5. The roof drawn below is made up of six pieces of lumber and is symmetrical. There is 1
foot of overhang on both sides.
Use the dimensions given in the diagram, determine how much total lumber would be
needed to create this roof (i.e. how many feet of wood does it take to build this roof?).
It is a good idea to label all of the vertices before beginning (6 marks).

The value of y= 5.49≈ 5.5cm

What is 30-60-90 traingle?

The 30-60-90 triangle is cut straight through the middle along its altitude, like one half of an equilateral triangle. Its name is derived from its three angles of 30 degrees, 60 degrees, and 90 degrees. Any triangle with angles of 30-60-90 will look like this: The hypotenuse is always twice as long as the shortest leg, and the length of the long leg can be calculated by multiplying the short leg by the square root of three. The shortest leg is across from the 30-degree angle.

By 30-60-90 triangle rule,

Side across 60° angle = x

Hypotenuse side = 2x= 15

Side across 30° angle = x√3

By solving,

2x= 15

x= 7.5cm

So side across 60° angle= 7.5 cm

Side across 30° angle = 7.5×√3

                                     = 7.5× 1.732= 12.99≈ 13cm

As the figure given us square so,

13= 7.5+y

y= 13-7.5

y= 5.5 cm

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a. Using the graph, the estimated solution is: (-2, -0.6).

b. Solving algebraically, the exact solution is: (-2, -4/6).

The solution 0f a system of equations is that point of intersection where the lines of the two equations meet when they are plotted on a graph.

a. Given the graph of the equations, 2x - 3y = -2 and x + 1.5y = -3, the estimated solution, which is the point of the intersection of both lines can be, (-2, -0.5)

b. To get the exact solution, we would solve algebraically as shown below:

2x - 3y = -2 --> eqn. 1

x + 1.5y = -3 --> eqn. 2

Rewrite eqn. 2:

x = -3 - 1.5y --> eqn. 3

Substitute the value of x into eqn. 1:

2(-3 - 1.5y) - 3y = -2

-6 - 3y - 3y = -2

-6 - 6y = -2

-6y = -2 + 6

-6y = 4

y = 4/-6

y = -4/6

Substitute the value of y into eqn. 3:

x = -3 - 1.5(-4/6)

x = -3 + 1

x = -2.

The exact solution is (-2, -4/6).

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The function g(x) = (x - 5)² has a translation of 5 units to the right.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over x-axis, (-x, y).

-f(x) = Reflection over y-axis, (x, -y).

The parent function is a quadratic f(x) = x².

Now, The transformed function g(x) = (x - 5)² is a horizontal transformation of 5 units to the right.

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Answer:

[tex]x < -7[/tex]

Step-by-step explanation:

First subtract 2 from both sides.

[tex]-5x+2-2 > 37-2[/tex]

[tex]-5x > 35[/tex]

Then divide both sides by -5.

[tex]\frac{-5x}{-5} > \frac{35}{-5}[/tex]

For x < - 7, the inequality {- 5x + 2 > 37} is satisfied.

Given is the inequality as follows -

- 5x + 2 > 37

The given inequality is -

- 5x + 2 > 37

- 5x + 2 > 37

- 5x + 2 - 2 > 37 - 2

- 5x > 35

x < - 7

Therefore, for x < - 7, the inequality {- 5x + 2 > 37} is satisfied.

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The labeled quadrants in the standard xy coordinate plane is Quadrant II

What is Quadrants?

The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces (the vertical number line). Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.

Concept:

The x and y coordinates are both positive in quadrant I. In quadrant II, the x and y coordinates are oppositely positive. The x and y coordinates are both negative in quadrant III. The x-coordinate is positive and the y-coordinate is negative in quadrant IV.

The origin, or the point where the x- and y-axes connect, is where both the x and y coordinates are zero (0, 0).

The point is in the first quadrant if both x and y are positive. If both x and y are negative, the point will be in the second quadrant. In the third quadrant if both x and y are negatives, the point is located.

The labeled quadrants in the standard xy coordinate plane is Quadrant II

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The Yolanda's taxable income is $62,500.

What is income tax?

An income tax is a charge levied against people or organizations in relation to the income or profits they make. In most cases, income tax is calculated as the sum of the tax rate and the amount of taxable income. The type of taxpayer and the type of income are two factors that can affect the tax rate.

Given:

In 2008, Yolanda paid $3,875 in Social Security tax.

The Social Security tax rate was 6.2% to the maximum income of $94,200 that year.

Lets assume Yolanda´s income be `x`.

Now, calculating the taxable income of Yolanda

6.2% x (x) = 3875

[tex]\frac{6.2}{100} (x) = 3875\\x = 3875(\frac{100}{6.2}) \\x = 62500[/tex]

Hence, the Yolanda's taxable income is $62,500.

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The money Trevor's family spend, in total, on shower water in the past month is $14.4

Two or more expressions with an Equal sign is called as Equation.

Given that the Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms.

In the past month, each person showered for an average of 480 minutes

an average 72 liters of shower water (over the entire month)

The cost of water per litre is 0.20 dollars.

We need to find the money Trevor's family spend, in total, on shower water in the past month

Cost of water used per minute = Water used by each person per month / Time each person spent bathing × Cost of water per liter

= 72 / 480 × 0.20

= 0.15 × 0.20

= $0.03.

Now 0.03×480=14.4.

Hence, 14.4 is the money Trevor's family spend, in total, on shower water in the past month.

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Answer:

(f ○ g)(x) = 3x² + 5

Step-by-step explanation:

substitute x = g(x) into f(x) , that is

(f ○ g)(x)

= f(g(x))

= f(x² + 2)

= 3(x² + 2) - 1

= 3x² + 6 - 1

= 3x² + 5

Answer:

2 1/4

Step-by-step explanation:

I know bc its basic math

A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.

A z-score is the value of an observation expressed in standard deviation units. The sign of the score indicates whether it is above (positive) or below (negative) the mean, and the value quantifies how many standard deviations the score is from the mean.

The purpose of z-scores is to identify and describe the exact location of each score in a distribution & to standardize an entire distribution to understand & compare scores from different tests.

Z-scores or Z-statistics represent a statistical technique of measuring the deviation of data from the mean. There are different formula used for Z-score or Z-statistics depending upon what is measured. Z-statistics is generally used with Z-test which is a hypothesis testing statistical technique.

Therefore,

A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

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The original price of the instrument is $60.

Discount Price:

50% of 120 = 50/100 * 120

                   = 0.5 * 120

                   = 60

Original Price = Sale Price - Discount Price                  

                       = 120 - 60

                       = 60

Therefore, the original price of the instrument is $60.

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G i.e m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

What is perpendicular bisector?

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

What is the perpendicular of two points?

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H) i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G)  i.e  m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f)  i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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Answer:

1/2

Step-by-step explanation:

Since 5 is one of the six possible numbers available, rolling a 5 is a 1/6 probability.

Since rolling a number less than 3 means rolling a 1 or 2, rolling a 1 or 2 is a 2/6 probability.

Add those probabilities up since you can get either of those outcomes and you get 1/6+2/6=3/6

3/6=1/2

Answer:

Below

Step-by-step explanation:

Area = pi r^2

r = sqrt ( area/pi) = sqrt( 676 ) = 26

Circumference = pi d  = 2 pi r  = 2 pi (26) = 163.4 mm

The carbinet has rectangular floor plan where the length is equal to 5 feet more than twice the width.  The the expression that represents the area in square feet is Option B 2w²+5. ∧where w is the width

The area of the rectangle is the floor space the rectangle can occupy at a given time.

The given parameters are

L= 2w+5

The width = w

Then area is given by the formula

A=L*W

A=2w*w+5

Simplify the expression you have

A=2w²+5 where w is the width

Therefore the area is b. 2w²+5, where w is the width

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By hypothesis testing, The chef believes the complaint rate is less than 8%, when in fact it is not less than 8%. The chef continues to use the new recipe but experiences a large number of unsatisfied customers.

What does testing your hypotheses mean?

To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample.

               First, a hazy assumption about the parameter or distribution is made.

What is hypothesis testing, and how can it be used?

A statistician will test a hypothesis about a population parameter in a process known as hypothesis testing. The type of data used in the study and its purpose will determine the methodology the analyst uses.

                     The plausibility of a hypothesis is evaluated using sample data in a process known as hypothesis testing.

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The points where the inequality x+ 5y <-30 intercepts is ( 30, 0 ) and (0,6).

Here given the inequality.

x + 5y ≤ 30

To find the x-intercepts.

We have to substitute 0 for y and solve x to determine the x-intercepts.

x + 5 × 0 = 30

By solving the equation.

x = 30

( 30, 0 ) is the x-intercepts.

To find the y-intercepts.

By substituting 0 for x and solving y will get the y-intercept(s).

0 + 5y = 30

5y =30

y = 30/5

y = 6

In the point form, y-intercept.

Y-intercept(s): ( 0, 6 )

(30, 0) is the x-intercept.

Y-intercepts at : ( 0, 6 ).

The points in which the inequality x+ 5y <-30 intercepts is (30, 0) and (0,6).

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The equivalent ratios to tan F = EL/ EF = OS/OJ

Similar triangles are those with the same shape but different sizes. Similar triangles include all equilateral triangles and squares with any side length.

All related pairs of angles will be equal and corresponding sides of similar triangles will have the same ratio. The symbol '∼' is used to represent the similarity.

Given that

△FEL∼△JOS

That means △FEL and △JOS are similar triangles

As we know tan θ = Opposite side / Adjacent side

From the triangle △FEL,

=> tan F = EL/EF      

By the given information,

The similar triangle's corresponding sides will have the same ratio  

=> EL/ EF = OS/OJ

Therefore

The equivalent ratios to tan F = EL/ EF = OS/OJ

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Answer: point form: (4,3) equation form: x=4 y=3

Step-by-step explanation:

Therefore , the probability that she selects none of those containing errors is 0.6798.

Calculating how likely or "possible" it is for an event to occur is the subject of probability. Words like "definitely," "impossible," or "likely" may be used to communicate the likelihood that a particular event will occur. Mathematics always expresses probabilities as fractions, decimals, or percentages, with values ranging from 0 to 1.

Here,

Number of ways of selecting 3 returns out of 59 is C(59,3).

Out of 59 returns, 59-7 = 52 returns has no error so number of ways of selecting 3 returns out fo 52 is C(52,3).

The probability that she selects none of those containing errors is

P( No errors )=[tex]\frac{C(52,3)}{C(59,3)}[/tex]=0.6798

Therefore , the probability that she selects none of those containing errors is 0.6798.

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z-score of a value is  -5.96

What is z-score in binomial distribution?

The Z score represents the number of standard deviations above or below the mean. The Z score of the mean is 0 by definition.

What is Probability?

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.

Given,

A random variable, let's call it X, has parameters that fit the Binomial distribution: n (number of trials) = 50 and p (success probability) 0.76.

We must ascertain the z-score (Z) of the value 20 =  that this random variable X has chosen.

Now, for a random variable, say X, its z-score (Z) is defined as ,

Z = (X - mean of X)/ Standard deviation of X

A binomial random variable with the parameters once more n and p, its mean is given as np and its standard deviation is given as [tex]\sqrt{n*p*(1-p)}[/tex]

The standard deviation of X is provided as [tex]\sqrt{50*0.76*0.24}[/tex] = [tex]\sqrt{9.12}[/tex] = 3.0199933  while the mean of X is given as 50*0.76 = 38.

Therefore, the required z-score (Z) for X = 20, is given as,

Z = 20-38/3.0199933

Z= -5.9602781238

Z= -5.96 that is the necessary z-score.

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Answer:

y=5x−2

I hope this helps!

Sam passed the marker of 483 miles, in 6 hours.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
An expression is given as M = 58h + 135. shows how many miles the same has traveled for h hours,
To evaluate the mile marker that sam passed at 6 hours, substitute the value with h in a given expression.
M = 58×6 +135

Simplifying the above expression gives the mile marker
M = 483 miles

Thus, the required miles are 483.

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The required percent decrease in the price of the skateboard is 40%.

What is the percentage?

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

Here, we have

Original price = $84.50

sale price = $50.70

Percent decrease = 84.50-50.70/84.50 × 100 = 40%

Hence, the required percent decrease in the price of the skateboard is 40%.

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the inequality model will be x+2y<19

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

x + y > 11

.05x + .10y < .95

by multiplying 20 in inequality we get x+2y<19

Hence, the inequality model will be x+2y<19

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Answer:

22

Step-by-step explanation:

Y is midpoint of WR.

Hence,

YR = 1÷2 of WR ( Half of WR )

So,

WR = 2YR

= 2×11

= 22

Answer:

1: B

2: A

3: D

4: A

5: A, B

Step-by-step explanation:

1: 6/5 is 1.2 2/10 is 1/5

2: 6/14= 3/7 or 6/14

3: 3/12 is 1/4 or 3/12

4: 28/13 is 2 2/13

5: 35/6 which is also 2 3/16

#/# means divide so 35/6 is 35 divided by 6

The cost of one liter of washing up liquid would be = $1.8

Liters is a variable that is can be used to denote the measurement of a liquid.

The quantity of the washing up liquid that was given= 1.5 liters.

The cost of 1.5 liters of washing up liquid =$2.70

If 1.5 L = 2.70

1 L = X

Make X the subject of formula;

X = 1× 2.70/1.5

X = $1.8

Therefore, the cost of one liter of washing up liquid would be = $1.8

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Answer: Y=mx+b

Step-by-step explanation: