In the following diagram, line m is parallel to line n and line q intersects the parallel lines at

Answer:

12 ounces

Step-by-step explanation:

168 divided by 14 = 12

Answer:

13.5 litres

Step-by-step explanation:

the ratios are 2 : 3 : 4 = 2x : 3x : 4x ( x is a multiplier )

given Henrietta produced 1.5 litres more than Gladys , then

4x = 3x + 1.5 ( subtract 3x from both sides )

x = 1.5

then total milk produced by the 3 cows is

total = 2x + 3x + 4x = 9x = 9 × 1.5 = 13.5 litres

Answer:

[tex]y + 6 = -1(x + 2).[/tex]

Step-by-step explanation:

Let's find the general equation of the given line:

[tex]y - x - 7 = 0\\\\y = x + 7.[/tex]

We can see that [tex]m = 1.[/tex]

Thus, the slope of any perpendicular line to the line [tex]y = x + 7[/tex] is [tex]-1.[/tex]

Given that the perpendicular line passes through (-2, -6), its point-slope form equation is as given:

[tex]y - y_1 = m(x - x_1)\\\\y - (-6) = -1(x - (-2))\\\\y + 6 = -1(x + 2).[/tex]

The unit measurement of the a volume in mm is mm³(millimetres cube.)

Volume is is defined as the space occupied within the boundaries. The objects are usually solid objects.

The volume of a 3 dimensional figure is the product of the base area and the height.

Therefore, the units of volume is measured in cubic units.

The volume of a prism with side lengths measured in millimetres is 20.

Therefore, the measurement can be represented as follows:

20 mm³

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Answer:

[tex]\text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]

Step-by-step explanation:

[tex]\text{f}^{-1}(x)[/tex] is the notation for the inverse of a function.  

The inverse of a function is a reflection in the line y = x.

Given function:

[tex]\text{f}(x)=15+12x[/tex]

To find the inverse of the given function:

Step 1

Replace f(x) with y to get an equation for y in terms of x:

[tex]\implies y=15+12x[/tex]

Step 2

Rearrange the equation to make x the subject:

[tex]\implies y-15=15+12x-15[/tex]

[tex]\implies y-15=12x[/tex]

[tex]\implies \dfrac{y-15}{12}=\dfrac{12x}{12}[/tex]

[tex]\implies x=\dfrac{y-15}{12}[/tex]

Step 3

Replace x with [tex]\text{f}^{-1}(x)[/tex] and y with x → this is the inverse function:

[tex]\implies \text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]

Step 4 (if necessary)

The domain of the function is the range of the inverse function.

The range of the function is the domain of the inverse function.

Therefore, as the domain and range of the given function are unrestricted, so too are the domain and the range of the inverse function:

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[tex]\\ \rm\leadsto y=15+12x[/tex]

Interchange x and y

[tex]\\ \rm\leadsto x=15+12y[/tex]

Solve for y

[tex]\\ \rm\leadsto 12y=x-15[/tex]

[tex]\\ \rm\leadsto y=\dfrac{x-15}{12}[/tex]

That's the inverse

Answer:

14

Step-by-step explanation:

If a baseball player records 4 hits in 8 games, then the player records 1 hit every 2 games. Therefore, the player will have 14 more hits in the next 28 games.

Answer:

Step-by-step explanation:

You want to save all the money you earn to buy a guitar that costs $400. You earn $9 per hour and

plan to work 15 hours each week for the next 3 weeks. Will you earn enough money in that time to buy

the guitar? Explain your answer.

15 hours × 3 weeks × $9 per hour

15 × 3 × 9 =

45 × 9 = 405$

The answer is YES

The tax that will be withheld is D. $16.48.

From the information, it was stated that Tim Worker is checking his earnings statement and that his weekly earnings are $520.00.

The tax that will be withheld will be:

= 3.16% × $520

= $16.48

In conclusion, the correct option is D.

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The value of the derivative of functions h'(6) as requested in the task content is; 55.

Since it follows from the task content that the function h(x)=4f(x)+5g(x)+1.

Hence, the derivative of h(x) can be evaluated as;

h'(x)=4f'(x)+5g'(x)

On this note, by substitution, it follows that;

h'(6)=4(5)+5(7)

h'(6) = 55.

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The value of x has a z-score of three is 20

The given parameters are:

Mean = 2

Standard deviation = 6

z = 3

The z-score is calculated as:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

So, we have:

[tex]3 = \frac{x -2}{6}[/tex]

Multiply through by 6

18 = x - 2

Add 2 to both sides

x = 20

Hence, the value of x has a z-score of three is 20

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Answer: [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]

Step-by-step explanation:

The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to [tex]y=5x+2[/tex] and crosses the origin.

We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.

Opposite Reciprocal of 5: [tex]-\frac{1}{5}[/tex]

Now that we have the slope and the point, we can use the point-slope form to get the equation of the perpendicular.

Point-Slope Form: [tex]y-y_1=m(x-x_1)[/tex] (m is slope, [tex]x_1[/tex] and [tex]y_1[/tex] are the point's coordinates)

[tex]y-0=-\frac{1}{5}(x-0)\\y=-\frac{1}{5}x[/tex]

Since we need to find a point on the original line that's closest to the origin, we need to find the intersection of the line and its perpendicular. We can do this by setting both lines equal to each other and solving for x and y.

[tex]5x+2=-\frac{1}{5}x\\25x+10=-x\\26x=-10\\x=-\frac{10}{26}\\x=-\frac{5}{13}[/tex]

Substituting x in any of the equations will give us y. Here, I will put it in the equation [tex]y=-\frac{1}{5}x[/tex]

[tex]y=-\frac{1}{5}*-\frac{5}{13}\\y=\frac{5}{65}\\y=\frac{1}{13}[/tex]

The closest point to the origin on the line [tex]y=5x+2[/tex] is [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]

The point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).

The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.

The given equation of a line is y=5x+2 ------(I)

The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to y=5x+2 and crosses the origin.

We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.

So, slope of perpendicular line is -1/5

The equation of the point slope form is: (y - y1) = m(x - x1)

Now, substitute m=-1/5 and (x, y)=(0, 0), we get

y-0=-1/5 (x-0)

y=-1/5 x -----(II)

Equate equation (I) and (II), we get

5x+2=-1/5 x

⇒ -x=25x+10

⇒ -26x=10

⇒ x= -5/13

So, y=-1/5 x =1/13

Therefore, the point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).

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The ratio of the area of ∆ABC to the area of ∆DEF is; 1:100.

Since, a major criterion for similarity and congruence of triangles is that the ratio of corresponding sides are equal.

On this note, since the task content suggest that the ratio of the perimeters is; 1:10, it follows from conventional mathematics that the ratio of their areas is given as; 1²:10²; 1:100.

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The average annual rainfall will be more than 40.6 inches in about 2.1 percent of the years.

Generally, the equation for the probability is mathematically given as

[tex]P( X < x) = p( Z < x - \mu / \sigma)[/tex]

Therefore

[tex]P( X > x) = 0.021[/tex]

[tex]P( X < x ) = 1 - 0.021\\\\\p( X < x) = 0.979[/tex]

[tex]P( Z < x - \mu / \sigma) = 0.979[/tex]

The z score for the probability of 0.979 is 2.034, according to the table of z values.

[tex]x - \mu / \sigma \\\\x= 2.034[/tex]

In the given equation, replace the values of mu and sigma with their respective values, and then solve for x.

[tex]x - 35.5 / 2.5 \\x= 2.034[/tex]

In conclusion, The average annual rainfall will be more than 40.6 inches in about 2.1 percent of the years.

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The percentage of students age 15 and above travel to school by bus is 47%

The table of values is given as:

                     Method of Travel to School

                            Walk/Bike    Bus    Car Row totals

Under age 15                            18                 165

Age 15 and above    65                                 195

Column totals          152          110        98      360

Using the column total of column 1, we have:

Under age 15 + 65 = 152

This gives

Under age 15 = 87

Using the column total of column 2, we have:

Age 15 and above + 18 = 110

This gives

Age 15 and above  = 92

Using the row total of row 1, we have:

Car + 87 + 18 = 165

This gives

Car = 60

Using the row total of row 2, we have:

Car + 65 + 92 = 195

This gives

Car = 38

So, the complete frequency table is

                     Method of Travel to School

                            Walk/Bike    Bus    Car Row totals

Under age 15           87              18      60        165

Age 15 and above    65          92        38        195

Column totals          152          110        98      360

The percentage of students age 15 and above travel to school by bus is:

Percentage = 92/195 * 100%

This gives

Percentage = 47%

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The two variables are; earnings, y and hours, x in which case, the former is the dependent variable while the latter is the independent variable.

It follows from the task content that Tiya earns $7 an hour mowing her neighbor's lawn.

On this note, it follows that the amount of money earned by Tiya is a dependent variable which solely depends on the number of hours spent on the job, which is the independent variable.

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The y-intercept of this function represents C. the minimum amount of electricity consumed

The function is given as:

y = 0.503x + 3.31

The y-intercept of a function represents the minimum or the initial value of the function

This means that the y-intercept of this function represents C. the minimum amount of electricity consumed

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The exact values of sec θ, tan θ and sin θ are 6.4/4, 5/4 and 5/ 6.4 respectively.

From the figure, we have the values of the sides to be;

Let's use Pythagorean theorem to find the hypotenuse(x)

Hypotebuse square = opposite side square + adjacent side square

Substitute the values deduced from the figures given

x² = 5² + 4²

x² = 25 + 16

x² = 41

x = [tex]\sqrt{41}[/tex]

x = 6. 4

sin θ = opposite/hypotenuse

Substitute the values

sin θ = 5/ 6. 4

tan θ = opposite/ adjacent

Substitute the values

tan θ = 5/ 4

sec θ = hypotenuse/ adjacent

substitute the values

sec θ = 6. 4/ 4

Thus, the exact values of sec θ, tan θ and sin θ are 6.4/4, 5/4 and 5/ 6.4 respectively.

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The domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.

The function is given as:

[tex]y=4\log_5(x-3)[/tex]

Set the expression in bracket greater than 0

x -3 > 0

Add 3 to both sides

x > 3

Hence, the domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.

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Using the normal distribution, there is a 0.8155 = 81.55% probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

The mean and the standard deviation for this problem are given, respectively, by:

[tex]\mu = 42.5, \sigma = 4.8[/tex]

The probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill is the p-value of Z when X = 48 subtracted by the p-value of Z when X = 35, hence:

X = 48:

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

[tex]Z = \frac{48 - 42.5}{4.8}[/tex]

Z = 1.15

Z = 1.15 has a p-value of 0.8749.

X = 35:

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

[tex]Z = \frac{35 - 42.5}{4.8}[/tex]

Z = -1.56

Z = -1.56 has a p-value of 0.0594.

0.8749 - 0.0594 = 0.8155.

0.8155 = 81.55% probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill.

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Answer: c. the mean is greater than the median

Explanation:

To find out the correct answer, we first must know the true meanings and the method of calculation of the terms, "mean", "mode" and "median".

Mean: The mean is a type of average. It is the sum of all the values in a set of data, such as numbers of measurements, divided by the numbers of values on the list.

[tex]\bar{x} = \dfrac{\sum x}{n}[/tex]                                      where, [tex]\bar{x}=[/tex] sample mean
                                                               [tex]\sum x =[/tex] sum of each value in sample
                                                               [tex]n =[/tex] number of values in the sample

Example: in {6, 3, 9, 6, 6, 5, 9, 3} the mean is 5.875 (6+3+9+6+6+5+9+3/8).
                           
                                         

Mode: The mode is the number which appears most often in a set of numbers.
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6.

Median: The median is the "middle" of a sorted list of numbers in ascending order (small to big). To find the Median, place the numbers in value order and find the middle.
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the median is 6. (in 3,3,5,6,6,9,9, the middle number is 6 )

with an even amount of numbers things are slightly different.
In that case we find the middle pair of numbers, and then find the value that is half way between them. This is easily done by adding them together and dividing by two. (basically averaging the middle two numbers incase there is an even set of numbers)
Example: 3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29

When we put those numbers in order we have:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56

There are now fourteen numbers and so we don't have just one middle number, we have a pair of middle numbers.

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56

In this example the middle numbers are 21 and 23.

To find the value halfway between them, add them together and divide by 2: 21 + 23 = 44, then 44 ÷ 2 = 22

So the Median in this example is 22.
(Note that 22 was not in the list of numbers ... but that is OK because half the numbers in the list are less, and half the numbers are greater.)

Now that you understand the terms clearly, let's find out the mean, mode and median from your given set of numbers.
                                           5, 15, 25, 30, 3

Mean: (5+15+25+30+3)/5  is, 15.6
Mode: None since none of the numbers repeated more than once.
Median: 3,5,15,25,30  , so the middle number is 15 .

Since there is no mode, option d. can never be the answer. And clearly, 15.6 is greater than 15 so the answer should be c. the mean is greater than the median.

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The number of pounds of blueberries and grapes sold are 11 and 22.

According to the statement

we have given that the:

Each pound of blueberries sells for $2.50 and each pound of grapes sells for $1.25.

And total money collected by selling pounds is $55

And total number of pounds sells = 33

And we have to find the Number of pounds of blueberries and grapes.

Let the number of pounds of blueberries is X

And Let the number of pounds of grapes is Y

So,

The equation becomes is:

X + Y = 33  -(1)

2.50X + 1.25Y = 55  -(2)

Now, From substitution method

From (1) equation

Y = 33 - X

put these in equation (2) then

2.50X + 1.25(33 - X ) = 55

2.50X + 41.25 - 1.25X = 55

1.25X = 13.75

X = 11

and the the value of Y becomes

Y = 33 - X

Y = 33 - 11

Y = 22.

So, The number of pounds of blueberries and grapes sold are 11 and 22.

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Step-by-step explanation:

the formula for the height in a right-angled triangle is

h = sqrt(p×q)

p and q being the segments of the Hypotenuse left and right from the point, where the height intersects with the Hypotenuse.

so, in our case

12 = sqrt(16×(x-16))

let's square this to eliminate the square root :

144 = 16×(x - 16) = 16x - 256

400 = 16x

x = 25

Answer:

B.) 19

Step-by-step explanation:

According to F(5), the question wants you to plug x = 5 into the equation. Then, you need to simplify to find the output.

F(x) = x² - 2x + 4                             <----- Original equation

F(5) = (5)² - 2(5) + 4                        <----- Plug 5 into "x"

F(5) = 25 - 10 + 4                            <----- Solve 5² and -2 x 5

F(5) = 19                                         <----- Combine like terms

The other sides measure:

All the measures must be multiplied by the same scale factor to get a similar pentagon.

If in the original pentagon the shortest side measures 2", and in the similar pentagon the shortest side measures 5", then we have:

5" = k*2"

5"/2" = k = 2.5

Then the scale factor is 2.5

To get the other sides of the pentagon, we just need to multiply the other sides of the original pentagon by 2.5

The other sides measure:

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Hello!

We are going to solve the question with our given functions.

We were given:

Those are our two given functions, we will use those to solve for (f + g)(x).

Keep in mind that (f + g)(x) could also be written as f(x) + g(x)

With this knowledge, we can solve our question.

Solve:

(ƒ + g)(x) = f(x) + g(x)

Plug in our f(x) and g(x) functions and solve.

f(x) + g(x) = |2x +1| + 3 - 2

Simplify.

|2x +1| + 3 - 2

|2x +1| + 1

Since we can't simplify this any further, the above will be our answer.

(f + g)(x) = |2x +1| + 1

Answer:

|2x +1| + 1

The score Macro needs in his next game to have a mean of 130 is 150.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

130 = (128 + 127 + 123 + 122 + x) / 5

Where x represents the fifth score

130 = (500 + x) / 5

130 x 5 = 500 + x

650 = 500 + x

650 - 500 = x

x = 150

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Answer: 8

Step-by-step explanation:

Since x=3, we can plug in 3 for x in the equation:

[tex]5(3-1)-2\\5(2)-2\\10-2\\8[/tex]

⊱________________________________________________________⊰

Answer:

8

Step-by-step explanation:

Plug in 3 for x

[tex]\sf{5(2)-2} \ \ \ \ \ \large\textbf{[Multiply 5 by 2 next]}[/tex]

[tex]\sf{10-2} \ \ \ \ \large\textbf{[Subtract]}[/tex]

[tex]\sf{8}[/tex]

Done !! Hope this made sense to you !!

⊱________________________________________________________⊰

[tex]\small\pmb{\tt{CALLIGRAPHY}}[/tex]

The test statistic, rounded to 2 decimal places is equal to

For this sample, the hypothesis is given by:

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

Assuming this sample has a normal distribution, we would use a pooled z-test to determine the value of the test statistic:

Substituting the given parameters into the formula, we have;

[tex]z = \frac{\frac{96}{150} \;-\;0.63}{\sqrt{0.63\; +\; \frac{1\;-\;0.63}{150}} }\\\\z = \frac{0.64 \;-\;0.63}{\sqrt{0.63\; +\; \frac{0.37}{150}}}\\\\z = \frac{0.01}{\sqrt{0.63\; +\; 0.0025}}\\\\z = \frac{0.01}{\sqrt{0.6325}}\\\\[/tex]

z = 0.01/0.7953

z = 0.013.

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Answer:

Step-by-step explanation:

According to the distribution table, the percent values within the interval of [- 2, 2] are:

Add them together to get the required answer:

The answer is 0.6 or 60%.

The respective probabilities that lie in the interval [-2, 2] are 0.33, 0.16, and 0.11. Therefore, the probability it lies in the interval is equal to the sum of the probabilities.