Answer:
80
Step-by-step explanation:
The cube Peggy wants to build will require 5×5×5 = 125 unit cubes. Since she has 45, she will need 80 more.
____
Peggy's cube will have 5 cubes along one edge. Then one layer will be 5 times that many, so 25 cubes. The 5 layers will be 5 times that many, so 125 cubes.
Find the indefinite integral by using the substitution x = 4 sec(θ). (Use C for the constant of integration.) x2 − 16 x d
Answer:
[tex]\frac{x^2-16}{2} + 16ln\frac{4}{x} +16C[/tex]
Step-by-step explanation:
Given the indefinite integral [tex]\int\limits{\frac{x^2-16}{x} } \, dx[/tex], using the substitute
x = 4 sec(θ)...1
The integral can be calculated as thus;
First let us diffrentiate the substitute function with respect to θ
dx/dθ = 4secθtanθ
dx = 4secθtanθdθ... 2
Substituting equation 1 and 2 into the integral function we will have;
[tex]\int\limits{\frac{(4sec \theta)^2-16}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\int\limits{\frac{16sec^2 \theta-16}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\int\limits{\frac{(16(sec^2 \theta-1)}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\\from \ trig \ identity,\ sec^2 \theta - 1 = tan^\theta\\\\\int\limits{\frac{16 tan^2 \theta}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\\\int\limits 16 tan^3 \theta d \theta\\\\[/tex]
Find the remaining solution in the attachment.
What is the pre-image of vertext A' if the rule that created the image is
Answer:
a
Step-by-step explanation:
the pythagorean theorem suggests it
At a particular chess club, it is quite common for a chess game to take over two hours to complete. Suppose that the lengths of these games are normally distributed with a mean of 153 minutes and a standard deviation of 45 minutes. Games which last in the longest 1% of all contests are given special recognition on an "Endurance Board" for all club members to see. How long would a game need to last to qualify for the "Endurance Board?"
Answer:
A game would need to be at least 257.67 minutes long to qualify for the Endurance Board.
257.67 minutes = 257 minutes, 40 seconds = 4 hours, 17 minutes, 40 seconds.
Step-by-step explanation:
Games that are given special recognition on the Endurance Board are the games that last in the longest 1% of all games.
If X is the random variable that represents the time a chess game takes before it is completed.
X is said to be normally distributed with
Mean = μ = 153 minutes
Standard deviation = σ = 45 minutes
Let games that last the longest 1% of the time last for a minimum of x' minutes.
P(X > x') = 1% = 0.01
P(X ≤ x') = 1 - P(X > x') = 1 - 0.01
P(X ≤ x') = 0.99
Indicating that such games are longer than 99% of all chess games.
This is a normal distribution problem
Let the z-score for these type of longest games with a minimum duration of x' minutes be z'.
P(X ≤ x') = P(z ≤ z') = 0.99
From the normal distribution table, z' = 2.326
z-score of any value is given as the value minus the mean divided by the standard deviation.
z = (x - μ)/σ
So,
z' = (x' - μ)/σ
2.326 = (x' - 153)/45
x' = (2.326×45) + 153
x' = 104.67 + 153 = 257.67 minutes = 257 minutes, 40 seconds.
Hope this Helps!!!
Suppose the eight committee members are ranked and the seating arrangements matter based off of rank. In how many ways can they sit in the 12 possible chairs
Answer:
They can sit in 19,958,400 ways
Step-by-step explanation:
The seating arrangements matter based off of rank, which means that we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
8 seats from a set of 12. So
[tex]P_{(12,8)} = \frac{12!}{(12-8)!} = 19,958,400[/tex]
They can sit in 19,958,400 ways
simplify
[tex] \sqrt{105} [/tex]
Answer:
C. √105
Step-by-step explanation:
105 = 3·5·7 has no square factors, so its root cannot be simplified.
√105 simplified is √105.
2. Solve the following.
a. 18:2/3
Answer:
Step-by-step explanation:
18 : 2/3
can also be written as 18 / 2/3 = 18 × 3/2
= 27
Hope it helps
plz mark as brainliest!!!!!
help help help pls pls
Answer:
C. 2y = -12
Step-by-step explanation:
Well a function is when all x values have only one corresponding y value and on a graph we can use the vertical line test and in doing so we know that the answer is C. 2y = -12
Answer:
Step-by-step explanation:hi
Given that Samuel is collecting data on the number of meals that students eat in a week, what type of data is he working with?
Answer:
discrete quantitative
Step-by-step explanation:
The number of meals that students eat is a numeric variable, which makes it a quantitative variable. However, it can only be measured in integers (assuming that there is no such thing as half a meal), which makes the data he is working with a discrete quantitative variable.
if 1/u=1/f-1/v is the formula Express f as the subject of the formula
Answer:
[tex]f = \frac{1}{\frac{1}{u}+\frac{1}{v} }[/tex]
Step-by-step explanation:
[tex]1/u=1/f-1/v\\\frac{1}{f} = \frac{1}{v} +\frac{1}{u} \\Divide- both- sides- by; 1\\\frac{1}{f} \div \frac{1}{1} = (\frac{1}{v} + \frac{1}{u}) \div \frac{1}{1}\\\\f = \frac{1}{\frac{1}{u}+ \frac{1}{v} }[/tex]
Answer:
f = uv/(v+u)
Step-by-step explanation:
1/u = 1/f - 1/v
1/u + 1/v = 1/f
(v+u) ÷ uv = 1 ÷ f
multiply both sides by uvf
f(v+u) = uv
f = uv / (v+u)
Lancelot Manufacturing is a small textile manufacturer using machineminus−hours as the single indirect − cost rate to allocate manufacturing overhead costs to the various jobs contracted during the year. The following estimates are provided for the coming year for the company and for the Case High School band jacket job.
Company Cae High School Job
Direct materials $40,000 $2,000
Direct labor $10,000 $400
Manufacturing overhead costs $45,000
Machine-hours 100,000 mh 900 mh
What is the bid price for the Case High School job if the company uses a 40% markup of total manufacturing costs?
A. $1,122.
B. $3,927.
C. $960.
D. $3,360.
Answer:
The correct answer is B.
Step-by-step explanation:
Giving the following information:
Job:
Direct materials= $2,000
Direct labor= $400
Machine-hours= 900 mh
Company:
Manufacturing overhead costs $45,000
Machine-hours 100,000 mh
Selling price= 40% markup of total manufacturing costs
First, we need to calculate the predetermined overhead rate to allocate overhead:
Predetermined manufacturing overhead rate= total estimated overhead costs for the period/ total amount of allocation base
Predetermined manufacturing overhead rate= 45,000/100,000
Predetermined manufacturing overhead rate= $0.45 per machine hour
Now, we can calculate the total cost and the selling price:
Total cost= 2,000 + 400 + 0.45*900= $2,805
Selling price= 2,805*1.4= $3,927
A repair shop repairs an average of 4.5 machines per hour. Let X be the time (in hours) before the first machine is repaired.(a) What is the probability that a repair time exceeds 4 hours?(b) What is the average time (in hours) it takes to repair the first machine?(c) The conditional probability that a repair takes at least 6 hours, given that it takes more than 4 hours?
Answer:
a) P(X>4)=e-4*4.5 =1.523*10-8 ~ 0.0000
b) 1/4.5 =0..2222 Hours
c) P(X>6|X>4) =P(X>2)=e-2*4.5 =0.000123
Step-by-step explanation:
y=x2+3x+1 has how many real roots?
Answer:
2 real solutions
Step-by-step explanation:
hello,
[tex]\Delta = b^2-4ac=3^2-4*1*1=9-4=5>0[/tex]
as this is > 0 there are 2 different real solutions
hope this helps
The quadratic equation, y = x² + 3x + 1 has two real roots.
How to define the nature of roots in a quadratic equation?In a quadratic equation of the form, ax² + bx + c = 0, the nature of the roots depends upon the value of the discriminant (D), which is calculated by the formula, D = b² - 4ac.
If the value of D > 0, the equation has real and distinct roots.
If the value of D = 0, the equation has real and equal roots.
If the value of D < 0, the equation has imaginary roots.
How to solve the questionIn the question, we are given an equation y = x² + 3x + 1 and are asked to say how many real roots it has.
To find the roots, we first equate y to 0.
∴ y = x² + 3x + 1 = 0.
Now comparing the equation x² + 3x + 1 to the standard equation ax² + bx + c, we get a = 1, b = 3, and c = 1.
Now, the nature of the roots depends upon the discriminant (D),
D = b² - 4ac = 3² - 4.1.1 = 9 - 4 = 5.
∵ Discriminant (D) > 0, the quadratic equation, y = x² + 3x + 1 has both its root real and distinct.
∴ The quadratic equation, y = x² + 3x + 1 has two real roots.
Learn more about quadratic equations at
https://brainly.com/question/1214333
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An oil company has two refineries. Refinery A produces 200 barrels of high-grade oil, 300 barrels of medium-grade oil, and 200 barrels of low-grade oil and costs $12,000 to operate. Each day, Refinery B produces 100 barrels of high-grade oil, 100 barrels of medium-grade oil, and 200 barrels of low-grade oil and costs $10,000 to operate. The company must produce at least 800 barrels of high-grade oil, 900 barrels of medium-grade oil, and 1,000 barrels of low-grade oil. What is the minimum cost to operate both refineries?
Answer:
$56,000
Step-by-step explanation:
If x is the number of days that Refinery A is in operation, and y is the number of days that Refinery B is in operation, then:
200x + 100y ≥ 800
300x + 100y ≥ 900
200x + 200y ≥ 1000
The total cost is:
C = 12,000x + 10,000y
x and y must be integers. Possible combinations are:
x = 0, y = 9
x = 1, y = 6
x = 2, y = 4
x = 3, y = 2
x = 4, y = 1
x = 5, y = 0
The costs of these combinations are:
[tex]\left[\begin{array}{ccc}x&y&C\\0&9&\$90,000\\1&6&\$72,000\\2&4&\$64,000\\3&2&\$56,000\\4&1&\$58,000\\5&0&\$60,000\end{array}\right][/tex]
The minimum cost is $56,000.
The mass of Box A and Box B is 0.6 kg. The mass of Box A and Box C is 1.3 kg.
Box C is 3 times as heavy as Box B. Find the mass of Box A.
Answer:
A=0.25
B=0.35
C=1.05
Step-by-step explanation:
1. A+B=0.6
2. A+C=1.3
3. C=3B
2 subtract 1:
C-B=0.73 substituted:
3B-B=0.7B=0.35C=0.7+0.35=1.05A=0.6-0.35=0.25www.g "7 Democrats and 6 Republicans. Four members are selected to attend a conference. Find the probability that the group will consist of all Republicans."
Answer:
2.10% probability that the group will consist of all Republicans.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the members are selected is not important. So we use the combinations formula to solve this question.
Combinations formula:
[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]
Desired outcomes:
4 republicans from a set of 6.
[tex]D = C_{6,4} = \frac{6!}{4!2!} = 15[/tex]
Total outcomes:
4 members from a set of 6 + 7 = 13.
[tex]T = C_{13,4} = \frac{13!}{4!9!} = 715[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{15}{715} = 0.021[/tex]
2.10% probability that the group will consist of all Republicans.
An exponential function has:
A. a straight line that can be increasing or decreasing.
B.a curved line that can be increasing or decreasing.
C. U-shaped curved lines that increase then decrease or decrease then increase.
D. None of these choices are correct.
Answer:
Answer B is the correct one: a curved line that can be increasing or decreasing.
Step-by-step explanation:
Exponential functions are one-to-one functions, which means that cannot have a U shape. Also, they are not a straight line, since they grow of decrease exponentially (based on a fixed numerical base with the variable as the exponent) They can represent exponential growth showing a curve with increasing values as we move from left to right, or can represent exponential decay showing a curve with decreasing values as we move from left to right.
Which absolute value function, when graphed, represents the parent function, f(x) = |x|, reflected over the x-axis and translated 1 unit to the right? f(x) = –|x| + 1 f(x) = –|x – 1| f(x) = |–x| + 1 f(x) = |–x – 1|
Answer:
Hello There. ♡ The correct answer is: f(x) = -|x-1|
The parent function is f(x) = |x|
Then the function is reflected over the x-axis, so the f(x) will become -f(x)'. The function will become:
f(x) = -|x|
-f(x)' = |x|
f(x)' = -|x|
After that, the function is translated 1 unit to the right. That mean x will become x'-1. The function will become:
f(x) = -|x|
f(x) = -|(x'-1)|
f(x) = -|x'-1|
Hope It Helps! :)
ItsNobody~ ♡
Answer:
its b on edge 2020
Step-by-step explanation:
how many are 4 x 4 ?
Answer: 16
Step-by-step explanation:
4 * 4 = 16
How many normal distributions are there? (1, 10, 30, infinite—pick one)
Answer:
Infinate
Step-by-step explanation:
The normal distribution is dependent on the standard deviation and what the value of the mean is. But this then implies that a different standard deviation or a different mean leads to a different normal distribution. Making there many possibilities for normal distributions.
There are infinitely many possibilities for normal distributions as there are indefinitely many values possible for both the mean and standard deviation.
HELP what transformation to the linear parent function , f(x)=x gives the function g(x)=x+8
Answer:
Vertical translation up 8.
Step-by-step explanation:
Vertical translation up 8.
John is a drummer who purchases his drumsticks online. When practicing with the newest pair, he notices they feel heavier than usual. When he weighs one of the sticks, he finds that it is 2.44 oz. The manufacturer's website states that the average weight of each stick is 2.00 oz with a standard deviation of 0.19 oz. Assume that the weight of the drumsticks is normally distributed. What is the probability of the stick's weight being 2.44 oz or greater? Give your answer as a percentage precise to at least two decimal places.
Answer:
1.02% probability of the stick's weight being 2.44 oz or greater
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 2, \sigma = 0.19[/tex]
What is the probability of the stick's weight being 2.44 oz or greater?
As a decimal, this is 1 subtracted by the pvalue of Z when X = 2.44. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.44 - 2}{0.19}[/tex]
[tex]Z = 2.32[/tex]
[tex]Z = 2.32[/tex] has a pvalue of 0.9898
1 - 0.9898 = 0.0101
1.02% probability of the stick's weight being 2.44 oz or greater
A candidate in an election lost by 5.4% of the vote. The candidate sued the state and said that more than 5.4% of the ballots were defective and not counted by the voting machine, so a full recount would need to be done. His opponent wanted to ask for the case to be dismissed, so she had a government official from the state randomly select 500 ballots and count how many were defective. The official found 19 defective ballots. Use a TI-83, TI-83 plus, or TI-84 calculator to test whether the candidate's opponent's claim is true and less than 5.4% of the ballots were defective. Identify the p-value, rounding to three decimal places
Answer: p value = 0.057
The candidate's opponent's claim of ( p < 0.054 ) is false
as p (0.057) is greater than 0.054.
(P > 0.054)
Step-by-step explanation:
p₀ = 5.4% = 0.054
Claim: p < 0.054
n = 500
x = 19
To perform z test for the proportion, we use TI-83, TI-83 plus, or TI-84 calculator
first;
Press STAT and go to TESTS menu.
Go to 1-Prop Z TEST
p₀ : 0.054
x : 19
n : 500
Prop < p₀
Calculate.
Output:
z = -1.582933013
p = 0.0567183695
therefore
p value = 0.057 ( three decimal place)
there the candidate's opponent's claim of ( p < 0.054 ) is false
as p > 0.054
Which of the following shows the union of the sets? {1, 5, 10, 15} {1, 3, 5, 7}
Answer:
{ 1,3,5,7,10,15}
Step-by-step explanation:
The union means join together, or all the elements of both sets
{1, 5, 10, 15} U {1, 3, 5, 7}
= { 1,3,5,7,10,15}
Answer:
Step-by-step explanation:
Union of two sets contains the elements that belongs to A set or B set or both
A= {1,5,10, 15}
B ={1,3,5,7}
A U B = {1,3,5,7,10,15}
Use the given information to determine if the geometric series converges or
diverges. If it converges, find the sum.
ai = 0.75; r = 5
a) The series converges to 3.75.
b) The series converges to 0.15.
c) The series diverges. There is no sum.
d) The series converges to 20.
Answer:
c) The series diverges. There is no sum.
Step-by-step explanation:
A geometric series is a series of the form:
[tex]S = \Sigma_{i=0}^{n} a\cdot r^{i}[/tex], [tex]\forall i \in \mathbb{N}_{O}[/tex]
Where:
[tex]a[/tex] - First term of the series, dimensionless.
[tex]r[/tex] - Common ratio, dimensionless.
A geometric series converges only if [tex]|r| < 1[/tex]. As [tex]r > 1[/tex], the geometric series diverges. Hence, the right answer is C.
Find the cardinal number for the given set
A = {6, 11, 16,...,76)
The cardinal number is
Answer:
15
Step-by-step explanation:
A={6,11,16,...,76}
a=6,d=11-6=5
[tex]a_{n}=a_{1}+(n-1)d\\76=6+(n-1)5\\76-6=(n-1)5\\n-1=70/5=14\\n=14+1=15[/tex]
so the cardinal number is 15
HELPSelect the correct answer.
Which table shows a proportional relationship between a and b?
Answer:
B
Step-by-step explanation:
table B: because when x increases y increases at the same rate and stay the same . the graph has proportional relation when it is a straight line passes through origin
for B :25/20=30/24=40/32=5/4
y=5/4 x
Can somebody help me with this math question?
Answer:
6(u-3)
Step-by-step explanation:
perimeter=2(length+width)
=2(2u-7+u-2)
=2(3u-9)
=6u-18
simplify 6(u-3)
How long will it take $4000 to grow into $5089.12 if it’s invested at 3.5% compounded annually?
Answer: 7 years
Step-by-step explanation:
From the formula A = P(1+(r/100))^t we have
5089.12 = 4000 (1+(3.5/100))^t
=> 1.27228 = (1.035)^t
Using calculator we find that 1.035^7 gives 1.272279
Hence in 7 years $4000 will grow to $5089.12 if it’s invested at 3.5%
factor the polynomial expression 16y^4-256x^12
Answer:
see explanation
Step-by-step explanation:
Given
16[tex]y^{4}[/tex] - 256[tex]x^{12}[/tex] ← factor out 16 from each term
= 16([tex]y^{4}[/tex] - 16[tex]x^{12}[/tex] ) ← difference of squares which factors in general as
a² - b² = (a - b)(a + b), thus
[tex]y^{4}[/tex] - 16[tex]x^{12}[/tex]
= (y² )² - (4[tex]x^{6}[/tex] )²
= (y² - 4[tex]x^{6}[/tex] )(y² + 4[tex]x^{6}[/tex] )
Now y² - 4[tex]x^{6}[/tex] ← is also a difference of squares
= y² - (2x³)²
= (y - 2x³)(y + 2x³)
Thus
16[tex]y^{4}[/tex] - 256[tex]x^{12}[/tex]
= 16(y - 2x³)(y + 2x³)(y² + 4[tex]x^{6}[/tex] )
Answer:
Step-by-step explanation:
4y^2+16x^6, 2y, 4x^3, 2y, 4x^3
Q2) The isoscsles right triangle has 2 of it’s sides 10,10 it’s area is
Answer:
Step-by-step explanation:
side a = 10
Area of isosceles triangle = [tex]\frac{\sqrt{3}a^{2}}{4}\\\\[/tex]
= [tex]\frac{\sqrt{3}*10*10}{4}\\\\=\sqrt{3}*5*5\\\\=25\sqrt{3}\\\\=25*1.732[/tex]
= 43.3 square units