Answer:
a)
The statistic value |Z| = 2.053 > 1.96 at 0.05 Level of significance
Null hypothesis is rejected
Alternative hypothesis is Accepted
Actually 30% of all drivers make not this mistake at the given intersection
b)
The test statistic value |Z| = 2.053 >2.576 at 0.01 Level of significance
Null hypothesis is Accepted
Actually 30% of all drivers make this mistake at the given intersection
Step-by-step explanation:
Step(i):-
Given Population proportion = 30% or 0.30
Given data In a random sample of 600 cars making a right turn at a certain intersection, 157 pulled into the wrong lane
sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{157}{600} = 0.2616[/tex]
Null hypothesis:- H₀: p = 0.30
Alternative hypothesis : H₁:p≠0.30
Step(ii):-
a)
Test statistic
[tex]Z = \frac{p^{-}-P }{\sqrt{\frac{p(1-p)}{n} } }[/tex]
[tex]Z = \frac{0.2616-0.30 }{\sqrt{\frac{0.30(1-0.30)}{600} } }[/tex]
Z = -2.053
|Z| = |-2.053| = 2.053
Level of significance = 0.05
Z₀.₀₅ = 1.96
The calculated value |Z| = 2.053 > 1.96 at 0.05 Level of significance
Null hypothesis is rejected
Alternative hypothesis is Accepted
Conclusion:-
Actually 30% of all drivers make not this mistake at the given intersection
b)
Given level of significance = 0.01
Z₀.₀₁ = 2.576
The calculated value |Z| = 2.053 >2.576 at 0.01 Level of significance
Null hypothesis is Accepted
Actually 30% of all drivers make this mistake at the given intersection
In Triangle A B C, what is the value of x? Triangle A B C. Angle A is (10 x minus 10) degrees, angle B is (8 x) degrees, angle C is (10 x + 8) degrees. 5.5 6.5 55 65
Answer:
x = 6.5
Step-by-step explanation:
The sum of the angles of a triangle is 180
8x+ 10x-10 + 10x +8 = 180
Combine like terms
28x -2 = 180
Add 2 to each side
28x-2+2 = 180+2
28x=182
Divide by 28
28x/28 = 182/28
x =6.5
Answer:
x = 6.5
Step-by-step explanation:
In a triangle, the sum of the measures of the angles equals 180 deg.
8x + 10x - 10 + 10x + 8 = 180
28x -2 = 180
28x = 182
x = 6.5
How many different simple random samples of size 5 cab be obtained from a population whose size is 46
Answer:
1370754
Step-by-step explanation:
From what I can see, you are probably studying combinations and permutations at the moment. Since this is a question about how many groups of five can be produced from a sample size of 46, the groups are random and not in order, which may rule for us to use the combination formula.
Once you compute this, this answer is basically saying that 1370754 groups of 5 can be created from a sample size of 46
Tammy and Lawrence like to bike competitively. Tammy biked seven less than three times the number of miles that Lawrence biked. If c represents the number of miles Lawrence biked, write an expression for the number of miles Tammy biked.
Answer:
3c - 7
Step-by-step explanation:
c - the number of miles Lawrence biked
Tammy biked seven less than three times the number of miles that Lawrence biked.
So, 3 x c (the # of miles Lawrence biked) - 7 (she biked seven less)
The answer is 3c - 7.
How do i find the remaining angles without a protractor?
Answer:
For Triangles:
To find remaining angles, implying that you have angles already given to you, you would mark your unknown angle as a variable, x per say, then you would add together the angles that you do have and you would subtract that by 180 degrees because all triangles angles sum up to 180 degrees. So when you subtract that you should be able to find your unknown angle.
What is the measure of angle S?
480
56°
930
101°
Answer:
m∠s = 93°
Step-by-step explanation:
We know that any quadrilateral's sum of angles adds up to 360°. In that case,
360 - (56 + 132 + 79) = m∠s
m∠s = 93°
Answer:
S° = 93 °
Step-by-step explanation:
[tex]The- diagram- is- a- trapezoid (quadrilateral)\\Sum- of- angles-in a- quadrilateral = 360\\ 132\° + 56\° + 79\° + x\° = 360\° \\267\° + x\° = 360\° \\x = 360 \° - 267 \° \\x\° = 93\°[/tex]
Quadrilaterals WXYZ and BADC are congruent. In addition, WX ≅ DC and XY ≅ BC.
If AD = 4 cm and AB = 6 cm, what is the perimeter of WXYZ?
18 cm
20 cm
22 cm
24 cm
Answer: 20 cm
If quadrilaterals WXYZ and BADC are congruent, then their corresponding sides are congruent.
Given that
WX≅DC,
XY≅BC,
you can state that
YZ≅AB,
WZ≅AD.
If AD = 4 cm and AB = 6 cm, then WZ = 4 cm and YZ = 6 cm. Opposite rectangle sides are congruent, then XY = 4 cm and WX = 6 cm.
The perimeter of WXYZ is
P = WX + XY + YZ + WZ = 6 + 4 + 6 + 4 = 20 cm.
Two identical decks of 52 cards are mixed together, yielding a stack of 104 cards. How many different ways are there to order this stack of 104 cards?
Answer:
here the order will be 104! =[tex]1.029e^{166}[/tex]
Step-by-step explanation:
since the cards are to arranged in no particular order that is why we used combination to find the result.
Combination can simply be explained as the method of selecting items from a collection of items where the order of the selections does not matter.
According to the graph, a person has a fever when his or her body temperature is .
ANSWER:
A number line going from 95 to 102. A closed circle is at 100. Everything to the right is shaded.
Dr. Hilton uses the graph to determine if a patient has a fever. The graph shows body temperatures, in degrees Fahrenheit, that indicate a fever.
According to the graph, a person has a fever when his or her body temperature is
✔ at least 100 degrees
.
It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that exactly three of five chosen calculators are defective
Answer:0.0081 or 0.81%
Step-by-step explanation:
The required probability is P(3,5,0.1)= C5 3 * p^3*q^2, where
C5 3= 5!/3/2=4*5/2=10
p is the probability that one randomly selected calculator is defective= 10%=0.1
q is the probability that one randomly selected calculator is non-defective.
q=1-p=1-0.1=0.9
So P(3,5,0.1)= 10*0.1^3*0.9^2=0.01*0.81=0.0081
The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, if the products are defined. A is 4 × 2, B is 2 × 4.
Answer:
AB: size 4 x 4
BA: size 2 x 2
Step-by-step explanation:
When we want to multiply two matrices, we need first to check if the number of columns of the first matrix is equal the number of rows of the second matrix. Then, the resulting matrix would have the number of rows equal the number of rows of the first matrix, and the number of columns equal the number of columns of the second matrix.
That is, if we have a matrix A with dimensions a x b and a matrix B with dimensions c x d, to calculate the product AB we must have b = c, and the resulting product would have dimensions a x d.
Finally, if A is 4 x 2 and B is 2 x 4, we would have:
AB = (4 x 2) (2 x 4)
2 = 2 -> product is possible.
Dimensions of the result: 4 x 4
BA = (2 x 4) (4 x 2)
4 = 4 -> product is possible.
Dimensions of the result: 2 x 2
The size of a matrix is its dimension,
The size of AB and BA are 4 x 4 and 2 x 2, respectively
The dimension of matrix A is given as 4 x 2, while the dimension of matrix B is 2 x 4
Product AB
The dimension of matrix AB is the row of matrix A by the column of matrix B.
Matrix A has 4 rows, while matrix B has 4 columns.
So, the dimension of matrix AB is 4 x 4
Product BA
The dimension of matrix BA is the row of matrix B by the column of matrix A.
Matrix B has 2 rows, while matrix A has 2 columns.
So, the dimension of matrix BA is 2 x 2
Hence, the size of AB and BA are 4 x 4 and 2 x 2, respectively
Read more about matrices at:
https://brainly.com/question/24810141
what is 82 times 0.3 /a is 246 /b is 24.6 /c is 2.46
Answer:
24.6
Step-by-step explanation:
Answer:
24.6
Step-by-step explanation:
82 times 3 is 246.
Remember your decimal mark.
24.6
Which number is equivalent to [tex]\frac{3^4}{3^2}[/tex]?
A. 2
B. 9
C. 81
D. 729
Answer:
B. 9
Step-by-step explanation:
When there are exponents with the same base in a fraction, they can be simplified by subtracting.
We can take out 2 on both the top and bottom, leaving us with 3^2 over 1
3x3 is 9 and 9/1 is still 9
Answer:
9
Step-by-step explanation:
Since the bases are the same, we can subtract the exponents to accomplish the division
a^b / a^c = a^ (b-c)
3^4 / 3^2
3^ (4-2)
3^2
9
If you are 16 16 years old now, which equation could be used to solve for your age, F , 15 15 years from now?
Answer:
F=16+15
Step-by-step explanation:
F=16+15
F-the age in fifteen years
16- the age right now
Answer:
F = 16 + 15
Explanation:
To write an equation, first establish any variables and their values, as well as the terms needed.
'F' - your age fifteen years from your current age
'16' - your current age
'15' - fifteen years added to your current age
Since we know that we have to find the total age fifteen years from your current age, that means we will be using addition in the equation. Now write your equation using the information we've established.
your age fifteen years from your current age = your current age + fifteen years
F = 16 + 15
Therefore, the equation that could be used to solve for you age is F = 16 + 15.
In a certain city, the true probability of a baby being a boy is 0.559. Among the next eight randomly selected births, find the probability that at least one of them is a boy. (round to three decimal places)
Answer:
99.86%
Step-by-step explanation:
What we have here is a binomial distribution, let x be the baby number among 8 births.
Binomial (n = 8, p = 0.559)
We want to find, P (X ≥ 1)
P (X ≥ 1) = 1 - P (X <1)
P (X ≥ 1) = 1 - P (X = 0)
P (X = 0) = 8C0 * (0.559) ^ 0 * (1 - 0.559) ^ (8-0)]
8C0 = 8! / (0! * (8-0)!) = 1
replacing we have:
P (X = 0) = 1 * 1 * 0.0014
P (X = 0) = 0.0014
P (X ≥ 1)) = 1 - 0.001 4
P (X ≥ 1) = 0.9986
Therefore the probability is 99.86%
algebra ...........................
Answer:
see explanation
Step-by-step explanation:
Given that y is inversely proportional to x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportion
(a)
To find k use the condition when y = 7 , x = 9, that is
7 = [tex]\frac{k}{9}[/tex] ( multiply both sides by 9 )
63 = k
y = [tex]\frac{63}{x}[/tex] ← equation of proportion
(b)
When x = 21, then
y = [tex]\frac{63}{21}[/tex] = 3
(right answer using ALGEBRA will get lots of points and brainliest!)
There are 23 boys and 35 girls on the school’s track and field team. After q boys and (q+4) girls graduate at the end of this year, the probability of selecting a boy at random to represent the school for an event becomes 2/5. Find the value of q.
Answer:
q=7
Step-by-step explanation:
So, right now, there are 23 boys and 35 girls.
After q boys and q+4 girls graduate, the probability of selecting a boy at random is 2/5. In other words, we can write the following equation:
(23-q)/(58-q-(q+4))=2/5
The numerator represents the number of boys after graduating.
The denominator represents the total numbers after boys and girls graduate. The 58 is the current total (23+35) and the -q and -(q+4) is the amount of students that will graduate. Now, find q:
(23-q)/(58-q-q-4)=2/5
(23-q)/(54-2q)=2/5
Cross multiply:
5(23-q)=2(54-2q)
115-5q=108-4q
-5q=-7-4q
-q=-7
q=7
We can check this: 23-7=16 and 35-11=24. 16/(24+16)=16/40=2/5
Answer:
7Step-by-step explanation:
Total students = 23 + 35 = 58
Now, it becomes,
[tex]58 - (q + q + 4)[/tex]
[tex] = 58 - (2q + 4)[/tex]
When there is a (-) in front of an expression parentheses , change the sign at each term .
[tex] = 58 - 2q - 4[/tex]
Collect like terms
[tex] = 54 - 2q[/tex]
Again,
[tex] \frac{23 - q}{54 - 2q} = \frac{2}{5} [/tex]
Apply cross product property
[tex]5(23 - q) = 2(54 - 2q)[/tex]
[tex]115 - 5q = 108 - 4q[/tex]
Move variable to L.H.S and change its sign
[tex] - 5q + 4q + 115 = 108[/tex]
Move constant to R.H.S and change its sign
[tex] - 5q + 4q = 108 - 115[/tex]
Calculate the sum or difference
[tex] - q = - 7[/tex]
The difference sign (-) will be cancelled in both sides
[tex]q = 7[/tex]
Hope this helps...
Good luck on your assignment ..
Rachel has completed 2/3 of her shift; Jose has completed 1/6 of his shift; Damon has finished 4/5 of his shift; and Stacy has 6/7 of her shift remaining. Out of the four employees, who has completed the most work time? A. Damon B. Rachel C. Stacy D. Jose
Answer:
C. Stacy
Step-by-step explanation:
One way to compare is to convert all the fractions into decimals
Rachel works 2/3 of her shift: Approximately= 0.667
Jose works 1/6: approx. = 0.1667
Damon works 4/5= 0.80
Stacy works 6/7: approx. = 0.8571
Now this makes it much easier to compare
And since 0.85714 (Stacy's shift) is the largest number, Stacy has completed the largest portion of her shift
Find the -scores that bound the middle 96 of the area under the standard normal curve by using the TI-84 calculator.
Answer:
[tex]\alpha=1-0.96 =0.04[/tex]
And [tex]\alpha/2= 0.02[/tex] and if we use the following function on the Ti84 plus we got:
invNorm(0.02,0,1)
invNorm(1-0.02,0,1)
And the values with the middle 96% of the values are:
[tex]z_{\alpha/2}= \pm 2.054[/tex]
Step-by-step explanation:
For this case we want to find the limits with the middle 96% of the area below the normal curve, then the significance level would be:
[tex]\alpha=1-0.96 =0.04[/tex]
And [tex]\alpha/2= 0.02[/tex] and if we use the following function on the Ti84 plus we got:
invNorm(0.02,0,1)
invNorm(1-0.02,0,1)
And the values with the middle 96% of the values are:
[tex]z_{\alpha/2}= \pm 2.054[/tex]
A student is given that point P(a, b) lies on the terminal ray of angle Theta, which is between StartFraction 3 pi Over 2 EndFraction radians and 2Pi radians. The student uses the steps below to find cos Theta. Which of the following explains whether the student is correct? The student made an error in step 3 because a is positive in Quadrant IV; therefore, cosine theta = StartFraction a Over StartRoot a squared + b squared EndRoot EndFraction = StartFraction a StartRoot a squared + b squared EndRoot Over a squared + b squared EndFraction. The student made an error in step 3 because cosine theta = StartFraction negative b Over StartRoot a squared + b squared EndRoot EndFraction = Negative StartFraction b StartRoot a squared + b squared EndRoot Over a squared + b squared EndFraction. The student made an error in step 2 because r is negative in Quadrant IV; therefore, r = Negative StartRoot a squared + b squared EndRoot. The student made an error in step 2 because using the Pythagorean theorem gives r = plus-or-minus StartRoot (a squared) minus (b squared) EndRoot = StartRoot a squared minus b squared EndRoot.
Answer:
A.
The student made an error in step 3 because a is positive in Quadrant IV; therefore,
[tex]cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}[/tex]
Step-by-step explanation:
Given
[tex]P\ (a,b)[/tex]
[tex]r = \± \sqrt{(a)^2 + (b)^2}[/tex]
[tex]cos\theta = \frac{-a}{\sqrt{a^2 + b^2}} = -\frac{\sqrt{a^2 + b^2}}{a^2 + b^2}[/tex]
Required
Where and which error did the student make
Given that the angle is in the 4th quadrant;
The value of r is positive, a is positive but b is negative;
Hence;
[tex]r = \sqrt{(a)^2 + (b)^2}[/tex]
Since a belongs to the x axis and b belongs to the y axis;
[tex]cos\theta[/tex] is calculated as thus
[tex]cos\theta = \frac{a}{r}[/tex]
Substitute [tex]r = \sqrt{(a)^2 + (b)^2}[/tex]
[tex]cos\theta = \frac{a}{\sqrt{(a)^2 + (b)^2}}[/tex]
[tex]cos\theta = \frac{a}{\sqrt{a^2 + b^2}}[/tex]
Rationalize the denominator
[tex]cos\theta = \frac{a}{\sqrt{a^2 + b^2}} * \frac{\sqrt{a^2 + b^2}}{\sqrt{a^2 + b^2}}[/tex]
[tex]cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}[/tex]
So, from the list of given options;
The student's mistake is that a is positive in quadrant iv and his error is in step 3
Answer:
a on e2020 :)
Step-by-step explanation:
Please answer question now
Answer:
∠CED
or
∠DEC
its the same thing
Step-by-step explanation:
E is the angle
Please answer this correctly
Answer:
1/9
Step-by-step explanation:
first, u need 9 ---> 1/3
then u need 8 ---> 1/3 also
Multiply them and get...1/9
what 4.2 times 0.7 /a is 294 /b is 2.94 /c 29.4
Answer:
29.4
Step-by-step explanation:
Answer:
2.94
Step-by-step explanation:
4.2 × 0.7 = 2.94
A 6-digit number has at least one even digit in its record. How many such numbers are there? (0 is an even digit)
Answer:
884,375
Step-by-step explanation:
The first digit can't be 0, so there are 9×10⁵ = 900,000 possible six-digit numbers.
Of those, the number of six-digit numbers that have only odd digits is 5⁶ = 15,625.
Numbers with at least one even digit are all numbers that don't have only odd digits. So the number of six-digit numbers with at least one even digit is:
900,000 − 15,625 = 884,375
Oli and Katrina are buying a new SUV. The sticker price is $47,500. They talked to their bank (loan A) and were offered a 6 year loan at 4.5% annual interest, resulting in monthly payments of $754.02. The dealership (loan B) claims the couple will pay less interest with them because the loan is shorter, 5 years, and the interest rate is barely higher at 6%, resulting in a monthly payment of $918.31.
Answer:
Following are the answer to this question:
Step-by-step explanation:
In the given equation some information is missing, that is Loans "A and B".
Formula:
[tex]\bold{Total \ Payback = \ Montly \ instalment \times \ Number \ of \ Instalments} \\\\[/tex]
calculating total amount of Loan A:
[tex]= $754.02 \times 72\\\\= 54289.44[/tex]
calculating total amount of Loan B:
[tex]= $918.31 \times 60\\\\= 55098.6[/tex]
Calculate loan A:
[tex]\bold{ \ Int = \ Total\ Payment - \ Loan}\\\\[/tex]
[tex]= $ 54289.44 - $ 47500\\\\= $ 6789.44[/tex]
Calculate loan B:
[tex]\bold{ \ Int = \ Total\ Payment - \ Loan}\\\\[/tex]
[tex]= $ 55098.60 - $ 47500\\\\= $ 7598.60[/tex]
The Additional value of the Int in loan B:
[tex]\bold{= \ Int \ in \ loan \ B - \ Int \ in \ loan \ A}[/tex]
[tex]= 7598.6 - 6789.44\\\\= 809.16[/tex]
If I ride a bicycle at a rate of 5m/s,how long will it take me to ride a distance of 12km at the same rate?
Step-by-step explanation:
given,velocity = 5 m/s
and distance=12×1000=12000m
now,time =?
we have , v=s/t
or, t= s/v
so,t=12000/5
2400sec.....ans
=
i will give brainliest and 50 points pls help ASP
Answer:
Step-by-step explanation:
A trapezoid and two rectangulars are in the opening form of the geometric shapes and you should calculate their surface areas seperately which is:
12 cm and 30 cm first rectangular and its surface area is 12 x 30 = 360 cm^2second rectangular has 30 cm and 26 cm and 30 x 26 = 780 cm^2A trapezoid surface area is = [(24+29) /2] * 25 = 662.5 cm^2total surface area = 360 + 780 + 662.5 = 1802.5Answer:
Total surface area = 3744 cm^2
Step-by-step explanation:
All linear measurements are in cm
Surface area of BOTH bases
Ab = 2* (12+29)*24/2
= 984
Circumference of base
Cb = (25+12+26+29)
= 92
Height of prism
H = 30 (given)
Surface area of sides of prism
As= Cb*H
= 2760
Total Surface area of Prism
A = Ab + As
= 984 + 2760
= 3744 cm^2
Copy the diagram and oaloulate the sizes of
a bº and cº. What is the sum of the angles of
the triangle?
Answer:
sum of the angles of the triangle are 180°
Step-by-step explanation:
To find the sum of the interior angles, we use the formula( s-2*180), where s is the number of sides of the shape. If it is a pentagon, 5-2*180= 3*180= 540,
which shows that the sum of the interior angles of a pentagon is 540.
since, it is a triangle in the figure with 3 sides, 3-2*180=1*180=180.
The interior angles are unknown= a, b and c. we know that a+b+c=180 degrees and the exterior angles are mentioned. And we know that, opposite angles are equal. So, a is 40 degrees considering that 40 degrees is the opposite angle of a, b is 95 degrees whereas c is 45 degrees.
now, lets check if the angles indeed have a sum of 180 degrees,
40+95+45= 135+45 which gives 180 degrees.
Answer:
180°
Step-by-step explanation:
→ Angles in a triangles always add up to 180, we can prove this by calculating a, b and c so,
a = 40° (vertical angles are equal)
b = 95° (vertical angles are equal)
c = 45° (vertical angles are equal)
40 + 45 + 95 = 85 + 95 = 180°
helpppppppppppppppppppppppp pleaseeeeeeeeeee
Answer:
6 stickers
Step-by-step explanation:
84/14 =6
Answer:
6 stickers each
Step-by-step explanation:
have a great day
Justin solved 15 problems of the recent math quiz. His classmate Jordan solved 3 more problems than Justin. Another classmate of Justin, Jeremy also solved some problems and they all together solved 37 problems. Who solved the most number of problems?
Answer:
Jordan
Step-by-step explanation:
Problems solved by Jordan = 15 + 3 = 18
Total problems solved = 37
Problems solved by Justin + problems solved by Jordan + problems solved by Jeremy = 37
15 + 18 + problems solved by Jeremy = 37
33 + problems solved by Jeremy = 37
Problems solved by Jeremy = 37 - 33
Problems solved by Jeremy = 4
So, Jordan solved most number of problems
Answer:
Jordan solved the most number of problems.
Step-by-step explanation:
Justin solved 15 problems
Jordan solved 15+3 = 18 problems
Jeremy solved 37 - (15+18) = 37 - 33 = 4 problems
I need help with Algebra.
Hey there! :)
Answer:
C. (f + g)(x) = 3x² + 3x/2 - 9
Step-by-step explanation:
(f + g)(x) requires you to add functions f(x) and g(x) together. Therefore:
(f + g)(x) = x/2 - 3 + 3x² + x - 6
Combine like terms:
(f + g)(x) = 3x² + x + x/2 - 3 - 6
Simplify:
(f + g)(x) = 3x² + 3x/2 - 9
Therefore, the correct answer is C.
Answer:
[tex](f+g)(x)=3x^2+\frac{3}{2} x-9[/tex]
agreeing with answer C in your list.
Step-by-step explanation:
If [tex]f(x)=\frac{x}{2} -3[/tex] and [tex]g(x)=3x^2+x-6[/tex] then the addition of the functions would be:
[tex](f+g)(x)=g(x)=\frac{x}{2} -3+3x^2+x-6=3x^2+\frac{3}{2} x-9[/tex]