The highest common factor (HCF) for the expression 4x³yz"; 30x²y²z² and 36x³y²z³ is 2x²yz.
What is H.C.FThe H.C.F. defines the highest common factor present in between given two or more numbers or mathematical expression.
We shall derive the HCF of the three expressions by expressing them as multiples of their factors as follows;
4x³yz = 2 × 2 × x × x × x × y × z
30x²y²z² = 2 × 3 × 5 × x × x × y × z × z
36x³y²z³ = 2 × 2 × 3 × 3 × x × x × x × y × y × z × z × z
HCF = 2 × x × x × y × z
HCF = 2x²yz
Therefore, the highest common factor for the expressions 4x³yz"; 30x²y²z² and 36x³y²z³ with the understanding of HCF is 2x²yz.
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A classroom has twenty-five students that are all 14-years old. If you list their ages and their heights as ordered pairs (age, height), which statement is true?
It is not a relation, but it is a function.
It is a relation but not a function.
It is neither a relation nor a function.
It is both a relation and a function.
When one lists their ages and their heights as ordered pairs (age, height), the statement that is true is D. It is both a relation and a function.
In mathematics, what is a relation?A relation between two sets is a collection of ordered pairs that each contain one object from the other set. If the ordered pair (x,y) is in the relation and the object x is from the first set and the object y is from the second set, the objects are said to be related. A relation is a type of function.
A function is a relation that states that there should be only one output for each input (or) we can say that a function is a special type of relation (a set of ordered pairs) that follows a rule, i.e., every X-value should be associated with only one y-value.
It should be noted that based on the information, only one value can be attributed to each person. Therefore, the correct option is D.
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What the answer pls help The distance from the tip of a slice of pizza to the crust is 6 inches.
The measurement of the distance from the tip of the slice of pizza to the crust is the radius.
The diameter of the pizza is 12 inches and the circumference is 37.7 inches
How to find the circumference?A slice of pizza is cut from the middle of the pizza to the crust. It is therefore cut from the middle of the pizza (circle) to the edge of the pizza (circle).
This is the radius because the radius is the straight - line distance from the edge of the middle of a circle to the edge.
If the radius is 6 inches, the diameter is:
= radius x 2
= 6 x 2
= 12 inches
The circumference is:
= π x diameter
= 22/7 x 12
= 37.7 inches
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What is one possible y coordinate
Answer:
Step-by-step explanation:
Answer x = 4 or x = -4.
Explanation: you can make what is called a 3-4-5 triangle. The base in this case is 3(from -2 to -5 there is 3 units), the hypotenuse is 5(length given in the question) therefore the height (also known as the y coordinate) is 4 or -4 if you flip the triangle.
Use the bar diagram to write an equation. Then solve. Drag numbers to complete the equations.
Step-by-step explanation:
as the graph shows :
4x + 12x = 320
16x = 320
x = 20
true or false? a large number of mba applicants are given an aptitude test. scores are normally distributed with a mean of 460 and standard deviation of 80. the probability that an applicant scores below 552 is 0.8329.
It is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.
Given, a large number of MBA applicants are given an aptitude test. scores are normally distributed with a mean of 460 and standard deviation of 80.
We are asked the probability that an applicant scores below 552.
Now, using the formula of probability, we get
P(X < 552) = 0.8329
when the mean is given i.e. 460 and standard deviation is given i.e. 80.
Hence, it is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.
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Can anyone state the vertex of the graph?
the graph above is the graph of a Cubic function, namely a polynomial with a degree of "3", and the behaviour is that it comes from the bottom from -infinity goes up up get to a smooth flat or horizontal plateau then it keeps on going right back up, its slope is never negative.
now, Cubic functions do not have a "vertex" as in a U-turn sense or a peak-sense.
please help Write each number as a percent. 1/200
The percent of the number is 0.5% when the number is 1/200.
Given that,
We have to find the percent of the number 1/200.
A percentage is a number or ratio that, in mathematics, represents a portion of one hundred. It's frequently represented by the symbol "%" or just "percent" or "pct."
Take the number.
1/200
Multiply by 100
1/200×100
We get
1/2
In decimal we get
0.5%
Or
Convert the number to decimal.
1/200= 0.005
Multiply 0.005 by 100 to convert to a percentage.
0.005×100
Simplify
0.5%
Therefore, The percent of the number is 0.5% when the number is 1/200.
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consider the polynomial function p given by p(x)=5x^3+6x^2+4x
evaluate the function at x=-5 and x=15
Answer:
p(-5) = -495p(15) = 18285Step-by-step explanation:
You want the value of p(x)=5x^3+6x^2+4x for x=-5 and x=15.
Horner formWriting a polynomial in Horner form can simplify evaluation.
p(x) = ((5x +6)x +4)x
p(-5)p(-5) = ((5(-5) +6)(-5) +4)(-5) = (-19(-5) +4)(-5) = 99(-5) = -495
p(15)p(15) = ((5(15) +6)(15) +4)(15) = (81(15) +4)(15) = 1219(15) = 18285
A 50 foot ladder is set against the side of a house so that it reaches up 48 feet. If Shaniece grabs the ladder at its base and pulls it 10 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 38 ft.) Round to the nearest tenth of a foot.
The distance up the house the ladder will reach after pulling it 10 feet further from the base of the house is 43.9 ft.
How to find the height of the ladder ?The ladder is set against the side of the house so that it reaches up 48 feet. Shaniece grabs the ladder at its base and pulls it 10 feet farther from the house.
The height of the ladder on the house can be computed as follows:
The situation form two right angle triangle.
The initial distance of the base of the ladder from the house can be calculated as follows;
using Pythagoras's theorem,
b² = 50² - 48²
b = √2500 - 2304
b = √196
b = 14 ft.
Therefore, the initial distance of the ladder from the base of the house is 14 feet.
Let's find the height of the ladder on the house after pulling it 10 ft further.
using Pythagoras's theorem,
b² = 50² - 24²
b = √2500 - 576
b = √1924
b = 43.8634243989
b = 43.9 ft
Therefore,
height of the ladder up the house = 43.9 ft
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couple has 5 kids, all sons. if they have a sixth kid, what is the probability that the sixth kid will be a son?
I need to know the answer
Step-by-step explanation:
The graph of [tex]p(x)=2x^3[/tex] is less steep than [tex]f(x)=2.5x^3[/tex] because the coefficient 2 is less than the coefficient 2.5. That makes points on the graph of p(x) lie closer to the x-axis than points on the graph of f. For example, if x = 2, the point (2, 20) is on the graph of f but the point (2, 16) is on the graph of p (so it lies under the point (2, 20).
The graph of [tex]p(x)=-x^3[/tex] is less steep than the graph of f and it is reflected over the x-axis. The negative coefficient -1 is doing that. The values of the function p(x) are opposite sign to values of f(x).
The graph of [tex]p(x)=3x^3[/tex] is steeper than the graph of f(x) because the coefficient 3 is larger than the coefficient 2.5, making the points on the graph of p lie farther away from the x-axis than points on the graph of f(x).
2. To paint a house, a painting company charges a flat rate of $500 for supplies, plus
$50 for each hour of labor.
a. How much would the painting company charge to paint a house that needs
hours of labor? A house that needs 50 hours?
Answer:
If a house need 50 hours to paint, it will cost $3000
Step-by-step explanation:
--- According to the problem, $500 is the cost for supplies, which means that for every house, that cost will be there. In other words, this payment never changes no matter the house. So far you pay $500
--- Now, the problem says that you pay $50 for each hour of labor. Since the house need 50 hours, we will multiply 50 (the cost) by 50 (the hours) = 2500.
--- Now we put the payments together. 500 + 2500 = 3000. So it will cost $3000 to paint a house that need 50 hours.
Rafe buys a cake for $12. The sales tax is 10%. How much is the sales tax?
A. $1.20
B.$10
C.$12
D.$13.20
Answer:
A $1.20
Step-by-step explanation:
Answer: A) $1.20
Step-by-step explanation: To get 10% of a number, you just need to divide by 10, so 12 ÷ 10 = 1.2.
Carol buys a house for £234,900
she pays a 10% deposit
work out the amount of deposit paid by carol
Answer:
£23, 490
Step-by-step explanation:
10% deposit by Carol of £234,900
10/100 *£234,900
0.1*£234,900=£23,490
Can anyone write the equation of the graph?
The function represented by the graph has an equation of f(x) = |x - 3| + 5
How to find the equation of the graph line?From the question, we have the following graph that can be used in our computation:
The graph is an absolute value graph
As a general rule, an absolute value is expressed as
y = |x - h| + k
In this case, the vertex is
Vertex = (h, k)
As a general rule, the vertex of a function is the minimum point on the graph
On the given graph, the minimum point is (3, 5)
This means that
(h, k) = (3, 5)
Substitute the values (h, k) = (3, 5) in the equation y = |x - h| + k
So, we have the following representation
y = |x - 3| + 5
Rewrite the equation as a function
f(x) = |x - 3| + 5
Hence, the equation of the graph represented by the figure is f(x) = |x - 3| + 5
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a standard die is rolled three times. what is the probability of rolling a number less than 5 on the first two rolls, then an even number on the third roll?
2/216 or 1/108 is the probability of rolling a number .
How does probability explain work?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.The great thing about this question is that all three of those rolls are Independent Scenarios.
The probability of the first roll does not effect the outcome of the second or third roll
1/6 ( we want a 1, and there are 6 options.)
1/6 ( We want a 3, and there are 6 options
2/6 ( We want a 5 or 6, and there are 6 options)
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Dominic needs a new bike mirror. His old mirror was a square with a side length of 9 cm. He wants the new mirror to have an area as close as possible to his old bike mirror.
Which circular bike mirror should Dominic buy? Answer Choices: 8 cm , 7 cm , and 6 cm Answer ASAP FOR Brainlist.
Answer:
6 cm
Step-by-step explanation:
The circular mirror Dominic should buy is the mirror with a side length of
8 cm.
Option A is the correct answer.
What is a square?A Square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side².
We have,
Old mirror.
Side = 9 cm
Area = 9 x 9 = 81 cm²
New mirror.
Side = 8 cm
Area = 64 cm²
Side = 7 cm
Area = 7 x 7 = 49 cm²
Side = 6 cm
Area = 6 x 6 = 36 cm²
64 cm² is closer to 81 cm².
Thus,
A circular mirror with a side length of 8 cm should be bought.
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help 100 points i need help asap
Answer:
Unclassified
Step-by-step explanation:
Which questions would you like answered?
PLEASE HELP ME THIS IS DUE TOMORROW!!!!!!!!
(a) The scatter plot and the line of fit are shown in the graph.
(b) The equation of the line of fit is y = -2.5x+18.3.
(c) The slope is -2.5 which indicates that the gamer losses 2.5 every week after getting a new game.
What is a scatter plot?A scatter plot is a graph of the given points or given data.
(a)
To make a scatter plot of the data, plot the points (x,y) on a graph.
To draw the line of fit, draw a line such that the distance between the line and the plotted points is minimum.
(b) The line passes through points (7.3,0)and (0,18).
The equation of the line is given by:
[tex]y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)[/tex]
Substitutes the points (x₁,y₁) = (7.3,0) and (x₂,y₂)=(0,18) into the above equation:
[tex]y-0=\frac{18-0}{0-7.3}(x-7.3)\\y=-2.5(x-7.3)\\y=-2.5x+18.3[/tex]
(c) The slope of a line of the form y=mx+c is m.
Therefore, the slope of the line y=-2.5x+18.3 is m = -2.5.
The slope indicates the change in y with respect to the change in x.
Therefore, the slope -2.5 indicates that the gamer losses 2.5 every week after getting a new game.
Hence,
(a) The scatter plot and the line of fit are shown in the graph.
(b) The equation of the line of fit is y = -2.5x+18.3.
(c) The slope is -2.5 which indicates that the gamer losses 2.5 every week after getting a new game.
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PLEASE HELP!!!!!!!!!!!!!
A handicapped ramp is being constructed for the front entrance of First National Bank in Springfield. ADA guidelines requires a rise angle from the foot of the ramp (point furthest from the entrance) not to exceed 4.8 degrees. This means the vertical to horizontal ratio cannot exceed 1:12. If the handicapped ramp must start 15 feet away from the front entrance, contractors estimate the rise to be about 3 feet.
Part A: Explain thoroughly whether or not these ramp dimensions meet the ADA guidelines.
Part B: If the rise estimate does not meet ADA requirements, provide a measurement that would meet the guidelines.
a) These ramp dimensions do not meet the ADA guidelines.
b) A measurement that would meet the guidelines is the ramp starting 39 feet away, with a height of 3 meters.
What is a slope?The slope of a situation is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
For the ramp in this problem, we have that the vertical change and the horizontal change are given as follows:
The vertical change is of: 3 feet.The horizontal change is of: 15 feet.The ratio between the vertical change to the horizontal change is of:
3/15 = 1/5.
Which is greater than 1/12, hence the ramp does not meet the ADA guidelines.
If the horizontal change was 13 times the vertical change, it would meet the ratio, hence a possible measurement is of:
3 feet vertical.39 feet horizontal.As the ratio would be of:
3/39 = 1/13 < 1/12.
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how many different two-letter initials can people have using the upper case characters in the english alphabet?
The different two-letter initials can people have using the upper case characters in the English alphabet is 676 (if no specifications are given)
The question has not specified other conditions so we have assumed it by cases and solved it
Case 1 -
“Everything” allowed, means that we are considering solutions like “AA” and “BA, AB”
If this is the case then there are => 26 x 26 = 676 Combinations,
Case 2-
No repetition allowed
Here, we are excluding cases like “AA, BB” etc so here we have
26 x 25 = 650 as our answer
Case 3-
no repetition allowed + unique set every time, So
here we will have ²⁶C₂ (this is basic combinatorics formula )
= (26 x 25)/2
= 325 combinations possible
Case 4 -
Repetition allowed + unique set every time
here we will assume along with the uniqueness of each combination we will add Repeated combinations, Here we have “AA, BB, CC,……..ZZ” 26 new combinations along with unique ones So,
²⁶C₂+ 26 = 325 + 26 = 391 possible cases.
and I would recommend adding more detail to your question specifying the conditions in a better way, but the technically correct answer to your questions if no conditions are CASE 1.
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The scatter plot shows the average price of major-league baseball ticket from 1997 to 2006
Predict the price of ticket in 2009.
The price of ticket will be $26 approximately in 2009 using the concept of the linear equation and slope.
What is linear equation?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is fairly simple (x and y). When attempting to solve systems of two linear equations, this form is also very helpful.
Here,
The line has 2 points,
(2001,18) and (2005,22)
m=(22-18)/(2005-2001)
m=1
y-y1=m(x-x1)
y-18=x-2001
x-y=1983
(2009,y) is on that line,
2009-y=1983
y=26
Using the idea of the linear equation and slope, the ticket price in 2009 will be approximately $26.
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PLEASE HELP I NEED IT TODAY
QUESTION IS ON THE IMAGE DOWN BELOW
PLEASE ANSWER QUESTION AS A double number line
Answer:
I agree with her the reason? because she is right
67.50/6= 11.25 meaning it's $11.25 per ticket
47/4= 11.75 meaning it's $11.75 per ticket
Step-by-step explanation: Jamar spent 11.25 per ticket
Aaron spent 11.75 per ticket meaning she spent more than Jamar
Anthony's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=57+7.4x, where y represents the expected quiz score and x represents hours spent on homework that week. What is the meaning of the x-value when y=90
The meaning of the x-value when y=90 means that Anthony will use 3.1 hours.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The relationship that can be represented by the equation y=57+7.4x,
where
y represents the expected quiz score
x represents hours spent on homework that week.
When y = 90, the value of x will be:
y=57+7.4x
57 + 7.4x = 90
Collect like terms
7.4x = 90 - 57
7.4x = 23
Divide
x = 23/7.4
x = 3.1
He'll use 3.1 hours.
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A Pringles chip can has a diameter of 8 cm and a height of 30 cm. Determine the volume of the cylindrical can.
The area of a circle is shown below.
A = πr²
The volume of the cylindrical Pringles chip can is 1508 cm³
Calculating the volume of a cylinderFrom the question, we are to determine the volume of cylindrical can
The volume of a cylinder is given by the formula
V = πr²h
Where V is the volume of the cylinder
r is the radius
and h is the height
From the given information,
Diameter = 8 cm
But,
Radius = Diameter / 2
Therefore,
r = 8 / 2 = 4cm
h = 30 cm
Thus,
Volume of the cylindrical can = π× 4² × 30
Volume of the cylindrical can = π× 16 × 30
Volume of the cylindrical can = 480π cm³
Volume of the cylindrical can = 1507.96447 cm³
Volume of the cylindrical can ≈ 1508 cm³
Hence,
The volume is 1508 cm³
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0.38 in standard form
each other.
с
D
1. The volume of box A is 64 cubic inches. The circumference of a regulation baseball is at least 9 inches but no more
than 9.25 inches. Can a baseball fit in box A? Explain.
2. Box B has a surface area of 216 square inches. What is the ratio of the side length of box B to the side length of box
A?
3. The ratios of the side lengths of B to A, C to B, and D to C are the same. How much more space do the boxes
occupy when stored separately in a closet than when they are stacked inside each other in the closet?
1.) Yes,it will fit because volume of the base ball is 13.36 cubic inch and the volume of box is 64 cubic inch which greater than the volume of baseball .
2) The ratio of the side length of box B to the side length of box
A is 1.472 inche : 6 inch.
What is cube ?
A Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.
What is circumference?
The circumference is the distance that surrounds a circle. We can measure the circumference of the earth by measuring the distance that we will have to walk all the way around the world.
To check whether the baseball is will till in the box we will check the maximum value of circumference.
⇒ [tex]2\pi r[/tex] = 9.25
⇒ [tex]r = \frac{9.25}{2\pi}[/tex]
⇒[tex]r = 1.472 in.[/tex]
Volume of the baseball [tex]= \frac{4}{3} \pi x^{3}[/tex]
[tex]= \frac{4}{3}\times \pi\times (1.472)^3 in^3[/tex]
[tex]= 13.36\ in^3 < 64 \ in^3\\[/tex]
So, it will fit inside the box.
2.)[tex]\sqrt[3]{216} = 6 \ (\therefore V = a^3)[/tex]
The length of each side of the box is 6 inches.
and the ratio of the side length of box B to the side length of box
A:
1.472 in : 6 inches
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P=2l+2w. Solve the formula for w in terms of P and l
The formula for w in terms of p and l is w = (p - 2l)/2
What is an expression?Numbers, symbols and operators grouped together that show the value of something.
Given that, an expression p = 2l + 2w
Solving for w, we get,
w = (p - 2l)/2
Hence, The formula for w in terms of p and l is w = (p - 2l)/2
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Solve the system of equations by the addition method.
3x + 4y = 7
6x - 4y= 2
I will give 100 pts for anwser asap Determine which integer(s) from the set S:{−24, 2, 20, 35} will make the inequality five sixths m minus five is less than one half m plus 3 false.
S:{−24, 2}
S:{35}
S:{−24, 2, 20}
S:{20}
None of the values in the given set makes the inequality false.
Given that,
To check for the expression 5m/6 - 5 < m/2 + 3, whether the set of values S:{−24, 2, 20, 35} holds or not.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
given expression,
5m/6 - 5 < m/2 + 3
5m/6 - m/2 < 3 + 5
(5m - 6m)/6 < 8
-m < 48
m > -48
Thus, none of the values in the given set make the inequality false.
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