The City of Irvine upgraded a bicycle lane in a section of road to have a physical barrier between the cyclists as opposed to just a painted white line on the road. They now want to do a study to see if the bicycle lane upgrades have encouraged more people to utilize the bike lane. Before the upgrade, on any given day, it was known that the section of road saw an average of 350 unique cyclists. After the upgrade, they took a random sample of 35 days in the year and counted the number of unique cyclists each day. The average was 405 cyclists with a standard deviation of 25. Test the hypothesis at the 0.05 significance level.
Answer:
The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.
Step-by-step explanation:
Before the upgrade, on any given day, it was known that the section of road saw an average of 350 unique cyclists. Test if more people are using now.
At the null hypothesis, we test if the same number of people is still using, that is, the mean is 350. So
[tex]H_0: \mu = 350[/tex]
At the alternate hypothesis, we test if this mean increased, that is:
[tex]H_1: \mu > 350[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
350 is tested at the null hypothesis:
This means that [tex]\mu = 350[/tex]
After the upgrade, they took a random sample of 35 days in the year and counted the number of unique cyclists each day. The average was 405 cyclists with a standard deviation of 25.
This means that [tex]n = 35, X = 405, s = 25[/tex].
Test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{405 - 350}{\frac{25}{\sqrt{35}}}[/tex]
[tex]t = 13.02[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 405, which is a right-tailed test with t = 13.02 and 35 - 1 = 34 degrees of freedom.
Using a t-distribution calculator, this probability is of 0.
The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.
Which of the following is most likely the next step in the series
Answer:
A
Step-by-step explanation:
The pattern is blue red blue red
+
The pattern is vertical horizontal vertical horizontal
Answer:
A.
The second figure adds another red horizontal line to the first. The third adds a vertical blue line to the second. The fourth must add a red horizontal line to the third.
ABC and XYZ are similar find the missing side length
Answer:
5
Step-by-step explanation:
Since both triangles are similar, the ratio of their corresponding side lengths would be equal.
This implies that:
AB/40 = 8/64
Cross multiply
AB*64 = 40*8
AB*64 = 320
AB = 320/64
AB = 5
Answer:
Step-by-step explanation:
the Answer is 4
Rewrite the quadratic function below in Standard Form.
y = (x - 4) (x + 3)
the standard form of a quadratic formula is
y = ax^2 + bx + c
in this case you will solve using foil method
(× - 4)(x + 3)
(x × x) +( x × 3 )(- 4 × x) ( -4)× 3))
x^2 + 3x - 4x -12
x^2 - x - 12
therefore
y = x^2- x - 12
Steven and his family ordered a meal the cost 136.50. Steven paid 14% sales tax and left a 20% tip on 136.50. What was the total cost
Answer:
The total cost was $182.91.
Step-by-step explanation:
Tax formula:
tax=tax percentage×amount
Tip formula:
tip=tip percentage×amount
solve
First find the tax. Write 14% as the decimal 0.14 before using it in the equation.
tax
= tax percentage×amount
= 0.14×136.50
= 19.11
The tax was $19.11.
Now find the tip. Write 20% as the decimal 0.20 before using it in the equation.
tip
= tip percentage×amount
= 0.20×136.50
= 27.3
The tip was $27.30.
Finally, find the total cost.
total cost
= cost + tax+tip
= 136.50+19.11+27.30
= 182.91
Answer:
182.91
Step-by-step explanation:
Matthew thought the price of a game was $40. When he got to the store the price
was $60. Calculate the percent error.
Answer:
It is 20%
Step-by-step explanation:
$60 - $40 = $20
Please help me with this
Answer:
–x² + 12x + 5
Step-by-step explanation:
x² + 3x
–2x² + 9x + 5
The sum of the above expression can be obtained as follow:
.... x² + 3x
+ –2x² + 9x + 5
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
–x² + 12x + 5
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Thus, the sum of x² + 3x and –2x² + 9x + 5 is –x² + 12x + 5
Find the surface area of the composite figure.
6 cm
5 cm
4 cm
6 cm
15 cm
3 cm
The surface area of the given composite figure will be 384 square cm.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
In the given image we have a composite figure one is a rectangular cuboid and the other is a triangular prism. The surface area will be equal to the sum of all the outer sides of the figure.
The surface area of the triangular shape will be calculated as:-
SA = 2( Area of triangle ) + Area of rectangular surfaces
SA = 2 ( (1/2) B x H ) + (5 x 6 ) + ( 6 x 3 )
SA = ( 3 x 4 ) + ( 30 ) + ( 18 )
SA = 12 + 30 + 18
SA = 60 square cm
The surface area of the rectangular cuboid will be calculated as:-
SA = ( 4 x 6 ) + 2 ( 158 x 4 ) + 2 ( 15 X 6 )
SA = 24 + 120 + 180
SA = 324 square cm
Total surface area will be = 324 + 60 = 384 square cm.
Therefore the surface area of the given composite figure will be 384 square cm.
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Is the point (3, -2) a solution to the following system of equations? How do you know?
y=−3x+7
y=2x−8
Answer:
YES
Step-by-step explanation:
Any straight line can be represented by an equation of the form
Y = mX + b
where m is the slope and b is the Y intercept, so these two equations are lines. The only solution is where the two lines cross, so must satisfy both equations. Plugging in 3 for X and -2 for Y we get
Y = -3X + 7
-2 = -3(3) + 7
-2 = -9 + 7
-2 = -2 True
AND,
Y = 2X - 8
-2 = 2(3) - 8
-2 = 6 - 8
-2 = -2 True
So since both are true, yes (3, -2) is the solution.
In the diagram below, AB, BC and CD are three sides of a regular polygon.
The polygon has 15 sides.
The length of each side is 8 cm.
The exterior angle of the polygon is x.
BRC is a right-angled triangle.
Calculate the length of BR.
Thanks in advance
Answer:
BR is about 7.3084 cm
Step-by-step explanation:
the sum of the exterior angles of any polygon is 360. The measure ox x would be 360/15= 24
since I want BR, I will use cos (adj/hyp)
cos24=s/8
.9135=s/8
7.3084=s
5/7 ÷ 2/3=?
Is it A?
Is it B?
Is it C?
Or is it D?
Answer:
[tex]C.[/tex] 5/7 × 2/3
Step-by-step explanation:
big help someone clutch up for me.TIMED!!
Answer:
B. 5
Step-by-step explanation:
Given expression;
n(n - x) = 25
From the given expression, x = 0
Substitute the value of x into the given equation and solve for n;
n(n - 0) = 25
this equation reduces to;
n(n) = 25
simplifying further to obtain the value of n;
n² = 25
n = √25
n = 5
Therefore, the correct option is B.
Find the surface area of the triangular prism.
Answer: 125.6
Step-by-step explanation:
The product of two positive integer numbers is 40 and the sum of the same two numbers is 13.
9514 1404 393
Answer:
5 and 8
Step-by-step explanation:
Factor pairs that make 40 are ...
40 = 1×40 = 2×20 = 4×10 = 5×8
The pair that has a sum of 13 is 5 and 8.
Solve the inequality
J+7>3j-4
Answer:
E. j<5.5
Step-by-step explanation:
Step by step explanation
y=-9x^2+571x-3884 find x
Answer:
I'm pretty sure it's either 3.1 or 4.1
Step-by-step explanation:
Answer:
x = (571 ± √186217) / 18
x ≈ 7.74840677368558702303.. or 55.69603767075885742140..
x ≈ 7.75 or 55.70
Step-by-step explanation:
y = -9x² + 571x – 3884.
x = (-b ± √b² – 4ac) / 2a
x =
(-(571) ± √((571)² – 4((-9) × (-3884))) / 2(-9)) →
(-571 ± √(326041 – 4(34956))) / -18) →
(-571 ± √(326041 – 139824)) / -18) →
(-571 ± √(186217)) / -18 →
(571 ± √186217) / 18 →
Question
A bottle of medicine contained 300 mL. Convert this to liters.
Provide your answer below:
L
Answer:
0.3L
Step-by-step explanation:
1000mL = 1L
300mL = 0.3L
When factoring the difference of two squares, what will the signs in the parenthesis be
Answer:
The signs will be + and -
Step-by-step explanation:
Required
The signs in the parenthesis of difference of two squares
Let the expression be:
[tex](x^2 - a^2)[/tex]
Expand
[tex]x^2 - a^2 = x^2 -ax + ax - a^2[/tex]
Factorize
[tex]x^2 - a^2 = x(x -a) + a(x - a)[/tex]
Factor out x - a
[tex]x^2 - a^2 = (x +a)(x - a)[/tex]
See that the sign in front of a is + and - in the parentheses
10. A new fish tank has a volume of 10x2 + 30x -40 cubic inches. Assuming V =
LWH, determine the expressions of the length, width and height of the fish tank.
9514 1404 393
Answer:
10, (x+4), (x -1)
Step-by-step explanation:
The given volume expression can be factored as ...
V = 10x² +30x -40
= 10(x² +3x -4)
= 10(x +4)(x -1)
The expressions representing length, width, and height might be ...
10, (x+4), (x -1)
help me plz god bless
Answer:
d.
Step-by-step explanation:
The gradient is -5 meaning that it's going downwards as x increases
The y-intercept is 3
Feel free to mark as brainliest :D
On a piece of graph paper, graph the line that passes through point (-2,3) with a slope of 2/3. Give me the coordinates of a first quadrant point that lies on this line, and has integer coordinates.
Answer:
Pic po nasan???????Step-by-step explanation:
-_-Here are some clues about my age. • Both my father’s age and mine are 2-digit numbers. • If you reverse the order of the digits of my father’s age, you get my age. • My father is 27 years older than I am. How old am I? Show your work and justify your thinking.
For the given condition the age of the son will be 69 years.
What is the equation?A mathematical equation asserts the equality of two expressions, which may or may not contain variables or integers. Equations are fundamental concerns, and efforts to rationally address them have served as the primary driving forces behind the creation of mathematics.
Suppose the two-digit number is x,
The father's and son's ages are 10x+y and 10y+x respectively.According to the given condition,
(10x+y) -(10y+x)=27
9x-9y=27
x-y=27/9
x-y=3
The value of x and y will be 4 and 1.
At x=9 and y=6, the age of the son is obtained as,
=10×6+9
=69 years
Thus, the age of the son will be 69 years.
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When you roll two number cubes, what are the odds, in simplest form, in favor of getting two numbers less than 3?
Answer:
1/3
Step-by-step explanation:
there are 4 numbers total that are less than 3 and there are 12 sides total
so 4/12 would be the total and 1/3 would be simplified
The Ballantyne area has 200 people over the age of eighty-five living in it of these people, 56 of them have a dog, 24 of them have a cat, and 16 of them have both of a person
is chosen at random, find the probability that they have a cat, if it is known they have a dog.
a. 1/2
b.3/7
c.2/7
d.2/25
HELP ME ASAP
I NEED YOUR HELP PLS
I NEED AN ANSWER NOW
Answer:
N=21 Degrees M=122 Degrees L= 37 Degrees X=21 Degrees
Step-by-step explanation:
Add all them up then make them equal 180 degrees
9x-9 = 180
Solve
9x=180 +9
9x= 189
9x/9= 189/9
x=21
Then plug in x to find each Angle.
N (x) Degrees
N=21 Degrees
M = 6x - 4
M = 6(21) - 4
M = 126 - 4
M = 122 Degrees
L = 2x - 5
L = 2(21) -5
L = 42 - 5
L = 37 Degrees
ames has 268 cookies to put into bags. Each bag holds 8 cookies.
If James uses as many of the cookies as possible, how many bags can he make, and how many cookies are left over?
Enter your answers in the boxes.
Step-by-step explanation:
Total amount of cookies= 268
One bag can hold 8 cookies
268 / 8 = 33 (remainder 4)
He can make as many as 33 bags, and there are 4 cookies left over.
In a survey of 554 U.S. adults, it is found that 360 favor a ban on stem cell research. Set up the null and the alternative hypotheses to test whether there is sufficient evidence that over 61% favor a ban on stem cell research. If alpha is set to 3.0%, should the null hypothesis be rejected
Answer:
The null hypothesis will be rejected
Step-by-step explanation:
The null hypothesis is that people who favour ban on stem cell research is less than or equal to 0.61
The alternate hypothesis is that people who favour ban on stem cell research is greater than 0.61
Proportion of population = 0.61
Total events = 360
Sample size = 554
Sample proportion = 360/554 = 0.649
As per test statistics –
Z = (p-p0)/sqrt {(p0 (1-p0))/n} = (0.649 -0.61)/ {(0.61 (1-0.61))/554}
= 0.039/0.021
= 1.857
P (Z<1.857) = 1- P (Z<1.857) = 1-0.9664 = 0.0336
So alpha value is 0.064.
Thus, we will reject the null hypothesis
Write the algebraic expression that matches each graph:
Answer:
follow me and I will answer it
how do you change a fraction to a unit rate
Answer:
A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.
Step-by-step explanation:
Unit 1: Geometry Basics Homework 3: Angle Relationships
Answer:
juicy no no square
Step-by-step explanation:
The value of x = z = 73 degrees and y = 107degrees
3) Geometry is a branch of mathematics that deals with the measurement of lines and angles.
From the diagram shown, we can see that the two lines intersect at a point. The following is therefore true:
y = 107° (vertically opposite angle)The sum of z and 107 is supplementary. Hence;
z + 107 = 180z = 180 - 107z = 73degreesAlso, the sum of x and y is also supplementary. This shows that:
x + y = 180x + 107 = 180x = 180 - 107x = 73dgreesFrom the calculations, hence x = z = 73 degrees and y = 107degrees
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