The monthly payments will thus be $1,612.81.
The annual effective rate on this loan is 5.78%.
What is the loan payment formulae?We can use the following loan payment formula to determine the loan payment:
Loan Payment = [tex]\\\frac{p * \frac{r}{n} }{1 - (1 + \frac{r}{n} )^{-n *t} }[/tex]
where P = borrowed amount = $69,300
r = yearly interest rate (decimal) = 0.056
n = number of times compounded per year = 12
t = number of years = 4
When we plug in the values, we get:
Loan Payment = [69300 x (0.056/12)] / [1 - (1 + 0.056/12)^(-12*4)]
= $1,612.81 (to the nearest cent)
The monthly payments will thus be $1,612.81.
We can use the following calculation to obtain the effective annual rate:
Annual Effective Rate =[tex](1 + r/n)^{n-1}[/tex]
When we plug in the values, we get:
Annual Effective Rate =[tex](1 + 0.056/12)^{12 - 1}[/tex]= 0.0578 or 5.78%
As a result, the annual effective rate on this loan is 5.78%.
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Consider the probability that exactly 91
out of 153
registered voters will vote in the presidential election. Assume the probability that a given registered voter will vote in the presidential election is 59%
.
Step-by-step explanation:
We can use the binomial distribution to compute the probability that exactly 91 out of 153 registered voters will vote in the presidential election, assuming that the probability that any given registered voter will vote in the presidential election is 59%.
The probability mass function of the binomial distribution is:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where:
- n is the number of trials (in this case, the number of registered voters)
- k is the number of successes (in this case, the number of registered voters who will vote in the election)
- p is the probability of success on any individual trial (in this case, the probability that a given registered voter will vote in the election)
Using this formula, we can calculate:
P(exactly 91 out of 153 voters will vote) = (153 choose 91) * 0.59^91 * (1 - 0.59)^(153 - 91)
= 0.037
Therefore, the probability that exactly 91 out of 153 registered voters will vote in the presidential election is approximately 0.037, or about 3.7%.
Find x. Round your answer to the nearest tenth of a degree.
Applying the tangent ratio, the value of x, to the nearest degree is determined as: 41.8 degree.
How to Find x Using the Tangent Ratio?The formula we would use to find the value of x is the tangent ratio, which is expressed as:
tan ∅ = length of opposite side / length of adjacent side.
reference angle (∅) = x
Length of opposite side = 17
Length of adjacent side = 19
Plug in the values:
tan x = 17/19
x = tan^(-1)(17/19)
x ≈ 41.8 degree (to nearest tenth of a degree)
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peters annual salary was 35000 he earned a 4% raise. what is his new salary
Peter’s new salary by the given data is $36,400.
We are given that;
Salary= 35000
Percentage= 4%
Now,
To find Peter’s new salary, we need to add the amount of his raise to his old salary. The amount of his raise is 4% of his old salary, which means we need to multiply his old salary by 0.04 (or 4/100).
The amount of his raise is:
0.04 × 35000
= 1400
35000 + 1400
= 36400
Therefore, by the given percentage the answer will be $36,400.
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Peter’s new salary by the given data is $36,400.
We are given that;
Salary= 35000
Percentage= 4%
Now,
To find Peter’s new salary, we need to add the amount of his raise to his old salary. The amount of his raise is 4% of his old salary, which means we need to multiply his old salary by 0.04 (or 4/100).
The amount of his raise is:
0.04 × 35000
= 1400
35000 + 1400
= 36400
Therefore, by the given percentage the answer will be $36,400.
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Show that " if x and y are odd integers, then x+y is even" using an indirect proof ( a proof by contraposition)
Using a proof by contraposition we can see that the sum must be even.
How to use the proof by contraposition?Here we know that x and y are odd integers, then we can write thes two numbers as:
x = 2n + 1
y = 2m + 1
Where n and m are integers.
If we use the proof by contraposition, then we will assume that the outcome is also an odd number 2k + 1
Then we can write:
2n + 1 + 2m + 1 = 2k + 1
We can simplify this to get:
2n + 2m + 1= 2k
2(n + m) + 1 = 2k
So there we have an odd number is equal to an even number, that does not make sense, thus, the outcome of the sum can't be odd.
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Need this asap help me
Answer:
-1
Step-by-step explanation:
You want the average rate of change of the function shown in the graph between x=-1 and x=2.
Y-valuesThe y-value at x = -1 is 9.
The y-value at x = 2 is 6.
Rate of changeThe graph changes by 6-9 = -3 units as x changes by 2 -(-1) = +3 units.
The average rate of change is ...
(change in y) / (change in x) = -3/3 = -1
The average rate of change from x = -1 to x = 3 is -1.
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Use the graph to answer the question. graph of polygon ABCD with vertices at 0 comma 0, 5 comma 2, 5 comma negative 5, 0 comma negative 3 Determine the coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180°. A′(0, 0), B′(−2, 5), C′(5, 5), D′(3, 0) A′(0, 0), B′(2, −5), C′(−5, −5), D′(−3, 0) A′(0, 0), B′(−5, −2), C′(5, −5), D′(3, 0) A′(0, 0), B′(−5, −2), C′(−5, 5), D′(0, 3)
The coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180° are A′(0, 0), B′(−5, 2), C′(−5, −5), D′(0, 3).
What are Transformation and Reflection?
Single or multiple changes in a geometrical shape or figure are called Geometrical Transformation.
A geometrical transformation in which a geometrical figure changes his position to his mirror image about some point or line or axis is called Reflection.
To find the coordinates of polygon A'B'C'D' after a 180° rotation, we need to reflect each vertex across the x-axis and then the y-axis.
To reflect a point across the x-axis, we change the sign of the y-coordinate.
To reflect a point across the y-axis, we change the sign of the x-coordinate.
Using this method, we can find the coordinates of A'B'C'D':
A(0, 0) reflects to A'(0, 0) (no change)
B(5, 2) reflects to B'(-5, 2) (reflect across y-axis)
C(5, -5) reflects to C'(-5, -5) (reflect across y-axis)
D(0, -3) reflects to D'(0, 3) (reflect across x-axis)
Therefore, the coordinates of polygon A'B'C'D' are:
A'(0, 0), B'(-5, 2), C'(-5, -5), D'(0, 3)
Hence, the coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180° are A′(0, 0), B′(−5, 2), C′(−5, −5), D′(0, 3) and the graph is attached is in the attached image.
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calculate the lengths a, b, c, d, e, f, g and h
A.) The length of the missing part of the triangle would be given as follows;
a = 4
b = 3
How to calculate the length of the missing sides of the triangle?To calculate the missing part of the triangle, the sine formula should be used such as follows;
x /SinX = b/sinB
where;
x= 5
X = 90
b = ?
B = 37°
That is;
5/sin90 = b/sin37
make b the subject of formula;
b = 5× 0.601815023/1
= 3
a² = C²- b²
= 25-9
= 16
a = √16 = 4
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Write an equation to represent the function: reflected over the x-axis, then translated 6 units left
The equation of the transformed function is y = -f(x + 6)
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = x
On simplifying , we get
Reflecting over the x-axis: To reflect a function over the x-axis, we multiply the function by -1. This changes the sign of the y-coordinate of each point on the graph of the function. So, the function after reflection over the x-axis would be y = -f(x).
Translating 6 units left: To translate a function 6 units to the left, we replace x with (x + 6). This shifts the graph of the function horizontally to the left by 6 units. So, the function after translation 6 units left would be y = -f(x + 6)
Hence , the function is y = -f(x + 6)
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Solve
3 (6 +0.5 - 1.47)
What happens to a consistent slope when the y value starts to decrease and the x value remains the same over time?
A. Y decreases and X decreases
B. Y decreases and X increases
C. Y increases and X increases
D. Y increases and X decreases
Answer:
If the y value decreases while the x value remains the same over time, then the correct answer would be A. Y decreases and X decreases.
Step-by-step explanation:
Sure! A slope is a measure of the steepness of a line. It is calculated by dividing the change in the y-coordinates (rise) by the change in the x-coordinates (run) between two points on a line. The formula for slope is m = (y2 - y1) / (x2 - x1).
In your question, if the y value decreases while the x value remains the same over time, it means that the change in y-coordinates (rise) is negative while the change in x-coordinates (run) is zero. This results in a vertical line with an undefined slope. Therefore, the correct answer would be A. Y decreases and X decreases.
5. The coffee shop recently sold 3 cappuccino and 7 espresso drinks.
What is the probability the next drink will be an espresso?
Answer:
To find the probability of the next drink being an espresso, we need to know the total number of drinks sold.
In this case, the total number of drinks sold is:
3 cappuccinos + 7 espresso drinks = 10 drinks
The probability of the next drink being an espresso can be calculated by dividing the number of espresso drinks sold by the total number of drinks sold:
Probability of next drink being an espresso = Number of espresso drinks sold / Total number of drinks sold
Probability of next drink being an espresso = 7/10
Probability of next drink being an espresso = 0.7 or 70%
Therefore, the probability of the next drink being an espresso is 0.7 or 70%.
1. An acrobat is on a platform that is 25 feet in the air. She jumps down
at an initial vertical velocity of 4 ft/s. Write a quadratic function to
represent the height h of the acrobat t seconds after the jump.
If a safety net is placed 5 feet above the ground, how long will it take
for her to land safely on the net?
It will take the acrobat 1/4 of a second to land safely on the net.
What is velocity?Velocity is a physical quantity that measures the rate at which an object moves in a particular direction. It is measured in terms of distance traveled per unit of time, usually expressed in terms of meters per second (m/s). Velocity is a vector quantity, meaning it has both a magnitude and a direction. It is an important concept in physics and is used to understand the motion of objects and forces.
The quadratic equation representing the height h of the acrobat t seconds after the jump can be written as follows: [tex]h=-16t^2+4t+25[/tex].
To find the time it takes for the acrobat to land safely on the net, we need to solve for t when h=5. We can do this by substituting 5 for h into the equation and solving for t:
[tex]h=-16t^2+4t+25\\\\5=-16t^2+4t+25\\\\=-16t^2+4t-20=0\\\\(4+\sqrt{64})/(-32)=t\\ \\t=(4+8)/(-32)\\\\t=1/4[/tex]
Therefore, it will take the acrobat 1/4 of a second to land safely on the net.
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brainliest! Pls help! Determine the relationship between the two triangles and whether or not they can be proven to be congruent.
Answer:
The two triangles are related by Angle-Angle-Side (AAS), so the triangles are congruent.
A company has 7000 arrivals of Internet traffic over a period of 16,780 thousandths of a minute. Let the random variable
× represent the number of such Internet traffic arrivals in one thousandth of a minute. It appears that these Internet
-M
arrivals have a Poison distribution. If we want to use the formula ply= l"•é
to find the probability of exactly 3
X!
arrivals in one thousandth of a minute, what are the values of y, ×, and e that would be used in that formula?
The values we used in the Poisson probability formula are:
μ = λ = 0.4168
x = 3
e ≈ 2.718
What is Poisson probability?The Poisson probability distribution is a statistical distribution that models the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence of the events.
The Poisson distribution has a mean and variance of λ. Therefore, in this case, the mean and variance of the number of Internet traffic arrivals in one thousandth of a minute are equal to λ.
We can find the value of μ by dividing the total number of arrivals (7000) by the total time period (16,780):
μ[tex]= 7000/16,780 = 0.4168[/tex]
We can use μ as the value of λ in the Poisson distribution since they are equal.
To find the probability of exactly 3 arrivals in one thousandth of a minute, we use the Poisson probability formula:
P(x=3) = (e^(-λ) * λ^x) / x!
where x = 3.
Substituting the values we have:
[tex]P(x=3)[/tex][tex]= (e^(-0.4168) * 0.4168^3) / 3![/tex]
Using a calculator, we can evaluate e^(-0.4168) to be 0.6596, and simplify the denominator:
[tex]P(x=3) = (0.6596 * 0.0287) / 6[/tex]
[tex]P(x=3) ≈ 0.000305[/tex]
Therefore, the values we used in the Poisson probability formula are:
μ = λ = 0.4168
x = 3
e ≈ 2.718
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The values we used in the Poisson probability formula are:
μ = λ = 0.4168
x = 3
e ≈ 2.718
What is Poisson probability?The Poisson probability distribution is a statistical distribution that models the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence of the events.
The Poisson distribution has a mean and variance of λ. Therefore, in this case, the mean and variance of the number of Internet traffic arrivals in one thousandth of a minute are equal to λ.
We can find the value of μ by dividing the total number of arrivals (7000) by the total time period (16,780):
μ[tex]= 7000/16,780 = 0.4168[/tex]
We can use μ as the value of λ in the Poisson distribution since they are equal.
To find the probability of exactly 3 arrivals in one thousandth of a minute, we use the Poisson probability formula:
P(x=3) = (e^(-λ) * λ^x) / x!
where x = 3.
Substituting the values we have:
[tex]P(x=3)[/tex][tex]= (e^(-0.4168) * 0.4168^3) / 3![/tex]
Using a calculator, we can evaluate e^(-0.4168) to be 0.6596, and simplify the denominator:
[tex]P(x=3) = (0.6596 * 0.0287) / 6[/tex]
[tex]P(x=3) ≈ 0.000305[/tex]
Therefore, the values we used in the Poisson probability formula are:
μ = λ = 0.4168
x = 3
e ≈ 2.718
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This is volume and factors and i’m having a hard time with it, please help.
The highest temperature on Day 7 is equal to 60 degrees.
The day in which the highest temperature was 60 degrees is day 3.
Yes, the high temperature is a function of the day because it is dependent variable.
No, the day is not a function of the high temperature because it is an independent variable.
What is an independent variable?In Mathematics, an independent variable can be defined as the variable that is being manipulated by an experimenter, scientist, or a researcher.
This ultimately implies that, an independent variable is always considered as the cause in an experiment and it is represented by the x-axis value on a graph.
In this context, we can reasonably infer and logically deduce that time measured in days represent the independent variable while the highest temperature measured in degree Fahrenheit represent the dependent variable.
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Ten pieces of paper with the number 1 to 10 are placed in a hat. What's the probability of pulling out a number that is divisible by 2 or 3?
A.1/10
B.6/10
C.8/10
D. some other response
The probability of pulling out a number which is divisible by 2 or 3 will be 7/10 which is not given here. So, option D will be the answer.
How do we find Probability?
The measurement through which we find the likelihood of an event to occur is called probability. We cannot predict a lot of events with total certainty. And thus, the chance of a event to occur (i.e. how likely they re going to happen) can be predicted using probability.
Probability of any event to happen can be find as: No of favorable outcomes/Total number of outcomes.
Here,
The total no of outcomes = 1,2,3,4,5,6,7,8,9,10
No of favorable outcomes ={2,3,4,6,8,9,10} = 7
Therefore, P(E) = 7/10
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Aiden gives his dog a dose of liquid vitamins every day. Each dose is 5/8 teaspoon. If the bottle of vitamins contains 12 1/2 teaspoons, how many days will the bottle last Aiden?
Answer:
20 days
Step-by-step explanation:
We can model this situation using the linear equation, whose general form is
f(x) = mx + b, where m is the slope and b is the y-intercept
f(x) = -5/8x + 25/2, where f(x) is the amount remaining in the vitamin bottle and x is the number of days
Explaining the formula:
We know that the slope must be negative since each successive dose depletes the bottleA slope of -5/8 means that the amount in the bottle decreases by 5/8 tsp for 1 day that passes25/2 is simply 12 1/2 (a mixed number) converted to an improper fraction25/2 is the y-intercept because the bottle starts with 25/2 tsp and when no doses are given (i.e., x = 0), there are 25/2 tsp in the bottleWe essentially want to find the x value that will make f(x) = 0 since that is when the bottle will be empty:
0 = -5/8x + 25/2
-25/2 = -5/8x
20 = x
We can check by plugging in 20 for x and see whether we get 0:
0 = -5/8(20) + 25/2
0 = -25/2 + 25/2
0 = 0
A machine that cost $170,000 has an estimated residual value of $17,000 and an estimated useful life of four years. The company uses double-declining-balance depreciation.
Calculate its book value at the end of year 3. (Do not round intermediate calculations.)
In the most recent reporting period, the amount of cash paid by Nike for property, plant and equipment was (in millions)?
a.
$171.
b.
$695.
c.
$3,800.
d.
$4,904.
In the most recent reporting period, the amount of cash paid by Nike for property, plant and equipment was $4,904 million. The Option D is correct.
What are recognized as cash payment under property, plant and equipment section?The cash payments under property, plant, and equipment (PP&E) are recognized in a company's financial statements when they represent actual expenditures for acquiring, constructing, or improving long-term assets.
Some examples of cash payments that could be recognized under PP&E include the purchase price of land or buildings, expenses related to preparing land for its intended use, costs incurred to construct new buildings or renovate existing ones, expenditures to install or upgrade equipment etc.
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HELP ME PLEASE
The average child in elementary school brings home 13 pieces of paper to show their parents each week. Students at Little Kids Elementary School are in a program that is supposed to be more focused on digital work than paperwork. In one week, five students brought home to following number of papers: 14, 12, 18, 8, 11
Conduct the steps of hypothesis testing to determine whether there is a different amount of papers brought home by the kids at Little Kids Elementary School compared to normal.
The steps of "hypothesis-testing" for papers bought home are stating the Null and Alternate Hypothesis, find level-of-significance, collecting data, determining p-value, and making decision.
The "Hypothesis-Testing" is defined as a statistical method used to make inferences about a population based on a sample of data. It involves making a assumption about a population parameter (such as its mean or proportion) and then collecting data to test whether the hypothesis is likely to be true or false.
The steps of hypothesis testing are:
Step 1: State the "Null-Hypothesis"
The null hypothesis (H₀) is = average number of papers brought home by the kids at Little Kids Elementary School is the same as the average for the general population, which is 13.
⇒ H₀: µ = 13,
Step 2: State the alternative hypothesis
The "Alternative-Hypothesis" (Hₐ) is = average number of papers brought home by the kids at Little Kids Elementary School is different from 13.
⇒ Hₐ: µ ≠ 13,
Step 3: Determine the level of significance
Let "significance-level" be "α = 0.05". This means we accept a 5% chance of making a "Type I Error"
Step 4: Collect the data and calculate test-statistic
The sample mean of the number of papers brought home by the kids at Little Kids Elementary School is:
⇒ x' = (14 + 12 + 18 + 8 + 11)/5 = 12.6,
The sample standard deviation is:
⇒ s = √[((14-12.6)² + (12-12.6)² + (18-12.6)² + (8-12.6)² + (11-12.6)²)/4] ≈ 3.71
The "test-statistic" ⇒ t = (x' - µ)/(s/√n);
where n = sample size = (5),
⇒ t = (12.6 - 13)/(3.57/√5) = -0.25,
Step 5: Determine of "p-value",
The "degrees-of-freedom" = 4, ..because 5 - 1 = 4,
We know that "p-value" for t = -0.63 with 4 "degrees-of-freedom" is approximately 0.8103.
Step 6: Making decision and interpreting results
The p-value is 0.8103 which is greater than "significance-level" of (0.05),
So we fail to reject the null hypothesis. and say that there is not enough evidence to conclude that the average number of papers brought home by the kids at Little Kids Elementary School is different from the population mean of 13.
Therefore, we can say that the digital work program did not have a statistically significant effect on the amount of papers brought home by the students at Little Kids Elementary School.
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Find the value of y in each triangle
A) cos 35⁰ = y/5
=> y = cos 35⁰ × 5 ≈ 0.82 × 5 ≈ 4,1
B) cos 45⁰ = y/6
=> y = cos 45⁰ × 6 = (√2)/2 × 6 = 3√2
Answer: a) 4,1 b) 3√2
Ok done. Thank to me >:333
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
1) Percent of time that customers at the old store bought milk shakes is: 20%
2) Percent of time that customers at the new store bought milk shakes is:
26%
3) Percent of total sales that were ice cream is: 78%
4) Percent of new store sales of both shops is: 35%
How to find the percentage?We are given the following parameters:
Number of Servings of Icecream in Old store = 52100
Number of milk shakes in old store = 13400
Number of Servings of Icecream in New store = 25800
Number of milk shakes in new store = 9200
1) Percent of time that customers at the old store bought milk shakes is:
Percentage = [13400/(52100 + 13400)] * 100%
≈ 20%
2) Percent of time that customers at the new store bought milk shakes is:
Percentage = [9200/(25800 + 9200)] * 100%
≈ 26%
3) Percent of total sales that were ice cream:
Percentage = [(52100 + 25800)/(52100 + 25800 + 13400 + 9200)] * 100%
≈ 78%
4) Percent of new store sales of both shops is:
Percentage = (25800 + 9200)/(52100 + 25800 + 13400 + 9200)] * 100%
≈ 35%
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Help with this math.
Answer:
17cm
Step-by-step explanation:
Perimeter is the sum of all the sides.
4.5+4.5=9
4+4=8
9+8=17
A rectangular pyramid is shown in the figure. A rectangular pyramid with a base of dimensions 7 centimeters by 5 centimeters. The two large triangular faces have a height of 7.6 centimeters. The two small triangular faces have a height of 8 centimeters. What is the surface area of the pyramid? 64.1 cm2 93.2 cm2 128.2 cm2 256.4 cm2
The surface area of the pyramid is 128.2cm².
What is the surface area of the pyramid?
A pyramid is a three-dimensional building with triangular lateral faces and a polygonal base. A pyramid's surface area is simply the total area of all of its faces.
Here, we have
Given: A rectangular pyramid with a base of dimensions 7 centimeters by 5 centimeters. The two large triangular faces have a height of 7.6 centimeters. The two small triangular faces have a height of 8 centimeters.
We have to find the surface area of the pyramid.
The rectangular base of the pyramid has a length of 7 centimeters and a width of 5 centimeters, so the area of the rectangular base is 35 cm².
The two large triangular faces have a height of 7.6 centimeters, so the area of each of these faces can be calculated as:
= (1/2)×7×7.6
= 26.6 cm²
Similarly, the two small triangular faces have a height of 8 centimeters, so the area of each of these faces can be calculated as:
= (1/2)×5×8
= 20cm²
The total surface area of the rectangular pyramid is:
= 35cm² + 2×26.6 cm² + 2×20 cm²
= 128.2cm²
Hence, the surface area of the pyramid is 128.2cm².
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Michael has an average daily balance on his credit card of $327.50. His credit card charges 11.99% annual interest. What will his monthly finance charge be?
Answer:
First, we need to calculate Michael's daily interest rate:
0.1199 / 365 = 0.0003282
Then, we can calculate his daily finance charge:
327.50 x 0.0003282 = 0.1075
To find his monthly finance charge, we multiply his daily finance charge by the number of days in a month:
0.1075 x 30 = 3.225
So Michael's monthly finance charge will be $3.23 (rounded to the nearest cent).
For what values of x are the following expressions equal to each other. the binomials x^2 - 10x +31 and x+1
Answer:
To find the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other, we can set them equal to each other and solve for x.
Setting x^2 - 10x + 31 equal to x + 1:
x^2 - 10x + 31 = x + 1
Rearranging the equation to standard quadratic form:
x^2 - 10x + 30 = 0
Now, we can factorize the quadratic expression:
(x - 5)(x - 6) = 0
Setting each factor equal to zero and solving for x:
x - 5 = 0 or x - 6 = 0
x = 5 or x = 6
So, the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other are x = 5 and x = 6.
Answer:
To find the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other, we can set them equal to each other and solve for x.
Setting x^2 - 10x + 31 equal to x + 1:
x^2 - 10x + 31 = x + 1
Rearranging the equation to standard quadratic form:
x^2 - 10x + 30 = 0
Now, we can factorize the quadratic expression:
(x - 5)(x - 6) = 0
Setting each factor equal to zero and solving for x:
x - 5 = 0 or x - 6 = 0
x = 5 or x = 6
So, the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other are x = 5 and x = 6.
Answer:
x = 5 or x = 6
Step-by-step explanation:
Given expressions:
[tex]\begin{cases}x^2-10x+31\\x+1\end{cases}[/tex]
To find the values of x for which the given expressions are equal to each other, first set the expressions equal to each other and rearrange so that we have a quadratic equal to zero:
[tex]\begin{aligned}x^2-10x+31&=x+1\\x^2-10x+31-x&=x+1-x\\x^2-11x+31&=1\\x^2-11x+31-1&=1-1\\x^2-11x+30&=0\end{aligned}[/tex]
Factor the quadratic:
[tex]\begin{aligned}x^2-11x+30&=0\\x^2-6x-5x+30&=0\\x(x-6)-5(x-6)&=0\\(x-5)(x-6)&=0\end{aligned}[/tex]
Using the zero-product property, set each factor equal to zero and solve for x:
[tex]\begin{aligned}x-5=0 \implies x&=5\\x-6=0 \implies x&=6\\\end{aligned}[/tex]
Therefore, the values of x that make the given expressions equal to each other are x = 5 or x = 6.
Answer:
x = 5 or x = 6
Step-by-step explanation:
Given expressions:
[tex]\begin{cases}x^2-10x+31\\x+1\end{cases}[/tex]
To find the values of x for which the given expressions are equal to each other, first set the expressions equal to each other and rearrange so that we have a quadratic equal to zero:
[tex]\begin{aligned}x^2-10x+31&=x+1\\x^2-10x+31-x&=x+1-x\\x^2-11x+31&=1\\x^2-11x+31-1&=1-1\\x^2-11x+30&=0\end{aligned}[/tex]
Factor the quadratic:
[tex]\begin{aligned}x^2-11x+30&=0\\x^2-6x-5x+30&=0\\x(x-6)-5(x-6)&=0\\(x-5)(x-6)&=0\end{aligned}[/tex]
Using the zero-product property, set each factor equal to zero and solve for x:
[tex]\begin{aligned}x-5=0 \implies x&=5\\x-6=0 \implies x&=6\\\end{aligned}[/tex]
Therefore, the values of x that make the given expressions equal to each other are x = 5 or x = 6.
it’s geometry and i HATE geometry
Answer: <ABC = <GHI transitive property
Step-by-step explanation:
<ABC = <GHI transitive property
this is because if you have <B=<E and <H=<E then <B=<H
thisis a tranisitive property
jackson well middle school find area.
multiply each shapes by length x width
Step-by-step explanation:
an example:
5x3 is 15
then do that for all of the shapes in this photo then add all of your answer together to get you're area
hope this helps
Tom jogs 4 1/6 miles from his house. He then jogs 5 4/5 miles farther. How many miles has Tom jogged in all? Write your answer as a mixed number in simplest form.
Tom has jogged 9 29/30 miles in all.
How to solve for the distanceJust add the values that tells us all the distamnce that he jogged
Write the values as improper fraction
(25/6) + (29/5)
To add these fractions, we need to find a common denominator, which is the least common multiple (LCM) of 6 and 5. The LCM of 6 and 5 is 30. Now we can convert each fraction to an equivalent fraction with a denominator of 30:
(25/6) * (5/5) = 125/30
(29/5) * (6/6) = 174/30
Now, add the fractions:
(125/30) + (174/30) = (125 + 174) / 30 = 299/30
Now, let's convert this improper fraction back into a mixed number:
299 ÷ 30 = 9 (remainder 29)
So, the mixed number is 9 29/30.
Tom has jogged 9 29/30 miles in all.
Read more on distance here:https://brainly.com/question/7243416
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For the pyramid below draw the net and then calculate its total surface area using your net. ( picture is uploaded)
The total surface area of the pyramid from the net is 286 square cm
Calculating the total surface area from the netTo calculate the total surface area of a pyramid from its net, you need to add up the areas of all its faces.
The net of a pyramid is a two-dimensional representation of the pyramid, where the edges of the net represent the edges of the pyramid.
In this case, the nets are
Rectangle of: 10 by 7Pair of triangles of: 10 by 12.5, 7 by 13Using the above as a guide, we have the following:
Area = 10 * 7 + 2 * (1/2 * 10 * 12.5 + 1/2 * 7 * 13)
Evaluate
Area = 286
Hence, the surface area is 286 square cm
Read more about surface area at
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