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Analyzing Intersections of Lines and Planes
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Use the given diagram to answer the question.
Which line is the intersection of two of the planes
shown?
Which line intersects one of the planes shown?
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Which line has points on three of the planes shown?

Answer:

Step-by-step explanation:

the fourth one

Answer:

first three answers.

Step-by-step explanation:

each bottle is 1/4d. so all three are 3*1/4d

Using the arithmetic operation, the number of worker in San Diego is obtained as 260, and the number line which represents the same is option 1.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The number of offices are = 3

The number of workers in the company is = 480

The number of workers in New York city = 90

The number of workers in Denver city = 130

The number of workers in San Diego city = x

To find the number of workers in San Diego use the formula -

Number of workers in San Diego = Total Number of Workers - (Number of workers in New York + Number of workers in Denver)

The arithmetic operation of addition and subtraction is used.

Substitute the values into the equation -

Number of workers in San Diego = 480 - (90 + 130)

Number of workers in San Diego = 480 - 220

Number of workers in San Diego = 260

The number line which represents the number of workers in San Diego is  option 1.

Therefore, the number of workers in 260.

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A company has offices in 3 different cities and a total of 480 workers. There are 90 workers in New York and 130 workers are in Denver. Which number line represents the number line represents the number of workers in San Diego?

Systematic random sampling is used when selecting every nth item from a list of items. In this example, every 49th student starting with the 3rd student is selected.

In systematic random sampling, a list of items is created and every nth item is selected for the sample. This technique is useful when selecting a representative sample from a large population of items. In the example given, 496 students were listed and every 49th student starting from the 3rd student was selected. This is a systematic random sampling technique because the items were selected in a systematic and random fashion. The selection of every 49th student starting from the 3rd student ensures that the sample is representative of the population while also randomizing it so that all students have an equal chance of being selected.

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A solution to the given system of equations include the following:

x = -2.

y = -1.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

y = 2x + 3      .......equation 1.

y = 3x + 5      .......equation 2.

By using the substitution method to substitute equation 1 into equation 2, we have the following:

2x + 3 = 3x + 5

By re-arranging and collecting like terms, we have the following:

3x - 2x = 3 - 5

x = -2.

For the value of y, we have the following:

y = 2x + 3

y = 2(-2) + 3

y = -4 + 3

y = -1.

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Answer:

D. I centimeter

Step-by-step explanation:

Since it is only 0.128 nm wide

0.128 nm x 100,000,000 =

1.28 centi meters

Answer:

D)  1 centimeter

Step-by-step explanation:

The SI base unit for length is meters (m).

The radius of a copper atom is 128 pm.

Picometer (pm) is a unit of length equal to 1 × 10⁻¹² meters.

Therefore, the radius of a copper atom in the SI base unit for length is:

[tex]\implies \sf 128 \times 10^{-12} = 1.28 \times 10^{-10}\;m[/tex]

One hundred million = 100,000,000 = 1 × 10⁸

Therefore, the length of a line of one hundred million copper atoms in meters is:

[tex]\implies \sf 1 \times 10^{8} \times 1.28 \times 10^{-10}[/tex]

[tex]\implies \sf 1.28 \times 10^{-10} \times 10^{8}[/tex]

[tex]\implies \sf 1.28 \times 10^{-10+8}[/tex]

[tex]\implies \sf 1.28 \times 10^{-2}\;\;m[/tex]

Centimeter (cm) is a unit of length equal to 1 × 10⁻² meters.

To convert meters to centimeters, divide by 1 × 10⁻²:

[tex]\implies \sf \dfrac{1.28 \times 10^{-2}}{1 \times 10^{-2}}=1.28\;cm[/tex]

Therefore, a reasonable estimate for the length of one hundred million copper atoms arranged in a line is 1 centimeter.

The equation of the plane  passing through point P with normal vector n A(x-2) + B(y-3) + C(z-4) = 0

(a) Normal Form:

The equation of the plane passing through point P with normal vector n can be written in normal form as:

n • (r - p) = 0

where r is a position vector in three-dimensional space and n is the normal vector of the plane.

Given n = (1,2,3) and p = (2,3,4).

Therefore, n • (r - p) = (1,2,3) • (r - (2,3,4)) = r1 + 2r2 + 3r3 -2 - 3 - 4 = 0

=> r1 + 2r2 + 3r3 - 8 = 0

=> Plane equation in normal form: 1x + 2y + 3z - 8 = 0

(b) General Form:

The equation of the plane passing through point P with normal vector n can also be written in general form as:

A(x-x0) + B(y-y0) + C(z-z0) = 0

where A, B and C are the components of the normal vector n and (x0,y0,z0) are the coordinates of the point p.

Given n = (1,2,3) and p = (2,3,4).

Therefore, A(x-2) + B(y-3) + C(z-4) = 0

=> 1(x-2) + 2(y-3) + 3(z-4) = 0

=> Plane equation in general form: x - 2y + 3z - 8 = 0

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Provide complete question here:Write the equation of the plane passing through p with normal vector n in (a) normal form and (b) general form.

An expression using the distributive property to find the earnings Jessica made on Friday and Saturday is 10(4 + 7).

The distributive property postulates that multiplying the sum of two or more addends by a number gives the same result as multiplying each addend by the number and then adding the products together.

The distributive property helps to solve mathematical expressions written in the form of a(b + c).

The amount Jessica makes per hour babysitting = $10

The number of hours of babysitting on Friday = 4 hours

The number of hours of babysitting on Saturday = 7 hours

According to the distributive property, the results from 'a' and 'b' below are the same.

a) 10(4 + 7) = 40 + 70 = 110

b) 10(4 + 7) = 10 x 11 = 110

Thus, using the distributive property, Jessica will make $110 for babysitting on Friday and Saturday, notwithstanding whether process A or B was followed.

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Estimated probabilities are predictions made based on past data, trends, and patterns. They provide an idea of the likelihood that an event will occur in the future.

Part A:

Answer: The probability of a drought within the next 4 years if the probability of a drought in any one year is 12% is approximately 48%.

Part B:

Answer: Pairs of digits starting at 00 and ending at 11 represent a drought happening. Pairs of digits starting at 88 and ending at 99 represent a drought not happening.

Part C:

Answer: Using the random numbers, the estimated probability that a drought happens at least once over the next 4 years is 68%.

Part D:

Answer: The probability that was calculated is greater than the probability predicted. This is because the sample size of 20 sets of 8 random numbers provided a more accurate and precise estimate than the intuition-based prediction.

Part E:

Answer: Yes, the estimated probability changes when the pairs of digits that represent a drought happening are changed so that they start at 10 instead of 00. Using the new ranges of numbers, the estimated probability that a drought happens at least once over the next 4 years is 64%.

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Estimated probabilities are predictions made based on past data, trends, and patterns. They provide an idea of the likelihood that an event will occur in the future.

Predictions based on historical data, patterns, and trends are known as estimated probability. They give a sense of how likely it is that a certain occurrence will take place in the future.

Estimated probabilities calculation Part A:

If the likelihood of a drought in any given year is 12%, the likelihood that one will occur within the next four years is roughly 48%.

Part B:

Answer: The drought is represented by pairs of numerals beginning at 00 and ending at 11. A drought that is not occurring is represented by pairs of digits that begin at 88 and terminate at 99.

Part C:

According to the random numbers, there is a 68% chance that a drought will occur at least once over the next four years.

Part D:

Answer: The calculated probability is higher than the expected probability. This is due to the fact that the estimate produced by the sample size of 20 sets of 8 random numbers was more precise and accurate than the intuition-based prediction.

Part E:

Answer: When the pairs of digits that represent the occurrence of a drought are modified so that they begin at 10 instead of 00, the predicted likelihood does indeed change. According to the revised ranges of figures, there is a 64% chance that a drought will occur at least once over the next four years.

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In the below we have compared deaths in A and B in terms of ratio, percentage and in terms of proportion.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The first comparison is in terms of rato.

The ratio of deaths due to a deadly disease in the United States at A and B is A : B = 17821 : 52093.

The second comparison in terms of percentage,

The percentage of people died in A is (52093/17821)×100 = 292.31% more than people died in B.

The third comparison is in terms of fractions.

The fraction of people died in A is (52093/17821) = 2.92 times more than people died in B.

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Answer:

no clue sorry I was not able to help

5/2 and 3 are the solutions to the equation 2x² - 10x + 15 = x.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

2x² - 10x + 15 = x

2x² - 11x + 15 = 0

2x² -6x -5x + 15 = 0

2x(x-3)-5(x-3)=0

x=5/2, 3

The solutions to the equation 2x² - 10x + 15 = x is 5/2 and 3.

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When calculating the finance charges, the monthly interest rate (MPR) is multiplied by the D. average daily balance.

The finance charge refers to the interest and other fees a borrower pays on a credit card.

To compute the finance charge, the annual percentage rate (APR) or the monthly percentage rate (MPR) is multiplied by the balance owed.

The balance commonly used for this calculation is the average daily balance.

Thus, Option D is multiplied by the MPR to compute the finance charges.

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By constructing 95% confidence intervals for each simulation, we can be 95% confident that the true proportion of wins lies within the range of each interval.

A confidence interval is a set of values that, given a specific level of certainty, are likely to include a population parameter like a mean or proportion.

The interval is derived using data drawn from a sample of the population and is frequently presented as a range of values with a 95% confidence level.

The probability that the range of values contains the genuine population parameter is quantified by the confidence level.

In the case of a 95% confidence interval, for instance, it means that 95% of the intervals would contain the real population parameter if we sampled the same population more than once and calculated a confidence interval each time.

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The absolute values of inequality equations totally depend on the symbols.

An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in unequal absolute values. By comparing the absolute valuesof two numbers on the number line, inequality is most frequently utilized. Different types of inequality are represented by a variety of different notations, including:

The symbol a b indicates that an is less than b.

A bigger value for a than a lesser value for b is indicated by the notation a > b.

a is not equal to b in either situation. These relationships are referred to be stringent inequalities since an is either strictly less than or strictly greater than b. Equivalence is not included.

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Answer:

4 cm.

Step-by-step explanation:

Area = pi r^2, so:

pi r^2 = 4 / pi

(pi)^2 r^2 = 4

r^2 = 4/ (pi^2)

r = 2/pi

Therefore, the circumference

= 2 pi r

= 2* pi * 2/pi

= 4

The ordered pair that represents (c•d)(4) on the graph of the combined function is (4, -12)

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

The graph

The function of the graph is a combined function (c . d)(x)

To calculate (c . d)(4), we trace the point x = 4 to the curve

So, we have

(c . d)(4) = -12

See attachment for the graph

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The upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles is 72.2 gallons.

R(t) gallons per hour of water leak from a tank. The values of the rate at two-hour intervals are shown in the table below. As time went on, the rate decreased. A Riemann sum is used to determine the overall volume of water that has leaked out.

An integral representation of the rate function would be the amount of water. Estimation with the Riemann sum and left endpoints:

F(x) ≅ ∑f(xi-1)Δx where Δx=10/5 = 2 for this case and i = 1 to 5

W = (10.7 + 8.6 + 6.6 + 5.2 + 5.0)2

= 36.1•2

= 72.2 gallons

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Answer: To find the area of a rectangle, you can use the formula:

Area = Length x Height

In this case, the length is given in cm and the height is given in mm. Therefore, you need to convert the length to mm before you can calculate the area.

1cm = 10mm.

So, 8.2 cm = 8.2 x 10 = 82mm

Now you can find the area of the rectangle:

Area = Length x Height = 82mm x 42mm = 3,444 mm^2

So, the area of the rectangle is 3,444 mm^2

Step-by-step explanation:

Option C. They will walk 9 laps and run 15 laps for a total of 24 miles.

The table is given as Walk (laps) 3 B 15

Run (laps) 5 10 D

Total (laps) A C 40

The total for walk and run is 3 + 5 = 8

Walk is 3

Run is 5

We are to find the laps of both categories with respect to the total distance of 24 miles

for walk = 3/8 * 24

= 9

For run we would have 5 / 8 * 24 = 15

Hence They will walk 9 laps and run 15 laps for a total of 24 miles.

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The function represented in Cartesian plane have the following features: Domain of function: - 4 ≤ x ≤ 2, Range of function: - 4 ≤ y ≤ 4. (Right choice: B)

In this question we find the representation of a function on Cartesian plane. There are two important hints to answer this question:

Then, by direct inspection we find the following results: Domain: - 4 ≤ x ≤ 2, Range: - 4 ≤ y ≤ 4.

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[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

As it is a triangle , so we know that sum of all angles of a triangle = 180°

=> 44 + 53 + x = 180

=> 97 + x = 180

=> x = 180 - 97

=> x = 83°

Answer: x = 13

Step-by-step explanation:

First you have to move 15+ to the other side to 28.Then when 15+ moves to the other side it will be 15-. After that you subtract 28 with 15 that will make 13. So x is equal to 13.

By numbers:

15+x=28

x=28-15

x=13

The student is trying to construct a bisector of a given Angle i.e. A.

what is a bisector?

In Geometry, a “Bisector” is a line that divides the line into two different or equal parts. It is applied to the line segments and angles. A line that passes through the midpoint of the line segment is known as the line segment bisector, whereas the line that passes through the apex of an angle is known as the angle bisector. The bisector of a segment always contains the midpoint of the segment. There are two types of bisectors based on what geometrical shape it bisects.

Line Segment Bisector (Perpendicular Bisector Theorem)

Angle Bisector (Triangle Bisector Theorem)

Now,

As we can see from the figure given that the bisector is dividing the angle in two equal segments.

Hence,

          The student is trying to construct a bisector of a given Angle.

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The two lines are perpendicular because the product of their slopes is equal to 1

The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line

Given here: The two lines  x-3y =15 and y = -3y + 4

Rewriting the given expressions in slop-intercept form we get

y=x/3-5

y = -3y + 4

The respective slopes are given as 1/3 and -3

Thus the product of the two slopes is 1/3×-3=-1

Hence, The given lines are perpendicular.

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The angle θ measures 53.13⁰ with the east direction.

The tangent of an angle is a trigonometric function that is defined as the ratio of the side opposite the angle to the side adjacent to the angle in a right triangle. In other words, it is a measure of the steepness of a line that is tangent to a point on a function's graph and is represented by the symbol tan. It is one of the three main trigonometric functions, along with sine and cosine. The value of tangent is always positive in the first and fourth quadrants.

let the angle made be θ degree to the north of east from the post office to the grocery shop

so tan θ = p/b

where p is perpendicular , b is base of the triangle

so tan θ = 3/4

=> θ = 53.13 degree

so the angle θ measures 53.13⁰ with the east direction.

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Complete question :

what is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.

When looking east, the angle is 53.[tex]13^{0}[/tex] degrees.

What does a tangent to any angle mean?

The ratio of a right triangle's side opposite to its side next to the angle is known as the tangent of an angle, which is a trigonometric function. It is a measurement of the steepness of a line that is tangent to a point on the graph of a function, and it is denoted by the symbol tan. One of the three primary trigonometric functions, together with sine and cosine, is it. In the first and fourth quadrants, tangent's value is always positive.

Let the angle formed between the post office and the grocery store be degrees to the north of east.

so tan θ = p/b

where p is perpendicular , b is base of the triangle

so tan θ = 3/4

=> θ = 53.13 degree

so the angle θ measures 53.13⁰ with the east direction.

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Complete question :

What is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.

Answer:

Look below

Step-by-step explanation:

Sale prince is $300

the commission is 3/4%

Commission amount is $2.25

Price + commission $302.25

Price - commission $297.95

I hope this gives you the answer you where looking for

The fraction of a pound of granola that Marty bought is 3/4 pounds.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 3/4.

The unit of conversion of ounces to pounds is :

1 pound = 16

12 ounces of granola =  12/16 pounds = 3 /4 pounds

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Given expression ?/(2/5)=4 where ?=x gives x=8/5.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression ? ÷ 2/5 = 4

let x=?

Therefore,

              x=4*2/5

             x=8/5

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Answer:

All you have to do is divide by -2 on both sides. You're trying to get x by itself, so divide by a number by cancels itself out. Don't forget the negative sign as well, or else you'll be left with -x instead of just x. A positive number divided by a negative number will become negative.

-2x=8

x=-4