Sure! To reduce the fraction 5 to its lowest terms, we need to find the greatest common factor of 5 and divide both the numerator and denominator by it.
The greatest common factor of 5 and 5 is 5, so we divide both the numerator and denominator by 5 to get:
5 / 5 = 1
So, 5 reduced to its lowest terms is 1.
To make it kid-friendly, you could explain it like this: "We can simplify the fraction 5 by dividing the top and bottom by the biggest number that they both share. In this case, 5 is the biggest number that 5 and 5 share, so we divide both 5 and 5 by 5 to get 1."
A function has the following properties:
• It is increasing and linear when the value of x is between -5 and -3.
• It remains constant when the value of x is between -3 and 0.
• It is decreasing and linear when the value of x is between 0 and 3.
• It is increasing and nonlinear when the value of x is between 3 and 5.
Which graph best represents this function?
Answer:
c
Step-by-step explanation:
trust me
Written as a simplified polynomial in standard form, what is the result when
(x − 2)² is subtracted from 4x?
Step-by-step explanation:
(x-2)(x-2)-4x
x²-2x-2x +4-4x
x²-4x-4x +4
x²-8x+4
Answer:
4x - (x - 2)² = 4x - x² + 4 = 3x + 4
Step-by-step explanation:
the preimter of a rectangel measures 78 centimterers the measure of the with is 15 cenimeters what is the area of the rectangel
Answer:
360 cm^2
Step-by-step explanation:
The length of the rectangle can be found using the formula for perimeter:
Perimeter = 2 * (length + width)
Rearranging the equation, we can solve for the length:
length = (Perimeter - 2 * width) / 2
Plugging in the given values:
length = (78 - 2 * 15) / 2 = (78 - 30) / 2 = 48 / 2 = 24 cm
Next, the area of the rectangle can be found using the formula:
Area = length * width
Plugging in the given values:
Area = 24 * 15 = 360 cm^2
Complete the table.
q=p+7
Р
q
0
1
8
2
3
4
11
Given expression q=p+7
Expression can be defined as contains one or more variables and constants with one or more arithmetic operators.
Simply put the p values in the expression. solve it and get the q values.
q=p+7 in the place of p submit p=0
q=0+7
q=7
q=p+7 in the place of p submit p=2
q=2+7
q=9
q=p+7 in the place of p submit p=3
q=3+7
q=10
Therefore, The values of q are 7,9,10
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The missing numbers are:
7,9 and 10 when 0, 2, and 3 respectively.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given:
An equation,
q = p + 7.
Substituting the values of p:
When p = 0,
q = 0 + 7
q = 7.
When p = 2,
then q = 9.
And when p = 3,
q = 10
Therefore, all the required values are given above.
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A student's course grades and their corresponding weights are given in the table.
What is the minimum grade needed on the final exam to earn an overall grade of 83% in the class
Answer: 75%
Step-by-step explanation: To calculate,
(0.1 x 100) + (0.3 x 80) + (0.2 x 95) + (0.4 x 75) = 83%
Out of 1000 students who appeared for Cost accounting examinations,750 failed in maths,600 failed in accounts and 600 in costing,150 failed in both accounts and costing,450 failed in both maths and accounts,400 failed in both maths and costing.the students who failed all three subjects were 75.Prove that the above data is not correct
Answer: This data can be proven to be incorrect using the Principle of Inclusion-Exclusion.
The Principle of Inclusion-Exclusion states that for two events A and B, the number of elements in the union of A and B is equal to the sum of the number of elements in A and the number of elements in B minus the number of elements in their intersection.
Let's denote the number of students who failed in Maths as M, Accounts as A, and Costing as C.
From the information given, we have the following relationships:
M = 750
A = 600
C = 600
A ∩ C = 150
M ∩ A = 450
M ∩ C = 400
M ∩ A ∩ C = 75
Applying the Principle of Inclusion-Exclusion, the number of students who failed in at least one subject is:
M + A + C - (A ∩ C) - (M ∩ A) - (M ∩ C) + (M ∩ A ∩ C) = 750 + 600 + 600 - 150 - 450 - 400 + 75 = 925
However, the number of students who appeared for the exams is 1000, which means that the number of students who passed in all subjects should be 1000 - 925 = 75.
But we have already determined that the number of students who failed in all subjects is 75, which means that there are 75 students who are counted twice. This leads to a contradiction, and therefore the data given cannot be correct.
Step-by-step explanation:
Last year Kristen had $ 20 , 000 to invest. She invested some of it in the first account that paid 7 % simple interest per year, and she invested the rest of it in a second account that paid 8 % simple interest per year. After one year, she received a total of $ 1 , 540 in interest. How much did she invest in each account?
The amount invested in the account that earns 7% interest is $6,000 and the amount invested in the account that earns 8% interest is $14,000.
How much is invested in each account?The system of equations that represent the information in the question is:
a + b = 20,000 equation 1
0.07a + 0.08b = 1540 equation 2
Where:
a = amount invested in the account that earns 7% interest
b = amount invested in the account that earns 8% interest
The elimination method would be used to solve the equations.
Multiply equation 1 by 0.07
0.07a + 0.07b = 1,400 equation 3
Subtract equation 3 from equation 2
0.01b = 140
Divide both sides of the equation by 0.01
b = 140/ 0.01
b = 14,000
Substitute for b in equation 1:
a + 14,000 = 20,000
a = 20,000 - 14,000
a = 6,000
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Statistics: Suppose the population variance for a given
population is 36. If we select all possible samples of a certain size from this population, then, on average, what will be the value of the sample variance?
If we select all possible samples of a certain size from this population, then, on average, the value of the sample variance is 36.
What is a population?In Science, a population can be defined as a set of similar items or events that comprises every member of a group and from which a researcher, scientist, or experimenter, obtains or generates data for a statistical study.
What is a sample?In Statistics and science, a sample can be defined as a set of data that is collected from a population based on a well-defined sampling procedure.
In this context, we can reasonably infer and logically deduce that the sample variance on average would be equal to 36 because all possible samples of a certain size are selected from a population of 36 members.
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Solving right triangle
Answer:
[tex]BC= 2.23[/tex]
Step-by-step explanation:
We can solve this problem using the trigonometric identity of [tex]sin[/tex].
We know:
[tex]sin(\theta) = \frac{opposite}{hypotenuse}\\\\sin(50 \textdegree) = \frac{?}{3}\\[/tex]
If we solve for [tex]?[/tex] we get:
[tex]3sin(50 \textdegree) \approx 2.23[/tex]
PLEASE ANSWER QUICKLY!
For students majoring in Hospitality Management, it was determined that 5% have visited 1–10 states, 16% have visited 11–20 states, 45% have visited 21–30 states, 19% have visited 31–40 states, and 15% have visited 41–50 states. Suppose a Hospitality Management student is randomly selected. What is the probability that the student has visited 21 or more states?
A. 0.15
B. 0.21
C. 0.45
D. 0.79
The probability is 0.79 that a randomly chosen student has visited 21 or fewer states.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
from the given data we get,
The categories are mutually exclusive, so we have ...
P(≥21) = P(21-30) +P(31-40) +P(41-50)
= 45% +19% +15%
P(≥21) = 79%
=0.79
The probability is 0.79 that a randomly chosen student has visited 21 or fewer states.
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A boat has a top speed of 26 knots and a displacement of approximately 81,000 tons. Express the top speed in miles per hour and the displacement in metric tons. The boat has a top speed of approximately______mile(s) per hour. (Round to the nearest tenth as needed.)
The boat has a top speed of approximately 29.7 miles per hour and a displacement of approximately 73,934 metric tons.
Answer:
[tex]29.9[/tex] miles per hour
[tex]73482[/tex] metric tons
Step-by-step explanation:
We are given:
top speed of 26 knots
displacement of 81,000 tons
It is asking us to convert knots to miles per hour.
It is asking us to convert tons to metric tons.
We can use conversion factors to complete the unit conversions.
1 knot (kt) = 1.15077945 miles per hour (mph)
1 ton = 0.907185 metric tons
Numerical Evaluation
Lets convert our top speed.
We can set up an equation like this
[tex]\frac{1}{1.15077945} =\frac{26}{x}[/tex]
Lets solve for [tex]x[/tex].
Cross multiply.
[tex]1x=26*1.15077945[/tex]
Evaluate [tex]26*1.15077945[/tex].
[tex]26*1.15077945 =29.9202657[/tex]
Round to the nearest tenth.
[tex]29.9[/tex] miles per hour
Lets convert our displacement.
We can set up an equation like this
[tex]\frac{1}{0.907185 } =\frac{81000}{x}[/tex]
Lets solve for [tex]x[/tex].
Cross multiply.
[tex]1x=81000*0.907185[/tex]
Evaluate [tex]81000*0.907185[/tex].
[tex]81000*0.907185=73481.985[/tex]
Round to the nearest tenth.
[tex]73482[/tex] metric tons
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The weight of potato chips in a medium sized bag is stated to be 10 ounces. The amount that
the packaging machine puts in these bags is believed to be normally distributed with a mean of 10.2
ounces and a standard deviation of 0.12 ounces. Is it unusual for a bag to contain 9.8 ounces of
chips? Explain your answer.
Step-by-step explanation:
a normal distribution with mean m and standard deviation d gives us a few regular pieces of information.
for example, we know that 68.2% of all events are within the interval
m ± d
and 95.4% of all events are in the interval
m ± 2d
and 99.7% of all events are in the interval
m ± 3d
that means only 0.3% of all events are outside the interval
m ± 3d = 10.2 ± 3×0.12 = 10.2 ± 0.36
now, when a bag is filled with 9.8 ounces, it is 0.4 off the mean (10.2).
that means it is outside the 10.2 ± 0.36 interval and inside the 0.3% "exception" range.
you have to see it also that way : 0.3% means 3 out of 1000 bags are in that range.
so, yes, it is considered unusual.
18 What is the solution to the system of equations x - y = -1 and x-3y = - 13?
A. (5, 6)
B.
(6,5)
C. (7,8)
D.
(8,7)
The value of a car deprecates by 35% each year.at the end of 2007 the value of the car was £5460. Work out the value of the car at the end of 2006
Answer:
£3549
Step-by-step explanation:
The value of the car depreciates by 35% each year, so we can calculate the depreciation for 2006 as follows:
Depreciation for 2006 = 0.35 * £5460 = £1911
The value of the car at the end of 2006 is:
£5460 - £1911 = £3549
Answer:
The depreciation rate:
Step-by-step explanation:
Step 1: Total depreciation = 35% x 2 years = 70%
Step 2: Find the value of the car at the end of 2006:
Value at the end of 2006 = 5460 x (100 - 70)/100 = 1638
Therefore, the value of the car at the end of 2006 was £1638.
The figure below shows a rope that circles the Earth. The radius of the Earth is
6371
63716371 kilometers.
Assuming the rope makes a perfect circle, what is the length of this rope?
Give your answer in terms of pi.
Answer:
The circumference of a circle can be calculated using the formula:
Circumference = 2πr
Where r is the radius of the circle.
Plugging in the value for the radius of the Earth, we have:
Circumference = 2π(6371 km) = 12,742 km
So the length of the rope, assuming it makes a perfect circle around the Earth, would be 12,742 km = 2π(6371) kilometers.
Step-by-step explanation:
I Given that x is an Intergen write down the three lowest values of x in each of the Following. al 10-3x > 8 62 5x-27 > 7x solution
The lowest values of x are;
1. x = 1/2, x = 2/4, x = 3/6
2. x = 14, 15, 16
How to determine the valuesFrom the information given, we have that;
10-3x > 8
collect the like terms, we get;
-3x > 8 - 10
subtract the values
-3x > -2
Make 'x' the subject
x > 2/3
5x-27 > 7x
collect the like terms
5x - 7x> 27
subtract the like terms
-2x> 27
Make 'x' the subject
x > -27/2
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the sum of three consecutive odd integers is 19 less than twice the smallest of the three integers.
-17, -15 and -13 are the three consecutive odd integers.
Word problem involving linear equationLinear equation are equation that has a leading degree of 1
Let the smallest integer is '2x - 1'
The next two integers are 2x + 1 and 2x + 3
If the sum of three consecutive odd integers is 19 less than twice the smallest of the three integers, hence;
2x - 1 + 2x + 1 + 2x + 3 = 2(2x-1) - 19
6x + 3 = 4x - 21
6x - 4x = -21 -3
3x = -24
x = -8
First number = 2(-8) - 1 = -17
Second number = 2(-8) + 1 = -15
Third number = 2(-8) + 3 = -13
Hence the 3 consecutive odd integers are -17, -15 and -13.
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Complete question
The sum of 3 consecutive odd integers is 19 less than twice the smallest of integers , what are the integers?
2. The population of chickadees in a certain region is smaller by 30% than the population of
phoebes, and the population of blue jays is 30% of the population of phoebes.
The population of phoebes is 12,000.
Find the sizes of the chickadee and blue jay populations in the region.
The population of chickadees in the region is 8,400 and the population of blue jays is 3,600.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
First, we can find the population of chickadees by multiplying the population of phoebes by 0.7 (100% - 30%):
Population of chickadees = 0.7 x 12,000 = 8,400
Next, we can find the population of blue jays by multiplying the population of phoebes by 0.3:
Population of blue jays = 0.3 x 12,000 = 3,600
Therefore, the population of chickadees in the region is 8,400 and the population of blue jays is 3,600.
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A total of tickets were sold for the school play. They were either adult tickets or student tickets. There were fewer student tickets sold than adult tickets. How many adult tickets were sold?
There were 375 adult tickets sold and 316 student tickets for the school play.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let the number of student tickets would be x and the number of adult tickets would be y
As per the question, we have a system of equations:
x + y = 691 ....(i)
x = y - 59 ....(ii)
Substitute the value of x = y - 59 in equation (i),
y - 59 + y = 691
2y = 691 + 59
2y = 750
y = 375
Substitute the value of y = 375 in equation (ii), and solve for x:
x = 375 - 59
x = 316
Thus, there were 375 adult tickets sold.
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The complete question would be as:
A total of 691 tickets were sold for the school play. There were 59 fewer student tickets sold than adult tickets. How many adult tickets were sold?
ite the equations of the lines with the following properties Two points, (1, 3) and (9,8)
The linear equation that passes through the two given points is:
y = (5/8)*x + 19/8
How to write the linear equation?We want to find the equation of a line that passes through (1, 3) and (9, 8).
Remember that the slope of a line that passes through two points (x₁, y₁) and (x₂, y₂) is given by the equation:
slope = (y₂ - y₁)/(x₂ - x₁)
Here we know the two points (1, 3) and (9, 8).
Then the slope is:
slope = (8 - 3)/(9 - 1) = 5/8
We can write the line as:
y = (5/8)*x + b
To find the value of b,we can evaluate in one of the given points, for example, if we use (1, 3) then we will get:
3 = (5/8)*1 + b
3 = 5/8 + b
3 - 5/8 = b
24/8 - 5/8 = b
19/8 = b
The linear equation is:
y = (5/8)*x + 19/8
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Will your battery capacity go down if you update your iphone?
Unfortunately, a lot of software apps tend to use up battery life even if you aren't currently using the phone. This leads to the phone feeling more sluggish over time. To help combat this, it's helpful to clear out any unused apps and clear up the cache.
Even if software was perfectly written the most efficiently, and apps weren't intrusive, the physical nature of the battery itself has limitations. The capacity of the battery will slowly decay each time you charge or use your phone. Even just sitting idle it slowly loses capacity. This loss is very small that it's hard to detect. But add it up over time and the losses will get more noticeable. This is why you cannot simply charge a battery an infinite number of times. As with all things in life, there's a limit.
Summary: Yes the capacity will go down but ever so slightly. It depends how often the updates are done and what software is being updated. Ideally the updated software should be more efficient with the battery life. However, life isn't perfect and there will likely be flaws.
In the critical value method, we find the area in the tail end and compare it to alpha to determine whether to reject or fail to reject the null hypothesis.
The critical value strategy entails deciding whether or not the observed test statistic is more extreme than would be anticipated if the null hypothesis were true in order to determine whether something is "likely" or "unlikely."
How do you determine the rejection zone and the crucial value?
The rejection zone is the area in which we have sufficient data to reject the null hypothesis if our test statistic falls within it. The rejection area, for the right-tailed test, for instance, is any value bigger than the critical value, or c 1 .
To execute any hypothesis test, the critical value technique entails four specific phases, which are as follows:
The null and alternative hypotheses should be specified.Calculate using the sample data and the null hypothesis as the default. the test statistic's value Using the t-statistic t=m−μ÷s/√n which follows a t-distribution with n - 1 degrees of freedom, we may test the population mean hypothesis.By determining the value of the known distribution of the test statistic such that the likelihood of making a Type I mistake is low, also known as the "significance level of the test," or (greek letter "alpha"), the crucial value can be found (typically 0.01, 0.05, or 0.10).Assess the critical value against the test statistic. Reject the null hypothesis in favor of the alternative hypothesis if the test statistic is more extreme in the alternative direction than the crucial value. When the test statistic falls inside the acceptable range,To know more about critical value method visit:
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Isaac Newton sat under an apple tree to drink some tea and think. While he was thinking, an apple fell off a branch of the tree. The equation v=(19.8d)12
can be used to find the velocity, in meters per second, of the apple after dropping a distance , in meters. If the apple was connected to a branch 9 meters above the ground, what was the velocity of the apple, to the nearest hundredth, when it hit the ground?
The velocity of the apple, to the nearest hundredth, when it hit the ground is equal to 13.35 meters per seconds.
What is a function?In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.
How to determine the velocity of the apple?From the information provided about an apple that fell off a branch of the tree, a function that models the velocity of the apple include the following:
Velocity = (19.8d)^{1/2}
Where:
d represents the distance in meters.
Velocity = (19.8 × 9)^{1/2}
Velocity = (178.2)^{1/2}
Velocity = 13.35 meters per seconds.
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A company that bottles mustard is allowed to advertise their bottle size as 21 ounces as long as the actual amount in the bottle is within 0.15 ounces of that amount. Which inequality shows all the possible actual bottle volumes (v) that the manufacturer would be able to advertise as 21 ounces?
Answer:
Step-by-step explanation:
the Answer is b
the company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays except on Saturdays which is limited to the minimum of 4 water tankers a day. Calculate the total number of water loads that were supplied to the project on the constitution site by the water tanker in March 2022
Note that in order to solve the above, we had to assume a start date for the construction. Hence, by March 2022, a total number of liters supplied is 3,380,000 liters.
What is the rationale for the above response?
To solve the problem, we need to know how many weekdays are in March 2022. March 2022 has 23 weekdays (31 days - 4 Saturdays - 4 Sundays).
Since the company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays, we can assume an average of 14 water tankers per weekday. Therefore, the total number of water tankers to be supplied on weekdays in March 2022 would be:
14 water tankers/day x 23 weekdays = 322 water tankers
On Saturdays, the company has to supply a minimum of 4 water tankers. Since there are 4 Saturdays in March 2022, the total number of water tankers to be supplied on Saturdays in March 2022 would be:
4 water tankers/day x 4 Saturdays = 16 water tankers
Therefore, the total number of water tankers to be supplied in March 2022 would be:
322 water tankers (weekdays) + 16 water tankers (Saturdays) = 338 water tankers.
Assuming each water tanker carries a load of 10,000 liters, the total volume of water supplied to the construction site in March 2022 would be:
338 water tankers x 10,000 liters/tanker = 3,380,000 liters
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Full Question:
The company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays except on Saturdays which is limited to the minimum of 4 water tankers a day. Assuming the start month for the construction was February 2022, Calculate the total number of water loads that were supplied to the project on the constitution site by the water tanker in March 2022
Which is stronger? 3 scoops of coffee for 4 cups of water, or 4 scoops of coffee for 6 cups of water? Show Your Work.
The stronger one is 4 scoops of coffee for 6 cups of water.
How strong coffee is made?Strong coffee is prepared by employing a greater coffee grounds-to-water ratio. Typically, 2 teaspoons of coffee grinds are used for every 6 ounces of water in a strong cup of coffee. To make a truly strong cup of coffee, use 3 teaspoons of ground coffee for every 6 ounces of water. If you use a French press, you need also increase the steeping time.
In the given question, it is stronger to use 4 scoops of coffee for 6 glasses of water. This is due to the fact that there are more coffee grounds in relation to the amount of water, resulting in a higher concentration of coffee in the combination.
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1) Find the 9th term of the sequence:
60, 30, 15, ...
*
Answer:
Step-by-step explanation:
Let me explain step by step:
Determine the common ratio: We see that each term is half the previous term, so the common ratio is 1/2.
Write the formula for the nth term: We can use the formula for an infinite geometric series to find the nth term:
a_n = a_1 * r^(n-1), where a_1 is the first term (60), r is the common ratio (1/2), and n is the term number.
Plug in the values: We want to find the 9th term, so we plug in the values into the formula:
a_9 = 60 * (1/2)^(9-1)
Calculate the expression: We can simplify the expression by using the exponent rule for powers of 1/2:
a_9 = 60 * (1/2)^8
Divide the result by 256: We can simplify the expression further by dividing both sides by 256:
a_9 = 60 * 1/256
a_9 = 60 / 256
Get the final answer: We divide 60 by 256 to get the final answer:
a_9 = 0.234375
So the 9th term of the sequence is approximately 0.234375.
A 10-ft board is cut into 2 pieces so that one piece of 6 feet longer than 3 times the shorter piece. If the shorter piece is x feet long find the lengths of both pieces
The lengths of the pieces are 1ft and 9ft
How to determine the length of sides
From the information given, we have that;
The shorter side = x
The longer side of the board = 6 +3x
The total length = 10
Substitute the values, we have;
x + 6 + 3x = 10
collect the like terms
x + 3x = 10 -6
Add or substract the like terms, we have;
4x = 4
Now, make 'x' the subject of formula by dividing by 4, we get;
4x/4 = 4/4
x = 1 ft
The longer side = 9ft
Hence, the values are 1 and 9
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Help quick!! Which of the following tables represents a relation that is a function?
Explained answer please
D because none of the inputs (x) are repeated. All the others have the same input with two or more different outputs.
Which is NOT a liability?
A. Debt owed by a business
B. Debt that must be paid within the current year
C. Debt that must be paid after the current year
D. Machines, vehicles, furniture and appliances
Answer:
D. Machines, vehicles, furniture, and appliances are not considered liabilities. Liabilities are obligations or debts that a business owes to others. They are usually in the form of loans or accounts payable and represent money that must be paid in the future.
Machines, vehicles, furniture, and appliances are assets, which are resources that a business owns and that have monetary value. Assets can be sold to generate cash or used to produce goods or provide services. While assets can be used to secure loans, they do not represent a debt or obligation that must be paid in the future like a liability
Answer:
D
Step-by-step explanation:
current liability is money owed to suppliers in the form of accounts payable . Current liabilities are typically settled using current assets, which are assets that are used up within one year.
