The factored form of 26x^5 - 13x is 13x(2x^4 - 1).
What is the greatest common factor?
The greatest common factor (GCF), also known as the greatest common divisor (GCD) or highest common factor (HCF), is a concept in mathematics that refers to the largest positive integer that divides two or more integers without a remainder.
To factor 26x^5 - 13x using the greatest common factor, we need to find the greatest common factor of the two terms.
26x^5 = 213x^5
13x = 13*x
The greatest common factor of the two terms is 13x.
So we can factor it out:
26x^5 - 13x = (13x) (2x^4 - 1)
Hence, the factored form of 26x^5 - 13x is 13x(2x^4 - 1).
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As a town gets smaller, the population of its high school decreases by 5% each year. The senior class has 320 students now. In how many years will it have about 100 students? Write an equation. Then solve the equation without graphing.
The number of years until the town will have 100 students is given as follows:
22.68 years.
How to model the situation?A decaying exponential function is modeled as follows:
y = a(1 - r)^x.
In which:
a is the initial value.r is the decay rate.The parameter values for this problem are given as follows:
a = 320, r = 0.05.
Hence the function is given as follows:
y = 320(0.95)^x.
The time it will take for the population to have 100 students is x when y = 100, hence:
100 = 320(0.95)^x
(0.95)^x = 100/320
(0.95)^x = 0.3125
x log(0.95) = log(0.3125)
x = log(0.3125)/log(0.95)
x = 22.68 years.
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what is the x-intercepts of the following equation: f(x)=x^2+1
X intercept is none , y intercept is (0,1)
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
the distance from the origin to a point where a graph crosses a coordinate axis. : interception.
The x- and y-intercepts of a line, or linear equation intercepts, are often used in problems involving lines and their graphs. Linear equation intercepts are important points to be able to understand and decipher in applications of linear equations problems and can also be used when graphing lines.
f(x)=x^2+1=0
so the x intercept is none and y intercept is (0,1)
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simplify (6 x 10^-3) (4 x 10^-3) Write the answer in scientific notation.
Answer: 2.4 x 10^-2
Step-by-step explanation:
6 x 4 = 24 (you can do this because powers are the same)
24 x 10^-3
2.4 x 10^-2
Part B
How does each inverse function from part A relate to its original function? Describe the relationship in terms of the context for each situation. Do this for each of the three models
The inverse function takes the output of the original function and gives the input that would produce that output.
In mathematics, the inverse function (f^-1) of a function f(x) is a function that "undoes" the action of the original function. The relationship between a function f(x) and its inverse function f^-1(y) is such that if f(x) = y, then f^-1(y) = x. In other words, the inverse function takes the output of the original function and gives the input that would produce that output.
It's important to note that not all functions have inverse functions, a function may not have an inverse if it's not one-to-one function, that is, if it's output has more than one input that produces it.
Correct Question :
How does each inverse function f^(-1)y relate to its original function? Describe the relationship in terms of the context for each situation.
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Solve quadratic functions
Identify the a,b and c for each quadratic equations . The substitute into the quadratic formula to solve .find the solutions using technology.
1) b^2 -4=0
The required solution of the given quadratic equation are 2 or -2.
What is Quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x ax² +bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution.
According to question:We have,
b² -4=0
Here we will use identity a² - b² = (a+b)(a-b)
Then,
b² -4=0
b² - (2)² = 0
(b + 2)(b - 2) = 0
b + 2 = 0
b = -2
Or b - 2 = 0
b = 2
Thus,required solution of the quadratic function are 2 or -2.
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a spinner has eight equal-sized sections numbered 1 through 8. the spinner is spun twice. what is the probability of first spinning an odd number then spinning an even number?
The probability of spinning an odd number first then spinning an even number is 3/8 x 4/8 = 12/64.
This can be expressed as a fraction, decimal, or percentage. As a fraction, this probability is 12/64. As a decimal, this probability is 0.1875. As a percentage, this probability is 18.75%.
To calculate this probability, we first need to calculate the probability of spinning an odd number first. Since there are eight sections and four of them are odd numbers (1, 3, 5, 7), the probability of spinning an odd number is 4/8. We then need to calculate the probability of spinning an even number. Since there are four even numbers (2, 4, 6, 8), the probability of spinning an even number is 4/8. Finally, we multiply these two probabilities together to get the probability of spinning an odd number first then spinning an even number, which is 3/8 x 4/8 = 12/64.
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What part of an hour is 5 minutes?
Answer:
1/12
Step-by-step explanation:
An hour consists of 60 minutes and 5 minutes would be 1/12 of an hour.
5 minutes / 60 minutes
divide both sides by 5
1/12 of an hour
A company want to decreae their energy ue by 11%. If their electric bill i currently $1,700 a month, what will their bill be if they are ucceful? Give your anwer accurate to at leat the nearet dollar.
$
If the company' electric bill for next month i $1547, hould that be conidered a ucce?
Ye, that i a ucce
No, that i not a ucce
No, that i not a ucce, the electric bill need to be amount $1530 or le to be conidered a ucce.
To calculate the electric bill after the 11% decrease, simply multiply the current electric bill by 0.89, which is 1-11%. This will give you the new electric bill.
$1700 x 0.89 = $1530
Therefore, if the company's electric bill for next month is amount $1530 or less, then that would be considered a success.
The company must reduce their electric bill to $1530 or less in order to be considered successful in decreasing their energy usage by 11%.
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i do a lot of exrcice but in the exame i can"t anwer any quetion i don t know what i the recent
Exercise can be beneficial for academic performance in a variety of ways.
Improved cardiovascular health, for example, can lead to improved blood flow to the brain, providing a better environment for learning and memory formation. Exercise can also improve mental health, reduce stress, and increase energy levels, helping to better prepare for tests and exams. Finally, exercise can help to improve concentration, focus, and overall cognitive function.
The formula for calculating the potential benefits of exercise on academic performance is:
Academic Performance = Exercise + Improved Cardiovascular Health + Mental Health + Stress Reduction + Energy + Concentration + Focus + Cognitive Function
By increasing the amount of exercise, the individual can increase their academic performance. This is done by improving cardiovascular health, mental health, stress levels, energy, concentration, focus, and cognitive function. All of these factors play a role in academic performance, and increasing any one of them can lead to an overall improvement in academic performance.
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you are talking with 3 friends and the conversation turns to birthdays what is the probability that no two peopl ein your group were born in the same month
The answer is [tex]\frac{55}{96}[/tex] .
If A, B, and C are three dependent events,
P(A∩ B∩C) =P(A). P(A|B) .P(C|A∩B)
Let us use your birthday as a starting point.
Let A be the first friend who has a different birth month than you. Let B be the second friend who has a different birth month than friend 1 and you
Let C be the third friend who has a different birth month than friend 1, friend 2, and you
there are 12 months in a year
P(A∩ B∩C) =P(A). P(A|B) .P(C|A∩B)
P(A∩ B∩C) [tex]= \frac{11}{12} .\frac{10}{12} .\frac{9}{12}[/tex]
P(A∩ B∩C) [tex]= \frac{990}{1728} =\frac{55}{96}[/tex]
So, the result is [tex]\frac{55}{96}[/tex] .
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The area of the cross section of the prism is 30 cm2.
The length of the prism is 25 cm.
Work out the volume of the prism?
The required volume of the prism when area of cross section of the prism and the length of the prism are given is calculated to be 750 cm³.
Area of cross section of the prism = 30 cm²
Length of the prism = 25 cm
Volume of the prism = ?
A prism is a polyhedron consisting of an n-sided polygon base. The relation between volume, base area and height of the prism is mathematically given as,
V = B H
where, B is Base area
H is Height of prism
V = 30 × 25 = 750 cm³
Thus, the required volume of the prism when area of cross section of the prism and the length of the prism are given is calculated to be 750 cm³.
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If Jimmy has five apples and eats two how many does he have?
Answer:3
Step-by-step explanation:
Answer: Jimmy has 3 apples left.
Step-by-step explanation: 5-2=3
-1 = 4
-2 = 3
Three equidistant dots on each of two parallel lines are joined in all possible ways, how many triangles can be formed ?
Answer:
only one triangle can be formed ...
7. If WXWZ, what theorem
can be used to show that
APXW = APZW?
8. If XZ LWY and XY = ZY, what
theorem can be used to show that
AXYP = AZYP?
9. If XW || YZ and ZXWZZZYX,
what theorem can be used to show
that AXWZ = AZYX?
Find the probability of rolling
a 7 when you toss two fair 6-
sided dice and add the result
from each die.
Answer:
B. [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
imma human calculator and no one can stop me
Find the 9th term of the geometric sequence
9
,
−
18
,
36
,
.
.
.
9,−18,36,...
Answer: This is a geometric sequence, because each term is obtained by multiplying the previous term by a constant ratio. In this case, the ratio is -2.
To find the 9th term, we can use the formula for the nth term of a geometric sequence:
a_n = a_1 * r^(n-1)
where:
a_n is the nth term of the sequence
a_1 is the first term of the sequence (9)
r is the common ratio (-2)
n is the term number (9)
Plugging in the values:
a_9 = 9 * (-2)^(9-1) = 9 * (-2)^8 = 9 * -256 = -2304
So the 9th term of the sequence is -2304
3.2 x 0.8 = ___
256
25.6
2.56
0.256
Question 3(Multiple Choice Worth 5 points)
(03.01 LC)
Solve 22.83 x 104 = ___.
2,283,000
228,300
22,830
2,283
Question 4(Multiple Choice Worth 5 points)
(03.03 MC)
The aquarium in Key West has a display of 486 fish. How many fish would be in 25 displays?
12,610
12,150
10,620
3,420
Question 5(Multiple Choice Worth 5 points)
(03.07 MC)
542.6 x 3.7 = ___.
2,007.62
1,941.02
1,885.22
542.60
Question 6(Multiple Choice Worth 5 points)
(03.03 MC)
6,325 x 48 = ___.
303,600
291,260
284,760
75,900
Question 7(Multiple Choice Worth 5 points)
(03.07 LC)
Estimate the product of 653.2 x 4.6. What numbers does it lie between?
Between 2,612 and 3,265
Between 3,000 and 2,612
Between 5 and 654
Between 4 and 653
Question 8(Multiple Choice Worth 5 points)
(03.02 LC)
Solve 147 x 3 = ___.
548
441
428
321
Question 9(Multiple Choice Worth 5 points)
(03.05 MC)
6.84 x 57 = ___.
342.68
389.88
34,268
38,988
Question 10(Multiple Choice Worth 5 points)
(03.02 LC)
A garden at the Hemingway House contains 236 plants. If each garden had the same number of plants, how many plants would be in 7 gardens?
1,652
1,422
1,412
1,282
Question 11(Multiple Choice Worth 5 points)
(03.01 LC)
Solve 16 x 103 = ___.
16,000
1,600
160
16
Question 12(Multiple Choice Worth 5 points)
(03.05 MC)
At the food stand near Fisherman's Wharf, a drink costs $2.98. What is the cost of 75 drinks?
$223.50
$412.60
$2,235.00
$4,126.00
Question 13(Multiple Choice Worth 5 points)
(03.06 LC)
Choose the answer that best describes the estimate for 1.2 x 1.2 = ___.
The answer will be 24 because 12 x 12 = 144.
The answer will be greater than 1 because the decimals are greater than 1.
The answer will be equal to 1 because the decimals are the same number.
The answer will be less than 1 because the decimals are less than 1.
Question 14(Multiple Choice Worth 5 points)
(03.04 LC)
Estimate the product of 2,456 x 38 by rounding to the nearest thousand and ten.
120,000
93,328
80,000
60,000
Question 15(Multiple Choice Worth 5 points)
(03.03 LC)
52 x 26 = ___.
1,122
1,232
1,342
1,352
Answer:
#1 is 2.56
#2 is 2374.32
#3 is 19
#4 is 2,007.62
Step-by-step explanation:
3.2 x 0.8 = 2.56
Solve 22.83 x 104 =2374.32
The aquarium in Key West has a display of 486 fish. How many fish would be in 25 displays=12150
542.6 x 3.7 =2007.62
6,325 x 48 =303600
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded. Number of Hours Total Number of Students 0 1 1 3 2 3 3 10 4 9 5 6 6 3 Determine the probability that a student studied for exactly 5 hours. Round to the nearest hundredth.
According to the given information in the question rounded to the nearest hundredth, the probability is 0.14.
How is probability determined?Probability is a measure of how likely something is to occur. The probability is computed by dividing the total possible outcomes by the number of possible ways the event could occur.
What is the simplest approach to answer questions about probability?Adding the probabilities together will yield the chance of a simple event occurring. Your total chances of acquiring something are 10% + 25% = 35%, for instance, if you have an 10% opportunity to win $10 and a 25 percentage chance of getting $20.
The probability of a student studied for exactly 5 hours can be calculated using the formula for probability of a discrete event:
P(X = 5) = (number of ways to get a 5) / (total number of outcomes)
From the data provided, we know that 5 students studied for 5 hours. And there were a total of 35 students surveyed. So the probability is:
P(X = 5) = 5/35 = 0.14
Rounded to the nearest hundredth, the probability is 0.14.
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Suppose the original quantity is $30 and the new quantity is $39 estimate the percent change is this an example of a percent increase or a percent decrease
The percentage change is by 30% and it indicates percentage increase due to increase in new quantity.
The percent change will be calculated using the formula -
Percentage change = difference in quantity ÷ original quantity × 100
Difference in quantity will further be expressed by the formula -
Difference in quantity = New quantity - original quantity
Keep the values in formula for calculation. Firstly finding the difference in quantity.
Difference in quantity = 39 - 30
Performing subtraction
Difference in quantity = $9
Percentage change = 9/30×100
Performing division and cancelling zero
Percentage change = 30%
The mentioned scenario represents percentage increase.
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If a steel nail is wrapped 8 times with an insulated copper wire and each end of is attached to a 1.5 V single-A battery we find that it will lift the weight of 2 paper clips. Hypothesis: If 8 more coils are added to the nail we will be able to pick up twice as many paper clips. When we ran the experiment, we observed and recorded that when we added 8 more wraps around the nail (16 coils) we could lift 4 paper clips and when we added 8 more wraps (24 coils) we could lift 6 paper clips. Which of the following is/are true?
I. Something went wrong with the experiment since it didn't give us the results we expected.
II. The hypothesis was supported with the results of the experiment.
III. It can be concluded that every time 8 wraps are added to the nail, the total number of paper clips lifted doubles.
II and III only
II only
I only
I and III only
All of the statements that are true include the following:
II. The hypothesis was supported with the results of the experiment.
III. It can be concluded that every time 8 wraps are added to the nail, the total number of paper clips lifted doubles.
Therefore, the correct answer option is: A. II and III only.
What is a hypothesis?In Science, a hypothesis is primarily considered to be a tentative or an educated guess and it can be defined as a testable explanation for an observation, result, or a specific experimentation (scientific) problem, especially through the use of the "if . . . then . . . because" format.
Based on the information provided about this experiment, we can reasonably infer and logically deduce that the hypothesis developed about the steel nail is true because when eight (8) wraps of an insulated copper wire are added to the steel nail, the total number of paper clips that would be lifted is twice as many paper clips.
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One angle of an isosceles triangle measures 120°. What measures are possible for the other two angles? Choose all that apply.
80°
20°
30°
120°
For the right triangles below, find the values of the side lengths c and h.
Answer:
the answer is
c = 4
and h = √2/10
the california state university (csu) system consists of 23 campuses, from san diego state in the south to humboldt state near the oregon border. a csu administrator wishes to make an inference about the average distance between the hometowns of students and their campuses. describe and discuss several different sampling methods that might be employed. would this be an enumerative or an analytic study? explain your reasoning
There are several different sampling methods that could be employed for this study, including:
Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.
Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.
Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.
Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.
This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.
It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.
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Determine whether the pairs of triangles are congruent.
~Circle yes, no, or not enough information. Explain your choice.
How can I set up an equation to help solve this problem?
Check the picture below.
Evaluate the following expressions to help the astronauts prepare for take off. These numbers will help calculate the amount of time it will take to prepare for take off. In this case x = 4, y = 5, z = ½ 7x – 5y = minutes to secure the door. 12z + 2y2 = minutes to complete the system check. 2xy + 8z = minutes to fill pantry with astronaut food
If x = 4, y = 5, z = 1/2 , then
(a) It will take 3 minutes to secure door ,
(b) It will take 56 minutes to complete system check ,
(c) It will take 44 minutes to fill pantry with astronaut food .
The values of x , y and z are x = 4, y = 5, z = 1/2 ;
Part(a) ;
The Number of minutes to secure door is calculated the by expression
⇒ 7x - 5y .
Substituting values as x = 4 and y = 5 ,
we get ;
⇒ 7(4) - 5(5) = 28 - 25 = 3 minutes .
Part(b) ;
The Number of minutes to fill pantry with astronaut food is calculated the by expression :
⇒ 12z + 2y² ,
Substituting values as z = 1/2 and y = 5 ,
we get ;
⇒ 12z + 2y² = 12(1/2) + 2(5)² = 6 + 2×25 = 6 + 50 = 56 minutes .
Part(c) ;
The Number of minutes to complete system check is calculated the by expression
⇒ 2xy + 8z ,
Substituting values as x = 4 , z = 1/2 and y = 5 ,
we get ;
⇒ 2xy + 8z = 2(4)(5) + 8(1/2) = 40 + 4 = 44 minutes .
The given question is incomplete , the complete question is
Evaluate the following expressions to help the astronauts prepare for take off. These numbers will help calculate the amount of time it will take to prepare for take off.
In this case x = 4, y = 5, z = 1/2 ;
(a) Number of minutes to secure door is found by expression ⇒ 7x - 5y .
(b) Number of minutes to complete system check is found by expression ⇒ 12z + 2y² ,
(c) Number of minutes to fill pantry with astronaut food is found by expression ⇒ 2xy + 8z .
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Liam and Bryan each create a pattern. Liam's pattern starts at 7 and increases by 7 each time. Bryan's pattern starts at 4 and increases by 4 each time.
Liam's Pattern
7
14
21
28
Bryan's Pattern
4
8
12
16
When the number in Liam's pattern is 49, what is the corresponding term in Bryan's pattern? Enter the answer in the box.
The comparable word in Bryan's pattern is 28 whereas the number in Liam's pattern is 49.
What is an arithmetic sequence?The difference between every two successive terms in an arithmetic series is always the same. The number "a" is the first term, and "d" is the common difference between the. sequence. The nth term of an arithmetic sequence is given by. aₙ = a + (n – 1)d
Given this, we must first determine what is the position of 49 in Liam's pattern. Since Liam's pattern starts at 7 and increases by 7 each time, we can say that
d = 7
a₁ = 7
Substituting these values, we will get
49 = 7 + (n - 1) * 7
49 = 7 + 7n - 7
49 = 7n
n = 7
we are asked what is the corresponding term in Bryan's pattern when the number in Liam's pattern is 49. Since 49 is the 7th term in Liam's pattern, we need to find the 7th term in Bryan's pattern. As stated in the problem, Bryan's pattern starts at 4 and increases by 4 each time. This means that
d = 4
a₁ = 4 n = 7
Substituting these values, we will get
a₇= 4 + (7 - 1) * 4
a₇ = 4 + (6) * 4
a₇ = 4 + 24
a₇ = 28
Therefore, when the number in Liam's pattern is 49, the corresponding term in Bryan's pattern is 28.
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Gib alle reellen Zahlen x an, die die Gleichung lösen.
a) x2 - 16 = 0
Answer:
x = +4 , -4
Step-by-step explanation:
Solving the equation:x² - 16 = 0
x² = 16
[tex]\sf x = \sqrt{16}\\\\x = \sqrt{4*4}\\\\[/tex]
x = ±4
a college runner set a school record of 3 minutes and 59.37 seconds in the mile run. assuming that the distance was measured accurately to five significant figures, what was the runner's average speed in kilometers per hour? assume 1 km
The runner's average speed in kilometers per hour is 24.257 km.
The total distance covered by the runner is 1 mile. The relation between kilometers and miles is given as 1 km = 0.62 mi. Converting 1 mile to km by using the given relation, we get-
Distance = 1 mile
= 1 mile × [1 km/0.62 mile]
= 1.6129 km
The time taken to complete a 1-mile run is 3 minutes and 59.37 seconds. The relation between hours and minutes is given below.
1 hour = 60 minutes ……(1)
Converting 3 minutes to hours using equation (1), we get-
3 minutes = 3 minutes × [1 hour/60 minutes]
= 0.05 hours
The relation between hours and seconds is given below.
1 hour = 3600 second …….(2)
Converting 59.37 seconds to hours using equation (2), we get-
59.37 seconds = 59.37 seconds × [1 hour/3600 seconds]
= 0.016492 hours
Total time to cover 1 mile = (0.05 + 0.016491) hours = 0.066492 hours
The average speed of the runner is calculated by the following relation-
Average Speed = Distance (km)/time (hours)
= 1.6129 km/0.066492 hours
= 24.257 km/hour
Therefore, the average speed in kilometers per hour is 24.257km.
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sing horizontal analysis, the increases and decreases are shown as a.amounts and percentages for each line item. b.amounts for the highest three lines. c.amounts only for each line item. d.percentages only for each line item.
Answer: D. percentages only for each line item.
Horizontal analysis, also known as trend analysis, is a method of financial statement analysis that compares line items over time by expressing them as a percentage of a base year. The base year is typically the most recent year, and the comparison is typically made to the prior year. In horizontal analysis, the increases and decreases are shown as percentages for each line item, so that the changes in the line items can be easily compared and analyzed. This is different from vertical analysis, which shows the line items as a percentage of a total, such as total assets or total revenue.
Step-by-step explanation: