Find the volume of the composite solid. Round your answer to the nearest hundredth.

In ΔFGH,  the length of h is 714.2 cm

Let us assume that in ΔFGH, f represents the opposite side to angle F, g represents the opposite side to angle G,  and h represents the opposite side to angle H.

Consider the following figure.

Using sine rule for triangle FGH,

sin F/f = sin G/g = sin H/h

Consider equation sin G/g = sin H/h

sin(98°) / 910 = sin(51°) / h

We solve this equation for h.

h = (sin(51°) × 910)/ sin(98°)

h =  (0.777 × 910)/ 0.99

h = 714.21

h = 714.2 cm

This is the required length of h.

Learn more about the equation here:

https://brainly.com/question/28243079

#SPJ1

Answer:

----------------------

Use the following identities:

Apply the identities to the given expression:

The expression can be simplified to get:

2.7^(1)*3.8^(5)

The correct option is C.

Remember that if we have the product of two powers with the same base, we only need to add the exponents.

Then we will get:

2.7^(-3) * 3.8^(2) * 2.7^(4) * 3.8^(3)

= (2.7^(-3)*2.7^(4)*3.8^(2)*3.8^(3))

= (2.7^(-3 + 4)*3.8^(2 + 3))

= 2.7^(1)*3.8^(5)

That is the expression simplified, we can see that the correct option is C.

Learn more about exponents at:

https://brainly.com/question/847241

#SPJ1

The solution set for each rational inequality:

Case 1: - 9 ≤ x < - 5

Case 3: Every real number except x = 1.

In this problem we find two cases of rational inequality, whose solution sets can be found by using algebra properties and sign laws. Now we proceed to solve on each case:

Case 1

(3 · x + 7) / (x + 5) ≥ 5

(3 · x + 7) / (x + 5) - 5 ≥ 0

[(3 · x + 7) - 5 · (x + 5)] / (x + 5) ≥ 0

(- 2 · x + 18) / (x + 5) ≥ 0

- 2 · (x - 9) / (x + 5) ≥ 0

The inequality is positive for - 9 ≤ x < - 5.

Case 3

(- x² - 1) / (- x² + 2 · x - 1) > 0

[(- 1) · (x² + 1)] / [(- 1) · (x² - 2 · x + 1)] > 0

(x² + 1) / (x² - 2 · x + 1) > 0

(x² + 1) / (x - 1)² > 0

The inequality is positive for all real number except x = 1.

To learn more on inequalities: https://brainly.com/question/30231017

#SPJ1

In the triangles given the analysis for same is given below

1) the corresponding vertices are

R ~ C and

E ~ 0

2) The corresponding angle are

∠E ~∠O  and

∠ R ~ ∠C

3)

The corresponding sides are;

ER ~ CO;
MO ~ EM
CM ~ RM

4)  the congruent angles are:

∠REM ≅ ∠MOC
∠ERM ≅ ∠MCO
∠CMO ≅ EMR

5) the congruent sides are:

ER ≅ CO;
MO ≅ EM
CM ≅ RM

6) the congruent triangles are;

ΔMER ≅ ΔMOC

Learn more about triangles:
https://brainly.com/question/2773823
#SPJ1

We know that cos(45) = sin(45) = √2/2.

Substituting these values, we can simplify the expression as follows:

4cos(45) - 2sin(45)

= 4(√2/2) - 2(√2/2) (substituting cos(45) and sin(45) values)

= 2√2 - √2

= √2

Therefore, the answer is √2.

Unit fractions are the fraction in which the value of numerator is 1. The multiple of the given fraction are,

1/9 = 2/9, 3/9, 4/9,5/9         ......so on.

Here, we have,

To find the multiple of the fraction 1/9 we need to know about the multiple of fraction.

We have,

Multiple of fraction is the number which is n times of the original function. Here  can be any whole or fraction number.

The given number in the problem is the fraction number which is,

The above number is the unit fraction.

Unit fraction-

Unit fractions are the fraction in which the value of numerator is 1.

The multiple of unit fraction is in times the original function. For the given fraction the multiple fraction can be given as,

1/9 = 2/9, 3/9, 4/9,5/9            .......so on.

Hence the multiple of the given fraction are,

1/9 = 2/9, 3/9, 4/9,5/9             ......so on.

Learn more about the multiple of fraction here;

brainly.com/question/9281754

#SPJ1

Step-by-step explanation:

y=m(x-x1)+y1

y=-2(x-4)+0

y=2x-8+0

y=2x-8

1. Find the vertex (turning point) of the parabola by using the formula x = -b/2a, where a = 4 and b = 8. This gives x = -1, which is the x-coordinate of the vertex. To find the y-coordinate, substitute x = -1 into the equation: y = 4(-1)² + 8(-1) + 3 = -1.

2. Plot the vertex at the point (-1, -1).

3. To find the x-intercepts, set y = 0 in the equation and solve for x. This gives x = (-8 ± √(8² - 4(4)(3)))/(2(4)) = (-8 ± √16)/8 = -1/2 or -3. Plot these points on the x-axis.

4. To find the y-intercept, set x = 0 in the equation and solve for y. This gives y = 3, so the y-intercept is at the point (0, 3).

5. Since the coefficient of x² is positive, the parabola opens upwards. Sketch the curve passing through the points found above.

6. Label the points of intersection and the turning point on the graph.

Answer:

Put your calculator in degree mode.

sin(35°) = 7/r

r sin(35°) = 7

r = 7/sin(35°) = 12.2 cm

Answer:

[tex]y = -2(x - 1)^2 + 3[/tex]

Step-by-step explanation:

The given figure which is a quadratic is the shape of a parabola

The general vertex form equation of a parabola is
[tex]y = a(x - h)^2 + k[/tex]

where,
( h, k ) is the vertex and a is a constant

Looking at the figure we see the vertex is at [tex](1, 3)[/tex]

So the equation of the parabola is

[tex]y = a(x - 1)^2 + 3[/tex]

To compute the constant [tex]a[/tex] take a point (x, y) through which the parabola passes, plug in these x, y values into the above equation and solve

The parabola passes through point   [tex](3, -5)[/tex]

Plugging

[tex]x = 3, y = -5[/tex]

gives
[tex]- 5 = a(3-1)^2 + 3\\\\-5 = a\cdot 2^2 + 3\\\\-5 = 4a + 3\\\\-5-3=4a\\\\-8 = 4a\\\\a = -8/4 = -2\\\\[/tex]

Therefore the equation of the given quadratic(parabola) is

[tex]y = -2(x - 1)^2 + 3[/tex]

Option D is the correct synthetic division of (x^2-4x+7) divided by (x-2)

Synthetic division is a shorthand procedure used to divide a polynomial by a linear factor of (x - a) form, in which "a" is constant. This method gives an expedient way to locate the quotient and remainder without carrying out long division.

x - 2 | x^2 - 4x + 7

            x^2 - 2x

           ---------

                 -2x + 7

                 -2x + 4

                 -------

                        3

read more on divisions here:https://brainly.com/question/31537400

#SPJ1

needs more explanation

Answer: you could reflect the points (2, 4) to both axisis to find the inverse, add a negative in front of both numbers, or multiply the function by -1.

Step-by-step explanation:

Have a great night.

There are 1100 many ways can be done that is when catering service offers 5 appetizers, 11 main courses, and 4 desserts.

Given that,

A catering service offers 5 appetizers, 11 main courses, and 4 desserts. A customer is to select 4 appetizers, 9 main courses, and 3 desserts for a banquet.

We have to find how many ways can this be done.

We know that,

Number of appetizers offered = 5

Number of appetizers customer is to select = 4

Number of main courses offered = 11

Number of main courses customer is to select = 9

Number of desserts offered = 4

Number of desserts the customer is to select = 3

So,

To determine the number of ways this can be selected,

By using the combination formula that is

[tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex]
[tex]^nC_r = ^5C_4\times ^{11}C_9\times^4C_3[/tex]

[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!(5-4)!} \times \frac{11!}{9!(11-9)!}\times \frac{4!}{3!(4-3)!}[/tex]

[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!1!} \times \frac{11!}{9!2!}\times \frac{4!}{3!1!}[/tex]

[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!} \times \frac{11!}{9!(2)}\times \frac{4!}{3!}[/tex]

[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 5 × 11 × 5 × 4

[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 1100

Therefore, There are 1100 many ways this can be done.

To know more about combination visit:

https://brainly.com/question/28998705

Answer:

i believe 67 its somewhat hard to tell but the line seems to be in the middle between 150 and 140

Step-by-step explanation:

since it heats up to 212 then the person lets it cool down for 10 mins the temp goes to 145 (Answer is 67)

The original price of this car is equal to $6,600.

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

Assuming the original price is represented by the variable x, we have the following:

12.5/100 × x = x - 5,775

0.125x = x - 5,775

5,775 = (x - 0.125x)

5,775 = 0.875x

x = 5,775/0.875

x = $6,600.

In conclusion, we can logically deduce that the percentage Pat Bain paid is 87.5%.

Read more on percentage here: brainly.com/question/28009735

#SPJ1

By the Principle of Mathematical Induction, 2ⁿ≥2n is true for all positive integers.

The given inequality is 2ⁿ≥2n.

Let n = 1

2^1 ≥ 2^1

2 ≥ 2 which is true

Inductive Step: Assume 2ⁿ≥2n is true for some arbitrary positive integer k.

We need to prove that 2^(k+1) ≥ 2^(k+1)

2^(k+1) ≥ 2*2^k (by the inductive hypothesis)

2^(k+1) ≥ 2*2^(k+1)

2^(k+1) ≥ 2^(k+1) which is true

Therefore, by the Principle of Mathematical Induction, 2ⁿ≥2n is true for all positive integers.

To learn more about the inequalities visit:

https://brainly.com/question/20383699.

#SPJ1

Answer:

198 ft^2

Step-by-step explanation:

l = 3

w = 3

h = 15

2(3*3) + 4(3*15) = 18 + 180

18 + 180 = 198 ft^2

The critical value that should be used in constructing the confidence interval is 2.132 (rounded to three decimal places).

What is Critical value ?

In statistics, a critical value is a threshold value that is used to determine whether to reject or fail to reject the null hypothesis in a statistical test. It is typically based on the significance level of the test, which is the probability of rejecting the null hypothesis when it is actually true.

To find the critical value for a 90% confidence interval with n = 5, we need to use a t-distribution with (n-1) degrees of freedom.

Using a t-distribution table or a calculator, we can find the critical value with a 90% confidence level and 4 degrees of freedom (n-1 = 5-1 = 4) to be approximately 2.132.

Therefore, the critical value that should be used in constructing the confidence interval is 2.132 (rounded to three decimal places).

To learn more about Critical value from given link.

https://brainly.com/question/30168469

#SPJ1

Therefore , the solution of the given problem of unitary method comes out to be once more administer maths and science quizzes on the same day.

The well-known minimalist approach, current variables, and any crucial elements from the initial Diocesan tailored query can all be used to accomplish the work. In response, you can be granted another chance to utilise the item. If not, important impacts on our understanding of algorithms will vanish.

Here,

List the multiples of each integer until we discover a common multiple as one method to determine the least common multiple:

=> 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80 are all multiples of 8.

=> 6, 12, 18, 24, 30, 36, 42, 48, 54, and 60 are multiples of 6.

As an alternative, we can use the prime factorization technique to identify the smallest common multiple:

=> 8's prime factors are 2 x 2 x 2

=> 6's prime factors are 2 x 3

=> 2 x 2 x 2 x 3 = 24

We can see that 24 is the smallest common multiple once more, and in 24 days,

Mrs Hopkins will once more administer maths and science quizzes on the same day.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1  

Answer:

$12,276.24

Step-by-step explanation:

22000 / (1 + 0.105/12)^4*12

12276.24

The half-life of the particular compound is approximately 9.4 days. (Correct choice: B)

The statement indicates the decay function of a particular compound, which is an exponential function of the form:

y = a · exp(- λ · t)

Where:

The half-life of the particular compound is determined by the following expression:

t = ㏑ 2 / λ

Where t is the half-life.

If we know that λ = 0.0736, then the half-life of the particular compound is:

t = ㏑ 2 / 0.0736

t = 9.4 days

To learn more on half-life: https://brainly.com/question/24710827

#SPJ1

Answer:

mt1= 995

mt2=975

Step-by-step explanation:

the line inside the box plot shows where the median is.

b) Josh would pay $741.15 for the refrigerator at the department store with 10% discount.

c)  The true statement is: Josh would pay more for the refrigerator at the superstore.

(b) If the department store marks up the wholesale price of the refrigerator by 50%, then the price at the store would be:

Wholesale price + (50% x Wholesale price) = $549 + (0.5 x $549) = $823.50

If Josh would receive a 10% discount off the in-store price, then the price he would pay would be:

In-store price - (10% x In-store price) = $823.50 - (0.1 x $823.50) = $741.15

(c) If the superstore marks up the wholesale price of the refrigerator by 40%, then the price at the store would be:

Wholesale price + (40% x Wholesale price) = $549 + (0.4 x $549) = $768.60

Therefore, Josh would pay $768.60 for the refrigerator at the superstore.

Comparing the prices, we can see that Josh would pay less for the refrigerator at the department store after factoring in the discount:

Price at department store = $741.15

Price at superstore = $768.60

So the true statement is: Josh would pay more for the refrigerator at the superstore.

To learn more about discount here:

https://brainly.com/question/3541148

#SPJ1

a) A function for the amount of money in the account, B, after t months with an initial deposit of $100 isB(t) = [tex]100(1 + 0.002)^t[/tex]

b) The amount in the account increases by a factor of approximately 1.002 every month, approximately 1.025 every year and approximately 1.099 every five years.

a) The function for the amount of money in the account after t months with an initial deposit of $100 and an increase of 0.2% per month can be written as:

B(t) = [tex]100(1 + 0.002)^t[/tex]

where t is the number of months.

b) To determine the factor by which the amount in the account increases every month, year, and five years, we can calculate the value of the function for t = 1, t = 12, and t = 60, respectively, and then divide each value by the previous one.

For each month:

B(1) = 100(1 + 0.002) = $100.20

B(2) = 100(1 + 0.002)² = $100.40

B(2)/B(1) = $100.40/$100.20 = 1.001993

The amount in the account increases by a factor of approximately 1.002 every month.

For each year:

B(12) = 100(1 + 0.002)¹² = $102.44

B(24) = 100(1 + 0.002)²⁴ = $105.01

B(24)/B(12) = $105.01/$102.44 = 1.0249

The amount in the account increases by a factor of approximately 1.025 every year.

For every five years:

B(60) = 100(1 + 0.002)⁶⁰ = $110.41

B(120) = 100(1 + 0.002)¹²⁰ = $121.20

B(120)/B(60) = $121.20/$110.41 = 1.0991

The amount in the account increases by a factor of approximately 1.099 every five years. Therefore, the amount in the account increases by a small factor every month, a moderate factor every year, and a larger factor every five years.

To learn more about account click on,

https://brainly.com/question/31354557

#SPJ1

The integer values that make the statement true are x = -3, -2, -1, 1, 2, 3

We have,

We can start by multiplying both sides of the inequality by -3x to get rid of the denominators:

-3/x < -x/3

Multiplying by -3x on both sides.

-9 < -x²

Rearranging.

x² < 9

Taking the square root of both sides.

|x| < 3

This means that x can take any integer value between -3 and 3, excluding 0.

Thus,

The integer values are x = -3, -2, -1, 1, 2, 3

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ1

The domain of the 1st piece is -10 < x < 0, for 2nd piece is 0 < x < 4, and for 3rd piece is 4 < x < 8.

A function is a particular kind of relationship where there is a set domain and range, and every input value in the domain is associated with a single output value in the range.

We have a piecewise function shown in the picture:

From the graph:

f(x) = -2, Domain: -10 < x < 0

f(x) = 2x + 1, Domain: 0 < x < 4

f(x) = (-1/2)x, Domaim: 4 < x < 8

Thus, the domain of the 1st piece is -10 < x < 0, for 2nd piece is 0 < x < 4, and for 3rd piece is 4 < x < 8.

Read more about functions here:

https://brainly.com/question/17043948

#SPJ1

Answer:

C

Step-by-step explanation:

Positive numbers represent a positive situation. And negative numbers coincide with a negative situation.

 Ex: An increase in temperature corresponds to a positive number, and a decrease in temperature with a negative number.