Petra invests $10 800. After 4 years she has earned $3240 in interest. At what amount rate of interest did she invest her money?

Answer:

196

Step-by-step explanation:

56*3.5=196

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The 17th term of the sequence is 289

The nth term is given as

Sn = n^2

The 17th term of the sequence implies that

n = 17

So, we have

S17 = 17^2

Evaluate

S17 = 289

Hence, the 17th term of the sequence is 289

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Answer:

The correct answer would be C

Step-by-step explanation:

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The choice which best compares the volume of the cylinders is; Choice B; The volume of cylinder B is the same as that of cylinder A.

From geometry, It can be concluded that the volume of a solid shape is the product of its cross sectional area and the height over which the area spans. On this note, since the volume of a cylinder is dependent on the radius and height of the cylinder, both cylinders have equal volumes.

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Answer:

1)(5x−3)(x−3)

2)(7m+10)(m−4)

3)(5y+6)(y+5)

4)(3p+10)(p+9)

Step-by-step explanation:

Have a nice day and hope this helps

Answer:

Purchasing Power

Step-by-step explanation:

None

Answer:

x = 30

y = 68

z = 82

Step-by-step explanation:

Let the first angle be X, the second angle be Y, and the third angle be Z.

You can write these 3 equations to represent the relationships between the angles:

\(x+y+z=180\\y+z=5x\\z=y+14\)

Step 1. Z is already isolated in the 3rd equation, so the first thing I would do is use that to eliminate the Z in the 1st and 2nd equations.

\(z=y+14\\\\x+y+z=180\\x+y+(y+14)=180\\\\y+z=5x\\y+(y+14)=5x\)

Step 2. Now, simplify both of those and treat them like a system of 2 equations. I'll simplify the top equation first and solve for x:

\(x+y+(y+14)=180\\x+y+y+14=180\\x+2y+14=180\\x+2y=166\\x=166-2y\)

Plug that into the other equation:

\(y+(y+14)=5x\\y+y+14=5(166-2y)\\2y+14=830-10y\\12y+14=830\\12y=816\\y=68\)

Step 3. Now we have the value of one variable. Use that to solve for x in the previous equation:

\(x=166-2y\\x=166-2(68)\\x=166-136\\x=30\)

Step 4. Now we have two variables. Pick any of the original 3 equations you want to solve for z:

\(x+y+z=180\\30+68+z=180\\98+z=180\\z=82\)

================================

Finally, you can confirm that by plugging these into all of the original equations to make sure they meet the conditions.

\(30+68+82=180\\180=180\\\\68+82=5(30)\\150=150\\\\82=68+14\\82=82\)

Answer:

15

Step-by-step explanation:

The equivalent expressions are B: 2(12m-6p+36) and (c): 12(2m-p+6)

From the question, we have the following parameters that can be used in our computation:

24m-12p+72

Factor out 2 from the expression

So, we have

2(12m-6p+36)

This represents the option (b)

Factor out 12 from the expression

So, we have

12(2m-p+6)

This represents the option (c)

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The probability that you select a Jack given that it is a Club P(Jack∣Club) is 1/13.

The probability that you select a Club given that it is a Jack is P(Club∣Jack) is 1/4.

The probability that you select a card that is NOT a Jack given that it is NOT a Club,P(NotJack∣NotClub) is 47/38

The probability that you select a card that is NOT a Club given that is it NOT a Jack is 38/47

The probability that you select a Jack given that it is a Club P(Jack|Club):

There are 4 Jacks in a deck (one for each suit), and since we are given that the selected card is a Club, we only need to consider the 13 cards in the Club suit.

So, the number of favorable outcomes is 1 (the Jack of Clubs), and the total number of possible outcomes is 13 (the number of cards in the Club suit)

P(Jack|Club) = 1 / 13

The probability that you select a Club given that it is a Jack

P(Club|Jack):

P(Club|Jack) = Number of favorable outcomes / Total number of possible outcomes

P(Club|Jack) = 1 / 4

The probability that you select a card that is not a Jack given that it is not a Club

P(NotJack|NotClub):

The number of cards that are not Jacks is 52 - 4 = 48 (since there are 4 Jacks in the deck), and the number of cards that are not Clubs is 52 - 13 = 39 (since there are 13 cards in the Club suit).

P(NotJack|NotClub) = Number of favorable outcomes / Total number of possible outcomes

P(NotJack|NotClub) = (48 - 1) / (39 - 1)

=47/38

P(NotClub|NotJack) = (39 - 1) / (48 - 1)

=38/47

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The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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The value of common ration r is 4.

Given that,

a₁ = 9

a₅ = 2304

We know that,

A geometric sequence  is a sequence in which each term (except from the first term) is multiplied by a fixed amount to obtain the following term.

The following term in the geometric sequence must be obtained by multiplying it by a set term (referred to as the common ratio), and the previous term in the sequence can be obtained by dividing it by the same common ratio.

Since we know that nth term of GP is,

\(a_{n}\) = a₁ \(r^{n-1}\)

Therefore,

a₅ = a₁ \(r^{4}\)  = 2304

⇒  9 x \(r^{4}\)  = 2304

⇒        \(r^{4}\)  = 256

⇒           r = 4

Hence, r = 4

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Answer: Let the length of the hypotenuse be x

Applying the Pythagorean theorem we have :

x²=20²+48²

⇒x²=2704

⇒x=52( ∀ x >= 0 )

Step-by-step explanation:

Let assume the hypotenuse(longest side of right triangle) be x

By Pythagoras theorem

\( \bf \large \longrightarrow \: {c}^{2} \: = \: {a}^{2} \: + \: {b}^{2} \)

Applying Pythagoras theorem

\( \bf \large \implies \: {x}^{2} \: = \: {20}^{2} \: + \: {48}^{2} \)

\(\bf \large \implies \: {x}^{2} \: = \:400 \: + \: 2304\)

\(\bf \large \implies \: {x}^{2} \: = \:2704\)

\(\bf \large \implies \: \sqrt{x} \: = \: \sqrt{2704} \)

\(\bf \large \implies \: \: x \: = \: 52\)

Hence , the length of hypotenuse is 52.

Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

An inequality to represent the cost of Jason’s food for the party is

An inequality to represent this situation "Jason knows that he will be buying at least 5 packages of hot dogs" is

The two options for buying wings and hot dogs include the following:

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of wings respectively, and then translate the word problem into algebraic equation as follows:

Since one package of wings costs $7 and Hot dogs cost $5 per package, and he must spend no more than $40, a linear inequality which represents this situation is given by;

7x + 5y ≤ 40

Additionally, since Jason knew he would buy at least 5 packages of hot dogs, a linear inequality which represents this situation is given by;

y ≥ 5

Next, we would use an online graphing calculator to plot the above system of linear inequalities as shown in the graph attached below.

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Answer:

Step-by-step explanation:

1.63 meters = 163 centimeters. Formula

Answer:

33.3%

Step-by-step explanation:

they're charging u 50 more

50 is 1/3 of 150 and 1/3 to percentage form is 33.3%

Answer:

33.3% I think

Step-by-step explanation:

Correct me if I'm wrong

200-150=50

150x33.3%=49.95

49.95+150=195.95

Close enough? nothing else works and 33.4% is over.

Answer:

right now if you were to have a coke depending on the weather is from where you are standing effect how long it will take to melt

Step-by-step explanation:

Answer:

None

Step-by-step explanation:

The answers are:

1. g(10) -31

2. x= -17/3

3. f(3)= 2

4.x= √30

5. h(-2)= 1

6. x= 0

7. h(a)= 1

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = x² – 7

g(x) = -3x - 1

j(x)= 2x-9

h(x) = 1

1. g(10)= -3(10) -1 = -30 - 1= -31

2. g(x) = 16

-3x- 1= 16

-3x = 17

x= -17/3

3. f(3)= (3)² – 7 = 9- 7= 2

4. f(x)= 23

x² – 7=  23

x² = 30

x= √30

5. h(-2)= 1

6. x= 0

7. h(a)= 1

8. S(-1) = 3

The value of function s(a) at a=-1 is 3.

10. g(4) = -1

The value of function g(a) at a=4 is -1.

11. h(2) = 8

The value of function h(a) at a=2 is 8.

12. k(2) = 9​

The value of function k(a) at a= 2 is 9.

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Answer:

Step-by-step explanation:

a-b=21

5a-2b=18

Using elimination, we have

5a-5b=105

5a-2b=18

So:

3b=-87 so b=-29

Substituting, a=-8

(a,b)=(-8,-29)

The angle 7 is the alternative interior angle to angle 2.

Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.

They are the angles that are on opposite sides of the transversal and inside the two parallel lines.

Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.

We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.

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The kitchen used \(2 \frac{4}{5}\) gallons of soup during the day.

To find out how many gallons of soup the kitchen used during the day, we need to subtract the amount of soup they had at the end of the day from the amount they had at the start of the day:

\(6 \frac{1}{2} - 2 \frac{7}{10}\)

First, let's convert both fractions to have a common denominator of 10:

\(6 \frac{5}{10} - 2 \frac{7}{10}\)

Now we can subtract the whole numbers separately and the fractions separately:

\(4 \frac{5}{10} - 2 \frac{7}{10} = 2 \frac{8}{10}\)

Finally, we can simplify the fraction to a mixed number:

\(2 \frac{8}{10} = 2 \frac{4}{5}\)

Therefore, the kitchen used \(2 \frac{4}{5}\) gallons of soup during the day.

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Answer:

wreck actually occurred in the year 1987. If the guilty part paid in the year the wreck actually happened, what would have been the equivalent payout in 1987?

Round your answer to the nearest penny.

HERES THE CPI CHART FOR IT

Step-by-step explanation:

with 1858 ‘Cuvee Leonie’ cognac) was sold in Australia for $12,000. What would have been the equivalent price just one year later, in 2014?

Round your answer to the nearest penny.

Question 2 Use the Consumer Price Index (CPI) value chart in Section 4 of your textbook to answer the following question:

The greatest payout for a personal injury was recorded at $163,882,660 in 1993. The car wreck actually occurred in the year 1987. If the guilty part paid in the year the wreck actually happened, what would have been

I think the equation should be x² + 4x + 11 = 0, so I am giving the solution of the same.

Hope it helps.

If you have any query, feel free to ask.

Answer:

sure if it is about something i know

Answer:

The margin of error is of 0.17.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

He surveyed 35 mortgage holders and found that the proportion of these that did expect to own their house within 10 years is 0.51.

This means that \(n = 35, \pi = 0.51\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

a)Calculate the margin of error that the high school student will have.

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(M = 1.96\sqrt{\frac{0.51*0.49}{35}}\)

\(M = 0.1656\)

Rounding to 2 decimal places, the margin of error is of 0.17.

Answer:

1st answer is correct y=(1/2)x+2

Step-by-step explanation:

Answer:

188 cm^2.

Step-by-step explanation:

This consists of 3 pairs of rectangles

= 2 * 4*7 + 2 * 4*6 + 2 * 6*7

=  56 + 48 + 84

=  188.