Answer:
g = 18 - 2t
Step-by-step explanation:
They start with 18 gal.
To find how much gas they use while driving:
(2 gal/hr)(t hr)
Subtract that amount from the 18 gal they had in the tank to start with.
g = 18 gal - (2 gal/hr)(t hr)
Work out
2 2/7 +1 1/4
Give your answer as a mixed number in its simplest form.
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.
Which statements are true regarding the sequence below? Check all that apply.
20.4, 24, 244.
It can be represented using the formula f(x + 1) = (f(x)) when f(1) = 10.
It can be represented using the formula x=4
It can be represented using the formula fox)=
The domain of the sequence is all real numbers.
The range of the sequence is all natural numbers.
The statements that are true regarding the sequence below are
It can be represented using the formula f(x) = 10/3 (6/5)ˣ⁻¹The domain of the sequence is all real numbers.How to find the true statementsThe 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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c.96 test to see if there is evidence that the lie detector says a person is lying more than 50% of the time, regardless of what the person reads.
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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Evaluate the line integral, where C is the given plane curve. 1649 (x®y + sin(x)) dy, C is the arc of the parabola y = x2 from (0, 0) to (1, x2)
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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A photograph is 8 centimeters wide. After Kari enlarges the photograph, it is 3 times as wide as the original. How wide is the photograph in millimeters?
answer: should be
8 *3 =24 centimeters
1cm = 10mm
24cm = 240mm
the photograph is 240 mm
The width of the photograph in millimeters is 240 mm.
How to illustrate the scale?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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Part A:
Describe two possible financial goals for which you may require $12,000. Classify each as a want or need. Do research to ensure that amount is enough for your goal.
Part B:
Create and describe three possible investments to reach your goal within five (5) years. Investment 1 is a simple interest investment with 3% annual interest. How much would you need to invest at the beginning? Investment 2 is a compound interest investment, with 3% annual interest compounded monthly. How much would you need to invest at the beginning?
Investment 3 is a regular deposit in an account that earns 3% compound interest, compounded once per year. How much do you need to deposit, and how often will you deposit it, to reach it Part C:
Calculate and describe the total interest earned on each of your three investments. Explain your thinking and show your work.
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:
Investment 1: initial investments of $10,435Investment 2: initial investments of $10,330.43Investment 3: Annual Deposit of $2,194.42.Part C: The total interest earned on each investment is as follows:
Investment 1: $1,565Investment 2: $1,669.57Investment 3: $1,027.90.How are the total interests computed?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.
Investment 1: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)
Investment 2: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
Investment 3: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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Solve for y:
2π=2y+6x
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
A fair coin is tossed 2 times in succession. The set of equally likely outcomes is {HH, HT, TH, TT}. Find the probability of getting exactly zero (0) heads.
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.
Probability of obtaining exactly 2 heads = (1 / 4) = 0.25Probability of obtaining no head = (1 / 4) = 0.25Probability of obtaining at least one head = (3 / 4) = 0.75Probability of obtaining a head and a tail = (2 / 4) = 0.5To know more about Probability:
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Consider the matrices
A= 4 7 , B= -2 3 . C= 3 4 -1, and D= 6
-3 8 0 5 2
-5 -2
What are the dimensions of the product matrix of two of these matrices?
Drag the matrix dimensions to each box to match the product.
BD 2 x 1
CA 3 x 3
DC 2 x 3
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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schoepfle 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 $12,500 (credit). accounts not yet due
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.
Use the diagram to answer the questions.
What is the value of x?
x =
What is the measure of angle B?
B =
What is the measure of the exterior angle ACD?
ACD =
The value of x is 21
The measure of angle B is 28°
The measure of exterior angle ACD is 63°
Calculating the measure of anglesFrom 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 mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. a sample of this radioactive substance was taken six days ago. if the sample has a mass of today, find the initial mass of the sample. round your answer to two decimal places.
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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Convert 13/50 to percent
Answer:
26%
Step-by-step explanation:
To convert a fraction to a percentage, you need to first convert the fraction to a decimal.To convert 13/50 to a decimal, you can divide 13 by 50, which gives you 0.26.To convert a decimal to a percentage, you need to move the decimal point two places to the right, which gives you 26%.So, 13/50 is equivalent to 26%.The value of number 13/50 into percentage is,
⇒ 26%
What is mean by Percentage?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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consider the table, which reports the fruit diameter and number of offspring obtained by the researcher in the f2 generation. in the parental lines, l. cheesmanii had a fruit diameter of 8 cm and l. esculentum had a fruit diameter of 16 cm .
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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you flip a weighted coin that comes up heads 40% of the time and tails 60%. if you flip this coin 5 times, what is the probability that you see at least 3 tails, rounded to the nearest percent? please input your answer as a decimal rounded to the nearest hundreth
The probability that in 5 flips, at least 3 tails will come will be 0.36.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.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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How do I solve this problem?
5 + 2/3 ( 2p - 6 ) = 9
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
A systems analyst is testing the feasibility of using a new computer system. He wants to see if the new system uses less processing time than the old system. (Assume the original populations are normally distributed.) A sample of 25 jobs was selected and the processing time for each in seconds was recorded on each of the two systems. The results are as follows:Old System: mean = 27.2 seconds, s = 3.2 seconds, n - 25New System: mean = 24.3 seconds, s = 2.1 seconds, n = 25Difference (Old -New): mean = 2.9 seconds, s = 1.4 seconds, n = 25What is the alternative hypothesis for this problem?a. HA: µD≠0b. HA: µD>0c. HA: µD=0d. HA: µD<0
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 post offices calculate shipping costs based on the weight of the item in addition to a fee. The cost to ship a 2 pound item is 6.09, while the cost to ship a 7 pound item is
8.84. Find the rate of change of the cost with respect to the weight of the item
The rate of change of the cost with respect to the weight of the item is equal to 0.55.
What is the rate of change?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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-10 (x+3) - 6x + 5
O -41x
0 -16x - 25
O 3x + 5
O 4x + 35
Can someone explain what the rules are for division algorithm and what it means?
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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2
2
2
18. 1. 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. How many
two-point and three-point shots did the Cruisers score?
The number of two-points and three points shot the cruisers scored are 24 and 19 respectively.
How to find the number of two and three points made?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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Calculate the slope over the interval 1≤ x<3.
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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In Las Vegas, Nevada, stores charge a 4.6% state sales tax and a 3.65% county sales tax. Yuki is purchasing a handbag priced at $220 before tax.
How much sales tax does Yuki pay for her handbag purchase?
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
Sarah budgeted $100 for new art supplies. When Sarah purchased the supplies, she
spend $75. What type of variance does this represent?
The variance is a positive variance because the actual amount spent by Sarah was less than the budgeted amount
How to know the type of variance?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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Find the vertex of each of the following parabolas by averaging the x-intercepts. Then write each equation in graphing form. y=(x-3)(x-11)
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
y = a(x - 7)^2.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
y = a(x - h)^2 + kwhere (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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Peter deposited some money in a new checking account. Over time, he withdrew the same
amount of money each week to spend on movies and music. The table shows the balance in
Peter's checking account, in dollars, over time.
Time (t)
4 weeks
8 weeks
10 weeks
15 weeks
Balance (B)
$537
$449
$405
$295
How much money did Peter deposit in his checking account?
Complete the equation to represent the situation.
B =
t+
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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the function f is continuous and differentiable on the closed interval [0,4]. the table above gives selected values of f on this interval. which of the following statements must be true?
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 Find B in degrees. B a A = 34° a = 6 b = 5 C b B = [?] degrees Round to the nearest tenth.
The measure of the angle B is 28 degrees
How to determine the measure of angle BFrom 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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What are the vertex and range of y = |2x + 6| + 2? 1 (0, 2); 2 < y < ∞ 2 (0, 2); −∞ ≤ y < ∞ 3 (−3, 2); 2 < y < ∞ 4 (−3, 2); −∞ ≤ y < ∞
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!
a paper company needs to ship paper to a large printing business. the paper will be shipped in small boxes and large boxes. each small box of paper weighs 50 pounds and each large box of paper weighs 80 pounds. a total of 28 boxes of paper were shipped weighing 1850 pounds altogether
On solving the provided question we can say that, 8 tiny boxes total were shipped and 13 huge boxes were dispatched.
What is equation?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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