Answer: X=0 , 1.03355778
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Find the number of solutions of the equation 6x^2+6x+3=0 by using the discriminant
Answer:
No real roots
Step-by-step explanation:
Given
[tex]6x^2 + 6x + 3 = 0[/tex]
Required
The number of solution
The discriminant (d) for [tex]ax^2 + bx + c = 0[/tex] is:
[tex]d = b^2 - 4ac[/tex]
So, we have:
[tex]d = 6^2 - 4*6*3[/tex]
[tex]d = 36 - 72[/tex]
[tex]d = -36[/tex]
Since [tex]d <0[/tex], then the equation has no real roots
A Driver’s Ed program is curious if the time of year has an impact on number of car accidents in the U.S. They assumethat weather may have a significant impact on the ability of drivers to control their vehicles. They take a randomsample of 150 car accidents and record the season each occurred in. They found that 27 occurred in the Spring, 39 inthe Summer, 31 in the Fall, and 53 in the Winter.
Required:
Can it be concluded at the 0.05 level of significance that caraccidents are not equally distributed throughout the year?
Answer:
p-value = 0.0145
Hence, Since p-value ( 0.0145 ) is less than significance level ( 0.05 )
we reject null hypothesis.
Therefore, there is sufficient evidence to conclude that Car accidents are NOT equally distributed throughout the year
Step-by-step explanation:
Given the data in the question;
Hypothesis;
Null hypothesis : H₀ : Car accidents are equally distributed throughout the year
Alternative hypothesis : Hₐ : Car accidents are NOT equally distributed throughout the year
significance level ∝ = 0.05
x ;
Spring = 27
Summer = 39
Fall = 31
Winter = 53
Test Statistics;
Chi Square = ∑[ (O – E)²/E ]
O E (O – E)²/E
Spring 27 37.4 2.94
Summer 39 37.4 0.06
Fall 31 37.4 1.1267
Winter 53 37.4 6.4067
Total 150 150 10.5334
so; z = ∑[ (O – E)²/E ] = 10.5334
{from table}
p-value = 0.0145
Hence, Since p-value ( 0.0145 ) is less than significance level ( 0.05 )
we reject null hypothesis.
Therefore, there is sufficient evidence to conclude that Car accidents are NOT equally distributed throughout the year
In this exercise we have to use probability knowledge to calculate the distribution during the year, so we find that:
There is sufficient evidence to conclude that car accidents are not equally distributed throughout the year.
Given the data in the question;
[tex]Null \ hypothesis: H_0[/tex][tex]Alternative \ hypothesis : H_a[/tex] [tex]Significance\ level = 0.05[/tex]Now the values given in the statement can be exemplified below as:
[tex]Spring = 27[/tex][tex]Summer = 39[/tex][tex]Fall = 31[/tex][tex]Winter = 53[/tex]In this way, we can assemble a table of values with the statistical data previously informed and using the formula given below:
[tex]Z=\sum[\frac{(O-E)^2}{E}][/tex]
[tex]Z = 10.5334[/tex]
So:
[tex]\ \ \ \ \ \ \ \ \ \ \ O \ \ \ \ \ E \ \ \ \ (O - E)^2/E\\Spring \ \ 27 \ \ 37.4 \ \ \ \ 2.94\\Summer \ 39 \ 37.4 \ \ \ \ 0.06\\Fall \ \ \ \ \ \ 31 \ 37.4 \ \ \ \ 1.1267\\Winter \ \ \ 53 \ 37.4 \ \ \ 6.4067\\Total \ 150 150 \ 10.5334[/tex]
Hence, Since pvalue ( 0.0145 ) is less than significance level ( 0.05 ), so we reject null hypothesis.
See more about probability at brainly.com/question/795909
What is the axis of symmetry for the graph of y=2x^2-6x+2
Use the formula below:
[tex] \large \boxed{h = - \frac{b}{2a} }[/tex]
From the given equation:
[tex] \large{y = 2 {x}^{2} - 6x + 2}[/tex]
Substitute a = 2 and b = -6 in the formula.
[tex] \large{h = - \frac{ - 6}{2(2)} } \\ \large{h = - \frac{ - 6}{4} } \\ \large{h = - \frac{ - 3}{2} \longrightarrow \boxed{h = \frac{3}{2} }}[/tex]
Since h is from (h,k). From an ordered pair, h = x and k = y. When answering the axis of symmetry, you should answer in term of x.
Answer
The axis of symmetry is x = 3/2Find the measures of the angles marked x and y Remember that ( 1 ) the sum of the measures of the angles of a triangle is 180 ° and (2) supplementary angles have a sum of 180 °
Answer:
gonna guess you're asked to find the measures of two interior angles given at least one exterior angle and one interior angle.
Two angles on the same line are SUPPLEMENTARY. Let's say your exterior angle is 95 degrees. That makes the corresponding interior angle 180 - 95 = 85 degrees. If your other interior angle is 79 degrees, then your last interior angle is 180 - (85 + 79) = 16 degrees.
The measure of x and y is -
x = 40°
y = 50°
We have a figure shown in the image.
We have to determine the measure of angle x and angle y.
What is the relation between the sides of any triangle ?The relation states that the sum of the any two sides of a triangle is always greater than the third side. Mathematically -
a + b > c
According to the question -
y + (2x + 50)° = 180° [supplementary angles have a sum of 180°]
2x + y = 130°
y = 130° - 2x
Therefore, in the right - angled triangle -
x + 130° - 2x + 90° = 180° [the sum of angles of a Δ = 180°]
- x + 220° = 180°
x = 220° - 180°
x = 40°
and
y = 130 - 2 x 40 = 50°
Hence, the measure of x and y is -
x = 40°
y = 50°
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HELPPP QUICK PLSS I WOULD REALLY APPRECIATE IT
Answer:
The colder it is, the more cups of hot chocolate will be sold.
Step-by-step explanation:
When it was 15 degrees Fahrenheit, 80 cups of hot chocolate were sold. When it was a 90 degree summer day, only 4 cups of hot chocolate were sold.
Find the radius of the circle,
Answer:
the correct answer is option D. 7
For each sequence, find the first 4 terms and the 10th term.
a) 12-n
B 5 - 2n
Answer:
Solution given:
a.
tn=12-n
1 st term =12-1=11
2nd term =12-2=10
3rd term=12-3=9
4th term=12-4=8
10th term=12-10=2
b.
tn=5-2n
1st term=5-2*1=3
2nd term=5-2*2=1
3rd term=5-2*3=-1
4th term=5-2*4=-3
10th term=5-2*10=-15
(a) Solution
T(n) = 12 - n
T(1) = 12 - 1 = 11
T(2) = 12 - 2 = 10
T(3) = 12 - 3 = 9
T(4) = 12 - 4 = 8
T(10) = 12 - 10 = 2
(b) Solution
T(n) = 5 - 2n
T(1) = 5 - 2 = 3
T(2) = 5 - 4 = 1
T(3) = 5 - 6 = -1
T(4) = 5 - 8 = -3
T(10) = 5 - 20 = -15
The board of directors of a corporation must select a president, a secretary, and a treasurer. In how many possible ways can this be accomplished if there are 25 members on the board of directors
Answer:
2400 ways
Step-by-step explanation:
Combination has to do with the idea of selection. Here we need to select a president, a secretary, and a treasurer.
This means to select three out of twenty five persons.
From;
nCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
Thus we have;
25C3 = 25!/(25 - 3)! 3!
=
1.6× 10^25/1.1×10^21 × 6
= 2400 ways
if it takes 53 seconds to walk from the first floor of a building to the third floor how long will it take you to walk from the first floor to the six floor
Answer: 106 seconds. (1 minute and 46 seconds.
Step-by-step explanation: If it takes 53 seconds to get through 3 floors and there are six, that means you have to multiply 53 by 2, because there are 2 sets of 3 floors.
Hope this helps! :)
the angle in a semi circle is?
24 rail cars is what % of 40 rail cars
Look at the angle shown below.
Estimate the measure of the angle.
Answer:
A
Step-by-step explanation:
It's only slightly bigger than 90 degrees, so 110 is the only plausible conclusion
Answer:
110
Step-by-step explanation:
Select the true statement about the relationship between sample size and the standard deviation of distribution of sample means, also known as the standard error.
a. As sample size increases, standard error increases.
b. Sample size does not have an impact on standard error.
c. As sample size increases, standard error decreases.
d. As sample size decreases, standard error decreases.
Answer:
c. As sample size increases, standard error decreases.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
Thus:
The standard error is inversely proportional to the square root of the sample size, that is, as the sample size increases, the standard error decreases, and the correct answer is given by option c.
Help find area of this
Answer:
120 sq feet
Step-by-step explanation:
1. 8 x 10 = 80
2. 8 x 5 = 40
3. 80 + 40 = 120 ft2 (sq feet)
Find the value of x.
A.6 B.5 C. 50/3 D.7
The value of x is 7.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The two triangles PQR and P'Q'R' are similar triangles
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Firstly let us find the P'Q' by using pythagoras theorem
R'Q'²=PR'²+P'Q'²
12²=10²+P'Q'²
144-100=P'Q'²
44=P'Q'²
P'Q'=6.6
The value of PR is x
The value of x is 7. as R it is a midpoint of P'Q'R'
Hence the value of x is 7
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please help with the steps
Answer:
2821.51
73425.64
28124.24
4124.24
Step-by-step explanation:
Effective rate: .058/2 = .029
This question is kind of ambigous and I'll make the assumption that there is no payment at time 0
[tex]175000=x\frac{(1+.029)^{2*18}-1}{.029}\\x=2821.511[/tex]
interested earned:
175000-2821.51*36= 73425.64
2.)
Same assumption as question 1 (there is no payment at time 0)
effective rate: .063/12= .00525
[tex]400(\frac{(1+.00525)^{60}-1}{.00525})=28124.24[/tex]
Interest earned: 28124-400*60=4124.24
Answer:
First problem: monthly payment $2741.99; interest earned $76,288.36
Second problem: amount in account $28,271.90; interest earned $4271.90
Step-by-step explanation:
First problem:
You open an account with a deposit. The deposit is the first monthly payment. This means that this is an annuity in which you pay at the beginning of the pay period. That makes it into an "annuity due."
[tex] A = \dfrac{F}{\frac{(1 + i)^n - 1}{i} \times (1 + i)} [/tex]
where A = periodic payment,
F = future value
i = interest rate per compounding period, n = number of compounding periods
[tex]A = \dfrac{175000}{\frac{(1 + \frac{0.058}{2})^{2 \times 18} - 1}{\frac{0.058}{2}} \times (1 + \frac{0.058}{2})}[/tex]
[tex] A = 2741.99 [/tex]
Interest earned:
[tex] 2 \times 18 \times 2741.99 - 175000 = 76288.36 [/tex]
Second problem:
Once again, the account starts with a deposit of the monthly payment, so this is also an annuity due, meaning the payments occur at the beginning of each compounding period. Here, we are given the monthly payment, an d we need to find the future value.
[tex] F = A \times \dfrac{(1 + i)^n - 1}{i} \times (1 + i)} [/tex]
[tex] F = 400 \times \dfrac{(1 + \frac{0.063}{12})^{5 \times 12} - 1}{\frac{0.063}{12}} \times (1 + \frac{0.063}{12})} [/tex]
[tex] F = 28271.90 [/tex]
The interest earned is:
[tex] 28271.90 - 12 \times 5 \times 400 = 4271.90 [/tex]
No links please :) Love you guys stay safe 3
Answer:
C
Step-by-step explanation:
I've completed the test before. :)
What is the volume, in cubic centimeters, of a rectangular prism with a height of 17 centimeters, a width of 17 centimeters, and a length of 11 centimeters?
Answer:
3179cm^3
Step-by-step explanation:
[tex]volum = height × width × length \\ = 17cm \times 17cm \times 11cm \\ = {3179cm}^{3} [/tex]
what is 12 take away 1 3/5
10 3/5
thank your guy for the pool work
I need the steps if possible:)
Answer:
3/6=1/2
Step-by-step explanation:
There are 3 ways you can roll an even number on a 6-sided die: 2, 4, and 6
Therefore, the probability of rolling an even number is 3/6 or 1/2.
Calculate half yearly payment required for each five year intervals
Answer:
bro im not going to download that pdf
Step-by-step explanation:
Find the length of DF will give brainliest to the right answer
Answer:
3.75
Step-by-step explanation:
DF = 6/24 × 15 = 3.75
________________
PLEASE HELPPP !!!!! WILL MARK BRAINLIEST TO WHOEVER GETS IT RIGHT
Answer:
128° because it is corresponding with <4
[tex] < 5 = \: < 3 \\ = \: < 4 \\ < 5 = 128 \degree[/tex]
PLSSSSSSS HELP ASAP !!! PLSSS
Answer:wpeleoe
Step-by-step explanation:
what is the system of equations shown in the graph?
Answer:
bugo.ka pag answer bobo ka bah ha wag kanang umasa dito piste ka
What is the range of the given function?
Answer:
-2
Step-by-step explanation:
range is y values
Answer:
-2
Step-by-step explanation:
That's the minimum range, which is basically the lowest point on the y-axis that the line touches
1.7p²q-1.5pq³+3.1p²q+7.1pq³
Answer:
see Image below:)
Step-by-step explanation:
Go here for steps
Volume of square based pyramid is 1568 cm3 and half of the length of the
side of the base is 7cm. Calculate the area of triangular faces of pyramid.
answer:
1393.84
Step-by-step explanation:
since the formula for a square base pyramid is a^2×h/3
we can find out the height for the pyramid by dividing the a^2×h/3 by a^2 =h/3
1568/7^2=32 since 32 = h/3 we multiply by 3 to find the height which = 96
now that we have the height we usee the pathagorean Therom to find the height of one of the face triangles
so 96^2+3.5^2=L^2 so L =96.06
so now that we have all we need
the surface area of the square at the bottom of the pyramid is 7×7
the surface area of the triangles are 96.06 ×7/2 since the area of a triangle is h×b/2
since there are 4 triangles and on square 49+4(96.06×7/2)= 1393.84
help me please thanks
Answer:
option 3
Step-by-step explanation:
ORIGINAL REFLECTED
A = ( 2, 0) A' = (-2, 0)
B = (5 , 0) B' = (-5, 0)
C = (5, -2) C' = (-5, -2)
D = (2, -2) D' = (-2, -2)
You roll a fair six-sided die. What are the chances the die shows an odd number or a number greater than one?
Answer:
4/3
Step-by-step explanation:
Out of the six sides 3 are odd and there's 5 numbers greater than 1. Basically these turn to the fractions 3/6 and 5/6 (these fractions stand for the probability they get rolled on this die).
Since the question says OR and not AND you add these fractions!
3/6 + 5/6 = 4/3