HELPP Write the equation of the given line in slope-intercept form:

a) By Pythagorean theorem, the value of variable x is equal to 10.2171 meters.

b) By trigonometric functions, the value of variable h is equal to 7.8620 meters.

Herein we have the representation of a geometric system formed by four right triangles, this formation has a known angle and a known side, and two unknown variables as well. The values of the variables can be found by means of trigonometric functions and Pythagorean theorem:

Trigonometric functions

sin 50° = h / x

h = 0.7660 · x

Pythagorean theorem

x² = L² + h²

8² = (0.25 · L)² + h²

64 = 0.0625 · L² + h²

Then, we eliminate L by equalizing second and third equations:

64 = 0.0625 · (x² - h²) + h²

64 = 0.0625 · x² + 0.9375 · h²

And by the first equation:

64 = 0.0625 · x² + 0.9375 · (0.7660 · x)²

64 = 0.0625 · x² + 0.5501 · x²

64 = 0.6126 · x²

8 = 0.783 · x

x = 10.2171 m

And the value of h is:

h = 0.7660 · (10.2171 m)

h = 7.826 m

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1. 8/3
2. 16/3
3. 123

*some words for 20 symbols*

Step-by-step explanation:

The volume of the packages is 1.5³=3.38ft³

The volume of the truck is a prism: A×B×C=10.5×8×9=756ft³

The amount of basketballs that can fit is: 756/3.38=223.6 boxes.

The maximum height reached from the ground is 242.75 m

Here, we have,

The horizontal speed of a projectile is regular, and there's a vertical acceleration because of gravity; its cost is 9.8 m/s/s, down, The vertical speed of a projectile changes via nine.8 m/s every second, The horizontal motion of a projectile is impartial to its vertical movement.

we know that,

Projectile motion is a form of motion experienced with the aid of an object or particle that is projected in a gravitational field, such as from Earth's floor, and movements alongside a curved route below the action of gravity best.

Projectile motion is the movement of an object thrown (projected) into the air. After the initial force that launches the item, it most effectively reports the pressure of gravity. The object is known as a projectile, and its route is called its trajectory.

Calculation:-

vertical velocity = 70 cos 35° = 57.34 m/s.

height = 64 m tall

time = ?

S = ut +1/2 at²

75 =  57.34t + 1/2×9.8 t²

4.9t² + 57.34t - 75 = 0

t = 1.50035 Sec

V² = U² - 2aS

0 =  U² - 2aS

U² = 2aS

S = U² /2a

  =  (57.34)²/2× 9.8

  = 167.75

Total height = 75 + 167.75

                    = 242.75 m

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complete question:

A man fired a bullet from the top of a tree whick is 64m tall. The bullet is fired with а velocity of 70ms-1 and angle of 35° to the horizontal line from the eye view of the man. If Sitting position the man is 0.8m Tall. Find the maximum height reached from the ground.

​

Answer:

2x+8-2y

Step-by-step explanation:

4x-2x+5+3-2y

2x+8-2y

Answer:

There you go!!

Step-by-step explanation:

4x - 2x - 2y + 3 + 5

All the singular points of the given differential equation. The singular points occur at x = 0.

Singular points are those points at which the coefficients of the derivatives of the given differential equation become infinite or the differential equation itself becomes undefined.

For the given differential equations, the singular points are as follows: 1. The given differential equation is(x+1)y" - x2y'+3y = 0

Comparing the given differential equation with the general form of the second-order linear differential equation (ay'' + by' + cy = 0), we get the coefficients of the derivatives as follows: a = x + 1b = -x2c = 3y

Therefore, the singular points occur at x = 0 and x = -1.2. The given differential equation isx2y"+3y' - xy = 0

Comparing the given differential equation with the general form of the second-order linear differential equation (ay'' + by' + cy = 0), we get the coefficients of the derivatives as follows: a = x2b = 3c = -x.

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The function notation will be:

f(x) = 3x - 2

Since y (the output) can be replaced with f(x).

First, we know that a relationship between two variables x and y maps the first variable (called the input) into the second variable (called the output)

In this case, the relationship between x and y is linear, and is of the form:

y = 3x - 2

Particularly, if for each value of "x" that we use we get only one value of y as the output, then the relationship is called a function, and in that case we can write:

y = f(x).

So here to use function notation we just write:

f(x) = 3x - 2

And in that way we know that we have a function.

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Answer:

Step-by-step explanation:

0.3

Answer:

It is 0.3 more or 0.300 more

Step-by-step explanation:

6.002 + 0.3 or 0.300 = 6.302

6.302- 0.300 or 0.3 = 6.002

Hope I helped

Answer:

Y=.833x-2

Step-by-step explanation:

correct y intercept and rise over run  gives you the slope.

Answer:

square root 162

Step-by-step explanation:

Answer:

\(9 \sqrt{2 } \)

Answer:

x=1 and y=1

Step-by-step explanation:

see attachment

Answer:

1.54034×10^5

Step-by-step explanation:

Therefore, by using a representative sample and appropriate statistical methods, it is possible to estimate the difference in expected muscle mass for women whose ages differ by one year without knowing the specific ages of the individuals in the population.

It is not necessary to know the specific ages of women to estimate the difference in expected muscle mass for women whose ages differ by one year because the confidence interval is based on a population-level estimate rather than individual-specific data.

In this case, the confidence interval is constructed based on a sample of women, which provides an estimate of the average difference in expected muscle mass for women whose ages differ by one year in the population. The sample is selected randomly and is assumed to be representative of the population of interest.

By using statistical techniques, such as hypothesis testing and confidence interval estimation, we can make inferences about population parameters, such as the difference in muscle mass for women of different ages. These techniques rely on the assumption that the sample is representative of the population, rather than requiring specific individual-level information.

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Answer:

20h + 4

Step-by-step explanation:

It's easy. Just disperse the multiplying by 4 to the others in the first group.

Multiply 1 by 4, and you get 4.

Multiply 5h by 4, and you get 20h.

The answer is 20h + 4.

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Answer:

All new reflected coordinates

T (-3, 6)

S (-2, 4)

U (-4, 4)

R (-3, 2)

Step-by-step explanation:

This is because the are reflected sideways on x = 1. This works like a mirror or opening a page of a book if that helps visualise it.

Answer:

The total volume is 62.5.-

Step-by-step explanation:

Giving the following information:

The equation below shows the total volume (V), in cubic units, of 4 identical boxes with each side equal to "s" units:

V = 4*(s^3)

Now, the total volume if s=2.5:

V= 4*(2.5^3)

V= 4*15.625

V= 62.5

The total volume is 62.5.-

Answer:

30 square units

Step-by-step explanation:

4 x 2.5 units= 10.

take the 3 from the V, (4s³).

Multiply that.

4 x 2.5 square units = 10

10 x ³ = 30 square units In total.

PS, Brainly has said answers were correct when they are actually wrong before, but it is also possible i am not correct. so Its up to you. :)

Answer:

x =6

Step-by-step explanation:

5(x-2) = 14+x

Distribute

5x-10 = 14+x

Subtract x from each side

5x-x -10 = 14+x-x

4x-10 = 14

Add 10 to each side

4x-10+10 = 14+10

4x= 24

Divide by 4

4x/4 = 24/4

x =6

Answer:

5(×-2)=14+×

5x-10=14+x

5x-x=14+10

4x=24

x=6

36 is  the number of possible pairs of outcomes by probability.

What is a probability answer?

Mathematics' branch of probability, where probability is the likelihood that any event will occur, deals with the occurrence of random events.      

                                                 The probability value is given as a number between 0 and 1. Probabilities are always between 0 and 1. The basic probability formula is: Probability = Number of Favorable Outcomes / Total Number of Outcomes.

We have two dice in this question. A die is known to be make up of 6 faces.

Therefore the number of faces for two dice = 6*6 = 36

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Answer:198.447

Step-by-step explanation:

just search 7 ounces to grams

The "d" format specifier is used to denote a signed decimal integer in various programming languages and formatting systems.

When used in format strings or printf-style functions, the "d" specifier indicates that the corresponding argument should be formatted as a signed decimal integer. It allows for the representation of both positive and negative whole numbers, including zero.

For example, in C programming, the printf function can be used with the "%d" format specifier to display a signed decimal integer value. Similarly, in other languages such as Python, the "{:d}" format specifier can be used with the format() function or string interpolation to represent a signed decimal integer.

Using the "d" specifier ensures that the output is formatted as a base-10 representation of a signed integer, taking into account the sign of the number.

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Answer:

number 3 maybe . sorry if wrong

Answer:

Slope is 20 and y-intercept is 40.

Step-by-step explanation:

First, let's find slope. I'll be using the points (1,60) and (3,100).

\(m=\frac{y2-y1}{x2-x1}=\frac{100-60}{3-1}=\frac{40}{2}=20\)

So the slope is \(m=20\). Now we need to find y-intercept. We can do this by using our slope and a point in the point-slope equation, \(y=mx+b\). I'll use the point (1,60).

\(y=mx+b\\60=20(1)+b\\60=20+b\\b=40\)

I hope this helps!

1. To determine the number of tubs John must sell per show to break even, we need to consider the fixed costs and the contribution margin per tub. The contribution margin is the difference between the selling price and the variable cost per tub.

In this case, the variable cost is the wholesale cost of $30 per tub. The contribution margin per tub is $80 - $30 = $50.  To calculate the break-even point, we divide the fixed costs by the contribution margin per tub:

Break-even point = Fixed costs / Contribution margin per tub

Break-even point = $900 / $50 = 18 tubs

Therefore, John must sell at least 18 tubs per show to break even.

2a. To earn a profit of $1,100 per show, we need to determine the sales volume in units necessary. The desired profit is considered an additional fixed cost in this case. We add the desired profit to the fixed costs and divide by the contribution margin per tub:

Sales volume for desired profit = (Fixed costs + Desired profit) / Contribution margin per tub

Sales volume for desired profit = ($900 + $1,100) / $50 = 40 tubs

Therefore, John needs to sell 40 tubs per show to earn a profit of $1,100.

2b. To determine the sales volume in dollars necessary to earn the desired profit, we multiply the sales volume in units (40 tubs) by the selling price per tub ($80):

Sales volume in dollars for desired profit = Sales volume for desired profit * Selling price per tub

Sales volume in dollars for desired profit = 40 tubs * $80 = $3,200

Therefore, John needs to achieve sales of $3,200 to earn a profit of $1,100 per show.

c. Income Statement (condensed version):

Sales Revene: 40 tubs * $80 = $3,200

Variable Costs: 40 tubs * $30 = $1,200

Contribution Margin: Sales Revenue - Variable Costs = $3,200 - $1,200 = $2,000

Fixed Costs: $900

Operating Income: Contribution Margin - Fixed Costs = $2,000 - $900 = $1,100

The condensed income statement confirms the answers from parts a and b, showing that the desired profit of $1,100 is achieved by selling 40 tubs and generating sales of $3,200.

3. The margin of safety represents the difference between the actual sales volume and the breakeven sales volume.

Margin of safety in sales dollars = Actual Sales - Breakeven Sales = $3,200 - ($50 * 18) = $2,300

Margin of safety in units = Actual Sales Volume - Breakeven Sales Volume = 40 tubs - 18 tubs = 22 tubs

Margin of safety as a percentage = (Margin of Safety in Sales Dollars / Actual Sales) * 100

Margin of safety as a percentage = ($2,300 / $3,200) * 100 ≈ 71.88%

Therefore, the margin of safety is $2,300 in sales dollars, 22 tubs in units, and approximately 71.88% as a percentage.

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Variance and standard deviation are both measures of the dispersion or spread of a dataset, but they differ in terms of the unit of measurement.

Variance is the average of the squared differences between each data point and the mean of the dataset. It measures how far each data point is from the mean, squared, and then averages these squared differences. Variance is expressed in squared units, making it difficult to interpret in the original unit of measurement. For example, if we are measuring the heights of individuals in centimeters, the variance would be expressed in square centimeters.

Standard deviation, on the other hand, is the square root of the variance. It is a more commonly used measure because it is expressed in the same unit as the original data. Standard deviation represents the average distance of each data point from the mean. It provides a more intuitive understanding of the spread of the dataset. For example, if the standard deviation of a dataset of heights is 5 cm, it means that most heights in the dataset are within 5 cm of the mean height.

To illustrate the application of these measures, consider a dataset of test scores for two students: Student A and Student B.

If Student A has test scores of 80, 85, 90, and 95, and Student B has test scores of 70, 80, 90, and 100, we can calculate the variance and standard deviation for each student's scores.

The variance for Student A's scores might be 62.5, and the standard deviation would be approximately 7.91. For Student B, the variance might be 125 and the standard deviation would be approximately 11.18.

These measures help us understand how much the scores deviate from the mean, and how spread out the scores are within each dataset.

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Answer:

The y-intercept is 8.

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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The interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.

The complete question is

A survey conducted by Conquest Communications Group randomly sampled 700 registered voters in the U.S. 258 of the 700 sampled voters correctly answered that fourth graders in the U.S. are above average for overall education compared to other countries.

Choose a number between 80 and 96. This is the level of confidence you will use for this section of problems. What is your number?

It is defined as the margin by which the values calculated will differ from the real values .

Let the chosen number is 95  %

95% Confidence Interval ,

\(\rm p = p \pm \dfrac{Z_{0.05}}{2} \sqrt \dfrac{p(1-p)}{n}}\\\\= \dfrac{258}{700} \pm 1.96 \sqrt \dfrac{\dfrac{258}{700}(1-\dfrac{258}{700})}{700}}\\\)

Therefore p at 95% Confidence Interval is given by 0.3329 , 0.4043

The margin of error is given by  0.4043-0.3329

= 0.0357

Therefore the interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.

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\(\\ \rm\Rrightarrow cos60=\dfrac{a}{500}\)

\(\\ \rm\Rrightarrow a=500(cos60)\)

\(\\ \rm\Rrightarrow a=500(1/2)\)

\(\\ \rm\Rrightarrow a=250m\)

Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. About how much farther is it to drive than to walk directly from building A to building B? Round to

the nearest whole number.

183 meters

we know that,

In a right angled triangle

\(⇒cos \: 60° \: = \frac{adjacent \: side}{hypotenuse} \\ \)

\(⇒cos \: 60° \: = \frac{BC}{AB} \\ \)

\(⇒ \frac{1}{2} \: = \frac{a}{500} \\ \)

\( ⇒a = 250 \)

Also, we know that,

\(⇒sin \: 60° \: = \frac{opposite \: side}{hypotenuse} \\ \)

\(⇒ \frac{ \sqrt{3} }{2} \: = \frac{AC}{AB} \\ \)

\(⇒ \frac{ \sqrt{3} }{2} \: = \frac{b \:}{500} \\ \)

\(⇒b = 250 \sqrt{3} = 433(approx)\)

Now,

Distance covered to walk directly from building A to buliding B ↷

\(⇒AC+BC-AB\)

\(⇒433 + 250 - 500\)

\(⇒683 - 500\)

\(⇒183m\)

Hence , 183m distance will be require to walk directly from building A to buliding B

Answer:

1: C) y = -x + 1

2: D) y = -3x + 8

Step-by-step explanation:

Well number 1,

c is the correct option because,

-2 -> 2

2+1 - 3

This rule applies for all the x values.

2,

X: -2, -1, 0, 1, 2

Y: 14, 11, 8, 5, 2

d is the correct option because -3*-2 is 6 + 8 = 14.

this rule applies for all x values.

Thus,

the answers are C and D.

Hope this helps :)