Answer:
31,783.5
Step-by-step explanation:
Half of 46601 = 23300.5
23300.5 + 8483 =31783.5
Which of the statements is true for the two division problems below? A: (x^2-3x-18)/(x-6) B. (x^3-x^2-5x-3)/(x^2+2x+1)
Answer:
B is the right statement
Answer:
add the answer choices
Step-by-step explanation:
You throw two four-sided dice. Let the random variable X represent the maximum value of the two dice. Compute E(X). Round your answer to three decimal places.
Answer:
E(X)=3.125
Step-by-step explanation:
We are given that two four sided dice.
Then , the sample space
{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}
Total number of outcomes=16
Let the random variable X represent the maximum value of the two dice
Outcomes X P(X)
(1,1) 1 1/16
(1,2),(2,1),(2,2) 2 3/16
(1,3),(2,3),(3,1),(3,2),(3,3) 3 5/16
(1,4),(3,4) ,(2,4),(4,1),(4,2),(4,3),(4,4) 4 7/16
Using the probability formula
[tex]P(E)=\frac{Favorable\;outcomes}{Total\;number\;of\;outcomes}[/tex]
Now,
[tex]E(X)=\sum_{i=1}^{n}x_iP(x_i)[/tex]
[tex]E(x)=1(1/16)+2(3/16)+3(5/16)+4(7/16)[/tex]
[tex]E(x)=\frac{1+6+15+28}{16}[/tex]
[tex]E(x)=\frac{50}{16}=3.125[/tex]
Match each set of vertices with the type of triangle they form.
A(2, 0), B(3, 2), C(5, 1)
obtuse scalene triangle
A(4, 2), B(6, 2), C(5, 3.73)
isosceles right triangle
A(-5, 2), B(-4, 4), C(-2, 2)
right triangle
A(-3, 1), B(-3, 4), C(-1, 1)
acute scalene triangle
A(-4, 2), B(-2, 4), C(-1, 4)
9514 1404 393
Answer:
rightacuteobtuserightobtuseStep-by-step explanation:
When the same problem is repeated, I like to solve it using a spreadsheet. That way, the formulas only need to be entered once, and the arithmetic is (almost) guaranteed to be done correctly.
A "form factor" computed from side lengths can be used to determine the type of triangle. Where 'c' is the long side, that factor can be computed as ...
f = a² +b² -c²
and interpreted as follows:
f = 0, right trianglef > 0, acute trianglef < 0, obtuse triangle(The sign of f matches the sign of the cosine of the largest angle computed using the law of cosines.)
Of course, a right triangle can also be identified by looking at the slopes of the sides of the triangle. If any pair of slopes has a product that is -1, or if any pair is 0 and "undefined", then the triangle will be a right triangle.
__
The attached spreadsheet is designed to accommodate a number of different problem requirements. It shows both side lengths and slopes, and it shows the "form factor" as described above. The final classification is shown at far right.
rectangle a is dilated to form rectangle b. what is the scale factor used .
Answer:
5
Step-by-step explanation:
The scale factor is 5. Answered by Gauthmath
The length and the width of rectangle a are expanded 5 times respectively.
What is a scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.
According to the question
Rectangle a is dilated to form rectangle b.
By division operation, the ratio
[tex]\frac{20}{4} =\frac{30}{6} =5[/tex]
The length and the width of rectangle a are expanded 5 times respectively.
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Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^4, y=1 and the y-axis and whose cross-sections perpendicular to the x axis are semicircles.
The base of the solid - call it B - is the set of points
B = {(x, y) : 0 ≤ x ≤ 1 and x ⁴ ≤ y ≤ 1}
Recall the area of a circle with radius r is πr ²; in terms of the diameter d = 2r, the area is π (d/2)² = π/4 d ². Then the area of a semicircle with the same diamater is half of this, π/8 d ².
Cross sections of the solid in question are semicircles arranged perpendicular to the x-axis, which means the diameters of each cross section corresponds to the vertical distance between y = x ⁴ and y = 1 for any given values of x between 0 and 1. So d = 1 - x ⁴, which makes the area of each cross section come out to π/8 (1 - x ⁴)².
Split up the solid into very thin cross sections with "base" area π/8 (1 - x ⁴)² and thickness ∆x. Take the sum of these half-cylinders' volumes, then let ∆x converge to 0. In short, we get the total volume by integrating,
[tex]\displaystyle \int_0^1\frac\pi8(1-x^4)^2\,\mathrm dx = \frac\pi8\int_0^1(1-2x^4+x^8)\,\mathrm dx = \boxed{\frac{4\pi}{45}}[/tex]
Mr Gardner is making 6 treat bags. He has 185 chocolate-covered raisins to share evenly among the treat bags.
Answer:
✎There will be 30 Chocolate-Covered raisins in each bag.
✎ And 5 Remaining.
Step-by-step explanation:
Take 185 and divide it by 6 and you should get 30 per bag with a remainder of 5 :)
The cost of an apple has decreased from $0.50 to $0.40. Work out the decrease cost of an apple as a percentage.
Answer:
Decreased by 20%
Step-by-step explanation:
0.5 x ? = 0.4
? = 0.4/0.5
? = 0.8
1 - 0.8 = 0.2
0.2 = 20%
To check, 20% of 0.5 is 0.1. 0.5 - 0.1 is 0.4. So the answer is correct.
In the figure, triangles ABC and DEF are congruent.
Find the measure of DF.
a. 13m
b. 12m
c. 7m
d. 13.928m
Simplify: x^d • x ^18
Answer:
x^(d+18)
Step-by-step explanation:
using the law of indices
you must add the powers
Answer:
[tex] {x}^{d + 18} [/tex]
Step-by-step explanation:
[tex]\sf{x^d.x^{18} }[/tex] [tex]\sf{ x^{d+18} }[/tex]Scores on the SAT are approximately normally distributed. One year, the average score on the Math SAT was 500 and the standard deviation was 120. What was the score of a person who did better than 85% of all the test-takers
Answer:
The score of a person who did better than 85% of all the test-takers was of 624.44.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
One year, the average score on the Math SAT was 500 and the standard deviation was 120.
This means that [tex]\mu = 500, \sigma = 120[/tex]
What was the score of a person who did better than 85% of all the test-takers?
The 85th percentile, which is X when Z has a p-value of 0.85, so X when Z = 1.037.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.037 = \frac{X - 500}{120}[/tex]
[tex]X - 500 = 1.037*120[/tex]
[tex]X = 624.44[/tex]
The score of a person who did better than 85% of all the test-takers was of 624.44.
Which of the binomials below is a factor of this trinomial?
x^2+8x+16
This is because the given expression factors to (x+4)(x+4), which condenses to (x+4)^2.
To factor, think of two numbers that A) multiply to 16, and B) add to 8. Those values would be 4 and 4
4+4 = 8
4*4 = 16
So that's how we end up with (x+4)(x+4). You can use the FOIL rule to expand that out and get x^2+8x+16 again to help verify you have the correct factorization.
How many gallons each of 15% alcohol and 10% alcohol should be mixed to obtain 5 gal of 13% alcohol?
9514 1404 393
Answer:
3 gallons 15%2 gallons 10%Step-by-step explanation:
Let x represent the quantity of 15% alcohol required. Then (5-x) is the amount of 10% alcohol needed. The amount of alcohol in the mix is ...
0.15x +0.10(5-x) = 0.13(5)
0.05x +0.5 = 0.65 . . . . . . . simplify
0.05x = 0.15 . . . . . . . . . subtract 0.5
x = 3 . . . . . . . . . . . . . divide by 0.05
3 gallons of 15% alcohol and 2 gallons of 10% alcohol should be mixed.
(2/3)^x-1=27/8, find x. Please add a step-by-step explanation.
[tex]( \frac{2}{3} ) {x - 1 = \frac{27}{8} }^{?} [/tex]
so basically after doing all the algebra, you will have to use the log function to solve. rearranging things and you will get the log expression that I obtained, then solve it using the change of base formula.
Choose the correct solution for the given equation x^2-6x=40
Answer:
10,-4
Step-by-step explanation:
not sure where the options are but if you were to solve this equation first bring everything to one side.
x^2 - 6x - 40 = 0
factor it
(x-10)(x+4) = 0
set each part to 0
x-10 = 0 and x+4 = 0
solutions are 10 and -4
A town recently dismissed 8 employees in order to meet their new budget reductions. The town had 9 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that at least 7 employees were over 50? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
The probability that at least 7 employees were over 50 is 0.0073%.
Step-by-step explanation:
Given that a town recently dismissed 8 employees in order to meet their new budget reductions, and the town had 9 employees over 50 years of age and 16 under 50, if the dismissed employees were selected at random, to determine what is the probability that at least 7 employees were over 50, the following calculation must be performed:
9/25 x 8/24 x 7/23 x 6/22 x 5/21 x 4/20 x 3/19 = X
0.36 x 0.33 x 0.304 x 0.272 x 0.238 x 0.2 x 0.157 = X
0.000073 = X
100X = 0.0073
Therefore, the probability that at least 7 employees were over 50 is 0.0073%.
porfavor se los agradeceria mucho y de corazon :D
Answer:
1=2p+3
2=
Step-by-step explanation:
Please helpppp me I really confused
Answer:
The answer would be D
Step-by-step explanation:
This is a piecewise function, meaning that it is split into two parts. The right side is an exponential and that part is greater than one, the left side is a line less than or equal to one. The only equation that matches the criteria for that is D.
What is the range of the data set shown below?
A. 36
B. 34
C. 32
D. 30
Answer:
b 34 the higest is 40 an the lowest 6 the diferens is 34
Step-by-step explanation:
Mark me brainlest pliz
Answer:
i would but this not my question this is theres he right A.
Step-by-step explanation:
(4-21)(1 + 71) help plz
the answer would be -1,224 because the parentheses is your multiplication and the it is a negative
Write the equation of a line in the slope-intercept form that has a slope of 4
and contains the point (4, 12).
Answer:
The equation of the point (4, 12) is y=4x+12
Which statement is true about the parts of this expression?
StartFraction 5 over 6 EndFraction + one-fourth x minus y
The constant is StartFraction 5 over 6 EndFraction.
The only coefficient is One-fourth.
The only variable is y.
The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.
Answer:
The constant is StartFraction 5 over 6 EndFraction
Step-by-step explanation:
StartFraction 5 over 6 EndFraction + one-fourth x minus y
5/6 + 1/4x - y
A. The constant is StartFraction 5 over 6 EndFraction.
True
B. The only coefficient is One-fourth.
False
There are two coefficients: the coefficient of x which is 1/4 and the coefficient of y which is 1
C. The only variable is y
False
There are 2 variables: variable x and variable y
D. The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.
False
5/6 and 1/4x are not like terms
The only true statement is: The constant is StartFraction 5 over 6 EndFraction
Answer:
It's A if you don't want to read. A). The constant is 5/6
Step-by-step explanation:
Based on a poll, among adults who regret getting tattoos, 24% say that they were too young when they got their tattoos. Assume that six adults who regret getting tattoos are randomly selected, and find the indicated probability.
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.
Answer:
a) 0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.
b) 0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c) 0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they say they were too young to get tattoos, or they do not say this. The probability of a person saying this is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
24% say that they were too young when they got their tattoos.
This means that [tex]p = 0.24[/tex]
Six adults
This means that [tex]n = 6[/tex]
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.24)^{0}.(0.76)^{6} = 0.1927[/tex]
0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
This is P(X = 1). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{6,1}.(0.24)^{1}.(0.76)^{5} = 0.3651[/tex]
0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.
This is:
[tex]p = P(X = 0) + P(X = 1) = 0.1927 + 0.3651 = 0.5578[/tex]
0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.
Random samples of size 81 are taken from a population whose mean is 45 and standard deviation is 9. Calculate the probability that a sample mean is less than 42. (round to 4 decimal places)
HINT: When you randomly select a group (n > 1) then you need to re-calculate the standard deviation using the formula:
σ n
Answer:
Using z table
= 0.0013
The probability = 0.0013
Step-by-step explanation:
Given that,
mean = μ = 45
standard deviation = σ = 9
n=81
μT = μ =45
[tex]\sigma T = \sigma / \sqrt n = 9 / \sqrt81 =1[/tex]
[tex]P(T <42 )\\= P[(T - \mu T ) / \sigma T < (42-45) /1 ]\\\\= P(z <-3 )[/tex]
Using z table
= 0.0013
probability= 0.0013
Our soccer team lost 9 games this season. That was 3/8 of all they played. How many games did they play this season?
Answer:
15
Step-by-step explanation:
3/8 = 9
9÷3= 3
the remainder of 3/8 is 5/8 so
5x3=15
Find the number of distinguishable arrangements of the letters of the word SEPTILLION
Answer:
10!
Step-by-step explanation:
Septillion-10 letters
1-s-10 places to be in
2-e-9
3-p-8
4-t-7
5-i-6
6-l-5
7-l-4
8-i-3
9-o-2
10-n-1
So, then
10×9×8×7×6×5×4×3×2×1=10!
or 3628800
The arrangement of the number will be equal to 3628800.
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a way to choose items or numbers from a collection or group of items without worrying about the items' chronological order.
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
The given word is SEPTILLION. The word has 10 characters. The different ways of the arrangement will be calculated as,
Arrangement = 10!
Arrangement = 10×9×8×7×6×5×4×3×2×1
Arrangement = 3628800
Therefore, the arrangement of the number will be equal to 3628800.
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Solve the following system of equations by using the inverse of a matrix.
Give your answer as an ordered triple (x , y , z)
Answer:
(x, y, z) = (-8,4,-2)
Step-by-step explanation:
.......................................
Translate To An Algebraic Expression:
S% of 1/r
Answer:
S/100r
Step-by-step explanation:
S% of 1/r = (1/r x S) : 100
(1/r x S) : 100
S/r : 100
S/100r
While planning a hiking trip, you examine a map of the trail you are going on hike. The scale on the map shows that 2 inches represents 5 miles.
If the trail measures 12 inches on the map, how long is the trail?
Answer:
30 miles
Step-by-step explanation:
Given that :
Scale = 2 inches represents 5 miles
This means that 2 inches in the map equals to 5 miles on ground ;
Hence, if the trail measures 12 inches on the map, the length on ground will be ; x
2 inches = 5 miles
12 inches = x miles
Cross multiply :
2x = (12 * 5)
2x = 60
x = 60 / 2
x = 30 miles
Consider the function z(x,y) describing the paraboloid \[z = (2x - y)^2 - 2y^2 - 3y.\]Archimedes and Brahmagupta are playing a game. Archimedes first chooses $x.$ Afterwards, Brahmagupta chooses $y.$ Archimedes wishes to minimize $z$ while Brahmagupta wishes to maximize $z.$ Assuming that Brahmagupta will play optimally, what value of $x$ should Archimedes choose?
Answer: -3/8
Step-by-step explanation:
Expanding z we get
z = 4x^2 - 4xy + y^2 - 2y^2 - 3y
= -y^2 - (4x + 3) y + 4x^2.
After Archimedes chooses x, Brahmagupta will choose
y=-(4x+3/2) in order to maximize z
Then
z=-((-4x+3)/2)^2 -(4x+3)(-4x+3)/2)^2)+4x^2
z=8x^2+6x+9/4
To minimize this expression, Archimedes should choose x=-3/8
one month is what percentage of a year given that there are 7 days in a week, and 12 months in a year
Answer:
it should be 8.333333%
Step-by-step explanation:
