an inequality is represented as

y > mx + c

Note that the symbol > can be replaced by the appropriate inequality symbol

When the given expressions are rewritten, we have

0 ≤ x

y > 4

5 ≥ x

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The height of the fabric is 8 ft.

Now, According to the question:

Rachel is making a tent.

The triangular piece of fabric for the front of her tent has an area of 24 [tex]ft^2[/tex]

and, it is 6 feet long at it's base.

We have to find the height of the fabric .

Now, Based on the given condition:

Formulate the problem:

24 × 2 ÷ 6

Cross out the common factor:

4 × 2

Calculate the product or quotient :

= 8

Hence, the height of the fabric is 8 ft.

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There is sufficient evidence at 0.10 level of significance that the machine is overfilling the bags. So the option 1 is correct.

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 418 gram setting.

For the given question,

The Hypothesis for the test would be:

H(0): μ = 418

H(1): μ > 418

The fact that the null hypothesis is rejected means that there is enough data to conclude that the machine is significantly overfilling the bags at the 0.10 level of significance.

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The complete question is:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 418 gram setting. Is there sufficient evidence at the 0.10 level that the bags are overfilled? Based on a 24 bag sample, the manufacturer decides to reject the null hypothesis. What is the conclusion?

1. There is sufficient evidence at the 0.10 level of significance that the machine is overfilling the bags.

2. There is not sufficient evidence at the 0.10 level of significance that the machine is overfilling the bags.

Here is one possible system of equations to represent the information provided:

Let x be the number of apple pies, y be the number of pumpkin pies, and z be the number of key lime pies.

The number of apple pies is the same as the number of pumpkin and key lime pies combined, since both tables have the same number of pies: x = y + z

There are twice as many pumpkin pies as key lime pies: y = 2z

There are 5 more apple pies than pumpkin pies: x = y + 5

Solving for y in the second equation, we have: y = 2z

Substituting that into the first equation we have: x = 2z + z = 3z + 5

Substituting that into the third equation we have: x = y + 5 = 2z + 5

So we have a system of equations:

Now we can solve for any of the variables. Let's find the number of PUMPKIN pies

y = 2z

We can substitute in any value of z to get y.

For example, if we let z=5, we can find that

y=2(5)=10 pumpkin pies

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Kwan is utilizing 8% of the entire garden to plant radishes.

Kwan is planting a garden and he is utilizing 1/5 of the garden to plant vegetables. That implies that 1 out of 5 pieces of the garden is being utilized to grow vegetables.

He then, at that point, expresses that he utilizes 2/5 of that 1/5 region for radishes. That implies that 2/5 of the area utilized for vegetables is being utilized to grow radishes.

To find the fraction of the entire garden that is being utilized for radishes, we want to join the two fractions. We can do this by multiplying them together.

At the point when we multiply 1/5 by 2/5, we get 2/25. This fraction can likewise be communicated as a rate by multiplying it by 100.

2/25 * 100 = 8%

So, Kwan is utilizing 8% of the entire garden to plant radishes.

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The age of Bryson today is 11 1/3 years

From the question, we have the following mathematical statements:

Bryson's dad age = 38

Bryson's dad age = 4 + 3 * Bryson's age

Represent Bryson's age with x

So, we have the following equation

Bryson's dad age = 38

Bryson's dad age = 4 + 3x

substitute the known values in the above equation, so, we have the following representation

4 + 3x = 38

Evaluatet the like terms

3x = 34

Divide by 3

x = 11 1/3 years

Hence, Bryson's age as per the mathematical statement is 11 1/3 years

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Each comic costs $4.71 and each novel costs $7.29.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

Let x be the cost of one comic and y be the cost of one novel.

From Amanda's purchase, we know that:

4x + y = $19

From Janelle's purchase, we know that:

x + 2y = $17

We can use the first equation to solve for y in terms of x:

y = $19 - 4x

We can substitute this expression for y into the second equation:

x + 2($19 - 4x) = $17

x + 2$19 - 8x = $17

-7x = $17 - 2$19

-7x = -$33

x = $33/-7 = $4.71

We can use this value of x to find the value of y:

y = $19 - 4($4.71) = $7.29

Hence, each comic costs $4.71 and each novel costs $7.29.

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Using inequality, the minimum number of towels in the pack is t = 6.

We can start by using the inequality 2.85t > 22, where t is the number of towels in the pack.

To find the minimum number of towels, we can use the smallest possible value for t that satisfies the inequality. Since the hand towels were available in packs of 4, 5, 6, and 8, we can use t = 4 in the inequality:

2.85(4) > 22

Simplifying the left side of the inequality gives:

11.4 > 22

This is not true, so t = 4 does not satisfy the inequality.

Next, we can use t = 5:

2.85(5) > 22

Simplifying the left side of the inequality gives:

14.25 > 22

This is also not true, so t = 5 does not satisfy the inequality.

We can keep doing this for t = 6, and t = 8, we will find out t=6 is the minimum value of t that satisfies the inequality.

2.85(6) > 22

Simplifying the left side of the inequality gives:

17.1 > 22

This is true, so t = 6 is the minimum number of towels in the pack.

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Answer: Points: (0, -3), and (9, 0)

Step-by-step explanation:

In order to graph an equation, you find 2 pairs of points and then just connect them into a line. (The x intercepts and the y intercepts are helpful)

One pair: (x, y) = (0, -3)

Another pair: (x, y) = (9, 0)

Now just connect them to get the line :>

The general solution of an exact differential equation can also be found by solving the associated homogenous equation and adding the particular solution obtained from the original equation.

1. Identify the exact differential equation.

2. Find the integrating factor by multiplying the equation by an expression of the form e^(f(x)).

3. Multiply the integrating factor with the equation to make it exact.

4. Integrate both sides of the equation to obtain the general solution.

5. Check the solution by differentiating it to confirm that it satisfies the original equation.

6. Add the particular solution obtained from the original equation to the homogenous solution to get the general solution.

The general solution of an exact differential equation can be found by using an integrating factor. An integrating factor is a function of the independent variable which can be multiplied with the equation in order to make it exact. Once the equation has been made exact, it can be solved using the standard integration techniques. In addition, the general solution can be found by solving the associated homogenous equation and then adding the particular solution obtained from the original equation.

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When White Oak is 15 miles from River City and the scale is 1 in.=3 mi, the distance in the map is 5 inches.

The ratio that describes the relationship between the actual figure and its model is called the scale. It serves as a representation of the actual figures in smaller units on maps. A scale of 1:5, for instance, means that 1 on the map is equivalent to the size of 5 in the real world.

A scale of 1:5, for instance, means that the size of 1 unit in the drawing corresponds to the size of 5 units in the real world. A scale of 1:5 is evident, for instance, if a giraffe that stands 150 inches tall in real life is depicted on the drawing as 30 inches tall.

In this case, when White Oak is 15 miles from River City and the scale is 1 in.=3 mi, the distance in the map is:

= 15 / 3

= 5 inches.

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The amount of money Rashon would need to invest is equal to $8,300.46.

Mathematically, the compound interest on an investment can be calculated by using this mathematical expression:

A(t) = P(1 + r/n)^{nt}

Where:

In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:

Quarterly interest rate = 0.069/4

Quarterly interest rate = 0.01725%

20,200 = P(1 + 0.01725)^{4 × 13}

20,200 = P(1.01725)^52

20,200 = 2.4336P

Principal, P = 20,200/2.4336

Principal, P = $8,300.46.

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Answer:

In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:

Quarterly interest rate = 0.069/4

Quarterly interest rate = 0.01725%

20,200 = P(1 + 0.01725)^{4 × 13}

20,200 = P(1.01725)^52

20,200 = 2.4336P

Principal, P = 20,200/2.4336

Principal, P = $8,300.46.

Answer: The equation provided is already solved, on the left side of the equation it shows the step by step solution of the equation:

3(x-2)+x-1 = 3(x-2) + x - 1 = 5

3x - 6 + x - 1 = 5

Combining like terms

4x - 7 = 5

Adding 7 to both sides

4x = 12

Dividing both sides by 4

x = 3

So the value of x that makes the equation true is x = 3

Step-by-step explanation:

The inequality for this problem is defined as follows:

The Cartesian plan representation of the inequality is given by the image presented at the end of the answer.

The two conditions for the inequality are given as follows:

These conditions are plotted as follows:

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