Jen opened a savings account at the bank. The amounts of her first 3 deposits are shown below:
• Deposit 1: $325
• Deposit 2: $280
• Deposit 3: $480
• Deposit 4: ?
How much does she need in the fourth deposit so that her average deposit is $365?

Answer:

1. x = 18

2. x = 154

Step-by-step explanation:

 2          12

------- = -------

  3          x

 3 × 12 = 36

2 × x = 2x

36 = 2x

÷2    ÷2

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

x = 18

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

  6         84

------- = -------

  11           x

6 × x = 6x

84 × 11 = 924

6x = 924

÷6     ÷6

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

x = 154

I hope this helps!

Answer:

k = 6 and k = -4

Step-by-step explanation:

To determine two integral values of k (integer values of k) for which the roots of the quadratic equation kx² - 5x - 1 = 0 will be rational, we can use the Rational Root Theorem.

The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -1) and q must be a factor of the leading coefficient (in this case, k).

Possible p-values:

Possible q-values:

Therefore, all the possible values of p/q are:

\(\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 1}{\pm k}=\pm 1, \pm \dfrac{1}{k}\)

To find the integral values of k, we need to check the possible combinations of factors. Substitute each possible rational root into the function:

\(\begin{aligned} x=1 \implies k(1)^2-5(1)-1 &= 0 \\k-6 &= 0 \\k&=6\end{aligned}\)

\(\begin{aligned} x=-1 \implies k(-1)^2-5(-1)-1 &= 0 \\k+4 &= 0 \\k&=-4\end{aligned}\)

\(\begin{aligned} x=\dfrac{1}{k} \implies k\left(\dfrac{1}{k} \right)^2-5\left(\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}-\dfrac{5}{k}-1 &= 0 \\-\dfrac{4}{k}&=1\\k&=-4\end{aligned}\)

\(\begin{aligned} x=-\dfrac{1}{k} \implies k\left(-\dfrac{1}{k} \right)^2-5\left(-\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}+\dfrac{5}{k}-1 &= 0 \\\dfrac{6}{k}&=1\\k&=6\end{aligned}\)

Therefore, the two integral values of k for which the roots of the equation kx² - 5x - 1 = 0 will be rational are k = 6 and k = -4.

Note:

If k = 6, the roots are 1 and -1/6.

If k = -4, the roots are -1 and -1/4.

Answer:

Answer 60 degrees

Step-by-step explanation:

70-10 60-5 55+7 62-2 60

The value of the standard deviation does not change and remains the same.

Given, a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5.

The mean μ = 82.4

The standard deviation σ = √[ ((x - μ)2 + (y - μ)2 + (z - μ)2)/3 ]

we have to find the variance,

We now add a constant k to each data value and calculate the new mean μ'.

μ' = ((x + k) + (y + k) + (z + k)) / 3 = (x + y + z) / 3 + 3k/3 = μ + k

We now calculate the new mean standard deviation σ'.

σ' = √[ ((x + k - μ')2 +(y + k - μ')2+(z + k - μ')2)/3 ]

Note that x + k - μ' = x + k - μ - k = x - μ

also y + k - μ' = y + k - μ - k = y - μ and z + k - μ' = z + k - μ - k = z - μ

Therefore σ' = √[ ((x - μ)2 +(y - μ)2+(z - μ)2)/3 ] = σ

If we add the same constant k to all data values included in a data set, we obtain a new data set whose mean is the mean of the original data set PLUS k. The standard deviation does not change.

Hence, the standard deviation does not change.

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More than once a week: 0.11

Once a week: 0.51

Every other week: 0.26

Every three weeks: 0.05

Less often than every three weeks: 0.07

To make a relative frequency distribution, follow these steps:

Count the number of occurrences of each category in the data. In this case, 11% of the 251 participants responded "more than once a week", so the number of occurrences for this category is 0.11 * 251 = 27.61 (rounded to 28). Similarly, 51% of the participants responded "once a week", so the number of occurrences for this category is 0.51 * 251 = 127.51 (rounded to 128). And so on for the other categories.

Divide the number of occurrences for each category by the total number of participants. In this case, the total number of participants is 251, so the relative frequency for "more than once a week" is 28 / 251 = 0.11. The relative frequency for "once a week" is 128 / 251 = 0.51. And so on for the other categories.

And that's it! These are the relative frequencies for each category in the data.

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Answer: 3/8

Step-by-step explanation:

i think it’s 3/8 because I’m also working on this one and it adds up to 3/8 because as you see there is 3 sections. (I’m not good at explaining so I added a photo)

Answer:

3/8

Step-by-step explanation:

me  class  said so

Answer:

n=\frac{x-1130}{452}

Step-by-step explanation:

Answer:

452n + 1130 [I think ] because you distribute the 226 by the inside

In mathematics, a sequence is an ordered list of elements, often denoted by brackets or parentheses.

The term "a sequence of length n" refers to a sequence that contains a specific number of elements, where the number of elements is denoted by "n."

When the domain of a function is the set of natural numbers (N), it is called an infinite sequence. An infinite sequence can be thought of as an ordered list that continues indefinitely.

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Answer:

55

Step-by-step explanation:

The calculated value of x at g(x) = 2 is x = 2.5

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

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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Answer:

1. true

2. false

3. supplementary

4. vertical

5. it would be 5

The table that represents the relationship between Lemon poppy and Bran muffins is as under:

Lemon poppy Muffins                    Bran Muffins

22                                                             2

66                                                             6

88                                                             8

Given that a backery sells 22 Lemon Poppy Muffins for every 2 Bran Muffins.

We are required to find the table that represents the relationship between lemon poppy and Bran Muffins.

To find the table we need to just multiply 1,2,3,4,5,etc.

Table contain rows and columns which shows some relationship between variables.

Table which shows represents the relationship between lemon poppy and Bran Muffins is as under:

Lemon Poppy Muffins                     Bran Muffins

22                                                            2

44                                                            4

66                                                            6

88                                                            8

Hence the table that represents the relationship between Lemon poppy and Bran muffins is as under:

Lemon poppy Muffins                    Bran Muffins

22                                                             2

66                                                             6

88                                                             8

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The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.

The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.

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The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.

The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we  two by the product of a number and 7, the result is at most -29 if the number is -31/7.

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Answer:

C. 6x+100<150

Step-by-step explanation:

Because yyour putting the two items together but they can't be more than 150

Answer:

9n+18(2n-6)+13

Step-by-step explanation:

First, use distributive property to eliminate the parenthesis:

9n + 18(2n -6) + 13

9n + 36n - 108 + 13

Next, combine like terms:

9n + 36n - 108 + 13

45n - 108 + 13

45n + 121

Hope this helps!!

Alan~

Answer:

hhffuutxu da ruzrxtoxotx suzs txyfyfxkfzfjzrzjrzurzi f2f jfizeyUrYsU

Step-by-step explanation:

that boi sus fo real nfcgxjfxiffxdkhdkydkgzxd lux kygksktskgxkhxyzjrztjztkxlyslyskt

Answer:32 DEGREES

Step-by-step explanation:

90+58=148

180-148=32

Answer:

-1 6/10

is greater than

- 5/3

Step-by-step explanation:

The statement about the unit prices which is true is Kitty Kibbles has a lower unit price of $1.30/pound.

The correct answer choice is option D.

Cost of 16-pound bag of Kitty Kibbles = $20.80

Unit price of kitty kibbles = Price / number of pounds

= $20.80 / 16

= $1.30 per pound.

Cost of 8-pound bag of Feline flavor = $11.20

Unit price of feline flavor = Price / number of pounds

= $11.20 / 8

= $1.40 per pound

Ultimately, the unit price of kitty kibbles and feline flavor is $1.30 and $1.40 respectively.

Complete question:

A 16-pound bag of Kitty Kibbles is $20.80. An 8-pound bag of Feline Flavor is $11.20. Which statement about the unit prices is true?

A. Feline Flavor has a lower unit price of $1.40/pound.

B. Feline Flavor has a lower unit price of $1.30/pound.

C. Kitty Kibbles has a lower unit price of $1.40/pound.

D. Kitty Kibbles has a lower unit price of $1.30/pound.

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Answer:

 The decision rule is  

Fail to reject the null hypothesis

  The conclusion is  

There no sufficient evidence to show that the proportion of salmonella in the region’s water differs from the proportion of salmonella in the region’s wildlife

Step-by-step explanation:

From the question we are told that

   The first  sample size is \(n_1 = 252\)

    The number that tested positive is  \(k_1 = 18\)

     The second sample size is  \(n_2 = 476\)

     The number that  tested positive is  \(k_2 = 20\)

     The level of significance is  \(\alpha = 0.01\)

Generally the first sample proportion is mathematically represented as

      \(\^ p _1 = \frac{k_1 }{ n_1 }\)

=>    \(\^ p _1 = \frac{18 }{ 252 }\)

=>    \(\^ p _1 = 0.071\)

Generally the second sample proportion is mathematically represented as

      \(\^ p _2 = \frac{k_2 }{ n_2 }\)

=>    \(\^ p _2 = \frac{20 }{ 476}\)

=>    \(\^ p _2 = 0.042\)

The  null hypothesis is            \(H_o : p_1 - p_2 = 0\)

The alternative hypothesis is  \(H_a : p_1 - p_2 \ne 0\)

Generally the test statistics is mathematically represented

       \(z = \frac{ \^ p_1 - \^ p_2 - ( p_ 1 - p_2 )}{ \sqrt{\frac{\^ p_1 (1-\^ p_1)}{ n_1 } + \frac{\^ p_2 (1-\^ p_2)}{ n_2 } } }\)

=>    \(z = \frac{ 0.071 - 0.042 - 0 }{ \sqrt{\frac{0.071 (1-0.071)}{ 252 } + \frac{0.042 (1-\^ 0.042)}{ 476 } } }\)

=>    \(z = 1.56\)

From the z table  the area under the normal curve to the right corresponding to  1.56   is  

        \(P(Z > 1.56 ) =0.05938\)

Generally the p-value is mathematically represented as

         \(p-value = 2 * P(Z > 1.56 )\)

=>      \(p-value = 2 * 0.05938\)

=>      \(p-value = 0.1188\)

From the value obtained we see that   \(p-value > \alpha\) hence

  The decision rule is  

Fail to reject the null hypothesis

  The conclusion is  

There no sufficient evidence to show that the proportion of salmonella in the region’s water differs from the proportion of salmonella in the region’s wildlife

A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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They can buy 120 vans, 60 small trucks, and 80 large trucks.

The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck

Therefore,

let

s = number of small truck

number of van = v

let

l = number of large truck

v + s + l = 260

25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000

v + 2s + 2l = 400

Hence,

v = 2s

So,

2s + 2s + 2l = 400

4s + 2l = 400

2s + s + l = 260

3s + l = 260

2s + l = 200

s = 60

l = 200 - 2(60)

l = 200 - 120

l = 80

v = 2(600 = 120

Therefore, they can buy the following:

number of small truck = 60

number of van = 120

number of large truck = 80

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24 - x = -12 so what do is just add the two together so 24  + 12 = 36 and since it ended on a negative number, the temperature change is -36!!

Answer:

4/185 or 0.0216...

Step-by-step explanation:

Given that,

P(x) = x⁴- 4x³ + x² - x + 10

substitute x = 1 in equation, we get

⇛P(1) = 1⁴ - 4(1)³ + 1² - 1 + 10

⇛ P(1) = (1*1*1*1) - 4(1*1*1) + (1*1) - 1 + 10

⇛ P(1) = 1 - 4(1) + 1 - 1 + 10

⇛P(1) = 1 - 4 + 1 - 1 + 10

⇛P(1) = 2 - 4 - 1 + 10

⇛P(1) = 12 - 4 - 1

⇛P(1) = 12 - 5

⇛P(1) = 7.

Therefore, the factor of the polynomial p(x) = x⁴- 4x³ + x² - x + 10 is 7.

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

To calculate your bi-weekly paycheck, follow these steps:

Step 1: Calculate the gross earnings:

Multiply the number of hours worked per week by the hourly rate.

20 hours/week * $9.00/hour = $180.00/week

Step 2: Calculate the total earnings for two weeks:

Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.

$180.00/week * 2 weeks = $360.00

Step 3: Calculate the deductions:

Calculate each deduction separately and subtract them from the gross earnings.

Federal Income Tax: $360.00 * 11.9% = $42.84

State Income Tax: $360.00 * 3.6% = $12.96

F.I.C.A: $360.00 * 7.65% = $27.54

Professional Dues: Amount varies depending on the specific dues.

Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues

Step 4: Calculate the net earnings:

Subtract the total deductions from the gross earnings.

Net Earnings = Gross Earnings - Total Deductions

Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.

It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.

Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.

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Answer:

$5.50

Step-by-step explanation:

The evaluation of the given Boolean expressions are:

a) A && !B =  false              b) B∥C = true

c) B==C = false                   d) A&&!C = true

e) (B∥C)&&(!A) =  false        f) (A!=B)∥(B!=C)  = true

Information available in the problem:

A = true

B = true

C = true

a) Since A and B are both true, !B (which means "not B") is false. Therefore, A && !B evaluates to false, because the logical AND operator returns true only if both of its operands are true.

Hence,

A && !B = true && false = false

b) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true.

Hence,

B∥C = true ∥ false = true

c) Since B is true and C is false, B and C have different values, and therefore B==C will evaluate to false. This is because the equality operator returns true only if its operands have the same value.

Hence,

B==C = true == false = false

d) Since A is true and !C (which means "not C") is true, A&&!C evaluates to true. This is because the logical AND operator returns true only if both of its operands are true.

Hence,

A&&!C = true && !false = true && true = true

e) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true. Therefore, B∥C evaluates to true.

Since A is true and !A (which means "not A") is false, !A evaluates to false.

Therefore, (B∥C)&&(!A) evaluates to false, because the logical AND operator returns true only if both of its operands are true.

Hence,

(B∥C)&&(!A) = true && false = false

f) Since A is true and B is true, A!=B (which means "A is not equal to B") is false, because A and B have the same value.

Since B is true and C is false, B!=C (which means "B is not equal to C") is true, because B and C have different values.

Therefore, (A!=B)∥(B!=C) evaluates to true, because the logical OR operator returns true if at least one of its operands is true.

Hence,

(A!=B)∥(B!=C) = false ∥ true = true

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Answer:360 degrees in a circle divide by 4 is 90

Step-by-step explanation: there are 360 degrees in a circle so divide that by 4 and you get 90