Answer:
[tex]h(g(t))=8t+8[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]h(t)=2t-2\text{ and } g(t)=4t+5[/tex]
And we want to find:
[tex]h(g(t))[/tex]
So, by substitution, we acquire:
[tex]h(g(t))=2(4t+5)-2[/tex]
Distribute:
[tex]h(g(t))=8t+10-2[/tex]
Simplify:
[tex]h(g(t))=8t+8[/tex]
An event that is guaranteed to happen has a probability of exactly
Answer:
100%
Step-by-step explanation:
It is confirmed to happen, or [tex]\frac{100}{100}[/tex]
Answer:
An event that is guaranteed to happen has a probability of exactly 1
Mark had 3 times as many quarters as nickels. He had $1.60 in all. How many nickels and how many quarters did Mark have? x represents . 3x represents .
Answer:
x represents nickels = 2
3x represents number of quarters = 6
Step-by-step explanation:
x represents nickels
3x represents number of quarters
We'll multiply each of those times the value of the coin they represent, and make that equal to the total amount of money Mark has to get the value of x
x(0.05) + 3x(0.25) = 1.60
0.05x + 0.75x = 1.60
0.80x = 1.60
x = 2 = number of nickels
So 3x = 6 = number of quarters
Checking the math:
2(0.05) + 6(0.25)= 0.10 + 1.50 = 1.60
The table represents equivalent ratios of x to y. Find the missing numbers in the table.
Х
y
15
20
16
25
o
30
24
Researchers investigated whether providing a fancy, foil-wrapped piece of chocolate with the dinner bill would lead to higher tips than not providing such a treat. Sixty-four dinner parties at a restaurant in Ithaca, NY were randomly assigned to receive such a piece of chocolate or not with their dinner bill. Of the 32 parties who received the chocolate, the average tip (as a percentage of the bill) was 17.84%, with a standard deviation of 3.06%. Of the 32 parties who did not receive the chocolate, the average tip (as a percentage of the bill) was 15.06%, with a standard deviation of 1.89%. Determine a 96% confidence interval for the size of the difference in average tips between the two groups
Answer:
The 96% confidence interval for the size of the difference in average tips between the two groups is (1.47%, 4.09%).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means while the standard deciation is the square root of the sum of the variances.
Of the 32 parties who received the chocolate, the average tip (as a percentage of the bill) was 17.84%, with a standard deviation of 3.06%.
This means that:
[tex]\mu_{C} = 17.84, s_{C} = \frac{3.06}{\sqrt{32}} = 0.541[/tex]
Of the 32 parties who did not receive the chocolate, the average tip (as a percentage of the bill) was 15.06%, with a standard deviation of 1.89%.
This means that:
[tex]\mu_{NC} = 15.06, s_{NC} = \frac{1.89}{\sqrt{32}} = 0.3341[/tex]
Difference in average tips
The distribution has mean:
[tex]\mu = \mu_{C} - \mu_{NC} = 17.84 - 15.06 = 2.78[/tex]
Standard deviation:
[tex]s = \sqrt{s_{C}^2 + s_{NC}^2} = \sqrt{0.541^2 + 0.3341^2} = 0.6358[/tex]
96% confidence interval
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.96}{2} = 0.02[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.02 = 0.98[/tex], so Z = 2.054.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 2.054*0.6358 = 1.31[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2.78% - 1.31% = 1.47%
The upper end of the interval is the sample mean added to M. So it is 2.78% + 1.31% = 4.09%
The 96% confidence interval for the size of the difference in average tips between the two groups is (1.47%, 4.09%).
Find the area of each figure. Round to the nearest tenth if necessary
Answer:
b. 869.6 ft²
Step-by-step explanation:
The figure is composed of an equilateral triangle and a trapezoid
Therefore,
Area of the figure = area of the triangle + area of the trapezoid
✔️Area of triangle = ½*a*b*Sin C
Where
a = 22 ft
b = 22 ft
C = 60° (mall angles of an equilateral triangle measures 60°)
Area = ½*22*22*Sin 60°
Area = 209.58 ft²
✔️Area of trapezoid = ½(a + b)h
a = 22 ft
b = 38 ft
h = 22 ft
Area = ½(22 + 38)22
Area = ½(60)22
Area = 960 ft²
✔️Area of the figure = 209.58 + 660 = 869.58 ≈ 869.6 ft²
Find the product? y ^4 · y ^3
Answer:
if it will help
y^7
Step-by-step explanation:
y^4+3 = y^7
Jose graphed the amount of money paid in relation to the Number of avocados bought. Which statement best describes the unit rate for the graph below?
Answer:
The Answer is C
Step-by-step explanation:
Evan purchased 6 boxes of sugar cookies, each box containing 10 snack bags and
each bag containing 12 cookies. Evan could have purchased the same amount of
cookies by buying how many family sized packs of 30 cookies each?
a. 12
b. 24
d. 72
C. 48
e. 180
Answer:
Doesn't make sense. There are 12 cookies in each box. 12 multiplied by 6 is 72 cookies. The snack bags don't count.
Step-by-step explanation:
Help me quickly!!! I'll try to give Brainlyest
Answer:
number 12 is A for sure
whats 25.28 in expanded form
The radius of each semicircle in the composite figure is x units. The width of the rectangular part of the figure is equal to the radius.
Which expression represents the distance around the composite figure
A. 6x+2πx
B. 6x +4πx
C. 10x +2πx
D. 10x +4πx
Answer:
A) 6x + 2πx
Step-by-step explanation:
left side of figure = 4x
top and bottom flat portion of figure = 2x
2 semi-circles with radius of x is equal to 1 full circle with diameter = 2xπ
distance around = 4x + 2x + 2xπ or 6x + 2πx
An event manager recorded the number of people in different age groups that attended a music concert.
A histogram titled Concert Audience is shown. The horizontal axis is labeled Age Group in years with bins 18 to 24, 25 to 31, 32 to 38, and 39 to 45. The vertical axis labeled Number of People with values from 0 to 120 at intervals of 20. The first bin goes to 20, the second goes to 40, the third goes to 120, and the last goes to 80.
Which data table accurately represents the data in the histogram? (5 points)
Age Group Number of People
18−24 80
25−31 120
32−38 40
39−45 20
Age Group Number of People
18−24 20
25−31 60
32−38 180
39−45 260
Age Group Number of People
18−24 260
25−31 180
32−38 60
39−45 20
Age Group Number of People
18−24 20
25−31 40
32−38 120
39−45 80
The data table that accurately represents the histogram is the last table since the information matches the one in the histogram.
How to identify the correct data table?Understand the histogram and in this case the number of people in each category. For example, from 18 to 24, there are 20 people.Compare the information to the data tablesChoose the one that matches.What is the correct data table?The correct option is the last one or:
Age Group Number of People
18−24 2025−31 4032−38 12039−45 80Because only in this one does the data match the one in the histogram.
Learn morea bout histogram in: https://brainly.com/question/16819077
#SPJ1
the function f(x) = -x^2 + 44x -384 models the daily profit in dollars that a shop makes
Find the circumference and area of a circle with diameter of 18 inches. Use 3.14 for pi. Write your answer as decimals rounded to the nearest hundredth.
a. C = 56.52 in, A = 1017.36 in2
b. C = 56.52 in, A = 254.34 in2
c. C = 113.04 in, A = 254.34 in2
d. C = 113.04 in, A = 1017.36 in2
e. None of the above are correct.
Answer: b
Step-by-step explanation:
Radius = 9 inches, Pi= 3.14
Circumference = 2 x pi x radius = 2 x (3.14) x 9 = 56.52
Area = pi x radius x radius = (3.14) x 9 x 9 = 254.34
Answer:
Answer attached
Step-by-step explanation:
Help me please its due in 20 minutes!!!!
Need help guys givin brainliest
fyi its tall not fall
Answer:
5 feet tall.
Step-by-step explanation:
So, it gives us the ratio of the Statue of Liberty
1 inch wide for each 61 feet tall.
Then it gives us the tallness of the actual thing:
305 feet tall.
To find out how wide it is, we should be able to divide 305 by 61.
305/61 is 5.
Ive been asking too many questions but Im really dmb so heres another one
Answer:
12(6)/2
B: 36
Step-by-step explanation:
Using the Pythagorean theorem: a right triangle has a side that is 24 in and one that is 25in (25 is the diagonal side) what is the length of the third side
Answer:
Third Side (Perpendicular side) = 7 inch
Step-by-step explanation:
Given:
First side (Base) = 24 inch
Second side (Diagonal/Hypotenuse side) = 25 inch
Find:
Third Side (Perpendicular side)
Computation:
Using Pythagorean theorem;
Perpendicular side = √Hypotenuse side² - Base²
Perpendicular side = √25² - 24²
Perpendicular side = √625 - 576
Perpendicular side = √49
Perpendicular side = 7 inch
Third Side (Perpendicular side) = 7 inch
How many quarters are there in 4
22?
2
134
Answer.
Please help this is Geometry
Answer:
solution given:
volume of lower one[V1]=l×b×h=1.5×0.5×0.5=0.378m³
volume of upper one [V2]=l×b×h=1×0.5×(0.75-0.5)=
0.125m³
total volume=V1+V2=0.378m³+0.125m³=0.503m³
0.503m³ is your answer
On the number line, plot and label all numbers with an absolute value of 32. Where did you place the points?
Answer:
on 32 and -32
Step-by-step explanation:
Please help me.. I don't undersand this
Answer:
45 degrees.
Step-by-step explanation:
When two angles are next to each other along a straight line, their sum = 180 degrees.
180 - 135 = 45
Answer:
I know i may be unwanted here but I just want you to know that you are incredible and that I love you for you! You are special to everyone you meet, and should not change who you are. I know your life may be tough, but you are strong and can get through it!
Step-by-step explanation:
How much money is 5 dollars, 10 dimes, and 10 pennies?
Answer:
6 dollars and 10 cents
Step-by-step explanation:
I'm sorry this isn't the answer, but I just want you to know that you are incredible and that I love you for you! You are special to everyone you meet, and should not change who you are. I know your life may be tough, but you are strong and can get through it!
Can a polygon have four sides and three angles
No a polygon only has 3 sides and 3 angles.
The area of a SQUARE is 22 ft2. Which of the following is the closest to
the length of each SIDE of the square?
Answer:
4.7ft
Step-by-step explanation:
Hello, the answer would be 4.7ft because 4.7^2 is closest to 22ft^2 with it being 22.09ft^2.
can anyone help me with this?
Answer:
First Blank (4) Second Blank (3)
Step-by-step explanation:
The square in the middle is the base and if you count the side units you will have 4 on each side. From the square the triangle points up 3 units on the graph.
Hope this helps : ) Mark Brainliest
Find the value of x in the triangle shown below x 42 106
Answer:
Step-by-step explanation:
where is the picture?
Answer:
you need a picture lol
Step-by-step explanation:
What is the value of n??
9514 1404 393
Answer:
73.6°
Step-by-step explanation:
The whole is the sum of the parts:
n = 44.5° +29.1°
n = 73.6°
Answer and Step-by-step explanation:
To find the value of n, we must add the two given angles first.
Why?
We add these two angles together because we are shown that angle n encompasses both angles, meaning that the value of n must be the combination of the angles added together.
29.1 + 44.5 = n
Add.
73.6° = n
The value of n is 73.6°.
#teamtrees #PAW (Plant And Water)
help please will give brainest.
Hi, you didn't add any picture or attached the info
If m=7 and r = 12, what is the value of the following algebraic expression
4m + 7r-5