1. We conclude that the conditions for calculating a confidence interval for a mean are satisfied.
2. Since interval was constructed and is reported, we assume that distribution of the sample mean is normal.
Do the conditions for a mean confidence interval calculation hold?Let x be the sample mean
Let s be the sample standard deviation
Let n be the sample size
Let α be the significance level
Let Z be the standard normal distribution value.
To determine if conditions for calculating confidence interval for a mean are met, we have to check the followings:
1. Random sampling:
The sample of 125 workers was selected randomly.
2. Independence:
We assume that each worker's commuting time is independent of each other.
3. Sample size:
n = 125 > 30. This satisfies the condition for the central limit theorem to apply.
4. Normality:
The 95% confidence interval was constructed using the formula x ± Zα/2(s/√n).
Since interval was constructed and is reported, we can assume that the distribution of the sample mean is approximately normal. Therefore, we can conclude that the conditions for calculating a confidence interval for a mean are satisfied.
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Please help I put 100 points
Answers:
26 math problems
16 science problems
===============================================
Work Shown:
m = number of math problems
s = number of science problems
Since "you have 10 more math problems than science problems", we can say m = s+10
Also, we can say m+s = 42 because there are 42 problems total.
Replace m with s+10, which is the substitution rule, and solve for s like so
m+s = 42
s+10+s = 42
2s+10 = 42
2s = 42-10
2s = 32
s = 32/2
s = 16
You have 16 science problems
m = s+10
m = 16+10
m = 26
and you have 26 math problems
To check this, we would say m+s = 26+16 = 42 which confirms the answer.
I cant see ur image.........
Container A holds 5 bottles of water each with a capacity of 250ml. Container B
holds 7 bottles of water each with a capacity of 175ml. Which container holds
more water? Explain your answer.
Answer:
Container A has more capacity, as it holds 1,250 milliliters of water against 1,225 milliliters that Container B contains.
Step-by-step explanation:
Since Container A holds 5 bottles of water each with a capacity of 250ml, while Container B holds 7 bottles of water each with a capacity of 175ml, to determine which container holds more water, the following calculation must be performed:
Container A:
250 ml x 5 bottles: Capacity
250 x 5 = X
1,250 = X
Container B:
175 ml x 7 bottles: Capacity
175 x 7 = X
1,225 = X
Therefore, Container A has more capacity, as it holds 1,250 milliliters of water against 1,225 milliliters that Container B contains.
Mason’s dad is renting a car for a 5-day business trip. He is paying a rental fee plus an additional fee for every mile driven (x). The rental cost can be modeled by the equation C=0.25x+200. Which statements are accurate interpretations of this model?
Select all that apply.
A There is a per-mile charge of $200.25 plus the rental fee.There is a per-mile charge of $200.25 plus the rental fee.
B The cost is less than $200 if fewer than 25 miles are driven.The cost is less than $200 if fewer than 25 miles are driven.
C There is a charge of $0.25 per mile in addition to the rental fee.There is a charge of $0.25 per mile in addition to the rental fee.
D There is a $200 charge per day plus $0.25 for every mile driven.There is a $200 charge per day plus $0.25 for every mile driven.
E The cost for renting a car for 5 days is $200, plus the per mile fee multiplied by the number of miles driven.The cost for renting a car for 5 days is $200, plus the per mile fee multiplied by the number of miles driven.
F The cost can be calculated by multiplying the total miles driven by 0.25 and adding 200.
Answer:
A, C, E, F
Step-by-step explanation:
...............
C= 0.25x + 200 represents the rental cost of renting a car with rental fees of $200 and additional fees per 'x' mile as $ 0.25.
What is equation?" Equation is defined as the representation the relation of variables with the sign of equality."
According to the question,
'x' represents the number of miles
'C' represents the rental cost
Rental fees of a car = $200
Additional fees per 'x' miles = $0.25
As per the condition given we have,
C = 0.25x +200
The given model states that total cost of the car is equals to the rental fees of the car is $200 and the additional fees per 'x' miles is $0.25.
Hence, Option(C), Option(E) and Option(F) are the correct answer.
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You have designed a concrete patio which is the shape of a parallelogram and a triangle combined. The parallelogram has a length of 12 m with a height of 4 m. The triangle has a base of 12 m with a height of 5 m. Calculate both the area and perimeter of this patio.
Answer:
perimeter is 35.6 area is 108
Step-by-step explanation:
it helps to draw a picture. first the perimeter of the rectangle is 4x2 +12=20 we wont be needing one of the twelves because it is connected to the triangle the area or the rectangle is 12x4=48. now for the triangle. we will need the Pythagorean theorem to find the sides first split the base in half 12/2=6 now we use the height and the base 6^{2} +5x^{2} =6
2
+5x
2
= 61 the square root of 61 is about 7.8 the perimeter is 7.8+7.8 +12 but we wont need the base because it is attached to the rectangle =15.6 the area of the triangle is like half a square Base times height though 12x5=60
the whole perimeter if 15.6+20=35.6 the area is 60+48=108
wlcm♥️
Please help I really need it for a grade boost.
Answer:
I hope This will Help u.. Plz mark me as Brilliant please
Step-by-step explanation:
Before you get started, take this readiness quiz.
Simplify: 
If you missed this problem, review (Figure).
Solve Equations with Constants on Both Sides
In all the equations we have solved so far, all the variable terms were on only one side of the equation with the constants on the other side. This does not happen all the time—so now we will learn to solve equations in which the variable terms, or constant terms, or both are on both sides of the equation.
Our strategy will involve choosing one side of the equation to be the “variable side”, and the other side of the equation to be the “constant side.” Then, we will use the Subtraction and Addition Properties of Equality to get all the variable terms together on one side of the equation and the constant terms together on the other side.
By doing this, we will transform the equation that began with variables and constants on both sides into the form  We already know how to solve equations of this form by using the Division or Multiplication Properties of Equality.
Solve: 
Solution
In this equation, the variable is found only on the left side. It makes sense to call the left side the “variable” side. Therefore, the right side will be the “constant” side. We will write the labels above the equation to help us remember what goes where.

Since the left side is the “”, or variable side, the 8 is out of place. We must “undo” adding 8 by subtracting 8, and to keep the equality we must subtract 8 from both sides.
Use the Subtraction Property of Equality.Simplify.Now all the variables are on the left and the constant on the right.
The equation looks like those you learned to solve earlier.Use the Division Property of Equality.Simplify.Check:Let .
Solve: 

Solve: 

Solve: 
Solution
Notice, the variable is only on the left side of the equation, so we will call this side the “variable” side, and the right side will be the “constant” side. Since the left side is the “variable” side, the 9 is out of place. It is subtracted from the , so to “undo” subtraction, add 9 to both sides. Remember, whatever you do to the left, you must do to the right.
Answer:
Division property of equality
Step-by-step explanation:
[tex] - 2m = 40[/tex]
[tex]m = \frac{40}{ - 2} [/tex][tex]m = - 20[/tex]
Hope it is helpful...You basically look at the bar graph on the right and see which statement is true. Brainliest and thank you!
Answer:
D
Step-by-step explanation:
To check this answer, you could obviously graph the points, but without graphing, you can tell the line would be straight because each x value is multiplied by the same number to get the corresponding y value.
3 x 5 = 15, 4 x 5 = 20, etc. This shows linear growth. If each x value were multiplied by twice itself (3 x 6, 4 x 8, and so on), you wouldn't have a straight line because the number that x is multiplied by changes depending on the value of x.
12. Three fifths of the children at my party like chocolate ice cream. How many of the 20 children at my party do not like chocolate ice-cream ? ……………………….
13. I have to pack 296 apples into 8 boxes. How many apples will there be in a box if each box contains the same number of apples? There will be 37
14. If I share 123 sweets equally among amongst 7 children, how many sweets will each child get?
……………………………………..
15. One soccer ball costs $4.50. How much will the soccer will balls in the picture cost?
The circumference of a circle is best modeled by the perimeter of which regular polygon below?
Answer:
The answer is "20-gon"
Step-by-step explanation:
As the number of the sides increases the perimeters of the regular polygon go more closer to the circumference of the large circle. therefore the circumference of a circle is best moduled by the perimeter of the zo-gon as it has the maximum sides (z0) compared to hexagon (6), 15 gon(15), and Dodecagon(12).
Find the night of the parallelogram wh hen it's :area is 2.5mm squared base is 5mm
Answer:
Height is 0.5
Step-by-step explanation:
height of parallelogram = area ÷ base
= 2.5 ÷ 5 = 0.5
Amy is going on a 4 1 4 4 4 1 mile hike. She has already hiked 2 3 4 2 4 3 miles. How many more miles does she have left
Answer:
1 1/2 miles
Step-by-step explanation:
Amy is going on a 4 1 /4 miles hike. She has already hiked 2 3 /4 miles. How many more miles does she have left?
We solve the above question using the operation of Subtraction
The number of miles she has left is calculated by:
Total number of miles she must hike - Number of miles she has hiked
Total number of miles she must hike
= 4 1/4 miles
Number of miles she has hiked = 2 3/4 miles
Therefore:
The number of miles she has left to hike is = 4 1/4 miles - 2 3/4 miles
Lowest Common Denominator = 4
4 - 2 + ( 1/4 - 3/4)
2 + (1 - 3/4)
2 + -2/4
1 2/4
= 1 1/2 miles
When f(n)=12, what is the value of n?
what is the length of the missing leg?
Answer:
[tex]a=\sqrt{609}\\\\a\approx 24.67793[/tex]
Step-by-step explanation:
To solve for the leg of the missing right triangle, one must use the Pythagorean theorem. The Pythagorean theorem states the following,
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the sides adjacent to or next to the right angle. (c) is the side opposite the right angle. Substitute in the given values and solve for the unknown,
[tex]a^2+b^2=c^2\\[/tex]
Substitute,
[tex]a^2+40^2=47^2\\[/tex]
Simplify,
[tex]a^2+1600=2209\\[/tex]
Inverse operations,
[tex]a^2=609[/tex]
[tex]a=\sqrt{609}\\\\a\approx 24.67793[/tex]
Answer:
b = 9 mm
Step-by-step explanation:
Using Pythagoras; identity in the right triangle
b² + 40² = 41²
b² + 1600 = 1681 ( subtract 1600 from both sides )
b² = 81 ( take the square root of both sides )
b = [tex]\sqrt{81}[/tex] = 9 mm
10) what is the area ratio
11) what is the area of RST
HELP ASAP EMERGENCY
9514 1404 393
Answer:
10) C 4/9
11) B 24
Step-by-step explanation:
10) The area ratio is the square of the ratio of side lengths. The ratio of side lengths is ...
RS/LM = 6/9 = 2/3
Then the area ratio is ...
(2/3)² = 4/9
__
11) Using the result of question 10, the area of ∆RST is ...
(4/9)(54 in²) = 24 in²
plzzz anserw ill give you more points and crown if correct plzzz =D
From midnight to 7:00 am, the temperature rose 3/10 °C each hour. If the temperature at midnight was −1°C, what was the temperature at 7:00 am?
Answer:
11/10°C
Step-by-step explanation:
7 x 3/10 = 21/10
Temperature at Midnight = -1°C
Temperature at 7.00am = 21/10 + (-1°C)
= 11/10°C
Please help!!!!!
the depth, g(x), of a nautical measuring instrument, is given in feet above or below the surface of the water given the number of days the instrument was in the water, x. if g(x)=-2x-1, which best gives the value of g(4)?
Answer:
x = 2x - 1
x - 2x = -1
-x = - 1
x = 1
g = 1
What is the value of the expression 1/3x − 3/4 when x = 1/4?
The angle of elevation to a nearby tree from a point on the ground is measured to be
44º. How tall is the tree if the point on the ground is 51 feet from the tree? Round
your answer to the nearest hundredth of a foot if necessary.
Answer: the tree is 49.25
Step-by-step explanation:
The height of the considered tree if the point on the ground is 91 feet from the tree is 49.2507 feet approximately.
What is angle of elevation?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
For this case, referring to the attached figure below, we get:
Angle of elevation =∠ACB=44°
Distance of the base of the tree from the point of the ground = 51 feet
Height of the considered tree = h feet (assume).
Angle ACB denotes internal angle made by AC and CB line segments). It is the angle of elevation here, taking BC as horizontal line, and AC as elevated line.
Then, using the tangent ratio from the perspective of angle ACB, we get:
tan44°= h/51
h= 0.9657×51
h= 49.2507 feet
Therefore, the height of the considered tree if the point on the ground is 91 feet from the tree is 49.2507 feet approximately.
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can someone pls finish this for me, ill give brainliest
What was the activity? Drawing Circles
How long did you spend doing your activity? 1 minute
How much of the activity did you complete in the time period? (Example: I did 24 sit-ups in one minute). Drew 29 circles
Which of these variables is your dependent variable?
Which one is the independent variable?
Write a sentence that describes the relationship between the dependent variable and the independent variable. (Hint: Ratio language can help.)
part 2
Assuming that you could complete the activity at the same rate over different time periods, how much of the activity could you complete in two minutes, three minutes, four minutes, and five minutes? (Note: If you spent two minutes doing your activity, then you should edit the table below and use multiples of 2 up to 10).
You may use the table below for your variables.
Time
(minutes)
0 0
1
2
3
4
Answer:
dependent variable: circles drawn
independent: time
the independent variable is what you control, which was the time spent. the amount of circles you were able to draw depended on the amount of time you had, so it was the dependent variable.
part 2:
if you drew circles at the same rate
0-0
1-29
2-58
3-87
4-116
hope that helped! lemme know if you need more
Anyone know how to skip a video on edge nuity???
Answer:
I dont think there is a way
Step-by-step explanation:
Find f(2) if f(x) = (x + 1)^2
answer options:
a. 6
b. 9
c. 5
HURRY PLZZZ
Answer:
c
Step-by-step explanation:
Replacing x with 2, you get 5 as your answer
Question and choices are in the photo please explain the answer
Answer:
51°
Step-by-step explanation:
Plain reasoning:
the arc of CD is 180°
78° is alrdy cut out for AB
the rest (102°) has to be equally decided between AC and BD
pls brainliest (although a second answer is needed to give the crown)
Please help me i'm struggling!
Answer:
y = [tex]\sqrt{x-5}[/tex]
This is the correct answer because I got it right.
A circle has a radius of 10 cm and a sector of the circle
has an arc length of 10.8 cm.
The angle at the centre of the sector is x.
Calculate the value of x to the nearest degree.
10.8 cm
10 cm
Estelle hosted a banquet for her extended family that cost $480.93. Estelle paid 9.25% sales tax and left an 18% tip on $480.93. What was the total cost?
Answer:
$563.89: total cost of the banquet
Step-by-step explanation:
Here we can to find the total cost, including tax and tip, by adding 9.25% and 18% together first. We obtain 17.25%, which translates into the decimal fraction 0.1725 and results in the amount added to the original cost, $480.93. The result is added to $480.93:
1.0000($480.93) + 0.1725($480.93) = $563.89
A shortcut would be to find the total cost, including the original $480.93 and the additional 17.25%, by multiplying $480.93 by 1.1725:
1.1725($480.93) = $563.89: total cost of the banquet
Isaias has a watering can that holds 3 liters of water. He uses 500 milliliters of water on each of her plants.
How many plants can he water? Enter your answer in the box. You just need to convert liters to milliliters. Please help, i will give brainliest
Answer:
6 plants.
Step-by-step explanation:
500 mls = 0.5 liters so the answer is
3 / 0.5
= 6.
Any fake or incorrect and links will be reported and you will have all answers taken away
Write a simplified expression for the perimeter of the triangle.
Answer:
Perimeter = 6s + 9 units
Step-by-step explanation:
Perimeter = 2s + 4 + 4s + 2 + 3
= 2s + 4s + 4 + 2 + 3
= 6s + 9 units
Consider the following statement. If r is any rational number and s is any irrational number, then r s is irrational. (a) Which of the following is a negation for the statement? If r is any rational number and s is any irrational number, then r s is rational. If r is any irrational number and s is any rational number, then r s is irrational. There is a rational number r and an irrational number s such that r s is irrational. There is a rational number r and an irrational number s such that r s is rational. (b) What are some values of r and s for which the given statement is false (that is, for which its
Answer:
(a) If r is any rational number and s is any irrational number, then r/s is rational
(b) The statement is false when r is 0
Step-by-step explanation:
Given
[tex]r \to[/tex] rational number
[tex]s \to[/tex] irrational number
[tex]\frac{r}{s} \to[/tex] irrational number
Solving (a): The negation
To get the negation of a statement, we only need to negate the end result
In other words, the number type of r and s will remain the same, but r/s will be negated.
So, the negation is:
[tex]r \to[/tex] rational number
[tex]s \to[/tex] irrational number
[tex]\frac{r}{s} \to[/tex] rational number
Solving (b): When r/s is irrational is false
Given that:
[tex]\frac{r}{s} \to[/tex] irrational number
Set r to 0
So:
[tex]\frac{r}{s} = \frac{0}{s}[/tex]
[tex]\frac{r}{s} = 0[/tex] -- rational
Hence, the statement is false when r is 0
Which numbers are irrational numbers?
Select each correct answer.
9√
12−−√
16−−√
20−−√
25−−√
Answer:
Square root of 12
Square root of 20
Step-by-step explanation:
An irrational number contains an infinite decimal.
All other numbers are perfect squares, resulting in whole numbers.
The square root of 9 is 3 because 3 × 3 = 9.
The square root of 12 is 3.464....
The square root of 16 is 4.
The square root of 20 is 4.472....
The square root of 25 is 5.
Determine the volume of the picture below. Please help
Answer:
6825 in
Step-by-step explanation:
Since the shape is a composite figure, we need to break it up into 2 shapes!
Rectangle and a triangular prism
Solving for Rectangle...
Volume = Length · Width · Height
Volume = 30 · 13 · 13
Volume = 5070 in
Solving for Triangular Prism
Volume = Length · Width · Height / 2
Volume = 30 · 9 · 13 / 2
Volume = 3510/2
Volume = 1755 in
Finally, add the volumes!
5070 + 1755 = 6825 in
there are 6 red 4 green 5 yellow and 5 blue marbles in a jar what is the probability of picking a green marble then blue
Answer:
Find the volume of this prism.