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The value of given expressions will be sin(F) = 3/5, cos(F) = 4/5, sin(G) = 4/5 and cos(G) = 3/5.

A triangle may be defined as a closed figure having three sides and three angle, the sum of which is equal to 180°. A right-angled triangle is the one which has one angle as 90°. We consider a right-angled triangle FGH which is right-angled at H. The sine of any angle is given by the division of Perpendicular to its Hypotenuse. The cosine of any angle is given by the division of Base to its Hypotenuse. Now, we need to find

sin(F) = Perpendicular/Hypotenuse, for angle at F perpendicular will be GH and Hypotenuse will be FG. So, sin(F) = 3/5

cos(F) = Base/Hypotenuse, for angle at F Base will be FH and Hypotenuse will be FG. So, cos(F) = 4/5

sin(G) = Perpendicular/Hypotenuse, for angle at G perpendicular will be FH and Hypotenuse will be FG. So, sin(F) = 4/5

cos(G) = Base/Hypotenuse, for angle at G Base will be GH and Hypotenuse will be FG. So, cos(F) = 3/5

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since

then

then it is the 100x0.66= 66%

According to the picture:

For the first statement

The reason is: Given.

This is because it is given in the information to solve the problem.

The second statement must be:

And the reason is also: Given.

For the third statement:

The reason is the Reflexive property.

The fourth statement must be:

The reason is Side Side Side congruence postulate.

The fifth statement must be:

The reason is congruent triangles definition.

Given

capacity of 500 pounds.

weights of the passengers are 107 pounds, 172 pounds and 129 pounds.

you weigh 136 pounds

Find

is it safe for you to enter the elevator?

Explanation

as total pounds in the elevator = 107 + 172 + 129 = 408 pounds

total pounds included my weight = 408 + 136 = 544 pounds

capacity = 500 pounds

so , extra pounds = 544 - 500 = 44 pounds

so , no it is not safe for you to enter the elevator.

Final Answer

Therefore , No the weigh capacity would be exceeded by 44 pounds

To determine the enrollment in 2009 we need to plug x=2009 in the equation given to determine the value of y:

Therefore, in the year 2009, there were 4589 students enrolled

=[2[tex]x^{2}[/tex]-y][3a-4b] This is the factorized form of 6a[tex]x^{2}[/tex]-3ay - 8 b[tex]x^{2}[/tex] + 4by

To factorize a number, use the factorization formula. Factorization is the process of dividing a whole into components that, when multiplied together, equal the original number. The factorization approach simplifies any algebraic or quadratic equation by using the basic factorization formula, which represents the equations as the product of factors rather than expanding the brackets. Any equation may have an integer, a variable, or the algebraic expression itself as a factor.

6a[tex]x^{2}[/tex]-3ay - 8 b[tex]x^{2}[/tex] + 4by

Rearrange the expression

6a[tex]x^{2}[/tex] -8bx² -3ay +4by

2[tex]x^{2}[/tex][3a-4b] - y[3a-4b]

=[2[tex]x^{2}[/tex]-y][3a-4b]

This is the factorized form of 6a[tex]x^{2}[/tex]-3ay - 8 b[tex]x^{2}[/tex] + 4by

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Using the z-distribution, it is found that:

b)

c) There is not enough evidence to conclude that the proportion of business owners providing gifts decreased using a 0.01 significance level.

At the null hypotheses, it is tested if there is no evidence that the proportion decreased from 49%, that is:

[tex]H_0: p \geq 0.49[/tex]

At the alternative hypotheses, it is tested if there is evidence that the proportion decreased from 49%, that is:

[tex]H_1: p > 0.49[/tex]

The test statistic is given according to the following rule:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which the parameters are described as follows:

Considering that 40% of the sample of 85 planned to provide a gift, and the proportion tested is of 49%, the values of the parameters are given as follows:

[tex]\overline{p} = 0.4, p = 0.49, n = 85[/tex]

Hence the test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.4 - 0.49}{\sqrt{\frac{0.4(0.6)}{85}}}[/tex]

z = -1.69.

Considering a left-tailed test, as we are testing if the proportion is less than a value, with z = -1.69, using a z-distribution calculator, the p-value is of 0.0455.

Since the p-value of the test is greater than 0.01, there is not enough evidence to conclude that the proportion of business owners providing gifts decreased using a 0.01 significance level.

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(1) d = rt so, r = d/t

(2) a = F/m so, F = ma

(3) p = w/t so, t = w/p

(4) h = V/B so, B = V/h

(5) A = (abc)/(4r) so, r = (abc)/(4A)

(6) P/Q = R/S so, S = QR/P

(7) a = (v-i)/t so, v = at + i

(8) E/e = (R + r)/r so, e = Er/(R+r)

(9) 1/p + 1/q = 1/f so, f = (pq)/(p+q)

(10) 1/p + 1/q = 1/f so, p = qf/(q-f)

(11) 1/R = 1/r1 + 1/r2 so, R = (r1 r2)/(r1 + r2)

(12) 1/t = (1/a) + (1/b) so, b = (at)/(a - t)

(13) A/B = C/D so, C = AD/B

(14) A = h(a+b)/2 so, b = 2A/h - a

(15) V = Q/r1 - Q/r2 so, Q = Vr1 r2/(r2 - r1)

(16) u = F(P/T - E) so, P = (uT + EFT)/F

Answer:

8x + 16 is your answer

Step-by-step explanation:

Answer:

Explanation:

The first step is to plot the graph of the parabola. It is shown below

Looking at the graph, the branches open up and down. Thus, the correct option is

c. The branches of the hyperbola open up and down.



A number is said to be rational if it can be written or transformed into the p/q form, where p and q are integers and q is a non-zero number; if it cannot be written in this form, it is said to be irrational.

Any number that can be written or stated in the p/q form, where p and q are integers and q is a non-zero number, is said to be rational.

A number that is irrational, on the other hand, cannot be stated in p/q form, and its decimal expansion is non-repeating and non-terminating.

Example: √2, √7, √11

Hence we get the required answer.

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The number of students that collected between 90 and 100 bottles is 3.

The number of students that collected more than 100 bottles are 7.

The number of students that collected less than 90 students are 2

The total number of classes represented is 10.

Here is the completed frequency table

Number of bottles collected  Classes

90 - 100                                         3

101 - 110                                          6

111 - 120                                          1

A stem-and-leaf plot is a table that splits a number into a stem and leaf.   The stem is the first number in the digit while the leaf is the last number. For example the stem in 45 is 4 and the leaf is 5.  

An advantage of the stem-and-leaf plot is that it provides an easy way to present and interpret a dataset. A disadvantage of the stem-and-leaf plot is that it cannot be used for a large dataset.

Bottles collected that are between 90 and 100 are 94, 98, 99

Bottles that are greater than 100 are 105, 107, 107, 113, 114, 119, 120

Bottles that are less than 99 are 94, 98

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Answer:

(-8.8)(-9)= 79.2

(0.5)(-0.5)= -0.25

(-0.2)(-5)= 1

Step 1

For perpendicular lines

Step 2

Find b, the y-intercept

Answer; Option D

Answer: 1) Each of the 126 cubes has a volume = (1/3)3 = 1/3 × 1/3 × 1/3 = 1/27 cubic feet.

2) It takes 126 cubes to fill the bin, so the bin has a volume of 126 × 1/27 = 126/27 cubic feet. (Don't do this division yet - leave it as an improper fraction)

3) The volume of the bin is also given by the formula Volume = Area of Base × Height. Plus we know the volume is 126/27 cubic feet and the height is 2 1/3 = 7/3 of a foot, so:

Step-by-step explanation: Volume = Area of Base × Height

126/27 = Area of Base × 7/3

126/27 × 3/7 = Area of Base

The  area of the base of bin is 2 feet².

The formula of volume of the cube is given by: Volume = a³, where a is the length of its sides or edges.

Given:

Edge = 1/3 feet

Volume of 1 cube= l³= (1/3)³ = 1/27

Totals cubes= 126

So, Volume of 126 cube= 126 x 1/27 = 126/ 27

Then, Volume of Plastic Bin= Area of base x height

126 / 27 =  Area of base x 7/3

Area of base = 126 /27 x 3 /7

Area of base = 2 ft²

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The quadrilateral have equal opposite sides, for example:

Then, (4x + 6) must be equal to (7x - 3), and (4y - 3) is equal to (3y + 1), therefore

We can solve that equation for x

Hence, x = 3. Now let's solve the other equation

Then the value of y is 4.

Final answers:

x = 3

y = 4

The value of x in the expression 42/100 of x over 35% is 0.147.

It should be noted that an expression is simply used to show the relationship between the variables or number given.

Therefore, the information will be expressed as:

42/100 × x/35%

= 42/100 × x/0.35

Cross multiply

100 × x = 0.35 × 42

100x = 14.7

Divide.

x = 14.7 / 100

x = 0.147

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4) [tex]m\angle XWY=m\angle HGY[/tex] (definition of congruent angles)

5) [tex]\angle HGY \cong \angle GTU[/tex] (corresponding angles theorem)

6) [tex]m\angle HGY=m\angle GTU[/tex] (definition of congruent angles)

7) [tex]\angle GTU[/tex] and [tex]\angle UTR[/tex] are supplementary (linear pair)

8) [tex]m\angle GTU+m\angle UTR=180^{\circ}[/tex] (definition of supplementary angles)

9) [tex]m\angle HGY+m\angle UTR=180^{\circ}[/tex] (substitution)

10) [tex]m\angle RTU+m\angle XWY=180^{\circ}[/tex] (substitution)

The total transmitted power is a. 340.3 W.

The transmitted and carrier power is related with modulation through the formula -

[tex] P_{t} = P_{c}(1 + \frac{ {m}^{2} }{2} )[/tex]

where [tex]P_{t}[/tex] is transmitted power, [tex]P_{t}[/tex] is carrier power and m is modulation.

Keep the values in formula to find the value of total transmitted power.

[tex]P_{t}[/tex] = 250 (1 + 85%²/2)

Taking square of percentage

[tex]P_{t}[/tex] = 250 (1 + 0.7225/2)

Performing division in the bracket

[tex]P_{t}[/tex] = 250 (1 + 0.36125)

Performing addition in the bracket

[tex]P_{t}[/tex] = 250×1.36125

Performing multiplication

[tex]P_{t}[/tex] = 340.3125

Thus, the total transmitted power when carrier power is 250 W and modulation is 85% is a. 340.3 W.

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The height of the pile increasing at the rate of  4.56 inches per minute when the pile is 10 ft high.

In given situation, the rate of change of height is equal to the rate of change of volume, divided by the base area.

First we find the base area.

base area = (π/4)d²

base area = (π/4)10²

base area = 25π ft²

base area ≈ 78.5 ft²

Then the rate of change of height would be,

(30 ft³/min)/(78.5 ft²)

≈ 0.38 ft/min

= 4.56 inches / minute

Therefore, the height of the pile increasing at the rate of  4.56 inches per minute when the pile is 10 ft high.

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Given the functions

You have to calculate

To solve this you have to apply the distributive property of multiplications, that is, you have to multiply each term of the first parenthesis with each term of the second parenthesis.

As follows:

Now simplify the like terms

The result in standard form is

For the sewing operator:

For cutter:

The two above equation is solve to obtain the graph

The solution of the graph is where the two lines meet

The coordinate is (10, 4), at the this point the maximum profit is made

So 10 ski pants and 4 ski jackets is made to get maximum profit

The profit made is given by

P = 3x + 2y

x =10 , y = 4

P = 3(10) + 2(4)

P = 30 + 8 = $38

One factory that obtained 90 kg of total beef from overseas. The company needs 390 oz of meat filler to make meatballs out of this shipment of beef.

In processed meat products, starches are frequently employed as fillers to bind water that would otherwise leak out of the product, increasing its texture and sensory qualities.

As cheap fillers or inferior fiber sources, items including corncobs, feathers, soy, cottonseed hulls, peanut hulls, citrus pulp, screening, weeds, straw, and cereal by-products are frequently used.

One factory that has obtained 135 kg of beef from overseas.

They want to add a total of 1.3oz of filler for each pound of beef.

Given is:

0.45 kg = 1 pound

So, 135 kg = 300 pounds

The company that wants to add a total of 1.3 oz of filler for each pound of beef.

So, for 300 pounds they will need = 390 oz of filler.

Therefore, the company needs 390 oz of filler.

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Hope it helped !! :)

.........

Answer:

Explanation:

Given:

Endpoints of the diameter of a circle as (-4, -8) and (6, -4)

To find:

Equation of a circle in standard form

The equation of a circle in standard form is generally given as;

where (h, k) is the coordinate of the center of the circle and r is the radius of the circle.

We'll go ahead and determine the coordinates of the midpoint of the endpoints of the diameter which will be the coordinates of the center of the circle as seen below wi;

So the center of the circle has coordinates (1, -6)

Since h = 1, and k = -6 and we have that x1 = -4 and y1 = -8, we can go ahead and solve for r as seen below;

We can now write the equation of the circle in standard form as;

You have:

mean = 45

standard deviation = 12

Use the following formula:

Solution

- The function given is:

- We have been given:

- We are required to find the time for the radioactive substance to decay. That means we need to find the value of t in the equation.

- Thus, we have that:

Final Answer

The answer is 236.65 years

Given

JK = 22

KN = 13

OL = 18

Procedure

Centroid formulation

KM = JK/2 = 22/2 = 11

KM = 11

NL = KN

NL = 13

KL = 2KN = 2(13) = 26

KL = 26

JO = OL = 18

JO = 18

JL = 2OL = 2(18)

JL = 36

Answer:

y=3/4x-2

Step-by-step explanation:

slope=3/4x

y-intercept=-2