A father is 48 years old and his son is 12 yeats old. in how many years will the father be twice as old as his son?​

The steps of elimination system of  equations are as follows.

1. Both equations should be written in standard form.

2. Make the opposites of a single variable's coefficients.

3. Step 2's equations are combined to remove one variable.

4. Calculate the value of the last variable.

5. In one of the original equations, substitute the step-four solution.

What is an equivalent system of equations?

Equation systems are referred to as equivalent systems when their solutions are the same. Given a system of two equations, we can create an equivalent system by substituting one equation with the sum of the two equations or by substituting one equation with a multiple of itself.

We have to write an equivalent system that will eliminate one of the variables when you add the equations.

The steps of elimination system of  equations are as follows.

1. Both equations should be written in standard form.

2. Make the opposites of a single variable's coefficients.

3. Step 2's equations are combined to remove one variable.

4. Calculate the value of the last variable.

5. In one of the original equations, substitute the step-four solution.

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The probability that the veterinarian will conclude that the h6n2 virus is not present in the flock is 0.988

Since there are only two possible outcomes for this problem—that the bird is infected or not—the probability of a binomial distribution is involved.

Let's now assume that in this case, x represents a random variable that represents the number of afflicted chickens.

P(false positive test)=0.05, suggests that.

False positive tests indicate that the bird is not infected but the veterinarian still reports that it is. P(false negative test)=0.10 where.

False negative results indicate that the bird is infected even though the veterinarian says it is not.

Then, P(bird tested false positive) = 1-0.05=0.95 and P(bird is not infected) = 1.

Similar to that, P(bird tested false negative) = 1 - P(bird tested positive) 1- 0.10=0.90

Now, according to the question, the flock is considered contaminated if at least three out of every ten chickens are infected.

Therefore, i, if the veterinarian does not declare the birds as infected, it merely signifies that less than 3 birds are infected.

P(vet declares uninfected) then equals P(x=0) + P(x=1) + P(x=2)

P= (0.05)⁰ (0.95¹⁰) + (0.05)¹ (0.95)⁹ +(0.05)² (0.95)⁸ = 0.988

This is calculated, and the result is 0.988.

your question is incomplete but most probably your full question was

suppose a veterinarian applies the procedure to a flock of 100,000 chickens at a commercial egg production farm. the elisa test is known to have probability 0.05 of producing a false positive result and probability 0.10 of producing a false negative result for a single chicken. if no chicken in the flock is infected with the h6n2 virus, what is the probability that the veterinarian will conclude that the h6n2 virus is not present in the flock? show how you found your answer.

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Yes , there can be a triangle that can have the side lengths as 10.2cm , 5.8cm and 4.5cm .

it is only possible to form a triangle , when the sum of the any two sides of the triangle is greater than the third side of triangle .

the side lengths of the triangle are given as : 10.2cm , 5.8cm and 4.5cm  ;

So , on adding any two side lengths and comparing it with third side ,

we get ;

⇒ 10.2 + 5.8 = 16 > 4.5 ; True

⇒ 5.8 + 4.5 = 10.3 > 10.2 ; True

⇒ 10.2 + 4.5 = 14.7 > 5.8 ;  True .

All the three sides follow the condition ,

Therefore , the given side lengths form a triangle .

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Answer:

(a) (9 , 5)

(b) (-9 , -5)

Step-by-step explanation:

When you are reflecting over the y-axis, you are changing the sign of the x value.

When you are reflecting over the x-axis, you are changing the sign of the y value.

1) Reflect the point (-9 , 5) across the y-axis.

Based on the rule stated above, when you reflect over the y-axis, you are changing the x value sign:

(x , y) = (-9 , 5)

Reflected over the y-axis: (-9 , 5) becomes (9 , 5).

2) reflect the point (-9 , 5) across the x-axis.

Based on the rule stated above, when you reflect over the x-axis, you are changing the y-value sign:

(x , y) = (-9 , 5)

Reflected over the x-axis: (-9, 5) becomes (-9 , -5).

~

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Answer:

Reflected across the y-axis:  (9, 5)

Reflected across the x-axis:  (-9, -5)

Step-by-step explanation:

The mapping rule for a reflection across the y-axis is:

Therefore, point (-9, 5) reflected across the y-axis is (9, 5).

The mapping rule for a reflection across the x-axis is:

Therefore, point (-9, 5) reflected across the x-axis is (-9, -5).

Answer:-20

Step-by-step explanation:

If he left home 50 minutes before the class started he was 53.7 minutes late for his class.

Given that,

Speed of the bike = 16 feet per second = 10.9091 miles/hour

Distance from home to bus stop = 5 miles

Total time taken to reach bus stop = distance/ speed = 5 miles/10.9091 miles/hour= 0.458 hours = 27.5 minutes

Then, speed of the bus = 25 miles per hour

Distance from bus stop to campus = 25 miles

Total time taken to reach campus = distance/ speed = 25 miles/25 miles/hour= 1 hour= 60 minutes

Then, speed of the bike = 16 feet per second = 10.9091 miles/hour

Distance from campus to bike rack = 480 yards =  0.2727 miles

Total time taken to reach bike rack = distance/ speed = 0.2727 miles/ 10.9091 miles/hour= 0.249 hour= 15 minutes (approximately)

Then, the Speed of walking = 2.5 miles per hour

Distance from bike rack to class = 250 feet =  0.047 miles

Total time taken to reach class = distance/ speed = 0.047 miles/ 2.5 miles/hour= 0.0188 hour= 1.2 minutes (approximately)

Thus, total time taken to reach class = 27.5 minutes+60 minutes+15 minutes+1.2 minutes = 103.7 minutes
Therefore, If he left home 50 minutes before the class started he was 53.7 minutes late for his class.

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2,352,071.15 ft^3 is closest to the volume, in cubic feet, of the sphere .

What does sphere refer to?

The shape and symmetry of a sphere are both round. All of its surface points are equally spaced from the center, making it a three-dimensional solid. Depending on the radius, it has a surface area and a volume.

The volume of a sphere = 4/3 π r^3    where r is the radius.

Here the radius = 1/2 * 165 = 82.5 ft.

So the volume  = 4/3 π (82.5)^3

= 2,352,071.15 ft^3

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Answer:

  4y

Step-by-step explanation:

You want the simplified form of -√(16y²) if y < 0.

The square root function returns the positive root, so this is ...

  [tex]-\sqrt{16y^2}=-4|y|[/tex]

The absolute value changes the sign of its negative arguments, so this is ...

  [tex]-4|y| = -4(-y) = \boxed{4y}\qquad\text{for $y < 0$}[/tex]

So on solving the provided question we can say we can plotting data by x = 0.83; y = 0.79; z = 0.83

The most typical approach to display data using a chart is a graph that shows the relationship between two additional variables. Diagrams created by hand or on a computer are also acceptable. Move 2 units to the right after starting at the origin before going 3 units up. The coordinates for the points 2, 3, should be shown on the coordinate plane. Clearly state your points. The pink dot with the letter P thus stands for 2.3. Before creating a line chart, you need first generate a number line for each value in your data collection. Put an X (or dot) over each value of the data on the number line after that. For each instance when a value appears in a record, place an X over the corresponding number.

x = 0.83

y = 0.79

z = 0.83

xa = 0.85

ya = 0.85

za = 0.85

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Answer: 8/100 or 2/25

Step-by-step explanation:

8% is automatically out of 100% so it would be

8/100

and the simplified version would be 2/25

Answer: 2/25

Step-by-step explanation:

Answer:

Let's call the number we're trying to find "x".

We know that 35% of x is 77, so we can set up the equation:

0.35x = 77

We also know that 90% of x is 198, so we can set up another equation:

0.9x = 198

We can use the first equation to find the value of x and then substitute that value into the second equation to find 55% of x.

To find x, we divide both sides of the first equation by 0.35:

x = 77 / 0.35 = 220

Now that we know x is 220, we can find 55% of x by multiplying 220 by 0.55:

0.55x = 220 * 0.55 = 121

So 55% of the number is 121.

Answer:

121

Step-by-step explanation:

Because one of the answers is already divisible by 10, allowing us to find 100% of the unknown number, we can first find 10% by dividing the 90% number by 9. 198/9 is 22, meaning 22 is 10% of the number. We can then multiply it by 10 to get 100%, 22(10)=220. Meaning our full number is 220

From here we can simply multiply by our desired percentage, which is 55%. In order to multiply by a percent, you have you divide the percent by 100 to get .55. From there you can do 220*.55= 121. Meaning our answer is 121.

The  718.85 < x inequality says that : He must print 719 photos or more.

Inequality:

In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. Most commonly used to compare two numbers on the number line based on size. There are several notations used to represent various types of inequalities.

Given,

In the question:

Rick bought a photo printer and supplies for $186. 90, which will allow him to print photos for $0. 29 each.

and, A photo store charges $0. 55 to print each photo.

To find the how many photos must Rick print before his total cost is less than getting prints made at the photo store?

Now,

According to the question:

Let the photos be x

Rick bought a photo printer be $186.90

A photo store charges $0. 55 to print each photo.

The question is based on inequality:

Photo Printer <  photo store

1.86.90 + 0.29x <  0.55x

            - 0.29x     - 0.29x

______________________

           1.86.90    < 0.26x

Divide by 0.26x on both sides = 718.85 < x

Hence, The  718.85 < x inequality says that : He must print 719 photos or more.

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Answer:

410cm^3

Step-by-step explanation:

The Volume of the upper rectangular prism is 10x3x8 which is 240

The volume of the middle prism is 6x5x3 which is 90

And the volume of the bottom prism is 8x2x5 which is 80

If you add them all up, the total volume is 410

Note(The volume of a rectangular prism is base x height x width)

The price difference between the two different frame sizes £25.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

let the price for small frame be x.

and, the price for large frame be y.

As, One small picture frame and one large frame costs £65.

It costs £170 to buy two of the larger frames and four of the smaller frames.

So, the system of equation are:

x+ y = 65..................(1)

4x+ 2y = 170

2x + y = 85.....................(2)

Solving equation (1) and (2) we get

2x + 65 -x = 85

x = 20

and, y = 65- 20 = 45

Hence, the difference if of £25.

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Answer:

y = - 7

Step-by-step explanation:

5y + 13 = - 43 - 3y ( add 3y to both sides )

8y + 13 = - 43 ( subtract 13 from both sides )

8y = - 56 ( divide both sides by 8 )

y = - 7

With substitution, you need to solve one of the equations for one of the unknown variables and substitute that value into one of the other equations, then solve for the remaining unknown variable.

To solve a 3 equation problem, you can use elimination or substitution. With elimination, you need to add or subtract the equations to eliminate one of the unknown variables. With substitution, you need to solve one of the equations for one of the unknown variables and then substitute that value into one of the other equations. You can then solve for the remaining unknown variable.

To solve a 3 equation problem, you can use elimination or substitution methods. With elimination, you need to add or subtract the equations to eliminate one of the unknown variables. With substitution, you need to solve one of the equations for one of the unknown variables and substitute that value into one of the other equations, then solve for the remaining unknown variable.

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

r1 (1) = r2.

An angle is a form in Euclidean geometry composed of two rays, called the hook's flanks, that converge at a point in the middle known as the vertex of the angle. In the plane that they are located, two ray may combine to make an angle. The collision of two planes also produces an angle. Dihedral angles are what we call them.

Here,

Make the pair of elements

r1 (t) = r2 (s) t = 7 - s

or

t + s = 7 equal to one another.

35 + t2 = s2, or 35 - t2 = 4, or s2 - t2 = 35

Step 2: Using the t value from equation 1, simplify equation 3.

35 + ( 7 - s ) ( 7 - s )

2 = s2 14s = 84 s = 6 and t = 1 are equivalent to.

Step 3: In formulas (1), (2), and, substitute these values of "t" and "s"

(3).

r1 (1) = r2

(6) = (1, 3, 36) (1, 3, 36)

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

r1 (1) = r2.

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The water is given on alternate days.

According to the explanation given in the question, the Saharan islands make strong efforts to conserve their water resources. Part of these efforts includes not wasting water on plants that don't require it. Sometimes, we overwater plants, and the extra water simply evaporates into the atmosphere.

Palm trees, on the other hand, only require watering every other day, which is why they are only watered on alternate days. The precise amount of water provided to each tree in a real-world oasis would depend on a number of variables, including the age and health of the tree, the climate, and the availability of water. However, this is a hypothetical situation.

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The probability of selecting a red or a blue tile from one of the bags is 1. This can be calculated by adding the probability of selecting a red tile (6/10) and the probability of selecting a blue tile (4/10) together. The equation for this is P(Red or Blue) = P(Red) + P(Blue), which simplifies to 10/10, or 1.

The probability of selecting either a red or blue tile from one of the bags can be calculated using the following equation:

P(Red or Blue) = P(Red) + P(Blue)

where P(Red) is the probability of selecting a red tile and P(Blue) is the probability of selecting a blue tile.

In this case, P(Red) = 4/10 and P(Blue) = 6/10. Therefore, the probability of selecting either a red or blue tile from one of the bags is:

probability of selecting

P(Red or Blue) = 4/10 + 6/10

P(Red or Blue) = 10/10

P(Red or Blue) = 1

This means that there is a 100% chance of selecting either a red or blue tile from one of the bags.

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Answer: one is 10 and one is 12. Holy why was this so hard shouldn't this be as SAT/ACT problem?

Step-by-step explanation: 1/X + 1/X+2 = 11/60. THEN DO ALGEBRA THAT TOOK ME FOREVER IT WAS SO HARD.

54.6 Btu is the value of 57,281 joules in btus .

What does Jule mean?

A measure of energy or work that is equivalent to the work completed by a force of one newton moving through a distance of one meter The term "joule" is frequently used in the context of physics to refer to units of energy.

                     Lifting an apple, which weighs roughly one Newton, is one example used to demonstrate a joule. One joule of work is expended if you lift the apple one meter into the air.

The conversion used from Joules to Btu is:

1 Btu = 1055.06 J

or,

 1J = 1/1055.06  Btu

 given that the energy 57281 J. Now we have to determine the energy in Btu.

As,    1J = 1/1055.06  Btu

      57281J = 57281J/1J * 1/1055.06 Btu

              = 54.6 Btu

Therefore, the correct option is, (B) 54.3 Btu.

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Answer: 54.3 Btus

Step-by-step explanation:

Answer:

[tex]f(g(x)) = \boxed{\dfrac{x}{2}}[/tex]

[tex]g(f(x)) = \boxed{2x - 5}[/tex]

Step-by-step explanation:

We have the following two functions
[tex]f(x) = \dfrac{1}{x-5}\\\\g(x) = \dfrac{2}{x}+\:5[/tex]

To find [tex]f(g(x))[/tex]  substitute the expression for [tex]g(x)[/tex]  wherever you see an [tex]x[/tex] in [tex]f(x)[/tex]

[tex]\mathrm{For}\:f=\dfrac{1}{x-5}\:\mathrm{substitute}\:x\:\mathrm{with}\:\dfrac{2}{x}+5[/tex]

[tex]=\dfrac{1}{\dfrac{2}{x}+5-5}\\\\[/tex]

[tex]=\dfrac{1}{\dfrac{2}{x}}\\\\\\= \dfrac{x}{2}[/tex]    ANSWER

To find [tex]g(f(x)[/tex], substitute the expression for [tex]f(x)[/tex]  wherever you see an [tex]x[/tex] in [tex]g(x)[/tex]

[tex]\mathrm{For}\:g=\dfrac{2}{x}+5\:\mathrm{substitute}\:x\:\mathrm{with}\:\dfrac{1}{x-5}\\\\=\dfrac{2}{\dfrac{1}{x-5}}+5\\\\[/tex]

[tex]=2\left(x-5\right)+5\\\\= 2x - 10 + 5\\\\= 2x - 5\\\\[/tex]ANSWER

Note:

[tex]\dfrac{2}{\dfrac{1}{x-5}}=2\left(x-5\right)\\\\[/tex]

Each side of the playground is 10[tex]\sqrt{2}[/tex] m.

We know that in a square,

                               d = [tex]\sqrt{2}[/tex] a

            where, d = diagonal of the square

                         a = side of the square

Now, according to the question the walkway forms a diagonal and is 20 meters long.

  So, d = 20 m

        a = ?

          d = [tex]\sqrt{2}[/tex] a

        20 =   [tex]\sqrt{2}[/tex] a

          a  =  20/ [tex]\sqrt{2}[/tex]

              =  [tex]\frac{10\sqrt{2}*\sqrt{2} }{\sqrt{2}}[/tex]

              = [tex]10\sqrt{2}[/tex]

Hence, the side of the playground is [tex]10\sqrt{2}[/tex] meters long.

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Answer:

Step-by-step explanation:

Based on the dot plot, it appears that the majority of the distances Roger ran in his tennis matches last month were between 4 and 6 kilometers. There are 3 dots representing 3 km, 4 dots representing 4 km, 5 dots representing 5 km, and 4 dots representing 6 km. There are no dots representing distances less than 3 km or greater than 7 km.

Therefore, a reasonable estimate of the probability that Roger runs less than 5 km in his next tennis match is low, as the data suggests that the majority of the distances he ran last month were at least 4 km.

Therefore , the solution of the given problem of function comes out to be A(x) = 23.

The subject of mathematics includes quantities including their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a group of inputs, of which each has an associated output. A  variable association between inputs and outcomes in which each input leads to a single, distinct result is known as a function. Each function is given a region and a require a small space, or scope.

Here,

As a result, h(x) = x2-10x+21 A(x) =y/x =-1 x 10 A(x)=?

A(x) = y/x =h(x-g)-h(x)/g

=> g = Xmax - Xmin

=> g = 10-(-1)

=> g = 10+1

=> g = 11.

A(x) =(x-11)

² - 10*(x − 11) + 21 − (x² - 10x+21) /11

=> A(x)= x²- 22x+121-10x + 110 + 21 - x² + 10x -21/11

=>A(x) =231 - 22x /11

=>A(x)= 11 * (21-2x)/11

A(x) = 21-2x.

x = Xmin => A(x) = 21-2 (−1)

=>A(x) = 21+ 2

=>A(x) = 23

Therefore , the solution of the given problem of function comes out to be A(x) = 23.

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On solving the provided question, we can say that the equation has infinitely many answers, c = 2

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

the equation

cx + d=4(0.5x - 5).

the equation has infinitely many answers

c = 2

as,  2x + d=4(0.5x - 5).

d = infinite

so has infinitely many answers

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Answer: Since he is in school for 5 days a week, in a school week he will have a balance of 25.

Step-by-step explanation:

The percentage of the 90 students on the Springfield High School varsity soccer team who are seniors is 31%.

The percentage is a portion of a whole number or value.

Using percentages is a way of expressing values compared to others in relative terms.

The percentage refers to the ratio, which is obtained as the quotient of a numerator and a denominator, which is then multiplied by 100.

The total number of students on the Springfield High School varsity soccer team = 90

The makeup of the soccer team = freshmen, sophomores, juniors, and seniors

The number of seniors on the soccer team = 28

The percentage of seniors on the soccer team = 31.11% (28/90 x 100)

Thus, we can conclude that about 31 percent of the soccer team consists of seniors.

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