Answer:
3x(x^2-4x+9)
Step-by-step explanation:
The polynomial 3x^3 - 12x^2 + 27x is factored by first taking out the greatest common factor of 3x, resulting in the final form of 3x(x^2 - 4x + 9), which cannot be factored further over the real numbers due to a negative discriminant.
To factor the polynomial 3x^3 - 12x^2 + 27x, we look for common factors in each term.
We can see that each term of the polynomial has a factor of 3x. So, we factor out 3x from the polynomial:
3x(x^2 - 4x + 9)
Now, we try to factor the quadratic expression x^2 - 4x + 9. However, this quadratic does not have real roots since the discriminant (b^2 - 4ac) is negative (-4^2 - 4 ×1 ×9 = -20). Therefore, it cannot be factored over the real numbers. Our final factored form of the polynomial is 3x(x^2 - 4x + 9), as we factored out the greatest common factor (GCF).
John is collecting data on the number of spots on ladybugs. He records it in this table. 2 7 5 4 3 3 5 5 6 5 The mean of the data is __ , and the median is __ .
The mean of the data is 4.5 and the median of the data is 5.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
To find the mean of the data, we add up all the values and divide by the total number of values:
2 + 7 + 5 + 4 + 3 + 3 + 5 + 5 + 6 + 5 = 45
There are 10 values, so:
mean = 45 / 10 = 4.5
Therefore, the mean of the data is 4.5.
To find the median of the data, we need to first put the values in order from smallest to largest:
2, 3, 3, 4, 5, 5, 5, 5, 6, 7
There are 10 values, which is an even number, so we take the average of the two middle values:
median = (5 + 5) / 2 = 5
Therefore, the mean of the data is 4.5 and the median of the data is 5.
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There are 20 entries in the chess tournament. How many ways can they finish in first, second,
and third place?
Answer:
6840
Step-by-step explanation:
Here, the order matters (1st, 2nd, and 3rd), so we need to use permutations.
There are 20 people who can get in first place. After that, there are 19 people who can get in second place. Finally, there are 18 people who can get in third place. So:
20 * 19 * 18 = 6840
Number of the ways can they finish in first, second, and the third-place is 6840
What is permutation?The linear arrangement of the set of the orders or the linear arrangements of the numbers is called the permutation.
Here, the order matters (1st, 2nd, and 3rd), so we need to use permutations.
There are 20 people who can get in first place. After that, there are 19 people who can get in second place. Finally, there are 18 people who can get in third place. So:
20 x 19 x 18 = 684
Therefore Number of the ways can they finish in first, second, and the third-place is 6840
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ima just get help so
Answer:
The answer is B 48 cm squared.
Step-by-step:
First divide into smaller sections. Then you will do Length times height.
9 x 4 = 36
6 x 2 = 12
36 + 12 = 48
Which of these is an example of a non-random sample?
A.
A cereal company surveys their employees about breakfast food preference.
B.
A farmer is choosing grains of wheat from a field to test for a new flavor of cereal.
C.
Ten college students at a college, population 50,000, are chosen to taste test a new cereal.
D.
A cereal company puts a winning ticket in one box of cereal out of 100,000 boxes.
I would go for C ten college students are chosen to taste test a new cereal
Angle dbc measures 5 degrees less than angle c and angle d measures 8 degrees more than angle c. What are the measures of each angle of the triangle?
Answer:
The measure of angle b (angle dbc) is [tex]54\°[/tex]
The measure of angle c is [tex]59\°[/tex]
The measure of angle d is [tex]67\°[/tex]
Step-by-step explanation:
Let
x-----> measure of angle b (angle dbc)
y----> measure of angle c
z----> measure of angle d
Remember that
The sum of the internal angles of a triangle must be equal to 180 degrees
so
[tex]x+y+z=180\°[/tex] -----> equation A
[tex]x=y-5[/tex] -----> equation B
[tex]z=y+8[/tex] ----> equation C
Substitute equation B and equation C in equation A and solve for y
[tex](y-5)+y+(y+8)=180\°[/tex]
[tex]3y+3=180\°[/tex]
[tex]3y=177\°[/tex]
[tex]y=59\°[/tex]
Find the value of x
[tex]x=59\°-5\°=54\°[/tex]
Find the value of z
[tex]z=59\°+8\°=67\°[/tex]
The measures of each angle of the triangle are
The measure of angle b (angle dbc) is [tex]54\°[/tex]
The measure of angle c is [tex]59\°[/tex]
The measure of angle d is [tex]67\°[/tex]
PROBLEM 1
Sam bought three folders and one
notebook from the office store and
spent $8.25. He went back the next
day and bought two more folders
and three more notebooks and
spent $16. If the prices did not
change between the days, find
the cost of one folder.
Answer:
Folder = 1.25$
Notebook = 4.5 $
Folder =x
Notebook = y
The cost of one folder if the prices did not change between the days, for this case, is $1.25
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
Given that:
Amount spent in buying 3 folders and 1 notebook = $8.25Amount spent in buying 2 folders and 3 notebook = $16Assumed that prices don't changeTo find:
Cost of one folder.
Assume that:
Cost of one folder = $xCost of one notebook = $yThen, from the given condition, we get:
Amount spent in buying 3 folders and 1 notebook = 3x + 1y dollars = $8.25
And, amount spent in buying 2 folders and 3 notebook = 2x + 3y dollars = $16
Thus, we get two equations as:
[tex]3x + 1y = 8.25\\2x + 3y = 16[/tex]
From the first equation, getting 'y' in terms of 'x', we get:
[tex]y = 8.25 - 3x[/tex]
Substituting this in second equation, we get:
[tex]2x + 3(8.25 - 3x) = 16\\2x +24.75 -3x = 16\\(2-9)x = 16 - 24.75\\-7x = -8.75\\7x = 8.75\\x = 8.75/7 =1.25 \: \rm dollars[/tex]
As we have Cost of one folder = $x
Thus, the cost of one folder if the prices did not change between the days, for this case, is $1.25
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8. PUZZLES Potter's Puzzles sells a wooden
pyramid puzzle. The base is a square
with side lengths of 6 inches. The slant
height is 10 inches. What is the surface
area of the puzzle? The internet gets 95.7squared inches, but how?
The surface area of the pyramid is 156 square inches. It is found by computing the area of the base, then adding it with the product of half of the base perimeter and the slant height.
Explanation:The problem involves finding the surface area of a pyramid with a square base. The surface area of a pyramid is given by the formula Base area + 1/2 * Perimeter of the base * Slant height.
First, let's compute the area of the base, the base is a square with sides of 6 inches. This gives us 6 * 6 = 36 square inches.
Secondly, the perimeter of a square is simply the length of one side multiplied by 4, which gives us 6*4 = 24 inches. Then multiply this by the slant height, which is 10 inches, then by 1/2, we have 0.5 * 24 * 10 = 120 square inches.
Finally, adding the base area and the latter computation gives: 36 + 120 = 156 square inches. Therefore, the surface area of the wooden pyramid puzzle is 156 square inches.
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The surface area of the wooden pyramid puzzle with a base side length of 6 inches and a slant height of 10 inches is 156 square inches.
Explanation:To find the surface area of the wooden pyramid puzzle, we need to calculate the area of each face and then sum them up. The base of the pyramid is a square with side lengths of 6 inches, so the area of the base is 6 inches multiplied by 6 inches, which gives us 36 square inches. The four triangular faces have the same area since the pyramid is symmetrical, so we just need to calculate the area of one triangular face.
The height of the pyramid is given as 10 inches, and since it is a right triangle, we can use the formula for the area of a triangle: (base x height) / 2.
The base of the triangle is the length of one side of the square base, which is 6 inches. Therefore, the area of one triangular face is (6 inches x 10 inches) / 2 = 30 square inches.
Since there are four triangular faces, the total area for all the triangular faces is 4 x 30 square inches = 120 square inches. Finally, we can sum up the areas of the base and the triangular faces to find the surface area: 36 square inches + 120 square inches = 156 square inches.
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Ms. Campbell recorded the number of cars each salesperson at her dealership sold last week.
Which of these statements is true?
A. The mean of the data summarizes the number of cars each salesperson sold last week.
B. The interquartile range of the data describes the change in the total number of cars sold last week.
C. The mean absolute deviation of the data summarizes the number of cars each salesperson sold last week.
D. The median of the data describes how the number of cars sold last week by each salesperson varies.
Answer:
the answer is A
Step-by-step explanation:
a measure of center for a numerical data set summarizes all of its' values with a single number; man and median are measures of center
a measure of variation describes how the numerical data varies with a single number; interquartile range and mean absolute deviation are measures of variation
***so the mean of the data summarizes the number of cars each salesperson sold last week***
Liang is ordering new chairs and cushions for his dining room table A new chair cost $88 and a new cushion cost $12 shipping costs $34 expression 88c + 12c + 34 gives the total cost for buying C sets of chairs and cushions simplify The expression by combining like terms
Answer:
100c + 34
Step-by-step explanation:
100c+4 that’s the answer
what value of r makes this equation true? justify your solution.
0.4r - 7 = -.3r +2.8
The answer is 14
0.4r-7=-.3r+2.8
Add 7 to both sides. -7+7=0 so it cancels on the left. 2.8+7=9.8.
0.4r=-.3r+9.8.
Add .3r to both sides. -.3r+3r=0 so it cancels on the right. 0.4r+.3r=0.7r.
0.7r=9.8
Divide 0.7 to both sides. 9.8 divided by 0.7 = 14
So r=14
Answer:
all work is pictured and shown
Events A and B are independent. Find the missing probability.
P(a)=3/10,p(b)=13/20,p(a and b)=?
ANSWER
[tex]P(A and B) = \frac{39}{200} [/tex]
EXPLANATION
If A and B are independent events, then,
P(A and B)=P(A)×P(B)
It was given that:
[tex]P(A) = \frac{3}{10} [/tex]
and
[tex]P(B) = \frac{13}{20} [/tex]
[tex]P(A \: and \: B) = \frac{3}{10} \times \frac{13}{20} [/tex]
[tex]P(A and B) = \frac{39}{200} [/tex]
the probability of events A and B occurring together, P(A and B), is 39/200 or, when simplified, 0.195.
The subject of the question is finding the probability of both independent events A and B occurring together, which is represented by P(A and B). To calculate this, you simply multiply the probability of event A by the probability of event B since they are independent. Given that P(A) = 3/10 and P(B) = 13/20, the calculation would be as follows:
P(A and B) = P(A) × P(B)P(A and B) = (3/10) × (13/20)P(A and B) = 39/200Thus, the probability of events A and B occurring together, P(A and B), is 39/200 or, when simplified, 0.195.
point o is the center if the circle. what is the value of x? mn and mp are tangent to
114
26
66
57
Answer:
[tex]x=66[/tex]
Step-by-step explanation:
Since MN and MP are tangent to circle O, they create 90° angles at the points of intersection.
We also know that this is a quadralateral, so the interior angles add up to 360.
We can make an equation with this information.
[tex]114+90+90+x=360[/tex]
[tex]294+x=360[/tex]
[tex]x=66[/tex]
By property of tangent, the value of x is Option(C) 66° .
What are the properties of tangent ?The properties of tangent are as follows -
Any tangent when intersect to a circle at the point, it subtends an angle of 90° at the interior segment. The total sum of the interior angle of the intersection of tangent at the points is always equal to 360° . How to find the given angle in the triangle ?Given that point O is the center if the circle also given MN and MP are tangent to O.
Thus by the property of tangent, ∠OPM and ∠ONM is equal to 90° as both the tangents intersect at the points P and N .
Also from property, we know that -
⇒ ∠ONM + ∠OPM + 114° + x° = 360°
⇒ 90° + 90° + 114° + x° = 360°
⇒ 294° + x° = 360°
∴ x = 360° - 294° = 66°
Therefore, by property of tangent, the value of x is Option(C) 66° .
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Please help! Due today!!!!!!!
Okay I have the same question as you so first cross out A and C. Because negative numbers are to the left ,and the Answer is D
There are some black and white buttons in a container.
7/10 of the buttons are black.
The difference between the number of black and white buttons is 24.
How many buttons are there in the container?
there are 80 buttons
7/10
3÷24=8 8×7=56 56+24=80
The total number of buttons in the container is 60. This was calculated by setting up an equation using the given proportion of black buttons and the difference between the number of black and white buttons.
Let the total number of buttons in the container be x. Given that 7/10 of the buttons are black, this means 7/10 of x, or (7/10)x, represent the number of black buttons. The remaining 3/10 of x are white buttons. The difference between the number of black and white buttons is 24, so we can set up the following equation:
(7/10)x - (3/10)x = 24.
Simplifying the equation by subtracting the fractions results in (4/10)x = 24.
We can then simplify this further by dividing both sides by the coefficient of x, which is (4/10), to find x.
x = 24 / (4/10) = 24 * (10/4) = 24 * (2.5) = 60.
So, there are 60 buttons in the container in total.
How do you calculate the area of a circle?
Area of a circle is equal to the diameterdiameter squaredradiusradius squared times diameterheightpiwidth.
Answer:
[tex]Area of circle = \pi (radius)^2 =\pi (r)^2[/tex]
Step-by-step explanation:
We need to find about how to calculate the area of a circle.
And match with the given choices. Where given choices are:
Area of a circle is equal to the diameterdiameter
squaredradiusradius squared times diameterheightpiwidth.
I'm not sure what exactly you have typed lol :)
But I can still answer that.
You just need to apply formula of the area of circle which is given by:
[tex]Area of circle = \pi (radius)^2 =\pi (r)^2[/tex]
Answer:
radius squared times pi
Step-by-step explanation:
edge
If a = 11 ft, b = 5 ft, and c = 7 ft, what is the surface area of the geometric shape formed by this net?
A. 167 sq. ft.
B. 145 sq. ft.
C. 117.5 sq. ft.
D. 147 sq. ft.
Answer:
the answer is B. 145 sq. ft.
Step-by-step explanation:
find the area of the first 2 triangles
A = 1/2 bh
A = 1/2 ba
a = 1/2 (11 ft.) (5 ft)
a = 27.5 sq ft.
A = 1/2 cb
a = 1/2 (5 ft) (7 ft)
a = 17.5 sq. ft
find the area of the rectangle
A = lw
a = (11 ft.)(5 ft.)
a = 55 sq. ft
Then add all together
2(27.5 sq.ft) + 2(17.5 sq. ft) + 55 sq.ft. = 145 sq. ft.
PLEASE HELP WILL MARK BRAINIEST
-see attachment-
Answer:
f(x) and g(x) are inverses
Step-by-step explanation:
* Lets check the inverse function
- If f(x) = y has a domain = x and a range = y, then f^-1 is the
inverse of f with a domain = y and a range = x
- f(x) = f^-1(x) = x
* Now lets solve the problem
∵ f(x) = 8/x
∵ g(x) = 8/x
∴ fg(x) = f(8/x)
∴ fg(x) = 8/(8/x) = 8 ÷ 8/x ⇒ change division sign to the multiplication
sign and reciprocal the fraction after the division sign
∴ fg(x) = 8 × x/8 = x
* Now lets find gf(x)
∴ gf(x) = g(8/x)
∴ gf(x) = 8/(8/x) = 8 ÷ 8/x
∴ gf(x) = 8 × x/8 = x
∵ f(x) = f^-1(x) = x
* fg(x) = gf(x) = x
∴ f(x) and g(x) are inverses
Lily has two times as much money invested in 8% stocks as she has in bonds paying 6%. How much she has invested in stocks if her annual income from stocks and bonds is $325.6?
Let's say Lily invested x amount of money in bonds and 2x in stocks. What the yield is annually from those is 6% of x plus 2 * 8% of x, as she gets 6% in bonds and 8% in stocks. Simplified is 0.06x + 0.16x. Add and you get 0.22x. Now you can solve a simple equation.
Equation:
0.22x = 325.6 (as annual income is $325.60)
----divide both sides by 0.22----
x = 1480
----multiply by 2 to get your answer----
2x = amount of stocks = 1480 * 2 = $2960
Noah is thinking of two numbers there sum is 10 and their difference is 4. What're the two numbers
Answer: 7 and 3
Step-by-step explanation: 7 + 3 = 10 and 7-3 = 4
Consider the diagram below. Choose the statement that correctly describes the pair <1 and <2
Answer:
Step-by-step explanation:
Same side interior angles
Answer:
Same-side interior angles.Step-by-step explanation:
Observe in the image that [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are inside the inclined pair of lines, that position is called interior angles, also notice that they are at the same side of the horizontal line.
Therefore, the correct description of that pair of angles is "same-side interior angles", because they are inside the pair of lines, and at the same side of the horizontal line.
mona wrote 7 tests. her average was 93 what is the lowest grade she can get for her average to be 90
15 POINTS AND THANKS
Answer:
69
Step-by-step explanation:
To find the total sum of all the tests, you multiply 93 by 7 or 651. Multiplying 90 and 8, you get 720. So 720-651 is 69.
If (-3, y) lies on the graph of y = 3x, then y =
1/27
-1
-27
Answer:
y =1/27
Step-by-step explanation:
Howdy!
If P = (-3, y) lies on the graph of y=3^x, then, to find the value of 'y' we need to substitute the point P into the equation:
To solve this, remember that [tex]a^{-b} = \frac{1}{a^{b}}[/tex]
Then:
y = 3^x
y = 3^(-3)
y = 1/27
So P= (-3, 1/27)
The correct option is y =1/27
Answer:
The correct answer option is 1/27.
Step-by-step explanation:
We are given the following equation and we are to find the value of y when the point (-3, y) lies on the graph of the given equation:
[tex] y = 3 ^ { x } [/tex]
So we will substitute the given value of x from the point (-3, y) in the equation to get y:
[tex] y = 3 ^ { - 3 } [/tex]
[tex] y = \frac { 1 } { 2 7 } [/tex]
how to solve this. it’s for angles
Answer:
x=36
Step-by-step explanation:
The angle right under 3x is 2x, because alternate exterior angles between parallel lines are equal. Those two angles add up to 180, because they are formed by a strait line intersecting with another straight line. This means that 5x = 180 or x=36.
What is the range of the function, f(x)=3x+4, given the domain is {-2, 4,,10, 16}
Select one:
a. {-2, 19, 40, 58}
b. {-2, 0, 2, 4}
c. {-2, 4, 8, 13}
d. {-2, 16, 34, 52}
Answer:
The range of f(x) is {-2 , 16 , 34 , 52} ⇒ answer d
Step-by-step explanation:
* Lets talk about the domain and the range of a function
- The domain is the values of x (input)
- The range is the value of y of the corresponding x (output)
∵ f(x) = 3x + 4
∵ The domain is {-2 , 4 , 10 , 16}
- To find the corresponding range substitute the values of x in f(x)
∵ x = -2
- Substitute x by -2 in f(x)
∴ f(-2) = 3(-2) + 4 = -6 + 4 = -2
∵ x = 4
- Substitute x by 4 in f(x)
∴ f(4) = 3(4) + 4 = 12 + 4 = 16
∵ x = 10
- Substitute x by 10 in f(x)
∴ f(10) = 3(10) + 4 = 30 + 4 = 34
∵ x = 16
- Substitute x by 16 in f(x)
∴ f(16) = 3(16) + 4 = 52
∴ The range of f(x) is {-2 , 16 , 34 , 52}
can someone tell me what to write for this?
Answer:
Step-by-step explanation:
You would take the area of half of a circle plus the area of a rectangle. You don't have measures there, but the formula would be
[tex]A=\frac{\pi r^{2} }{2}+(l*w)[/tex]
Brenda is asked to make 3 quarts of apple cider. The recipe that she reads for how to make apple cider states that she should use 10 apples to make 2 quarts. How many apples does she need to make 3 quarts of apple cider?
Answer:
15 apples
Step-by-step explanation: if you need 10 apples for two quarts, then you need 5 for 1. add those together and you get 15
Simplify. (-2)^-3
A.-8
B.-1/8
C.1/8
D.8
ANSWER
[tex]{( - 2)}^{ - 3} =- \frac{1}{ 8} [/tex]
EXPLANATION
We want to simplify;
[tex] {( - 2)}^{ - 3} [/tex]
Recall that,
[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]
[tex]{( - 2)}^{ - 3} = \frac{1}{{( - 2)}^{ 3}} [/tex]
We multiply out to get,
[tex]{( - 2)}^{ - 3} = \frac{1}{{- 2} \times - 2 \times - 2} [/tex]
[tex]{( - 2)}^{ - 3} = \frac{1}{ - 8} [/tex]
The correct choice is B.
what is the diffrenc e between a 1 1/4 and 3/8
Answer:
7/8
Step-by-step explanation:
Answer:
7/8
Step-by-step explanation:
Given: 4x - 7 = 2x + 9
Prove: x = 9
What is the missing reason?
1. 4x - 7 = 2x + 9 ------------- 1. Given
2. 2x - 7 = 9 ------------------- 2. ?????
3. 2x = 18 --------------------- 3. Addition Property of Equality
4. x = 9 ------------------------ 4. Division Property of Equality
A) Multiplication property of equality
B) Subtraction property of equality
C) Transitive property of equality
D) Substitution property of equality
Since the difference between steps 1 and 2 is that 2x was subtracted from both sides, i'm pretty sure the answer is B, the Subtraction property of equality. Hope this helps you!
Answer:
B) Subtraction property of equality
Step-by-step explanation:
4x - 7 = 2x + 9
Subtract 2x from each side using the subtraction property of equality
4x -2x - 7 = 2x-2x + 9
2x -7 = 9
How do you calculate the area of a circle?
Area of a circle is equal to the diameterdiameter squaredradiusradius squared times diameterheightpiwidth.
The answer is:
[tex]Area_{circle}=\pi *radius^{2}[/tex]
or
[tex]Area_{circle}=\pi *(\frac{diameter}{2})^{2}[/tex]
Why?We can calculate the area of any circle using the following formula:
[tex]Area_{circle}=\pi *radius^{2}[/tex]
Where,
π, is a constant used to calculate the area of the circle.
radius, is the distance from the center to any point of the circle.
Also, we have that:
[tex]radius=\frac{diameter}{2}[/tex]
So, we can rewrite the equation by the following way:
[tex]Area_{circle}=\pi *(\frac{diameter}{2})^{2}[/tex]
Have a nice day!
Answer:
Use formula:
[tex]Area of circle = \pi (radius)^2 =\pi (r)^2[/tex]
Step-by-step explanation:
We need to find about how to calculate the area of a circle.
And match with the given choices. Where given choices are:
Area of a circle is equal to the diameterdiameter
squaredradiusradius squared times diameterheightpiwidth.
I'm not sure what exactly you have typed as choices are not written in proper way.
But I can still answer that.
You just need to apply formula of the area of circle which is given by:
[tex]Area of circle = \pi (radius)^2 =\pi (r)^2[/tex]