The Shaffer family started on a trip in their car with 18 gallons of gasoline. The car uses 2 gallons of gasoline every hour. If t represents the number of hours spent driving and g represents the number of gallons of gasoline left in the car, which equation could be used to calculate the value of g, if 0 ≤t ≤9
Multiple Choice
g = 18 - 2t
g = 18t - 2
g = 2t - 18 g = 2t + 18

Answer: y=pi-3

Step-by-step explanation:

2pi=2y+6

2pi-6=2y

(2pi-6)/2=y

pi-3=y

y=pi-3

hope this helped

625 is the total amount deposited by Peter in his checking account.

1) According to question

Balance after 4 weeks= 537                                     (equation 1)

Balance after 8 weeks= 449                                     (equation 2)

Each week Peter withdraws same amount.

Let the same amount be x.

From equation 1 and 2

Money spent in 4 weeks = 537-449=88

Therefore money spent in one week = 88/4=22

So the amount deposited by Peter=537 +22x 4 weeks

=537+88=625

2) B=625-22t

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Answer: The vertex is at (-6, 2). The range is 2 < y < ∞.

Step-by-step explanation:

      y = |2x + 6| + 2 is almost in vertex form, which is y = |x - h| + k. We will divide both values by 2, so the 2 coefficient is on the outside, y = 2|x + 3| + 2.

      After this, we can see that the vertex is at (-h, k). This means the vertex is at (-3, 2).

      For the range, since this V (the shape of an absolute value graph) opens upwards, it will be everything greater than and equal to the y value of the vertex, in this case, 2. That means our range is;

           2 < y < ∞

Answer:

The answer is c, or (3, 2), 2 less than y is greater than infinity

Step-by-step explanation:

I got it right on the test

Have a good day and hope it helps!

Answer:

p = 6

Step-by-step explanation:

5 + 2/3 (2p - 6) = 9

5 + 4/3p - 4 = 9

1 + 4/3p = 9

4/3p = 8

p = 6

Answer:

p= 6

Step-by-step explanation:

Solve for p:

(2 (2 p - 6))/3 + 5 = 9

Put each term in (2 (2 p - 6))/3 + 5 over the common denominator 3: (2 (2 p - 6))/3 + 5 = 15/3 + (2 (2 p - 6))/3:

(15/3 + (2 (2 p - 6))/3) = 9

15/3 + (2 (2 p - 6))/3 = (2 (2 p - 6) + 15)/3:

((2 (2 p - 6) + 15)/3) = 9

2 (2 p - 6) = 4 p - 12:

((4 p - 12) + 15)/3 = 9

Grouping like terms, 4 p - 12 + 15 = 4 p + (15 - 12):

(4 p + (15 - 12))/3 = 9

15 - 12 = 3:

(4 p + 3)/3 = 9

Multiply both sides of (4 p + 3)/3 = 9 by 3:

(3 (4 p + 3))/3 = 3×9

(3 (4 p + 3))/3 = 3/3×(4 p + 3) = 4 p + 3:

(4 p + 3) = 3×9

3×9 = 27:

4 p + 3 = 27

Subtract 3 from both sides:

4 p + (3 - 3) = 27 - 3

3 - 3 = 0:

4 p = 27 - 3

27 - 3 = 24:

4 p = 24

Divide both sides of 4 p = 24 by 4:

(4 p)/4 = 24/4

4/4 = 1:

p = 24/4

The gcd of 24 and 4 is 4, so 24/4 = (4×6)/(4×1) = 4/4×6 = 6:

Answer: p = 6

The dimensions of the product matrix of two of these matrices is BD = 2 * 1 , CA = 1 * 3 and DC = 2 * 3 .

Given :

The dimension of BD :

B dimensions = ( 2 * 2 )

D dimensions = ( 2 * 1 )

Product of BD dimensions = Numbers of rows of B * number of columns in D

= 2 * 1

The dimension of CA :

C dimensions = ( 1 * 3 )

A dimensions = ( 3 * 3 )

Product of CA dimensions = Numbers of rows of C * number of columns in A

= 1 * 3

The dimension of DC :

D dimensions = ( 2 * 1 )

C dimensions = ( 1 * 3 )

Product of CA dimensions = Numbers of rows of D * number of columns in A

= 2 * 3

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The statements that are true regarding the sequence below are

The given sequence include 10/3, 4, 24/5, 244/25

Applying the formula f(x) = 10/3 (6/5)ˣ⁻¹ to it

for x = 1, f(x) = 10/3 (6/5)¹⁻¹ = 10/3

for x = 2, f(x) = 10/3 (6/5)²⁻¹ = 4

for x = 3, f(x) = 10/3 (6/5)³⁻¹ = 24/5

This shows that the formula works for it hence a correct statement

Real numbers include all positive and negative numbers, fractions and decimals alike and the domain are natural numbers which are part of real numbers

The range are also all real numbers and this go beyond natural numbers

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As per the given function, the value of x is lies between the closed interval [0, 4].

The term function in statistics is defined as a function from a set X to a set Y assigns to each element of X exactly one element of Y.

Here we have given that the function f is continuous and differentiable on the closed interval [0,4].

And we need to find correct statement about this interval.

As per the concept of function, we know that if there is a number c in the closed interval [a , b] such that f(c) ≥ f(x) for all x in [a , b].

Here let us consider that a be the number that has been selected.

So, based on the rule of function can be written as,

=> f(a) ≥ f(x)

where a lies between [0, 4].

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a. total estimated uncollectible accounts is $21,190

b. to entry the adjustment, we have to debit bad debt expense and credit allowance for doubtful accounts in the amount of $14,690

a. to compute the estimated uncollectible accounts, we have to multiply the specific % to the accounts receivable plus the beginning balance;

•Accounts not due

$36,000 x 4% = $1,440

•Accounts 1 - 60 days past due

$21,000 x 25% = $5,250

•Accounts more than 60 days past due

$16,000 x 50% = $8,000

So the total uncollectible accounts would be; $6,500 + $1,440 + $5,250 + $8,000 = $21,190

b. to record the year-end adjustment of the uncollectible accounts, we have to debit bad debt expense and credit allowance for doubtful accounts in the amount of $14,690. This figure is the uncollectible amount we computed earlier based on the aging.

Therefore, the total estimated uncollectible accounts is $21,190 and to entry the adjustment, we have to debit bad debt expense and credit allowance for doubtful accounts in the amount of $14,690

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Disclaimer

The question given by you is incomplete, so the above answer has been done as per a similar question

Spade Agency separates its accounts receivable into three age groups for purposes of estimating the percentage of uncollectible accounts. In addition, the balance of Allowance for Uncollectible Accounts before adjustment is $6,500 (credit).Accounts not yet due = $36,000; estimated uncollectible = 4%.Accounts 1–60 days past due = $21,000; estimated uncollectible = 25%.Accounts more than 60 days past due = $16,000; estimated uncollectible = 50%.Required:a. Compute the total estimated un-collectible accounts.b. Record the year-end adjustment for estmated un-collectable accounts.

The initial mass of the sample is =2.39 kg

Radioactivity=Radioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.Radioactive describes something that exhibits or is caused by radioactivity. If something is radioactive, it emits radiation, which usually takes the form of electromagnetic waves or fast-moving elementary particles, such as protons or neutrons.

M(t)= Mo E =2.546 M(3)=2.54-02(3)

=2.54e -0.06

=2.39 kg (initial mass of the sample)

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The slope over the interval 1 ≤  x < 3 is m = 3 / 2 .

Given :

the slope over the interval 1 ≤  x < 3

From the graph :

take two points which lies on the interval

( 1 , 0 ) and ( 3 , 3 )

slope :

Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line .

slope m = y2 - y1 / x2 - x1

= 3 - 0 / 3 - 1

= 3 / 3 - 1

= 3 / 2

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The vertex of the parabola is at the point (7, 0) and since the vertex of this parabola is (7, 0), the equation of the parabola in graphing form is

The vertex of a parabola is the point on the graph where the parabola reaches its highest or lowest point. To find the vertex of the parabola y = (x - 3)(x - 11), you can average the x-intercepts of the parabola, which are the points where the parabola crosses the x-axis. The x-intercepts of this parabola are at x = 3 and x = 11, so the average of these two points is (3 + 11) / 2 = 7.

To write the equation of the parabola in graphing form, you can use the vertex form of a parabola, which is written as

where (h, k) is the vertex of the parabola and a is a coefficient that determines the direction of the parabola (whether it opens upwards or downwards). Plugging in the values for the vertex and the y-coordinate of the vertex (which is 0), we get

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The rate of change of the cost with respect to the weight of the item is equal to 0.55.

Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the shipping costs (y) with respect to the weight of the item (x), with the following data points (2, 7) and (6.09, 8.84):

Rate of change, m = (8.84 - 6.09)/(7 - 2)

Rate of change, m = 2.75/5

Rate of change, m = 0.55.

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The variance is a positive variance because the actual amount spent by Sarah was less than the budgeted amount

A variance is the difference between the budgeted amount and the actual amount. It can be positive or negative, depending on whether the actual amount is more or less than the budgeted amount

Given that, Sarah budgeted $100 for new art supplies and spent $75

Variance = $100 - $75 = $25

Therefore, the variance is a positive variance, since the actual amount spent was less than the budgeted amount. A positive variance represents a favorable situation, where the actual amount spent was less than the budgeted amount

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Answer:

26%

Step-by-step explanation:

The value of number 13/50 into percentage is,

⇒ 26%

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

The number is,

⇒ 13/50

Now, We get;

The value of number 13/50 into percentage is,

⇒ 13/50 x 100%

⇒ 13 x 2%

⇒ 26%

Thus, The value of number 13/50 into percentage is,

⇒ 26%

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The total number of genes involved in fruit diameter in tomatoes is 4.

[tex]1/4^{n}[/tex] = ratio of F2 individuals expressing either extreme Phenotype

In the above equation, 'n' represents the number of genes involved.

The term 'extreme phenotype' refers to the phenotype of one of the parents from the P1 generation. In this case, it denotes the parents with fruit diameters of 8 cm and 16 cm. In the F2 generation, which consists of a total of 256 offspring, there is only 1 offspring that resembles either P1 parent.

The ratio of individuals expressing either extreme phenotype = Number of springs with either extreme phenotype / Total number of off spring.

ratio of F2 individuals expressing either extreme Phenotype = 1/256

Apply the value of 1/256 to the first equation.

That is, [tex]1/4^{n}[/tex]  = 1/256

1[tex]1/4^{4}[/tex] = 1/256

As shown above, the value of 'n' is 4.

Therefore, the total number of genes involved in fruit diameters is 4.

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Part A: Two possible financial goals that may require $12,000 is to save for home ownership and education.

Part B: Three possible initial investments to reach the goal of having a future value of $12,000 in 5 years are:

Part C: The total interest earned on each investment is as follows:

The total interest for investment 1 is a product of simple interest formula, which multiplies the principal, interest rate, and time.

The total interests for investments 2 and 3 are the results of the online finance calculator., which inputs the future value, compound interest rate, and compounding period.

Future value = $12,000

Investment Period = 5 years

Simple interest rate = 3% or 0.03

Initial investment, P = A/(1 + rt)

Where P = principal

A = Future Value

r = interest rate

t = time

P = $12,000/(1 + 0.03 x 5)

= 12,000/(1.15)

= $10,435

Total Interest = $1,565 ($12,000 - $10435) or ($10,435 x 3% x 5)

Future value = $12,000

Investment Period = 5 years

Compound interest rate = 3% or 0.03 monthly

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 3%

PMT (Periodic Payment) = $0

FV (Future Value) = $12,000

Results:

Present Value (PV) = $10,330.43

Total Interest = $1,669.57

Future value = $12,000

Investment Period = 5 years

Compound interest rate = 3% or 0.03 annually

N (# of periods) = 5 years

I/Y (Interest per year) = 3%

PV (Present Value) = $0

FV (Future Value) = $12,000

Results:

Periodic Deposits = $2,194.42

Sum of all periodic payments = $10,972.10

Total Interest = $1,027.90

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Answer:

It is 3 15/28.

Step-by-step explanation:

To solve this problem, we first need to add the whole numbers: 2 + 1 = 3. Next, we need to add the fractions. To do this, we need to find a common denominator for the fractions 2/7 and 1/4. A common denominator for these two fractions is 28, so we can convert the fractions to equivalent fractions with a denominator of 28: 2/7 is equivalent to 8/28 and 1/4 is equivalent to 7/28. With the fractions written in this form, we can add them to get 8/28 + 7/28 = 15/28.

Finally, we need to add the whole number 3 and the fraction 15/28 to get our final answer. To do this, we need to convert the fraction 15/28 to a mixed number. We can do this by dividing 15 by 28 to get a quotient of 0 and a remainder of 15. This means that the mixed number equivalent of 15/28 is 0 + 15/28. Therefore, our final answer is 3 + 0 + 15/28 = 3 + 15/28 = 3 15/28. This is the simplest form of the mixed number, so our final answer is 3 15/28.

The value of x is 21

The measure of angle B is 28°

The measure of exterior angle ACD is 63°

From the question, we are to determine the measure of the angles.

From the given diagram, we can write that

35° + (x + 7)° = 3x° (Exterior angle theorem)

Solve for x in the equation

35° + (x + 7)° = 3x°

35° + x° + 7° = 3x°

35° + 7° = 3x° - x°

42° = 2x°

Divide both sides by 2

42°/2 = 2x°/2

21° = x°

Therefore,

x = 21

The measure of angle B is

Measure of angle B = (x + 7)°

Measure of angle B = (21 + 7)°

Measure of angle B = 28°

The measure of exterior angle ACD

Measure of exterior angle ACD = 3x°

Measure of exterior angle ACD = 3(21)°

Measure of exterior angle ACD = 63°'

Hence, the measure of the exterior angle is 63°

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the null hypothesis is that the mean difference between the two systems is 0 (H0: µD=0).The alternative hypothesis for this problem is HA: µD>0.

The alternative hypothesis (HA) is the opposite of the null hypothesis (H0).

In this problem, the null hypothesis is that the mean difference between the two systems is 0 (H0: µD=0).

Therefore, the alternative hypothesis is that the mean difference between the two systems is greater than 0 (HA: µD>0).The mean difference of the two systems is 2.9 seconds. Therefore, the alternative hypothesis is that the mean difference between the two systems is greater than 0 (HA: µD>0).

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The probability of getting exactly zero(0) means which comes with no head is P(no head)=1/4.

When a fair coin is tossed; any of the two outcomes are equally likely: head or tail denoted as 'h' and 't' respectively.

So, when a fair coin is tossed twice; the set of all possible outcomes is: {hh, ht, th, tt}.

Thus, there are 4 possible outcomes.

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The width of the photograph in millimeters is 240 mm.

It should be noted that a scale factor simply shows the relationship between a shape abd the original value given.

In this situation, the photograph is 8 centimeters wide and after Kari enlarges the photograph, it is 3 times as wide as the original.

The photograph in millimeters will be:

= 8 × 3 × 10

= 240 millimeters.

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The measure of the angle B is 28 degrees

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

A = 34 degrees

a = 6

b = 5

The measure of angle B can be calculated using the following sine ratio

a/sin(A) = b/sin(B)

Substitute the known values in the above equation, so, we have the following representation

6/sin(34) = 5/sin(B)

So, we have

10.73 = 5/sin(B)

Rewrite as

sin(B) = 5/10.73

Evaluate

sin(B) = 0.4660

Take the arc sin of both sides

B= 28

Hence, the angle is 28 degrees

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The number of two-points and three points shot the cruisers scored are 24 and 19 respectively.

The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots.

Therefore, the number of two-points and three-points the cruiser scored is as follows:

let

x = number of two-points

y = number of three-points

Hence, using equation

x + y = 43

2x + 3y = 105

Multiply equation(i) by 2

2x + 2y = 86

2x + 3y = 105

subtract equation(i) from equation(ii)

y = 19

Let's find x as follows:

x = 43 - 19

x = 24

Therefore,

number of two points = 24

number of three points = 19

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The probability that in 5 flips, at least 3 tails will come will be 0.36.

Given is that you flipped a weighted coin that comes up heads 40% of the time and tails 60%.

The coin shows up heads 40% of the time and tails 60%, this means that the probability of turning to tails would be 0.6 . For 5 flips that, the probability that at least 3 tails will come will be -

P{A} = (0.6 + 0.6 + 0.6)/5 = 1.8/5 = 0.36

P{A} = 0.36

Therefore, the probability that in 5 flips, at least 3 tails will come will be 0.36

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Line integral will be ∫c(x²y + sinx )dy = 1/3π²×π³ + 2π

Given:

C is the arc of parabola y = x² from (0,0) to (π,π²)

Let x be the parameter ; since the parabola is given as function of x

the parametric equations are

x=x,y=x², for 0≤x≤π

By using concept

∫c(x²y + sinx)dy = [tex]\int\limits^0_x {(x^2(x^2) + sinx} \, ).2xdx[/tex]

by applying the limits of integration we get ,

= 2 [ π².π³/6 + [ -πcosπ + sinπ - (0 + sin0)] ]

by calculating,

= 2 ( π².π³/6 + π )

= 1/3 π².π³ + 2π

Thus,

∫c(x²y + sinx )dy = 1/3π²×π³ + 2π

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Answer:

$18.15 of taxes

Step-by-step explanation:

based on the givens: 220 (4.6%  + 3.65% )

calculate the sum or difference: 220 x 0.0825

calculate the product: 18.15

It is not possible for a lie detector, or any other type of technology, to accurately determine whether a person is lying more than 50% of the time. Lie detectors, also known as polygraph machines, measure physiological responses such as changes in heart rate, blood pressure, and respiration to determine if a person is telling the truth or not. However, these responses can be affected by many factors, such as anxiety or stress, and are not always reliable indicators of deception. In addition, people can learn how to manipulate their physiological responses in order to deceive the polygraph machine. Therefore, it is not accurate to say that a lie detector can determine whether a person is lying more than 50% of the time

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On solving the provided question we can say that, 8 tiny boxes total were shipped and 13 huge boxes were dispatched.

A formula is a statement that the values ​​of two expressions are equal. The formula essentially says that two things are equal. An equals sign or '=' indicates that. 8+2=12-2 is an example equation. According to the above formula, the left side of the formula is equal to the right side. So the equation is the statement "this is equal to that".

Let x represent the quantity of tiny boxes, and y represent the quantity of large boxes.

21 cartons in all were despatched, according to the first statement.

Equation 1 is as follows:

[tex]x+y=21[/tex]

For the equation's solution, use the substitution approach.

x's value being entered into equation 2

[tex]25(21-y) +70y =1110 \\ 525-25y+70y = 1110\\ 45y = 585\\ Y=13[/tex]

x+13 = 21

X = 8

8 tiny boxes total were shipped.

13 huge boxes were despatched.

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Division algorithm also known as Euclid division lemma.

This algorithm says when a number a is divided by a number b it gives the quotient q and the remainder r .

then a = bq + r where 0 ≤ r < b.

Dividend = Divisor × Quotient + Remainder

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