What is the answer to this word problem??

Answer:

a₉ = 50

Step-by-step explanation:

The sum to n terms of an arithmetic series is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term, d is the common difference and n the number of terms

Here a₁ = - 6, S₃₀ = 2865, n = 30 and d has to be found

\(\frac{30}{2}\) [ (2 × - 6) + 29d ] = 2865 ( divide both sides by 15 )

- 12 + 29d = 191 ( add 12 to both sides )

29d = 203 ( divide both sides by 29 )

d = 7

The nth term is

\(a_{n}\) = a₁ + (n - 1)d , then

a₉ = - 6 + (8 × 7) = - 6 + 56 = 50

A function for the area A of the enclosure in terms of w is A = W(750 - 2W).

The width w that would maximize the area is 187.5 feet.

The maximum area is equal to 70,312.5 square feet.

Mathematically, the perimeter of a rectangular shape can be calculated by using this mathematical expression;

P = 2(L + W) or P = 2L + 2W

Where:

From the information about the fencing (perimeter), we have:

P = L + 2W

750 = L + 2W

Making L the subject, we have:

L = 750 - 2W

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

A = W(750 - 2W).

A = 750W - 2W².

For the width that would maximize the area, we have:

Width, W = 750/4

Width, W = 187.5 feet.

L = 750 - 2W = 750 - 2(187.5) = 375 feet.

Maximum area = LW

Maximum area = 375 × 187.5

Maximum area = 70,312.5 square feet.

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Answer:

2:5

Step-by-step explanation:

Please mark me brainlest, i really nead it

Answer:

0.3333333333333333....

1/3 of the pizza is left. 1/3 of the 1/3 was eaten

so

1/3 × 1/3 = 1/9

same ate 1/9 of the pizza

It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

In the given statement is:

λ = 2.5 x 10^-2 \(min^{-1}\)is the rate constant of the nucleus

To solve this problem, we use

N(t) = \(N_{0}\)e^-λt

and since we are looking for the time it takes to decay the nucleus to one -fourth of its original amount, we set

N(t) = 1/4 \(N_{0}\) = 0.25\(N_{0}\)

We can substitute this in the decay equation:

0.25\(N_{0}\) =\(N_{0}\) e^-λt

Cancel the like terms

0.25 = e ^-λt

Take the natural logarithm of both sides:

㏑(0.25) =㏑(e^-λt)

㏑(0.25)= -λt

Solve for the time t:

t = - ㏑(0.25)/λ

Substitute the given rate constant :

t = ㏑(0.25) / 2.5 x 10^-2 \(min^{-1}\)

t = -1.3863 /2.5 x 10^-2 \(min^{-2}\)

t = 55.452mins

It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

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Answer:

x(x-1)

Step-by-step explanation:

\(x^{2} -x\)

look for what both functions share, they both share an x,

which you can factor out,

x(x-1)

and you have your answer :)

Answer:

17

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

The answer is 17 because We noticed that 5 is 4 more than 1, 9 is 4 more than 5, and 13 is 4 more than 9. They are all a +4 pattern so you just simply add 4 to 13 which is 13 + 4 + 17 So our answer is 17

Answer:

alternate interior,x=2

Step-by-step explanation:

they are alternate interior angles

so 36x+3=-1+38x

   -36x         -36x

3=-1+2x

+1|+1

4/2=2x/2

x=2

Hello,

\(f(x) = 4 {x}^{2} - 9\)

\(g(x) = 4 {x}^{2} - 9 + 8 = 4 {x}^{2} - 1\)

Answer:

Step-by-step explanation:

4

Hello names smiley!

for your answer for this is  A  circle with diameter 10cm will have a circumference of approximately 31.4cm

or

10cm x 3.14 = 31.4 Circumference = 3.14 x diameter

Step-by-step explanation:

its ok if you dont give brainliest i just want to help!  

bye!

Answer:

it takes 48 days for 15 men to work

it takes 16 days for 15/48*16

the answer is 5 men

Answer:

45 men

Step-by-step explanation:

If you 1/3 the amount of time (from 48 to 16 ) to weed the plot, you will need to TRIPLE the number of men    to     45  men

Jamie should accept the second option to buy a new refrigerator for his apartment.

What is the Annual Interest?

The annual interest rate on an amount borrowed or a loan is the increment added to the loan at a particular rate over the desired period of time.

The objective of this question is to weigh the two options and determine the best means by which Jamie could get a new refrigerator for his apartment.

Option 1:

The annual interest rate for the first card = $1300 x 16.5%

The annual interest rate = $214.5

The monthly finance charge on a credit card can be estimated by finding the average daily balance using the Annual interest rate and the days of the billing cycle.

The monthly finance charge

= 1300 x 0.165/12

The monthly finance charge = $17.88

Now, The minimum monthly payment is 100 + 17.88

The minimum monthly payment for the first month = $117.88

In 12 months, Jamie would have paid off the loan with an additional interest of $214.5

Total amount paid = (117.88 x 12) + 247.5

= $1629.06

Option 2.

The appliance store offers an installment loan;

Using;

S.I. = PRT / 100

Since the loan must be paid in 12 equal payments; we can say the loan is paid monthly which is equivalent to 1 year.

i.e., Time(T) = 1 year

S.I. = 1300 x 12.5 x 1 / 100

The down payment = $300

In the total amount of $1300, Jamie has an outstanding amount of $1000 to pay.

Thus, In 12 equal payment times,

Jamie gets to pay = $1000/12

Jamie gets to pay = $ 83.33 each time .

Total amount paid = $162.5 + 1300

Total amount paid = $1462.5

Therefore, we can conclude that Jamie should accept the second option

to buy a new refrigerator for his apartment since the total amount paid in option 2 is lesser than that of option 1.

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Answer:

y=(x+5)²-3.

Step-by-step explanation:

1) the coordinates of the vertex are (-5;-3), it means (x+5)², not (x-5)²;

2) the vertex of the given graph is in bottom side, it means no minus before the '(x+5)';

3) according the items 1 and 2 and the given answers, the correct answer is y=(x+5)²-3.

p(male) * p(fail) = 0.2069 and P(male and fail) = 0.2034. The two results are different and so the events are independent

Independent Events are said to be when the probability of one event does not affect the probability of a second event. Dependent Events are said to be when the probability of one event affects the probability of a second event.

Now, the total number of people both male and female are:

48 + 70 = 118

Thus, probability of selecting a male = 48/118 = 0.4068

Probability of selecting someone that failed = (36 + 24)/118 = 0.5085

p(male) * p(fail)= 0.4068 * 0.5085 = 0.2069

P(male and fail) = 24/118 = 0.2034

The two results are different and so the events are independent

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Answer:

P=0.025x+100

Step-by-step explanation:

The y-intercept of the function is 100 which represents the base pay Sydney makes regardless of computer sales.

that's the correct answer^^^

y = 1/40x + 100 is  an equation that represents P as a function of X

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.

Given, Sydney is a salesperson who sells computers at an electronics store. She makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from her sales that day.

Let the equation of line y = kx + b

Where b is 100

Since the given line passes through (0, 100) and (4000,200)

since For a line k = (y₂ - y₁)/(x₂ - x₁)

Thus, k = (200 -100)/(4000-0)

k = 1/40

Thus,

y = 1/40x + 100

Therefore, an equation that represents P as a function of X is y = 1/40x + 100.

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Complete question:

Answer:

the shape has ,9 edges,,,

The rectangular blocks with the measure of 7 cm by 8 cm by 9 cm will not fit in the smallest cylindrical cup with the radius of 5cm.

Rectangular block with the least dimensions, 7cm by 8cm side.

Circle with radius r is x² + y² = r²

∴ x² + y² = 5² or x² + y² = 25

Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)

Its observed that the block cannot fit inside the cup. We can confirm this if

y >4 when x = 3.5

3.5² + y² = 25

12.25 + y² = 25

y² = 12.75

taking positive square root, y≈3.57

Since this is <4, the block cannot fit the 5 cm radius cup.

equation for the cup with r = 6cm,

x² + y² = 6² or x² + y² = 36

Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)

it is observed the block will fit inside the cup as y>4 when x = 3.5

3.5² + y² = 36

12.25 + y² = 36

y² = 23.75

taking positive square roots, y≈4.87

Since this is >4, the block can fit the 6 cm radius cup.

equation for the cup with r = 7cm,

x² + y² = 7² or x² + y² = 49

Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)

it is observed the block will fit inside the cup as y>4 when x = 3.5

3.5² + y² = 49

12.25 + y² = 49

y² = 36.75

taking positive square roots, y≈6.06

Since this is >4, the block can fit the 7 cm radius cup.

∴ the block will not fit the smallest cup

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The equation of the line that is perpendicular to line y = 7x/4+7 is y = -4x/7+12/7 and the equation of the line that is parallel to this line is y = 7x/4+11.

According to the question,

We have the following information:

y = 7x/4+7

Now, the slope of this line is 7/4 which will be the slope of the parallel line and the slope of the perpendicular line will be -4/7 (-1/m).

Points through line is passing = (-4,4)

x' = -4 and y' = 4

Now, we know that following formula is used to find the equation of the line:

(y-y') = m(x-x')

Perpendicular line:

y-4 = -4/7(x+4)

y-4 = -4x/7-16/7

y = -4x/7-16/7+4

y = -4x/7+12/7

Parallel line:

y-4 = 7/4(x+4)

y-4 = 7x/4+7

y = 7x/4+7+4

y = 7x/4+11

Hence, the equation of the line that is perpendicular to line y = 7x/4+7 is y = -4x/7+12/7 and the equation of the line that is parallel to this line is y = 7x/4+11.

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Step-by-step explanation:

at 3=3

at 0=9

at 4=1

\(y = ax + b\)

\(1 = 4a + b \\ 3 = 3a + b \\ 2 = - a \\ a = - 2 \\ 1 = - 4 \times 2 + b \\ b = 1 + 8 = 9 \\ y = - 2x + 9\)

Answer:

y=-2x+9

Step-by-step explanation:

From looking at the line you can already tell that the slope is going to be negative, and the y-intercept is going to be 9, since that's where y is when x is 0. You can see that when x is one, y is 7. When x is 2, y is 5. And when x is 3, y is 3.

So:

0: 9

1:7

2:5

3:3

And the difference of y over the difference of x is the slope

-2/1=-2

So the slope is -2

Therefore, putting the equation together makes:

y=-2x+9

Hope this helps!

It is not of exponential order for h(t) = et2. F is of exponential order and has order. F is piecewise continuous. No function's Laplace transform is possible. g(t) = eat, where t [0,.

Non-exponential form:

To represent a scientifically notated number as a non-exponential quantity: • Remove the exponential component of the number by moving the decimal point the same number of places as the exponent's value. The decimal is moved to the right by the same number if the exponent is positive.

Here are a few instances of functions other than exponential ones. y = 3 1 x as a result. n = 0 3 p as a result. Because y = ( 4) x. Since b = 1, y = 6 0 x.

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hello

to solve this question, we should let the unknown number be represented by x

the first number (x) is equal to 11, we can find the other number.

from the calculations above, the numbers are 11 and 22

Nine cans must be chosen to guarantee that we have three cans of the same type of soft drink.

To guarantee that we have three cans chosen from the same type of soft drink, we need to consider the worst-case scenario, which is that we choose two cans from each type of soft drink (a total of eight cans) and none of them is the same type. In this case, we would need to choose at least nine cans to guarantee that we have three cans chosen from the same type of soft drink.

To see why this is the case, imagine choosing eight cans from the four different types of soft drinks. There are two possibilities:

1. We choose two cans from each type of soft drink, and none of them is the same type. In this case, we would need to choose at least one more can from any of the types of soft drinks to guarantee that we have three cans chosen from the same type.

2. We choose three cans from at least one type of soft drink. In this case, we already have three cans chosen from the same type.

Therefore, we need to choose at least nine cans to guarantee that we have three cans chosen from the same type of soft drink, regardless of which cans we choose.

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Answer:

The graph with a y-intersect of (0, -3) and x-intercept of (12, 0)

Step-by-step explanation:

So the graph goes 1 unit up every 4 units to the right

The graph which represents the linear function y = 1/4x – 3 is A. A line on a graph passes through the (-4, -4), (0, -3), and (4, -2).

A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.

Given linear function is,

y = 1/4x – 3

Substitute x = 0.

y = 0 - 3 = -3

So the graph passes through (0, -3).

Let x = 4.

y = (1/4 × 4) - 3 = -2

So the graph passes through (4, -2).

Let x  = -4,

y = (1/4 × -4) - 3 = -4

So the graph passes through (-4, -4).

Hence the graph passes through (-4, -4), (0, -3), and (4, -2).

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The complete question is given as follows.

Which graph represents the linear function y = 1/4x – 3?

A. A line on a graph passes through the (-4, -4), (0, -3), and (4, -2).

B. A line on a graph passes through the (-4, -2), (0, -3), (4, -4).

C. A line on a graph passes through the points (0, -3), (1, 1), (2, 5).

D. A line on a graph passes through the points (-4, 2), (0, 3), (4, 4).

Answer:

Hence the greatest number of books that could be on the shelf is 30.

Step-by-step explanation:

Step 1:-

Here the given number of books is m,  

m < 45.  

If they are arranged into piles of five books, each no books would remain.  

m is divisible by 5.  

The last digit of m would be 5 or 0.    

The same number of books, when arranged with piles of 7 books each, two books remain.  

m-2 is divisible by 7.  

Step 2:-  

The last digit of m is 5 or 0.  

m-2 will have the last digit 3 or 8.    

Multiples of 7 are 7,14,21,28,35, 42;  

among which only number 28 has the last digit 8 or 3.    

m - 2 = 28  

m = 30  

The greatest number of books that could be on the shelf is 30.

Answer:

yeah the answer is in the question just needed the points

Step-by-step explanation:

\(\begin{bmatrix}4 & 0 & -4& |& -8 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix} \xrightarrow{\text{4R3+R1}\rightarrow \text{R1}} \begin{bmatrix}\bold{4} & \bold{0} & \bold{0}& |& \bold{4} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)

and,

\(\begin{bmatrix}4 & 0 & -4& |& 4 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix} \xrightarrow{\frac{1}{4} \text{R1}\rightarrow \text{R1}} \begin{bmatrix}\bold{1} & \bold{0} & \bold{0}& |& \bold{1} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)

"A set of numbers arranged in rows and columns so as to form a rectangular array."

"A matrix formed by combining the columns of two matrices to form a new matrix."

"The mathematical operations that are performed on rows of a matrix."

For given question,

We have been given an augmented matrix.

\(\begin{bmatrix}4 & 0 & -4& |& -8 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)

We need to perform the row operation 4R3 + R1 → R1

To perform above row operation,

- First multiply the third row by 4. (\(4R_3\))

- Add the new third row (4\(R_3\)) with the first row.

- Then replace Row 1 with the result.

The resultant augmented matrix would be,

\(\begin{bmatrix}\bold{4} & \bold{0} & \bold{0}& |& \bold{4} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)

That is,

\(\begin{bmatrix}4 & 0 & -4& |& -8 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix} \xrightarrow{\text{4R3+R1}\rightarrow \text{R1}} \begin{bmatrix}\bold{4} & \bold{0} & \bold{0}& |& \bold{4} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)

Now, we need to perform the row operation  \(\frac{1}{4}\) R1 → R1 on the above resultant augmented matrix.

To perform above row operation,

- Multiply the Row 1 by the reciprocal of 4.

- Then replace Row 1 with the result.

The resultant augmented matrix would be,

\(\begin{bmatrix}4 & 0 & -4& |& 4 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix} \xrightarrow{\frac{1}{4} \text{R1}\rightarrow \text{R1}} \begin{bmatrix}\bold{1} & \bold{0} & \bold{0}& |& \bold{1} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)

Therefore,

\(\begin{bmatrix}4 & 0 & -4& |& -8 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix} \xrightarrow{\text{4R3+R1}\rightarrow \text{R1}} \begin{bmatrix}\bold{4} & \bold{0} & \bold{0}& |& \bold{4} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)

and,

\(\begin{bmatrix}4 & 0 & -4& |& 4 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix} \xrightarrow{\frac{1}{4} \text{R1}\rightarrow \text{R1}} \begin{bmatrix}\bold{1} & \bold{0} & \bold{0}& |& \bold{1} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)

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The expected amount of each cube in the complete bag is given as follows:

20 blue cubes.

20 red cubes.

12 green cubes.

8 white cubes.

The expected amounts are obtained by applying the proportions in the context of the problem.

We are told that a bag has 60 cubes a random sample of 15 cubes is collected from the bag the results from the random sample.

15 cubes were selected from a bag of 60, hence the fraction collected is given as follows:

15/60 = 1/4.

Meaning that the expected amounts on the bag are given by the amounts on the sample multiplied by 4.

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Answer:

18/20

Step-by-step explanation:There are 20 total cards and 2 are brown so answer would be 18/20.

Word form One hundred three and five hundred three thouandth

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