Answer:
Step-by-step explanation:
Consider the sets A and B
(A − (A ∩ B)) ∩ (B − (A ∩ B))
= (A ∩ (A ∩ B)c) ∩ (B ∩ (A ∩ B)c) by the set difference law
= (A ∩ (Ac ∩ B)c) ∩ (B ∩ (Ac ∩ B)c) by De Morgan's law
= {(A ∩ Ac) ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ (B ∩ Bc)} by the distributive law
= {∅ ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ ∅} by complementation
= {A ∩ Bc} ∩ {B ∩ Ac} by identity law
= (A ∩ Ac) ∩ (B ∩ Ac) by the associative law
= ∅ ∩ ∅ by complementation
= ∅ by the universal bound law
Therefore, (A − (A ∩ B)) ∩ (B − (A ∩ B)) = ∅
Answer:
Considere los conjuntos A y B
(A − (A ∩ B)) ∩ (B − (A ∩ B))
= (A ∩ (A ∩ B)c) ∩ (B ∩ (A ∩ B)c) por la ley de diferencia establecida
= (A ∩ (Ac ∩ B)c) ∩ (B ∩ (Ac ∩ B)c) por la ley de De Morgan
= {(A ∩ Ac) ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ (B ∩ Bc)} por la ley distributiva
= {∅ ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ ∅} complementando
= {A ∩ Bc} ∩ {B ∩ Ac} por ley de identidad
= (A ∩ Ac) ∩ (B ∩ Ac) por la ley asociativa
= ∅ ∩ ∅ complementando
= ∅ por la ley universal consolidada
Step-by-step explanation:
What to you think 28.6×100
Answer:
28.6 × 100
⇒ 286/10 × 100
⇒ 286 × 10
⇒ 2860
What is the value of the expression?
458+56−134
Answer:
380
Step-by-step explanation:
Order of operations!
(458+56)-134
(514)-134
514-134
380
done!
Answer:
3.8%
Step-by-step explanation:
After evaluating the expression you get 380. You take 380, and turn it into a percentage, move the decimal to the left twice. Giving you 3.8%
Makayla invested $630 in an account paying an interest rate of 5.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $1,860?
Answer:
19.7 or 20 rounded
Step-by-step explanation:
A = $ 1,861.65
A = P + I where
P (principal) = $ 630.00
I (interest) = $ 1,231.65
Continuous Compounding Formulas (n → ∞)
Calculate Accrued Amount (Principal + Interest)
A = Pe^rt
Calculate Principal Amount, solve for P
P = A / e^rt
Calculate rate of interest in decimal, solve for r
r = ln(A/P) / t
Calculate rate of interest in percent
R = r * 100
Calculate time, solve for t
t = ln(A/P) / r
Factor the trinomial completely
8a^2+65ab+8b^2
what is the following quotient,
sqrt96/ sqrt8
Answer:
The answer is option 1.
Step-by-step explanation:
Firstly, you have to get rid of square root at the denorminator by multiply both side with √8 :
[tex] \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} [/tex]
[tex] \sqrt{a} \times \sqrt{a} = a[/tex]
[tex] \frac{ \sqrt{96} }{ \sqrt{8} } [/tex]
[tex] \frac{ \sqrt{96} }{ \sqrt{8} } \times \frac{ \sqrt{8} }{ \sqrt{8} } [/tex]
[tex] \frac{ \sqrt{96} \times \sqrt{8} }{ \sqrt{8} \times \sqrt{8} } [/tex]
[tex] \frac{ \sqrt{768} }{8} [/tex]
Next, you have to simply by looking which factor is a perfect square :
[tex] \frac{ \sqrt{256 \times 3} }{8} [/tex]
[tex] \frac{16 \sqrt{3} }{8} [/tex]
[tex]2 \sqrt{3} [/tex]
Answer:
its a
Step-by-step explanation:
on edge 2022
Do people walk faster in an airport when they are departing(getting on a plane) or after they have arrived (getting off aplane)? An interested passenger watched a random sample of people departing and a random sample of people arriving and measured the walking speed (in feet per minute) of each. A hypothesis test is to be performed to determine if the mean walking speed is different between departing and arriving passengers at an airport. One of the conditions that must be satisfied for conclusions from atwo-sample t-test to be valid is that the samples are representative of their respective populations. Is the condition satisfied in this problem?
A. The samples will be representative of their respective populations only if both sample sizes are at least 50% of the population sizes.
B. Because the people observed in the study were randomlyselected, the passengers in each sample should be representative of all departing and arriving passengers at the airport where the samples were taken.
C. The departing and arriving passengers in the samples will be representative of all departing and arriving passengers at the airport where the samples were taken as long as walking speeds in both populations follow a normal distribution.
D. As long as each sample size is at least 30, the samples will be representative of their respective populations.
Answer:
B
Step-by-step explanation:
The sample must be represenatative of whole population. Random selection ensures this.
The sets F and H are given below.
F={c,f,g}
H= {d,e,h)
Find the union of F and H.
Find the intersection of F and H.
Answer:
F ∪ H = {c, d, e, f, g, h}
F ∩ H = { }
Step-by-step explanation:
The union is the list of elements that are in either of the two sets.
F ∪ H = {c, d, e, f, g, h}
The intersection is the list of only those elements that appear in both sets. (There are none.)
F ∩ H = { } . . . . the empty set
a trapazoid is a quadrilateral with one or more pairs of paralllel sides true or false
yes the answer is( true).
Answer:
The answer is (True)
Step-by-step explanation:
You are building a curio cabinet in the form of a rectangular prism that must be 4 feet tall with a volume of 48 cubic feet. The length and with each must be no more than tot. Which of the following dimensions are the possible width and length of the cabinet? a) 15 foot by feet b) 24 feet by 5 foot c) 25 feet by 4.8 feet d) 3 feet by 4 feet e) 4 feet by 12 feet 19
Answer:
d) 3 feet by 4 feet
Step-by-step explanation:
Volume of the prism = 48 feet³
Height if the prism = 4 feet
To determine the possible values of the length and width of the prism let's divide the volume by the height.
So 48/4 = 12
So we'll be looking for a product of two numbers to give us 12
And it's between 12 and 1, 4 and 3 , and 6 and 2.
We have only 4 and 3 in the option.
Charlie wants to order lunch for his friends hell order 6 sandwiches and a $2 kids meal for his little brother Charlie has $32 how much can he spend on each sandwich if they are all the same price
Answer:
Charlie spent 5$ per sandwich
Step-by-step explanation:
He ordered 6 sandwiches
6x5 =30
He spent 2$ on kids meal
30+2 = 32$
Hope this helped, if you want please mark branliest it would be appreciated
Answer:
5
Step-by-step explanation:
remove the kids meal first
32-2=30
now, divided 30 dollars by the 6 sandwiches
30÷6 = 5
each sandwhich is 6 dollars
Isaac is working as a security guard. He earns $8.45 an hour. He earns double time for any overtime over 40 hours. Last week he worked 44 hours. How much did he earn last week? ( HInt: double time means 2 times the regular hourly rate. )
Answer:
$405.60
Step-by-step explanation:
If Isaac works for 40 hours will earn $8.45×40=$388. Since he worked 4 extra hours, he will earn $8.45×2×4 since he worked 4 extra hours. $8.45×2=$16.90, which is the amount he earns for every extra hour he works. $16.90×4=$67.60. Now if we add $67.60+$388=$405.60.
Hope this helps!
In tests of a computer component, it is found that the mean time between failures is 937 hours. A modification is made which is supposed to increase reliability by increasing the time between failures. Tests on a sample of 36 modified components produce a mean time between failures of 960 hours, with a standard deviation of 52 hours. Using a significance level of .01, test the claim that, for modified components, the mean time between failures is greater than 937 hours. Find the appropriate p-value.
Answer:
Null hypothesis is [tex]\mathbf {H_o: \mu > 937}[/tex]
Alternative hypothesis is [tex]\mathbf {H_a: \mu < 937}[/tex]
Test Statistics z = 2.65
CONCLUSION:
Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.
P- value = 0.004025
Step-by-step explanation:
Given that:
Mean [tex]\overline x[/tex] = 960 hours
Sample size n = 36
Mean population [tex]\mu =[/tex] 937
Standard deviation [tex]\sigma[/tex] = 52
Given that the mean time between failures is 937 hours. The objective is to determine if the mean time between failures is greater than 937 hours
Null hypothesis is [tex]\mathbf {H_o: \mu > 937}[/tex]
Alternative hypothesis is [tex]\mathbf {H_a: \mu < 937}[/tex]
Degree of freedom = n-1
Degree of freedom = 36-1
Degree of freedom = 35
The level of significance ∝ = 0.01
SInce the degree of freedom is 35 and the level of significance ∝ = 0.01;
from t-table t(0.99,35), the critical value = 2.438
The test statistics is :
[tex]Z = \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \dfrac{960-937 }{\dfrac{52}{\sqrt{36}}}[/tex]
[tex]Z = \dfrac{23}{8.66}[/tex]
Z = 2.65
The decision rule is to reject null hypothesis if test statistics is greater than critical value.
CONCLUSION:
Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.
The P-value can be calculated as follows:
find P(z < - 2.65) from normal distribution tables
= 1 - P (z ≤ 2.65)
= 1 - 0.995975 (using the Excel Function: =NORMDIST(z))
= 0.004025
Suppose a certain item used to sell for 30 cents per pound, and you see that it’s been marked up to 45 cents per pound. What is the percent increase?
Answer:
50%
Step-by-step explanation:
45 cents is 15 cents more than 30 cents. The increase in cents is 15.
15 is half of 30. Half is also 0.5, 1/2, or 50%. The increase is 50%.
You can also answer this using the percent change formula.
percent change = (new number - old number)/(old number) * 100%
percent change = (45 - 30)/30 * 100%
percent change = 15/30 * 100%
percent change = 0.5 * 100%
percent change = 50%
If the result is positive, it is a percent increase.
If the result is negative, it is a percent decrease.
Which equation has the same solution as x^2+8x-33 =0 ?
1) (x+4)2 =49
3) (x+4)2 =17
2) (x-4)2 =49
4) (x-4)2=17
Please show work
Answer:
1) (x+4)2 =49
Step-by-step explanation:
x^2+8x-33 = 0 Factor this equation
(x + 11)(x - 3) = 0 Set each equation equal to 0
x = -11 and 3
Test the first equation to see if it has the same solution
(x+4)2 = 49 Simplify the parentheses
(x+4)(x+4) = 49 FOIL the equation
x^2 + 8x + 16 = 49 Subtract 49 from both sides
x^2 + 8x - 33 = 0 This is the correct solution.
Answer: correct answer is A
Step-by-step explanation:
Urgent help!
QUESTION 1
A fruit basket has both mangoes and oranges and can accommodate only 80 mangoes and oranges when
full. If there are x mangoes in a full basket,
(i) Write an expression for the number of oranges in it.
(ii) If an orange costs 50 cents and a mango costs 40 cents, write an expression for the amount of
money collected (in dollars) for the sale of all the mangoes and oranges in the full basket, S ( x ) .
(iii) Find the total amount collected from selling all the fruits in the full basket if there are 35 mangoes
in it.
Answer:
(i) [tex]80-x[/tex]
(ii) [tex]S(x) = 40 - 0.10x[/tex]
(iii) $36.5
Step-by-step explanation:
Given that:
1. Total Number of fruits = 80
2. Number of mangoes = x
3. Both mangoes and oranges are there in the basket.
Solution (i):
Only mangoes and oranges are there in the basket and the basket is full.
so, Number of mangoes + Number of oranges = Total number of fruits
x + Number of oranges = 80
Number of oranges = [tex]80 -x[/tex]
Solution (ii):
Given:
Cost of an orange = 50 cents = $0.50
Cost of a mango = 40 cents = $0.40
Cost for x mangoes = [tex]\$ 0.40x[/tex]
Cost for ([tex]80-x[/tex]) oranges = [tex]\$ 0.50 \times (80-x)[/tex]
[tex]\Rightarrow S(x) = 0.50 (80-x) + 0.40x\\\Rightarrow S(x) = 40 -0.50x + 0.40x\\\Rightarrow S(x) = 40 - 0.10x[/tex]
Solution (iii):
Put value of x = 35 in S(x)
[tex]S(35) = 40 - 0.10 (35)\\\Rightarrow S(35) = 40 - 0.35\\\Rightarrow S(35) =\$ 36.5[/tex]
Hence, answers are:
(i) [tex]80-x[/tex]
(ii) [tex]S(x) = 40 - 0.10x[/tex]
(iii) $36.5
Find the area of the triangle
Need help fast
Answer:
118.3
Step-by-step explanation:
area = base * height / 2
The two sides forming a right angle can be used as base and height.
area = 13 m * 18.2 m / 2
area = 118.3 m^2
Answer:it is 118.2977011m^2 because the instruction says do not round
Step-by-step explanation:
Round your answer to the nearest hundredth.
B
35°
6
A
Someone help pls!
Scientists use carbon-14 dating to determine the age of a sample of organic material. a. The amount C (in grams) of a 100-gram sample of carbon-14 remaining after t years is represented by the equation C=100(0.99988)t C = 100 ( 0.99988 ) t . Use a calculator to find the amount of carbon-14 remaining after 4 years. Round your answer to the nearest hundredth. The amount of carbon-14 remaining is about grams. b. What percent of the carbon-14 remains after 4 years? Round your answer to the nearest hundredth. The percent of carbon-14 remaining is about %.
Answer:
a) 99.95 grams are remaining after 4 years.
b) The percent of carbon-14 remaining is about 99.95%
Step-by-step explanation:
The amount of carbon 14 remaining after t years is given by the following equation:
[tex]C(t) = 100(0.99988)^{t}[/tex]
a) Amount remaining after 4 years.
[tex]C(t) = 100(0.99988)^{4} = 99.95[/tex]
99.95 grams are remaining after 4 years.
b) Percentage remaining after 4 years:
[tex]p = \frac{100*C(4)}{C(0)} = \frc{100*99.95}{100} = 99.95[/tex]
The percent of carbon-14 remaining is about 99.95%
a) 99.95 grams are remaining after 4 years.
b) The percent of carbon-14 remaining is about 99.95%
The calculation is as follows:a.
The amount of carbon should be
[tex]C=100(0.99988)^4[/tex]
= 99.95 grams
b. The percent is
[tex]= 100 \times 99.95100[/tex]
= 99.95%
Learn more: https://brainly.com/question/6269728?referrer=searchResults
The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.50. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.20 and P(B | A2) = 0.05. If needed, round your answers to three decimal digits. (a) Are A1 and A2 mutually exclusive?
The inclusion-exclusion principle says
P(A1 ∩ A2) = P(A1) + P(A2) - P(A1 ∪ A2)
We know the probability of intersection is 0, so
P(A1) + P(A2) = P(A1 ∪ A2)
which means A1 and A2 are indeed mutually exclusive.
Quarters are currently minted with weights normally distributed and having a standard deviation of 0.065. New equipment is being tested in an attempt to improve quality by reducing variation. A simple random sample of 25 quarters is obtained from those manufactured with the new equipment, and this sample has a standard deviation of 0.047 . Use a 0.05 significance level to test the claim that quarters manufactured with the new equipment have weights with a standard deviation less than 0.065. Does the new equipment appear to be effective in reducing the variation of weights?
Answer:
Yes, the new equipment appear to be effective in reducing the variation of weights.
Step-by-step explanation:
We are given that Quarters are currently minted with weights normally distributed and having a standard deviation of 0.065.
A simple random sample of 25 quarters is obtained from those manufactured with the new equipment, and this sample has a standard deviation of 0.047.
Let [tex]\sigma[/tex] = standard deviation of weights of new equipment.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma \geq[/tex] 0.065 {means that the new equipment have weights with a standard deviation more than or equal to 0.065}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma[/tex] < 0.065 {means that the new equipment have weights with a standard deviation less than 0.065}
The test statistics that would be used here One-sample chi-square test statistics;
T.S. = [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex] ~ [tex]\chi^{2}__n_-_1[/tex]
where, s = sample standard deviation = 0.047
n = sample of quarters = 25
So, the test statistics = [tex]\frac{(25-1)\times 0.047^{2} }{0.065^{2} }[/tex] ~ [tex]\chi^{2}__2_4[/tex]
= 12.55
The value of chi-square test statistics is 12.55.
Now, at 0.05 significance level the chi-square table gives critical value of 13.85 at 24 degree of freedom for left-tailed test.
Since our test statistic is less than the critical value of chi-square as 12.55 < 13.85, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the new equipment have weights with a standard deviation less than 0.065.
Find the volume. Round your answer to one decimal place.
(PLZ SOMEBODY HELP ASAP)
Answer:
32.738ft³
32.7ft³
Step-by-step explanation:
This is half a sphere therefore volume=4/3πr³×1/2
4/3×22/7×2.5³×1/2
=32.738ft³
Cherry Trees: Timber yield is approximately equal to the volume of a tree, however, this value is difficult to measure without first cutting the tree down. Instead, other variables, such as height and diameter, may be used to predict a tree's volume and yield. Researchers wanting to understand the relationship between these variables for black cherry trees collected data from 31 such trees in the Allegheny National Forest, Pennsylvania. Height is measured in feet, diameter in inches (at 54 inches above ground), and volume in cubic feet. (Hand, 1994)Estimate Std. Error t value P(>|t|)(Intercept) -57.99 8.64 -6.71 0.00height 0.34 0.13 2.61 0.01diameter 4.71 0.26 17.82 (c) Are each of the predictors, "height" and "diameter" significant predictors of volume? PICK ONEOnly diameter is a significant predictor since it has the smallest p-valueYes, since the p-values associated with each predictor are less than 0.05No, since the p-values associated with each predictor are less than 0.05(d) How much volume is expected from a tree that measures 79 feet tall and has a diameter of 11.3 inches?(please round to the nearest cubic foot)________ cubic feet(e) A tree in the data set measures 79 feet tall, has a diameter of 11.3 inches, and is 24.2 cubic feet in volume. Determine whether the model gives an overestimate or underestimate of the volume of this tree. PICK ONEoverestimateunderestimate
Answer:
(c) Yes, since the p-values associated with each predictor are less than 0.05
(d) 22.093 cubic feet
(e) underestimate
Step-by-step explanation:
Our main objective is to determine the following
(c) Are each of the predictors, "height" and "diameter" significant predictors of volume? PICK ONE Only diameter is a significant predictor since it has the smallest p-value
Yes, since the p-values associated with each predictor are less than 0.05
No, since the p-values associated with each predictor are less than 0.05
Assuming our significance level ∝ = 0.05
From the data given;
p-value for height is = 0.00
p - value for diameter = 0.01
where, p-value ( = 0.01 and 0.00 ) < ∝ (= 0.05 )
Hence, according to the rejection rule; the null hypothesis is rejected and the predictors "height" and " diameter" are significant predictors of volume.
Thus
The answer is :
Only diameter is a significant predictor since it has the smallest p-value
Yes, since the p-values associated with each predictor are less than 0.05
(d) How much volume is expected from a tree that measures 79 feet tall and has a diameter of 11.3 inches?(please round to the nearest cubic foot)________
[tex]\hat y = -57.99+ 0.34 \ \mathbf{height }+4.71 \ \mathbf{diameter}[/tex]
[tex]\hat y = -57.99+ 0.34 \ \mathbf{(79)}+4.71 \ \mathbf{(11.3)}[/tex]
[tex]\hat y = 22.093 \ cubic foot[/tex]
(e)
A tree in the data set measures 79 feet tall, has a diameter of 11.3 inches, and is 24.2 cubic feet in volume. Determine whether the model gives an overestimate or underestimate of the volume of this tree. PICK ONE
overestimate
underestimate
We can posits that the model gives an underestimate of the volume of this tree due to the fact that the predicted value is 22.093 and which is less than the observed value of 24.2 cubic feet.
Find f(-7) if f(x) = 2x + 8
Answer:
-6
Step-by-step explanation:
f(x) = 2x + 8
Put x as -7.
f(-7) = 2(-7) + 8
Multiply first.
f(-7) = -14 + 8
Add.
f(-7) = -6
I need this asap
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle:
A(2,-3) B(4, -3) C(4, 5) D(2,5)
What is the perimeter of the rectangle ABCD?
Answer:
20
Step-by-step explanation:
The rectangle is 2 x 8.
2 + 2 + 8 + 8
What is the difference between a centroid, orthocenter, and a circumcenter?
Giving Brainliest. :D
Please help.
Answer:
Take an example in a triangle:
The orthocenter is the intersection point of 3 altitudes.
The centroid is the intersection point of 3 medians.
The circumcenter is the intersection point of 3 bisectors.
Centroid, orthocenter, and circumcenter are collinear.
Hope this helps!
:)
The Trapezoidal rule Tn on the interval [0,5) will be exact for
all polynomial of degree at most
Select one
O A 5
OB. None
C. 3
O 0.9
OE
Answer:
degree 1
Step-by-step explanation:
The trapezoidal rule is exact when the second derivative is zero. This occurs when the polynomial is degree one or less
Solve for kkk.
\dfrac{k}{4} = \dfrac{3}{8}
4
k
=
8
3
Answer:
[tex]k=\frac{3}{2}[/tex]
Step-by-step explanation:
Given:
[tex]\frac{k}{4}=\frac{3}{8}[/tex]
To find: value of [tex]k[/tex]
Solution:
Cross-multiplying is a method in which the numerator of each (or one) side is multiplied by the denominator of the other side.
[tex]\frac{k}{4}=\frac{3}{8}[/tex]
On cross-multiplication, the equation becomes [tex]k\times 8=4\times 3[/tex]
[tex]8k=12[/tex]
Divides both sides by 8
[tex]\frac{8k}{8}=\frac{12}{8}\\k=\frac{12}{8}=\frac{3}{2}[/tex]
What is the domain of g?
Answer:
domain is [-6,6] or -6 ≤ x ≤6
Step-by-step explanation:
domain is x value of given function
dark circle means that that number is included in domain
1, 2, 5, 10, 17, 26, 37, whats next
Answer:
50, 65, 82, 101,122,145,170.
Step-by-step explanation:
hope this helps
(Add two to an odd number and continue doing so)
example: 1+1 =2, 2+3 = 5, 5+5 = 10, 10+7 = 17, and so on so forth.
Is 49 + –56 positive or negative?
Answer:
-7. negative
Step-by-step explanation:
49 + -56
49 - 56
-7
