Solve the equation. 3 4 (2a − 6) 1 2 = 2 5 (3a 20) a =

The equation of the line passing through the points (-3,5) and (6,5) is y = x/9 + 13/3  .

In the question ,

it is given that ,

the required line passes through the points (-3,5) and (6,5) ,

we need to find equation of line ,

to find the equation , we first need to calculate the slope (m) .

slope(m) = (6-5)/(6-(-3))

= 1/9

So , the equation of the line passing through the point (6,5) with slope 1/9 in point slope form is

(y - 5) = 1/9(x - 6)

9(y - 5) = 1(x - 6)

9y - 45 = x - 6

9y = x - 6 + 45

9y = x + 39

y = x/9 + 39/9

y = x/9 + 13/3

Therefore , The equation of the line passing through the points (-3,5) and (6,5) is y = x/9 + 13/3  .

The given question is incomplete , the complete question is

What is the equation of the line in the point slope form passing through the points (-3,5) and (6,5) ?

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Answer:

64 milliliters of 25% juice

96 milliliters of 50% juice.

Step-by-step explanation:

Answer:

96 mL of the 50% juice

64 mL of the 25% juice

Step-by-step explanation:

Declaration

Let the number of mL of 25% juice = x

Let the number of mL of 50% juice = y

Equations

25/100 * x + 50/100 y = 40/100 * 160        Combine

x + y = 160 mL

Solution

0.25x + 0.5y = 0.4 * 160

0.25x +0.5y = 64                            Multiply this equation by 4

0.25*4x + 0.5*4y = 64*4                Combine

x + 2y = 256                                   Put the first equation underneath and subtract

x + 2y = 256

x + y = 160                                    Subtract

     y = 96                                       mL of 50% fruit juice

x + y = 160

x + 96 = 160                                    Subtract 96 from both sides.

x + 96 - 96 = 160-96

x = 64                                              mL of the 25% fruit juice.

Ratio of the sundae with nut to total number is 2:3.

The ratio will be written as numerator and denominator seperated by colon. The numerator will be number of sundae with nut and denominator will be total number of sundae. So, writing the numbers in mentioned description of ratio.

Ratio of the number of sundae with nut to the total number of sundae = 4 : 6

The ratio can be further simplified by dividing both numerator and denominator by 2.

Ratio of the number of sundae with nut to the total number of sundae = 2 : 3

Thus, the required ratio fo sundae is 2:3.

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Answer:

2728

Step-by-step explanation:

Answer:

20 sq units

Step-by-step explanation:

A quick sketch graph will show the right angle is at (-3 ,4)

The lengths of the shorter sides are both sqrt(2^2 + 6^2) = sqrt(40)

Area = 1/2 x (sqrt(40))^2 = 20

If you didn’t have a right angle you could find the lengths of all sides a, b and c

Calculate the semi perimeter s = (a+b+c) / 2

And the area = sqrt(s(s-a)(s-b)(s-c))

Try and use this method to check the first one

a) About 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.

b) About 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.

c) The estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.

To answer these questions, we'll use the properties of the normal distribution and the given mean and standard deviation.

(a) To find the percentage of test takers who earn a score less than 500 on the GRE Chemistry test, we need to calculate the cumulative probability up to the score 500.

z-score = (X - mean) / standard deviation

where X is the score we are interested in.

z-score = (500 - 694) / 112

z-score ≈ -1.732

Now, we look up the cumulative probability for a z-score of -1.732 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.0416 or 4.16%.

So, about 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.

(b) To find the proportion of test takers who earn a score greater than or equal to 900, we need to calculate the cumulative probability from 900 to positive infinity.

z-score = (X - mean) / standard deviation

where X is the score we are interested in.

z-score = (900 - 694) / 112

z-score ≈ 1.839

Now, we look up the cumulative probability for a z-score of 1.839 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.9664 or 96.64%.

So, about 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.

(c) To estimate the score at the 99th percentile on the GRE Chemistry test, we need to find the value that separates the lowest 99% of the scores from the highest 1%.

We use the z-score formula to find the z-score corresponding to the 99th percentile:

z-score = invNorm(0.99)

z-score ≈ 2.326

Now, we use the z-score to find the score corresponding to the 99th percentile:

X = mean + (z-score * standard deviation)

X = 694 + (2.326 * 112)

X ≈ 694 + 260.512

X ≈ 954.512

So, the estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.

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Answer:

12

Step-by-step explanation:

3x4

The slope of the line in the graph is -3/4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane. Calculating the slope of a line is similar to finding the slope between two different points. In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.

Taking two points from the line;

The slope of a line is given as

m = y₂ - y₁ / x₂ - x₁

Substituting the values into the formula;

m = 0 - 3 / 4 - 0

Slope = -3/4

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The equation of linear function is y=x-1.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

The given values are

x=1, y=0

x=2, y=1

x=3, y=2

x=4, y=3

The table represents that for the value of x the value of y is x-1,

Since for any two points from the table, let (1,0) and (2,1)

The slope = 2-1/1-0 = 1

And the interception of y is 0 when x=1

Therefore, the equation of the function can be written as,

y=x-1

Y=x-1 is the required equation.

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Answer:

35

Step-by-step explanation:

18+17=35

We list the operations done between two functions below:

In this problem we find three functions, two of them defined by quadratic equations (f(x), g(x)) and the other defined by a linear equation (h(x)). There are five operations that can be used b two functions:

Now we proceed to determine the result of each operation:

Case 1:

g(x) / h(x) = (4 · x² + 2 · x - 1) / (2 · x - 3)

Case 2:

h(x) - g(x) = (2 · x - 3) - (4 · x² + 2 · x - 1)

h(x) - g(x) = - 4 · x² - 2

Case 3:

h(f (x)) = 2 · (3 · x² + 2) - 3

h(f (x)) = 6 · x² + 1

Case 4:

f(x) + g(x) = (3 · x² + 2) + (4 · x² + 2 · x - 1)

f(x) + g(x) = 7 · x² + 2 · x + 1

Case 5:

h(f(x)) = 6 · x² + 1

h(f(2)) = 6 · 2² + 1

h(f(2)) = 25

Case 6:

f(h(x)) = 3 · (2 · x - 3)² + 2

f(h(x)) = 3 · (4 · x² - 12 · x + 9) + 2

f(h(x)) = 12 · x² - 36 · x + 29

f(h(3)) = 12 · 3² - 36 · 3 + 29

f(h(3)) = 29

Case 7:

g(x) + h(x) = (4 · x² - 12 · x + 9) + (2 · x - 3)

g(x) + h(x) = 4 · x² - 10 · x + 6

g(2) + h(2) = 4 · 2² - 10 · 2 + 6

g(2) + h(2) = 2

Case 8:

2 · f(x) - g(x) = 2 · (3 · x² + 2) - (4 · x² + 2 · x - 1)

2 · f(0) - g(2) = 2 · (3 · 0² + 2) - (4 · 2² + 2 · 2 - 1)

2 · f(0) - g(2) = 4 - 19

2 · f(0) - g(2) = - 15

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Inequality which shows the number of phone calls in order to make Plan 1 more economical is, x> 375.

It means if customer calls for more than 375 times Plan 1 is more economical for him/her.

Given that Plan 1 offers unlimited calls against $29 per month.

and Plan 2 offers each call against $0.04 and with an adiditional charge $14 per month.

Let if there are x calls in a month then Plan 1 is more economical.

Plan 1 is more economical means Plan 1 costs the customer less than the Plan 2.

So for x calls the bill according to Plan 2 = 14 +0.04x

And the charge $29 fixed for Plan 1.

So the required inequality is,

14+0.04x > 29

Solving the inequality we get,

0.04x > 15

.x > 375

So the calls should be more than 375.

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At the 0.05 level of confidence, there is enough data to say that Gentle Ben's blood glucose is higher than 85 mg/100 ml.

A probability distribution that is symmetric about the mean is the normal distribution, also referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph. Data are symmetrically distributed and skew-free in a normal distribution. As one moves away from the center, values start to taper off and the majority of values are concentrated in this area. In a normal distribution, the mean, mode, and median are identical measures of central tendency.

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The solution for f(3) in the function when the function f(x) = 0.75(10 - x) + 1 is 6.25

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

f(x) = 0.75(10-x)+1

To make the equation legible, we need to rewrite it

So, we have the following representation

f(x) = 0.75(10 - x) + 1

Also from the question, we have

f(3)

This means that the value of x is 3, and we calculate f(x) when x = 3

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

f(3) = 0.75(10 - x) + 1

So, we have the following equation

f(3) = 0.75(10 - 3) + 1

There are constants to add or subtract to both sides of the equation

Also, there are factors to multiply or divide from both sides of the equation

So, we have the following representation

f(3) = 0.75 * 7 + 1

Solving further, we have

f(3) = 5.25 + 1

Evaluate the sum

f(3) = 6.25

Hence, the solution is 6.25

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Possible question

Given f(x) = 0.75(10-x)+1, find f(3).

Population in 2011 is 361.606 million, Population in 2025 is 438.094 million, Year when population will be 2 billion is 2136

What is Function?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

Given the function of the population = P(t) = 3111(1+0.0138)^t

1. Population of Indonesia in 2011

= P(11) = 311 (1.0138)^11

= P(11) = 361.606 million

2. Population of Indonesia in 2025

= P(25) = 311 (1.0138)^25

= P(25) = 438.094 million

3. Year when population is 2 billiion

2000 million= 311(1.0138)^x

x = 136 years approx. i.e. 2136

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Answer:

A

Step-by-step explanation:

40% = 40/100 = 4/10 = 2/5

2/5 * 2/5 = 4/25 = 0.16

Answer:

  C.  all real numbers

Step-by-step explanation:

You want the domain of the function F(x) = 1.

The domain of a function is the set of values of the independent variable for which the function is defined. The function F(x) is defined for all possible values of x, so its domain is all real numbers.

Answer: A. 4/3 x

Step-by-step explanation:

x miles in 90 minutes to ? miles in 120 minutes

90 miles to 120 miles is 1.3333 which is equal to 4/3.

Multiply it to x and you have A. 4/3x

Answer:

Step-by-step explanation:

the answer would be 1 and 2/3

3 goes into 5 one time and you have 2 left

Answer:  E has no solution

Step-by-step explanation: It is a contradiction

If A = 21 bh, b= 16, and A= 40, then value of h is 0.1190.

∴ A= 21 bh, b = 16, A= 40

Putting the values in A = 21 bh, we get

A= 21 bh

⇒ 40 = 21×16×h

⇒h = 40/21×16

⇒h = 0.1190

So the value of h is 0.1190.

Answer:

20

Step-by-step explanation:

add 1 to both sides

3/4x=15

multiply both by 4

3x=60

divide by 3

x=20

To find the area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees.

Area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees is 459.36.

A triangle's feature known as SAS, or "Side, Angle, Side," has two sides and an angle that are both known.

The space occupied between the sides of the SAS triangle in a plane can thus be calculated with the use of the SAS triangle area formula.

The formula to find area of SAS triangle is:

Area = ½ ab Sin C = ½ × 29 × 36 × sin 62

Thus, Area = 522 × sin 62 = 522 × 0.88 = 459.36

Hence the answer is, Area of SAS triangle with side lengths 29 and 36 and included angle 62 degrees is 459.36.

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Answer:

ccccccccc

Step-by-step explanation:

Answer:

x<1

Step-by-step explanation:

10-2x-6<15-4x-9 (distributive property)

4-2x<6-4x (simplified both sides)

-2x<2-4x (1st step to get x isolated)

2x<2 (2nd step to get x isolated)

x<1 (divide 2 from each side)

and that's how! :)

Answer:

x is 13 and y is 10

Step-by-step explanation:

Multiply the second equation by 3

Answer:

 D. Multiply the second equation by 3. The solution is x = 12, y = 10.

Step-by-step explanation:

You want the multiplier for the elimination of the y-variable in the system of equations x +3y = 42; 2x -y = 14.

The coefficients of y are +3 and -1, so multiplying the second equation by 3 will make it the opposite of the former. Then their sum is zero, which is what you want when eliminating the y-variable.

Multiplying the second equation by 3 and adding the first gives ...

  3(2x -y) +(x +3y) = 3(14) +(42)

  7x = 84 . . . . . . . . . simplify. Note the y-variable has been eliminated.

  x = 12 . . . . . . . . . divide by 7

  2(12) -y = 14 . . . . substitute for x in the second equation

  24 -14 = y = 10 . . . . add y-14

The solution is (x, y) = (12, 10).

The appropriate t-multiplier for a 95% confidence interval for the mean μ is t(0.025,14) = 2.15.

Given:

The t-multiplier for a 95% confidence interval for a population mean, using a well-behaved sample of size 14.

It is the 97.5%-quantile of the t-distribution with 14 degrees of freedom.

In the figure the dashed line shows the value such that the yellow shaded area has size 0.975: the 97.5%-quantile is the value such that 97.5% of the probability mass is to the left of it and the rest to the right.

so t - multiplier = 2.15.

Therefore the appropriate t-multiplier for a 95% confidence interval for the mean μ is t(0.025,14) = 2.15.

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Answer:

1:38

Step-by-step explanation:

i think that is the answer

Answer: Its started driving through the neighborhood at 1:37

Step-by-step explanation:

The cost of per ounce of water at store A is $0.08 and at store B is $0.07  , the water in the store B  will cost less per ounce .

In the question ,

it is given that

in store A the cost of 16 ounce of water is $1.28 ,

so the cost of 1 ounce of water in store A is = 1.28/16

= $0.08

in store B the cost of water is represented by the equation

y = 0.07x

where "x" is the number of ounces of water ,

which means

the cost of 1 ounce of water in store B is = $0.07

hence , the water in store B will cost less  .

Therefore , The cost of per ounce of water at store A is $0.08 and at store B is $0.07  , the water in the store B  will cost less per ounce .

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