Answer:
a) Null hypothesis:[tex]\mu \leq 120[/tex]
Alternative hypothesis:[tex]\mu > 120[/tex]
b) [tex]t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236[/tex]
The degrees of freedom are given by:
[tex] df = n-1 = 80-1=79[/tex]
The p value for this case taking in count the alternative hypothesis would be:
[tex]p_v =P(t_{79}>2.236)=0.0141[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=130[/tex] represent the sample mean for the amount spent each shopper
[tex]s=40[/tex] represent the sample standard deviation
[tex]n=80[/tex] sample size
[tex]\mu_o =120[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value f
Part a
We want to verify if the shoppers participating in the loyalty program spent more on average than typical shoppers, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 120[/tex]
Alternative hypothesis:[tex]\mu > 120[/tex]
The statistic for this case would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236[/tex]
The degrees of freedom are given by:
[tex] df = n-1 = 80-1=79[/tex]
The p value for this case taking in count the alternative hypothesis would be:
[tex]p_v =P(t_{79}>2.236)=0.0141[/tex]
Describe each pattern formed. Find the next three terms. 4,8,16,32
Answer:
The pattern is multiplying by 2.
Next three terms: 64,128,256
Step-by-step explanation:
4,8,16,32
To get from 4 to 8 we can multiply by 2.
To get from 8 to 16 we can multiply by 2.
To get from 16 to 32 we can multiply by 2.
So the pattern is multiplying by 2.
To find the next three terms:
32*2=64
64*2=128
128*2=256
Help timed test! At which root does the graph...
Answer:
x = -2
Step-by-step explanation:
The way you can tell if the graph is going to cross the x-axis or just touch the x-axis is by looking at the power of the factor.
(x - 5)^3 has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.
(x + 2)^2 has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.
To find where it will touch the axis set the factor equal to zero and solve.
(x + 2) = 0
subtract 2 from both sides
x = -2
Find the solution to the system of equations.
−2x+2y=−4
3x+3y=−18
Answer:
Step-by-step explanation:
-6x + 6y = -12
6x + 6y = -36
12y = -48
y = -4
3x - 12 = -18
3x = -6
x = -2
(-2, -4)
Hannah is setting up chairs for the class play. The room has 20 chairs. What are the different ways she can arrange the chairs in a rectangle?
Answer:
Have them 4 by 5.
Step-by-step explanation:
If you she but 5 chairs in a row, then 3 on the side of the chairs. That would create a backward "L" type of shape.
For example, (The "o" is a chair)
OOOOO
O
O
O
As you see the the top are the 5 chairs, then side are are the 4 chairs.
Then, you will do the exact same thing but on the opposite side.
Here is the next example.
OOOOOO
O O
O O
O O
OOOOOO
Basically, arranging the chairs 4x5, it would make a rectangle.
Which equation describes a line
that passes through (0, 3) and is
perpendicular to the line described
by y = -5x - 4?
Answer:
A line has equation y = ax + b, perpendicular to the line y = -5x - 4
=> a x (-5) = -1 => a = 1/5.
This line passes (0, 3) => (1/5)*0 + b = 3 => b = 3
=> Equation of this line: y = (1/5)x + 3
Hope this helps!
:)
The equation of the line passes through the point (0, 3) and is perpendicular to the line → y = - 5x - 4 is y = x/5 + 3.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Given is a line that passes through (0, 3) and is perpendicular to the
line → y = - 5x - 4
Since the line is perpendicular to the line → y = - 5x - 4. We can write -
m[L] = -1/-5
m[L] = 1/5
Assume that the equation of the line is -
y = m[L]x + c
y = x/5 + c
Since the line passes through the point (0, 3), we can write -
3 = 0 + c
c = 3
The final equation of the line will be -
y = x/5 + 3
Therefore, the equation of the line passes through the point (0, 3) and is perpendicular to the line → y = - 5x - 4 is y = x/5 + 3.
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Which formula will find the area of the composite figure below ?
Answer:
Last formula
[tex] {side}^{2} + \frac{\pi {r}^{2} }{2} [/tex]
Step-by-step explanation:
Composite figure is made up of a square and a semicircle.
Therefore,
Area of composite figure= area of square + area of semicircle
[tex] \huge\purple {\boxed {= {side}^{2} + \frac{\pi {r}^{2} }{2}}} [/tex]
There are 12 inches in 1 foot. Write 75 inches in feet and inches
Answer:6.25
Step-by-step explanation:
If a zero is
then the graph of its function only touches the x-axis at that zero.
Ifa zero is
then the graph of its function crosses the x-axis at that zero.
Answer: The first one is of even multiplicity and the second one is of odd multiplicity.
Answer:
even
odd
Step-by-step explanation:
What is the vertex of the graph of the function f(x) = x2 + 8x - 2 ?
(-4, 18)
(0, -2)
(-8, -2)
(-4, -18)
Answer: (-4,-18)
Step-by-step explanation: If you use desmos you can graph the equation to find the vertex.
The vertex of the graph of function f(x) = x² + 8x - 2 is (-4, -18)
What is the vertex of the graph of a quadratic function?In a quadratic function, the vertex of the graph refers to the highest or lowest possible outcome of the function. In a graph, the vertex is the highest or lowest point on the parabola,
Given that:
f(x) = x² + 8x - 2
where;
a = 1b = 8c = - 2By using the vertex formula to find the x-value;
[tex]\mathbf{x = \dfrac{-b}{2a}}[/tex]
[tex]\mathbf{x = \dfrac{-8}{2(1)}}[/tex]
x = -4
So,
y = (-4)² + 8(-4) - 2
y = 16 -32 -2
y = -18
Therefore, the vertex of the graph of function f(x) = x² + 8x - 2 is (-4, -18)
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PLS HELP ASAP !!!! Giving brainlist!
First one (on the left) is 2) associative property because we are regrouping terms or re-associating them based on the parenthesis. Think of the parenthesis like a tent or a house that separates off the stuff outside. First 27 and 36 are grouped, then we move the parenthesis so that 52 and 27 are grouped now.
Second one (on the right) is 1) commutative. The commutative multiplication property says we can multiply two numbers in any order. For example, 4*9 = 36 and 9*4 = 36. The 4 and 9 swap places. In this problem, the 3 and 4x swap places. The use of parenthesis isn't necessary, though it is sometimes used to imply multiplication.
Answer:
1) Associative property
2) Commutative property
2x + 3y = 12
Complete the missing value in the solution to the equation.
,8)
4 ÷ 1/5 = 20 because
Step-by-step explanation:
BECAUUUUSE ;
[tex]4 \div \frac{1}{5} = 20 \\ \frac{4}{1} \div \frac{1}{5} = 20 \\ \frac{4}{1} \times \frac{5}{1} = 20 \\ \frac{20}{1} = 20[/tex]
Answer:Because the divide sign change to multiplication sign, and when this happens denominator in the right hand side will become numerator,while the formal numerator will become denominator.
Step-by-step explanation:
4 ➗ 1/5
4 x 5/1=20
lan ran 24 laps in a charity run and then walked 0.2 kilometer to the presentation table the total; distance lan traveled was 29.6 kilometer what was the distance of each lap explain how you solve the problem
Answer:
Step-by-step explanation:
1.225km is equal to each laps
Step-by-step explanation:
Since Kristy total distance traveled = 29.6km
And Kristy ran 24 laps and later walk 0.2km. it simply implies that
Total distance traveled = distance covered running + distance covered walking
Since we know that
Total distance traveled = 29.6km
distance covered running = 24 laps
distance covered walking = 0.2km
Distance covered running in km = total distance traveled - distance covered walking
Distance covered running in km = 29.6km - 0.2km = 29.4km.
To now find the distance for each lap.
Since we have:
Distance covered running in km = 29.4km.
Distance covered running in lap = 24 laps
i.e
24 laps = 29.4km
1 lap = x
Use cross-multiple
24 laps * x = 29.4km × 1 lap
x = 29.4km / 24
x = 1.225km
Therefore
1.225km is equal to each laps.
Answer:1.225km is equal to each laps
Step-by-step explanation:
Can someone help me please
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY
Step-by-step explanation:
D.12
A.26
........................
Answer:
D and A
Step-by-step explanation:
D= 132
A is larger than 132
What is true when you rent? A.you build equity in your house,B.you are responsible for any repairs,c. You pay fewer up front costs
Answer: C you pay fee fewer upfront cost
Step-by-step explanation:
Is z = 5 in the solution set of the inequality 6z > 15
YES
OR
NAA
Answer:
Yes
Step-by-step explanation:
6z > 15
z > 15/6
z > 2.5
So all numbers greater than 2.5 is in the solution set of the inequality 6z > 15.
A car can travel 480 miles on a full tank of petrol. The tank holds 60 litres. A driver fills the tank and sets off on a journey. How many litres of petrol will be left when the car has travelled 360 miles?
Answer:
15 liters
Step-by-step explanation:
60/480= 0.125
0.125*360= 45
60-45= 15
If a pair of standard dice are rolled,
what is the probability that at least
one die shows a 5?
?
Answer:
The correct answer is 11/36
Step-by-step explanation:
The probability that at least one die shows a '5' is 11/36.
What is the probability of an event?The probability of an event is the chance of happening that particular event.
Here, a pair of standard dice are rolled.
Therefore, the total number of combinations of two dice is = 6² = 36.
The case at which one die shows a '5' are: (1, 5); (2, 5); (3, 5); (4, 5); (5, 5); (6,5); (5, 1); (5, 2); (5, 3); (5, 4); (6, 5)
Therefore, the total number of cases at which one die shows a '5' is = 11.
Therefore, the required probability of the given event is
= 11/36
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Which expression is equivalent to 2(3x − 1.75) − 3(1.5x − 2.5)?
Answer:
1.5x+4
Step-by-step explanation:
Step-by-step explanation:
Step 1: Distribute
[tex]2(3x - 1.75) - 3(1.5x - 2.5)[/tex]
[tex](2 * 3x) + (2 * -1.75) + (-3 * 1.5x) + (-3 * -2.5)[/tex]
[tex](6x) + (-3.5) + (-4.5x) + (7.5)[/tex]
Step 2: Combine like terms
[tex](6x - 4.5x) + (7.5 - 3.5)[/tex]
[tex]1.5x + 4[/tex]
Answer: [tex]1.5x + 4[/tex]
Suppose the round-trip airfare between Philadelphia and Los Angeles a month before the departure date follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between these two cities will be between $325 and $425?
Answer:
52.74% probability that a randomly selected airfare between these two cities will be between $325 and $425
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 387.20, \sigma = 68.50[/tex]
What is the probability that a randomly selected airfare between these two cities will be between $325 and $425?
This is the pvalue of Z when X = 425 subtracted by the pvalue of Z when X = 325. So
X = 425
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{425 - 387.20}{68.50}[/tex]
[tex]Z = 0.55[/tex]
[tex]Z = 0.55[/tex] has a pvalue of 0.7088
X = 325
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{325 - 387.20}{68.50}[/tex]
[tex]Z = -0.91[/tex]
[tex]Z = -0.91[/tex] has a pvalue of 0.1814
0.7088 - 0.1814 = 0.5274
52.74% probability that a randomly selected airfare between these two cities will be between $325 and $425
Giving brainliest to CORRECT answer.
Answer:
A. 2
Step-by-step explanation:
[tex] y = 16x^2 - 8x + 1[/tex] is a quadratic function, hence on solving it will give two zeros, therefore graph of the function will intersect x axis in two points.
The length of a rectangle is seven less than twice the length of its width. If the area of the rectangle is 15 square meters, find the value of x.
Answer:
Length is 3 meters and the Width is 5 meters
Step-by-step explanation:
L*W=15
L=2W-7
(2W-7)W=15
[tex]2W^{2} -7W=15\\2W^{2} -7W-15=0[/tex]
(2W+3)(W-5)=0, don't use (2W+3)=0, because it gives you a negative dimension.
W=5, L=3
What is the disciminant of 3x^2-10x=-2
Answer:
76
Step-by-step explanation:
First get the equation into the form
ax^2 +bx+c =0
3x^2-10x+2=-2+2
3x^2-10x+2 =0
The discriminant is
b^2 -4ac where a=3 b = -10 c =2
(-10)^2 - 4(3)(2)
100 - 24
76
The measures of the angles of a triangle are 25 degrees, 87 degrees, and 68 degrees. Is the triangle acute, right, or obtuse?
Answer:
their all less than 90 degress so its acute
Step-by-step explanation:
Which unit would be best for measuring the thickness of a coin?
kilometer
()) centimeter
meter
)) milli
Answer:
Since 1 mm = . 03937 inches, mm would seem to be the units appropriate for defining the thickness of a coin measuring 2 units.
Step-by-step explanation:
Plz help ..............!!!!!
Answer:
1.8
is the median
Answer: 1.8
Step-by-step explanation: 1.8 is the median
hurry plz im timed. i have 20 minutes left
Which shows how the distributive property can be used to evaluate 7 times 8 and four-fifths?
56 + StartFraction 28 over 5 EndFraction = 56 + 5 and three-fifths = 61 and three-fifths
56 times StartFraction 28 over 5 EndFraction = StartFraction 1568 over 5 EndFraction = 313 and three-fifths
15 + (StartFraction 35 over 5 EndFraction + four-fifths) = 15 + StartFraction 39 over 5 EndFraction = StartFraction 75 over 5 EndFraction + StartFraction 39 over 5 EndFraction = StartFraction 114 over 5 EndFraction = 22 and four-fifths
15 times (StartFraction 35 over 5 EndFraction + four-fifths) = 15 times StartFraction 39 over 5 EndFraction = StartFraction 15 over 1 EndFraction times StartFraction 39 over 5 EndFraction = StartFraction 585 over 5 EndFraction = 117
Answer:
First one:
56 + StartFraction 28 over 5 EndFraction = 56 + 5 and three-fifths = 61 and three-fifths
Step-by-step explanation:
7 × 8⅘
7(8) + 7(4/5)
56 + 28/5
56 + 5 + 3/5
61 3/5
Answer:
its A
Step-by-step explanation:
56 + StartFraction 28 over 5 EndFraction = 56 + 5 and three-fifths = 61 and three-fifths
and pls mark me as brainliest if this is correct! :D
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
C. x=2 ± √13
Explanation:
What’s the correct answer for this?
Answer:
A.
Step-by-step explanation:
tan x= 6/8
usually tan θ = perpendicular / base
So,
we get perpendicular = 6, base = 8
Now using Pythagorean Theorem to find hypotenuse
hyp² = base² + Perp²
hyp² = 8² + 6²
hyp²= 64 + 36
hyp²=100
Taking sq root on both sides
hypotenuse = 10
Now
sin θ = Perpendicular / Hyp
sin x = 6 / 10
Now
cos θ = base / Hyp
cos x = 8 / 10
