6. Tom's cousin, George, is three times as old as Tom. In 15
years, Tom will be two-thirds as old as his cousin, George.
How old is each of them in 15 years?

Answer: x = 4

Step-by-step explanation:

Divide each term in 5x = 20 by 5 and simplify

[tex]\frac{5}{5} x[/tex] = [tex]\frac{20}{5}[/tex]

[tex]x=4[/tex]

Answer:

x=4

Step-by-step explanation:

5x4=20

Answer: 1-squareroot of 11 (Nominator) over 2 (dominator), 1+ of 11 (Nominator) over 2 (dominator

Step-by-step explanation:

The time take would be 1 hour and 18 minutes

What is Linear Equation in One Variable?

Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable).

Solution:

Given: Growth rate of bacteria = (3*I + 2)*t

I is the Initial Number of Bacteria

t is the time in hours

So,

42 = (3*10 + 2)t

42 = 32*t

t = 1.3 hours

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Answer:

66

Step-by-step explanation:

[tex]\binom{12}{2}=\frac{12!}{10!21}=\frac{12 \cdot 11}{2}=66[/tex]

Answer:

The correct values for points A, B, C, and D on a number line going from negative 2 to positive 2 in increments of 1 are:

A = negative 2

B = negative 3/4

C = negative 1/4

D = 1/4

This can be determined by noting that each mark on the number line represents a distance of 1/4, and by counting the number of marks to the right or left of the given points. For example, point B is 1 mark to the right of negative 2, which means it is located at negative 2 + 1/4 = negative 3/4. Similarly, point C is 1 mark to the left of negative 1, which means it is located at negative 1 - 1/4 = negative 1/4. The other points can be determined in the same way.

Step-by-step explanation:

Answer:

It is A the 1st one

Step-by-step explanation:

A = negative 2, B = negative 1 and three-fourths, C = negative 1 and one-fourth, D = negative one-fourth

The ratio of  a: b is = 5:7

Here the ratio is a:b

When the prices are both decreased by £10, the new ratio

= a-10 : b-10

When the prices are both increased by  £5, the new ratio

= a+5 : b+5

By the given conditions,

a-10 : b-10 = 3:5

or, [tex]\frac{a-10}{b-10\\}[/tex] =[tex]\frac{3}{5}[/tex]

or, 5(a-10) = 3(b-10)

or, 5a -50 = 3b-30

or, 5a -3b = 20 .... ...(1)

and a+5 : b+5 =3 : 4

or,[tex]\frac{a+5}{b+5}[/tex] = [tex]\frac{3}{4}[/tex]

or, 4(a+5) = 3(b+5)

or, 4a +20 = 3b+15

or, 4a-3b= -5 .... ...(2)

subtract the equation(2) from equation(1)

   5a -3b - (4a -3b) =20 - (-5)

or, 5a-3b-4a+3b = 20+5

or, 5a-4a = 25

Therefore,  a =25

Putting a=25 in equation (1), we get

 125-3b=20

or, 3b= 105

therefore, b=35

a :b =25:35

       = 5:7

Hence, the ratio of  a: b = 5:7

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Answer: 103

Step-by-step explanation:i think

Answer: 140 I think actually

Step-by-step explanation: Because if you use the well comonlmonly used method you would see that MAYBE the equivilancalence is 140, not  130.

The lower bound for given equation of  M is 25.45.

What is lower bound?

An element of K that is greater than or equal to each element of S is referred to as an upper bound or majorant in mathematics, particularly in order theory.

An element of K that is less than or equal to each element of S is referred to as a lower bound or minorant of S.

Let,

[tex]M = \frac{p-2b}{2} \\p = 68.3\\b = 8.7[/tex]

We have to find the lower bound for M.

Plug the values of p and b in the given equation.

[tex]M = \frac{68.3 - 2(8.7)}{2}\\ M = \frac{68.3 - 17.4}{2} \\M = \frac{50.9}{2}\\ M = 25.45[/tex]

Hence, the lower bound for M is 25.45.

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The required rate of change for the given equation is 57.

What is the rate of change?

A measure of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.

For the given equation,

Health club charges a one-time sign-up fee and a monthly membership fee

y = 57x +30

So, the rate of change, [tex]\frac{dy}{dx}[/tex] = 57

hence, the required rate of change for the given equation is 57.

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-5x^4 is the 3rd term when 5 3x2 − 5x4 2x3 is arranged in descending order.

Given ,

the 3rd term when 5 3x2 − 5x4 2x3 is arranged in descending order.

It is said to be in descending order if the information is arranged from highest to lowest. Examples of numbers that are organized in descending order include 10, 9, 8, 7, 6, 5, 4, 3, 2, and 1. In other words, the order is said to be declining if the numbers are listed from largest to smallest.

5 3x^2 - 5x^4 2x^3

=> 5x^4 - 5 3x^2 2x^3

=> 5x^4 - 10x^5

=> -5x^4

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The equation of the line passing through the two points [tex](1,1)[/tex] and [tex](3,5)[/tex] is [tex]\frac{3}{1}[/tex] i.e.  [tex]y=2x-1[/tex]

For finding the equation of lien if two points are given then we will use the two-point form i.e.

[tex]y-y_{1}=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } (x-x_{1})[/tex]

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{5-1}{3-1} \\m=\frac{4}{2} \\m=\frac{2}{1}\\m=2[/tex]

The slope of the line is [tex]2[/tex]

The point [tex](x_{1} ,y_{1} )=(1,1)[/tex]

Plug in these values

[tex]y-1=2(x-1)\\y-1=2x-2\\y=2x-2+1\\y=2x-1[/tex]

The equation of the line is [tex]y=2x-1[/tex]

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Answer:

Step-by-step explanation:

To solve use tangent(63) to solve for x

tan(63)=x/90

Multiple by sides by 90

90tan(63)=x

x=176.6

Answer:

176.6

Step-by-step explanation:

tan(63°) = x/90

1.962 • 90 = 176.58

When I round to the nearest tenth I get 176.6

I hope this helps:)

The dimensions of the rectangle is 25m × 25m.

Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth.

The three dimensions of a three-dimensional shape are length, width, and depth.

It is given that

Perimeter of the rectangle = 100m

Area is as large as possible if both the values are the same number.

The measurements must be equivalent for the rectangle to attain its maximum area.

Consider the dimensions as x

So perimeter can be written as

2 (x + x) = 100

2 (2x) = 100

By additional computation

4x = 100

Divide both sides by 4

x = 25

Therefore, the dimensions of a rectangle is 25m × 25m.

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Answer: 20/3

Step-by-step explanation:

When we multiply improper fractions, we multiply the numerator by numerator and denominator by denominator. So we do:

5/4 * 16/3

= 80/12

= 20/3

So the answer is 20/3.

Answer:30

Step-by-step explanation:

30%x100

Answer:

x=12

Step-by-step explanation:

_-----------------------

When the scale factor of the map is less than 1, then the location will be above the map projection plane

The scale factor is used in the UTM mapping systems.

UTM stands for Universal Transverse Mercator, it is the coordinate grid used for the map projection.

The scale factor is an important part in the UTM mapping. Because it is used to show the distortion from the mapping system. Distortion is because of the Earth is mapped into flat surface.

So we can divide the surface into two, the surface above the mapping projection and the surface below the mapping projection

If the scale factor is less than 1 the location will be above the map projection plane and if the scale factor is greater than 1 the location will be below the map projection plane

Therefore, the scale factor less than 1 shows the location above the projection

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The sampling distribution of the sample mean is a normal distribution with a mean of 2.3 crimes per day and a standard deviation of 0.2 crimes per day centered around population mean.

This distribution is centered around the population mean, and its standard deviation is much smaller than the population standard deviation, indicating that the sample mean is a more reliable measure of the population mean than individual observations.

1. The number of violent crimes committed in a day possesses a distribution with a mean of 2.3 crimes per day and a standard deviation of 2 crimes per day.

2. A random sample of 100 days was observed, and the mean number of crimes for the sample was calculated.

3. The sampling distribution of the sample mean is a normal distribution with a mean of 2.3 crimes per day and a standard deviation of 0.2 crimes per day.

4. This distribution is centered around the population mean, and its standard deviation is much smaller than the population standard deviation, indicating that the sample mean is a more reliable measure of the population mean than individual observations.

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The ordered pair which does not satisfy the equation f ( x ) = ( 1/2 ) x - 7 is

A ( 2 , 8 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Now , the value of A is

f ( x ) = ( 1/2 ) x - 7

The value of f ( x ) = y

So , the ordered pair will be of the point A ( x , y )

a)

( 1 , -6 1/2 )

The value of the point A ( x , y ) = A ( 1 , -6 1/2 )

So , the equation is f ( x ) = ( 1/2 ) x - 7

Substitute the value of x and y in the equation , we get

y = ( 1/2 ) x - 7

-6 1/2 = ( 1/2 ) 1 - 7

-6 1/2 = 1/2 - 7

-6 1/2 = -6 1/2

Therefore , the ordered pair A ( 1 , -6 1/2 ) satisfies the equation

b)

( 2 , 8 )

The value of the point A ( x , y ) = A ( 2 , 8 )

So , the equation is f ( x ) = ( 1/2 ) x - 7

Substitute the value of x and y in the equation , we get

y = ( 1/2 ) x - 7

8 = ( 1/2 ) 2 - 7

8 = 1 - 7

8 ≠ -6

Therefore , the ordered pair A ( 2 , 8 ) does not satisfy the equation

c)

( -2 , -8 )

The value of the point A ( x , y ) = A ( -2 , -8 )

So , the equation is f ( x ) = ( 1/2 ) x - 7

Substitute the value of x and y in the equation , we get

y = ( 1/2 ) x - 7

-8 = ( 1/2 ) ( -2 ) - 7

-8 = -1 - 7

-8 = -8

Therefore , the ordered pair A ( -2 , -8 ) satisfies the equation

d)

( 0 , -7 )

The value of the point A ( x , y ) = A ( 0 , -7 )

So , the equation is f ( x ) = ( 1/2 ) x - 7

Substitute the value of x and y in the equation , we get

y = ( 1/2 ) x - 7

-7 = ( 1/2 ) ( 0 ) - 7

-7 = 0- 7

-7 = -7

Therefore , the ordered pair A ( 0 , -7 ) satisfies the given equation

Hence , the ordered pair A ( 2 , 8 ) does not satisfy the equation

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Answer:

1/4

Step-by-step explanation:

[tex]\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{2 \cdot 2}=\frac{1}{4}[/tex]

Answer:

Step-by-step explanation:

-50 since an integer is the opposite of a whole number positive or negative.

Answer: -50

Step-by-step explanation:

The probability of the given event is 1/9.

The odds against the event are 8 to 1.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

When we roll 2 dice, then

Sample space i. e possible outcomes are

{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

n(S) = 36

Let A be the event of getting a total of 5.

Therefore,

A = {(1, 4), (2, 3), (3, 2), (4, 1)}

⇒ n(A) = 4

⇒ P(A) = Probability of A = n(A) / n(S) = 1 / 36 = 1/9

(a) Probability of given event = 1/9

(b) Odds against the event = 1- P(A) / P(A)

                                             = (1 - 1/9) / (1/9)

                                             = (8/9) / (1/9)

                                             = 8/9 x 9/1

  Odds against the event    = 8/1

The reduced odds against the event are 8 to 1.

Hence, the probability of the given event is 1/9.

The odds against the event are 8 to 1.

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After calculating the angles, we know that the value of x is (C) 99°.

An angle is formed when two straight lines or rays meet at a single terminal.

The place where two points converge is known as an angle's vertex.

The name "angel" comes from the Latin word "angulus," which means "corner."

Angles are also produced when two planes intersect.

These are what are known as dihedral angles.

So, according to the given figure of the diagram:

We can say that:

y + 116 = 180

y = 180 - 116

y = 64°

Now, calculate for x inside the given figure:

125 + 72 + 64 + x = 360

261 + x = 360

x = 360 - 261

x = 99°

Therefore, after calculating the angles, we know that the value of x is (C) 99°.

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For the given pair of equations, the given ordered pair does not represent the solution.

Given is the equation -

7a + 8b = 3

For [a] = 0 and [b] = 1, we can write -

7 x 0 + 8 x 1 = 3

8 ≠ 3

Therefore, the points does not represent the solution to the equation given.

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Answer:

0.5ft

Step-by-step explanation:

The percent of decrease in the number of tokens is 30%.

From the information illustrated, Reggie bought 40 tokens to use at a family fun center. He used some of the tokens to ride go-carts and use the batting cages. He now has 28 tokens left.

The number used will be:

= 40 - 28

= 12

Therefore, the percentage decrease will be:

= Number used / Total tokens × 100

= 12 / 40 × 100

= 30%

The percentage is 30%.

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To enlarge a figure by scale factor of 1 , multiple the coordinates of pre-image by 1 though scale factor 1 won't affect anything .

Scale factor is a number by which the size of any geometrical figure or shape can be changed with respect to its original size. It is the ratio of the sizes of the original figure with the dilated figure.

The scale factor can either increase the size of an object or decrease the size of an object.

The basic formula:

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

Enlarging a shape means to change its size. To enlarge a shape, multiply all lengths of the shape by the scale factor. The scale factor tells us how many times larger the shape will be.

When the scale factor is 1 , a copy of a pre-image form . No, change in the image will happen . You will produce you an original image.

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A distribution of the means of two independent groups serves as the comparison distribution for an independent-samples t-test.

By using the one-sample t-test formula

If s is the sample standard deviation, n is the sample size, and x is the sample mean, is the population mean.

The between-groups variance measures the variability of the group means, whereas the within-groups variance measures the variability of the individual scores within the groups. This is a key distinction between variance terms for between-groups and within-groups.

By using the formula,

df = (n1 - 1) + (n2 - 1) (n2 - 1)

where the sample sizes for the two groups are n1 and n2.

The mean of the differences between the scores in the two groups can be used to compute the mean of the difference scores for the original data. The mean of the difference scores would be determined as follows, for instance, if the first group has scores of 3, 5, and 7, while the second group has scores of 4, 6, and 8.

[tex]\frac{(3 - 4) + (5 - 6) + (7 - 8)}{3}[/tex]

= [tex]\frac{(-1 + -1 + -1)}{3}[/tex]

= [tex]\frac{- 3}{3}[/tex]

= -1

The name of the statistical test, the sample sizes, the averages and standard deviations of the groups, the estimated t-value and degrees of freedom, and the p-value would all be included in a report of statistical results that follows proper APA format. The research question and hypothesis being examined should be stated clearly in the report, together with a discussion of the findings and their implications.

The standard error of the difference scores for the provided data can be calculated as

SE = [tex]((\frac{s12}{n1}) + (\frac{s22}{n2}))[/tex]

where n1 and n2 are the sample sizes, s1 and s2 are the standard deviations of the two groups, and

Calculating the t-value and comparing it to the critical value of t from the appropriate degrees of freedom in the t-distribution is the fifth step in performing a single-sample t-test. The null hypothesis can be rejected if the estimated t-value is greater than the critical value since it shows that the observed differences between the sample and the population are statistically significant.

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Johnny will pay a least possible amount of $25 and for 10 miles, the cost for both services will be same.

Given are two taxi service companies.

For Yellow Taxi service, John will pay -

C(x) = 15 + 2.5x = 15 + 2.5 x 5 = 15 + 12.5 = 27.5

C(x) = $27.5

For white taxi service, we can write -

C(x) = 10 + {(16 - 10)/(2 - 0)}x

C(x) = 10 + 3x = 10 + 3 x 5 = $25

C(x) = $25

Johnny will pay $25 as the least possible amount.

For equal amount, we can write -

10 + 3x = 15 + 2.5x

3x - 2.5x = 15 - 10

0.5x = 5

x/2 = 5

x = 10

Therefore, we can write -

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Answer:

Step-by-step explanation: No f(x) is not an inverse of g(x)