suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table. the time t is measured in seconds and the units for r(t) are measured in tonnes (metric tons) per second. note that r(t) is increasing over the interval [0, 6]. t 0 1 2 3 4 5 6 r(t) 2 10 18 32 44 54 60 (a) give upper and lower estimates (in tons) for the total quantity q(6) of erupted materials after six seconds. (use six equal subintervals.)

Answer:

C)  The range of the function is all real numbers less than or equal to 0.

Step-by-step explanation:

Given function:

[tex]f(x)=-\sqrt{x}[/tex]

Domain

The domain of a function is the set of all possible input values (x-values).

As the square root of a negative number cannot be taken, x ≥ 0.

Therefore, the domain of the function is all real numbers greater than or equal to 0.

Range

The range of a function is the set of all possible output values (y-values).

As the domain is x ≥ 0, the range of the function is all real numbers less than or equal to 0.

Answer:

C) The range of the function is all real numbers less than or equal to 0.

The length of unknown side of the triangle will be 18 inch.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The two triangles are shown in figure.

Now,

Since, Both the triangle are similar.

Hence, There corresponding sides of the triangle are similar.

So, We get by definition of proportion visit:

⇒ 4 / 12 = 6 / x

⇒ 1/3 = 6/x

⇒ x = 6 × 3

⇒ x = 18 in

Thus, The length of unknown side of the triangle = 18 inch.

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Answer: B. $13,720

Step-by-step explanation: To calculate Ford's proceeds, we need to first find the discount, which is equal to the interest on the loan multiplied by the principal amount of the loan. The interest is 8% of $14,000, or $1,120. The discount is then $1,120 * 90/360, or $310. The proceeds are equal to the principal amount minus the discount, or $14,000 - $310 = $13,720.

The expected value of the extended warranty is $687.90 assuming it is replaced in the first 2 years.

Here, we are assuming that the dishwasher is replaced in the first 2 years in order to calculate the expected value of the extended warranty.

Because there is 14% chance of replacement:

Value of warranty = 14%*$800 - $112.10

Value of warranty = $112.00 - $112.10

Value of warranty = -$0.10

Now, because it is assumed that replacement will be done in first 2 years, then,

Value of warranty will increase to $687.90 ($800 - $112.10).

Therefore, the expected value of the extended warranty is $687.90 assuming it is replaced in the first 2 years.

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The sell order with the fifth lowest price (lowest bid) will be ranked fifth and will be executed last. In this case, the sell order with a price of $14 and a quantity of 10 will be executed last.

1. $10 - 20

2. $11 - 30

3. $12 - 50

4. $13 - 40

5. $14 - 10

1. The sell order with the lowest price (highest bid) is ranked first and will be executed first. In this case, the sell order with a price of $10 and a quantity of 20 will be executed first.

2. The sell order with the second lowest price (second highest bid) will be ranked second and will be executed second. In this case, the sell order with a price of $11 and a quantity of 30 will be executed second.

3. The sell order with the third lowest price (third highest bid) will be ranked third and will be executed third. In this case, the sell order with a price of $12 and a quantity of 50 will be executed third.

4. The sell order with the fourth lowest price (fourth highest bid) will be ranked fourth and will be executed fourth. In this case, the sell order with a price of $13 and a quantity of 40 will be executed fourth.

5. The sell order with the fifth lowest price (lowest bid) will be ranked fifth and will be executed last. In this case, the sell order with a price of $14 and a quantity of 10 will be executed last.

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The function f in slope - intercept form is y = -3x + 6 .

Given :

For linear function f, f(2)=0 and f(4)=-6.

Examples :

f(5)=0 means (5,0) is a point on the line.

f(3)=-2 means (3,-2) is a point on the line.

so f ( 2 ) = 0 means ( 2 , 0 )

f ( 4 ) = -6 means ( 4 , -6 )

slope m = -6 - 0 / 4 - 2

= -6 / 2

= -3

substitute m and ( 2 , 0 ) in y = mx  + b

0 = -3 * 2 + b

b = 6

substitute m and b value

y = -3x + 6

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The addition of function f(x) = 3 · x² - 1 and function g(x) = x + 2 is equal to (f + g)(x) = 3 · x² + x + 1. (Correct choice: B)

New functions can be created by combining functions, the most common operations are listed below:

In this problem we must determine the expression that is the result of the addition of two functions, whose definition is shown below:

(f + g) (x) = f(x) + g(x)

First, use the definition of the addition of two functions:

(f + g)(x) = (3 · x² - 1) + (x + 2)

Second, simplify the algebraic expression:

(f + g)(x) = 3 · x² + x + 1

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The monthly payment on a principal of $156000 with interest rate of 4% over a time period of 15 years is $1153.91

The monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.

The formula of monthly payment is given as;

A = P [r(1 + r)ⁿ] / [(1 + r)ⁿ - 1]

The principal of the loan can be calculated as 20 % of 195000

20 / 100 = x / 195000

0.2 = x / 195000

x = 39000

The principal is 195000 - 39000 = 156000

The principal is 156000, rate is 4% and time is 15 year

Substituting the values into the formula

A = 156000[0.04(1 + 0.04)¹⁸⁰] / [(1 + 0.06)¹⁸⁰ - 1]

A = 1153.91

The monthly payment is $ 1,153.91

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The expected value of X + 1 (Y - 1) can be calculated using the formula E(X + 1)(Y - 1) = E(X)E(Y) + E(X) - E(Y) + 1. Thus, the expected value of X + 1 (Y - 1) = 9/2 * 9/2 + 9/2 - 9/2 + 1 = 17. Therefore, the correct answer is d) 17.

The expected value of X + 1 (Y - 1) is a measure of the average value of the product of two independent random variables, X and Y. To calculate this expected value, we can use the formula E(X + 1)(Y - 1) = E(X)E(Y) + E(X) - E(Y) + 1. Since X and Y are independent random variables, we know that E(X) = E(Y) = 9/2. Plugging this value into the formula, we get E(X + 1)(Y - 1) = 9/2 * 9/2 + 9/2 - 9/2 + 1 = 17. This is the expected value of X + 1 (Y - 1). Therefore, the correct answer is d) 17.

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The standard deviation of the difference in the weights of the two oranges is equal to sqrt(1.2^2 + 1.2^2) = 1.7 ounces.

What do you mean by standard deviation?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

The standard deviation of the difference in the weights of the two oranges is equal to the square root of the sum of the squares of the standard deviations of the two oranges. This is because the weights of the two oranges are independent random variables.

Therefore, the standard deviation of the difference in the weights of the two oranges is equal to sqrt(1.2^2 + 1.2^2) = 1.7 ounces.

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Answer:

representa 48

Step-by-step explanation:

The proof that shows that ∠B ≅ ∠D by the CPCTC is explained in the table below.

CPCTC is a postulate that stands for "corresponding parts of congruent triangles are congruent". It says that if you prove that two triangles are congruent to each other, then every of their corresponding parts are congruent.

Therefore, the proof below shows how to use CPCTC to prove that ∠B ≅ ∠D.

Statement                           Reason                                                  

1. BC ≅ CD                          1. Given

2. AC ≅ EC                         2. Given

3. ∠ACB ≅ ∠ECD               3. Vertical angles theorem

4. ΔACB ≅ ΔECD               4. SAS theorem

5. ∠B ≅ ∠D                         5. CPCTC

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Answer:

Step-by-step explanation:

in similar triangles

sides are proportional.

By Side - Angle - Side Congruence Rule the given triangles are Congruent

What is SAS Rule of Congruence?

That is stated in the SAS regulation. If two sides and the included angle of one triangle equal two sides and the included angle of another, the triangles are congruent. An included angle is one created by the intersection of two specified sides.

Solution:

By Side - Angle - Side Congruence Rule the given triangles are Congruent

Since, two sides are equal andd the angle included between the sides is equal to

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The monthly payment is $966.76.

What is monthly payment?

The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original lent amount, but also the interest that accrues, must be repaid.

Given the amount of the loan is $1,450.

The number of installment is 18.

The APR of the loan is 8%.

The monthly rate of interest is 8%/12 = 2/3%

The formula of monthly installment is

[tex]M=P[\frac{r}{1-(1+r)^{-n}} ][/tex]

P =  principal = 1,450

r = rate of interest = 2/3%

n = number of instalment = 18

[tex]M=1450[\frac{0.67}{1-(1+0.67)^{-n}} ][/tex]

M = 966.76

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Answer:

D

Step-by-step explanation:

Since this we have rose petal, the equation will be either

[tex]r = a \sin(n \alpha ) [/tex]

or

[tex]r = a \cos( n\alpha ) [/tex]

Since we have 3 petals, which is a odd number, n=3

so the answer must be either

[tex]r = a \cos(3a) [/tex]

[tex]r = a \sin(3 \alpha ) [/tex]

Where a is some constant real number.

So D is the answer

Answer:

y=4x+11

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The 18 is the intitial value.  It does not change.  What does change is the height every month.  You would substitute in the number of months for x to find the height of the plant.

Answer: x=3y-1/2 or y=(x+1/2)/3

Step-by-step explanation:

f^-1(x) is just the inverse so all you need to do is switch x and y.

right now you have y=3x-1/2

so switch the x and y to get your answer of x=3y-1/2

if you're asked to solve for y, follow these steps:

1. x +1/2 = 3y-1/2 +1/2 -> x+1/2=3y

2. divide both sides by 3 -> (x+1/2)/3=y

The expected number of transitions is 22p(1-p) when take into account n separate coin flips with a p percent chance of landing on heads.

Given that,

Take into account n separate coin flips with a p percent chance of landing on heads. Say a changeover happens any time an outcome diverges from the one that came before it. For instance, there are 3 changeovers if n=5 and the result is HHTHT.

We have to determine the anticipated number of transitions.

We know that,

Independent flips,

n =12

Probability of heads =p

Probability of tails =(1-p)

Let m=1,2,...n

If mth term may be head then (m+1)th outcome could be head or vice-versa.

Probability of change overs from mth to (m+1)th outcome =2p(1-p)

So, the  expected changeovers is given by

E[change overs] = (n-1) *2p(1-p)

= (12-1) × 2p(1-p)

=11 × 2p(1-p)

=22p(1-p)

Therefore, the expected number of transitions is 22p(1-p) when take into account n separate coin flips with a p percent chance of landing on heads.

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Answer:

z = 20

Step-by-step explanation:

We can use the elimination method in a systems of 3 equations, just as we did when we were solving systems of 2 equations. While the method we apply it is the same, we have to apply it multiple times as elimination gets rid of one variable (usually) and since we're dealing with 3 variables, that still leaves us with 2 variables and we need to cancel once more.

We want to develop two linear equations, by applying elimination twice to each equation at least once, and then from there we can apply elimination once more.

Since we're solving for "z", we don't want to immediately cancel it out. So let's use the following two equations:
[tex]x+y-z=-5\\\\x-4y+3z[/tex]

Let's cancel out the "x", by manipulating one equation to be -x. We can do this by multiplying one equation by -1, but remember we have to apply this to both sides of the equation. Let's do it to the top one (you could also do it to the bottom one)

[tex]-1(x+y-z)=-(-5)\implies -x-y+z=5[/tex]

So now let's add the two equations:

[tex]\ \ \ (-x-\ y+\ z)=5\\+(\ \ x-4y + 3z) = 5\\ ------------\\ -5y+4z=10[/tex]

Now let's apply the same thing, but to the middle and bottom equation. Since they don't have the same absolute value coefficients (ignoring the sign) we need to multiple one by a value other than just negative one. So let's multiply the bottom equation by -2 so that the bottom will have a -2x which will cancel when adding it to 2x

[tex]-2(x - 4y + 3z) = -2(5)\\-2x + 8y - 6z = -10[/tex]

Now let's add the equations:

[tex]\ \ \ (\ \ 2x-y+z)=8\\+(-2x + 8y - 6z)=-10\\\\-----------\\7y - 5z = -2[/tex]

So now we have the two equations:

[tex]7y-5z=-2\\-5y+4z=10[/tex]

From here we can apply any method we want, from here I'll use substitution. Since we want to get rid of the "y", let's solve for "y" in terms of z, so once we substitute we have no "y" terms left.

[tex]7y-5z=-2\\7y=5z-2\\y=\frac{5z-2}{7}[/tex]

Now let's plug this into the second two-variable equation we made.

[tex]-5(\frac{5x-2}{7})+4z=10\\\\\frac{-25x+10}{7}+4z=10\\\\\frac{-25}{7}z+\frac{10}{7} + \frac{28}{7}z = \frac{70}{7}\\\\\frac{-25+28}{7}z = \frac{70-10}{7}\\\\\frac{3}{7}z = \frac{60}{7}\\\\z = \frac{60}{7} * \frac{7}{3}\\\\z = 20[/tex]

The critical value is 13.28 when the distribution of final marks in the statistics department.

Given that,

According to a teacher, the distribution of final marks in the statistics department is: A, 25%; B, 25%; C, 40%; D, 5%; and F, 5%. The following number of grades were recorded at the conclusion of a randomly chosen semester.

We have to recognize the important value.

We know that,

Given a=0.01,

The critical value of chi-square with 0.99,

df=n-1=4  is

13.28 (From chi-square table)

Therefore, The critical value is 13.28 when the distribution of final marks in the statistics department.

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Answer:

x =  e^3   +7

Step-by-step explanation:

ln ( x-7) = 3

To solve for x, raise each side to base e

e ^ ( ln ( x-7) ^= e^3

x-7 = e^3

Add 7 to each side

x-7+7 = e^3   +7

x =  e^3   +7

The expression in terms of first power of cosine cos4x*sin2x = 1/16 + cos(2x)/16 - cos(4x)/16 - cos(4x)cos(2x)/16.

How to lower the power of expression in trigonometry?

sin2x+cos2x = 1 and cos2x = (1+cos(2x))/2

Using the first identity, we have sin2x = 1-cos2x.

So we have that cos4x*sin2x = cos4x(1-cos2x)

Expanding, we have cos4x-cos6x.

Since cos2x=  (1+cos(2x))/2, this implies cos4x = ((1+cos(2x))/2)² and cos6x=((1+cos(2x))/2)³.

Expanding each one, we have

cos4x - cos6x = 1/4(1+2cos(2x) + cos2(2x)) - 1/8(1+3cos(2x) + 3cos2(2x) + cos3(2x)).

Simplifying we get

cos4x - cos6x = 1/8 + 1/8(cos(2x) - cos2(2x) - cos3(2x)).

cos2(2x) = 1/2(1+cos(4x)) and cos3(2x)

= cos2(2x)*cos(2x)

= 1/2(1+cos(4x)) * cos(2x)

= 1/2(cos(2x) + cos(4x)*cos(2x))

Substituting, we get

cos4x - cos6x = 1/8 + 1/8(cos(2x) - 1/2(1+cos(4x)) - 1/2(cos(2x) + cos(4x)*cos(2x)))

Cleaning it up, we get

cos4x*sin2x = 1/16 + cos(2x)/16 - cos(4x)/16 - cos(4x)cos(2x)/16.

Hence, The expression in terms of first power of cosine cos4x*sin2x = 1/16 + cos(2x)/16 - cos(4x)/16 - cos(4x)cos(2x)/16.

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Answer:

+2 or –10

Step-by-step explanation:

x² + 8x –5 = 15

x² + 8x = 15 + 5

x² + 8x = 20

using completing the square method

(½(8))² to be applied in both sides

x² + 8x + 16 = 20 + 16

factorise the LHS

(x+4)² = 36

x + 4 = √36

x + 4 = ±6

x = –4±6

x = –4 + 6 or –4–6

x = +2 or –10

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The rational numbers are √9, √4, √1. Options A, B and F

A rational number is defined as a number expressed as the ratio of two integers, such that the denominator should not be equal to zero.

These numbers can be expressed as quotients of two integers.

It is a number whose decimal form is finite or recurring in nature.

It is determined by dividing an integer with another integer, an exception is made with zero.

It is important to note the following;

From the numbers given, the rational numbers are;

√9, √4, √1

Hence, the values are √9, √4, √1

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The number of pounds of peanuts needed is 29.167.

Multiply the number of pounds of each type and multiply by the cost per pound to get the total cost of that part contribution to the total. Add them together and set it equal to the final total pounds (50) multiplied by its cost per pound ($2.90)

There are 5 pounds of mixed nuts.

let x = pounds of peanuts

cost of each pound of peanuts is $1.50

45 - x = pounds of cashews

Cost of each pound of cashew is $4.50

This way total pounds = 50

5 pounds($6) + x pounds ($1.50) + (45-x)pounds($4.50) = 50 pounds($2.90)

30 + 1.50x + 202.5 - 4.50x = 145

-3x = -87.5

x = 29.167

Therefore, the number of pounds of peanuts needed is 29.167.

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Disclaimer

The question given by you is incomplete, the abouve asnwer is done as per a similar question, the question is

A merchant has 5 pounds of mixed nuts that cost $30. he wants to add peanuts that cost $1.50 per pound and cashews that cost $4.50 per pound to obtain 50 pounds of a mixture that costs $2.90 per pound. how many pounds of peanuts are needed?

The surface area of the figure given which is a rectangular prism is 1362cm²

The total region or area covered by all the faces of a rectangular prism is defined as the surface area of a rectangular prism. A rectangular prism is a three-dimensional shape. It has six faces, and all the faces are rectangular-shaped. Therefore, both the bases of a rectangular prism must also be rectangles.

The surface area of the prism is calculated by the formula

A = 2[(lw) + (lh) + (wh)]

To solve this problem, we have to divide the prism into two different parts and solve for the area.

For the first rectangular prism;

A = 2[(lw) + (lh) + (wh)]

A = 2[(8 * 14) + (8 * 14) + (14 * 14)]

A = 840cm²

The area of the second figure will be;

A = 2[(8 * 17) + (17 * 5) + (8 * 5)]

A = 552cm²

The total surface area of the figure is 840cm² + 552cm² = 1362cm²

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By solving a simultaneous linear equation, it can be calculated that-

Value of ab = 60

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a simultaneous linear equation needs to be solved

[tex]3^a = 81^{b+2}[/tex] and [tex]125^b = 5^{a-3}[/tex]

[tex]3^a = 3^{4(b+2)}[/tex]

a = 4(b + 2)

a = 4b + 8

a - 4b = 8 ... (1)

[tex]125^b = 5^{a-3}\\5^{3b} = 5^{a-3}\\[/tex]

3b = a - 3

a - 3b = 3 .... (2)

Subtracting (1) from (2)

b = -5

Putting the value of b in (2)

a - 3(-5) = 3

a + 15 = 3

a = 3 - 15

a = -12

Value of ab = (-12) [tex]\times[/tex](-5) = 60

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