Answer:
3/20
Step-by-step explanation:
By question it's given that ,
[tex]\implies \dfrac{a}{b}=\dfrac{2}{5}[/tex]
[tex]\implies \dfrac{b}{c}=\dfrac{3}{8}[/tex]
And we need to find out the value of a/c .For that Multiply both of them , we have ;
[tex]\implies \dfrac{a}{b} \times\dfrac{b}{c}=\dfrac{2}{5}\times \dfrac{3}{8} \\\\\implies \dfrac{a}{c}= \dfrac{3}{20}[/tex]
Hence the required answer is 3/20 .
The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms. Statistical analysis of the output suggests that the resistances can be approximated by a normal distribution with known standard deviation of 0.005 ohms. We are interested in testing the hypothesis that the resistors conform to the specifications.
Requied:
a. Determine whether a random sample of 10 resistors yielding a sample mean of 0.152 ohms indicates that the resistors are conforming. Use alpha = 0.05.
b. Calculate a 95% confidence interval for the average resistance. How does this interval relate to your solution of part (a)?
Answer:
a) The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.
b) The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.
Step-by-step explanation:
Question a:
The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms.
At the null hypothesis, we test if this is the average resistance, that is:
[tex]H_0: \mu = 0.15[/tex]
We are interested in testing the hypothesis that the resistors conform to the specifications.
At the alternative hypothesis, we test if it is not conforming, that is, the mean is different of 0.15, so:
[tex]H_1: \mu \neq 0.15[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.15 is tested at the null hypothesis:
This means that [tex]\mu = 0.15[/tex]
Sample mean of 0.152, sample of 10, population standard deviation of 0.005.
This means that [tex]X = 0.152, n = 10, \sigma = 0.005[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.152 - 0.15}{\frac{0.005}{\sqrt{10}}}[/tex]
[tex]z = 1.26[/tex]
P-value of the test and decision:
The p-value of the test is the probability of the sample mean differing from 0.15 by at least 0.152 - 0.15 = 0.002, which is P(|z| > 1.26), given by two multiplied by the p-value of z = -1.26.
Looking at the z-table, z = -1.26 has a p-value of 0.1038.
2*0.1038 = 0.2076
The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.
Question b:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.005}{\sqrt{10}} = 0.003[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.15 - 0.003 = 0.147.
The upper end of the interval is the sample mean added to M. So it is 0.15 + 0.003 = 0.153.
The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.
The distance between Ali's house and 1 point
college is exactly 135 miles. If she
drove 2/3 of the distance in 135
minutes. What was her average speed
in miles per hour?
Ali's average speed was 40 miles per hour.
What is an average speed?
The total distance traveled is to be divided by the total time consumed brings us the average speed.
How to calculate the average speed of Ali?
The total distance between the college from Ali's house is 135 miles.
She drove 2/3rd of the total distance in 135 minutes.
She drove =135*2/3miles
=90miles.
Ali can drive 90miles in 135 mins.
Therefore, her average speed is: 90*60/135 miles per hour.
=40 miles per hour.
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Solve x∕3 < 5 Question 5 options: A) x ≥ 15 B) x > 15 C) x < 15 D) x ≤ 15
Answer:
C
Step-by-step explanation:
Given
[tex]\frac{x}{3}[/tex] < 5 ( multiply both sides by 3 to clear the fraction )
x < 15 → C
3 write the factor of the following (1) 48 (2) 36 (3) 28 (4) 100 (5) 125
Answer:
FACTORING THE NUMBERS :-
well u didnt say to prime factors so i am writing all factors
1) 48 => 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 ( all are plus and minus )
2) 36 => 1, 2, 3, 4, 6, 9, 12, 18 and 36 ( all are plus and minus )
3) 28 => 1, 2, 4, 7, 14 and 28 ( all are plus and minus )
4) 100 => 1, 2, 4, 5, 10, 20, 25, 50, and 100 ( all are plus and minus )
5) 125 => 1, 5, 25, 125 ( all are plus and minus )
is it worth brainliest...
yes ofc
pls help me asap !!!
Answer:
11
Step-by-step explanation:
Hopefully you can see that this is an isosceles triangle and remembering the inequality theorem of a triangle (4,4,11 triangle cannot exist). Iso triangle has two side the same length - as well as two angles the same.
190 of 7
6 7 8 9 10
-3
4
5
6
The slope of the line shown in the graph is
and the intercept of the line is
Answer:slope 2/3
Y-int 6
Step-by-step explanation:
The ratio of frogs to toads was 3 to 7. If there were 1280 frogs and toads in all, how many were frogs?
Answer:
348 frogs
Step-by-step explanation:
ratio = 3:7
total of ratio = 10
frogs = 3/10 × 1280 = 348 frogs
Answer:
let the ratio be 3x and 7x.
3x+7x=1280
10x=1280
x=128
Now
frogs =3x=3*128=384
toads =7x=7*128=896
a farmer needs 5 men to clear his farm in 10 days. How many men will he need if he must finish clearing the farm in two days if they work at the same rate?
Answer:
25 workers
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
,
Analyze the key features of the graph of the quadratic function f(x) = –x^2 + 4x – 3.
1. Does the parabola open up or down?
2. Is the vertex a minimum or a maximum?
3. Identify the axis of symmetry, vertex and the y-intercept of the parabola.
9514 1404 393
Answer:
downmaximumx=2; (2, 1), -3Step-by-step explanation:
1. The negative leading coefficient (-2) tells you the parabola opens downward.
__
2. The fact that the parabola opens downward tells you the vertex is a maximum.
__
3. For quadratic ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For this parabola, that is x = -4/(2(-1)) = 2. The y-value of the vertex is f(2) = -2^2+4(2)-3 = -4+8-3 = 1. The y-intercept is the constant, c = -3.
axis of symmetry: x = 2vertex: (2, 1)y-intercept: (0, -3)the number of multiples of a given number is infinite ( )
Answer:
make an 8 horizontal
oooookkkk
Answer:
TRUE
The number of multiples of a given number is finite is a false statement. The number of multiples of a given number is infinite.
Examples:
Multiples of 2 = 2,4,6,8,10,…..
Multiples of 3 = 3,6,9,12,15,18,…
Multiples of 4 = 4, 8, 12, 16, 120, 24….
∴ The number of multiples of a given number is infinite .
Answer From Gauth Math
Tyler and Gabe went to the arcade and played the same two games, Tyler played five rounds of each game for 30$. Write two equations for the amounts the two boys spent. Then find the cost for one round each game.
Equations:
1. (30)(5)= 150
2. 30 + 30 + 30 + 30 + 30 = 150
I round:
30 dollars divided by 5 rounds = 6 dollars per round.
The total amount spent by the two boys is $300.
What is algebraic expression?An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is that Tyler and Gabe went to the arcade and played the same two games. Tyler played five rounds of each game for 30$.
We can write the total amount spent by the two boys as -
total amount = 2 x cost of each game x total number of games played
total amount = 2 x 30 x 5
total amount = 10 x 30
total amount = 300
Therefore, the total amount spent by the two boys is $300.
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Một công ty sản xuất ván trượt có thể bán một cái ván trượt với giá $60.
Tổng chi phí cho sản xuất bao gồm chi phí cố định là $1200 và chi phí để sản xuất một cái ván trượt là $35.
Nếu công ty đó bán được 80 cái ván trượt thì công ty đó
Use the commutative law of multiplication to rewrite 67 x 13.
A. 3 X 671
B. 13 x 67
C.6 X 7 X1 X3
D.80
Answer:
A. 671*3
B. 67*13
C. 3*1*7*6
D. 1*80
You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten.
Answer:
[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]
Step-by-step explanation:
There are 52 cards in a standard deck, and there are 4 suits for each card. Therefore there are 4 twos and 4 tens.
At first we have 52 cards to choose from, and we need to get 1 of the 4 twos, therefore the probability is just
[tex]\frac{4}{52}[/tex]
After we've chosen a two, we need to choose one of the 4 tens. But remember that we're now choosing out of a deck of just 51 cards, since one card was removed. Therefore the probability is
[tex]\frac{4}{51}[/tex]
Now to get the total probability we need to multiply the two probabilities together
[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]
There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.10 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.04 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm. What is the probability that the first machine produces an acceptable cork
Answer:
0.6827
Step-by-step explanation:
Given that :
Mean, μ = 3
Standard deviation, σ = 0.1
To produce an acceptable cork. :
P(2.9 < X < 3.1)
Recall :
Z = (x - μ) / σ
P(2.9 < X < 3.1) = P[((2.9 - 3) / 0.1) < Z < ((3.1 - 3) / 0.1)]
P(2.9 < X < 3.1) = P(-1 < Z < 1)
Using a normal distribution calculator, we obtain the probability to the right of the distribution :
P(2.9 < X < 3.1) = P(1 < Z < - 1) = 0.8413 - 0.1587 = 0.6827
Hence, the probability that the first machine produces an acceptable cork is 0.6827
Doyle Company issued $500,000 of 10-year, 7 percent bonds on January 1, 2018. The bonds were issued at face value. Interest is payable in cash on December 31 of each year. Doyle immediately invested the proceeds from the bond issue in land. The land was leased for an annual $125,000 of cash revenue, which was collected on December 31 of each year, beginning December 31, 2018
Answer:
f
Step-by-step explanation:
Evaluate:
[tex]{ \int \limits^\pi_{ \frac{1}{4}\pi}{ {e {}^{2 \sigma} (\sqrt{1 - { \sigma}^{2} } ) d \sigma}}}[/tex]
Answer:
hope this answer helps.
Please help!!
Find BD
Answer: [tex]8\sqrt{2}[/tex]
==========================================================
Work Shown:
Focus entirely on triangle ABD (or on triangle BCD; both are identical)
The two legs of this triangle are AB = 8 and AD = 8. The hypotenuse is unknown, so we'll say BD = x.
Apply the pythagorean theorem.
[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\x = \sqrt{8^2 + 8^2}\\\\x = \sqrt{2*8^2}\\\\x = \sqrt{8^2*2}\\\\x = \sqrt{8^2}*\sqrt{2}\\\\x = 8\sqrt{2}\\\\[/tex]
So that's why the diagonal BD is exactly [tex]8\sqrt{2}\\\\[/tex] units long
Side note: [tex]8\sqrt{2} \approx 11.3137[/tex]
QUESTION 3.1 POINT
An investment pays 25% interest compounded monthly. What percent, as a decimal, is the effective annual yied? Enter your
answer as a decimal rounded to four decimal places.
9514 1404 393
Answer:
0.2807
Step-by-step explanation:
The relationship between the effective annual yield (e) and the nominal annual interest rate (r) compounded n times per year is ...
e = (1 +r/n)^n -1
e = (1 +0.25/12)^12 -1 = 0.2807 . . . . . . about 28.07%
The PTA sells 100 tickets for a raffle and puts them in a bowl. They will randomly pull out a ticket for the first prize and then another ticket for the second prize. You have 10 tickets and your friend has 10 tickets. What is the probability that your friend wins the first prize and you win the second prize?
[tex]\sqrt{25}[/tex]
Answer:
5
Step-by-step explanation:
Calculate the square root of 25 and get 5.
Police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. Listed below are shoe print lengths, foot lengths, and heights of males. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Based on these results, does it appear that police can use a shoe print length to estimate the height of a male? Use a significance level of α=0.01
It does not appear that police can use a shoe print length to estimate the height of a male.
The given parameters are:
[tex]\begin{array}{cccccc}{Shoe\ Print} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} \ \\ Height (cm) & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} \ \end{array}[/tex]
Rewrite as:
[tex]\begin{array}{cccccc}{x} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} \ \\ y & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} \ \end{array}[/tex]
See attachment for scatter plot
To determine the correlation coefficient, we extend the table as follows:
[tex]\begin{array}{cccccc}{x} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} & y & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} & x^2 & {817.96} & {864.36} & {1036.84} & {1049.76} & {745.29} & y^2 & {29756.25} & {31222.89} & {35494.56} & {28934.01} & {32112.64} & x \times y & {4933.5} & {5194.98} & {6066.48} & {5511.24} & {4892.16} \ \end{array}[/tex]
The correlation coefficient (r) is:
[tex]r = \frac{\sum(x - \bar x)(y - \bar y)}{\sqrt{SS_x * SS_y}}[/tex]
We have:
[tex]n =5[/tex]
[tex]\sum xy =4933.5+5194.98+6066.48+5511.24+4892.16 =26598.36[/tex]
[tex]\sum x =28.6+29.4+32.2+32.4+27.3=149.9[/tex]
[tex]\sum y =172.5+176.7+188.4+170.1+179.2=886.9[/tex]
[tex]\sum x^2 =817.96+864.36+1036.84+1049.76+745.29=4514.21[/tex]
[tex]\sum y^2 =29756.25+31222.89+35494.56+28934.01+32112.64=157520.35[/tex]
Calculate mean of x and y
[tex]\bar x = \frac{\sum x}{n} = \frac{149.9}{5} = 29.98[/tex]
[tex]\bar y = \frac{\sum y}{n} = \frac{886.9}{5} = 177.38[/tex]
Calculate SSx and SSy
[tex]SS_x = \sum (x - \bar x)^2 =(28.6-29.98)^2 + (29.4-29.98)^2 + (32.2-29.98)^2 + (32.4-29.98)^2 + (27.3-29.98)^2 =20.208[/tex]
[tex]SS_y = \sum (y - \bar x)^2 =(172.5-177.38)^2 + (176.7-177.38)^2 + (188.4-177.38)^2 + (170.1-177.38)^2 + (179.2-177.38)^2 =202.028[/tex]
Calculate [tex]\sum(x - \bar x)(y - \bar y)[/tex]
[tex]\sum(x - \bar x)(y - \bar y) = (28.6-29.98)*(172.5-177.38) + (29.4-29.98)*(176.7-177.38) + (32.2-29.98)*(188.4-177.38) + (32.4-29.98)*(170.1-177.38) + (27.3-29.98) *(179.2-177.38) =9.098[/tex]
So:
[tex]r = \frac{\sum(x - \bar x)(y - \bar y)}{\sqrt{SS_x * SS_y}}[/tex]
[tex]r = \frac{9.098}{\sqrt{20.208 * 202.028}}[/tex]
[tex]r = \frac{9.098}{\sqrt{4082.581824}}[/tex]
[tex]r = \frac{9.098}{63.90}[/tex]
[tex]r = 0.142[/tex]
Calculate test statistic:
[tex]t = \frac{r}{\sqrt{\frac{1 - r^2}{n-2}}}[/tex]
[tex]t = \frac{0.142}{\sqrt{\frac{1 - 0.142^2}{5-2}}}[/tex]
[tex]t = \frac{0.142}{\sqrt{\frac{0.979836}{3}}}[/tex]
[tex]t = \frac{0.142}{\sqrt{0.326612}}[/tex]
[tex]t = \frac{0.142}{0.5715}[/tex]
[tex]t = 0.248[/tex]
Calculate the degrees of freedom
[tex]df = n - 2 = 5 - 2 = 3[/tex]
The [tex]t_{\alpha/2}[/tex] value at:
[tex]df =3[/tex]
[tex]t = 0.248[/tex]
[tex]\alpha = 0.01[/tex]
The value is:
[tex]t_{0.01/2} = \±5.841[/tex]
This means that we reject the null hypothesis if the t value is not between -5.841 and 5.841
We calculate the t value as:
[tex]t = 0.248[/tex]
[tex]-5.841 < 0.248 < 5.841[/tex]
Hence, we do not reject the null hypothesis because they do not appear to have any correlation.
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Find the measure of the incanted angle to the nearest degree
Answer:
15.5⁰ or approximately 16⁰
Step-by-step explanation:
let unknown side be x
cos x= 53/55
cos x= 0.9636
x=cos inverse of 0.9636
x=15.5⁰
Answer:
[tex]cosx = \frac{53}{55} \\ x = {cos}^{ - 1} ( \frac{53}{55} ) \\ x = 15.4987[/tex]
The answer to this math problem need help
Step-by-step explanation:
you know that you can copy and paste and give the answer
Answer this question that is given
Answer:
See explanation
Step-by-step explanation:
2) (10+4) x 2 = 28
3) (13 + 6) x 2 = 38
4) (8+4) x 2 = 24
5) (11+8) x 2 = 38
Answered by Gauthmath
A rectangle has a length of 7 in. and a width of 2 in. if the rectangle is enlarged using a scale factor of 1.5, what will be the perimeter of the new rectangle
Answer:
27 inch
Step-by-step explanation:
Current perimeter=18
New perimeter=18*1.5=27 in
-5 + 3 and also what is 1/4 of 24
What is the answer i am struggling
Answer:
-5+3=-2
1/4 of 24 = 6
Step-by-step explanation:
If lan does a job in 132 hours and with the help of Danielle they can do it together in 44 hours, how long
would it take Danielle to do it alone
Answer:
88 hours
Step-by-step explanation:
Ian = 132
Daniel + Ian = 44
Daniel = Ian - 44
= 132-44 = 88 hours
PLEASEE HELP ME ASAPPP (geometry)
Answer:AE=EC và BF=FC => EF là đường trung bình của tam giác ABC
=> EF // và bằng 1/2 AB
=> AB = 16
Step-by-step explanation:
Answer:
AB=16
Step-by-step explanation:
Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.
The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle.
AD=DB
AD+DB=AB=2EF
AB=2×8=16
how many distinct permutations can be formed using the letters of the word robberies
Answer:
45360 arrangements
Step-by-step explanation:
Given the word 'robberies'
Number of letters = 9 letters in total
Repeated letters ; r = 2 ; b = 2 ; e = 2
Therefore, the number of distinct arrangement of letters is :
(total letters)! / repeated letters!
The number of distinct arrangement of letters is :
9! / (2! * 2! * 2!) = (9*8*7*6*5*4*3*2*1) / (2*2*2)
362880 / 8 = 45360 arrangements
