Find the distance the point P(3, 1, 7), is to the plane through the three points
Q(5, 0, 3), R(0, -1, 7), and S(7, 5, 0).

The lengths for which the area will be less than 175 cm² are less than 25 cm

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

Width = 7 cm

Area = Less than  175 cm²

The formula of area is represented as

Area = Length * Width

Using the above as a guide, we have the following:

Length * Width < 175

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

Length * 7 < 175

Divide by 7

Length < 25

Hence, the length is less than 25

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Answer:

860,000.

Step-by-step explanation:

If the sales in 2022 were up 75% from 800,000, the sales in 2022 would be 800,000 + (800,000 * 75%) = 800,000 + 600,000 = 1,400,000.

To find the sales for 2021, we'll have to use the average annual growth rate to find the sales in between 2012 and 2022.

Let's assume that the sales grew linearly, so the average annual growth rate would be (1,400,000 - 800,000) / (2022 - 2012) = 600,000 / 10 = 60,000.

The sales in 2021 would then be 800,000 + 60,000 = 860,000.

Answer:(4x^2 + y^2)(2x + y)(2x - y)

Step-by-step explanation:

16x^4 - y^4

= (4x2)^2 - (y^2)^2

= (4x^2 +y^2)(4x^2 - y^2)

=(4x^2 + y^2)( (2x)^2 -y^2)

= (4x^2 + y^2)(2x + y)(2x - y).

The equivalent trigonometric expression to sin(2x)cos(x) is given as follows:

sin(2x)cos(x) = 2sin(x)cos²(x).

The expression for this problem is defined as follows:

sin(2x)cos(x).

The trigonometric identity used to simplify sin(2x) is given as follows:

sin(2x) = 2sin(x)cos(x).

Hence the expression can be written as follows:

sin(2x)cos(x) = 2sin(x)cos(x)cos(x)

sin(2x)cos(x) = 2sin(x)cos²(x).

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In the given equilateral triangle XYZ the relation which is true is WX = 2WZ. So option C is correct.

An equilateral triangle is a particular kind of triangle in which the lengths of the three sides are equal. These are a few of its main characteristics:

Congruent angles exist for all three: An equilateral triangle has 60 degrees for each angle.

The three parties all agree: The perimeter of an equilateral triangle is three times the length of any one side because each side is the same length.

For any side, the same line serves as the altitude, median, and angle bisector:

A line segment perpendicular to the other side and drawn from one vertex is the altitude. A line segment called the median is drawn from one vertex to the middle of the other side. The line segment known as the angle bisector divides the angle made up of two sides.

Given that,

The triangle XYZ,

It is known that,

All the sides in the equilateral triangle are equal,

So it can be written as,

⇒ WX = WY = XY

⇒ WY = 2WZ = 2ZY

Therefore,

⇒ WX = 2WZ

Hence, the correct relationship is WZ = 2WZ.

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Answer:

WX=2 times WZ

Step-by-step explanation:

i just took the quiz on apex

The value of delta such that the statement is true is:

δ = 0.0002

We want to find δ such that:

if |x -3| < δ, then |5x - 15| < ε

So we have two absolute value inequalities to work with.

With ε = 0.001

If we take the second inequality and replace epsilong, we will get:

|5x - 15| < 0.001

We can take 5 as a common factor on the left side to get:

5*|x - 3| < 0.001

Dividing both sides by 5 gives:

|x - 3| < 0.001/5

|x - 3| < 0.0002

Then the value of delta is 0.0002.

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Answer:

2570 is ten times smaller than 25700

Step-by-step explanation:

The function g(x) = (x - 3)³ is shown in the graph. The solution has been obtained by using the concept of transformation.

What is transformation?

Any action that moves a polygon or other two-dimensional object on a plane or coordinate system is referred to as a transformation.

Translation, rotation, reflection, and dilation are all methods of transformation.

We are given a graph, from which we can say that when x = 3, then y = 0

The function must satisfy these values.

The functions g(x) = (x + 3)³ , g(x) = x³ + 3 and g(x) = x³ − 3 does not satisfy the point (3,0).

Also, the translation is 3 units to the right.

So the function shown in the graph is g(x) = (x - 3)³.

Hence, the transformed function is g(x) = (x - 3)³.

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Question: If the parent function is f(x) = x³, which transformed function is show in the graph?

g(x) = (x − 3)³ , g(x) = (x + 3)³ , g(x) = x³ + 3 , g(x) = x³ − 3

Four rational numbers between 1/5 and 1/6 are; 41/240, 42/240, 43/240, 44/240

A rational number is defined as a number that can be expressed as the quotient of fraction p/q of two integers, a numerator p, and a non-zero denominator q.

First, we have to make the denominators the same.

We multiply 1/5 by 48 and 1/6 by 40 to get:

48/240 and 40/240

Thus, the other rational numbers between them are;

41/240, 42/240, 43/240, 44/240

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Complete question is;

Find four rational numbers between 1/5 and 1/6 ​

The algebraic equation for the statement is 21 = 2 x - 5

Algebraic equations can be written using mathematical symbols and operations to represent relationships between variables or quantities. Variables are the quantities that the equation is trying to represent or solve for.

There is only one variable here and we can call it x.

The number is doubled so the representation would be :

= 2 x

This is then decreased by 5 and becomes :

= 2 x - 5

This is equated to 21 to become:

21 = 2 x - 5

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Answer:

See below

Step-by-step explanation:

My man, how did you even get these numbers??? no whole number multiplied by 6.65 even equals 22??? Regardless, here's what I did.

a) r = 40/2 = 20

A = πr^2 = (3.14)(20)^2 = 1256

b) 1256/50 = 25.12 basically, 26

c) 26 x 6.65 = 172.9

Thoughts and prayers my guy. Keep trying

Answer:

A. 1256[tex]ft^{2}[/tex] B. 26 pounds C. $172.90

Step-by-step explanation:

PART A

1st find the radius of the area

radius = diameter / 2

r = 40/2

radius = 20ft

Area of circle = radius^2* pi

Area = 400 * 3.14

Area = 1256 [tex]ft.^{2}[/tex]

PART B

1256 / 50 = 25.12

Because we can only buy full pounds and we need the whole area to be reseeded, we round 25.12 to 26.

26 pounds of seeds will be needed to reseed the whole area.

PART C

Multiply the number of pounds of seeds needed to be bought by 6.65

26 x 6.65

$172.90 for the total cost of grass seeds

The length of the both pieces are 1ft and 9ft respectively. Option C

We have from the information given that;

Now, substitute the values, we get

x + 6 + 3x =10

Collect the like terms

x + 3x = 10 -6

Add the like terms

4x = 10 - 6

Substract the like terms

4x = 4

Make 'x' the subject of formula by dividing both sides by 4, we get;

x = 4/4

divide the values

x = 1

Thus, the values are 1ft and 9ft

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Answer: 6 pounds and 12 pounds.

Step-by-step explanation:

1.5(x)+2.4(18-x)=2.1(18)

1.5x+43.2-2.4x=37.8

1.5x+43.2=37.8+2.4x

0.9x=5.4

x=6 pounds of $1.50 candy

18-6=12 pounds of $2.40 candy

(check my work to see if it's correct :))

1. The difference between the temperature is 14°C.

2. The value of the expression will be -3x - 6y + 27.

The difference between the temperature will be:

= -10 + 24

= 14°C.

For the second part of your question, to clear the parenthesis in the expression "12 - 3(x + 2y - 5)", you can first simplify the expression inside the parenthesis:

x + 2y - 5

Next, multiply this expression by 3:

3(x + 2y - 5) = 3x + 6y - 15

Finally, substitute this back into the original expression:

12 - 3(x + 2y - 5) = 12 - (3x + 6y - 15) = 12 - 3x - 6y + 15 = -3x - 6y + 27

So, the final expression after clearing the parenthesis and combining like terms is -3x - 6y + 27.

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Answer:

122.3°

Step-by-step explanation:

Vertical angles are congruent.  That means that they have the same measurement.

A physical quantity with both magnitude and direction is called a vector quantity.

A vector quantity is a physical quantity that has both magnitude and direction. One example of a vector quantity is velocity, which is defined as the rate of change of an object's position with respect to time. Velocity is a vector quantity because it has both a magnitude (speed) and a direction (the object's motion). For instance, if an object is moving with a speed of 20 meters per second to the north, its velocity would be 20 meters per second north. If the object's direction changes to east, its velocity would become 20 meters per second east. Therefore, velocity is a vector quantity because its value depends not only on the speed of the object but also on the direction in which it is moving.

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Complete Question

Write down a vector quantity and explain your response.

The Ratios, Rate and unit rate are used to solve many real-world problems.

Let us defined ratios, rates and unit rates and see the real world examples below.

As a ratio is a comparison of two numbers or measurements.

For example, if a store sells 5 black color pens and 7 blue color pens, then the ratio of black to blue pens is 5 to 7.

A rate is also a ratio in which the two terms are in different units.

For example, if 2 galloons of milk costs 8 dollar, then the rate is 2galloons for

8 dollar. And the unit is galloons per dollar.

As Rates are used in our daily life, such as when we work 40 hours per week or take 2 liters of water per day. When rates are expressed as a quantity of 1, such as 2 liters of water per day  that is, per 1 day or 6 miles per hour that is, per 1 hour. So they can be defined as unit rates.

Hope this helps

Answer:

to describe the same relationship between quantities or to compare two quantities. A rate is a special type of ratio that compares quantities with unlike units. A unit rate compares a quantity of something with a single unit of a different quantity.

The required value of x is equivalent to 30 units.

The state of likeness can be referred to as a similarity. When two elements, things, ideas, or people resemble one another, they are said to be similar. Example: In terms of the number of sides, a square and a rectangle are comparable ( four sides for each). The state of being different can be used to define a difference.

To find the value of x we will use the similarity which corresponding sides of similar triangle are Proportional.

So;

50/x = 75/45

2/x = 3/45

x = 30 units

Thus, required value of x is  30 units.

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There are 36 possible outcomes from rolling a die twice (or two dice once) and these result in sums from 2 to 12.

Possible ways to make a sum of 2: 1

Possible ways to make a sum of 3: 2

Possible ways to make a sum of 4: 3

Possible ways to make a sum of 5: 4

Possible ways to make a sum of 6: 5

Possible ways to make a sum of 7: 6

Possible ways to make a sum of 8: 5

Possible ways to make a sum of 9: 4

Possible ways to make a sum of 10: 3

Possible ways to make a sum of 11: 2

Possible ways to make a sum of 12: 1

This means there are 21 ways to make a sum greater than 6.

21/36 ≈ 58.33%

There are 24 ways to make sums that are not divisible by 3 and not divisible by 6.   (Note that if a number isn't divisible by 3, it's also not divisible by 6, so that's a weird thing to include.)

24/36 ≈ 66.67%

The value of the camper after 5 years is given as follows:

$15,155.2.

An exponential function is defined as follows:

y = a(b)^x.

In which:

From the table, the rate of change is given as follows:

b = 29600/37000

b = 0.8.

Then the value of the camper after five years can be obtained applying the recursion, multiplying the value after 4 years by the rate of change of 0.8, as follows:

18944 x 0.8 = $15,155.2.

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Answer:

To perform a t-test for the equality of two population means with unequal variances, we can use the Welch's t-test. In this test, the formula for the t-statistic is:

t = (x1 - x2) / sqrt(s1^2/n1 + s2^2/n2)

Where x1 and x2 are the sample means, s1^2 and s2^2 are the sample error variances, and n1 and n2 are the degrees of freedom for the two samples.

Plugging in the given values, we have:

t = (52.8 - 48.4) / sqrt(20.31/36 + 45.06/24) = 4.25

Next, we need to find the critical t-value from the t-distribution table with degrees of freedom equal to the smaller of n1 and n2, which is 24. With a 95% confidence level, the critical t-value is approximately 2.492.

Since our calculated t-statistic (4.25) is greater than the critical t-value (2.492), we reject the null hypothesis that the two population means are equal. This suggests that there is strong evidence that the mean yield of oats is different between the two experiments.

Step-by-step explanation:

The given expressions {4x^3+2x^2+6x+7}/{2x+1} and 2x^2+3+(4/{2x+1}) are equal at x = 10, they are not equal at x = -1/2, and they are equal for all x other than -1/2.

Substitute x = 10 in the given expressions, we get

{4x^3+2x^2+6x+7}/{2x+1}

= (4000+200+60+7)/21

=203.19

2x^2+3+(4/{2x+1}.)

200+3+4/21

=203.19

Hence, the given expressions are equal when x = 10

Now substitute x = -1/2 in the given expressions

={4x^3+2x^2+6x+7}/{2x+1}

=(4*-1/8+2*1/4+6*-1/2+7)/0

2x^2+3+(4/{2x+1}.)

=2*1/4+3+4/0

When we substitute the value x= -1/2 then it divide by 0 and value will be infinite and hence we can say that the values are not equal at x = -1/2

2x^2+3+(4/{2x+1}.) take LCM

{4x^3+2x^2+6x+7}/{2x+1} here both expression are equal and  we can't able find the value at x = -1/2 but for other value of x they are equal.

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Answer:

Below

Step-by-step explanation:

2^3  /  2^7 =   2^(3-7)   =   2^(-4)   =   1/ (2^4)   =   1/16   =   .0625  

   ~~~~pick your poison

The required expression [tex]2^3/2^7[/tex], after simplification is equivalent to 1/16.

To simplify the expression [tex]2^3/2^7[/tex], we can apply the rule of exponentiation that states when dividing two numbers with the same base, we subtract the exponents.

In this case, the base is 2.

Using the rule, we subtract the exponent of the denominator from the exponent of the numerator:

[tex]2^3/2^7 = 2^{7} = 2^{-4}[/tex]

The expression [tex]2^{-4}[/tex] can be further simplified by using the rule that states any number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent:

[tex]2^{-4} = 1/2^4[/tex]
      = 1/16

Therefore, the expression [tex]2^3/2^7[/tex] is equivalent to 1/16.

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Answer:  

Translates to x-(x+6) which simplifies to -6

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

Explanation:

x = some number

x+6 = the sum of x and 6

x-(x+6) = subtract the previous amount from x

x-x-6 .... distribute the negative through to each term

-6

No matter what number you started with, you'll always end up with -6 as the fully simplified answer. The x variables cancel.

Example:

Pick 10 as the starting number. Subtract off 10+6 = 16 to get 10-16 = -6.

The least possible total number of cookies are 21.

A total is a whole or complete amount, and "to total" is to add numbers or to destroy something. In math, you total numbers by adding them: the result is the total.

Given that, Bailey is making festive cookie bags. She tried to split all her cookies evenly by putting 15 per bag, but the last bag had only 14 cookies.

Here, 15+14=29

29 is our first number. Bailey cannot evenly split the cookies into each bag with that amount of cookies, so we must move on to the next number.

Now, 10+9+2=21

21 can be divided 3 times by 7. Now we know the least amount of cookies total, is 21.

Therefore, the total number of cookies are 21.

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The production possibility frontier based on the information is attached.

PPF0 is the curve before technological progress. PPF1 is the the curve after the advance in technology.

Before the advance in technology, the opportunity cost of treating HIV/AIDS increases as the world moves down along its PPF.

After the advance in technology, the opportunity cost of treating more HIV/ AIDS cases decreases as the world has to give up less other goods and services to treat additional HIV/AIDS patients. Or, by giving up the same amount of other goods and services, world can treat more HIV/AIDS patients now.

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Answer:

y = |x - 3| - 1

Step-by-step explanation:

The vertex of the absolute value function graphed is (3, -1). The formula for absolute value is y = a |x - h| + k, where (h, k) is the vertex. The a stretches the graph, although this graph isn't stretched. So a is 1, which is the same as multiplying by 1. Plugging 3 as h and -1 as k into the formula results in y = |x - 3| - 1.

In total, the number of greetings will be 1159.

Mathematical symbols used to represent quantities or values include numbers. They are employed in the measurement, comparison, addition, subtraction, multiplication, and division processes in mathematics. According to their qualities and properties, numbers can be categorized into a variety of groups, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. There are specific properties and guidelines for mathematical operations for each group of numbers. Mathematics depends on numbers, which are also utilized in many other disciplines, including science, engineering, economics, and statistics.

The number of greetings exchanged between the host and the other mothers and daughters must be counted first. Since there is only one host, the number of mother-daughter pairs is 20 - 1 = 19. There are thus a total of 38 greetings, 19 between the host and the other moms, and 19 between the host and the other daughters.

The number of pleasantries exchanged between the guest mums and everyone else must next be tallied. The host, the other mothers, and the daughters must all be greeted, making a total of 20 - 1 = 19 guest mothers. Thus, each host mother must extend 1 + 19 + 20 = 40 greetings. There will be 760 greetings exchanged between the guest mothers and everyone, or 19 x 40.

The number of pleasantries exchanged between the mothers and the invited girls must also be tallied. Moreover, there are 20 guest girls, so 19 of them must welcome the mothers. As a result, there will be 361 pleasantries exchanged between the mothers and the guest daughters.

In total, the number of greetings will be 38 + 760 + 361 = 1159.

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