Answer:
[tex]x^3+y^3[/tex]
Step-by-step explanation:
[tex](x+y)(x^2-xy+y^2)= \\\\x(x^2)+x(-xy)+x(y^2)+y(x^2)+y(-xy)+y(y^2)= \\\\x^3-x^2y+xy^2+x^2y-xy^2+y^3= \\\\\boxed{x^3+y^3}[/tex]
Hope this helps!
What is the value of a3 - b2 for a=3 and b = 1/2
Answer:
Answer = 26.75
Answer = 27
Step-by-step explanation:
[tex]a^{3} -b^{2} \\a =3\\b =\frac{1}{2} \\3^{3} -(\frac{1}{2} )^{2} \\27 -\frac{1}{4} \\\\\\Answer = 26.75\\Answer = 27[/tex]
Answer:
26 3/4 God bless!
Step-by-step explanation:
A country commits to decreasing spending for infrastructure in various ways at a rate of 30% per year. At the time of the announcement, the country is spending $12 billion per year. Which graph models the amount of infrastructure spending for future years?
Answer:
You want the curve to be decreasing from left to right since they are decreasing the amount spent so we can eliminate options 2 and 3. The initial amount (when x = 0) has to be 12 so the answer is the last option.
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8548 g and a standard deviation of 0.0512 g. A sample of these candies came from a package containing 444 candies, and the package label stated that the net weight is 379.3 g. (If every package has 444 candies, the mean weight of the candies must exceed 379.3/444 = 0.8543 g for the net contents to weigh at least 379.3 g.)
(a) If 1 candy is randomly selected, find the probability that it weighs more than 0.8542g. (Round to four decimal places as needed.)
(b) If 447 candies are randomly selected find the probability that their mean weight is at least 0.8542 g. (Round to four decimal places as needed.)
(c) Given these results does it seem that the candy company is providing consumers with the amount claimed on the label?
Answer:
a) 0.5047
b) 0.5978
c) Yes
Step-by-step explanation:
Given:
Mean, u = 0.8548
Standard deviation = 0.0512
Sample mean, X' = 0.8542
a) If 1 candy is randomly selected, the probability that it weighs more than 0.8542 would be:
[tex] z = \frac{X' - u}{\sigma} = \frac{0.8542 - 0.8548}{0.0512} = -0.0117 [/tex]
From standard normal table, NORMSTD(-0.0117) = 0.4953
P(z > -0.0117) = 1 - 0.4953 = 0.5047
Probability = 0.5047
b) If 447 candies are randomly selected the probability that their mean weight is at least 0.8542:
Here, we are to find the probability that the men weight is greater or equal to 0.8542
[tex] z = \frac{X' - u}{\sigma / \sqrt{n}} = \frac{0.8542 - 0.8548}{0.0512/ \sqrt{447}} = -0.24776 [/tex]
From standard normal table, NORMSTD(-0.24776) = 0.40216
P(z > -0.0117) = 1 - 0.40216 = 0.5978
Probability = 0.5978
c) Yes, it seems the candy company is providing consumers with the amount claimed on the label, because the probability of getting a sample mean of 0.8542 or greater when 447 candies are selected is not exceptionally small
is dilated by a scale factor of 3 to form . Point O, which lies on , is the center of dilation.
Answer:
qui qeruete va a lmismiasima mierda hjo dle uta pyalae mculosso
Step-by-step explanation:
Simplify (5^-2)^4 Please Help i don’t understand
Answer:
5^ -8 or 1/ 5^8
Step-by-step explanation:
(5^-2)^4
We know that a^b^c = a^(b*c)
(5^-2)^4 = 5^(-2*4) = 5^(-8)
We know that a^ - b = 1/ a^b
5^ -8 = 1/ 5^8
Consider the test of Upper H 0: The defendant is not guilty against Upper H Subscript a: The defendant is guilty. a. Explain in context the conclusion of the test if Upper H 0 is rejected. b. Describe the consequence of a Type I error. c. Explain in context the conclusion of the test if you fail to reject Upper H 0. d. Describe the consequence of a Type II error.
Answer:
(a) The conclusion of the test if null hypothesis is rejected is that we conclude that the null hypothesis that the defendant is not guilty is false and the defendant is found guilty and should be convicted.
(b) The consequence of a Type I error would be that an innocent defendant was found guilty and will be hanged but in actual he was not guilty.
(c) The conclusion of the test if we fail to reject the null hypothesis is that we conclude that the null hypothesis is true and the defendant is not guilty. The defendant should be set free.
(d) The consequence of a Type II error would be that a guilty defendant was set free but in actual it is found guilty and should be convicted.
Step-by-step explanation:
We are given the following hypothesis below;
Null Hypothesis, [tex]H_0[/tex] : The defendant is not guilty.
Alternate Hypothesis, [tex]H_A[/tex] : The defendant is guilty.
(a) The conclusion of the test if null hypothesis is rejected is that we conclude that the null hypothesis that the defendant is not guilty is false and the defendant is found guilty and should be convicted.
(b) Type I error states that the null hypothesis is rejected given the fact that null hypothesis was true.
So, here the Type I error would be to conclude that the defendant is guilty but in fact it was not guilty.
Hence, the consequence of a Type I error would be that an innocent defendant was found guilty and will be hanged but in actual he was not guilty.
(c) The conclusion of the test if we fail to reject the null hypothesis is that we conclude that the null hypothesis is true and the defendant is not guilty. The defendant should be set free.
(d) Type II error states that the null hypothesis is accepted given the fact that null hypothesis was false.
So, here the Type II error would be to conclude that the defendant is not guilty but in fact it was found guilty.
Hence, the consequence of a Type II error would be that a guilty defendant was set free but in actual it is found guilty and should be convicted.
Lots of points if answer is serious
Find the image of Z(1, 1) after two reflections, first across line 1, and then across line 2.
Line 1: y = 2
Line 2: x-axis
Answer:
The image of Z would be (1, -3).
Step-by-step explanation:
After reflecting across y = 2, Z' is (1, 3). Reflecting across the x-axis would make the y value negative, making it (1, -3).
Triangles L O A and L A M share side L A. Angles O L A and A L M are congruent. What additional information is needed to prove that the triangles are congruent using the AAS congruence theorem? LO ≅ LM OA ≅ MA AngleLOA ≅ AngleLMA AngleLAO ≅ AngleLAM
Answer:
Angle LOA = angle LMA
Step-by-step explanation:
I just took the test
From the diagram, the two triangles have an indication of a pair of
congruent angles.
The additional information needed is; ∠LOA ≅ ∠LMAReasons:
The given parameters of ΔLOA and ΔLAM are;
The shared side of the triangles = Side LA
From the attached diagram, we have;
∠ALO = ∠ALM
Required:
The additional information needed to prove that the triangles are congruent using AAS
Solution:
The AAS congruency is an acronym for Angle Angle Side, which states
that, two triangles are similar if two angles and a non included side of one
triangle are equal to two angles and a non included side on another
triangle, then the two triangles are congruent.
The angle on ΔLOA that will make the side LA a non included side is ∠LOA.
Similarly;
The angle on ΔLAM that will make the side LA a non included side is ∠LMA.
Therefore, the additional information needed to prove that the triangle are congruent using the AAS congruency theorem is; ∠LOA ≅ ∠LMA
Learn more about Angle Angle Side, AAS, rule of congruency here:
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Retro Rides is a club for owners of vintage cars and motorcycles. Every year the club gets together for a ride. This year, 50 vehicles
participated in the ride. The total number of tires of all the vehicles was 148. Assuming each car has 4 tires and each motorcycle has
2 tires, how many each of cars and motorcycles participated in the ride?
Answer:
24 cars, 26 motorcycles
Step-by-step explanation:
x = number of motorcycles
y = number of cars
x + y = 50
x = 50 - y
2x + 4y = 148
2(50 - y) + 4y = 148
100 - 2y + 4y = 148
100 + 2y = 148
2y = 48
y = 24 cars
x = 50 - 24
x = 26 motorcycles
Please answer this correctly
Answer:
1-5: Make it 1 unit tall
6-10: Make it 4 units tall
11-15: Make it 1 unit tall
16-20: Make it 0 units tall (Change nothing)
21-25: Make it 5 units tall
Step-by-step explanation:
1-5: 1 (1 number)
6-10: 7, 9, 9, 10 (4 numbers)
11-15: 13 (1 number)
16-20: (0 numbers)
21-25: 21, 23, 23, 25, 25 (5 numbers)
A publisher reports that 41% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually less than the reported percentage. A random sample of 320 found that 36% of the readers owned a laptop. Is there sufficient evidence at the 0.05 level to support the executive's claim? Find the value of the test statistic. Round your answer to two decimal places. Specify if the test is one-tailed or two-tailed. Determine the decision rule for rejecting the null hypothesis, H0. Make the decision to reject or fail to reject the null hypothesis. State the conclusion of the hypothesis test.
Step 1 of 6: State the null and alternative hypotheses.
Answer:
Step-by-step explanation:
Hello!
The objective is to test the claim that less than 41% of the publisher's readers own a laptop.
To do so, a sample of 320 readers was taken and the proportion of readers that own a laptop resulted in 36%
Be X: number of readers that own a laptop.
X~Bi(n;p)
n=320
Sample proportion p'= 0.36
The hypotheses are:
H₀: p ≥ 0.41
H₁: p < 0.41
α: 0.05
[tex]Z=\frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]≈N(0;1)
[tex]Z_{H_0}=\frac{0.36-0.41}{\sqrt{\frac{0.41(1-0.41)}{320} } }= -1.82[/tex]
This test is one-tailed to the left, meaning, that you'll reject the null hypothesis to small values of Z, there is only one critical value that defined the rejection region:
[tex]Z_{\alpha }= Z_{0.05}= -1.645[/tex]
The decision rule is:
If [tex]Z_{H_0}[/tex] ≤ -1.645, reject the null hypothesis.
If [tex]Z_{H_0}[/tex] > -1.645, do not reject the null hypothesis.
The calculated value is less than the critical value, then the decision is to reject the null hypothesis.
So at a 5% significance level, the test is significant. You can conclude that the population proportion of the publisher's readers that own a laptop is less than 41%.
I hope this helps!
SOMEONE PLEASE HELP ME !! ASAP!!
Answer:
A
Step-by-step explanation:
RT=12
TU=5
RU=12+5=17
RS=17+7=24
SU=√(RS²-RU²)=√(24²-17²)=√(24-17)(24+17)=√(7×41)=√287
area=1/2×12×√287=6×√287≈101.6 unit²
How many ways can Carlos choose 2 pizza toppings from a menu of 4 toppings if each topping can only be chosen once?
Answer:
30 different ways
Step-by-step explanation:
Hi
for the first topping she can choose 1 of 6 items
so she has 6 choices
and then the second topping she has 5 choices as each topping can only be chosen once
so it comes 6 * 5 = 30
URGENT I NEED HELPPPPP
Answer:
8/15
Step-by-step explanation:
Using Pythagorean Theorem the length of XZ is 15.
tan X = opposite / adjacent = YZ / XZ = 8 / 15.
Answer:
I think it is C, 8/15, sorry If I am wrong
Step-by-step explanation:
Find the difference between points P (4,6) and Q (8,9)
[tex]distance = \sqrt{x2 - x1 + y2 - y1} \\ here \\ \: \: \: \: x1 = 4 \\ \: \: \: \: x2 = 8 \\ \: \: \: \: y1 = 6 \\ \: \: \: \: y2 = 9 \\ now \: we \: have \: to \: substitute \: the \: given \: values \: in \: the \: above \: formula \\ we \: get \\ \: \: \: \: \: \: = \sqrt{8 - 4 + 9 - 6} \\ \: \: \: \: \: \: = \sqrt{4 + 3} \\ \: \: \: \: \: \: = \sqrt{7} \\ \\ hope \: it \: helped[/tex]
13 different cut flowers and I plan on using 7 of them. How many different selections of the 7 flowers are possible?
Answer:
7/13
Step-by-step explanation:
The orthocenter of a triangle may lie outside the triangle because an altitude does not necessarily intersect the____
of the triangle
A. Median
B. Angles
C. Sides
D. Vertices
Answer: sides
Step-by-step explanation:
The orthocenter of the triangle will be the intersection of the three altitudes of a triangle. The orthocenter has several vital properties with other parts of a triangle, including the area ,incenter circumcenter and more. Typically, the orthocenter is represented by letter H.
The altitude of a triangle is a line that passes through the vertex of a triangle and it is also perpendicular to the opposite side. The orthocenter of a triangle can lie outside the triangle because an altitude may not necessarily intersect the side.
Hep me on this please
Answer:
The answer is 2240m².
Step-by-step explanation:
Given that the formula of area of trapezium is A = 1/2×(a+b)×h where a and b represents the length and h is height :
[tex]area = \frac{1}{2} \times (a + b) \times h[/tex]
[tex]let \: a = 50 \\ let \: b = 90 \\ let \: h = 32[/tex]
[tex]area = \frac{1}{2} \times (50 + 90) \times 32[/tex]
[tex]area = \frac{1}{2} \times 140 \times 32[/tex]
[tex]area = 70 \times 32[/tex]
[tex]area = 2240 \: {m}^{2} [/tex]
Answer:
2,240 square meters
Step-by-step explanation:
The shape above is a trapezoid. Therefore, we can use the area formula for a trapezoid:
A=1/2(a+b) *h
where a is the short base, b is the long base is h is the height.
In this trapezoid, the short base is 50 meters , the long base is 90 meters and the height is 32 meters.
a= 50
b=90
h=32
A=1/2(50+90)*32
Add inside the parentheses first.
A=1/2(140)*32
Multiply 1/2 and 140, or divide 140 by 2.
A=70*32
Multiply 70 and 32
A=2240
Add appropriate units. In this case, the units are meters^2
A=2240 meters^2
The area of the playground is 2,240 meters^2
12 m 20 m 16 m 6m 10m x find the length represented by x for each pair of similar triangles
Answer:
x = 8mStep-by-step explanation:
Let the two triangles be represented as A and B.
Given two triangles with sides 12m 20m 16m and 6m 10m x.
Lengths of sides of triangle A = 12m, 20m, 16m
Lengths of sides of triangle B = 6m, 10m, x
It can be seen that each length of triangle A are twice that of B i.e triangle B dilated by a factor of 1/2.
A = 2B
Considering the 16m length in triangle A and comparing it with the 'x'm length in triangle B, we can get the unknown length x as shown;
16 = 2x
x = 16/2
x = 8m
a tree needs to be stake with four wires, each wire is attached to the trunk 6 feet above the ground, and then anchored to the ground 8 feet from the base of the tree. How many feet of the wire is needed for 5 trees???
Answer:
89
Step-by-step explanation:
What is the frequency of the function y=2sin(1/2 x)-3 *
Options::
1
1/2
2π
-3
Answer:
-3
Step-by-step explanation:
y = 2sin (1/2 x 0) -3
y = -3
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 95% confidence level with an error of at most 0.02
Complete question:
A state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.18.
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 95% confidence level with an error of at most 0.02? Round your answer up to the next integer.
Answer:
1418
Step-by-step explanation:
Given:
Sample proportion = 0.18
Level of significance = 1 - 0.95 = 0.05
u.E = 0.02
Required:
Find the sample size.
To find the sample size, n, use tge formula:
[tex] n = \frac{(Z_a_/_2)^2 p(1 - p)}{u.E^2} [/tex]
Using the Z table, [tex] Z_0_._0_5_/_2 [/tex] = 1.96
Thus,
[tex] n = \frac{1.96^2 * 0.18(1 - 0.18)}{0.02^2} [/tex]
[tex] n = 3.8451 * 0.1476}{0.0004} [/tex]
[tex] n = 1417.55[/tex]
Approximately 1418
Sample size woulb be 1418
A poster of area 3840 cm? has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the sides. Find the
dimensions that maximize the printed area.
(Use decimal notation. Give your answers as whole or exact numbers.)
width:
cm
height:
cm
Answer:
Dear user,
Answer to your query is provided below
The dimensions to maximise the printed area to 2160 is length = 100cm and width = 60cm
Step-by-step explanation:
Explanation for the answer is attached in the image
Put this equation into slope-
intercept form.
3x – 2y = 4
Answer:
y= 3/2x -2
Step-by-step explanation:
make y be on one side by itself ( -2y = -3x + 4 )
divide by negative 2 in order to get y by itself ( -2y/-2 = -3/-2 + 4/-2 )
two negatives make a positive ( y = 3/2 + -2 )
G(x) =19.60 + 1.75x what is the value of g (30) ?
Answer:
72.1
Step-by-step explanation:
G(x) =19.60 + 1.75x
Let x = 30
G(30) =19.60 + 1.75*30
=19.60 +52.5
72.1
A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 51 months and a standard deviation of 11 months. Using the Empirical Rule rule, what is the approximate percentage of cars that remain in service between 73 and 84 months
Answer:
The approximate percentage of cars that remain in service between 73 and 84 months
P( 73 < x < 84 ) = 0.02145 = 2.1 %
Step-by-step explanation:
Explanation:-
Given mean of the Population 'μ ' = 51 months
Standard deviation of the Population 'σ' = 11 months
Let 'X' be the random variable of Normal distribution
Let 'X' = 73
[tex]Z = \frac{x-mean}{S.D} = \frac{73-51}{11} = 2[/tex]
Let 'X' = 84
[tex]Z = \frac{84-51}{11} = 3[/tex]
The approximate percentage of cars that remain in service between 73 and 84 months
P( 73 < x < 84 ) = P( 2 < Z < 3)
= P( Z<3) - P( Z <2)
= 0.5 + A(3) - ( 0.5 + A(2))
= A(3) - A( 2)
= 0.49865 - 0.4772 ( From Normal table)
= 0.02145
P( 73 < x < 84 ) = 0.02145
The approximate percentage of cars that remain in service between 73 and 84 months
P( 73 < x < 84 ) = 0.02145 = 2.1 %
suppose you add 10^10 + 10^100. What, approximately, is the answer? A. 10^10 B. 10^100 C. 10^110 B. 10^1000
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
1 × 10^100.
So the answer's B
Answer:
B. 10^100
Step-by-step explanation:
10^10 + 10^100
10^10 ( 1 + 10^10)
10^10 x 10^10 = 10^100 bc 10 times 10 equals 100
Mark as brainliest if this helped! :))
A store that sells skis buys them from a manufacturer at a wholesale price of $87. The store’s markup rate is 50%
Answer: $130.50
Step-by-step explanation: $87 x .50 = $43.50 / $87 + $43.50 = $130.50
Help ?!!!!?!?????????????????
Suppose we want to choose a value of x within 3 units of 11. [This means a value of x that is less than 3 units away from 11.] Think about some values of x that meet this constraint. Write an inequality that represents all values of x that meet this constraint. On the number line below, represent all values of x that meet this constraint.
Answer:
(a) [8, 14]
(b) [tex]8 \leq x \leq 14[/tex]
(c)See attachment
Step-by-step explanation:
We want to choose a value of x within 3 units of 11.
(a)Now, 11-3=8 and 11+3=14
The possible values of x ranges is in the closed interval [8,14]
(b) Since x is within 3 units of 11., we have:
[tex]|11-x|\leq3[/tex]
Solving the absolute inequality
[tex]-3 \leq 11-x \leq 3\\$In $ -3 \leq 11-x\\ x \leq 11+3\\x \leq 14\\\\$In $ 11-x \leq 3\\ 11-3 \leq x\\8 \leq x\\$Therefore,an inequality that represents all values of x that meet this constraint is:$\\8 \leq x \leq 14[/tex]
(c)To draw the number line, we use a closed dot since we have the less than or equal to sign.
The solution of the inequality is [tex]8\leq x\leq14[/tex]
According to the question, we need to choose a value of x within 3 units of 11. This can be represented by the inequality
[tex]|11-x|\leq3[/tex]
The expression in modulus can be negative or positive:
For the positive inequality
[tex]11-x \leq3\\-x \leq3 -11\\x\geq8\\8\leq x[/tex]
For the negative inequality
[tex]-11+x \leq3\\x \leq3 +11\\x\leq14\\[/tex]
Combining the inequalities
[tex]8\leq x\leq14[/tex]
Hence the solution of the inequality is [tex]8\leq x\leq14[/tex]
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