Find the common difference of the arithmetic sequence − 19 , − 11 , − 3

Prime numbers of the form p and p+2, where p is a prime number, are known as twin prime numbers.

A twin prime is a prime number that is either 2 less or 2 more than another prime number. For example, the number 3 and 5 are twin primes, because they are both prime and the number 5 is 2 more than 3. Similarly, the number 5 and 7 are also twin primes, because they are both prime and the number 7 is 2 more than 5.

Therefore, Twin primes are considered as interesting numbers in number theory because of their relative rarity, rare in nature and because they are the building blocks for certain types of primes such as Sophie Germain primes and safe primes.

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The density in terms of  pounds per cubic foot is 101.2 pounds/ft³

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here; 6900 g for every 4.05 quarts thus expressing in terms of pounds per cubic foot we get = 15.22/0.15039

                                                  = 101.2

Hence, The density in terms of  pounds per cubic foot is 101.2 pounds/ft³

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The percent change in population is 90.65%.

A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".

Given population of country in 1965 = 192 thousand = 1,92,000.

population of country in 2020 = 366 thousand = 3,66,000

the increase in population is = 366000 - 192000 = 1,74,000

the percentage increase =  (100)(increase in population)/(1965 population)

the percentage increase = (100) (174000)/(192000)

the percentage increase =  90.625%

Hence the percent increase is 90.62%.

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If a student made two patterns to show multiplication of a decimal by powers of ten. All the value are incorrect. The correct value are: 36.75, 367.5, 3,675, 36.75, 0.03675, 0.003675.

Pattern A

3.675×10 =3.7650 Incorrect

3.675×10 = 36.75 Correct

3.675× 100= 3.67500  Incorrect

3.675×100= 367.5 Correct

3.675×1,000= 3.675000 Incorrect

3.675×1,000 = 3,675 Correct

Pattern B

3.675×10=3.0675 Incorrect

3.675× 10= 36.75 Correct

3.675×0.01= 3.00675 Incorrect

3.675×0.01= 0.03675 Correct

3.675×0.001= 3.000675 Incorrect

3.675×0.001= 0.003675 Correct

The correct value are: 36.75, 367.5, 3,675, 36.75, 0.03675, 0.003675.

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Answer:

11 AM

Step-by-step explanation:

Mile Calculation:

200 miles away and 50 miles per hour.
200 divided by 50 is equal to 4

Answer:
Now, 7 am + 4 hours is equal to 11 AM.

Answer:

pretty sure it's B. Let me know if im wrong

Step-by-step explanation:

From the graph we got two equations of line -3x+ y -9 =0 and x+y-7 =0

and solution of these equations are x = -1/2 and y= 15/2

An algebraic expression that represents a number of points which creates a line in the XY coordinate system or another coordinate plane.

we are given a graph containing two equations of line named a and b. The lines are plotted in XY coordinate system.

From the graph, we can detect two locations of point (5, 6) and (1, -6) for line a  and detect two location of point (1, 6) and (6, 1) for line b.

As per the formula for equation of straight line, a line passes through two points can be written as y-y₁ = [(y₂-y₁) / (x₂-x₁)] × (x- x₁)

hence, line a can be written as (y- 6) = [(-6 -6) / (1-5)] × (x- 5)

                                                 y-6 = 3(x-5)

                                               y-6 = 3x -15

                                             y-3x -9 = 0

In the next, line b can be written as (y-6) = [(1-6) / (6-1)] × (x-1)

                                                       y-6 = -1(x-1)

                                                     y-6 = -x+1

                                                   x+ y -7 =0

 now, we get two equations, -3x+ y -9 =0

                                                  x+ y -  7 =0

Solving these two equations by addition method, we get x= -1/2 and y = 15/2

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The number of seconds it takes ball to before hit the ground is 6 seconds.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

Given that, a ball is thrown from the top row of seats in a stadium the function h(t)=-16t²+80t+96 gives the height, in feet, of the ball t seconds after it is thrown.

When ball hits the ground h=0

So, -16t²+80t+96=0

-16(t²-5t-6)=0

t²-5t-6=0

By using splitting middle term method, we get

t²-6t+1t-6=0

t(t-6)+1(t-6)=0

t-6=0 or t+1=0

t=6 or t=-1

Time can not be negative integer.

Therefore, the number of seconds it takes ball to before hit the ground is 6 seconds.

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Answer: A right triangular prism is a 3-dimensional geometric shape that has a triangular base and three rectangular faces that connect the base to the top. A rectangular prism has three pairs of rectangular faces that are congruent, these faces are perpendicular to each other and connected by edges.

So, in a right triangular prism there are 3 rectangular faces which are the lateral faces (the one that connects the base and the top)

A triangular prism also has 3 triangular faces which are the base faces

So in total, a right triangular prism has 3 rectangular faces and 3 triangular faces.

Step-by-step explanation:

The probability that on average these students spend more than $425 on books is given as follows:

0.0009 = 0.09%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 400, \sigma = 80, n = 100, s = \frac{80}{\sqrt{100}} = 8[/tex]

The desired probability is one subtracted by the p-value of Z when X = 425, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{425 - 400}{8}[/tex]

Z = 3.125.

Z = 3.125 has a p-value of 0.9991.

1 - 0.9991 = 0.0009 = 0.09%.

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Answer:

Given that we know the base of the parabola is at the origin, and that it is symetrical about the y-axis, we can simplify the equation to

y=ax2=14px2" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">y=ax2=14px2y=ax2=14px2

which corresponds to the given equation a=14p" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">a=14pa=14p given above.

Since y=6" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">y=6y=6 when x=2" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">x=2x=2,

6=a(2)2=4a" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">6=a(2)2=4a6=a(2)2=4a

and

a=32" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">a=32a=32

Thus we have

32=14p12p=2p=16" role="presentation" style="display: table-cell !important; line-height: 0; text-indent: 0px; text-align: center; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 3.337em; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; width: 10000em; position: relative;">32=14p12p=2p=1632=14p12p=2p=16

So, the receiver should be placed 16" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">1616 of a foot, or 2 inches, above the base.

A function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20

A relation is a function if it has only One y-value for each x-value.

Given a a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45

and that g(0) = -2 and g(-9) = 6,

x=-20 then g(-20)=-5

x=-19 then g(-19)=-4

x=-18 then g(-18)=-3

x=-17 then g(-17)=-2

x=-16 then g(-16)=-1

x=-15 then g(-15)=0

x=0 then g(0)=-2

x=-9 then g(-9)=6

By observing this we can say that as x values are decreasing the function values are increasing and vice versa

So option D is correct

Hence, a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20

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Answer:

r = 7.50 + (1.10 × (m - 1))

r = 7.50 + (1.10 × (9 - 1))

r = 16.40

The total uber rate for 9 miles is $16.3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

First-mile charge = $7.50

Additional charges after the first mile = $1.10

The total charge for 9 miles.

r = 7.50 + 1.10 x 8

r = 7.50 + 8.8

r = $16.3

Thus,

The total rate for 9 miles is $16.3.

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The solution is Option A.

The shortest distance is given by the two hypotenuses of the triangles and the distance is X = 7.8 cm

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the shortest distance be represented as X

Let the first triangle be the first face of the rectangular box ΔABC

The length of the triangle AB = 3 cm

The height of the triangle BC = 2 cm

Now ,

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

The measure of AC = √ ( 3² + 2² )

The measure of AC = √13 cm

And , the second triangle is the second face of the rectangular box ΔDEF

The length of the triangle DE = 4 cm

The height of the triangle EF = 2 cm

The measure of DF = √ ( 4² + 2² )

The measure of DF = √18 cm

Now , the shortest distance X = The measure of AC  + measure of DF

Substituting the values in the equation , we get

The shortest distance X = √13 cm + √18 cm

The shortest distance X = 3.60 + 4.24

The shortest distance X = 7.8 cm

Therefore , the value of A is 7.8 cm

Hence , the shortest distance for the ant is 7.8 cm

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I believe it's A

I hope this helps and if I'm wrong I apologize

Answer:

All four are equivalent fractions with the LCD of 12

Step-by-step explanation:

Answer:

$22.5

Step-by-step explanation:

$27.00/3/5=45

45*1/2=$22.5

On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

by graphs of the function f (x) and g( x)

[tex]lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5[/tex]

from the graphs n f (x) and g( x) are 1 and 5 .

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Answer:

$100 + $375 + $41(4) = $516

$516 - $425 = $91

$91 / $5 = 18.2 cars

Therefore, the four student government officers must wash 18 cars in order to have enough money to pay for the trip.

Therefore , the solution of the given problem of function comes out to be satisfies the given function is x=9 and y=21.

Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.

Here,

Given : A table of values of x and y

To find : the function is linear or not

Thus,

F(x) = y -3x =0

So,

Putting the values of x and y in given function

The value which satisfies the given function is x=9 and y=21.

Therefore , the solution of the given problem of function comes out to be

satisfies the given function is x=9 and y=21.

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Answer: Tonya's calculation is incorrect because she mixed units of measurement. She used feet to measure one dimension of the room (10 feet) and inches to measure the other dimension (120 inches) and then calculated the area as 10 x 120 = 1200 square feet.

Area is a measure of the amount of space inside a two-dimensional shape, and it's typically measured in square units. To calculate the area of a rectangular room, you multiply the length of the room by the width of the room,

However in this case, Tonya used different units of measurement for length and width (feet and inches), and therefore the answer is incorrect.

You would need to convert inches to feet before multiplying 10 feet by 120 inches to get the area.

120 inches = 10 feet

So, the correct calculation of the area would be 10 feet * 10 feet = 100 square feet

It's worth mentioning that before calculating any area or volume, it's important to make sure that all units of measurement are consistent and the same.

Step-by-step explanation:

The multiplicative rate of change for the exponential function is 0.4.

The exponential function in mathematics is represented by the symbols f(x)=exp or ex. The word, unless otherwise stated, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

In mathematics, an exponential function has the following form: f (x) = an x, where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

Given: Exponential function [tex]$f(x)=2\left(\frac{5}{2}\right)^{-x}$[/tex]

To find The multiplicative rate of change for the exponential function.

Solution :

The general form of the exponential function is [tex]$f(x)=a b^x$[/tex]

where $b$ is the rate of change of the function.

First we write the given function In proper form:

[tex]$$\begin{aligned}& f(x)=2\left(\frac{5}{2}\right)^{-x} \\& f(x)=2\left(\frac{2}{5}\right)^x\end{aligned}$$[/tex]

The rate of change is [tex]$f(x)=a b^x$[/tex]

Therefore, The multiplicative rate of change for the exponential function Is $0.4$

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Answer: h=14

Step-by-step explanation:

If x=-18, then

h=17+(-18)/6

h=17+(-3)

h=17-3

h=14

Answer:

Step-by-step explanation:

so, the calculation was :  h = 17 + [tex]\frac{-18}{6\\}[/tex]

To subtract "[tex]\frac{-18}{6}[/tex] " we need to make it the same denominator  as "17"

(it's not written but technically 17 = [tex]\frac{17}{1}[/tex] )

Yet, we see that [tex]\frac{-18}{6} =\frac{-3* 6}{1*6}[/tex]

We just need to remove both the 6 that are not useful here and :

[tex]\frac{-3*6}{1*6} =\frac{-3}{1}= -3[/tex]

We obtain h = 17 - 3 = 14

hope it helped :)

Answer:

m∠5+m∠6=180°

m∠2+m∠3=m∠6

m∠2+m∠3+m∠5=180°

Step-by-step explanation:

Verify each option

case A) we have

m∠5+m∠3=m∠4 ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

Therefore Is not always true

case B) we have

m∠3+m∠4+m∠5=180° ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

so

Their sum is always 180 degrees

Therefore this option is always true

case D) we have

m∠2+m∠3=m∠6 -----> equation A

we know that

m∠5+m∠6=180° ----> by supplementary angles

m∠6=180°-m∠5 ----> equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

Therefore this option is always true

case E) we have

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

This option is always true

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Answer:

c=200+0.4Yd find determine equlibirum level investment is =400

Answer:im pretty sure its D

Step-by-step explanation:it goes through the origin