Answer:
6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Poisson distribution with a mean of 1 crack per 100 ft.
So [tex]\mu = \frac{ft}{100}[/tex], in which ft is the length of the pavement.
What is the probability that there will be exactly 8 cracks in a 500 ft length of pavement
500ft, so [tex]\mu = \frac{500}{100} = 5[/tex]
This is P(X = 8).
[tex]P(X = 8) = \frac{e^{-5}*5^{8}}{(8)!} = 0.0653[/tex]
6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement
how many are 5 x 5 ?
what is the answer to the problem i need help with?
Answer:
C
Step-by-step explanation:
Recall the equation for a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex], where the center is (h,k) and the radius is r.
The given equation is:
[tex](x+5)^2+(y+7)^2=21^2[/tex]
Another way to write this is:
[tex](x-(-5))^2+(y-(-7))^2=21^2[/tex]
Thus, we can see that h=-5 and k=-7.
The center is at (-5, -7).
need answer asap!!! pls help ?
Answer:
what is your problem
Step-by-step explanation:
What is the average rate of change of the function over the interval x = 0 to x = 6? f(x)=2x−1 3x+5 Enter your answer, as a fraction, in the box.
Answer:
-11
Step-by-step explanation:
Our function is 2x-13x+5
2x-13x+5= -11x+5 F(0)= 5 and F(6)= -11*6+5 = -61 let m be the average change : m= (-61-5)/6= -11Determine the function which corresponds to the given graph. (3 points) a natural logarithmic function crossing the x axis at negative two and y axis at one. The asymptote is x = -3
Answer:
[tex]y=\log_3{(x+3)}[/tex]
Step-by-step explanation:
The parent log function has a vertical asymptote at x=0, so the asymptote at x=-3 indicates a left shift of 3 units.
The parent log function crosses the x-axis 1 unit to the right of the vertical asymptote, which this one does, indicating there is no vertical shift.
The parent log function has an x-value equal to its base when it has a y-value of 1. Here, the y-value of 1 corresponds to an x-value 3 units to the right of the vertical asymptote, so the base of this logarithm is 3.
The function is ...
[tex]\boxed{y=\log_3{(x+3)}}[/tex]
What is the inverse of the function f(x) = 2x + 1?
1
1
h(x) =
X-
2
2
1
1
Oh(x) =
- x +
O h(x) =
3x-2
Oh(x) =
= {x+2
Mark this and return
Save and Exit
Next
Submit
Answer:
[tex]f^{-1} = \frac{x-1}{2}[/tex]
Step-by-step explanation:
[tex]f(x) = 2x+1[/tex]
Replace it with y
[tex]y = 2x+1[/tex]
Exchange the values of x and y
[tex]x = 2y+1[/tex]
Solve for y
[tex]x = 2y+1[/tex]
Subtracting 1 from both sides
[tex]2y = x-1[/tex]
Dividing both sides by 2
[tex]y = \frac{x-1}{2}[/tex]
Replace it by [tex]f^{-1}[/tex]
So,
[tex]f^{-1} = \frac{x-1}{2}[/tex]
Answer:
[tex]\displaystyle f^{-1}(x)= \frac{1}{2}x - \frac{1}{2}[/tex]
Step-by-step explanation:
f(x) = 2x + 1
f(x) = y (output)
y = 2x + 1
Solve for x.
y - 1 = 2x
Divide 2 on both sides.
y/2 - 1/2 = x
1/2y - 1/2 = x
Switch variables.
1/2x - 1/2 = y
[tex]f^{-1}(x)= \frac{1}{2}x - \frac{1}{2}[/tex]
pls help me pls pls pls
Answer: 1x + 2y = 4
Step-by-step explanation:
The equation of the line is y = -1/2x + 2.
First, let's make 4 on one side of the equation. First, bring x to the left. y + 1/2x = 2. Then multiply the whole equation by two. Thus, 1x + 2y = 4.
Hope it helps <3
Which expression is equivalent to 8 - (6r + 2)? A. -6r + 6 B. 2r + 2 C. 6r + 10 D. -6r + 10
Answer:
6 -6r
Step-by-step explanation:
8 - (6r + 2)
Distribute the minus sign
8 - 6r -2
Combine like terms
6 -6r
Answer:
A. -6r+6
Step-by-step explanation:
We are given the expression:
8-(6r+2)
First, let's distribute the negative sign. Multiply each term inside the parentheses by -1.
8+ (-1*6r) + (-1*2)
8-6r-2
Now, combine like terms. Add the constants, or terms without a variable.
-6r + (8+-2)
-6r + (8-2)
-6r + (6)
-6r+6
The answer is A. -6r+6
a lorry is travelling at 13.5 m/s along a road whereto speed limit is 50km/h. She that the lorry is travelling below the speed limit
Answer:
First, convert 13.5 m/s to km/hr
13.5 x 3.6 = 48.6 km/hr
This is below the speed limit of 50 km/hr
Answer:
48600/hour × 1/1000= 48.6km/h
Step-by-step explanation:
4(x+1)=16 HELP MEEEEEE
Answer:
4(x + 1) = 16
x + 1 = 4 (Divide equation by 4)
x = 3 (subtract 1)
Answer:
x = 3
Step-by-step explanation:
4(x + 1)=16
Expand the brackets.
4x + 4 = 16
Subtract 4 on both sides.
4x + 4 - 4 = 16 - 4
4x = 12
Divide both sides by 4.
4x/4 = 12/4
x = 3
2. Write an equation of a line in slope-intercept form
that passes through a point (4,-6) and has a slope of -3.
Answer:
y = -3x+6
Step-by-step explanation:
The slope intercept form of a line is given by
y = mx+b where m is the slope and b is the y intercept
y = -3x +b
Substitute the point into the equation
-6 = -3*4+b
-6 =-12+b
Add 12 to each side
-6+12 =-12+12+b
6=b
y = -3x+6
[tex](2 + 6)(2 + 3)[/tex]
Answer:
40 because (8)(5)=40 when you add the numbers inside the parenthesis
Step-by-step explanation:
Look at my picture for the written work for ANOTHER method
To solve this problem, you use the method called FOIL.
F= multiply the FIRST terms
O= multiply the OUTTER terms
I= multiply the INNER terms
L= multiply the LAST terms
Please rate this the brainlist if this helped, thanks!
Answer:
[tex]40[/tex]
Step-by-step explanation:
[tex](2+6)(2+3)[/tex]
Solve brackets.
[tex](8)(5)[/tex]
Multiply.
[tex]=40[/tex]
Evaluate the expression ( 1 + 2 i ) ( − 2 − 1 i ) and write the result in the form a + b i .
Answer:
- 5i.
Step-by-step explanation:
( 1 + 2 i ) ( − 2 − 1 i )
= 1 * -2 + 1*-1i + 2i*-2 - 2i*1i
= -2 - i - 4i - 2i^2 i^2 = -1 so we have:
-2 - 5i +2
= 0 - 5i
= -5i.
Plz answer what is in the screen shot!
Answer:
([tex]\sqrt{15}[/tex])/7
Step-by-step explanation:
Let b be the tird side of the triangle
tanθ= b/c
using the pythagorian theorem we get :
a²+b²= c² ⇒ b²= c²-a²= 8²-7²=15 ⇒b=√15
so: tanθ= √15/7
What is the length of AC?
Answer:
16Option A is the right option
Step-by-step explanation:
BO is bisector of line AC
so,
AB=BC
AC=AB+BC
=8+8
= 16
Hope this helps...
Good luck on your assignment....
Answer:
16
Step-by-step explanation
BD is perpendicular bisector of AC so BC is 8.
8+8=16
Find the circumference of a circle with a radius of 15 centimeters. Round your answer to the nearest centimeter
Answer:
94 cm
Step-by-step explanation:
The formula for finding the circumference of a circle is;
Circumference = 2πr
where π = [tex]\frac{22}{7}[/tex] or 3.14 and
r = radius
Here radius is 15 cm so;
Circumference = [tex]2 * \frac{22}{7} * 15[/tex]
= [tex]\frac{660}{7}[/tex]cm
= 94.28cm
= 94 cm ( rounded to the nearest centimetre )
[tex](\sqrt{5})(\sqrt[3]{5})[/tex] answers [tex]6\frac{5}{6}\\5\frac{1}{6}\\5\frac{2}{3}\\5\frac{7}{6}[/tex]
Answer:
A : [tex]5^{\frac{5}{6} }[/tex]
Step-by-step explanation:
Because you're multiplying two numbers with the same base, you can add their exponents:
[tex]\sqrt{5} = 5^{\frac{1}{2} } = 5^{\frac{3}{6} } \\\sqrt[3]{5} =5^{\frac{1}{3} } = 5^{\frac{2}{6} }[/tex]
[tex]5^{\frac{3}{6} } * 5^{\frac{2}{6} } = 5^{\frac{5}{6} }[/tex]
Which of the following are examples of statistical questions?
a
How many pairs of shoes do you own?
b
What types of music does the 6th grade like?
c
How many sodas do Jack and his friends drink in a week?
d
How many cats does Jack have?
The correct answers are B. What types of music does the 6th grade like? and C. How many sodas do Jack and his friends drink in a week?
Explanation:
Statistical questions are those that can only be answered by collecting and analyzing numerical data. This often implies gathering data from a group of individuals and using this to answer the question. Additionally, statistics questions are complex and do not have a direct or unique answer. In this context, the question "What types of music does the 6th grade like?" is statistical because to answer this, it is necessary to collect data from all students in 6th grade and analyze it. This occurs in "How many sodas do Jack and his friends drink in a week?" because it is necessary to know the number of sodas each person drinks in a week.
On the other hand, the questions "How many pairs of shoes do you own?" or "How many cats does Jack have?" are not statistical because it is not necessary to collect a lot of data to know the answer and they can be answered through only one number.
If x ∥ y and y ∥ z, then _____
Answer:
x ║ z
Step-by-step explanation:
Lines parallel to the same line are parallel to each other.
x and z are both parallel to y, so are parallel to each other:
x ║ z
7•(6+2)2squared-3squared=What
Answer:
215
Step-by-step explanation:
7*(6+2)4-9
7*8*4-9
56*4-9
224-9=215
Answer:
7.12.2= 168
Step-by-step explanation:
168 x 168 =28224
28224-3= 28221
28221 x 28221 = 796424841
Stacy goes to the county fair with her friends. The total cost of ride tickets is given by the equation c = 3.5t, where c is the total cost of tickets and t is the number of tickets. If Stacy bought 15 tickets, she would spend $
Answer:
She would spend $52.50.
Step-by-step explanation:
c = 3.5t
c = 3.5(15)
c = $52.50
Hope this helped! :)
Answer:
328.48
Step-by-step explanation:
Will give brainliest, can somebody help me with this question
Answer:
A = 5x + 5
Step-by-step explanation:
Area of Parallelogram Formula: A = bh
Since we are given b = 5 and h = x + 1, simply plug it into the formula:
A = 5(x + 1)
A = 5x + 5
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▹ Answer
A = 5x + 5
▹ Step-by-Step Explanation
A = bh
A = 5(x + 1)
A = 5x + 5
Hope this helps!
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Brainliest is greatly appreciated!
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Evaluate the following integral using trigonometric substitution.
Integral from 7 StartRoot 49 - x2 EndRoot dx
1. What substitution will be the most helpful for evaluating thisintegral?
2. Find dx?
3. Rewrite the given integral using substitution.
Answer:
Step-by-step explanation:
1. Given the integral function [tex]\int\limits {\sqrt{a^{2} -x^{2} } } \, dx[/tex], using trigonometric substitution, the substitution that will be most helpful in this case is substituting x as [tex]asin \theta[/tex] i.e [tex]x = a sin\theta[/tex].
All integrals in the form [tex]\int\limits {\sqrt{a^{2} -x^{2} } } \, dx[/tex] are always evaluated using the substitute given where 'a' is any constant.
From the given integral, [tex]\int\limits {7\sqrt{49-x^{2} } } \, dx = \int\limits {7\sqrt{7^{2} -x^{2} } } \, dx[/tex] where a = 7 in this case.
The substitute will therefore be [tex]x = 7 sin\theta[/tex]
2.) Given [tex]x = 7 sin\theta[/tex]
[tex]\frac{dx}{d \theta} = 7cos \theta[/tex]
cross multiplying
[tex]dx = 7cos\theta d\theta[/tex]
3.) Rewriting the given integral using the substiution will result into;
[tex]\int\limits {7\sqrt{49-x^{2} } } \, dx \\= \int\limits {7\sqrt{7^{2} -x^{2} } } \, dx\\= \int\limits {7\sqrt{7^{2} -(7sin\theta)^{2} } } \, dx\\= \int\limits {7\sqrt{7^{2} -49sin^{2}\theta } } \, dx\\= \int\limits {7\sqrt{49(1-sin^{2}\theta)} } } \, dx\\= \int\limits {7\sqrt{49(cos^{2}\theta)} } } \, dx\\since\ dx = 7cos\theta d\theta\\= \int\limits {7\sqrt{49(cos^{2}\theta)} } } \, 7cos\theta d\theta\\= \int\limits {7\{7(cos\theta)} }}} \, 7cos\theta d\theta\\[/tex]
[tex]= \int\limits343 cos^{2} \theta \, d\theta[/tex]
What is the explicit rule for the following sequence? 48, 24, 12, 6, ……
I NEED HELP PLEASE, THANKS! :)
Write 18(cos169° + isin169°) in rectangular form. Round numerical entries in the answer to two decimal places. (Show work)
Answer:
-17.67 +3.43i
Step-by-step explanation:
Carry out the indicated math:
18 cis 169° = (18·cos(169°) +i·18·sin(169°)) = (18·(-0.9816) +i·18·0.1908)
= -17.67 +i·3.43
Answer:
The rectangular form is z = -17.67 + i 3.43
Step-by-step explanation:
A consumer electronics company is comparing the brightness of two different types of picture tubes for use in its television sets. Tube type A has mean brightness of 100 and standard deviation of 16, and tube type B has unknown mean brightness, but the standard deviation is assumed to be iden- tical to that for type A. A random sample of n = 25 tubes of each type is selected, and XB - Xis computed. If us equals or exceeds ua, the manufacturer would like to adopt type B for use. The observed difference is XB - XA = 3.5. What decis would you make, and why?
Answer:
________________________________________________
someone please help me!!!
Explanation:
Surface area of a cone = pi*r^2 + pi*r*sqrt(r^2+h^2)
r = radius
h = height of cone
In this case,
r = 8 is the radius
h = 41
So,
SA = surface area
SA = pi*r^2 + pi*r*sqrt(r^2+h^2)
SA = pi*8^2 + pi*8*sqrt(8^2+41^2)
SA = 1250.936884057 use a calculator for this step
SA = 1251 square meters approximately
what is the volume of a 1 by 2 by 3 box? Is it 6^3 or 216?
Answer:
[tex]6 \text{ unit}^3[/tex]
Step-by-step explanation:
[tex]\text{Volume}=\text{Base * Height * Depth}\\1*2*3=6\\\text{So neither of your options are correct.}[/tex]
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▹ Answer
6ft³
▹ Step-by-Step Explanation
Since we are using the measurement of cubic feet, the answer is always going to be (cf³) .
1 × 2 × 3 = 6
Cubic feet - 6 ft³
Hope this helps!
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What will happen (other things being equal) if you increase the sample size used to construct a given confidence interval?
Answer:
So if you increase the sample size used to construct a given confidence interval, the confidence interval will be narrower, that is, more precise.
Step-by-step explanation:
The sample size is important to find the margin of errror of a confidence interval.
The margin of error is given by a formula in the following format:
[tex]M = \frac{c*s}{\sqrt{n}}[/tex]
In which c is the critical value(depends on the distribution used, can be T or Z), s is the standard deviation(of the sample or the population) and n is the size of the sample.
As n increases, M decreases, which leads to a lower margin of error.
The lower the margin of error, the more precise the interval is.
So if you increase the sample size used to construct a given confidence interval, the confidence interval will be narrower, that is, more precise.
It is thought that the front cover and the nature of the first question on mail surveys influence the response rate. An article tested this theory by experimenting with different cover designs. One cover was plain; the other used a picture of a skydiver. The researchers speculated that the return rate would be lower for the plain cover.
Cover Number Sent Number Returned
Plain 209 103
Skydiver 215 109
Does this data support the researchers' hypothesis? Test the relevant hypotheses using ? = 0.10 by first calculating a P-value.
State the relevant hypotheses. (Use p1 for the plain cover and p2 for the skydiver cover.)
H0: p1? p2 = 0
Ha: p1? p2 > 0H0: p1? p2 = 0
Ha: p1? p2 ? 0 H0: p1? p2 = 0
Ha: p1? p2? 0H0: p1? p2 = 0
Ha: p1? p2 < 0
Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z =
P-value =
State the conclusion in the problem context.
Reject H0. The data does not suggest that the front cover and nature of the first question on mail surveys influence the response rate.Fail to reject H0. The data does not suggest that the front cover and nature of the first question on mail surveys influence the response rate. Reject H0. The data suggests that the front cover and nature of the first question on mail surveys does influence the response rate.Fail to reject H0. The data suggests that the front cover and nature of the first question on mail surveys does influence the response rate.
Answer:
The null and alternative hypothesis are:
[tex]H_0: \pi_1=\pi_2\\\\H_a:\pi_1\neq \pi_2[/tex]
Test statistic z = -0.29
P-value = 0.7709
Fail to reject H0. The data does not suggest that the front cover and nature of the first question on mail surveys influence the response rate.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the return rate is different for the Plain cover and the Skydiver cover.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The significance level is 0.1.
The sample 1 (plain cover), of size n1=209 has a proportion of p1=0.493.
[tex]p_1=X_1/n_1=103/209=0.493[/tex]
The sample 2 (skydiver cover), of size n2=215 has a proportion of p2=0.507.
[tex]p_2=X_2/n_2=109/215=0.507[/tex]
The difference between proportions is (p1-p2)=-0.014.
[tex]p_d=p_1-p_2=0.493-0.507=-0.014[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{103+109}{209+215}=\dfrac{212}{424}=0.5[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.5*0.5}{209}+\dfrac{0.5*0.5}{215}}\\\\\\s_{p1-p2}=\sqrt{0.001196+0.001163}=\sqrt{0.002359}=0.049[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.014-0}{0.049}=\dfrac{-0.014}{0.049}=-0.29[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=2\cdot P(z<-0.29)=0.7709[/tex]
As the P-value (0.771) is bigger than the significance level (0.1), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the return rate is different for the Plain cover and the Skydiver cover.