The factors of given polynomial are (x+3), (x-3), (x+2) and (x-2).
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The given polynomial is x⁴-13x²+36
Here, x⁴-13x²+36 can be written as x⁴-9x²-4x²+36
= x²(x²-9)-4(x²-9)
= (x²-9)(x²-4)
= (x²-3²)(x²-2²)
By using the identity a²-b²=(a+b)(a-b)
So, (x+3)(x-3)(x+2)(x-2)
Therefore, the factors are (x+3), (x-3), (x+2) and (x-2).
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Someone pls help me with the bottom question 30 points
Answer: 9/4
Step-by-step explanation:
A scale factor is the number by which all components of an object are multiplied in order to create a proportional enlargement or reduction.
A mechanic had412 gallons of motor oil at the start of the day. At the end of the day, only 5 pints remained.
How many pints of motor oil did the mechanic use during the day?
Answer:
3,291 pints used
Step-by-step explanation:
There are 8 pints in a gallon
Started with 412 gallons, multiply that by 8 to get 3,296 pints
At the end of day, he only had 5
So we can subtract 5 from the 3,296 that he started the day with, and we get the answer of 3,291 used throughout the day.
88
myUT
Courses
Mortgage B: 381.93 12-30 = $137.494.80
Content attribution
Module 2.5 Unders
Content
Question
Stephen is comparing two mortgage options for his $80, 000 mortgage.
Mortgage A: 15 years at 4.5% with monthly payments of $611.99 and a total payb
$110, 158.20.
Mortgage B: 30 years at 4% with monthly payments of $381.93and a total paybac
$137, 494.80.
Provide your answer below:
Which option requires more interest to be paid over the life of the mortgage? How
Mortgage B requires $27,336.60 more interest than mortgage A. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
There are four fundamental mathematical operations that can be used to express any real number; these are referred to as "arithmetic operations." The four operations are multiplication, division, addition, and subtraction.
We are given the principal amount as $80,000.
So, interest on Mortgage A = Total amount payable - principal amount
Interest = $110,158.20 - $80,000
Interest = $30,158.20
Similarly, interest on Mortgage B = Total amount payable - principal amount
So,
Interest = $137,494.80 - $80,000
Interest = $57,494.80
So, difference in interest = $57,494.80 - $30,158.20 = $27,336.60
Hence, mortgage B requires $27,336.60 more interest than mortgage A.
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Each worker at a store gets paid $15.90 for that first 40 hours worked. After 40 hours, they earn time and a half wages. Every employee has a 28% of his/her gross pay deducted for taxes, insurance etc. how much of a net pay does each worker take home?
Each worker would take home a net pay of $586.71.
What is the net pay?
The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.
To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.
To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.
For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:
Gross Pay for 40 hours = $15.90/hour x 40 hours = $636
For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:
Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88
Therefore, their total gross pay would be:
Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88
Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:
Total Deductions = 28% x $814.88 = $228.17
Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:
Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71
Therefore, each worker would take home a net pay of $586.71.
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A certain antihistamine is often prescribed for allergies. A typical dose for a 100-pound person is 22 mg every six hours. Following this dosage, how many 12.3 mg chewable tablets would be taken in a week?
Answer:
x = 50 tablets
Step-by-step explanation:
Ket's call the number of tablets taken in a week "x".
A typical dose for a 100-pound person is 22 mg every six hours, so in 24 hours, they would take 22 mg * 24 hours / 6 hours = 88 mg.
In one week, they would take 88 mg * 7 days = 616 mg.
And since each tablet is 12.3 mg, they would take 616 mg / 12.3 mg/tablet = 50 tablets in a week.
So the answer is x = 50 tablets.
A researcher tested two groups (females and males) of rats on memory performance. The following scores are for the number of correct choices they made on the task:
The probability distribution does not add up to 1.0, in other words.
What is meant by probability?Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes.The study of events susceptible to probability is known as statistics. The probability is frequently stated as a ratio between the total number of outcomes in the sample space and the number of positive outcomes.This is how it is written: Number of Favorable Outcomes P(E) = Probability of an Event (Sample space).Probability can be divided into four main categories: axiomatic, axiomatic, classical, and empirical. The area of mathematics known as probability studies the likelihood that a random event will occur.The complete question is:
A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?
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Answer:
It is not accurate
Step-by-step explanation:
If the complete question is:
A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?
THEN:
To determine whether the probability distribution is accurate, we need to check two conditions:
The sum of the probabilities should be equal to 1.
All probabilities should be between 0 and 1.
Let's check these conditions:
Sum of probabilities:
p(0) + p(1) + p(2) + p(3) + p(4 or more) = 0.22 + 0.30 + 0.16 + 0.12 + 0.25 = 1.05
The sum of the probabilities is greater than 1, which violates the first condition. Therefore, this is not a valid probability distribution.
All probabilities should be between 0 and 1:
The probability of making 0, 1, 2, or 3 mistakes are all between 0 and 1, so they satisfy this condition.
However, the probability of making 4 or more mistakes is 0.25, which is a valid probability, but it implies that the probability of making 0, 1, 2, or 3 mistakes is negative, which is impossible. Therefore, this distribution does not satisfy this condition.
Since this probability distribution violates both conditions for a valid probability distribution, it is not accurate, and the researcher should revise their data.
find the sum of 10+3x,25-4x+2x^,3x^-5x and -x^+2x+15
Answer:
50 + 5x^2 + 4x.
Step-by-step explanation:
To find the sum of the expressions, we need to simplify each expression first and then add them up.
10 + 3x represents the first expression.
25 - 4x + 2x^2 represents the second expression. By simplifying this expression, we get 25 + 2x^2 - 4x.
3x^2 - 5x represents the third expression.
-x^2 + 2x + 15 represents the fourth expression.
Adding all four expressions gives us:
10 + 3x + 25 + 2x^2 - 4x + 3x^2 - 5x - x^2 + 2x + 15
By combining like terms, we get:
10 + 5x^2 + 4x + 25 + 15
The final simplified sum is:
50 + 5x^2 + 4x.
Please help!
An object is dropped from the top of a tower with a height of 1170 feet. Neglecting air resistance, the height of the object at time
t seconds is given by the polynomial -16t² +1170. Find the height of the object at t=2 seconds.
The height of the object at 2 seconds is _____ feet.
The height of the object at a time of 2 seconds is given as follows:
1106 feet.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
h(t) = -16t² + 1170.
At a time of 2 seconds, the height is found replacing the lone instance of t by two, hence:
h(2) = -16(2)² + 1170
h(2) = 1106 feet.
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A crew of construction workers are disassembling the inside of a building and dropping things into dumpsters at the base of the building. The equation Va=(64d)122
is used to find the average velocity, or speed, in feet per second of an object that has fallen a distance of d feet. What is the average velocity, to the nearest hundredth, of a ceiling tile that fell 43 feet ?
The average velocity, to the nearest hundredth, of a ceiling tile that fell 43 feet is 344 feet per second
What is speed?Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.
Given that the formula for the speed of a falling object is v= √64d,
where v is the speed of the object in feet per second and d is the distance the object has fallen, in feet.
And also given that d = 43 feet.
Substituting the value to the formula,
v = √64 (43)
v = 8 x 43
v = 344
Therefore, 344 feet per second is the velocity.
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Learning Page
QUESTION
We'd like to simulate the probabilities involved when Ivanna shoots two penalty kicks.
The table below gives a simulation of Ivanna shooting penalty kicks.
The table shows 10 trials. Each trial has two simulated penalty kicks.
Each simulated penalty kick is a random number from 1 to 100.
Trial
1
2
3
4
5
6
7
8
an
First
penalty kick
91
10
33
88
92
56
More Practice
4
92
45
40
39
Second
penalty kick
43
82
29
58
86
45
11
36
6
43
The correct answers are given below:
(a) 1 to 55
(b) 40%
How to solve thisSince Mansour scores 55% of his kicks, we'd want exactly 55% of the simulated numbers to denote Mansour scoring a penalty, thus, 1 to 5 is a possible range.
To find the percentage of trials where Mansour scored exactly one penalty, we have to count the trials where one of the simulated numbers is in the range of 1 to 5 (denoting Mansour scoring the penalty) and the other is in the range of 56 to 100 (denoting Mansour missing the penalty)
Trails 1, 3, and 4, 6 are such trials. Thus, Mansour scored exactly one penalty kick in 40% of the trials.
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Which of the following WAS NOT an impact of the crusades?
A. Change in culture in Europe
B. End of the Roman Empire
C. Monarchs grew more powerful
D. Many Christians were killed or badly injured
The option that was not an impact of the crusades is B. End of the Roman Empire.
What is the impact of the crusades?The Crusades were a series of religious wars fought between Christians and Muslims in the Middle East during the medieval period. The Crusades had a significant impact on European society and culture, including:
Monarchs grew more powerful: The Crusades helped to strengthen the power of monarchs in Europe, as they became more involved in financing and organizing the Crusades.
However, the Crusades did not bring about the end of the Roman Empire. The Roman Empire had already collapsed centuries earlier, in the 5th century AD, and the Crusades took place in the 11th-13th centuries AD, during the medieval period.
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A) In a geometric sequence, t_(1)=625 and the common ratio is r=(1)/(5). For what value of n is t_(n)=(1)/(25)?
b) Determine whether each sequence is arithmetic, geometric, or neither. Then find a formula for the n-th term of the sequence.
(2)/(5),(3)/(6),(4)/(7),(5)/(8),dots
Answer:
Step-by-step explanation:
A) In a geometric sequence, t_(1)=625 and the common ratio is r=(1)/(5). For what value of n is t_(n)=(1)/(25)?
Step 1: Write the formula for the nth term
The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.
Step 2: Substitute the given values into the formula
t_n = 625 * (1/5)^(n-1)
Step 3: Solve for n when t_n = (1/25)
(1/25) = 625 * (1/5)^(n-1)
(1/25) / 625 = (1/5)^(n-1)
(1/5)^(n-1) = (1/25) / 625
(n-1) = log base (1/5) of ((1/25) / 625)
Step 4: Solve for n
n = 1 + log base (1/5) of ((1/25) / 625)
The value of n is the number of terms that have passed when t_n = (1/25).
B) (2)/(5),(3)/(6),(4)/(7),(5)/(8),...
Step 1: Determine the type of sequence
A sequence is an arithmetic sequence if the difference between any two consecutive terms is constant. Since this sequence does not have a constant difference, it is not an arithmetic sequence.
A sequence is a geometric sequence if the ratio between any two consecutive terms is constant. We can see that the ratio between any two consecutive terms is constant, so this sequence is a geometric sequence.
Step 2: Find the common ratio
To find the common ratio, we can divide any two consecutive terms. For example, the common ratio is (3/6) / (2/5) = (3/2) / (6/5) = 5/6.
Step 3: Write the formula for the nth term
The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.
Step 4: Substitute the given values into the formula
To use this formula, we need to know the value of t_1. We are given t_1 = (2/5), so:
t_n = (2/5) * (5/6)^(n-1)
This is the formula for the nth term of the sequence (2)/(5),(3)/(6),(4)/(7),(5)/(8),...
10p - 3p/4- 2 +5 when p= 10
The value of 10p - 3p/4- 2 +5 for p=10 is 95.5.
What is Solution of Equation?An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Given:
We have 10p - 3p/4- 2 +5.
Now put the value of p =10 we get
= 10p - 3p/4- 2 +5
= 10(10) - 3(10)/4- 2 +5
= 100 - 30/4 -2 + 5
= 100 -7.5 -2 +5
= 95.5
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3. Juanita put $2,000 in a 6-month CD. The interest rate is 3%. The interest is compounded quarterly. What is the interest for the first quarter? What will be the value of the CD when it matures?
The interest for the first quarter would be $ 15
The value of the CD when it matures is $ 2, 030. 11
How to find the value of the CD ?The interest is said to compound quarterly which means that the periodic interest rate per quarter is:
= 3 % / 4
= 0. 75 % per quarter
The interest in the first quarter :
= 0. 75 % x 2, 000
= $ 15
The value of the CD at maturity is:
= 2, 000 x ( 1 + 0. 75% ) ²
= $ 2, 030. 11
Note : 2 periods because 6 months is 2 quarters.
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2.2 Kiri's older brother asked the 25 students in his class. 11 students said they think aliens exist. Which class has a greater percentage of students who think aliens exist: Kiri's or her brother's? Explain your thinking.
Answer:
The percentage of students in Kiri's brother's class who think aliens exist is 11/25 = 44%.
Since the number of students in Kiri's class is not given, it's not possible to compare the percentage of students in Kiri's class who think aliens exist to the percentage in her brother's class. We need to know the number of students in Kiri's class and the number of students who believe in aliens in order to compare the percentages.
Isabel wants to pour 90.45 grams of salt into a container. So far, she has poured 55.2 grams. How much more salt should Isabel pour?
By subtraction we get that, Isabel has to pour 35.25 grams of salt into the container.
What is subtraction?The operation or process of finding the difference between two numbers or quantities is known as subtraction. To subtract a number from another number is also referred to as 'taking away one number from another'.
According to the information in question:
Total salt = 90.45 grams
Amount of salt poured = 55.2 grams
Thus, the total amount of salt left with her which has to be poured will be calculated by subtraction:
Amount of salt left = 90.45 - 55.2
= 35.25 grams
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Does 0% percent on battery health of capacity mean your iphone will never turn on again or it will?
Answer asap for brainlist
Answer:
It will turn on again, just charge it. All phones come with a charger.
Stats Determine the y-intercept and slope from the equation: y = 5.8 +2.5x
The slope is 2.5
The y-intercept is 5.8.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
y = 5.8 + 2.5x
This is in the form of y = mx + c
So,
m = 2.5
And,
The y-intercept is when x = 0.
So,
y = 5.8 + 2.5x
Substitute x = 0,
y = 5.8
Thus,
Slope is 2.5
The y-intercept is 5.8.
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Use numerical evidence to estimate the value of the limit to at least 2 decimal places.
If the equation be [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex] then the value is 1.22222
What is meant by numerical evidence?The term "numerical evidence" describes information that is expressed in a numerical manner, such as numbers, quantities, or statistical data. It is thought to be objective and quantifiable, and it is used to support a claim or argument.
The quantity of sales made during a specific business quarter is an example of numerical data. Simply put, if the response includes a number, the data is quantitative (numerical).
Let the equation be [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex]
Simplifying the above equation, we get
[tex]$\frac{x^2-x-30}{x^2-3 x-18}= \frac{x+5}{x+3}$[/tex]
[tex]$=\lim _{x \rightarrow 6}\left(\frac{x+5}{x+3}\right)$$[/tex]
Plug in the value x = 6
= (6 + 5)/(6 + 3)
= 11/9 = 1.22222
Therefore, the equation of [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex] be 1.22222.
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Rewrite in simplest terms:-2(-10v+1)-6v
Answer:
14v-2
Step-by-step explanation:
1. distribute
2. combine like terms
see photo for more information
A cylinder shaped dispenser holds 5,652 cubic centimeters of liquid soap and is now full. The radius of the dispenser is 7. 5 centimeters. What is the difference between the height of the soap in the full dispenser and the height when 4,239 cubic centimeters of soap remains in the dispenser? use 3. 14 for pi. Enter your answer in the box.
Answer:
The difference in height is 8cm
Step-by-step explanation:
Volume of a cylinder=hπr²
When the bottle is full 5652:
5652=hπr²
5652=h*3.14*7.5²
5652=h*176.625
5652/176.625=h
Height=32cm
When the bottle is full by 4239:
4239=hπr²
4239=h*3.14*7.5²
4239=h*176.625
4239/176.625=h
Height=24cm
Difference in height:
32-24=8
The difference in height is 8cm
According to government data 22 percent of children in the United States under the age of 6 years live in households with incomes that are closed a pincome A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood if the government data are correct, which of the following best approximates the probability that at 27 percent of the children in the sample live in households that are closed at the particulo income level o represents a standard normal random variable)
Answer: [tex]p(z > \frac{0.27-0.22}{\sqrt{\frac{(0.22)(0.78)}{300} } } )[/tex]
Step-by-step explanation:
[tex]P=\frac{22}{100} =0.22, n=300[/tex] [tex]q=1-p=0.78[/tex]
[tex]p' = \frac{27}{100}=0.27[/tex]
[tex]p(z > \frac{p'-p}{\sqrt{\frac{p*q}{n} } } )[/tex]
[tex]p(z > \frac{0.27-0.22}{\sqrt{\frac{(0.22)(0.78)}{300}} }[/tex]
A rectangular field is four times as long as it is wide. If the perimeter of the field is 400 yards, what are the field’s dimensions?
Answer:
Answer is in the attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note the perimeter of the rectangle is:
2 x Length + 2 x Width.
Answer:
2 x Length + 2 x Width.
Step-by-step explanation:
Put the equation y=x^2-8x+12 into the form y= (x-h)^2+k
Answer:
y = ( x - 4 )² - 4
Step-by-step explanation:
a² ± 2ab + b² = ( a ± b )²
~~~~~~~~~~~~
y = x² - 8x + 12
y = ( x² - 2(4)(x) + 4² ) - 4² + 12 = ( x - 4 )² - 4
y = ( x - 4 )² - 4
Courtney can run a 1/4 mile in 2 minutes. At this rate, how many minutes will it take Courtney to
run 1.25 miles?
Answer:
10 minutes
Step-by-step explanation:
1/4 in 2 minutes
1 1/4 = 1/4 x 5
2 x 5 = 10
(That's REALLY good honestly)
7. Jane was shopping for oranges, which were listed $0.75 each. She brought seven the discount, she was charged $4.30 before tax. What was the percent discount on each oranges to the checkout lane, where she learned that there was a sale on oranges. With orange?
The discount on each orange is 81.3%
What is discount?The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.
A sales discount is a reduced price offered by a business on a product or service.
The total price for the oranges is;
0.75 × 7 = $5.25
She paid $ 4.30 for the oranges, this means that the discount = 5.25-4.30 = $0.95
Therefore the percentage discount on all the oranges = 0.95/5.25 × 100
= 18.1%
by discount each orange = 4.30/7 =$ 0.61
Therefore the discount on each orange = 0.61/0.75 ×100 = 81.3 %
Therefore the discount on each orange is 81.3%
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A helicopter hovers 1025 feet above a small island.The figure shows that the ang;e of depression from the helicopter to point P is 32 degrees. How far off the coast, to the nearest foot, is the island?
Answer:
The island is 728 feet off the coast.
Step-by-step explanation:
If 4x² = 16, then x =
A20
B12
C4
D2
The solution to the equation 4x² = 16 is x = 2.
What is the solution to the given equation?Given the equation in the question;
4x² = 16
x = ?
To solve for x, first divide both terms by 4.
4x² = 16
4x²/4 = 16/4
x² = 4
Take the square roots of both sides
√x² = ±√4
x = ±2
x = -2 or 2.
Therefore, the value of x is 2.
Option D)2 is the correct answer.
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Answer:
D.2
Step-by-step explanation:
[tex]4 {x}^{2} = 16 \\ \frac{4 {x}^{2} }{4} = \frac{16}{4} \\ {x}^{2} = 4 \\ \sqrt{ {x}^{2} } = \sqrt{4} \\ x = \sqrt{4} \\ x = 2[/tex]
Given: log a 2 = 4, log a 3 = 5, log a 5 = 8. Find log a 60.
A. 2.9
B. 1.46
C. .32
D. 2.1
The solution of the logarithm expression logₐ 60 is 2.1. Therefore, the answer is D.
How to solve logarithm?The logarithm expression can be solved as follows; Using the logarithm rule,
Law of multiplication of logarithm,
logₐ x + logₐ y = logₐ xy
Therefore,
logₐ 2 = 4
logₐ 3 = 5
logₐ 5 = 8
Hence, let's find logₐ 60.
logₐ 5 + logₐ 3 + logₐ 2 + logₐ 2 = logₐ (5 × 3 × 2 × 2) = logₐ 60
Hence,
0.8 + 0.5 + 0.4 + 0.4 = 2.1
Therefore,
logₐ 60 = 2.1
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The value of log a 60 is 21. The correct option is D.
What is a Logarithm?Logarithms are another way of writing exponents.
Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only.
log a 60 = log a (12 x 5)
log a 60 = log a 12 x log a 5
log a 60 = log a (4 x 3) x log a 5
log a 60 = log a 4 x log a 3 x log a 5
log a 60 = 2 log a 2 x log a 3 x log a 5
Substituting the values for the logs
log a 60 = 2 (4) + 5 + 8
log a 60 = 21
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Samir made a scale drawing of a city. He used the scale 5 inches = 1 yard. What scale factor
does the drawing use?
Simplify your answer and write it as a fraction.
Answer:
the scale factor that Samir used in his drawing is 5/1.
Step-by-step explanation:
Here's a step by step explanation of how to find the scale factor of a drawing:
Identify the scale used in the drawing. In this case, the scale used in Samir's drawing is 5 inches = 1 yard.
Express the scale as a ratio between the two sizes. In this case, the ratio is 5 inches : 1 yard.
Simplify the ratio, if possible. In this case, the ratio 5 inches : 1 yard can be simplified to 5/1.
The simplified ratio, 5/1, is the scale factor of the drawing. This means that for every 5 inches on the drawing, the actual length in the real world is 1 yard.
So, the scale factor that Samir used in his drawing is 5/1.
