Using the z-distribution, it is found that we reject the null hypothesis, which means that her claim is not validated.
What are the hypotheses tested?At the null hypotheses, it is tested if the mean is of 110, that is:
[tex]H_0: \mu = 110[/tex].
At the alternative hypotheses, it is tested if the mean is less than 110, that is:
[tex]H_1: \mu < 110[/tex].
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In this problem, we have that the parameters are given as follows:
[tex]\overline{x} = 105, \mu = 110, \sigma = 15, n = 50[/tex]
Hence the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{105 - 110}{\frac{15}{\sqrt{50}}}[/tex]
z = -2.36.
What is the decision?Using a z-distribution calculator, z = -2.36 has a p-value that is less than the standard significance level of 0.05, hence we reject the null hypothesis, which means that her claim is not validated.
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please answer asap! 20 points!!
A new car is purchased for 23,900 dollars. The value of the car depreciates at a rate of 6.4% per year. Which equation represents the value of the car after 4 years?
1) V= 23,900(0.936)(0.936)(0.936)(0.936)
2) V=23,900(1+0.064)⁴
3) V= 23,900(1−0.064)(1−0.064)
4) V= 23,900(0.064)⁴
Answer:
1) V= 23,900(0.936)(0.936)(0.936)(0.936)
Step-by-step explanation:
Each year, the car depreciates to 1 -0.064 = 0.936 of its previous value. After 4 years, the original value has been multiplied by this factor 4 times:
__
depreciated value = 23,900(0.936)(0.936)(0.936)(0.936)
_____
This could be represented by ...
V = 23,900(1 -0.064)⁴ . . . . . . not an answer choice
Amelia's car used 16 gallons to travel 656 miles. How many gallons of gas would she need to travel 533 miles?
Answer:
13 gallons of gas.
Step-by-step explanation:
If amelia used 16 gallons of gas for 656 miles, she is traveling 41 miles per gallon. (656 divided by 16). So we take the amount she needs to travel which is 533, and divide it by 41 because 41 miles is equal to one pound of gas, so, 533 divided by 41 is 13, she needs 13 gallons of gas to travel 533 miles.
Help with this question please
Answer:
See below
Step-by-step explanation:
(a)
[tex]\angle A\cong \boxed{\angle Z}[/tex][tex]\angle B\cong \boxed{\angle Y}[/tex][tex]\angle C\cong \boxed{\angle X}[/tex](b)
[tex]\overline{AB}\cong \boxed{\overline{ZY}}[/tex][tex]\overline{AC}\cong \boxed{\overline{ZX}}[/tex][tex]\overline{BC}\cong \boxed{\overline{YX}}[/tex](c)
[tex]\triangle CAB \cong \triangle \boxed{XZY}[/tex]A right circular cone has a base radius of 4 and a height of 6. A right circular cylinder also has a base radius of 4 and a height of 6. Let A be the lateral surface area of the cone, and let B be the lateral surface area of the cylinder. Find A/B.
Answer:
A/B = 0.6Step-by-step explanation:
Given dimensions of
Right circular cone: r = 4 and h = 6Right circular cylinder: r = 4 and h = 6Find the lateral surface area of both figures
The cone[tex]A= \pi r\sqrt{h^2+r^2}=3.14*4\sqrt{6^2+4^2}= 90.57[/tex]The cylinder[tex]B=2\pi rh=2*3.14*4*6 = 150.72[/tex]Find the ratio A/B
A/B = 90.57/150.72 = 0.6 (rounded0Write in scientific notation:
0,007 832
Answer:
The scientific notation for this will be
[tex]7.832 \times {10}^{ - 3} [/tex]
As there are three zero in expression
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
pls help with this question asap
Answer:
30 ft
Step-by-step explanation:
Perimeter
= 3 + 4 + 4 + 7 + 4 + 4 + 4
= 30 ft.
Leah bought a bicycle for $118 that was originally priced at $472. What is the discount
percentage?
Write your answer using a percent sign (%).
Answer:
75%Step-by-step explanation:
the discount percentage :
[tex]\frac{472-118}{472} \times100 = 75 \%[/tex]
The percentage decrease ( discount percentage ).
Solution:[tex]\large\boxed{\sf{formula = 100 \times \frac{(final - initial)}{initial} }}[/tex]
We'll have to subtract 472 ( initial value ) from 118 ( final value).
[tex]472 - 118[/tex]
[tex] = 354[/tex]
Now, we'll have to divide 354 ( difference ) by 118 ( initial value ) and multiply by 100.
[tex] 100 \times \frac{354}{118} [/tex]
[tex]\large\boxed{\sf{ = 75\% }}[/tex]
Hence, the discount percentage is 75.
Which equation can be used to find A, the area of the parallelogram shown?
Explanation:
The area of a parallelogram is equal to base times height.
The base and height are always perpendicular to one another. Usually the base is horizontal along the ground (if not then you'd need to rotate your paper until it is, but that step is optional).
The base is 6 meters and the height is 7 meters.
Therefore, area = base x height = 6 x 7
The side of 11 meters is not used at all. It's likely put in there as a distraction.
Answer:
A = 6 * 7
Step-by-step explanation:
A parallelogram follows the same rules as a regular quadrilateral, as the only difference is that both its sides have been moved along.
The diameter of a circle is 14 miles. What is the circle's area?
Use 3.14 for .
Answer:
153.86cm^2
Step-by-step explanation:
area of a circle= πr^2
where r = radius= 14/2= 7miles
area= 3.14×(7×7)
area= 3.14×49= 153.86cm^2
A can has a height of 11cm and a volume of 486cm^3 . Find the radius of each can . Correct to two decimal places
If the height is 11 cm and the volume is486 cubic cm. Then the radius of the can will be 3.75 cm.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
A can has a height of 11 cm and a volume of 486 cubic cm.
Then the radius of the can will be
We know that the volume is given as
Volume = πr²h
486 = π r² x 11
r² = 14.06
r = 3.75 cm
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need help with this one geometry problem asap
Answer:
Step-by-step explanation:
A date is picked at random on the calendar for april. what is the probability that the date chosen will be on a two digit odd number
Answer:
1/3
Step-by-step explanation:
That is the simplified version of the number of all the double-digit odd days (11,13,15,17,21,23,25,27,29), 10, over the total number of days in April, 30
10/30=1/3
Students must purchase a ticket to attend the show. the committee wants to
have $500 remaining from ticket sales, after paying for equipment, lighting,
and costumes.
the tickets will cost $5.60 for each ticket, and the committee expects to sell
as many tickets as there are seats available.
what is the greatest amount of money, in dollars, the committee can spend
on equipment and costumes?
Answer:
The total number of seats is also needed to answer the question.
Step-by-step explanation:
For example, if there were 100 seats the committee would make $560 in all, therefore having $60 to spend on equipment and costumes.
Help pls!!!!!!
A family sized box of cereal with dimensions 3x9x12 inches costs $6, while the regular size with dimensions 2x8x9 inches costs $4.50. What is the difference in price per cubic inch?
Answer:
$0.01
Step-by-step explanation:
Family size rate (per cubic inch)
Volume of box = 3 x 9 x 12 = 324 in³Cost = $6Rate = 6/324 = 1/54 = $0.02 per cubic inchRegular size rate
Volume of box = 2 x 8 x 9 = 144 in³Cost = $4.50Rate = 4.50/144 = 1/32 = $0.03 per cubic inchDifference in price
$0.03 - $0.02$0.01Volume of family sized box
LBH3(9)(12)27(12)324in³Price per inch
6/324=0.02$/inVolume of regular size
2(8)(9)144in³Price per in
4.5/144=0.03$/inDifference:-
|0.02-0.03|=0.01$
Tim tried to use Cavalieri's principle to show that the two figures have the same volume.
"The base areas are the same. Therefore, corresponding cross-sections have the same area. So the volumes must be the same."
What is the first mistake Tim made?
Answer:
The base areas aren't same
Step-by-step explanation:
The base areas arent same
Answer:
He did not establish that heights are the same.
( i will give brainlist ) please help is the following equation linear, quadratic, exponential or none of these?
Answer:
exponential
Step-by-step explanation:
It is exponential because the variable is in the exponent
Find a function y of x such that 2yy′=x and y(2)=6
Answer:
[tex]y=\sqrt{\frac{x^{2}}{2} +34}[/tex]
Step-by-step explanation:
[tex]2y\left( x\right) y^{\prime }\left( x\right) =x[/tex]
[tex]\Longrightarrow \int 2y\left( x\right) y^{\prime }\left( x\right) dx=\int x\ dx[/tex]
[tex]\Longrightarrow y^{2}\left( x\right) =\frac{x^{2}}{2} +c\ \text{(c is a constant)}[/tex]
[tex]y\left( 2\right) =6\Longleftrightarrow y^{2}\left( 2\right) =36[/tex]
[tex]y^{2}\left( 2\right) =36\Longleftrightarrow \frac{\left( 2\right)^{2} }{2} +c=36\ \Longleftrightarrow c=34[/tex]
[tex]\Longrightarrow y\left( x\right) =\pm\sqrt{\frac{x^{2}}{2} +34}[/tex]
Which expression represents the volume, in cubic units, of empty space in the cube? four-thirdsπ(4.53) – (4.5)3 (9)3 – four-thirdsπ(4.52) four-thirdsπ(4.53) – (9)3 (9)3 – four-thirdsπ(4.53)
The expression that represents the volume of the empty space is 9³ - 4/3π(4.5)³
How to determine the volume of the empty space?The cube box has a side length of 9.
So, the volume of the box is:
V = 9³
The sphere has a radius of 4.5.
So, the volume of the sphere is:
v = 4/3π(4.5)³
Calculate the difference between both volumes:
d = 9³ - 4/3π(4.5)³
Hence, the expression that represents the volume of the empty space is 9³ - 4/3π(4.5)³
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Answer: that is answer d
Step-by-step explanation:
2023 edge
Solve 6^x+2 = 10 for x using the change of base formula
Answer:
[tex]x\approx-0.7149[/tex]
Step-by-step explanation:
[tex]\displaystyle 6^{x+2}=10\\\\\log_6(6^{x+2})=\log_6(10)\\\\x+2=\frac{\log(10)}{\log(6)}\\\\x+2\approx1.2851\\\\x\approx-0.7149[/tex]
Recall that the change of base formula is [tex]\displaystyle \log_a(b)=\frac{\log(b)}{\log(a)}[/tex]
What are the values of a and b? a = 14, b = 6 a = 14, b = 8 a = 17, b = 6 a = 17, b = 8
The value of a and b given that the opposite side are equal are 17 and 6 respectively
Properties of a kiteThe kite is a quadrilateral with 4 sides and the opposite side of the side are equal. If they are, then;
2a - 4 = 30
2a = 34
a = 17
Similarly
3b+6 = 24
3b = 18
b = 6
Hence the value of a and b given that the opposite side are equal are 17 and 6 respectively
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a) What percentage of 5³ is 5?
b) What percentage of 5³ is 5²?
Step-by-step explanation:
a) 5³= 5*5*5 = 125
5/125*100%
4%
b) 5²=5*5=25
25/125*100%
20%
How far does the unicycle move if the wheel turns once?
Pierre enters a 100m unicycle race. How many times must the wheel rotate completely in order for Pierre to travel 100m?
The unicycle moves a distance of 251.20cm if the wheel turn once and the wheel must rotate 32 times to cover a distance of 100m
Circumference of a circleThe formula for calculating the circumference of a circle is given as:
C = 2pi r
r is the radius of the circle
a) r = 80/2 = 40cm
C = 2(3.14)(40)
C = 251.20 cm
Hence the unicycle moves a distance of 251.20cm if the wheel turn once
b) Number of revolution * 2pi r = distance covered
n * 2(3.14)(50) = 10000
314n = 10000
n = 10000/314
n =32
Hence the wheel must rotate 32 times to cover a distance of 100m
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An object is fired from a cannon. Its height after t seconds is given by the function
h(t)= 16t² + 128t + 140 feet. How high was the object after 2 seconds?
=
The object was
feet high.
Answer:
332 feet
Step-by-step explanation:
Height = h(2) = - 16(2^2) + 128t + 140 ( NOTE: I added the minus sign)
= 332 feet
The maximum height is 908 feet.For a parabola, h = ax^2 + bx + c, the vertex at point (h,t), is first found by the equation t = b / 2a, and then plugging that point into the equation to find h.
What is more about the problem?For a parabola, h = ax^2 + bx + c, the vertex at point (h,k), is first found by the equation t = b / 2a, and then plugging that point into the equation to find h.
Given the equation h = 16t^2 + 128t + 140, we know a = 16, b = 128, c = 140.
t = -b/2a
t = -(128) / 2(16)
t = -128 / 32
t = 4 seconds
let's plug in t=4 to our equation:
h = 16t^2 + 128t + 140
h = 16*(4)^2 + 128*(4)+ 140
h = 908ft
h = 908 feet
answer is that the maximum height is 908 feet.
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The length of AB is four times the length of BC.
AC = 75 cm.
=
Someone help me find the length of ST please!
Answer:
10
Step-by-step explanation:
I calculated and it's 10 I'm in car so I can't give the whole explanation
PLEASE HELP WILL MARK BRAINLIEST WITH 100 POINTS
What is the best way to describe the center of the data represented in this line plot?
Select from the drop-down menus to correctly complete the statement.
The
median
mean
is
1 inch
1.5 inch
1.8 inch
2 inches
Line plot titled Daily Rainfall. The number line is labeled Number of inches. There are 3 dots above 0, 3 dots above 1, 1 dot above 2, 1 dot above 3, 1 dot above 4, and 1 dot above 6.
.
Answer:
Mean = 1.8 in
Step-by-step explanation:
MedianThe Median is the middle value when all data values are placed in order of size.
Ordered data values: 0, 0, 0, 1, 1, 1, 2, 3, 4, 6
As there is an even number of data values, the middle value is the mean of the middle two data values. Therefore, the Median = 1 in
MeanThe Mean is the sum of all data values divided by the total number of data values.
[tex]\implies \textsf{Mean}=\dfrac{0+0+0+1+1+1+2+3+4+6}{10}=1.8[/tex]
Therefore, the Mean = 1.8 in
ConclusionThe Median is a better measure of central tendency when the data includes outliers (data values that are far away from the majority), as it is not affected by those outliers. As there does not appear to be any outliers in this data set, the mean can be used to best describe the center of the data.
Therefore, the Mean = 1.8 in
PLEASE HELP SUPER EASY bottom question please!!
Answers:
The histogram is shown below.7/10 of the class passed the assignment.============================================================
Explanation:
Part 1
Sort the data values to get
51, 54, 58, 60, 60, 62, 70, 72, 72, 75, 76, 80, 85, 88, 90, 90, 95, 100, 100, 100
Now let's say we had these intervals
51-6061-7071-8081-9091-100Notice each interval is 9 units wide.
The 5 scores 51,54,58,60,60 are in the interval 51-60, which means the first interval has a bar that's 5 units tall.
The scores 62,70 are in the interval 61-70, which means the second bar is 2 units high.
Keep this process going to create the histogram shown below.
It looks like you have the right idea, but your class interval widths aren't the same each time.
Because the class interval widths can change, this means other histograms are possible. Just be sure to stick to one interval width.
-----------------------------------
Part 2
Set A = set of scores that are 70 or larger, i.e. those who passed
Set A = {70, 72, 72, 75, 76, 80, 85, 88, 90, 90, 95, 100, 100, 100}
Set B = set of all scores in the class
Set B = {51, 54, 58, 60, 60, 62, 70, 72, 72, 75, 76, 80, 85, 88, 90, 90, 95, 100, 100, 100}
There are 14 items in set A and 20 in set B
This means 14/20 = 7/10 of the students passed.
Work out
m
and
c
for the line:
y
=
x
+
4
Answer:
m = 1
c = 4
Step-by-step explanation:
First let's review what a slope-intercept form is.
Slope-intercept form is a specific form of linear equations. It always has y on one side and all the other terms on the other. Its structure is:
[tex]y = mx + c[/tex],
where m is the slope and c is the y-intercept.
You can easily read slope (m) and intercept (c) in your equation.
[tex]y = mx + c\\y = x + 4[/tex]
You can see that m in front of x is 1, because x = 1x. Multiplying with 1 perserves the number.
So:
[tex]m = 1\\c = 4[/tex]
For any positive numbers a,b, and d, with b=1, logb a+logb d=
Answer the right answer is a
Whats the product 72x0.45
Answer:
72 times 0.45 is equal to 33.75
Step-by-step explanation:
You can use a calculator to find this out.
Answer:
32.4
Step-by-step explanation:
After repeatedly adding 0.45 a total of 72 times. You end up getting 32.5
To check the answer you divide 32.5 by 72 and receive 0.45. Checking the answer
