A large right triangle is going to be a part of a geometric sculpture, as shown below. The hypotenuse will be 55​ feet long. The length of one leg of the triangle is 22​​ feet​ less​ than twice the other leg. Find the length of each leg, in feet, and separate them with a comma.

Answer:

195 mL of the 90% solution

Step-by-step explanation:

Let the number of mL of 90% mixture = x

Hence, our equation is

780mL × 15% + x mL × 90% = (780mL + x) 30%

117 + 0.9x = 234 + 0.3x

Collect like terms

0.9x - 0.3x = 234 - 117

0.6x = 117

x = 117/0.6

x = 195 mL

Therefore, You will need 195 mL of the 90% solution

All the roots of the polynomial equation that we have in the equation x³ + 6x²+ 9x + 2= 0 are;

x = -1, x = -2, x = -2.

We know that when we talk about a cubic equation, we would be looking at the kind of equation that has the highest power of the variable x in it to be 3.

We know that we can be able to solve the equation by factorization and then when we do that, we would have that;

x³ + 6x²+ 9x + 2= 0 would become  (x+1)(x+2)(x+2) = 0.

Therefore, the solutions to the equation are x = -1, x = -2, x = -2.

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Answer:

x = 6.5

Step-by-step explanation:

square is rectangle

9x+26 = 84.5

84.5 - 26 = 58.5

9x = 58.5

x = 58.5 divided by 9

x = 6.5

Answer: lisa should have about 1006 cal minah should have 2014 cals thequestion has some spelling errors like "How much calories do Lisa have?" and "How much calories do Minah have?"

Answer:

The answer is: WHAT IS YOUR QUESTION!????

Hope that helps! :D

Step-by-step explanation:

Answer:

Once you post the pic, I will see if I can help at all

Step-by-step explanation:

The answer of the given question based on the cost of mailing is , the cost of mailing a 2.5-ounce letter to Vienna, Austria would be $6.63 (rounded to the nearest cent).

An equation is  mathematical statement that shows  two expressions are equal. It contains variables, constants, and mathematical operations like  addition, subtraction, multiplication, and division.

For example, a simple equation could be:

2x + 3 = 9

The equation y = 0.25x + 6.00 represents the cost y of mailing a letter to Vienna, Austria based on the weight x of the letter in ounces. The flat rate of $6.00 is represented by the constant term 6.00 in the equation, and the additional charge of $0.25 per ounce is represented by the coefficient of x, which is 0.25.

To use this equation to determine the cost of mailing a specific letter, you would need to know the weight of the letter in ounces. You could then substitute this value for x in the equation and solve for y, which would give you the cost of postage in dollars.

For example, if a letter weighs 2.5 ounces, you could plug in x = 2.5 into the equation:

y = 0.25(2.5) + 6.00

y = 0.625 + 6.00

y = 6.625

So the cost of mailing a 2.5-ounce letter to Vienna, Austria would be $6.63 (rounded to the nearest cent).

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Answer:

1. 11 married females because out of the 19 married, only 8 had more than 15 years of service and 19 - 8 = 11.

2. 10 married males because of out the 18 married with more than 15 years of service, 8 were females and 18 - 8 = 10.

3. 9 single females because out of the 17 with more than 15 years of service, 8 were married and 17 - 8 = 9.

4. 8 married females because it literally says, "8 married female with more than 15 years of service".

gotta go hope this helps sry

Answer:

a) 0.0169

b) 0.19

c) 0.651                  

Step-by-step explanation:

Given:

Number of samples = 20

X denote the number of parts in the sample of 20 that require rework

A process problem is expected if X exceeds its mean by more than three standard deviations

Solution:

Let X be the random variable that denotes the number of parts that require rework

Then X follows a binomial distribution with parameters:

n = 20

p = 0.01

Probability mass function of X:

Pr(X=k) = \((\left \ {{n} \atop {k}} \right.)p^{k}(1-p)^{n-k}\)

where k = 0, 1, 2, ..., 20

and

\((\left \ {{n} \atop {k}} \right.) = \frac{n!}{k!(n-k)!}\)

a)

Compute mean and standard deviation:

percentage of parts that require rework remains at 1% so p = 0.01

n = 20

Compute Mean:

E(X) = np = 20 * 0.01 = 0.2

Compute Standard Deviation:

σ\(_{X}\) = √np(1-p) = √20 * 0.01 ( 1 - 0.01 ) = √0.2 (0.99) = √0.198 = 0.444972

Compute upper bound:

U = E(X) + 3 * σ\(_{X}\) = 0.2 + 3 ( 0.444972 ) = 0.2 + 1.334916 = 1.534916 = 1.53

Compute probability of X exceeds its mean by more than three standard deviations.:

P(X> 1.53 ) = 1 - P(X = 0) - P(X = 1)  

P ( X = 0 ) =  \((\left \ {{20} \atop {0}} \right.)0.01^{0}(1-0.01)^{20-0}\)

                = 20! / 0! ( 20 - 0 ) ! 1 ( 0.99 )²⁰

                = 1 * 1 * 0.99²⁰

                = 1 * 1 * 0.817907

                = 0.817907

P ( X = 1 ) =  \((\left \ {{20} \atop {1}} \right.)0.01^{1}(1-0.01)^{20-1}\)

                =  20! / 1! ( 20 - 1 ) ! 0.01 (0.99 )¹⁹

                = 20 * 0.01 * 0.826169

                = 0.165234

P(X> 1.53 ) = 1 - P(X=0) - P(X=1)= 1 - 0.817907 - 0.165234 = 0.016859 = 0.0169

b)

Compute mean and standard deviation:

rework percentage increases to 4% so p = 0.04

Compute the probability that X exceeds 1?

P(X>1) = 1 - P(X=0) - P(X=1)

P (X=0) =  \((\left \ {{20} \atop {0}} \right.)0.04^{0}(1-0.04)^{20-0}\)

            = 20! / 0! ( 20 - 0 ) ! 1 ( 0.96 )²⁰

            = 1 * 1 * 0.96²⁰

            = 0.442002

P (X=1) =  \((\left \ {{20} \atop {1}} \right.)0.04^{1}(1-0.04)^{20-1}\)

                =  20! / 1! ( 20 - 1 ) ! 0.04 (0.96 )¹⁹

                = 20 * 0.04 * 0.460419

                = 0.368335

P(X>1) = 1 - P(X=0) - P(X=1) = 1 - 0.442002 - 0.368335 = 0.189663 = 0.19

c)

Let Y be a random variable which denotes the number of hours in which X exceeds 1.  

Since the probability that X exceeds 1 is constant in every hour, so compute p and n for Y

p\(_{Y}\) =  P(X>1)

From part (b) P(X>1) = 0.19 So,

p\(_{Y}\) =  P(X>1) = 0.19

Then Y follows a binomial distribution with parameters:

n\(_{Y}\) = 5

p\(_{Y}\) = 0.19

Probability mass function of Y:

Pr(Y=k) = \((\left \ {{n} \atop {k}} \right.)p^{k}(1-p)^{n-k}\)

Pr (Y=k) = \((\left \ {{n} \atop {k}} \right.)\) \(p_{k}\)\(_{Y}\) (1-p\(_{Y}\)\()^{5-k}\)

where k = 0, 1, 2, ... ,5

and

\((\left \ {{5} \atop {k}} \right.) = \frac{5!}{k!(5-k)!}\)

Compute the probability that X exceeds 1 in at least one of the next five hours of samples:

P (Y≥1) = 1 - P (Y=0)

P(Y=0) = \((\left \ {{5} \atop {0}} \right.)0.19^{0}(1-0.19)^{5-0}\)

           = 1 * 1 * 0.81⁵

           = 0.348678

P (Y≥1) = 1 - P (Y=0) = 1 - 0.348678 = 0.651322 =  0.651

Answer:

i hope this helpes

Step-by-step explanation:

a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.

b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.

c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.

Answer:

a) $52

b) C(x) = 40 + 2x, if x > 10 and x ≤ 50

C(x) = 40, if x ≤ 10

c) Domain = {x ≥ 1 and x ≤ 50}

Range = { from 40 to 140}

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

She will be paid $1,350

Step-by-step explanation:

Linear Modeling

Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

y=mx+b, where m and b are constants.

The payments for a salesperson will be linearly modeled. There are two known points: When the sales were $16,000, the payment was $1,600. This makes the point (16,000;1,600).

We also know when the sales were $12,000, the payment was $1,400. The point is (12,000;1,400)

Let's use the points to find the values of m and b.

Using (16,000;1,600):

1,600=m*16,000+b

Using (12,000;1,400):

1,400=m*12,000+b

Subtracting both equations:

200=16,000m-12,000m

200=4,000m

Solving:

m=200/4,000=0.05

Using the first equation and the value of m:

1,600=0.05*16,000+b

1,600=800+b

Solving:

b=800

The equation is now complete:

y=0.05x+800

She sold $11,000 this month, so the payment is:

\(y=0.05\cdot 11,000+800\)

Y=550+800=1,350

She will be paid $1,350

Answer:

1350

Step-by-step explanation:

(Note: this method is not the best to use in future problems, please refer to the other answer if you want something better to use.)

16,000-12,000=4,000

1,600-1,400=200

To find the rate of change in 1000s:

200/4 = 50

Essentially this means the rise is 50 and the run is 1000, so, just remove $50 from the payment from 2 months ago to find your answer

We are given the following expression:

To simplify this expression we will first add the terms inside the parenthesis:

Now, we will solve the exponents:

Now we solve the products:

Now we solve the addition:

therefore, the expression reduced to 522.61

Answer:

y = -3x + 3

Step-by-step explanation:

use the formula y - y1 = m ( x - x1)

y - 3 = -3 ( x - 0)

y - 3= -3x

y = -3x + 3

The expected number of employees working at Sprockets R Us in 2006 will be 8069.45.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

Given that:-

The number of employees working for Sprockets R Us in 2005 was 8110, with an expected decrease of 0.5% per year. At the rate of decrease given, what is the expected number of employees working at Sprockets R Us in 2006?

The number of the employees in 2006 will be calculated as:-

Number of employees decreased   = 0.5% x 8110

Number of employees decreased   = (0.5/100) x 8110

Number of employees decreased   = 40.55

The number of the employees in 2006 will be

N = 8110 - 40.55 = 8069.45

Therefore the expected number of employees working at Sprockets R Us in 2006 will be 8069.45.

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Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

The equation which represents the proportionality relationship is:

y=16x.

Given, we have the pairs as:

(1,16),(2,32) and (3,48)

calculate the value of y/x for the ordered pairs:

For (1,16), the value of y/x is = 16/1 = 16

For (2,32), the value of y/x is = 32/2 = 16

For (3,48), the value of y/x is = 48/3 = 16

now, compare ratios:

for each ordered pair, y/x = 16

Since, k=y/x, you know that the constant of proportionality , k is 16.

Substitute 16 for k in the equation for a proportional relationship.

y = kx

y = 16x

Hence we get the equation as y=16x.

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Answer:

to graph an inequality you need a variable. please rewrite your question.

The length of the fence must be 618cm

The volume that it can hold is 1,909,620 cm³

First, the fence is just equal to the circumference of the cylinder, remember that the circumfernce of a circle of diameter D is:

C = П*D

Here we use П = 3, then:

C = П*206cm

C = 3*206cm = 618cm

Now the volume, for a cylinder of diameter D and height H, the volume is:

V = П*(D/2)²*H

Replacing the values that we know we will get:

V = 3*(206cm/2)²*60cm = 1,909,620 cm³

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Answer: 21

Step-by-step explanation:  im not guessing im a certified expert at calculus and have a masters degree in mathmatics so yeah

Answer:

21

Step-by-step explanation:

I did the test

Hope this helps :)

Answer:

See Explanation

Step-by-step explanation:

(a) Proof: Product of two rational numbers

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

\(A = \frac{1}{2}\)

\(B = \frac{2}{3}\)

The product:

\(A * B = \frac{1}{2} * \frac{2}{3}\)

\(A * B = \frac{1}{1} * \frac{1}{3}\)

\(A * B = 1 * \frac{1}{3}\)

\(A * B = \frac{1}{3}\)

Proved, because 1/3 is rational

(b) Proof: Quotient of a rational number and a non-zero rational number

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

\(A = \frac{1}{2}\)

\(B = \frac{2}{3}\)

The quotient:

\(A / B = \frac{1}{2} / \frac{2}{3}\)

Express as product

\(A / B = \frac{1}{2} / \frac{3}{2}\)

\(A / B = \frac{1*3}{2*2}\)

\(A / B = \frac{3}{4}\)

Proved, because 3/4 is rational

(c) x + y is rational (missing from the question)

Using direct proofs.

Let x and y be

Such that:

\(x = \frac{1}{2}\)

\(y = \frac{2}{3}\)

The sum:

\(x + y = \frac{1}{2} + \frac{2}{3}\)

Take LCM

\(x + y = \frac{3+4}{6}\)

\(x + y = \frac{7}{6}\)

Proved, because 7/6 is rational

The above proof works for all values of A, B, x and y; as long as they are rational values

Answer:

d>2

Step-by-step explanation:

\(14-3d<8d-22+7d \\ \\ 14-3d<15d-22 \\ \\ 14<18d-22 \\ \\ 18d>36 \\ \\ d>2\)

Answer: 120\(m^{2}\)

Step-by-step explanation:

The top part of this polygon is a triangle and the bottom is a rectangle. In this way, we can use the are of a triangle formula and the area of a rectangle formula to find the total area of the polygon.

Area of a triangle:

A = (base * height) / 2

= (6m*8m)/2

= (48m)/2

= 24\(m^{2}\)

Area of a rectangle:

A = base * height

= 12m * 8m

= 96\(m^{2}\)

Area of the polygon:

A = area of triangle + area of rectangle

= 24m + 96m

= 120\(m^{2}\)

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is: ∠A = 39.6°

3) The length of side x is: x = 39.5 mm

The six trigonometric ratios of a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is gotten from:

∠A = cos⁻¹ (47/61)

∠A = 39.6°

3) The length of side x using trigonometric ratios is:

21/x = tan 28

x = 21/tan 28

x = 39.5 mm

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Answer:

£11.064

Step-by-step explanation:

55.32/5 = 11.064

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer:

well... oop my FIRE ALARM WENT OFF gtg

Step-by-step explanation:

Answer:

1+1=2

Step-by-step explanation:

Answer:

the correct answer is 15011.428571

Step-by-step explanation:

=525.4 ÷ 0.035

=15011.428571

hope this works out!!!!

The division of decimal values 525.4 ÷ 0.035 = 15011.428571........

To divide decimals we make them integers by multiplying the numerator and denominator by 10ⁿ, where n is the number of decimal places in the numerator or denominator, whichever has more.

Then we follow the steps of normal numeric divisions.

In the question, we are asked to divide the equation 525.4 ÷ 0.035.

We can write this as 525.4/0.035.

Now, 0.035 has more decimal places, with n = 3, where n is the number of decimal places.

Thus, we multiply the numerator and denominator by 10³ = 1000.

Therefore, 525.4/0.035

= (525.4*1000)/(0.035*1000)

= 525400/35

= 15011 3/7

= 15011.428571........

Thus, the division of decimal values 525.4 ÷ 0.035 = 15011.428571........

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The range of the function m is [1, ∞). Thus, B is correct option.

The dοmain οf a functiοn is the cοllectiοn οf values that can be plugged intο it. This set represents the x values in a functiοn like f. (x). A functiοn's range is the set οf values that the functiοn can take οn. This is the set οf values returned by the functiοn when we enter an x value.

Tο determine the range οf functiοn m, we must first determine the set οf all pοssible functiοn οutput values.

Looking at the function graph, we can see that the lowest point is (3, 1) and the highest point is (∞, ∞).

As a result, the function m has a range of [1, ∞).

We can write: in interval notation:

m ∈ [1, ∞) range.

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