Answer:
1
Use the quadratic formula
=
−
±
2
−
4
√
2
x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=2a−b±b2−4ac
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
2
+
5
−
2
=
0
x^{2}+5x-2=0
x2+5x−2=0
=
1
a={\color{#c92786}{1}}
a=1
=
5
b={\color{#e8710a}{5}}
b=5
=
−
2
c={\color{#129eaf}{-2}}
c=−2
=
−
5
±
5
2
−
4
⋅
1
(
−
2
)
√
2
⋅
1
Step-by-step explanation:
this should help
A population is equally divided into three class of drivers. The number of accidents per individual driver is Poisson for all drivers. For a driver of Class I, the expected number of accidents is uniformly distributed over [0.2, 1.0]. For a driver of Class II, the expected number of accidents is uniformly distributed over [0.4, 2.0]. For a driver of Class III, the expected number of accidents is uniformly distributed over [0.6, 3.0]. For driver randomly selected from this population, determine the probability of zero accidents.
Answer:
Following are the solution to the given points:
Step-by-step explanation:
As a result, Poisson for each driver seems to be the number of accidents.
Let X be the random vector indicating accident frequency.
Let, [tex]\lambda=[/tex]Expected accident frequency
[tex]P(X=0) = e^{-\lambda}[/tex]
For class 1:
[tex]P(X=0) = \frac{1}{(1-0.2)} \int_{0.2}^{1} e^{-\lambda} d\lambda \\\\P(X=0) = \frac{1}{0.8} \times [-e^{-1}-(-e^{-0.2})] = 0.56356[/tex]
For class 2:
[tex]P(X=0) = \frac{1}{(2-0.4)} \int_{0.4}^{2} e^{-\lambda} d\lambda\\\\P(X=0) = \frac{1}{1.6} \times [-e^{-2}-(-e^{-0.4})] = 0.33437[/tex]
For class 3:
[tex]P(X=0) = \frac{1}{(3-0.6)} \int_{0.6}^{3} e^{-\lambda} d\lambda\\\\P(X=0) = \frac{1}{2.4} \times [-e^{-3}-(-e^{-0.6})] = 0.20793[/tex]
The population is equally divided into three classes of drivers.
Hence, the Probability
[tex]\to P(X=0) = \frac{1}{3} \times 0.56356+\frac{1}{3} \times 0.33437+\frac{1}{3} \times 0.20793=0.36862[/tex]
Find the measure of angle FGE
35 degrees
40 degrees
100 degrees
30 degrees
60 degrees
The measure of angle FGE is 52.5°.
What is the Angles of Intersecting Secants Theorem?Angles of Intersecting Secants Theorem states that, If two lines intersect outside a circle, then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs.
Thus, applying the angles of intersecting secants theorem
m∠FGE = 1/2[(100 + 35) - 30]
m∠FGE = 1/2[(105]
m∠FGE = 52.5°
Learn more about angles of intersecting secants theorem here :
https://brainly.com/question/15532257
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Which of the following is a solution to 6x - 5y=4?
(2,7)
(-1, -2)
(-2, -1)
(2, -7)
Answer:
2,7
Step-by-step explanation:
Answer:
(-1,-2)
Step-by-step explanation:
(6 x -1) -(-2 x 5) = 4
-6 + 10 = 4
Use the discriminant to describe the roots of each equation. Then select the best description.
7x² + 1 = 5x
Answer:
Imaginary roots
Step-by-step explanation:
The discriminant of a quadratic in standard form [tex]ax^2+bx+c[/tex] is given by [tex]b^2-4ac[/tex].
Given [tex]7x^2+1=5x[/tex], subtract 5x from both sides so that the quadratic is in standard form:
[tex]7x^2-5x+1=0[/tex]
Now assign variables:
[tex]a\implies 7[/tex] [tex]b\implies -5[/tex] [tex]c\implies 1[/tex]The discriminant is therefore [tex](-5)^2-4(7)(1)=25-28=\textbf{-3}[/tex].
What does this tell us about the roots?
Recall that the discriminant is what is under the radical in the quadratic formula. The quadratic formula is used to find the solutions of a quadratic. Therefore, the solutions of this quadratic would be equal to [tex]\frac{-b\pm \sqrt{-3}}{2a}[/tex] for some [tex]b[/tex] and [tex]a[/tex]. Since the number under the radical is negative, there are no real roots to the quadratic (whenever the discriminant is negative, the are zero real solutions to the quadratic). Therefore, the quadratic has imaginary roots.
Find the measure of x. X=8, x=7, x=9, x=11
Answer:
[tex]\frac{135}{15} =\frac{15(x+2)}{15}[/tex]
[tex]9=x+2[/tex]
[tex]x=7[/tex]
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How many more barrels of gasoline than desiel were produced
Answer:
15
Step-by-step explanation:
Wayne has a rectangular painting. The width of the painting is
5/6
of a foot, and the length is
3/4
of a foot. What is the area of the painting?
Answer:
5/8 ft^2
Step-by-step explanation:
The area of a rectangle is given by
A = l*w where l is the length and w is the width
A = 5/6 * 3/4
A = 3/6 * 5/4
A = 1/2 * 5/4
A = 5/8 ft^2
WHAT IS X³-27 SIMPLIFIED
Answer:
It is (x - 3)³ - 9x(3 - x)
Step-by-step explanation:
Express 27 in terms of cubes, 27 = 3³:
[tex] = {x}^{3} - {3}^{3} [/tex]
From trinomial expansion:
[tex] {(x - y)}^{3} = (x - y)(x - y)(x - y) \\ [/tex]
open first two brackets to get a quadratic equation:
[tex] {(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)[/tex]
expand further:
[tex] {(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}[/tex]
take y to be 3, then substitute:
[tex]( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)[/tex]
The circle graph above shows the distribution of utility expenses for the Hierra family last year. If the family’s total utility expenses last year were $3,600, what were their expensive go water and sewer.
Water and sewer=X%
Electric=30%
Heating and gas=50%
Answer:
The correct answer is - $720 or 20%.
Step-by-step explanation:
Given:
Total expense = 3600
Electric=30%
Heating and gas=50%
Water and sewer=X%
Solution:
For electric: 3600*30/100 = 1080
for heating and gas: 3600*50/100 = 1800
Left money for expense of water and shower = total - (electric and heating)
= 3600-1880
= 720
Percentage of water and shower = 720*100/3600
= 20%
Answer:
Correct!
Step-by-step explanation:
Thank you this is correct :) I took the test
thank you for the help every one
Answer:
1. 1.66in
2. 6.66in
3. 3.33in
4. 1inch
Step-by-step explanation:
the area of a rectangle is found by multiplying the length times width or the two sides.
5 x 1/3 is about 1.66 inches
5 x 4/3 is about 6.66 inches
5/2 x 4/3 is about 3.33 inches
and 7/6 x 6/7 is 1 inch
can anybody help me with this?
Answer:
Option (a)
Step-by-step explanation:
[tex]\sqrt[6]{1000m^{3} n^{12} } = \sqrt[6]{10^{3} } \sqrt[6]{m^{3} } \sqrt[6]{n^{12} } =\\\sqrt{10} \sqrt{m} n^{2} = n^{2} \sqrt{10m}[/tex]
What is the sum of the geometric sequence 1, 3, 9, ... if there are 10 terms? (5 points)
Answer:
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Step-by-step explanation:
There's a handy formula we can use to find the sum of a geometric sequence, and here it is
[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]
The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.
First lets visualize this sequence
[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]
Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.
[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]
Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.
[tex]S_n = \sum{a*r^{n-1}}[/tex]
To finish up lets plug these coefficients in and get our sum after 10 terms.
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Solve this question:Зх <-24
Answer:
x< - 8
Step-by-step explanation:
3x <-24
x < - 24
3
x< - 8
x < - 8
Step-by-step explanation:
3x < - 24
Divide 3 on both sides,
3x / 3 < - 24 / 3
x < - 8
What is the discriminat of 2x+5x^=1
Answer:
don't know...........
Write an explicit formula for the sequence.
-4,7,-10,13,-16
Step-by-step explanation:
Sequence is
4
,
7
,
10
,
13
,
16
,
.
.
.
a
1
=
4
,
a
2
=
7
,
a
3
=
10
,
.
.
.
If it is Arithmetic sequence,
a
2
−
a
1
=
a
3
−
a
2
=
a
4
−
a
3
& so on
In the given sum,
a
2
−
a
1
=
7
−
4
=
3
a
3
−
a
2
=
10
−
7
=
3
a
4
−
a
3
=
13
−
10
=
3
Since the difference between the successive terms is same and
hence
common difference
d
=
3
find the perimeter of 6 CM 6 CM 6 CM 6 CM
Answer:
P = 24
Step-by-step explanation:
Since all the sides are the same length, the shape is a square.
Multiply all sides by 6.
6 cm x 4 sides = 24
A particle is moving with the given data. Find the position of the particle.
a(t) = [tex]t^{2}[/tex] − 4t + 5, s(0) = 0, s(1) = 20
How do I find s(t)=?
Recall that
[tex]\dfrac{dv(t)}{dt} = a(t) \Rightarrow dv(t) = a(t)dt[/tex]
Integrating this expression, we get
[tex]\displaystyle v(t) = \int a(t)dt = \int(t^2 - 4t + 5)dt[/tex]
[tex]\:\:\:\:\:\:\:= \frac{1}{3}t^3 - 2t^2 + 5t + C_1[/tex]
Also, recall that
[tex]\dfrac{ds(t)}{dt} = v(t)[/tex] or
[tex]\displaystyle s(t) = \int v(t)dt = \int (\frac{1}{3}t^3 - 2t^2 + 5t + C_1)dt[/tex]
[tex]\:\:\:\:\:\:\:= \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + C_1t + C_2[/tex]
Next step is to find [tex]C_1\:\text{and}\:C_2[/tex]. We know that at t = 0, s = 0, which gives us [tex]C_2 = 0[/tex]. At t = 1, s = 20, which gives us
[tex]s(1) = \frac{1}{12}(1)^4 - \frac{2}{3}(1)^3 + \frac{5}{2}(1)^2 + C_1(1)[/tex]
[tex]= \frac{1}{12} - \frac{2}{3} + \frac{5}{2} + C_1 = \frac{23}{12} + C_1 = 20[/tex]
or
[tex]C_1 = \dfrac{217}{12}[/tex]
Therefore, s(t) can be written as
[tex]s(t) = \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + \frac{217}{12}t[/tex]
Solve -9 < 4x + 3 5 19.
Answer:
C -3 < x ≤ 4
Step-by-step explanation:
-9 < 4x + 3 ≤ 19.
Subtract 3 from all sides
-9-3 < 4x + 3-3 ≤ 19-3
-12 < 4x ≤ 16
Divide by 4
-12/4 < 4x/4 ≤ 16/4
-3 < x ≤ 4
Which of the following is an advantage of using systematic random sampling?
Systematic random sampling reduces sampling variability.
Systematic random sampling does not require a finite population size.
Systematic random sampling could inadvertently miss patterns in the population.
Systematic random sampling uses clusters, which are close in proximity, making data collection easier.
This is a question that asks about the advantages of a systematic random sampling. Thus, we first take a look at the types of sampling, and then we see the advantage of systematic random sampling.
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
Systematic:
One of the bigger advantages is that the systematic sampling eliminate clusters, which means that the last option is wrong.
Inadvertently missing patterns is a problem in systematic sampling, and not an advantage, thus the third option is also wrong.
It also does not reduce sampling variability, thus the first option is wrong.
From this, it can be concluded that the correct option is:
Systematic random sampling does not require a finite population size.
For another example of systematic random sampling, you can check https://brainly.com/question/21100042
If it takes 247.2 yards of yarn to knit 2.5 baby bibs, how many yards of yarn would it take to knit 4 baby bibs? SHOW ALL WORK! ONLY ANSWER IF YOU KNOW THE ANSWER!
Answer:
395.52
Step-by-step explanation:
247.2/2.5=98.88(1 bib)
98.88x4=395.52(4 bibs)
Each Friday, the sixth grade students in Mr. Shin's physical education class spend the first five minutes doing crunches. Instead of keeping track of the weekly total number of crunches, Mr. Shin keeps track of how they do compared to the week before, and then records the result as a positive or negative number. Record the number for each of the following:
Ben did 10 more crunches this week than last week. What number would Mr. Shin record?
Gail did 8 less crunches this week than last week. What number would Mr. Shin record?
Nathaniel did the same number of crunches this week as last week. What number would Mr. Shin record?
awnser asap
Answer:
Mr. Shim would record the number +10 or 10 for Ben because of the word "more".
For Gail, Mr. Shin would record the number -8 because of the word, "less''.
Since Nathaniel did not improve or decrease the number of crunches, Mr. Shin would record the number 0.
I hope this helps better
Give the domain and range of G={(6.0),(-9,-3),(1,-3)}
Answer:
Step-by-step explanation:
D={ 6 , -9 , 1 }
R={ 0 ,-3 }
i need help figuring it out
I don’t get it. If u can actually answer it
Answer:
A is the answer! I think you know because the formula is given at the top.
What is the domain of the function represented by the graph
Answer:
C
Step-by-step explanation:
Domain of the function is the whole R
In the figure above, AABC is an equilateral
triangle and each circle is tangent to the other
two circles. If each circle has diameter 10, what
is the distance h?
(A) 103
(B) 1513
(C) 15+513
(D) 10+1013
(E) 10+5/5
Answer:
B
Step-by-step explanation:
The range is the set of________
A) First Coordinates
B) Ordered Pairs
C) Second coordinates
Answer:
The range is the set of first coordinates
From the figure, the cylinder glass has a height of 6 inches and a radius of the mouth of the glass 1.25 inches. Find the length of SK in inches.
Answer:
D. 6.5
Step-by-step explanation:
The diameter of the cylinder is 1.25 x 2 = 2.5
SK = √1.25² + 6² = √42.25 = 6.5
Working for a car company, you have been assigned to find the average miles per gallon (mpg) for acertain model of car. you take a random sample of 15 cars of the assigned model. based on previous evidence and a qq plot, you have reason to believe that the gas mileage is normally distributed. you find that the sample average miles per gallon is around 26.7 with a standard deviation of 6.2 mpg.
a. Construct and interpret a 95% condence interval for the mean mpg, , for the certain model of car.
b. What would happen to the interval if you increased the condence level from 95% to 99%? Explain
c. The lead engineer is not happy with the interval you contructed and would like to keep the width of the whole interval to be less than 4 mpg wide. How many cars would you have to sample to create the interval the engineer is requesting?
Answer:
a) The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.
b) Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.
c) 37 cars would have to be sampled.
Step-by-step explanation:
Question a:
We have the sample standard deviation, and thus, the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.1448\frac{6.2}{\sqrt{15}} = 3.4[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 26.7 - 3.4 = 23.3 mpg.
The upper end of the interval is the sample mean added to M. So it is 26.7 + 3.4 = 30.1 mpg.
The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.
b. What would happen to the interval if you increased the confidence level from 95% to 99%? Explain
Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.
c. The lead engineer is not happy with the interval you constructed and would like to keep the width of the whole interval to be less than 4 mpg wide. How many cars would you have to sample to create the interval the engineer is requesting?
Width is twice the margin of error, so a margin of error of 2 would be need. To solve this, we have to consider the population standard deviation as [tex]\sigma = 6.2[/tex], and then use the z-distribution.
We have that 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 pvalue 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.
How many cars would you have to sample to create the interval the engineer is requesting?
This is n for which M = 2. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 1.96\frac{6.2}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 1.96*6.2[/tex]
[tex]\sqrt{n} = \frac{1.96*6.2}{2}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*6.2}{2})^2[/tex]
[tex]n = 36.9[/tex]
Rounding up:
37 cars would have to be sampled.
5^3×25=
Simplify as much as possible
