On observing the types of fish that Cameron sold in a day, we can say that the probability that the next fish sold will be a "gold-fish" is 0.3 or 30%.
To find the probability of the next-fish Cameron sells being a goldfish, we use the formula:
⇒ probability = (number of desired outcomes)/(total number of possible outcomes),
In this case, the "desired-outcome" is selling a "goldfish", and
The total number of possible outcomes is the total number of fish sold so far.
To find the number of "gold-fish" sold, we need to count the number of times "goldfish" appears in the list : betta, goldfish, neon tetra, betta, guppy, guppy, swordtail, betta, goldfish, goldfish
We see that "goldfish" appears three times, so the number of desired outcomes is = 3.
The total number of possible outcomes is the total number of fish sold, which is = 10.
So, probability of the next fish Cameron sells being a goldfish is = 3/10 = 0.3,
Therefore, there is a 30% chance that the next fish Cameron sells will be a goldfish.
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Calculating Perpetuity Values
Curly’s Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $25,000 per year forever. A representative for the company tells you the policy costs $500,000. At what discount rate would this be a fair deal?
Provide the formula through excel
Answer:
a discount rate of 5%
Step-by-step explanation:
The formula to calculate the present value of a perpetuity is:
PV = PMT / r
Where PV is the present value, PMT is the constant payment, and r is the discount rate.
In this case, the PMT is $25,000 and the PV is -$500,000 (negative because it represents a cash outflow). So we can rearrange the formula to solve for r:
r = PMT / PV
r = $25,000 / -$500,000
r = -0.05 or -5%
Therefore, at a discount rate of 5%, the policy would be a fair deal.
To calculate this in Excel, you can use the following formula in a cell:
=r(-25000/500000)
This will give you a result of -0.05, or -5%, which represents the fair discount rate.
Hope this helps!
The Karns Recreation Hall needs to build a ramp. The height of the ramp must be 2 feet. The ramp will start 6 feet from the door. To the nearest tenth of a foot, how long will the ramp be?
Using the Pythagorean's theorem we can see that the length of the ramp is 6.32ft
How long the ramp will be?We know that the ramp is a right triangle whose legs are 2 ft and 6 ft. Remember that by Pythagorean's theorem we know that the square of the hypotenuse is equal to the sum of the squares of the legs.
Then the length of the ramp L will be:
L² = (2ft)² + (6ft)²
L = √((2ft)² + (6ft)²)
L = 6.32ft
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Mariano has $3.55 in nickels and quarters. The total number of coins is 5 less than twice the number of nickels. Which system of equations can be used to determine q, the number of quarters, and n, the number of nickels, that Mariano has?
The system of equations that can be used to determine q and n is:
25q + 5n = 355
q = 2n - 5
We have,
Let's use q to represent the number of quarters and n to represent the number of nickels.
The value of q quarters is 25q cents, and the value of n nickels is 5n cents.
The total value of Mariano's coins is 3.55, or 355 cents.
We can write the first equation based on these values:
25q + 5n = 355
The second sentence tells us that the total number of coins is 5 less than twice the number of nickels.
Since each nickel is one coin, the number of quarters must be two less than the total number of coins.
We can write the second equation based on this information:
q = 2n - 5
Therefore,
The system of equations that can be used to determine q and n is:
25q + 5n = 355
q = 2n - 5
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I need the area choices below
Answer:
Area of the shape is 244.98cm² is B
Step-by-step explanation:
Area of shape=Area of semi circle+Area of trapezoid
A=1/2 πr² + 1/2(a+b)h
A=1/2×3.142×7² + 1/2(14+18)10.5
A=1/2×3.142×49 + 1/2×32×10.5
A=76.98+168
A=76.98+168
A=244.98cm²
Answer the following questions
1. Order the following rational numbers from least to greatest: -5/6, -0.2001, 20%, -78
Answer:
-78, -5/6, -0.2001, 20%
Step-by-step explanation:
The first step is to convert all of the numbers into the same form. In this case, it is easiest to use decimal form.
-5/6 = -0.8333...
-0.2001
20% = 0.2
-78
-78 is the smallest by far
-0.8333... is the next smallest
-0.2 is next
and 0.2 is the largest
7.54 Torque on a rusty bolt.
(a) Do you think it is reasonable to apply ANOVA in this case?
(b) Regardless of your answer in part (a), describe hypotheses for ANOVA in this context, and use the table below to carry out the test. Give your conclusion in the context of the data.
(c) The table below are p-values for pairwise t-tests comparing each of the different groups. These p-values have not been corrected for multiple comparisons. Which pair of groups appears most likely to represent a difference?
(d) There are 28 p-values shown in the table in part (c). Determine if any of them are statistically significant after correcting for multiple comparisons. If so, which one(s)? Explain your answer.
Answer:
Answer is obstacle by giving up yours
5. (10 points) The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed with a mean of 367 ml and a standard deviation of 3 ml. If all cans less than 358 or greater than 373 ml are scrapped, what proportion of cans is scrapped? Solution:
The proportion of cans that are scrapped is approximately 0.0241.
We know that the fill volume of cans follows a normal distribution with a mean of 367 ml and a standard deviation of 3 ml. Let's define X as the fill volume of a single can. Then we can write:
X ~ N(367, 3)
We want to find the proportion of cans that are scrapped, i.e., the proportion of cans with a fill volume less than 358 ml or greater than 373 ml. Let's call this proportion p:
p = P(X < 358 or X > 373)
To solve this problem, we can use the standard normal distribution and the z-score formula:
z = (X - μ) / σ
where μ is the mean and σ is the standard deviation of the distribution. We can standardize the values 358 and 373 using this formula:
z1 = (358 - 367) / 3 = -3
z2 = (373 - 367) / 3 = 2
Now we can find the probabilities of the two events separately using the standard normal distribution table or a calculator:
P(X < 358) = P(z < -3) ≈ 0.0013
P(X > 373) = P(z > 2) ≈ 0.0228
The probability of either event happening is the sum of the probabilities:
P(X < 358 or X > 373) = P(X < 358) + P(X > 373) ≈ 0.0241
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$900 is deposited in an account with 4%
interest rate, compounded continuously.
What is the balance after 10 years?
F = $[?]
Answer:
[tex]\$1342.64[/tex]
Step-by-step explanation:
We can represent the value [tex]A[/tex] of a quantity [tex]P[/tex] compounded continuously for [tex]t[/tex] years at [tex]r[/tex] rate of interest as:
[tex]A = P\cdot e^{rt}[/tex]
This formula uses the mathematical constant [tex]e[/tex] (approx. 2.72), which is the theoretical limit for continuous compounding.
Plugging the given values into the formula:
[tex]A = \$900 \cdot e^{(0.04 \, \cdot \, 10)}[/tex]
We can now solve for [tex]A[/tex].
↓ simplifying [tex]e[/tex]'s exponent
[tex]A = \$900 \cdot e^{0.4}[/tex]
↓ plugging into a calculator
[tex]A \approx \$1342.64222788[/tex]
↓ rounding to the nearest cent
[tex]\boxed{A \approx \$1342.64}[/tex]
Jenna threw a disc 18 yards to Karl, who threw it 11 yards in the same direction to Alice.
Start at 0 on the number line and move _____ to the right to represent Jenna throwing the disc to Karl.
Then move ______ to the right to represent Karl throwing the disc to Alice the result shows that.
Start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl. Then move 11 yards to the right to represent Karl throwing the disc to Alice the result shows that.
To represent Jenna throwing the disc to Karl, we need to move 18 yards to the right on the number line. This is because Jenna threw the disc directly to Karl, so the distance between them is 18 yards. Therefore, we can start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl.
To represent Karl throwing the disc to Alice, we need to move 11 yards to the right from Karl's position on the number line. This is because Karl threw the disc 11 yards in the same direction as Jenna threw it to him.
So, we can start at Karl's position on the number line (which is 18 yards to the right of 0) and move 11 yards to the right to represent Karl throwing the disc to Alice.
Overall, to represent the entire throwing sequence from Jenna to Karl and then to Alice, we can start at 0 on the number line and move 18 + 11 = 29 yards to the right.
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school administrator believes that the mean class GPAs for a given course are higher than the preferred mean of 2.75 at a significance level of 0.05, and checks a randomly chosen sample of 50 classes. Create a histogram, and calculate x, the t-statistic, and the p-value.
3.09
2.73
2.58
2.68
2.84
2.68
2.64
2.62
2.35
2.72
2.63
2.77
2.72
3.03
2.71
2.96
2.74
3.01
2.88
2.68
2.83
3.02
2.83
2.71
2.67
2.79
2.65
2.56
2.78
2.89
2.40
2.38
2.41
2.83
2.86
3.01
2.80
2.84
2.95
2.75
2.93
2.48
2.34
2.97
2.85
2.74
2.84
3.10
2.62
2.77
It can be concluded that there exists ‘insufficient evidence’ depicting that the ‘new mean GPA is more than 2.75’.
Therefore, X= 2.7532; T = 0.1203; P = 0.4524.
How to solveH0: ‘The mean class GPAs for a given course’ is equal to 2.75.
H1: ‘The mean class GPAs for a given course’ exceeds 2.75.
Our 'sample size' n = 50 and we calculate the ‘sample mean and sd’ with 'Excel', through its respective code ‘AVERAGE()’.
The resultant ‘sample mean’ xbar equals to 2.7532, while implementing the code ‘STDEV.S()’ gives us the ‘sample sd’ s being 0.188164.
The ‘hypothesized mean’ μ0 is again fixed at 2.75. Given that the ‘population sd is unknown’, we are obliged to perform a ‘t-test’ in order to receive our data.
Evaluating this test statistic provides us with-
T = (xbar-μ0)/(s/√n)
= (2.7532-2.75)/(0.188164/√50)
= 0.0032/0.0266
= 0.1203
Also, taking into account the 'degrees of freedom', which is (n-1), we figure out that it sums up to 49.
After conjuring a 'students t distribution', we get a P-value of 0.4524. Hereby, as the ‘P-value surpasses the significant level of 0.05’, the ‘null hypothesis fails to be dismissed’.
Consequently, it can be concluded that there exists ‘insufficient evidence’ depicting that the ‘new mean GPA is more than 2.75’.
Therefore, X= 2.7532; T = 0.1203; P = 0.4524.
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distinguish the number of solutions . show your work. explain how you know the number of solutions. -6x-4y=-4, 3x +2y=6
The number of solutions to the system of equations is n = 0
Given data ,
Let the first equation be represented as A
-6x - 4y = -4 be equation (1)
Let the second equation be represented as B
3x + 2y = 6 be equation (2)
Now , on simplifying , we get
-6x - 4y = -4
Multiply by -1 on both sides , we get
6x + 4y = 4
Divide by 2 on both sides , we get
3x + 2y = 2 be equation (3)
Now , the equation (2) and ( 3) are similar but the constant term is different
The slope of the first equation is -3/2 and the slope of the second equation is also -3/2. Since the slopes are the same, the two lines are parallel to each other.
When two lines are parallel, they never intersect, which means there are no common solutions for the system of equations
Hence , the equations are solved
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Please help.
Draw a sketch to show two
figures that have the same number of unit cubes
that look different from each other.
The two figures that have the same number of cubes are given.
We have,
The number of cubes in each figure drawn = 5 cubes
We can also find the area of each figure,
Consider each cube has a side of 2 cm
Figure 1:
Two rectangles.
So,
Area = 6 x 2 + 4 x 2 = 12 + 8 = 20 square units
Figure 2:
Area = 10 x 2 = 20 square units.
Thus,
The two figures that have the same number of cubes are given.
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The mean score, overbar(x), on an aptitude test for a random sample of 5 students was 73. Assuming that σ = 15, construct a 95.44% confidence interval for the mean score, μ, of all students taking the test.
Question 14 options:
A)
67.0 to 79.0
B)
59.6 to 86.4
C)
43 to 103
D)
62.9 to 83.1
The 95.44% confidence interval for the mean score, μ, of all students taking the test is 59.6 to 86.4.
What is confidence interval?A confidence interval is a range of values that is calculated from a sample of data. It provides a level of certainty, usually expressed as a percentage, that a population parameter lies within this range. It is used to estimate a population parameter, such as a mean, a proportion, or a difference between two means.
The 95.44% confidence interval for the mean score, μ, of all students taking the test can be calculated using the formula:
Confidence Interval = overbar(x) ± (1.96 x (σ/√n))
where overbar(x) is the mean score on the aptitude test, σ is the standard deviation of the population (15 in this case), and n is the sample size (5 in this case).
Plugging in the given values, we get:
Confidence Interval = 73 ± (1.96 x (15/√5))
= 73 ± (1.96 x 3)
= 73 ± 5.88
Therefore, the 95.44% confidence interval for the mean score, μ, of all students taking the test is 59.6 to 86.4.
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Express the answers in simplest form. A list contains the names of six anthropology students, two sociology students, and four psychology professor's new study, find the probability that the chosen student (a) A psychology student (c) A psychology student or an anthropology (d) Not a sociology student.
a) P(psychology student) = 1/3. b) P(psychology or anthropology student) = 5/6. c) P(not sociology student)= 5/6
How to find the probability that the chosen student(a) The probability of choosing a psychology student is the number of psychology students divided by the total number of students:
P(psychology student) = 4/(6+2+4) = 4/12 = 1/3
(b) The probability of choosing a psychology student or an anthropology student is the sum of the number of psychology and anthropology students divided by the total number of students:
P(psychology or anthropology student) = (4+6)/(6+2+4) = 10/12 = 5/6
(c) The probability of not choosing a sociology student is the number of non-sociology students divided by the total number of students:
P(not sociology student) = (6+4)/(6+2+4) = 10/12 = 5/6
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Mrs. Thomas made 31⁄2 gallons of tea for the family reunion. She estimates that each of the 17 family members will drink about 3 cups of tea that day. Did she prepare enough?
To wrap gift boxes joelle uses 24 yards if ribbon which us 8% of her total amount of ribbon. How many ribbons does she gave jn all
Joelle gave a total of 300 yards of ribbon in all
How many ribbons does she gave in allLet's assume that the total amount of ribbon Joelle has is "x" yards.
We know that 24 yards of ribbon is 8% of her total amount of ribbon. So we can write an equation:
0.08x = 24
To solve for x, we divide both sides of the equation by 0.08:
x = 24 ÷ 0.08
x = 300
Therefore, Joelle has a total of 300 yards of ribbon.
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Answer:
Step-by-step explanation: the answer is 300 just divide and you’ll get the answer that simple
Victoria bought a box of raisins and gave of the raisins to her younger brother.
About what percent of the raisins did she keep for herself?
F 30%
G 33%
H 66%
J 70%
The percent of the raisins that Victoria she keep for herself is 70%
How to calculate the percentageBased on the information, a percentage simply has to do with the a value or ratio which can be stated as a fraction of 100.
Since Victoria bought a box of raisins and gave 3/10 of the raisins to her younger brother. The percent of the raisins she keep for herself will be:
= (1 - 3/10) × 100
= 70%
Therefore, the percent of the raisins that Victoria she keep for herself is J 70%
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Victoria bought a box of raisins and gave 3/10 of the raisins to her younger brother.
About what percent of the raisins did she keep for herself?
F 30%
G 33%
H 66%
J 70%
If 30% of (B-A)= 18% of (A+B), then the ratio A:B will be
Answer:
1:4
Step-by-step explanation:
30% of (B - A) = 18% of (A + B)
0.3(B - A) = 0.18(A + B) (converting percentages to decimals)
0.3B - 0.3A = 0.18A + 0.18B (distributing on both sides)
0.3B - 0.18B = 0.18A + 0.3A (grouping like terms)
0.12B = 0.48A
Simplifying further gives:
B/A = 0.48/0.12 = 4/1
Therefore, the ratio of A:B is 1:4.
Let's start by simplifying the given equation:
30% of (B-A) = 18% of (A+B)
0.3(B-A) = 0.18(A+B)
0.3B - 0.3A = 0.18A + 0.18B
0.12B = 0.48A
B = 4A
Now we know that B is 4 times A.
To find the ratio A:B, we can express B in terms of A:
B = 4A
A:B = A/4A = 1/4
Therefore, the ratio A:B is 1:4.
Look at the simultaneous equations below. (1) 18 = 7x - y (2) 3x + y = 2 a) Rearrange equation (1) to make y the subject. b) Using your answer to part a), solve the simultaneous equations ck to task Watch video
Answer:
Explanation:
The solution to the simultaneous equations is x = 2 and y = -4. To obtain these values, 18 = 7x - y is rearranged to y = 7x - 18, and then substituted into 3x + y = 2 to obtain the value of x and y.
Rearranging equation (1) to make y the subject
18 = 7x - y
Add y to both sides
18 + y = 7x
Subtract 18 from both sides
y = 7x - 18
Using the answer to part a) to solve the simultaneous equations
Substitute the expression for y from equation (1) into equation (2)
3x + (7x - 18) = 2
Simplify
10x - 18 = 2
Add 18 to both sides
10x = 20
Divide both sides by 10
x = 2
Substitute x = 2 into equation (1) to find y
18 = 7(2) - y
18 = 14 - y
Subtract 14 from both sides
4 = -y
Multiply both sides by -1
-4 = y
Therefore, the solution to the simultaneous equations is x = 2 and y = -4.
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PLEASE HELP ME PLEASE LOOK AT THE PICTURE BELOW
Answer:
162 square units
Step-by-step explanation:
You want the surface area of the trapezoidal prism.
Base areaThe triangle at the top of each base is a right triangle with leg 3 units and hypotenuse 5 units. This tells you it is a 3-4-5 right triangle and the width of the prism is 4 units.
The area of each trapezoidal base is ...
A = 1/2(b1 +b2)h = 1/2(3 +6)(4) = 18 . . . . . square units
Lateral areaThe lateral area is the product of the height of the prism (7) and the perimeter of the base. The vertical edges of the base are 3 and 6, the horizontal edge is 4 (see above), and the slant edge is shown as 5. This means the perimeter is 3+6+4+5 = 18 units.
The lateral area of the prism is ...
LA = Ph = (18)(7) = 126 . . . . . square units
Total surface areaThe total surface area of the prism is the sum of the areas of the two bases and the lateral area:
2(18) +126 = 162 . . . . . . square units
The surface area of the composite solid is 162 square units.
__
Additional comment
If you have forgotten about the 3-4-5 right triangle, you can find the missing side length using the Pythagorean theorem.
a² +b² = c²
3² +b² = 5²
b² = 25 -9 = 16
b = √16 = 4 . . . . . . the missing triangle side is 4 units long
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The distribution of scores on the SAT is approximately normal with a mean of μ- 500 and a standard deviation of a 100. or the population of students who
have taken the SAT
a. What proportion of students have scores less than 380?
b. What proportion of students have scores greater than 639
a. The proportion of students have scores less than 380 is 11.51%.
b. The proportion of students have scores greater than 639 is 8.23%.
What is the proportion with SAT scores below 380 and above 639?1. Using the z-score formula:
We can calculate that score of 380 corresponds to a z-score of -1.2 since z = (x - μ) / σ.
Using a standard normal distribution table, we find that:
The proportion of students with scores less than 380 is 0.1151.2. Similarly, a score of 639 corresponds to a z-score of 1.39.
Using a standard normal distribution table, we find that:
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Given f(x)=x−1‾‾‾‾‾√ and g(x)=12x+5, what is the value of (f∘g)(2)?
Enter your answer in the box.
If f(x)= √(x−1) and g(x)=12x+5, then the value of (f∘g)(2) is 2√7.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
To find the value of (f∘g)(2), we first need to evaluate g(2), and then use the result as the input for f.
So,
g(2) = 12(2) + 5 = 24 + 5 = 29
Now, we use the value g(2) = 29 as the input for f:
f(g(2)) = f(29)
Since f(x) = √(x-1), we have:
f(29) = √(29-1) = √28 = 2√7
Therefore, the value of (f∘g)(2) is 2√7.
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A rectangle has sides measuring (2x + 7) units and (5x + 9) units.
Part A: What is the expression that represents the area of the rectangle? Show your work. (4 points)
Part B: What are the degree and classification of the expression obtained in Part A? (3 points)
Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
Answer:
A: (2x + 7)(5x + 9) = 10x^2 + 53x + 63
B: second-degree (quadratic) polynomial
C: The product of two polynomials is a polynomial.
Part A: we simply need to multiply this out using the distributive property:
Area = 2x5x + 2x9 + 75x + 79
= 10x² + 18x + 35x + 63
= 10x² + 53x + 63 (4 points)
Part B:A polynomial of degree 2 is called a quadratic polynomial. So, the classification of this polynomial is "quadratic". (3 points)
Part C:In the case of the set of polynomials, the closure property for multiplication says that multiplying any two polynomials results in another polynomial. This is demonstrated in Part A where we multiplied two polynomials - (2x + 7) and (5x + 9) - and the result was another polynomial - 10x² + 53x + 63. This shows that the set of polynomials is closed under multiplication. (3 points)
Part A:
The area of a rectangle is given by the product of its length and width. Therefore, for a rectangle with sides measuring (2x + 7) units and (5x + 9) units, the area can be represented as:
Area = (2x + 7)(5x + 9)
Now, we simply need to multiply this out using the distributive property:
Area = 2x5x + 2x9 + 75x + 79
= 10x² + 18x + 35x + 63
= 10x² + 53x + 63 (4 points)
Part B:
The degree of a polynomial is the highest power of x in the polynomial. Here, the highest power of x is 2 (in the term 10x²), so the degree of this polynomial is 2.
A polynomial of degree 2 is called a quadratic polynomial. So, the classification of this polynomial is "quadratic". (3 points)
Part C:
The closure property of an operation (like addition, multiplication, etc.) on a set says that applying the operation to any elements in the set always results in an element that is also in the set.
In the case of the set of polynomials, the closure property for multiplication says that multiplying any two polynomials results in another polynomial. This is demonstrated in Part A where we multiplied two polynomials - (2x + 7) and (5x + 9) - and the result was another polynomial - 10x² + 53x + 63. This shows that the set of polynomials is closed under multiplication. (3 points)
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You have a credit card with a current balance of $1500. The interest rate is 15.99%. If your minimum payment is 15% of your new balance, what is the balance of your card month 24? If your minimum payment is $75, what is the balance of your card month 24?
a) If the minimum payment is 15% on a credit card with a current balance of $1,500 and an interest rate of 15.99%, the balance of the card at month's end is $1,291.99.
b) If the minimum payment is $75 on a credit card with a current balance of $1,500 and an interest rate of 15.99%, the balance of the card at month's end is $1,293.99.
What is the credit card balance?The credit card balance refers to the difference between the beginning balance, payments, and interests.
a) Current balance on a credit card = $1,500
Interest rate = 15.99%
Minimum payment = 15%
= $225 ($1,500 x 15%)
Interest = $16.99 ($1,500 - $225 x 15.99% x 1/12)
Ending Balance = $1,291.99 ($1,500 +$16.99 - $225)
b) Current balance on a credit card = $1,500
Interest rate = 15.99%
Minimum payment = $75
Interest = $18.99 ($1,500 - $75 x 15.99% x 1/12)
Ending Balance = $1,293.99 ($1,500 +$18.99 - $225)
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what’s the value of x and y?
Answer:
the answer os 53
Step-by-step explanation:
The weatherman predicted that today's temperature would be 64°F. It was actually 38°F. What was the percent error of the weatherman's
prediction?
A 68.42%
B
40.63%
C 42.55%
D 64.82%
Answer:
Step-by-step explanation:
B. 40.63
Answer:
Step-by-step explanation:
B. 40.63
Plsss help this is hard giving 20 pnts!!!
Answer:I need part A to answer
Step-by-step explanation:
Wenona sketched the polynomial P(X) as shown on the axes below.
Which equation could represent P(X)
A.P(X)=(x+1)(x-2)^2
B.P(X)=(x-1)(x+2)^2
C.P(X)=(x+1)(x-2)
D.P(X)=(x-1)(x+2)
An equation that could represent P(x) include the following: A. P(x) = (x + 1)(x - 2)²
What is a polynomial graph?In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
Also, the graph has a zero of multiplicity 2 at x = 2 and zero of multiplicity 1 at x = -1;
x = 2 ⇒ x - 2 = 0.
(x - 2)²
x = -1 ⇒ x + 1 = 0.
(x + 1)
In this context, an equation that represent the polynomial function is given by:
p(x) = a(x - 2)²(x + 1)
By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, 4), we have;
4 = a(0 - 2)²(0 + 1)
4 = a4
a = 4/4.
a = 1
Therefore, the required polynomial function is given by:
p(x) = (x - 2)²(x + 1)
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You are biking to the library. When you are 75% of the way there, you realize you forgot a book. So you turn around and head back. When you are 1/3 of the way back, you realize you don't need the book, so you turn around again and bike 3.2 miles to the library. How far do you live from the library
The distance you live from the library, would be 6. 4 miles.
How to find the distance ?Assigning the distance between your house and where you can find books as x miles, we could approximate that initially you cycled 0.75x miles before retracing your route back a third of what had already been travelled; converting to 0.25x mile. Thus, at this stage, you will have covered an accumulated distance of 0.5x - taking into account earlier computations.
Realizing that borrowing such book would be unnecessary, you rode back to the library from whence you started- making it 3.2 miles. As you have advanced some length by travelling a cumulative distance of 0.5x from your private residence on previous trial, only another 0.5x miles stands between you and the target place after spinning around anew.
The equation is:
0. 5 x = 3. 2
x = 3. 2 / 0. 5
x = 6. 4 miles
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