There are 720 different 6-letter arrangements that can be formed using the letters in the word QUASAR, calculated by 6 factorial (6!).
Explanation:The question asks for the total number of different 6-letter arrangements that can be formed using the letters in the word QUASAR. This is a problem of permutations where all the letters are distinct. To find the number of different permutations of the letters in QUASAR, we multiply the number of choices available at each position. There are 6 choices for the first letter, 5 for the second, and so on, until 1 choice for the last letter.
Therefore, the permutations are calculated as 6 × 5 × 4 × 3 × 2 × 1, which is equal to 6! (6 factorial).
The calculation of 6! is as follows:
6 × 5 × 4 × 3 × 2 × 1 = 720.So, there are 720 different 6-letter arrangements that can be formed from the word QUASAR.
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Shawn bought 8 boxes of erasers. Each of the erasers is either pink or blue. Each box has x pink erasers and y blue erasers in it. The expression shown below represents the total number of erasers Shawn bought.
8(x + y)
Which expression also represents the total number of erasers Shawn bought?
Question 7 options:
a 8x + 8y
b 8x + y
c 8xy
d 8 + x + y
Answer:
A
Step-by-step explanation:
You need to distribute the 8 to everything in the equation. You need to keep the sign in the middle. So in the end you would get 8x+8y.
Final answer:
Option a), 8x + 8y, accurately represents the total number of erasers Shawn bought since it's obtained by distributing the number of boxes, 8, to both x and y inside the parentheses.
Explanation:
The expression 8(x + y) represents the total number of erasers Shawn bought, where x is the number of pink erasers in each box and y is the number of blue erasers in each box. Since Shawn bought 8 boxes, and each box contains x pink erasers and y blue erasers, we need to multiply the sum of pink and blue erasers in one box by the number of boxes to get the total. Hence, the correct expression that also represents the total number of erasers Shawn bought is option a), 8x + 8y which is obtained by distributing the 8 to both x and y inside the parentheses.
a large rectangular swimming pool is 1,000 feet long 100 feet wide and 10 feet deep how much water does the pool hold?
ANSWER
The swimming pool can hold 1,000,000 cubic feet of water.
EXPLANATION
The capacity of water the pool holds is the volume of water in the swimming pool.
The swimming pool is rectangular, therefore its volume can be calculated using the formula,
[tex]V = l \times w \times h[/tex]
where l=1000ft is the length, w=100ft is the width and h=10ft is the height of the pool.
We substitute all these values into the formula to get:
[tex]V = 1000 \times 100 \times 10 = 1000000 {ft}^{3} [/tex]
The swimming pool can hold 1,000,000 cubic feet of water.
The amount of water the pool can hold is 1,000,000 ft³.
What is the amount of water the pool can hold?In order to determine the amount of water the pool can hold, we have to determine the volume of the rectangular swimming pool. Since the swimming pool has the shape of a cuboid, the formula for the volume of a cuboid would be used.
Volume = length x width x height
1000 x 100 x 10 = 1,000,000 ft³
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What is the range of the following relation?
{(5,0), (6, -1), (1, 4), (0,5), (2,3)}
ANSWER
The range is
{-1,0,1,3,4,5}
EXPLANATION
The relation is given to us as an ordered pair.
The range is the set of all the y-values of the relation.
We list the set of all the values in ascending order without any repetition.
We then obtain the range as:
{-1,0,1,3,4,5}
Scott went snowboarding down a mountain. The trail was 2 miles long and took him 5 minutes to complete. If Tom snowboards three times as fast, how long would it take him to get down the mountain?
Answer:
1 minute and 40 seconds or 1 2/3 minute
Step-by-step explanation:
If it took Scott 2 miles for 5 minutes, than it took him 2.5 minutes to do 1 mile. For 3 times as fast, we need to divide by 3. 2.5/3= 5/2*1/3=5/6. It is 2 miles, so 5/6*2=10/6=5/3=1 2/3 minute. 2/3 minute=40 seconds. So, the answer is 1 minute and 40 seconds or 1 2/3 minute.
Answer:
1 minute and 40 seconds or 1 2/3 minute(s)
Step-by-step explanation:
Find the difference between (15,-17) and (-20,-5)
Answer:
37 units
Step-by-step explanation:
The horizontal distance between these two points is 35 and the vertical is 12.
Treat these distances as the lengths of the legs of a right triangle whose hypotenuse we want to determine:
d^2 = 35^2 + 12^2 = 1369, so d = the distance between these two points = d = sqrt(1369) = 37 units
The difference between the points (15,-17) and (-20,-5) is calculated by subtracting the coordinates, resulting in a difference of (35, -12).
To find the difference between the two points (15,-17) and (-20,-5), we need to subtract the coordinates of the second point from the coordinates of the first point.
For the x-coordinates: 15 - (-20) = 15 + 20 = 35
For the y-coordinates: -17 - (-5) = -17 + 5 = -12
Therefore, the difference between the two points is (35, -12).
find the length of the missing side. if necessary, round to the nearest tenth.
A. 44
B. 22
C. 15.6
D. 484
the answer to this question would be c- 15.6
(a-b)^2/(1/a-1/b) simplify
The solution of the expression (a-b)²/{(1/a)-(1/b)} is ab² - a²b.
What is factorization?Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.
Given:
An expression,
(a-b)²/{(1/a)-(1/b)}.
Simplifying,
(a-b)²/{(1/a)-(1/b)},
= (a-b)²/{(b-a)/ab},
= -(a-b)² (ab)/(a-b)
= -(a-b)(ab)
= ab² - a²b.
Therefore, ab² - a²b is the solution.
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Final answer:
The expression (a-b)²/(1/a-1/b) simplifies by first finding a common denominator, then multiplying to remove the fraction, resulting in the simplified form -ab(a-b).
Explanation:
To simplify the expression (a-b)²/(1/a-1/b), we can start by finding a common denominator for the terms in the denominator 1/a and 1/b. The common denominator is a × b, so we rewrite the expression as:
((a-b)²) / ((b - a) / (ab))
Now, we can simplify by multiplying both the numerator and the denominator by ab to eliminate the fraction in the denominator:
(a-b)² × (ab) / (b - a)
Note that (a - b) is equal to -(b - a), so:
(a-b)² × (ab) / -(a - b)
Because (a - b)² is (a - b) × (a - b), one (a - b) in the numerator cancels with the (a - b) in the denominator, leaving us with:
-(a - b) × (ab)
Which simplifies to:
-ab(a - b)
Which set of coordinates satisfies the system of equations y = x − 3 and y = -2x + 1?
A. a
B. b
C. c
D. d
Point c.
You can graph the two points in a calculator to find out the answer OR you can identify the lines using the y-intercept aka b in the y=mx+b format.
Y=x - 3 has a y-intercept of -3, so look for the line where it goes through -3 on the y axis. (do the same for the other except when the y-intercept is 1)
From this, you can identify the lines and just find where they intersect.
Answer:
CCCCCCCCCCCCCC
Step-by-step explanation:
Which is the approximate measure of this angle?
Answer:
120 degrees aka answer D
Step-by-step explanation:
Answer:
D. 120°.
Step-by-step explanation:
Since the angle is obtuse (greater than 90), it cannot be 30°, since 30° is an acute angle.
The angle cannot be 90° since the angle is obtuse, and red curved line is not a square.
The line would be straight if the angle was 180°, so the most reasonable answer would be D. 120°.
sweet t has 1,258 staples that he will use to create art canvases. Each canvas requires 24 staples. How many canvases can he make AND how many staples will he have remaining
Answer:
He can make 52 canvases and will have 10 remaining staples
Step-by-step explanation:
1258/24=52 10/24
Answer:
52 canvases can be prepared and 10 staples will be remaining
Step-by-step explanation:
Sweet t has number of staples to create art canvases = 1258
Each canvas requires number of staples = 24
Let n canvases can be prepared by these staples.
Number of staples used in n canvases = 24n
The expression representing this process will be
24n = 1258
n = [tex]\frac{1258}{24}[/tex]
= 52.42 canvases
Staples used to prepare 52 canvases = 52 × 24
= 1248
Remaining staples = 1258 - 1248
= 10 staples
Therefore, 52 canvases can be prepared and 10 staples will be remaining.
what is the midpoint between (-8,5) and (2,-2)
Answer:
the midpoint between (8,5) and (2,-2) is P(5,1.5)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{2-8}{2}~~,~~\cfrac{-2+5}{2} \right)\implies \left( \cfrac{-6}{2}~,~\cfrac{3}{2} \right)\implies \left(-3~~,~~1\frac{1}{2} \right)[/tex]
8.What is the lateral area and the surface area of the cone shown below? Round the answers to the nearest tenth.the figure is not drawn to scale.
if you have the answers for the whole test I'll take them too please
Answer:
Part 1) The lateral area is [tex]LA=791.7\ ft^{2}[/tex]
Part 2) The surface area is [tex]SA=1,244.1\ ft^{2}[/tex]
[tex]LA=791.7\ ft^{2}[/tex], [tex]SA=1,244.1\ ft^{2}[/tex]
Step-by-step explanation:
step 1
Find the lateral area of the cone
we know that
The lateral area of the cone is equal to
[tex]LA=\pi rl[/tex]
we have
[tex]r=12\ ft[/tex]
[tex]l=21\ ft[/tex]
substitute
[tex]LA=(3.1416)(12)(21)=791.7\ ft^{2}[/tex]
step 2
Find the surface area of the cone
we know that
The surface area of the cone is equal to
[tex]SA=\pi r^{2}+LA[/tex]
we have
[tex]r=12\ ft[/tex]
[tex]LA=791.7\ ft^{2}[/tex]
substitute
[tex]SA=(3.1416)(12)^{2}+791.7=1,244.1\ ft^{2}[/tex]
To investigate a community’s reading habits, a magazine invites readers to complete and mail in a survey. What is the sampling method?
A. Convenience Sampling
B. Systematic Sampling
C. Self-Selected Sampling
D. Random Sampling
Does the sampling method have any bias?
A. Yes, because the survey is leading. It suggests that a certain answer is wanted.
B. Yes, because the people who respond to the survey may underrepresent the number of readers in the community.
C. No, the sampling method has no bias because part of the population equally represents the entire population.
D. Yes, because the people who respond to the survey may overrepresent the number of readers in the community.
The sampling method used in this case is Self-Selected Sampling (C) and it has bias because those who respond to the survey may overrepresent the number of readers in the community.
Explanation:The sampling method used in this case is Self-Selected Sampling (C). The magazine invites readers to complete and mail in a survey, therefore the readers themselves choose whether or not to participate. There is no random selection involved in this sampling method.
The sampling method used in this case does have bias. (D) Yes, because the people who respond to the survey may overrepresent the number of readers in the community.
This is because only those who choose to respond will be included in the sample, and those who are more interested in the magazine or have strong opinions about reading may be more likely to respond.
Final answer:
The sampling method used in this situation is Convenience Sampling, and it does have bias because it may underrepresent the number of readers in the community.
Explanation:
The sampling method used in this situation is Convenience Sampling. This is because the magazine invites readers to complete and mail in a survey based on their convenience, rather than using a random or systematic method to select the sample.
The sampling method used in this situation does have bias. The correct answer is B. Yes, because the people who respond to the survey may underrepresent the number of readers in the community. This is because the sample is based on self-selection, meaning that only those who choose to respond to the survey are included. This can result in a biased sample that may not accurately represent the entire community's reading habits.
Three 3/10 converted into a decimal
Answer:
3.3
Step-by-step explanation:
3 3/10 = 3 + 3/10 = 3 + 0.3 = 3.3
A store had 800 T-shirts in stock for a weekend sale.T-shirts are sold in packs of 4 each.During the sale,20 packs of T-shirts were sold on Saturday, and 70 more packs were sold on Sunday.
During the weekend sale, a total of 360 T-shirts were sold from the initial stock of 800 T-shirts in packs of 4. This resulted in 440 T-shirts leftover in stock after the sale.
Explanation:In the context of the store scenario, we have an initial stock of 800 T-shirts, which are sold in packs of 4 each. On Saturday, 20 packs are sold, resulting in a reduction of 20 packs times 4 shirts per pack, which equals 80 shirts. On Sunday, 70 more packs are sold, which corresponds to 70 packs times 4 shirts per pack, totaling 280 shirts sold on Sunday. Adding up the shirts sold on both days, we get 80 + 280, which equals 360 shirts sold in total during the weekend. To find the remaining stock, we subtract the total shirts sold from the initial stock: 800 shirts - 360 shirts = 440 shirts remaining after the sale.
Complete the following statement ( round your answer to the nearest hundredth)
f(7)=
Okay so in this question it says to solve f(7). This means to plug in the 7 every where you see an x, so that it looks like this: [tex]\frac{3}{7+2} -\sqrt{7-3}[/tex]Then you'll solve it like a normal equation.
Hope this helped! Let me know if there is anything I need to clarify or explain more in depth!
Answer:
- 1.67
Step-by-step explanation:
To evaluate f(7) substitute x = 7 into the expression
f(7) = [tex]\frac{3}{7+2}[/tex] - [tex]\sqrt{7-3}[/tex]
= [tex]\frac{3}{9}[/tex] - [tex]\sqrt{4}[/tex]
= [tex]\frac{1}{3}[/tex] - 2
= [tex]\frac{1}{3}[/tex] - [tex]\frac{6}{3}[/tex]
= - [tex]\frac{5}{3}[/tex] ≈ - 1.67
Jana finished 1/4 of her homework at school and 2/3 of it before dinner how much of her homework has she finished so far
Answer:
11/12
Step-by-step explanation:
1/4+2/3
1/4×3/3+2/3×4/4
3/12+8/12
a shopper gives a cashier $60 to pay for a $49 how much does the cashier of the shopper
Answer:
$11.00
Explanation:
$60 given - $49 order = $11 change
Answer:
It's 11 because 60-49 equals 11.
Step-by-step explanation:
Solve for x.
A.
x = 4
B.
x = 3
C.
x = 12
D.
x = 1v
Answer:
the answer is a
Step-by-step explanation:
One number is 5 times another number. The product of the two numbers is 245. Find the two numbers.
Let's assume the unknown number is x and as another one is 5 times the number then second number is 5x
》x × 5x = 245
》5x square =245
》x square =245÷5
》x square =49
》x=7
So 5x = 5×7=35
Two quadratic functions are shown.
Function 1:
f(x) = 2x2 - 8x + 1
Function 2:
x g(x)
-2 2
-1 -3
0 2
1 17
Which function has the least minimum value and what are its coordinates? (5 points)
Function 1 has the least minimum value and its coordinates are (0, 1).
Function 1 has the least minimum value and its coordinates are (2, -7).
Function 2 has the least minimum value and its coordinates are (0, 2).
Function 2 has the least minimum value and its coordinates are (-1, -3).
Answer:
Function 1 has the least minimum value and its coordinates are (2, -7).
Step-by-step explanation:
Two quadratic functions are shown.
Function 1:
[tex]f(x) = 2x^2 - 8x + 1[/tex]
Function 2:
x g(x)
-2 2
-1 -3
0 2
1 17
LEts find the vertex to get the minimum value
to get the minimum value for function 1 we use formula [tex]x=\frac{-b}{2a}[/tex]
[tex]f(x) = 2x^2 - 8x + 1[/tex], a=2, b=-8
[tex]x=\frac{-b}{2a}=\frac{8}{2(2)}=2[/tex]
when x=2, the value of [tex]f(2) = 2(2)^2 - 8(2) + 1=-7[/tex]
minimum point of function 1 is (2,-7)
For function 2, we find the minimum point using the table
minimum point of function 2 is (-1,-3)
Function 1 has the least minimum -7.
Function 1 has the least minimum value and its coordinates are (2, -7).
The true statement is (b) function 1 has the least minimum value and its coordinates are (2, -7).
The first quadratic function is given as:
[tex]f(x)= 2x^2 - 8x +1[/tex]Factor out 2 in the above equation
[tex]f(x)= 2(x^2 - 4x) +1[/tex]
Rewrite the expression in the bracket, as follows:
[tex]f(x)= 2(x^2 - 4x + 4 - 4) +1[/tex]
This gives
[tex]f(x)= 2(x^2 - 4x + 4 ) -8+1[/tex]
[tex]f(x)= 2(x^2 - 4x + 4 ) -7[/tex]
Express x^2 - 4x + 4 as a perfect square
[tex]f(x)= 2(x - 2)^2 -7[/tex]
A quadratic function is represented as:
[tex]f(x)= a(x - h)^2 +k[/tex]
Where
[tex]Vertex = (h,k)[/tex]
By comparison, we have:
[tex]Vertex = (2,-7)[/tex] --- this represents the minimum of function 1From the graph, the minimum of function 2 is:
[tex]Vertex = (-1,-3)[/tex](2,-7) is lesser than (-1,-3).
Hence, the function 1 has the least minimum value at a coordinate of (2,-7)
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What is M
A.
42°
B.
50°
C.
58°
D.
100°
Answer:
C. 58°
Step-by-step explanation:
m∠ACB=(180-138)°
m∠B + m∠A +∠mACB =180
80+ m∠A + (180 -138) =180
80 + m∠A - 138 = 0
m∠A = 58
Answer:
C
Step-by-step explanation:
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ACD is an exterior angle of the triangle and
∠A and ∠B are the 2 opposite interior angles, hence
∠A + ∠B = 138, that is
∠A + 80 = 138 ( subtract 80 from both sides )
∠A = 58° → C
Order the following measures from least to greatest: 0.5 m, 30 in, 1.25 ft, 17cm
Answer:
30 in, 0.5 m, 1.25 ft, 17 cm
30in, 0.5m, 1.25, 17cm
42x^3+35×^2-36x-30 factor
Answer:
(6x + 5)(7x² - 6)
Step-by-step explanation:
Factor the first/second and third/fourth term
42x³ + 35x² - 36x - 30
= 7x²(6x + 5) - 6(6x + 5) ← factor out (6x + 5) from each term
= (6x + 5)(7x² - 6)
Answer:
(6x+5)(7x2−6)
Step-by-step explanation:
Factor 42x3+35x2−36x−30
42x3+35x2−36x−30
=(6x+5)(7x2−6)
Line AB is parallel to Line CD. Line AC and Line BD are perpendicular to Line AB and Line CD. What is the relationship between AC and BD?
Line AC and Line BD are perpendicular to each other.
Explanation:In this scenario, we have Line AB parallel to Line CD, and both Line AC and Line BD are perpendicular to Line AB and Line CD. Since two perpendicular lines intersect at a 90-degree angle, we can say that Line AC and Line BD are also perpendicular to each other. This means that Line AC forms a 90-degree angle with Line BD.
Order numbers to least to greatest 0.8,8%,18%,1/8,8/18
Answer 8%, 1/8, 18%, 8/18, 0.8
Step-by-step explanation:
0.8 = 80%
1/8 = 12.5%
8/18 = 44.4%
8% < 12.5% < 18% < 44.4% < 80%
Four resistors are connected in series such that their total resistance is 50ohm . If the resistance of resistors is 5 ohm , 10ohm and 15 ohm respectively .find tue resistance of the fourth resistor
[tex]\boxed{R_{4}=20\Omega}[/tex]
Step-by-step explanation:If resistors are in series, so the current [tex]I[/tex] is the same in all of them. In this problem we have four resistors. So, we can get a relationship between the Equivalent resistance of series combination and the four resistors as follows:
[tex]R_{eq}=R_{1}+R_{2}+R_{3}+R_{4}[/tex]
[tex]R_{eq}[/tex] is the total resistance [tex]50\Omega[/tex]. Moreover:
[tex]R_{1}=5\Omega \\ R_{2}=10\Omega \\ R_{3}=15\Omega[/tex]
Therefore:
[tex]50=5+10+15+R_{4} \\ \\ R_{4}=50-(5+10+15) \\ \\ R_{4}=50-30 \\ \\ \boxed{R_{4}=20\Omega}[/tex]
Choose all of the rectangular prisms that have a volume of 24
Answer:
pictures 1, 2, 4, and 6
Step-by-step explanation:
The chart shows the marginal revenue of producing apple pies.
According to the chart, the marginal revenue
decreases by ten dollars as production increases.
increases by ten dollars as production increases.
falls to zero dollars as production increases.
remains the same as production increases.
Answer:
(d) remains the same as production increases
Step-by-step explanation:
All of the numbers in the Marginal Revenue column are the same. That means we can conclude marginal revenue ...
remains the same as production increases.
Answer:
(d) remains the same as production increases
Step-by-step explanation:
what is the distance in units between (-1, -5) and (-9,-5) on a coordinate plane
Answer:
8 units
Step-by-step explanation:
Calculate the distance (d) using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 1, - 5) and (x₂, y₂ ) = (- 9, - 5)
d = [tex]\sqrt{(-9+1)^2+(-5+5)^2}[/tex]
= [tex]\sqrt{(-8)^2+0^2}[/tex]
= [tex]\sqrt{64}[/tex]
= 8 units