(03.02 MC)

Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown:

A support structure is shown in which a right triangle PQR is formed with the right angle at Q. The length of PQ is shown as 14 feet, and the length of QR is shown as 9 feet.
Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer stating the theorem you used. Show all your work. (5 points)

Part B: The length of rod PR is adjusted to 18 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work. (5 points)

The statement made by Diego is correct.

In order to determine the number of groups of 5/6 that are in 1, 1 would be divided by 5/6.

1 ÷ 5/6

= 1 x 6/5 = 6/5

6/5 is called an improper fraction because the numerator is greater than the denominator.

6/5 can also be rewritten as a mixed fraction. If it is rewritten as a mixed fraction, it becomes 1 1/5.

Learn more about mixed fractions at:

brainly.com/question/29264210

#SPJ1

Given question is incomplete , the complete question is given below:

Diego said that the awnser to the question "How many groups of 5/6 are in 1?" Is 6/5 or 1 1/5.Do you agree with his statement? Explain or show your reasoning.

The input is 8, the output of the function f(x) would be -5.

What is the function?

Function is a relationship or expression involving one or more variables.  It has a set of input and outputs.

Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet

To find the output of the function f(x) when x is 8, we substitute x = 8 into the function and simplify:

f(x) = 8/x - 6

f(8) = 8/8 - 6

f(8) = 1 - 6

f(8) = -5

Hence, if the input is 8, the output of the function f(x) would be -5.

To learn more about function, Visit

https://brainly.com/question/11624077

#SPJ1

The expression can be simplified to: [tex]tan(x) + cot(x)/sec(x) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]

We can simplify the expression as follows:

tan(x) + cot(x)/sec(x) = tan(x) + 1/tan(x) / 1/cos(x) = tan(x) + cos(x) / tan(x) * cos(x) = tan(x) + cos^2(x) / tan(x)

Using the identity: tan(x)^2 + 1 = sec^2(x), we can simplify further:

tan(x) + cos^2(x) / tan(x) = tan(x) + cos^2(x) / (sqrt(sec^2(x) - 1)) = tan(x) + cos^2(x) / sqrt(tan^2(x) + 1 - 1) = tan(x) + cos^2(x) / sqrt(tan^2(x))

Using the identity sin^2(x) + cos^2(x) = 1, we can simplify further:

[tex]tan(x) + cos^2(x) / \sqrt(tan^2(x)) = tan(x) + (1 - sin^2(x)) / \sqrt(tan^2(x)) = tan(x) + \sqrt(1 - sin^2(x)) / \sqrt(tan^2(x)) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]

Therefore, the expression can be simplified to:

[tex]tan(x) + cot(x)/sec(x) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]

Read more about trig expressions here:

https://brainly.com/question/26270284

#SPJ1

Answer:

If the ratio of the length to width of the rectangle is 3 to 2, we can write the length and width as:

length = 3x and width = 2x

where x is a common factor that can be determined once we know one of the dimensions.

Since the length of the rectangle is given as 1 3/4 feet, we can set x = 1 3/4:

length = 3x = 3 * 1 3/4 = 5 1/4 feet

width = 2x = 2 * 1 3/4 = 3 1/2 feet

Now that we know the length and width of the rectangle, we can calculate its area in square inches:

area = length * width = 5 1/4 * 3 1/2 = 18 3/8 square feet

To convert from square feet to square inches, we multiply by 12^2 = 144:

area = 18 3/8 * 144 = 2664 square inches

So the area of the rectangle is 2664 square inches.

The expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased and multiplying by x gives the total revenue from selling x units at that price.

Revenue can be defined as the total amount of income generated by the sale of goods and services related to the primary operations of the business.

The revenue (R) from a particular distributor that buys x units can be calculated using the following function statement:

R(x) = (4000 - 0.03x) * x

Where

The expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased, and multiplying by x gives the total revenue from selling x units at that price.

Learn more about revenue here : brainly.com/question/16232387

#SPJ1

(x - 10)² = -12 (y + 4)  represents a parabola with a vertical axis of symmetry, vertex at (10, –4), and p = –3 .

What's a vertical parabola?

A vertical parabola has its axis of symmetry at x = h, and the vertex is (h, v). With this information, you can find the focus and directrix. The focus is the distance from the vertex to the focus is 1/(4a), where a can be found in the equation of the parabola (it is the scalar in front of the parentheses).

we know that

If the axis of symmetry is parallel to the y-axis, then we have a vertical parabola

The equation of a vertical parabola is equal to

4p(y - k) = (x - h)²

where

(h,k) is the vertex

In this problem we have

(h,k) = (10, –4)

p= -3

substitute

4*(-3)(y - (-4)) = (x - 10)²

-12 (y + 4) =  (x - 10)²

or

(x - 10)² = -12 (y + 4)

Hence , option D is correct.

Learn more about parabola at:
https://brainly.com/question/25651698

#SPJ1

On solving the provided question we cans ay that the statistical data In this instance, the subject is not treated by the researcher.

Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts A data element is a feature (or attribute) data such as height, origin country, income, etc. that is measured or tallied. Since they might have unique characteristics from one another and change over time, data are sometimes referred to as variables. Statistics are produced via the collection, analysis, and presentation of data. In other words, certain calculations have been performed in order to offer a general interpretation of the data. Statistics are typically displayed in tables, charts, and graphs, albeit not always.

Due to the fact that these replies are not random, they may not accurately represent the population.

because they chose themselves.

The majority of the sample proportion demonstrates that it is statistical in (b)

(c) In this instance, the subject is not treated by the researcher.

The observational research is presented here.

To know more about statistical data visit:

https://brainly.com/question/14893265

#SPJ1

Answer:

Step-by-step explanation:

Yes, the ratios 4:6 and 2:3 are equivalent.

To see why, we can compare the proportions of the two ratios by dividing each term by the smaller term in each ratio.

In the ratio 4:6, if we divide both terms by 4, we get:

4/4 : 6/4 = 1 : 3/2

In the ratio 2:3, if we divide both terms by 2, we get:

2/2 : 3/2 = 1 : 3/2

Since both ratios reduce to the same proportion of 1 : 3/2, we can conclude that the ratios 4:6 and 2:3 are equivalent.

Ratios are mathematical expressions that compare two or more quantities. When two ratios are equivalent, it means that they represent the same proportion, even if the numbers in the ratios are different.

To compare the ratios 4:6 and 2:3, we divided each term in each ratio by the smallest term. This is because dividing each term by the same number will keep the proportion of the ratio the same.

For example, in the ratio 4:6, dividing both terms by 4 gave us the proportion of 1 : 3/2, which is the same as the proportion of 2:3 when divided by 2. This means that, even though the numbers in the two ratios are different, they represent the same proportion, and therefore the ratios are equivalent.

It's important to note that when comparing ratios, it's best to reduce the ratios to their simplest form so that the proportions are more easily compared.

Answer:

The solution to the equation 20 = m ÷ -5 is m = -100

To see this, we can multiply both sides of the equation by -5 to isolate the variable m:

20 × -5 = m ÷ -5 × -5

Expanding the right side of the equation:

20 × -5 = m × 1

Combining like terms:

-100 = m

And the solution is:

m = -100

Verification:

To verify the solution, we can plug in the value of m back into the original equation and see if it is true:

20 = -100 ÷ -5

Expanding -100 ÷ -5:

20 = 20

Since 20 = 20 is a true statement, we have verified that the solution m = -100 is correct.

∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°

→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°

→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°

angle Y and W are supplementary angles

so

→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°

angle X and Z are supplementary angles

so

→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

Therefore, the answer is

The value of the angle is 120°.

The corresponding angle of a given angle refers to the angle in a congruent position in another figure. For example, if two lines intersect, the angle formed at one vertex of the intersection is called a vertex angle. The corresponding angle in the other figure is the angle in a congruent position, meaning that it has the same measure.

We are given two lines to be parallel

Hence the angle adjacent to x is 40°

Now Sum of All three angle is 180° (Angles in linear pair)

Hence we have

40 + x + 20 = 180°

x = 120°

Hence the measure of angle x is 120°

Given below is sample of Angles in linear pair please refer the link

https://brainly.com/question/1757859

#SPJ1

Based on the information, we can infer that the graph would be a curve like the one shown in the attached image.

First of all, to graph the information about the body temperature of children, we must consult on the internet or other sources what is the body temperature of children. Below is the information:

According to the above, the graph should present a higher frequency at a temperature of 98.6, so the highest point on the graph would be at that temperature. On the other hand, the other temperatures would decrease because they are less frequent among children.

Learn more about body temperature in: https://brainly.com/question/18883752

#SPJ1

Answer:

Center = (-3, -3)

Step-by-step explanation:

[tex](x-h)^2+(y-k)^2=r^2\\\\Center=(h,k)[/tex]

[tex]x^2+6x+y^2+6y=18\\(x^2+6x \,\,\,\,\,\,\,) + (y^2+6y\,\,\,\,\,\,\,)=18\\\\\frac{6}{2} =(3)^2=9\,\,\,\,\,\,\,\,\,\,\,\,\,\, \frac{6}{2}=(3)^2 =9\\\\(x^2+6x+9)+(y^2+6y+9)=18+9+9\\(x+3)^2+(y+3)^2=36\\\\Center=(-3,-3)[/tex]

Answer:

1. 32 divided by 2 is 16

2.  2 x 16 = 36

Step-by-step explanation:

The solution set for the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex] is (-4, -3) ∪ (-3, ∞).

What is inequality?

An inequality is a mathematical statement that describes a relationship between two values or expressions, where one is greater than, less than, or not equal to the other.

To solve the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex], we can use the concept of interval notation and test each interval to see if it satisfies the inequality. Here are the steps:

Find the critical points of the expression, which are the values that make the expression equal to zero. In this case, the critical points are -5, -4, and -3.

Use these critical points to divide the number line into four intervals: (-∞, -5), (-5, -4), (-4, -3), and (-3, ∞).

Test a value in each interval to see if the inequality is true or false. We can use the sign of the expression to determine this:

For x < -5, all three factors are negative, so the product is negative. Therefore, this interval does not satisfy the inequality.

For -5 < x < -4, the first factor is positive and the other two factors are negative. The product is therefore negative. This interval does not satisfy the inequality.

For -4 < x < -3, the first and third factors are positive and the second factor is negative. The product is therefore positive. This interval satisfies the inequality.

For x > -3, all three factors are positive, so the product is positive. Therefore, this interval satisfies the inequality.

Write the solution set using interval notation. We have found that the solution set is (-4, -3) union ( -3, ∞).

Therefore, the solution set for the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex] is (-4, -3) ∪ (-3, ∞).

To learn more about inequality, visit:

https://brainly.com/question/24372553

#SPJ1

The system of linear equations representing the given situation is: 2x + y = 10 and 2x + 3y = 22. Solving this system, we find that it takes 6 minutes to jog around the park.

a. Let's use x to represent the number of minutes it takes to jog around the block and y to represent the number of minutes it takes to jog around the park.

From the problem statement, we know that:

2x + y = 10 (jog around the block twice and the park once in 10 minutes)

2x + 3y = 22 (jog around the block twice and the park three times in 22 minutes)

These are the two linear equations that represent the given situation.

b. We can solve this system of equations to find the value of y, which represents the number of minutes it takes to jog around the park.

We can start by eliminating x from the equations. Subtracting the first equation from the second, we get:

(2x + 3y) - (2x + y) = 22 - 10

2y = 12

y = 6

So, it takes 6 minutes to jog around the park.

Learn more about linear equations here: brainly.com/question/11897796

#SPJ4

Complete question:

You can jog around your block twice and the park once in 10 minutes. you can jog around your block twice and the park 3 times in 22 minutes.

a. write a system of linear equations that represents this situation. let x represent the number of minutes it takes you to jog around your block and y represent the number of minutes it takes you to jog around the park. system of equations:

b. how long does it take you to jog around the park? it takes you minutes to jog around the park.

Answer:

try this

Step-by-step explanation:

E1, E3, and E2, E3 are independent variables.

[tex]$& \mathrm{P}\left(\mathrm{E}_1\right)=\frac{1}{6} \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_2\right)=\frac{1}{6} \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_3\right)=\frac{2+4+6+4+2}{36}=\frac{1}{2} \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_2 \cap \mathrm{E}_3\right)=\frac{1}{2} \times \frac{1}{6}=\mathrm{P}\left(\mathrm{E}_2\right) \times \mathrm{P}\left(\mathrm{E}_3\right) \\[/tex]

Then,

[tex]$& \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_3\right)=\frac{1}{2} \times \frac{1}{6}=\mathrm{P}\left(\mathrm{E}_1\right) \times \mathrm{P}\left(\mathrm{E}_3\right) \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_2 \cap \mathrm{E}_3\right)=0 \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_1\right) \mathrm{P}\left(\mathrm{E}_2\right) \mathrm{P}\left(\mathrm{E}_3\right) \equiv 0 \\[/tex]

Simplify,

[tex]$& \therefore \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_2 \cap \mathrm{E}_3\right) \equiv \mathrm{P}\left(\mathrm{E}_1\right) \mathrm{P}\left(\mathrm{E}_2\right) \mathrm{P}\left(\mathrm{E}_3\right)[/tex]

E1, E3 are independent

E2, E3 are independent

The complete question is:

Let two fair six-faced dice A and B are thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

To learn more about independent variable, refer to:

https://brainly.com/question/27894163

#SPJ1

The common difference of the given arithmetic sequence is 8.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

The given arithmetic sequence is -1, 7, 15,....

Common difference = Second term - First term

= 7-(-1)

= 7+1=8

Common difference = Third term - Second term

= 15-7

= 8

Therefore, the common difference is 8.

To learn more about an arithmetic sequence visit:

https://brainly.com/question/10396151.

#SPJ1

The solution is, the common differences are -3, -20, -10, -2, 5.

In an arithmetic sequence, the difference between any two consecutive terms must always be the same number, which is known as the common difference.

here, we have,

So we just need to take different pairs of consecutive terms and see if their difference is always the same:

1) The differences are:

32 - 35 = -3

29 - 32 = -3

26 - 29 = -3

So yes, this is an arithmetic sequence and the common difference is -3

2) The differences are:

-23 - (-3) = -20

-43 - (-23) = -20

-63 - (-43) = -20

This is an arithmetic sequence, and the common difference is -20

3) The differences are:

-64 -(-34) = -30

-94 -(-64) = -30

-124 -(-94) = -30

This is an arithmetic sequence and the common difference is -30

4) The differences are:

-40 -(-30) = -10

-50 - (-40) = -10

-60 - (-50) = -10

This is an arithmetic sequence and the common difference is -10

5) The differences are:

-9 - (-7) = -2

-11 - (-9) = -2

-13 - (-11) = -2

This is an arithmetic sequence, and the common difference is -2

6) The differences are:

14 - 9 = 5

19 - 14 = 5

24 - 19 = 5

This is an arithmetic sequence, and the common difference is 5.

To learn more on common difference click:

https://brainly.com/question/21726804

#SPJ1

Hakeem made 10 shots. The solution has been obtained by using proportions.

What is proportion?

Two numbers are compared. It is known as a proportion in mathematics. The law of proportion states that if two sets of given numbers rise or decrease in the same ratio, they are considered to be directly proportionate to one another.

We are given that Hakeem made 5% of his free throws over the season.

He shot 200 free throws and was able to make 5% from them.

So,

Number of throws he made = Number of free throws x Percentage made

Using this, we get

⇒Number of throws he made = 200 x 5%

⇒Number of throws he made = 10

Hence, Hakeem made 10 shots.

Learn more about proportions from the given link

https://brainly.com/question/870035

#SPJ1

=$50

Step-by-step explanation:

Total amount to be earn

if one women cut and add a colour

35$ + 15$

= $50

The salon earn if the women get a cut and a colour is $50.

There are many meanings of total, but they all have something to do with completeness. A total is a whole or complete amount, and "to total" is to add numbers or to destroy something.

In math, you total numbers by adding them: the result is the total. If you add 8 and 8, the total is 16. If a car is totalled in an accident, it has been completely destroyed. A total defeat is a complete and utter defeat with no chance of recovering. The total resources of a company are all its resources, everything it has.

Step-by-step explanation:

Total amount to be earn

if one women cut and add a colour

35$ + 15$

= $50

Learn more about Total amount

https://brainly.com/question/28000147

#SPJ1

Answer:

(a) Possible number(s) of positive real zeros:  3

(b) Possible number(s) of negative real zeros:  1

Step-by-step explanation:

Descartes' Rule of Signs tells us the maximum number of positive and negative roots.

Positive root case

[tex]f(x)=-3x^4+2x^3-x^2+9x+7[/tex]

As there are 3 sign changes, the maximum possible number of positive roots is 3.

Negative root case

[tex]\begin{aligned}f(x)&=-3(-x)^4+2(-x)^3-(-x)^2+9(-x)+7\\&=-3x^4-2x^3-x^2-9x+7 \end{aligned}[/tex]

As there is one sign change, the maximum possible number of negative roots is 1.

Answer:

a. The probability that a married couple watches the show can be calculated by multiplying the probabilities that each spouse watches the show:

P(Married couple watches the show) = P(Husband watches the show) * P(Wife watches the show) = 0.4 * 0.5 = 0.2

Step-by-step explanation:

b. The probability that a wife watches the show, given that her husband does, can be calculated using Bayes' theorem:

P(Wife watches the show | Husband watches the show) = P(Husband watches the show | Wife watches the show) * P(Wife watches the show) / P(Husband watches the show)

P(Wife watches the show | Husband watches the show) = 0.7 * 0.5 / 0.4 = 0.875

c. The probability that at least one member of a married couple will watch the show can be calculated as the sum of the probabilities that either the husband or the wife watches the show:

P(At least one member of a married couple watches the show) = P(Husband watches the show) + P(Wife watches the show) - P(Married couple watches the show) = 0.4 + 0.5 - 0.2 = 0.7

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

The federal loan at 2.8% is approximately 11000, and the private bank loan at 4.8 percent is around 39000 (which is 50000 - 11000).

Let's use f and p to denote the amounts of Josie's federal and private bank loans, respectively.

We know that the total amount of loans is 50000, so:

f + p = 50000

We also know that the interest on federal loans at 2.8% and the interest on private bank loans at 4.8% add up to 1600 per year. The interest on the federal loans is 0.028f and the interest on the private bank loans is 0.048p, so:

0.028f + 0.048p = 1600

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for p:

p = 50000 - f

Substituting this into the second equation, we get:

[tex]0.028f + 0.048(50000 - f) = 1600[/tex]

Simplifying and solving for [tex]f[/tex], we get:

[tex]f = \frac{1600 - 0.048 \cdot 50000}{0.02} \approx 11000[/tex]

Therefore, the federal loan at 2.8% is approximately 11000, and the private bank loan at 4.8% is approximately 39000 (which is 50000 - 11000).

To know more about interest visit:

https://brainly.com/question/30393144

#SPJ1

The side RT of the triangle is 13 m.

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

The sine law is a mathematical formula used in trigonometry to relate the sides and angles of a triangle. The sine law states that:

a/sin(A) = b/sin(B) = c/sin(C)

where:

a, b, and c are the lengths of the sides of the triangle

A, B, and C are the angles opposite those sides

Using sine law:

RT/sin 34° = ST/sin 109°

RT/sin 34° = 22/sin 109°

RT = (22 * sin 34°)/(sin 109°)

RT = 13 m

Learn more about Trigonometry on:

brainly.com/question/11967894

#SPJ1

Answer:

x = 2.4 inch

Step-by-step explanation:

Tall retangular prism = lwh = 6 x 9 x 3 = 162 in^3

378 - 162 = 216

Long rectangular prism = lwh = (15)(6)(x) = 90x

216 = 90x

x = 2.4