please help with this practice question, thank you

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

Learn more about Right-angled triangle at:

brainly.com/question/22790996

#SPJ1

The conversion from yards to miles is given by:

The conversion factor is:

Now, if we want to know how many miles are 39 yards, we multiply 39 yards by the conversion factor:

Initially, Joshua had $155 in his account.

Deposits of $25 and $40

Withdrawals = $15, $35

At the end of the month, he had $170 in his account.

Solution:

Let x be the amount of money he had initially.

Then,

x + 25 + 40 - 15 -35 = 170

x + 65 - 50 = 170

x = 170 + 50 - 65

x = 220 - 65

x = 155

Therefore, initially, he had $155 in his account.

To learn more about the amount, refer

https://brainly.com/question/25793394

#SPJ13

h(g(x)) is equivalent to the expression 1/2|x|-10

Given g(x) = 1/2|x|-6 and h(x) = x-4

h(g(x)) = h(1/2|x|-6)              

Put the value of g(x) in the expression

Now, evaluate the expression using the  definition of h(x) by replacing x in x-4 with 1/2|x|-6:

h(g(x)) = 1/2|x|-6 - 4 = 1/2|x|-10

Since  h(g(x)) = 1/2|x|-10. Therefore, 1/2|x|-10 is the expression equivalent to h(g(x)) so the third option is the answer.

Learn more about function h(g(x))  on:

https://brainly.com/question/13048549

#SPJ1

The equation of the line perpendicular to y = - (2 / 3) · x and the point (4, - 8) is y = (3 / 2) · x - 14.

Mathematically speaking, lines are represented by equations of the form y = m · x + b, where m and b are the slope and the intercept of the line. Additionally, two lines are perpendicular to each if the product of their slopes is equal to - 1.

First, we determine the slope of the perpendicular line:

m' = - 1 / m

m' = - 1 / (- 2 / 3)

m' = 3 / 2

Second, the intercept of the perpendicular line is:

b = y - m · x

b = - 8 - (3 / 2) · 4

b = - 8 - 6

b = - 14

Then, the equation of the perpendicular line is y = (3 / 2) · x - 14.

To learn more on perpendicular lines: https://brainly.com/question/17565270

#SPJ1

The time that David left the money in the account would be = 4 years

An earned interest is the amount of money that is regularly paid to an individual who invested a specific amount of money for a stipulated period of time.

The principal amount(p)= $300

The time (T)= X

The rate of interest yield (R)= 5 %

Simple interest( SI)= $ 60

Using the formula;

SI = P×T×R/100

Make T the subject of formula;

T = SI×100/P*R

T= 60×100/300×5

T= 6000/1500

T = 4 years.

Learn more about simple interest here:

https://brainly.com/question/25793394

#SPJ1

a)The smaller break even quantity is 10

b)The quantity that must be sold to maximize the profit= 14.25

c)The maximum profit = $36.13

STEP - BY - STEP EXPLANATION

What to find?

• The smaller break even quantity is

• The quantity that must be sold to maximize the profit

• The maximum profit.

Given:

C(x)= 13x + 370

R(x)=70x - 2x²

a) At the break even quantity, the revenue = cost, that is no profit and no loss.

R(x) = C(x)

So that we have;

70x - 2x² = 13x + 370

Re-arrange.

-2x² + 70x - 13x - 370 =0

-2x² +57x - 370 =0

2x² - 57x + 370 = 0

We can now solve the quadratic equation above.

Using the qudaratic formula

a=2 b=-57 c=370

Substitute the values into the formula and evaluate.

Or

x = 37/2 or x=10

We take the smaller value.

Hence, x=10

Therefore, the smaller break even quantity is 10.

b)To find the quantity that will maximize the profit, find the profit function.

p(x) = R(x) - C(x)

P(x) = 70x - 2x² - (13x +370)

= 70x - 2x² - 13x - 370

P(x) =-2x² + 57x - 370

Equate to zero

-2x² + 57x - 370 = 0

2x² - 57x + 370 =0

The maximum is at x = -b/2a

b= -57 and a=2

Substitute the values

x= - (-57) /2(2)

x= 57 /4

x= 14.25

c) To find the maximum profit, simply substitute x=14.25 into the profit function and simplify.

That is;

P(x) =-2x² + 57x - 370

P(14.25) =-2(14.25)² + 57(14.25) - 370

= -406.125 + 812.25 - 370

= 36.125

≈ 36.13

Hence, the maximum profit is $36.13

If the area of a trapezoid is A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex], then the equation represents the value of [tex]b_{1}[/tex] is [tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]

The trapezoid is a quadrilateral with at least one pair of parallel sides is called trapezoid. There are four vertices and four edges in the trapezoid.

The area of the trapezoid  A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex]

Where [tex]b_{1}[/tex] and [tex]b_{2}[/tex] are the length of the parallel sides of  the trapezoid

h is the height of the trapezoid

A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex]

Move 1/2  to other side

[tex](b_{1}+ b_{2})h[/tex] = 2A

Move h to other side

[tex](b_{1}+ b_{2})[/tex]  = [tex]\frac{2A}{h}[/tex]

Move [tex]b_{2}[/tex]  to other side

[tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]

Hence, if the area of a trapezoid is A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex], then the equation represents the value of [tex]b_{1}[/tex] is [tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]

Learn more about trapezoid here

brainly.com/question/7328615

#SPJ1

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.

The inequality is lies between the 5.26 < 5.71

The correct option is (a)

Given,

From the figure,

To see the number line and determine the which of the expression is true.  

What is Inequality?

Inequality is defined as an equation that does not contain an equal sign.

Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The number line goes from 5.0 to 6.0 with 9 labeled marks in between.

Each mark increases by point one

There are five labeled points.

A point labeled 5.04 is between 5.0 and 5.1.

A point labeled 5.26 is between 5.2 and 5.3.

A point labeled 5.4 is at the mark labeled 5.4

A point labeled 5.520 is between 5.5 and 5.6.

A point labeled 5.71 is between 5.7 and 5.8.

Then the ascending order of the number line will be :

5.04 < 5.26 < 5.4 < 5.52 < 5.71

Hence, The correct option is (a)i.e., 5.26 < 5.71

Learn more about Number line at:

https://brainly.com/question/13425491

#SPJ1

(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:

When one-third of a number is at least four less than the number, the inequality to represent the information is C. n ≥ 6.

It should be noted that an inequality is simply used to illustrate the expressions that aren't equal.

Let the number be n.

This will be illustrated as:

1/3n ≥ n - 4

Collect like terms

1/3n - n ≥ -4

-2/3n ≥ -4

Multiply through by -3/2

n ≥ -4 × -3/2

n ≥ 6

The value is n ≥ 6.

Learn more about inequalities on:

brainly.com/question/24372553

#SPJ1

Answer:

y=3/4x-2

Step-by-step explanation:

slope=3/4x

y-intercept=-2

The ratio of both men and women 15:22

What is Ratio ?

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Given,

The ratio of men and children = 5:2

The ratio of women and children = 11:3

To find the ratio of men and women we have to divide both the ratio:

men/children/women/children

or,

men/children x children/women

putting the values

=5/2 x 3/11

=15/22

Hence, the ratio of men:women is 15:22

To learn more about Ratio click on the link

https://brainly.com/question/2914376

#SPJ9

Answer:

the second quadrant is negative but the reference angle is exactly the same but positive

Step-by-step explanation:

looking at 150 on the unit circle in the second quadrant you will see the cosine is negative square root 3 divided by 2 but the reference angle is 30 degrees and when we look at the cosine of that which is the x value of what we see it is positive square root of 3 divided by 2

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

The following that represent the sales price and the regular prices are:

regular price: $55.43, sales price: $45.45

regular price: $29.99,  sales price: $24.59

regular price: $652.30, sales price: $534.89

Percentage is the fraction of a number out of hundred. The sign that is used to represent percentages is %.

When a discount is given on the price of an item, the price of the item would reduce by the given price or by the percent reduction.

Sales price = regular price x (1 - discount)

Sales price = regular price x (1 - 0.18)

Sales price = regular price x 0.82

Sales price when the initial price is $55.43: $55.43 x 0.82 = $45.45

Sales price when the initial price is $29.99: $29.99 x 0.82 = $24.59

Sales price when the initial price is $215.33: $215.33 x 0.82 = $176.57

Sales price when the initial price is $849.50: $849.50 x 0.82 = $696.59

Sales price when the initial price is $652.30: $652.30 x 0.82 = $534.89

Please find attached the complete question. To learn more about how to calculate discounts, please check: https://brainly.com/question/26061308

#SPJ1

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

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

Answer:

-0.07

Step-by-step explanation:

Find the average

This statement is justified by the angle addition postulate.

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.

To know more about meat fillers, visit:

https://brainly.com/question/9220872

#SPJ13

• The Same roots

• The same axis of symmetry

1) If we compare two parabolas from this family, like:

Note that the difference is in the leading coefficient "a".

2) Both parabolas will have the same roots, the same x-intercepts:

In addition to this, we can state that both will share the same axis of symmetry:

As well as:

Hence, the answer is:

0. Same roots

1. Same axis of symmetry

1. 3x - 4 = 23

add 4 to both sides

3x - 4 + 4 = 23 + 4

3x = 27

Divide both sides by 3

3x/3 = 27/3

x = 9

2. 9 -4x = 17

subtract 9 from both sides

9 -9 -4x = 17 - 9

-4x = 8

Divide both sides by -4

-4x/-4 = 8/-4

x = -2

3. 6(x-7) = 36

Divide both sides by 6

x -7 = 6

add 7 to both sides

x - 7 + 7 = 6 + 7

x = 13

4. 2(x-5) -8 = 34

Expand

2x -10 -8 = 32

2x - 18 = 32

2x = 32 + 18

2x = 50

Divide both sides by 2

x =25

The number of red marbles in the bag is 114 .

in the question ,

it is given that ,

total number of marbles in the bag = 120 marbles

let the number of red marbles [tex]=[/tex] r

let the  number of black marbles [tex]=[/tex] b

so , According to the question

b + r = 120   ...eqn(1)

also given that for every black marble there is 19 red marbles

which is represented by , r = 19b

Substituting  r = 19b in eqn (1) , we get

b + 19b = 120

simplifying further , we get  

20b = 120

b = 6

and r = 19(6) = 114

Therefore , The number of red marbles in the bag is 114 .

Learn more about Equations here

https://brainly.com/question/11461055

#SPJ1

Use the next property:

Answer: 36.00%

60% can be written as 0.60 and/or 6/10, which simplifies to 3/5 for easier operations. The probability of 2 students both drink coffee with breakfast can be shown as 0.60 • 0.60 = 0.36. This means there is a 36% chance of both students drinking coffee with breakfast in the morning.

Step-by-step explanation:

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.

Learn more about Irrational numbers here:

brainly.com/question/20400557

#SPJ9

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.

More can be learned about the z-distribution at https://brainly.com/question/13873630

#SPJ1

=[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

To learn more about factorization visit :

brainly.com/question/24182713

#SPJ10