PLEASE HURRY!!

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)

Answer:

11x

Step-by-step explanation:

Answer:

1.) x = 1, 2/3  

2.) x = -3±[tex]\sqrt{6}[/tex]

3.) x = [tex]\frac{4+/-\sqrt{37} }{3}[/tex]  or x = −3.36092084, 0.69425417

Step-by-step explanation:

These are quadratic equations so we use the quadratic formula method.

Use the quadratic formula by taking:

[tex]ax^{2}+bx^{2} +c=0[/tex]

1.) a = 3, b = -5, c = 2

2.) a = 1, b = 6, c = 3

3.) a = -3, b = -8, c = 7

Then, substitute into the quadratic formula:

(Check the picture provided for the quadratic formula)

Answer:

1.4 people out of 10

Step-by-step explanation:

Just divide it by 10

Answer:

only 4 people

An example of an exponential function is the growth of bacteria. the growth of the bacteria is by exponential growth in the number of cells in a specimen of bacteria doubles every hour.

Some bacteria double her size every hour. Starting with 1 bacterium, every hour he doubles, after x hours he doubles as bacterium. This can be written as f(x) = 2x.

Bacteria replicate by binary fission, the process by which one bacterium divides into two. Bacteria therefore multiply in number by a geometric progression, doubling the population with each generation. The binary fission is the actual multiplication procedure of the cells division where cells grows fastly and further divided itself into other groups or colony.

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These scatterplots show that model type A is best suited to summarize the relationship between year and stock price. The scatterplot of the processed data is nearly linear, so a linear model is suitable.

These scatterplots show that model type A is best suited to summarize the relationship between year and stock price. The scatterplot of the processed data is nearly linear, so a linear model is suitable.

A linear model is applicable if we can create a linear equation based on the connection between the independent and dependent variables (because there is no constant rate of change).

Otherwise, we can simulate the relationship using an exponential model.

An exponential model is:When the rate of increase representing the relationship between the year and stock price is proportional or constant, we utilize the exponential model.

By determining whether the ratio of the dependent values is the same, one can choose to describe the connection as an exponential equation.

As a result, even though the time and price scatterplot is curved, a linear model is adequate.

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Answer:

Step-by-step explanation:

To find the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly, we can use the formula:

compound interest = principal * (1 + rate/n)^(n*t) - principal

where "principal" is the initial amount of money, "rate" is the annual interest rate, "n" is the number of times the interest is compounded per year, and "t" is the number of years.

Plugging in the given values, we get:

compound interest = $50,000 * (1 + 0.064/4)^(4*10) - $50,000

= $50,000 * (1.016)^40 - $50,000

= $50,000 * 2.6335 - $50,000

= $78,167.50 - $50,000

= $28,167.50

Therefore, the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly is $28,167.50.

The most horizontal line is straight so it equal 180°. You know that one side (lower left section) is 67° meaning the other side is 180° - 67° = 113° (lower right side).

The most vertical line is straight so it equal 180°. You know that one side (lower right side) is 113°. The entire right side you have: 113°, 42°, and f.

f =  180° - (113° + 42°)

f = 25°

Answer:25 deegrees

Step-by-step explanation:

When a number is first increased by 25% then if it is decreased by 25% , we will get the same starting number. hence the net increased or decreased value is zero.

A decline in net income is a change from one period to the next in the amount of money you have after deducting your expenses from your revenues.

There are two possible outcomes for net income. Your business has a positive net income when revenues exceed expenses. You have a negative net income, commonly referred to as a net loss, if all of your expenses exceed all of your revenues.

let the number is x

first it is increased by 25%

so,

x+(25/100)x=(125/100)x

now according to second condition,

we have to find a value by which it is decreased so we get the same number.

so, let that decreased value is y;

(125/100)x-y=x

-y=x-(125/100)x

-y=-(25/100)x

cancelation of sign;

y=25%

so this is our required value.

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Answer:

f(-4)=1

Step-by-step explanation:

f(x) = 2x² + 3x - 19

f(-4)=2(-4)² + 3(-4)-19

f(-4)=2(-16)+3(-4)-19

f(-4)=-32+3(-4)-19

f(-4)=32-12-19

f(-4)=20-19

f(-4)=1

The  value of inserting area of an array is 0.02

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

The region that an object's shape defines as its area. The amount of space occupied by a figure or any other two-dimensional geometric shape in a plane is known as its area.

Given:

5 column (hundred grid) = 5/100 = 0.05

4 row (hundred grid) = 4/100 = 0.04

Find:

Area equation

Computation:

Area equation = 0.05 x 0.04

0.05 x 0.04 = 0.002

Therefore the  value of inserting area of an array is 0.02

The complete question is : Which product is represented by the model? A hundred grid model shows 5 columns shaded and 4 rows shaded. The intersecting area is an array that is 5 by 4. A. 0 . 05 × 0 . 04 = 0 . 002 B. 5 × 0 . 4 = 2 C. 0 . 5 × 0 . 4 = 0 . 2 D. 0 . 5 × 0 . 04 = 0 . 02

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Answer:

To find the dimensions of the fish tank, we can set up the equation:

(width) * (length) * (height) = 1440 cubic inches

Substituting the given expressions for the dimensions of the tank, we get:

(w) * (w + 8) * (18 - w) = 1440

This is a quadratic equation in w, and we can solve it using the quadratic formula:

w = (-(w + 8) +/- sqrt((w + 8)^2 - 4*(18 - w)11440)) / (2*1)

This simplifies to:

w = (-(w + 8) +/- sqrt(w^2 + 16w + 64 - 72w + 5760)) / 2

= (-(w + 8) +/- sqrt(w^2 - 56w + 5760)) / 2

We can further simplify this equation by factoring:

w = (-(w + 8) +/- sqrt((w - 40)(w - 144))) / 2

We can then solve for w by setting each factor equal to zero:

w - 40 = 0 => w = 40

w - 144 = 0 => w = 144

Since the width of the fish tank must be greater than 6 inches, the only valid solution for w is 40 inches. Substituting this value back into the equation for the volume of the tank, we find that the length of the tank is 48 inches (w + 8 = 40 + 8 = 48) and the height of the tank is 12 inches (18 - w = 18 - 40 = 12).

Therefore, the dimensions of the fish tank are:

width: 40 inches

length: 48 inches

height: 12 inches

The correct answer is therefore (a) width: 12 in., length: 20 in., height: 6 in.

Step-by-step explanation:

A value of lawn care is negetive because the profits are decreasing after month-3. So it is sloping downards. Had the profits been raising the a-value would have been positive.

Based on the plot the profits of each month can be found out using a qudratic function?

The lawn care business shows diminishing returns after month 3 . So it is not a viable business to conitnue for the long term. Based on the projections around month 8 profit becomes -$14.44. This is loss.

The other two businesses are profitable. The show upward growing trend as the months progress. Following table shows projected earnings for 1 year based on the equations showed in the graph.

3. A quadratic funtion can be used to represent the profits. The equation is given in the plots

4. A value of lawn care is negetive because the profits are decreasing after month-3. So it is sloping downards. Had the profits been raising the a-value would have been positive.

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Number of nails to finish the project by buying are required = 2964 units

1 package of nails contains per unit  = 52 units

To find the no. of packages we have to simply divide the total no. of nails required by the total of no. of nails of unit given in the one package of nails.

So,

Number of package required to the builder

= Total number of nails required to buy by the builder / no. of nails provided  per package

=2964/52

=57 packages

Therefore, No. of packages required by the builder to buy to complete the project

=57 packages needed.

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Answer: 57

Step-by-step explanation:

Just plug it into a calculator.

2964/52 = 57

He needs to buy 57 packages

The value of u is 21.

Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.

Given:

DG=FG=7, m ∠DEG=u+21°, and m ∠FEG=2u,

As, from the Diagram

DE = FE  (Given)

DG= FG  ( Given)

GE= GE (Common)

So, ΔDEG ≅ ΔFEG by SSS Rule.

<DEG = <FEG (CPCT)

u + 21 = 2u

2u - u= 21

u=21

Hence, the value of u is 21.

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Size will be 37 L x 15 W.

Perimeter is the distance around the edge of a shape. Discover how to calculate a shape's perimeter by adding its side lengths.

Finding the dimension is required, if the perimeter is 104 meters and the length is 7 meters longer than twice the  breadth.

Let L be the length and W be the width

L = 7 + 2*W

P = 2(L + W) ; 104 = 2(7 + 2W + W) ; 104 = 2(7 + 3W) ;

104 = 14 + 6W

6*W = 90 ;

W = 15 L = 37

Hence the dimension is 37*15

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Volunteer/voluntary response bias, also known as self-selection bias, occurs when research participants exert control over the decision to engage in the study.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

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4 is the value of w which makes the equation true.

What is an equation?

It is given that,

3(−4w−5)=−7(5+w)

by solving the equation,

-12w-15=-35-7w

12w-7w=35-15

5w=20

w=20/5

∴w=4

Hence, 4 is the value of w which makes the equation true.

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Answer:

x=  -22d/44    x = -48d/44  is your answer

where d =2x  

Step-by-step explanation:

22d²- 35d + 12 = -3d²

22d²- 35d + 12 +3d²

25d²- 35d + 12 = a b c formula= - b-/+ / b^2 - 4 ac   / 2a

= -35d -+/ 35^2 - 4 *22d *12 / 2*22d

= -35d -+/1225d-4 (22) (12) /44d

= -35d -+/1225d- (88) (12) /44d

= -35d -+/1225d- (1056) /44d

= -35d -+/169d-  /44d

=-35d -/+ 13d   /44     x=  -22d/44    x = -48d/44  

The discriminant b2−4ac>0

so, there are two real roots.

Step-by-step explanation:

it seems like you understood the law of cosine (extended Pythagoras for non-right-angled triangles) and applied it mostly correctly for a).

but you made a little typo : suddenly, in the second half of the formula you changed the side length BC from 83.1 to 81.3. but it is 83.1.

so, the correct calculation is

a² = 83.1² + 95.5² - 2×95.5×83.1×cos(101) =

= 16,025.86 - 15,872.1×cos(101) =

= 16,025.86 - -3,028.539456... =

= 19,054.39946...

a = sqrt(19,054.39946) = 138.037674...

the rounded result is the same (138 km), but just for your information, and also, I want to use the correct numbers for b)

for b) we need to know :

bearings are angles, measured clockwise from north (north would be 0°).

when ship A looks to station C, the bearing is 146°.

when ship A looks to ship B, the corresponding bearing is 146 - the triangle angle at A (because that is how far we have to turn from looking at C to looking at B).

so, now, we need to apply the law of cosine again. this time to get angle A, as we have now side a.

c² = a² + b² - 2ab×cos(C)

and we want to get C, means now (since you called the baseline "a" in the first part)

83.1² = 95.5² + a² - 2×a×95.5×cos(angle A)

6,905.61 = 9,120.25 + 19,054.39946... - 2×138.037674...×95.5×cos(angle A)

6,905.61 = 28,174.64946... - 26,365.19574...×cos(angle A)

-21,269.03946... = -26,365.19574...×cos(angle A)

cos(angle A) = -21,269.03946.../-26,365.19574...

= 0.806708953...

angle A = 36.22437773...°

therefore, the bearing from A to B is

146 - 36.22437773... = 109.7756223...°

Answer: No, because they are not the same in slope - intercept form

Step-by-step explanation:

    First, we will distribute and simplify into slope-intercept form.

   Equation 1:

y - 3 = 4(x - 2)

y = 4(x - 2) + 3

y = 4x - 8 + 3

y = 4x - 5

   Equation 2:

y + 2 = 4(x + 7)

y = 4(x + 7) - 2

y = 4x + 28 - 2

y = 4x + 26

      We see that the answer to this question is "No, because they are not the same in slope - intercept form" as they have different y-intercepts, one being -5 and one being 26.

The missing number in the equation 1/2 of 30 = 1/4 is 60

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

1/2 of 30 = 1/4

This equation can be properly expressed as

1/2 of 30 = 1/4 of __

Represent the blank with a variable x

So, we have the following representation

1/2 of 30 = 1/4 of x

Express as products

1/2 * 30 = 1/4 * x

Multiply both sides by 4

This gives

x = 4 * 1/2 * 30

Evaluate

x = 60

Hence, the missing number is 60

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Answer:

4/15

Step-by-step explanation:

reciprocal of 1/3 then cross multiply

Answer: [tex]y-1=-\frac{1}{2}(x-4)[/tex]

Step-by-step explanation:

The equation of the given line can be rearranged as [tex]y=2x-4[/tex].

Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we need to find is -1/2.

Using point-slope form, the equation is [tex]y-1=-\frac{1}{2}(x-4)[/tex].

The possible number of ways the 7-question test can be answered: 128

In this question, we have been given a true-false test contains 7 questions.

We need to find the possible number of combinations (ways)  the 7-question test can be answered.

As, it is a true-false test, there are 2 choices per problem.

The number of problems = 7

so,  the possible number of ways  the 7-question test can be answered: 2*2*2*2*2*2*2

= 2^7

= 128

Therefore, in 128 different ways the 7-question test can be answered.

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Answer:

x=15.56

Step-by-step explanation:

You need to use pythagoras for this question.

Formula for pythagoras: a^2 + b^ =c^2

a= 11

b=11

c=?

11^2+11^2=c^2

121+121=c^2

242=c^2

[tex] \sqrt{242} [/tex]

=c

c=15.56

Answer: True

Step-by-step explanation:

Simple.

Therefore, the probability that their hospital stay is from 5 to 6 days is 0.03310 .

Probability deals with calculating or making estimates of how probable or "possible" an event is to occur. To convey the probability of an event occurring, words like "certainly," "impossible," or "likely" might be employed. Probabilities are always represented in mathematics as fractional, decimals, or percentages, with values that range from 0 to 1.

Here,

Given:

Mean, μ =7.37 days

Standard Deviation, σ =  2.75 days

Given: hospital stays are distributed in a bell-shaped manner, which is a typical distribution.

Formula:

Z = [tex]\frac{x-u}{\alpha }[/tex]

a) P( 5 to 6 days are spent in the hospital.)

P(5≤x≤6)

=>P([tex]\frac{5-7.37}{2.75}[/tex] ≤x≤ [tex]\frac{6-7.37}{2.75}[/tex])

=>P(-0.861≤x≤-0.498)

=>P(Z≤-0.498) - P(Z<-0.861)

=>0.034 - 0.001 = 0.03310

=> P(5≤x≤6) =3.3%

Therefore the probability that their hospital stay is from 5 to 6 days is 3.3%.

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Answer:

numerator = 4x + 6

Step-by-step explanation:

x²+3x + 2

(x+2)(x+1)

x/(x+2)(x+1) + 3(x+2)/(x+2)(x+1)

(x+3x+6)/(x+2)(x+1)

(4x+6)/(x+2)(x+1)