the solution set of a linear system involving variables x1; : : : ; xn is a list of numbers.s1; : : : ; sn/that makes each equation in the system a true statement when the values s1; : : : ; sn are substituted for x1; : : : ; xn, respectively.

21ft = 7yd or 21 feet is equivalent to 7 yards.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

The sentence states an equality between units of length: feet and yards.

From there, we can say that we are asked how many yards are there in 21 feet

Converting feet to inches, we must use the conversion

3 feet = 1 yard

21ft = 21/3 yards

21ft = 7yd

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The coordinates weighted average is 6.

The whole query is as follows:

The weights of the coordinates 3 and 8 are 2 and 3, respectively. Additionally, we must determine the weighted average.

The parameters are as follows:

Three has a weight of two.

The weight of coordinate 8 is 3.

Next, the weight average is determined as follows:

Weight average is equal to the product of the weight and the coordinates.

We thus have:

Average weight: (3 * 2 + 8 * 3)/(2 + 3)

Assess the quotient.

Average weight = 6

Consequently, the coordinates' weighted average is 6

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Answer: B

Step-by-step explanation:

I think it's B because if you solve the x and numbers by themselves then you get 4x-2

2x+3x = 5x

5x-1x= 4x

-5-2 = -7

-7+5= -2

4x-2

If at sunset a thermometer had a reading of 4°F and during the night the temperature decreased by 15°F, then after the decrease the total number of degrees that the temperature must change for the thermometer to read 0°F is equal to 11°F.

The total number of degrees that the temperature must change for the thermometer to read 0°F can be determined by using subtraction.

Subtraction can be defined as an act of calculating the difference between numbers or values.

As the temperature decreased by 15°F during the night, the temperature after the decrease can be calculated as follows,

4°F - 15°F = -11°F

The total number of degrees the temperature must change for the thermometer to read 0°F can be calculated as follows,

-11°F + x = 0

x = 11°F

Hence, the temperature must increase by 11°F for the thermometer to read 0°F.

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Answer: 11’F

Step-by-step explanation:

4’F-15’F=-11

-11+11’F=0’F

Probability that the mother in this sample had a premature baby given that the mother admitted to smoking is 50 percent.

Likelihood is the part of science concerning mathematical depictions of how likely an occasion is to happen, or how likely it is that a suggestion is valid. The likelihood of an occasion is a number somewhere in the range of 0 and 1, where, generally talking, 0 demonstrates difficulty of the occasion and 1 shows conviction.

P (A) is the probability of an event “A”

n (A) is the number of favorable outcomes

n (S) is the total number of events in the sample space

The higher the likelihood of an occasion, the more probable it is that the occasion will happen. A straightforward model is the throwing of a fair coin. Since the coin is fair, the two results are both similarly likely; the likelihood of "heads" approaches the likelihood of "tails"; and since no different results are conceivable, the likelihood of by the same token "heads" or "tails" is 1/2.

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The minimum and maximum distance from Earth to the Sun will be 90.7 million miles and 93.80 million miles.

From the information, The average distance from Earth to the Sun is 92.95 million miles. The actual

distance varies from the average by up to 1.55 million miles.

The minimum value will be:

= 92.25 - 1.55

= 90.7 million miles.

The maximum distance will be:

= 92.25 + 1.55

= 93.80 million miles.

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In order to make 4.5 gallons of orange juice, she will need 12 cartons of concentrated orange juice.

So,

The orange juice concentrate to water ratio is 12:36.

Now, let's call 'x' the amount of concentrated orange juice in 4.5 gallons of orange juice and 'y' the amount of water in the 4.5 gallons of orange juice we have;

We can conclude the following from equations (1) and (2):

x = 1.125 gallons of concentrated orange juice in 4.5 gallons of orange juice:

y = 3.375, the amount of water in 4.5 gallons of orange juice.

As a result, we have;

The number of fluid ounces in a carton is 12 ounces.

In 4.5 gallons of orange juice, x = 1.125 gallons = 144 fluidounces = 12 cartons of concentrated orange juice

Therefore, in order to make 4.5 gallons of orange juice, she will need 12 cartons of concentrated orange juice.

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Using scientific notation, it is found that:

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

For this problem, the number is given by:

982.1 m².

In scientific notation, the base has to be a number between 1 and 10(open interval at 10), hence the base has to be divided by 100.

To compensate for the division by 100, the number has to be multiplied by 100 somewhere, which happens when we add 2 to the exponent, as 10² = 100.

Hence:

The number is written as follows: [tex]9.821 \times 10^2[/tex] m².

The significant digits are all the digits that are not zero, and the zeros at the beginning or between other numbers, hence they are:

9, 8, 2 and 1.

Meaning that the number has 4 significant digits.

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Answer:

A $78.50

Step-by-step explanation:

Pennies $2.50

nickels $6.00

dimes $30.00

quarters $40.00

Answer:

3.87298335

Step-by-step explanation:

Answer:

3.872

Step-by-step explanation:

Answer:

2y^2+4y

Step-by-step explanation:

7y^2-5y+9y-5y^2

=7y^2+4y-5y^2

=7y^2-5y^2+4y

=2y^2+4y

The square root of 9801 is 99.

√9801 = 99

A number can be obtained by multiplying the square root of that integer by itself.

The equation √y = √y12 can be used to express the square root of any number. In other words, if a number's exponent is 1/2, we must determine the number's square root.

The context of complex numbers can be used to discuss square roots of negative numbers. More broadly, square roots can be taken into account in any situation where the concept of an object's "square" is established. Among other mathematical structures, these include square matrices and function spaces.

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The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

The midpoint formular used in finding the midpoint of a segment is expressed as;

( [x₁+x₂]/2 , [y₁+y₂]/2 )

Given the data in the question;

Point V(-2,5)

Point Z(3,-17)

Plug these values into the equation above.

( [x₁+x₂]/2 , [y₁+y₂]/2 )

( [(-2) + 3]/2 , [5 + (-17)]/2 )

( 1/2 , -12/2 )

( 1/2, -6 )

The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

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Answer:

0.82%

Step-by-step explanation:

Answer:

Step-by-step explanation:

divide both sides by 3

3z>6

3z/3>6/3

z>2

4 is less than 5, so 4.241 is less than 4.25.

Given the numbers are 4.241 and 4.25.

Because 4.241 and 4.25 have the same units and tenth digit (4.2 = 4.2)

so we need to compare the hundredths place that is, 0.041 with 0.05.

A decimal's distance from one whole increases as it increases in size. A decimal is further away from one whole the smaller it is. The amount of digits in each decimal should be your primary point of focus. Each of them contains two digits, allowing for immediate comparison.

The number following the decimal point is called the hundredths place. Round up the number of hundredths if the third number after the decimal is 5 or above. Keep the hundredths number constant if the number in the third position after the decimal point is 4 or less.

0.041 < 0.05

hence we get 4.241 < 4.25

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The odds of selecting a red 9 is 1/26.

Probability of an event E is represented by P(E)  can be defined as (the number of favorable outcomes) / (Total number of outcomes).

Given the total number of cards in a standard deck = 52

there can be  only two red9 as one 9 from heart and one red from diamond.

So the number of outcome for red 9 =2

the probability of odds of selecting red 9 is [tex]\frac{2}{52}[/tex] which can be further simplified into [tex]\frac{1}{26}[/tex].

Therefore , The odds of selecting a red 9 is 1/26.

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If the points lie on straight line then, the points should be collinear.

We enter the values and check to see whether we receive a true statement, such as "10 Equals 10," to determine whether a point (x, y) is on the graph of a line. The point is not on the line if we obtain a result other than 6 = 4, as it does not meet the equation. Two lines will coincide if they have a same point and have the same slope. To put it another way, if A, B, and C are three points in the XY plane, they will all lie on a line, or three points will be collinear, but only if AB's slope and BC's slope are both equal.

(a) ab=kac

(3-2,8-6,0-1)=k(1-2,4-6,2-1)

⇒(1,2,-1)=k(-1,-2,1)=-k(1,2,-1) these are the points lie on stright line.

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Answer:

-1.96312.. is a real, irrational number while √(-5) is imaginary. There is no value for a root of a negative number

Step-by-step explanation:

You should understand that numbers are naturally classified as real and imaginary. Under the real numbers, they are additionally classified into rational and irrational numbers. Under rational numbers, these possess fractions and integers. Irrational numbers are in decimal forms that cannot be converted to fractions. Thus, the difference between the two is that: -1.96312.. is a real, irrational number while √(-5) is imaginary. There is no value for a root of a negative number.

Answer:

Step-by-step explanation:

a. f(-3d) = (-3d)^2 - 2(-3d) - 8 = 9d^2 + 6d - 8

b. f(3) = (3)^2 - 2(3) - 8 = 9 - 8 - 8 = 1 - 8 = -7

c. f(2a - 1) = (2a - 1)^2 - 2(2a - 1) - 8 = 4a^2 - 4a + 1 -4a + 2 - 8 = 4a^2 - 8a - 5

d. g(5)= (2(5)+3)/(5^2 -2(5) + 1) = (10 + 3)/(25 - 10 + 1)= 13/15+1= 13/16

e. g(3x)= (2(3x) + 3))/((3x)^2 - 2(3x) + 1))= (6x + 3)/(9x^2 - 6x + 1)

f. g(-4a + 8) = (2(-4a + 8)) +  3/(-4a + 8)^2 - 2(-4a +8) +1))

         (-8a + 16 + 3)/(16a^2 - 32a + 64 + 8a - 16 + 1)

                    (-8a + 19)/(16a^2 - 24a + 49)

There is only one value greater than 19, which is 20, indicating that the data set contains one high outlier.

Because the dot plot demonstrates the frequency of each inspection, the total data-set is given by:

The following are the quartiles:

The IQR is calculated as follows:

The high outliers are values that are higher than 1.5 standard deviations above Q3, so the threshold is given by:

Therefore, there is only one value greater than 19, which is 20, indicating that the data set contains one high outlier.

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The correct question is given below:
The following dot plot shows the number of songs on each album in Sal's collection. Each dot represents a different album.

A dot plot with an axis labeled "number of songs" and numbered from 0 to 20 in increments of 1, with 19 points. 4, frequency 1. 7, frequency 1. 8, frequency 2. 9, frequency 2. 10, frequency 4. 11, frequency 1. 12, frequency 2. 13, frequency 2. 14, frequency 1. 16, frequency 1. 18, frequency 1. 20, frequency 1.

Here is the five-number summary for these data:

Five-number summary

min \text{Q}_1Q

1

start text, Q, end text, start subscript, 1, end subscript median \text{Q}_3Q

3

start text, Q, end text, start subscript, 3, end subscript max

444 999 101010 131313 202020

According to the 1.5\cdot \text{IQR}1.5⋅IQR1, point, 5, dot, start text, I, Q, R, end text rule for outliers, how many high outliers are there in the data set?

Choose 1 answer:

[tex]\dfrac{z-1}3 = \dfrac8{z+1}[/tex]

Eliminate the denominators.

[tex]3(z+1)\cdot\dfrac{z-1}3 = 3(z+1)\cdot\dfrac8{z+1}[/tex]

[tex]z^2 - 1 = 24[/tex]

Solve for [tex]z[/tex].

[tex]z^2 = 25[/tex]

[tex]\boxed{z = \pm5}[/tex]

Answer: You will have 12 plants in 4 weeks.

Step-by-step explanation: You will 12 plants because you get 3 new plants every week. So 4 weeks times 3 plants each week gives you 12 plants in 4 weeks.

Answer:

Step-by-step explanation:

Write an equation and solve: y decreased by 23 is 52.9

y - 23 = 52.9

y = 52.9 + 23

y = 75.9

------------------------

check

75.9 - 23 = 52.9

52.9 = 52.9

the answer is good

The ratio HD:HA is 5/11 when the sides of a triangle are of lengths 13, 14, and 15.

When the lengths of all three sides are known, the geometry formula Heron's formula, which bears Hero of Alexandria's name, determines the area of a triangle. There is no need to first determine the angles or other distances in the triangle, unlike other triangle area formulas. Heron of Alexandria is credited with developing the Heron's formula, which determines the area of a triangle in terms of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: Area is equal to the square root of (a + b + c)/2, where s is half the perimeter.

By Heron's Formula, the area of this triangle is 84 Thus the height perpendicular to  AB  has a length of 11.2, and by the Pythagorean Theorem,  AE  and  EB  have lengths  6.6  and  8.4,  respectively. These lengths tell us that  C  is at.

The slope of  BC  is (0-11.2)/(15-6.6)=-4/3,  and the slope of  AD  is 3/4 by taking the negative reciprocal of -4/3.  Therefore, the equation of line  AD  can best be represented by  y=(3/4) x.

We next find the intersection of  CE  and  AD . We automatically know the  x -value; it is just  6.6  because  CE  is a straight line hitting  (6.6,0).  Therefore, the  y -value is at  (3/4)* 6.6=4.95.  Therefore, the intersection between  CE  and  AD  is at  (6.6,4.95) .

We also need to find the intersection between  BC  and  AD . To do that, we know that the line of  AD  is represented as  y=3/4x,  and the slope of line  BC  is  -4/3.  We just need to find line  BC 's y-intercept. So far, we have  y=-4/3x+b,  where  b  is a real y-intercept. We know that  B  is located at  (15,0),  so we plug that into the equation and yield  b=20.  Therefore, the intersection between the two lines is

(3/4)x=-(4/3)x+20

⇒9x=-16x+240

⇒25x=240

⇒x=9.6

Now y=(3/4)*x=(3/4)*9.6=7.2

⇒y=7.2

After that, we use the distance formula:  HA  has a length of

√(6.6-0)²+(4.95-0)²=√(1089/25)+(9801/400)

=√(1089*16+9801)/400

=√27225/400=√1089/16=33/4=8.25

and  HD  has a length of

√(9.6-6.6)²+(7.2-4.95)²=√(3)²+(36/5-99/20)²

=√(9)+(81/16)

=√225/16=15/4=3.75

So the ratio os HD:HA is

⇒3.75/8.25=15/33=5/11

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Answer:

$8.75

Step-by-step explanation:

y = 6x + 19

71.50 = 6x + 19  Subtract 19 from both sides of the equation

52.50 = 6x Divide both sides by 6

8.75 = x

Answer:

KL = 10

Step-by-step explanation:

Given:

 [tex]JL=26[/tex]

 [tex]KL=3x+7[/tex]

 [tex]JK=8x+8[/tex]

From inspection of the given diagram:

[tex]JK+KL=JL[/tex]

Substitute the given values into the found equation and solve for x:

[tex]\implies 8x+8+3x+7=26[/tex]

[tex]\implies 11x+15=26[/tex]

[tex]\implies 11x+15-15=26-15[/tex]

[tex]\implies 11x=11[/tex]

[tex]\implies \dfrac{11x}{11}=\dfrac{11}{11}[/tex]

[tex]\implies x=1[/tex]

Substitute the found value of x into the expression for KL:

[tex]\implies KL=3(1)+7[/tex]

[tex]\implies KL=3+7[/tex]

[tex]\implies KL=10[/tex]

Formula we use,

→ JK + KL = JL

Now the value of x will be,

→ (8x + 8) + (3x + 7) = 26

→ 11x + 15 = 26

→ 11x = 26 - 15

→ x = 11/11

→ [ x = 1 ]

Then the value of KL will be,

→ 3x + 7

→ (3 × 1) + 7

→ 3 + 7 = 10

Hence, the value of KL is 10.

Answer:

(29x +4) cm

Step-by-step explanation:

The perimeter of a figure is the sum of the lengths of all its sides.

Perimeter of figure

= 5x +5 +x +8x -3 +7x +2 +8x           (sum up the lengths)

= 5x +x +8x +7x +8x +5 -3 +2           (group like terms together)

= (5 +1 +8 +7 +8)x +4

= (29x +4) cm

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