The required greatest common factor in the given expression is 3x²y.
What is the greatest common factor?The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers include of.
here,
Given expression,
= 18x⁴y+3x³y²-39x²y³+12x²y⁴
Taking common 3x²y from every term,
= 3x²y(6x² + xy - 13y² + 4y³)
Where 3x²y id the greatest common factor,
Thus, In terms of the given expression 3x²y is the greatest common factor.
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7 (-5r+3) - 7r ≤ -29+8r solve the inequality
The value of r for the given inequality 7(-5r + 3) - 7r ≤ -29 + 8r is r ≥ 1.
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
7(-5r + 3) - 7r ≤ -29 + 8r
To determine the value of r, simplify the inequality,
-35r + 21 - 7r ≤ -29 + 8r
21 - 42r ≤ -29 + 8r
21 + 29 ≤ 42r + 8r
50 ≤ 50r
1 ≤ r
Or r ≥ 1.
The value of r is greater than or equal to 1.
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. Stanley needs to get 12 gallons of gas. He finds a gas station that is advertising their price at $3.479/gallon.
A. What will the cost be if the gas station rounds the final cost of gas (to the nearest hundredth) after all calculations?
B. What will the cost be if the gas station rounds their price per gallon (to the nearest hundredth) and then calculates the total price?
C. Which option will save Stanley money?
In case A:
The amount to be paid = $41.75
In case B :
The amount to be paid = $41.76
So, the Case A is better option.
Finding the right answer using the round off to nearest hundredth.
How to change any value to it's nearest hundredth ?
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.
Steps to find nearest hundredth of any value:
Step 1:
Since we need to round the given decimal number to the nearest hundredth, we mark the digit at the hundredths place.
Step 2:
Then, we observe the 'thousandths' place digit, which lies to the right of the hundredths column.
Step 3:
If the digit at the thousandths place is less than 5, we write the hundredths place digit as it is and remove all the digits to its right.
Step 4:
If the digit at the thousandths place is 5 or more than 5, we add 1 to the digit at the hundredths place, that is, we increase the hundredths place by 1 and remove all the digits to its right.
Case A :
The price for each gallon = $3.479
So, the total price for 12 gallon = $41.748
In case A total amount is rounded off
So, the price = $41.75
Case B :
The price for each gallon = $3.479
Rounding off the price for each gallon = $3.48
So, the total amount for 12 gallon = $41.76.
So, the case A is better option.
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Question 1 of 7 ✓
Question 1
>
The relationship between the amount of time a car is parked, in hours, and the cost of parking, in dollars, can be described with a function. Which
statements about the function are true? Select all that apply.
A
The parking cost is the function of the amount of time the car is parked and for 1 hour the cost of parking is $3 with a maximum amount of $12 for parking. The correct statements are C and D.
What is a function?A function is a relationship between the dependent and independent variables. The independent variables are function inputs, while the dependent variables are function outputs. The value of a dependent variable is determined by the input.
Here in the graph, the cost of parking is varying with time. It means that the cost of parking is dependent on the time of parking but the maximum amount for parking is $12 for any number of hours of car parking.
Hence, the correct statements are C and D.
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Simplify the fractions, show your work
35/90
3/36
Answer:
Step-by-step explanation:
35/90 gets devided by 5
7/18
3/36 gets devided by 3
1/12
Answer:35/90 = 7/18
3/36=1/12
Step-by-step explanation:
for 35/90 you divide both sides by 5 giving you 7/18 and 3/36 you divde both by 3 giving you 1/12.
Hope this helped
PLEASE HELP!
determine the truth value of each conditional.
1. Explain your reasoning or give a counterexample. if a figure has four congruent angles then the figure is a square.
2. if the sidewalks are wet, then it has been raining.
3. Write a biconditional for the following conditional. Determine the truth value of the new statement. If two lines have the same slope, then they are parallel.
the idea that there is a relationship in the population and that the relationship in the sample reflects this relationship in the population is referred to as:
The idea that there is a relationship in the population and that the relationship in the sample reflects this relationship in the population is referred to as Alternative Hypothesis.
Alternative Hypothesis:
In statistical hypothesis testing, the alternative hypothesis is one of the statements proposed in the hypothesis test. In general, the purpose of a hypothesis test is to show that, given the conditions, there is sufficient evidence to support the reliability of the alternative hypothesis rather than the sole assertion in the test (the null hypothesis) . It is usually consistent with research hypotheses because it is generated from literature reviews, previous studies, etc. However, in some cases the research hypothesis is consistent with the null hypothesis.
In statistics, the alternative hypothesis is often denoted by Ha or H1. Hypotheses are formulated to compare them in statistical hypothesis testing. In the field of inferential statistics, two competing hypotheses can be compared for their explanatory and predictive power.
For scalar parameters, there are four main types of alternative hypotheses:
Points: The point alternative arises when the hypothesis test is designed such that the population distribution under the alternative is a fully defined distribution with no unknown parameters. Such hypotheses are usually of no practical interest, but are fundamental to the theoretical considerations of statistical inference and form the basis of the Nyman-Pearson lemma.Unidirectional: The one-sided alternative addresses the rejection region on only one side of the sample distribution.Bidirectional: The two-sided alternative addresses both rejection regions of the sample distribution.Undirected: The undirected alternative hypothesis does not address any of the areas of rejection, only that the null hypothesis is not true.Learn more about Alternative Hypothesis:
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The sum of two numbers is 57 and the difference is 3. What are the numbers?
Answer:
The 2 numbers are 27 and 30
Step-by-step explanation:
Let call them x and y where x is the larger number and y is the smaller number :
x + y = 57 (obtained from the first line of the question)
x - y = 3 (obtained from the second line of the question)
Now we are going to use the rules of simultaneous equations to find x and y :
I will use elimination method :
Add the 2 equations to eliminate the y :
2x = 60
x = 30
Substitute x into equation 1 :
(30) + y = 57
Subtract 30 from both sides :
y = 57 - 30
y = 27
So
x = 30 and y = 27
As you can see the difference is also 3
The 2 numbers are 27 and 30
Hope this helped and have a good day
Please please please help me I need it asap! Please!!
Point A, located at (-11, -7) on the coordinate plane, is reflected over the x-axis to form point B. Then point B is reflected over the y-axis to form point C.
What are the coordinates of points B and C?
A: Point B: (-11, 7) Point C: (11, -7)
B: Point B: (11, -7) Point C: (11, 7)
C: Point B: (11, -7) Point C: (-11, 7)
D: Point B: (-11, 7) Point C: (11, 7)
presence, a statistical issue, refers to the finding that a systematic relationship exists between the two variables of interest in the population. true false
Presence: a statistical issue, refers to the finding that a systematic relationship exists between the two variables of interest in the population.
The above statement is False.
Presence refers to the finding that there is a systematic relationship between two variables in the population of interest.
Direction means knowing if the relationship is positive or negative.
Strength means knowing how long the relationship will last.
Systematic relationship is also known as Covariance. Covariance is a statistical term that refers to the systematic relationship between two random variables such that changes in the other reflect changes in one.
The relationship between probability and statistics usually falls into one of three categories: deterministic, random, or statistical. Statistical relationships are a hybrid of deterministic and random relationships.
A deterministic relationship involves an exact relationship between two variables. For example, let's say you earn $10 an hour. Earn $10 more for every hour you work.The random relationship is a bit misleading, as there is no relationship between the variables. However, random processes may make it seem related. For example, he spent $20 in the lottery and he won $25. This "win" is a coincidence, but you might think that for every $20 he spends on tickets, he gets $25 more (which is wrong, of course). TheStatistical relation is a hybrid of his two relations above. This is a relationship that is part deterministic and part random. For example, there is a statistical relationship between caloric intake and weight gain. However, the relationship is not exact. How much weight you gain depends on many other factors as well as randomness.Learn more about systematic relationship:
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An elected official surveyed residents of a town to assess their satisfaction with city services. the survey includes both those who own and those who rent their homes. level of satisfaction high medium low total owners 26 34 18 78 renters 15 12 5 22 total 41 46 23 110 what proportion of those surveyed have low satisfaction with city services? 0.2091 0.2308 0.2644 0.3727
The proportion we get is 0.291 and that matches up with our first choice that we see.
What is proportion?A proportion simply means the amount or quantity of a thing present in another thing taken as whole.
What are the applications of proportion?The main purpose of stating stuff in proportions is to compare shares. If 2 people receive shares in a 1:1 proportion, it means they have exactly equal shares. If 2 people invest in something and one partner invests $3 for every $2 the other invested, the major partner would expect the profits to be divided 3:2 in their favor.
This issue informs us that a town's residents were polled by an elected official to see how satisfied they were with the town's services. Both homeowners and renters were included in the survey. The following charts show the percentage of respondents that are unsatisfied with city services. In order to calculate the percentage of surveys with low satisfaction, we only need to consider the third column to the right, which is labeled "low satisfaction," and the number we are interested in is the 1, which corresponds to the row labeled "total," because it represents the total number of survey respondents who have low satisfaction, whether or not they are home owners or renters. This number is 23 points.
But that only represents the whole population of those with low levels of satisfaction. We can find the total number of respondents in the cross section between the total column and the total row, giving us 110 points. We wish to multiply that total for the low level by the entire number of respondents. Therefore, if we want that proportion right away, we need divide 23 by 110 points. When we round off to four decimal places, the result is 0.291, which corresponds to our initial option that we see.
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Answer:
A - 0.2091
Step-by-step explanation:
I took it
A triangle has side lengths of (9v-7w)(9v−7w) centimeters, (7v+10x)(7v+10x) centimeters, and (8x+5w)(8x+5w) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Perimeter of triangle is P= 18x+16v-2w.
How do triangles work?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a single point.
The triangle's three angles add up to a total of 180 degrees.
.
side lengths of a triangle are (9v-7w),(7v+10x),(8x+5w) centimetres.
We know that perimeter of the triangle is sum of all the three sides.
So here perimeter p= addition of all sides of a triangle.
Therefore ,
P = ( 9v - 7w) + (7v + 10x ) + ( 8x + 5w)
= 9v - 7w + 7v + 10x + 8x + 8w
= 18x + 16v - 2w
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32 feet
21 feet
< Previous
8 feet
12 feet
Which of these boards could be used for his project?
OA, B, and C
OA, B, and D
OD, C, and A
OD, C, and B
Work is done by A in one day [tex]$=\frac{1}{15}$[/tex]
By B [tex]$=\frac{1}{12}$[/tex]
[tex]\mathrm{C}=\frac{1}{20}[/tex]
boards could be used for his project
Together in 1 Day [tex]\text { Together in } 1 \text { Day }=\frac{1}{15}+\frac{1}[/tex][tex]{12}+\frac{1}{20}=\frac{4+5+3}{60}=\frac{12}{60}=\frac{1}{5}[/tex]
2 days work [tex]$=\frac{2}{5}$[/tex]
Remaining work [tex]$=1-\frac{2}{5}=\frac{3}{5}$[/tex]
one day work of [tex]$\mathrm{A}, \mathrm{B} \Rightarrow \mathrm{A}+\mathrm{B}=\frac{1}{15}+\frac{1}{12}=\frac{4+5}{60}=\frac{9}{60}=\frac{3}{20}$[/tex]
[tex]$$\begin{aligned}& (A+B) \text { work for } t \text { days }=\frac{3}{20} t=\frac{3}{5} \\& t=4 \text { days }\end{aligned}$$[/tex]
A and B will complete the work in 4 days.
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Y-2/3x=-6. Find the value of y.
20 POINTS!!!!!!
Write 0.000000648 in scientific notation.
648 × 109
6.48 × 107
6.48 × 10−7
648 × 10−9
The scientific notation of the given number will be equal to 6.48 × 10⁻⁷. Hence, option C is correct.
What is a scientific notation?A way to express numbers that are either too large or too little to be conveniently stated in decimal form is through scientific notation. It is also known as "scientific form" in Britain because researchers, mathematicians, and engineers frequently use it for intricate calculations involving large numbers.
As per the given information in the question,
The given number is,
0.000000648
As we move towards the right of the given point then the power will be in negative form.
So, it can also be written as,
6.48 × 10⁻⁷
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the answer is C:
6.48 × 10−7
Your algebra final exam is worth 150 points and contains 60 questions. Some of the questions are worth two
points and some are worth five points. How many two-point and five-point questions are on the test?
There are 50 two-point questions and 10 five-point questions on the test.
What is a linear equation in two variables?
A linear equation in two variables is an equation that can be written in the form Ax + By = C, where A, B, and C are constants and x and y are variables. The graph of a linear equation in two variables is a straight line, and the equation represents a linear relationship between the variables.
To solve this problem, you can use the fact that the total number of points on the test is 150 and that some of the questions are worth two points and some are worth five points.
Let x represent the number of two-point questions on the test, and let y represent the number of five-point questions on the test.
We can set up the following system of equations to represent the given information:
2x + 5y = 150
x + y = 60
To solve this system, you can use the substitution method. First, solve the second equation for y:
y = 60 - x
Substitute this expression for y into the first equation:
2x + 5(60 - x) = 150
This simplifies to:
2x + 300 - 5x = 150
Combine like terms:
-3x = -150
Divide both sides by -3:
x = 50
Substitute this value for x into the second equation to find the value of y:
y = 60 - 50 = 10
Hence, there are 50 two-point questions and 10 five-point questions on the test.
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Greg the doggo has a rectangular playpen that he and the other dogs can "chill" in. The playpen has an area of 32 square feet . The pen's length is 4 feet longer than its wide.
Include an equation to represent this situation.
The required equation for the width of the rectangular playpen is w² + 4w -32 = 0.
What is a rectangle?The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.
here,
let the length be l and width be w,
According to the question,
l = w + 4
Now,
Area of the pen = length × width
Area of the pen = (w + 4) × w
32 = w² + 4w
w² + 4w -32 = 0
Thus, w² + 4w -32 = 0 is the required equation that represents the rectangular playpen.
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What is the solution of the system of equations below?
x + 3y = 7
2x - y = 7
Answer:
y = 1
x = 4
Step-by-step explanation:
x + 3y = 7 → ( 1 )
2x - y = 7 → ( 2 )
First, let us make x the subject in equation ( 1 ).
x = 7 - 3y → ( 3 )
Let us find the value of y.
For that let us take equation (1) & replace x with ( 7 - 3y ).
2x - y = 7
2 ( 7 - 3y ) - y = 7
Solve the brackets.
14 - 6y - y = 7
Combine like terms.
14 - 7y = 7
Subtract 14 from both sides.
-7y = 7 - 14
-7y = -7
Divide both sides by -7.
y = 1
Let us find value of x
For that let us take equation (3) & replace y with 1.
x = 7 - 3y
x = 7 - 3 × 1
x = 7 - 3
x = 4
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The true statements about the circle are
The radius of the circle is 3 units.The center of the circle lies on the x-axis.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. How to determine the true statements about the circle?From the question, we have the following parameters that can be used in our computation:
x² + y² - 2x - 8 = 0
Generally, To convert this equation to standard form, we need to complete the square.
First, we can rearrange the terms on the left-hand side of the equation so that all the x terms are together and all the y terms are together:
x² - 2x + y² - 8 = 0
Then, we need to add and subtract a value that allows us to rewrite x² - 2x term as a perfect square.
To do this, we take half of the coefficient of the x term (which is -2), square it, and add it to both sides of the equation:
So, we have
x² - 2x + (1²) + y² - 8 = 0 + (1²)
Evaluate
(x - 1)² + y² - 8 = 1
Finally, we can rearrange the terms
So, we have
(x - 1)² + y² = 9
Express 9 as the square of 3
(x - 1)² + y² = 3²
So, the standard form of the equation is (x - 1)² + y² = 3²
The standard equation of a circle is represented as
(x - a)² + (y - b)² = r²
Where
Center = (a, b)
Radius = r
When these equations are compared, we have
Center = (a, b) = (-1, 0)
Radius = r = 3
The point (-1, 0) lies on the x-axis
This means that the center is on the x-axis.
Also, it means that the radius of the circle is 3 units
This radius is the same for a circle that has the form x² + y² = 9
This is so because 9 can be expresses as the square or 3, and r = 3
Hence, the correct statements are (a), (b) and (e)
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Complete Question
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true?
Select three options.
The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.A game uses an unbiased die with faces numbered 1 to 6. The die is thrown once. If it shows an even number this number is doubled to get the final score. If an odd number is thrown then the die is thrown again and the final score is the sum of the numbers shown on the two throws.
Given that the dice was thrown twice. What is the probability that the final score is 8
HELP ME PLEASE!!!!!!!!!
The length of a cell phone is 1.41.4 inches and the width is 3.43.4 inches. The company making the cell phone wants to make a new version whose length will be 1.541.54 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answer:
Step-by-step explanation:7.48521878104
Convert 940 hours into a year Round answer to the nearest hundredth
Answer:
0.41 years
Step-by-step explanation:
940 hours is equivalent to 0.41 years. When rounded to the nearest hundredth, that would be 0.00 years. It is not possible to convert hours directly to years because they are different units of time measurement. Years are a measure of the time it takes for the Earth to orbit around the Sun, while hours are a measure of time within a day. To convert hours to years, you would need to know the number of hours in a year, which can vary depending on the number of days in the year and the number of hours in a day.
Answer:
Hi!
I think the answer you might be looking for is 0.11
I hope this helped you :)
A man spends 70% of his income and craves rs 2580 What is his income? Full explanation please
Answer:
• Statement of the given problem,
⚫ A man spends 70% of his income and saves Rs. 2550. What is his income?
According to above data,
⚫ the required income of the
given man
= 2550/(1 - 70/10)
☐ = 2550/0.30
= 8,500 (Rs) [Ans]
Harry owns a rare baseball card that is valued at $13.00. If he originally purchased the card for $5.00, by what percentage has its value increased?
Answer: The Value has increased by 800%
Step-by-step explanation:
what is the difference between a squared number and a cubed number
this is the explanation above with some examples
Using the function f(x) = 7+ 4x, what is the value of f(-5) ?
Using the function f(x) = 7+ 4x, -13 is the value of f(-5).
What is function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
We might create a function with a set of persons as the domain X and a set of numbers as the codomain. For instance, if the codomain Y is the collection of whole integers, then define the function c so that its output, c(x), equals the number of offspring of every given x.
Four main categories may be used to classify different sorts of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
Given that,
f(x) = 7 + 4x
now, putting the value of f(-5), we get -
f(-5) = 7 + 4(-5)
or, f(-5) = -13
Using the function f(x) = 7+ 4x, -13 is the value of f(-5).
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a. 1 /2 + 5 12 greater than 1 less than 1 b. 2 7/8 – 1 7/9 greater than 1 less than 1.
Find the area of the figure.
The area of the figure in the first, second, and third cases will be 76 square ft, 120 square cm, and 87.5 square in, respectively.
What is a trapezoid?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.
The area of the trapezoid will be calculated as,
A = 1/2(sum of parallel sides) x height
8. The area of the figure is calculated as,
A = 1/2 (6 + 6 + 7) x 8
A = 76 square ft
9. The area of the figure is calculated as,
A = 1/2 (8 + 4) x 4 + 8 x 12
A = 24 + 96
A = 120 square cm
10. The area of the figure is calculated as,
A = 1/2 (5 + 10) x 5 + 5 x 10
A = 37.5 + 50
A = 87.5 square in
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If the price of a certain stock is $55.00 per share and its earnings are $2.75 per share, what is the ratio of the earnings to the stock’s price in lowest terms?
The earnings-to-stock-price ratio in simplest terms is 20.
What is PE ratio?A stock's P/E ratio is calculated by dividing its price by its annual earnings per share.The P/E ratio assists investors in determining whether a company's stock is overvalued or undervalued in relation to its earnings. The ratio measures what the market is willing to pay for the company's current operations as well as its potential growth. If a company has a high P/E ratio, the market believes in its growth potential and is willing to overspend today based on future earnings.
Here given,
Stock price = $55.00
Earnings per share = $2.75
We have to find ratio od earnings,
The formula is,
Ratio is : P/E
By substituting the values,
Ratio = $55.00 / $2.75
= 20
A car dealership pays $8350 for a car. They mark up the price by 17.4% to get the retail price. What is the retail price of the car at this deallership
The retail price of the car is $ 9802.9.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.A percentage is a figure or ratio that shows a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The symbol "%" is frequently written after the number to indicate percentages.A car dealership pays $8350 for a car.
They mark up the price by 17.4%
8350 * 17.4% = 1452.9
retail price = 8350 + 1452.9 = $ 9802.9
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if 87.5 percent of a sample of pure 131i decays in 24 days, what is the half-life of 131i?
If 87. 5 percent of a sample of pure 131 I decays in 24 days, then the half-life of 131 i is 8 days.
In this question we have been given 87.5 percent of a sample of pure 131i decays in 24 days
We need to find the the half-life of 131i
We know that the rate constant expression is given as :
k = (2.303/t)*(log (a / a-x))
where, t = 24 days
a = 100
a -x = 100 - 87.5
= 12.5 g
From the rate constant expression,
k = (2.303 / 24) * (log(100/12.5))
k = 0.0866
Now, the half life is given as :
k = 0.693 / t(1/2)
t1/2 = 0.693 / 0.0866
t1/2 = 8 days.
Therefore, the half-life of 131 i is 8 days.
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