Answer:
The calculated Z= 10/4.61 = 2.169
The P value is 0.975 .
Since the calculated value of z= 2.169 falls in the rejection region we therefore reject the null hypothesis at 5 % significance level . On the basis of this we conclude that the students at University A do not spend more on textbooks then the students at University B.
Step-by-step explanation:
We set up our hypotheses as
H0 : x 1= x2 and Ha: x1 ≠ x2
We specify significance level ∝= 0.05
The test statistic if H0: x1= x2 is true is
Z = [tex]\frac{x_1-x_2}\sqrt\frac{s_1^2}{n_1}+ \frac{s_2^2}{n_2}[/tex]
Z = 260-250/ √400/50 + 529/40
Z= 10 / √8+ 13.225
Z= 10/4.61 = 2.169
The critical value for two tailed test at alpha=0.05 is ± 1.96
The P value is 0.975 .
It is calculated by dividing alpha by 2 for a two sided test and subtracting from 1. When we subtract 0.025 ( 0.05/2)from 1 we get 0.975
Since the calculated value of z= 2.169 falls in the rejection region we therefore reject the null hypothesis at 5 % significance level . On the basis of this we conclude that the students at University A do not spend more on textbooks then the students at University B.
Prove that the statement (ab)^n=a^n * b^n is true using mathematical induction.
Answer:
see below
Step-by-step explanation:
(ab)^n=a^n * b^n
We need to show that it is true for n=1
assuming that it is true for n = k;
(ab)^n=a^n * b^n
( ab) ^1 = a^1 * b^1
ab = a * b
ab = ab
Then we need to show that it is true for n = ( k+1)
or (ab)^(k+1)=a^( k+1) * b^( k+1)
Starting with
(ab)^k=a^k * b^k given
Multiply each side by ab
ab * (ab)^k= ab *a^k * b^k
( ab) ^ ( k+1) = a^ ( k+1) b^ (k+1)
Therefore, the rule is true for every natural number n
Hello, n being an integer, we need to prove that one statement depending on n is true, let's note it S(n).
The mathematical induction involves two steps:
Step 1 - We need to prove S(1), meaning that the statement is true for n = 1
Step 2 - for k integer > 1, we assume S(k) and we need to prove that S(k+1) is true.
Imagine that you are a painter and you need to paint all the trees on one side of a road. You have several colours that you can use but you are asked to follow two rules:
Rule 1 - You need to paint the first tree in white.
Rule 2 - If one tree is white you have to paint the next one in white too.
What colour do you think all the trees will be painted?
Do you see why this is very important to prove the two steps as well ?
Let's do it in this example.
Step 1 - for n = 1, let's prove that S(1) is true, meaning [tex](ab)^1=a\cdot b =a^1\cdot b^1[/tex]
So the statement is true for n = 1
Step 2 - Let's assume that this is true for k, and we have to prove that this is true for k+1
So we assume S(k), meaning that [tex](ab)^k=a^k\cdot b^k[/tex]
and what about S(k+1), meaning [tex](ab)^{k+1}=a^{k+1}\cdot b^{k+1}[/tex] ?
We will use the fact that this is true for k,
[tex](ab)^{k+1}=(ab)\cdot (ab)^k =(ab) \cdot a^k \cdot b^k[/tex]
We can write it because the statement at k is true and then we can conclude.
[tex](ab)^{k+1}=(ab)\cdot (ab)^k =(ab) \cdot a^k \cdot b^k=a^{k+1}\cdot b^{k+1}[/tex]
In conclusion, we have just proved that S(n) is true for any n integer greater or equal to 1, meaning [tex](ab)^{n}=a^{n}\cdot b^{n}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
find x, if sq.root(x) +2y^2 = 15 and sq.root(4x) - 4y^2=6
Answer:
Example: solve √(2x−5) − √(x−1) = 1
isolate one of the square roots:√(2x−5) = 1 + √(x−1) square both sides:2x−5 = (1 + √(x−1))2 ...
expand right hand side:2x−5 = 1 + 2√(x−1) + (x−1) ...
isolate the square root:√(x−1) = (x−5)/2. ...
Expand right hand side:x−1 = (x2 − 10x + 25)/4. ...
Multiply by 4 to remove division:4x−4 = x2 − 10x + 25.
Answer:
Step-by-step explanation:
ewrerewrwrwerrwer
If the discriminant of a quadratic equation is equal to -8 , which statement describes the roots?
Answer: There are no real number roots (the two roots are complex or imaginary)
The discriminant D = b^2 - 4ac tells us the nature of the roots for any quadratic in the form ax^2+bx+c = 0
There are three cases
If D < 0, then there are no real number roots and the roots are complex numbers.If D = 0, then we have one real number root. The root is repeated twice so it's considered a double root. This root is rational if a,b,c are rational.If D > 0, then we get two different real number roots. Each root is rational if D is a perfect square and a,b,c are rational.If (x - 2) and (x + 1) are factors of
x + px? + qx + 1, what is the sum of p and q?
Answer:
p + q = -3
Step-by-step explanation:
First we need to take the original equation, and factor it to a form that's easier to get two binomial factors from (i.e., let's get a quadratic):
x^3 + px^2 + qx + 1
= x (x^2 + px + q) + 1
Now that we have factored out the x, we have a quadratic trinomial which we know can be broken down into two linear binomials. The problem gives us two linear binomials, so let's take a look.
(x - 2) (x + 1) = (x^2 + px + q)
x^2 - 2x + x -2 = x^2 + px + q
Now let's solve.
x^2 - x - 2 = x^2 + px + q
-x - 2 = px + q
From here, we can easily see that p = -1 (the coefficient of x) and q = -2.
Hence, p + q = -1 + -2 = -3.
Cheers.
name all the pairs of angles which are vertical angles , alternate interior angles , alternate exterior angles , co interior angles , co exterior angles , and corresponding angles from the given figure . (co interior - interior angles on the same side of transversal)
Answer:
Step-by-step explanation:
Since m and k are the parallel lines and a transverse 'l' is intersecting these lines at two different points.
- Opposite angles at the point of intersection of parallel lines and the transverse will be the vertical angles.
∠1 ≅ ∠3, ∠2 ≅ ∠4, ∠5 ≅ ∠8 and ∠6 ≅ ∠7 [Vertical angles]
- Pair of angles between parallel lines 'k' and 'm' but on the opposite side of the transversal are the alternate interior angles.
∠4 ≅ ∠6 and ∠3 ≅ ∠5 [Alternate interior angles]
- Angles having the same relative positions at the point of intersection are the corresponding angles.
∠2 ≅ ∠6, ∠3 ≅ ∠8, ∠4 ≅ ∠7 and ∠1 ≅ ∠5 [Corresponding angles]
- Co interior angles are the angles between the parallel lines located on the same side of the transversal.
∠4 and ∠5, ∠3 and ∠6 [Co interior angles]
- Co exterior angles are the angles on the same side of the transverse but outside the parallel lines.
∠2 and ∠8, ∠1 and ∠7 [Co exterior angles]
A linear regression analysis uses two distinct types of data. The first are variables that are at least nominal level.
a) true
b) false
Answer:
The answer is
A. True
Step-by-step explanation:
In linear regression, Linear models make a prediction using a linear function of the input features, with one being
For regression, the general prediction formula for a linear model looks as follows:
ŷ = w[0] * x[0] + w[1] * x[1] + ... + w[p] * x[p] + b
Here, x[0] to x[p] denotes the features (in this example, the number of features is p)
of a single data point, w and b are parameters of the model that are learned, and ŷ is
the prediction the model makes. For a dataset with a single feature, this is
ŷ = w[0] * x[0] + b
which you might remember from high school mathematics as the equation for a line.
Here, w[0] is the slope and b is the y-axis offset. For more features, w contains the
slopes along each feature axis. Alternatively, you can think of the predicted response
as being a weighted sum of the input features, with weights (which can be negative)
given by the entries of w.
Find the particular solution of the differential equation that satisfies the initial condition. f '(x) = −8x, f(1) = −3
Step-by-step explanation:
f(x) = integral (-8x) dx = -4x^2 + C
f(1) = -3 = -4 + C
C = 1
f(x) = -4x^2 + 1
The particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is: f(x) = -4x² + 1.
Here, we have,
To find the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3,
we can integrate the equation and use the initial condition to determine the constant of integration.
First, integrate both sides of the equation with respect to x:
∫ f'(x) dx = ∫ -8x dx
Integrating, we get:
f(x) = -4x² + C
Now, we can use the initial condition f(1) = -3 to find the value of the constant C.
Substituting x = 1 and f(x) = -3 into the equation, we have:
-3 = -4(1)² + C
-3 = -4 + C
C = -3 + 4
C = 1
Therefore, the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is:
f(x) = -4x² + 1
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36 minus 20 minus 32 times 1/4
Answer:
6
Step-by-step explanation:
36 - 20 - 32 x 1/4
=> 36 - 20 - 32/4
=> 36 - 20 - 8
=> 36 - 28
=> 6
Finding Side Lengths in a Right Triangle
What is the value of s?
15 units
С
5
B
15
S
D
Answer:
maybe it's 10.because c is 10,b is 10,and so as s.
hence s is 10 also.
a Find the amount compounded annually on Rs 25,000 for 2 years if the rates of
interest for two years ore 10 % and 12 % respectively,
Answer:
Amount = Rs. 30250 when Rate = 10%
Amount = Rs. 31360 when Rate = 12%
Step-by-step explanation:
Given
[tex]Principal, P = Rs.\ 25,000[/tex]
[tex]Time, t = 2\ years[/tex]
[tex]Rate; R_1 = 10\%[/tex]
[tex]Rate; R_2 = 12\%[/tex]
Number of times (n) = Annually
[tex]n = 1[/tex]
Required
Determine the Amount for both Rates
Amount (A) is calculated by:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
When Rate = 10%, we have:
Substitute 25,000 for P; 2 for t; 1 for n and 10% for r
[tex]A = 25000 * (1 + \frac{10\%}{1})^{1 * 2}[/tex]
[tex]A = 25000 * (1 + \frac{10\%}{1})^{2}[/tex]
[tex]A = 25000 * (1 + 10\%)^{2}[/tex]
Convert 10% to decimal
[tex]A = 25000 * (1 + 0.10)^{2}[/tex]
[tex]A = 25000 * (1.10)^{2}[/tex]
[tex]A = 25000 * 1.21[/tex]
[tex]A = 30250[/tex]
Hence;
Amount = Rs. 30250 when Rate = 10%
When Rate = 12%, we have:
Substitute 25,000 for P; 2 for t; 1 for n and 10% for r
[tex]A = 25000 * (1 + \frac{12\%}{1})^{1 * 2}[/tex]
[tex]A = 25000 * (1 + \frac{12\%}{1})^{2}[/tex]
[tex]A = 25000 * (1 + 12\%)^{2}[/tex]
Convert 12% to decimal
[tex]A = 25000 * (1 + 0.12)^{2}[/tex]
[tex]A = 25000 * (1.12)^{2}[/tex]
[tex]A = 25000 * 1.2544[/tex]
[tex]A = 31360[/tex]
Hence;
Amount = Rs. 31360 when Rate = 12%
Which expression is equivalent to 73 ⋅ 7−5? 72 77 1 over 7 to the 2nd power 1 over 7 to the 7th power
Answer:
1/7^2
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^-b = 1/a^b
__
Then your expression simplifies to ...
[tex]7^3\cdot 7^{-5}=7^{3-5}=7^{-2}=\boxed{\dfrac{1}{7^2}}[/tex]
Answer:
The answer is 1/7^2
Step-by-step explanation:
I took the test lol
Please answer this correctly without making mistakes
Answer:
The answer is 68 6/11
Step-by-step explanation:
If you enter the number into a calculator it shows you the exact decimal, therefore you can identify the answer.
Answer:
It is 68 6/11
Step-by-step explanation:
First I made all of the improper fractions into whole numbers and fractions and just saw which one was in the middle .
2,17,82,257,626,1297 next one please ?
The easy thing to do is notice that 1^4 = 1, 2^4 = 16, 3^4 = 81, and so on, so the sequence follows the rule [tex]n^4+1[/tex]. The next number would then be fourth power of 7 plus 1, or 2402.
And the harder way: Denote the n-th term in this sequence by [tex]a_n[/tex], and denote the given sequence by [tex]\{a_n\}_{n\ge1}[/tex].
Let [tex]b_n[/tex] denote the n-th term in the sequence of forward differences of [tex]\{a_n\}[/tex], defined by
[tex]b_n=a_{n+1}-a_n[/tex]
for n ≥ 1. That is, [tex]\{b_n\}[/tex] is the sequence with
[tex]b_1=a_2-a_1=17-2=15[/tex]
[tex]b_2=a_3-a_2=82-17=65[/tex]
[tex]b_3=a_4-a_3=175[/tex]
[tex]b_4=a_5-a_4=369[/tex]
[tex]b_5=a_6-a_5=671[/tex]
and so on.
Next, let [tex]c_n[/tex] denote the n-th term of the differences of [tex]\{b_n\}[/tex], i.e. for n ≥ 1,
[tex]c_n=b_{n+1}-b_n[/tex]
so that
[tex]c_1=b_2-b_1=65-15=50[/tex]
[tex]c_2=110[/tex]
[tex]c_3=194[/tex]
[tex]c_4=302[/tex]
etc.
Again: let [tex]d_n[/tex] denote the n-th difference of [tex]\{c_n\}[/tex]:
[tex]d_n=c_{n+1}-c_n[/tex]
[tex]d_1=c_2-c_1=60[/tex]
[tex]d_2=84[/tex]
[tex]d_3=108[/tex]
etc.
One more time: let [tex]e_n[/tex] denote the n-th difference of [tex]\{d_n\}[/tex]:
[tex]e_n=d_{n+1}-d_n[/tex]
[tex]e_1=d_2-d_1=24[/tex]
[tex]e_2=24[/tex]
etc.
The fact that these last differences are constant is a good sign that [tex]e_n=24[/tex] for all n ≥ 1. Assuming this, we would see that [tex]\{d_n\}[/tex] is an arithmetic sequence given recursively by
[tex]\begin{cases}d_1=60\\d_{n+1}=d_n+24&\text{for }n>1\end{cases}[/tex]
and we can easily find the explicit rule:
[tex]d_2=d_1+24[/tex]
[tex]d_3=d_2+24=d_1+24\cdot2[/tex]
[tex]d_4=d_3+24=d_1+24\cdot3[/tex]
and so on, up to
[tex]d_n=d_1+24(n-1)[/tex]
[tex]d_n=24n+36[/tex]
Use the same strategy to find a closed form for [tex]\{c_n\}[/tex], then for [tex]\{b_n\}[/tex], and finally [tex]\{a_n\}[/tex].
[tex]\begin{cases}c_1=50\\c_{n+1}=c_n+24n+36&\text{for }n>1\end{cases}[/tex]
[tex]c_2=c_1+24\cdot1+36[/tex]
[tex]c_3=c_2+24\cdot2+36=c_1+24(1+2)+36\cdot2[/tex]
[tex]c_4=c_3+24\cdot3+36=c_1+24(1+2+3)+36\cdot3[/tex]
and so on, up to
[tex]c_n=c_1+24(1+2+3+\cdots+(n-1))+36(n-1)[/tex]
Recall the formula for the sum of consecutive integers:
[tex]1+2+3+\cdots+n=\displaystyle\sum_{k=1}^nk=\frac{n(n+1)}2[/tex]
[tex]\implies c_n=c_1+\dfrac{24(n-1)n}2+36(n-1)[/tex]
[tex]\implies c_n=12n^2+24n+14[/tex]
[tex]\begin{cases}b_1=15\\b_{n+1}=b_n+12n^2+24n+14&\text{for }n>1\end{cases}[/tex]
[tex]b_2=b_1+12\cdot1^2+24\cdot1+14[/tex]
[tex]b_3=b_2+12\cdot2^2+24\cdot2+14=b_1+12(1^2+2^2)+24(1+2)+14\cdot2[/tex]
[tex]b_4=b_3+12\cdot3^2+24\cdot3+14=b_1+12(1^2+2^2+3^2)+24(1+2+3)+14\cdot3[/tex]
and so on, up to
[tex]b_n=b_1+12(1^2+2^2+3^2+\cdots+(n-1)^2)+24(1+2+3+\cdots+(n-1))+14(n-1)[/tex]
Recall the formula for the sum of squares of consecutive integers:
[tex]1^2+2^2+3^2+\cdots+n^2=\displaystyle\sum_{k=1}^nk^2=\frac{n(n+1)(2n+1)}6[/tex]
[tex]\implies b_n=15+\dfrac{12(n-1)n(2(n-1)+1)}6+\dfrac{24(n-1)n}2+14(n-1)[/tex]
[tex]\implies b_n=4n^3+6n^2+4n+1[/tex]
[tex]\begin{cases}a_1=2\\a_{n+1}=a_n+4n^3+6n^2+4n+1&\text{for }n>1\end{cases}[/tex]
[tex]a_2=a_1+4\cdot1^3+6\cdot1^2+4\cdot1+1[/tex]
[tex]a_3=a_2+4(1^3+2^3)+6(1^2+2^2)+4(1+2)+1\cdot2[/tex]
[tex]a_4=a_3+4(1^3+2^3+3^3)+6(1^2+2^2+3^2)+4(1+2+3)+1\cdot3[/tex]
[tex]\implies a_n=a_1+4\displaystyle\sum_{k=1}^3k^3+6\sum_{k=1}^3k^2+4\sum_{k=1}^3k+\sum_{k=1}^{n-1}1[/tex]
[tex]\displaystyle\sum_{k=1}^nk^3=\frac{n^2(n+1)^2}4[/tex]
[tex]\implies a_n=2+\dfrac{4(n-1)^2n^2}4+\dfrac{6(n-1)n(2n)}6+\dfrac{4(n-1)n}2+(n-1)[/tex]
[tex]\implies a_n=n^4+1[/tex]
A survey of undergraduates revealed the follwoing information: WOMEN MENsample mean weight 124.7 183.3sample standard deviation of weight 23.32 25.41sample proportion Roman Catholic 0.40 0.32Sample mean GPA 3.34 3.24Sample standard deviation of GPA 0.35 0.44Sample size 20 25Assume the populations are normally distributed. Suppose you want to determine whether the proportion of SCU women who are Roman Catholic is greater than the proportion of SCU men that are Roman Catholic.a. What are the null and alternative hypothesis to run this test?b. What is the calculated value of the test statistic?c. What is the p-value of the calculated test statistic?d. What is the conclusion of the hypothesis test, at 5% the significance level?
Answer:
the answers are below:
Step-by-step explanation:
a. null hypothesis:
H0: Pw - Pm = 0 (so Pw = Pm)
alternate hypothesis:
H1: Pw - Pm > 0 (so Pw > Pm)
where Pw is the proportion of women
Pm is the proportion of men
b.) proportion of women = o.40
proportion of men = 0.32
sample size of women = 20
sample size of men = 25
[tex]z = 0.4 - 0.32/ \sqrt{((0.4 *0.6)/20) * (0.32 * 0.68)/25)}[/tex]
[tex]z = 0.56[/tex]
c.) p value =
p(z>0.56)
= 0.7123
= 1 - 0.7123
= o.2877 which can be approximated to be 0.288
d. alpha value was set at 0.05
the p value is greater than alpha.
therefore it is not statistically significant.
we conclude that the proportion of roman catholic women is not greater than men.
I will mark u brainleiest if u help me and 5 stars
Answer:
[tex]\boxed{50}[/tex]
Step-by-step explanation:
Because the initial temperature is 40 degrees and it increases by 10, add the two values together to get the final temperature.
40 + 10 = 50
Therefore, the final answer is 50 degrees.
Answer:
50
Step-by-step explanation:
If it starts at 40 degrees and increases 10 degrees, it is going to be 50 degrees. Increases means adding, so it is asking you to add 10 to 40 which is 50. If it asks decreases in the future you will have to subtract.
Determine the value(s) for which the rational expression 2x^2/6x is undefined. If there's more than one value, list them separated by a comma, e.g. x=2,3.
Answer:
0
Step-by-step explanation:
Hello, dividing by 0 is not defined. so
[tex]\dfrac{2x^2}{6x}[/tex]
is defined for x different from 0
This being said, we can simplify by 2x
[tex]\dfrac{2x^2}{6x}=\dfrac{2x*x}{3*2x}=\dfrac{1}{3}x[/tex]
and this last expression is defined for any real number x.
Thank you
Given the following diagram, find the required measures. Given: l | | m m 1 = 120° m 3 = 40° m 2 = 20 60 120
Step-by-step explanation:
your required answer is 60°.
Hello,
Here, in the figure;
angle 1= 120°
To find : m. of angle 2.
now,
angle 1 + angle 2= 180° { being linear pair}
or, 120° +angle 2 = 180°
or, angle 2= 180°-120°
Therefore, the measure of angle 2 is 60°.
Hope it helps you.....
1. Transform the polar equation to a Cartesian (rectangular) equation: 2. Transform the Cartesian (rectangular) equation to a polar equation: y^2 = 4x
Answer:
Attachment 1 : 5x + 6y = 5, Attachment 2 : 4cotθcscθ
Step-by-step explanation:
Remember that we have three key points in solving these types of problems,
• x = r cos(θ)
• y = r sin(θ)
• x² + y² = r²
a ) For this first problem we need not apply the third equation.
( Multiply either side by 5 cos(θ) + 6 sin(θ) )
r [tex]*[/tex] ( 5 cos(θ) + 6 sin(θ) ) = 5,
( Distribute r )
5r cos(θ) + 6r sin(θ) = 5
( Substitute )
5x + 6y = 5 - the correct solution is option c
b ) We know that y² = 4x ⇒
r²sin²(θ) = 4r cos(θ),
r = 4cos(θ) / sin²(θ) = 4 cot(θ) csc(θ) = 4cotθcscθ - again the correct solution is option c
You have a jar containing 55 coins, consisting entirely of nickels and quarters, worth a
total of $7.15. How many quarters are in the jar?
Answer: 22 quarters
Step-by-step explanation:
Let N be the number of nickels.
Then the number of quarters is (55-N)
The nickels contribute 5N cents to the total.
The quarters contribute 25*(55-N) cents to the total.
5N + 25*(55-N) = 715
5N + 1375 - 25N = 715
-20N = 715 - 1375 = -660
[tex]N=\frac{-660}{-20}[/tex]
[tex]=33[/tex]
[tex]55-33=22[/tex]
So there is 22 quarters inside the jar.
Check to see if my answer is correct-
33*5 + 22*25 = 715 cents
Write the polar form of a complex number in standard form for [tex]8[cos(\frac{\pi}{2}) + isin(\frac{\pi}{2})][/tex]
Answer:
Solution : 8i
Step-by-step explanation:
We can use the trivial identities cos(π / 2) = 0, and sin(π / 2) = 1 to solve this problem. Let's substitute,
[tex]8\left[cos\left(\frac{\pi }{2}\right)+isin\left(\frac{\pi \:}{2}\right)\right][/tex] = [tex]8\left(0+1i\right)[/tex]
And of course 1i = i, so we have the expression 8(0 + i ). Distributing the " 8, " 8( 0 ) = 0, and 8(i) = 8i, making the fourth answer the correct solution.
For a closed rectangular box, with a square base x by x cm and height h cm, find the dimensions giving the minimum surface area, given that the volume is 18 cm3.
Answer:
∛18 * ∛18 * 18/(∛18)²
Step-by-step explanation:
Let the surface area of the box be expressed as S = 2(LB+BH+LH) where
L is the length of the box = x
B is the breadth of the box = x
H is the height of the box = h
Substituting this variables into the formula, we will have;
S = 2(x(x)+xh+xh)
S = 2x²+2xh+2xh
S = 2x² + 4xh and the Volume V = x²h
If V = x²h; h = V/x²
Substituting h = V/x² into the surface area will give;
S = 2x² + 4x(V/x²)
Since the volume V = 18cm³
S = 2x² + 4x(18/x²)
S = 2x² + 72/x
Differentiating the function with respect to x to get the minimal point, we will have;
dS/dx = 4x - 72/x²
at dS/dx = 0
4x - 72/x² = 0
- 72/x² = -4x
72 = 4x³
x³ = 72/4
x³ = 18
[tex]x = \sqrt[3]{18}[/tex]
Critical point is at [tex]x = \sqrt[3]{18}[/tex]
If x²h = 18
(∛18)²h =18
h = 18/(∛18)²
Hence the dimension is ∛18 * ∛18 * 18/(∛18)²
Which angle of rotation is determined by the matrix below?{1/2 -sqrt3/2 sqrt3/2 1/2] 30° 60° 120° 300°
Answer:
60°
Step-by-step explanation:
You have the rotation matrix ...
[tex]\left[\begin{array}{cc}\cos{\theta}&-\sin{\theta}\\\sin{\theta}&\cos{\theta}\end{array}\right]=\left[\begin{array}{cc}\dfrac{1}{2}&-\dfrac{\sqrt{3}}{2}\\\dfrac{\sqrt{3}}{2}&\dfrac{1}{2}\end{array}\right][/tex]
This tells you the angle of rotation is ...
[tex]\tan{\theta}=\dfrac{\sin{\theta}}{\cos{\theta}}=\dfrac{\left(\dfrac{\sqrt{3}}{2}\right)}{\left(\dfrac{1}{2}\right)}=\sqrt{3}\\\\\theta=\arctan{\sqrt{3}}=60^{\circ}[/tex]
The angle of rotation is 60°.
Answer:
B----- 60
Step-by-step explanation:
Two brothers, Tom and Allen, each inherit $39000. Tom invests his inheritance in a savings account with an annual return of 2.9%, while Allen invests his inheritance in a CD paying 5.7% annually. How much more money than Tom does Allen have after 1 year?
Answer:
Tom:
initial money = $ 39000
% increased per annum = 2.9%
money gained per annum = 39000 * 2.9/100 = $1131
Allen:
initial money = $ 39000
% increased per annum = 5.7 %
money gained per annum = 39000 * 5.7/100 = $2223
Allen has $ (2223 - 1131) = $ 1192 more than Tom
PLEASE HELP SOON! A 2011 study by the National Safety Council estimated that there are nearly 5.7 million traffic accidents year. At least 28% of them involved distracted drivers using a cell phones or texting. The data showed that 11% of drivers at any time are using cell phones. Car insurance companies base their policy rates on accident data that shows drivers have collisions approximately once every 19 years. That's a 5.26% chance per per year. Given.
A - Let dc= event that a randomly selected driver is using a cell phone. what is P(DC)? B - Let ta = event that a randomly selected driver has a traffic accident. what is P(ta) C - how can you determine if cell phone use while driving and traffic accidents are related? D - Give that the driver has an accident, what is the probability that the driver was distracted by a cell phone? Write this event with the correct conditional notation.
Answer:
(A) 0.11
(B) 0.0526
(C) Related
(D) 0.28
Step-by-step explanation:
The data provided is:
DC = event that a randomly selected driver is using a cell phone
TA = event that a randomly selected driver has a traffic accident
(A)
From the provided data:
P (DC) = 0.11
(B)
From the provided data:
P (TA) = 0.0526
(C)
To determine whether the events DC and TA are dependent, we need to show that:
[tex]P(DC\cap TA)\neq P(DC)\times P(TA)[/tex]
The value of P (DC ∩ TA) is,
[tex]P(DC\cap TA)=P(DC|TA)\time P(TA)[/tex]
[tex]=0.28\times 0.0526\\=0.014728[/tex]
Now compute the value of P (DC) × P (TA) as follows:
[tex]P (DC) \times P (TA)=0.11\times 0.0526=0.005786[/tex]
So, [tex]P(DC\cap TA)\neq P(DC)\times P(TA)[/tex]
Thus, cell phone use while driving and traffic accidents are related.
(D)
The probability that the driver was distracted by a cell phone given that the driver has an accident is:
P (DC | TA) = 0.28
If the occurrence of one event does not influence the outcome of another event, then two events are:
A. conditional
B. disjoint
C. independent
D. interdependent
Answer:
C. Independent
Step-by-step explanation:
Independent events are events that have no impact on each other.
So, if the occurrence of an event doesn't influence the outcome of another, this means that they are independent because they do not impact each other.
This must mean C is correct because the two events have to be independent.
write a letter to your friend in Ghana stating your experience in your presentation school in nigeria
Answer:
hi Ghana how are you doing I am fine here. I really miss u and my friends in the old.U know what in Nigeria this school is really awesome and fantastic we have a swimming pool here and we can go to trip and we can have many things here I really loved this school.
at starting I was not have any friends and know I have many friends. But I really miss u this is what about our . Come to my house I can show you my school it is very near to my house .
Ur friend
writ ur name
The time, X minutes, taken by Tim to install a satellite dish is assumed to be a normal random variable with mean 127 and standard deviation 20. Determine the probability that Tim will takes less than 150 minutes to install a satellite dish.
Answer: 0.8749
Step-by-step explanation:
Given, The time, X minutes, taken by Tim to install a satellite dish is assumed to be a normal random variable with mean 127 and standard deviation 20.
Let x be the time taken by Tim to install a satellite dish.
Then, the probability that Tim will takes less than 150 minutes to install a satellite dish.
[tex]P(x<150)=P(\dfrac{x-\text{Mean}}{\text{Standard deviation}}<\dfrac{150-127}{20})\\\\=P(z<1.15)\ \ \ [z=\dfrac{x-\text{Mean}}{\text{Standard deviation}}]\\\\=0.8749\ [\text{By z-table}][/tex]
hence, the required probability is 0.8749.
PLZ HELPPPPPP. 25 POINTS.
A store sells books for $12 each. In the proportional relationship between x, the number of books purchased, and y, the cost per books in dollars" to "y, the total cost of the books in dollars, the constant of proportionality is 12. Which equation shows the relationship between x and y?
A. y=12/x
B. y=12x
C. y=12+x
D. y=12−x
Answer:
b
Step-by-step explanation:
because its right dummy
The Venn diagram shows 3 type numbers odd even in prime
what are the next terms in the number pattern -11, -8, -5, -2, 1
Answer:
4, 7, 10, 13
Step-by-step explanation:
Hey there!
Well in the given pattern,
-11, -8, -5, -2, 1
we can conclude that the pattern is +3 every time.
-11 + 3 = -8
-8 + 3 = -5
-5 + 3 = -2
-2 + 3 = 1
And so on
4, 7, 10, 13Hope this helps :)
