Answer:
4)13
Step-by-step explanation:
In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
Ignacio is curious about the average age of cars in the commuter lot at Mis large university. He takes a random
sample of 16 cars and finds that their average age is 2 = 14.5 years and their standard deviation is 8, = 4.6
years. The distribution of ages in the sample was roughly symmetric with no obvious outliers.
Based on this sample, which of the following is a 90% confidence interval for the mean age of cars (in years) in
this commuter lot?
Therefore, the correct answer is (D) [tex]$(12.61,16.39)$[/tex]
To calculate the confidence interval for the mean age of cars in the commuter lot, we'll use the formula:
[tex]\[ \text{Confidence interval} = \bar{x} \pm t \left( \frac{s}{\sqrt{n}} \right) \][/tex]
where:
- [tex]\(\bar{x}\)[/tex] is the sample mean age (14.5 years),
- [tex]\(s\)[/tex] is the sample standard deviation (4.6 years),
- [tex]\(n\)[/tex] is the sample size (16),
- [tex]\(t\)[/tex] is the critical value from the t-distribution corresponding to the desired confidence level (90% in this case).
First, we need to find the critical value \(t\) for a 90% confidence level with [tex]\(n-1 = 15\)[/tex] degrees of freedom. Using a t-distribution table or calculator,[tex]\(t \approx 1.753\).[/tex]
Now, we can plug in the values:
[tex]\[ \text{Confidence interval} = 14.5 \pm 1.753 \left( \frac{4.6}{\sqrt{16}} \right) \][/tex]
[tex]\[ \text{Confidence interval} = 14.5 \pm 1.753 \times \frac{4.6}{4} \][/tex]
[tex]\[ \text{Confidence interval} = 14.5 \pm 1.753 \times 1.15 \][/tex]
[tex]\[ \text{Confidence interval} = 14.5 \pm 2.12595 \][/tex]
[tex]\[ \text{Confidence interval} = (12.37405, 16.62595) \][/tex]
Complete question:
Ignacio is curious about the average age of cars in the commuter lot at his large university. He takes a random sample of 16 cars and finds that their average age is [tex]$\bar{x}=14.5$[/tex] years and their standard deviation is [tex]$s_x=4.6$[/tex]years. The distribution of ages in the sample was roughly symmetric with no obvious outliers.
Based on this sample, which of the following is a [tex]$90 \%$[/tex] confidence interval for the mean age of cars (in years) in this commuter lot?
Choose 1 answer:
(A) [tex]$(6.44,22.56)$[/tex]
(B) [tex]$(12.05,16.95)$[/tex]
(c) [tex]$(12.48,16.52)$[/tex]
(D)[tex]$(12.61,16.39)$[/tex]
(E) [tex]$(13.35,15.65)$[/tex]
The 90% confidence interval for the mean age of cars in the commuter lot is (12.48, 16.52). The correct answer is: c) (12.48, 16.52)
Step 1
To determine the 90% confidence interval for the mean age of cars in the commuter lot, we can use the formula for the confidence interval of the mean for a normally distributed sample:
[tex]\[ \text{CI} = \bar{x} \pm t \left(\frac{s}{\sqrt{n}}\right) \][/tex]
Where:
- [tex]\(\bar{x}\)[/tex] is the sample mean (14.5 years)
- [tex]\(s\)[/tex] is the sample standard deviation (4.6 years)
- n is the sample size (16)
- t is the t-value for the 90% confidence level with [tex]\(n-1\)[/tex] degrees of freedom (df = 16 - 1 = 15)
First, we find the t-value for 90% confidence and 15 degrees of freedom. Using a t-table or a calculator, the t-value (two-tailed) is approximately 1.753.
Step 2
Next, we calculate the margin of error:
[tex]\[ \text{Margin of Error} = t \left(\frac{s}{\sqrt{n}}\right) = 1.753 \left(\frac{4.6}{\sqrt{16}}\right) = 1.753 \left(\frac{4.6}{4}\right) = 1.753 \times 1.15 \approx 2.016 \][/tex]
Now, we calculate the confidence interval:
[tex]\[ \text{CI} = 14.5 \pm 2.016 \][/tex]
So, the lower bound is:
[tex]\[ 14.5 - 2.016 = 12.484 \][/tex]
And the upper bound is:
[tex]\[ 14.5 + 2.016 = 16.516 \][/tex]
Thus, the 90% confidence interval for the mean age of cars is approximately:
[tex]\[ (12.48, 16.52) \][/tex]
This interval suggests that we are 90% confident that the true mean age of cars in the commuter lot lies between 12.48 and 16.52 years.
Complete question : Ignacio is curious about the average age of cars in the commuter lot at Mis large university. He takes a random sample of 16 cars and finds that their average age is 2 = 14.5 years and their standard deviation is 8, = 4.6
years. The distribution of ages in the sample was roughly symmetric with no obvious outliers. Based on this sample, which of the following is a 90% confidence interval for the mean age of cars (in years) in this commuter lot?
a) (6,44,22,56)
b) (12,05,16,95)
c) (12,48,16,52)
d) (12,61,16,39)
e) (13,35,15,65)
To find the square root of 12, what is most likely to be an ancient Babylonian’s first guess?
please help. I don't understand it. Please and thank you to whoever answers :')
Answer:2 root 3
Or 3.464101615
Step-by-step explanation:
Answer:
b. 3
Step-by-step explanation:
plz hurry 50 points!
solve n -> which number?
this is an inequality problem.
n - 4 -> 13
<-14-15-16-17-18-19-20-21-22-> # number line
9
11
17
18
Answer:
see below
Step-by-step explanation:
n-4 ≥ 13
Add 4 to each side
n-4+4 ≥ 13+4
n ≥17
There will be a closed circle at 17 because of the equal sign and the line will go to the left because of the greater than sign
The perimeter of the triangle shown is 30 inches. What is the length of the longest side of the triangle
Answer:
The length of the longest side of the triangle is 13 inches
Step-by-step explanation:
step 1
Find the value of x
we know that
The perimeter of triangle is equal to the sum of its three length sides
so
[tex]P=x+(2x+3)+(4x-8)[/tex]
[tex]P=(7x-5) \ in[/tex]
we have
[tex]P=30\ in[/tex]
substitute
[tex]30=(7x-5)[/tex]
solve for x
[tex]7x=30+5\\7x=35\\x=5[/tex]
step 2
Find the length of the longest side of the triangle
Remember that in a right triangle, the longest side is the hypotenuse
so
(2x+3) is the longest side
substitute the value of x
[tex]2(5)+3=13\ in[/tex]
6/10 + 20/100 = 8/10
6/10 can be simplified but we don't need to worry about it right now. We only need to worry about simplifying 20/100:
20/100 → 10/50 → 5/25 → 1/5
Find common denominators
1/5 → 2/10
6/10
Now, add.
6/10 + 2/10 = 8/10
Therefore, the equation is true.
Best of Luck!
Answer:
6/10+20/100 does not equal 8/10
Step-by-step explanation:
If triangle ABC is similar to triangle DEC, find the values of x and y.
The values are x=8 and y=35, if the given ΔABC and ΔDEC are equal, it is obtained by Pythagoras theorem.
Step-by-step explanation:
The given are,
From ΔABC,
AB= 6
BC= 10
AC = x
From ΔDEC,
CD= 28
DE= 21
CE = y
Step:1
Pythagoras theorem from ΔABC,
[tex]BC^{2}=AB^{2} + AC^{2}[/tex]...............(1)
Substitute the values,
[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]AC^{2}[/tex]
100 = 36 + [tex]AC^{2}[/tex]
[tex]AC^{2}[/tex] = 100 - 36
= 64
AC = [tex]\sqrt{64}[/tex]
AC = 8
AC = x = 8
Step:2
Pythagoras theorem for ΔDEC,
[tex]CE^{2} = CD^{2} + DE^{2}[/tex]................(2)
From the values,
[tex]CE^{2}[/tex] = [tex]28^{2}[/tex] + [tex]21^{2}[/tex]
[tex]CE^{2}[/tex] = 784 + 441
= 1225
CE = [tex]\sqrt{1225}[/tex]
CE = 35
CE = y = 35
Result:
The values are x=8 and y=35, if the given ΔABC and ΔDEC are equal.
Rhonda tutors students after school. She charges $25 per hour to tutor math students and $30 per hour to tutor science students.
She tutored math students for 3 hours on Thursday and science students for 5 hours on Monday.
Which of the following expressions can be used to find the total amount of money that Rhonda earned?
A. (50 + 30) × (5 + 3)
B. (3 + 25) × (5 + 30)
C. (5 × 25) + (3 × 30)
D. (3 × 25) + (5 × 30)
Answer:D
Step-by-step explanation:
Answer:
[3x25]+[5x30]
Step-by-step explanation:
Kevin has 30% less money than Erin. Kevin has $140. How much money does Erin have
Answer:
Erin has $200
Step-by-step explanation:
Kevin = K
Erin = E
30% of Erin = 0.3E
K = E - 0.3E
K = 140
Substitute
140 = E - 0.3E
140 = 0.7E
Divide both sides of the equation by 0.7
E = 200
Erin has $200
Hope this helps :)
Please help on number 5, multiple choice
Answer:
Final Answer B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Answer B is correct because all the side lengths are multiply by 3.
5 times 3= 15, 12 times 3=36, and 13 times 3=39.
Have a nice day and stay safe!
If (2, −7) and (8, 15) are the endpoints of a diameter of a circle, what is the equation of the circle?
A) (x + 5)2 + (y − 4)2 = 60
B) (x − 5)2 − (y − 4)2 = 80
C) (x − 5)2 − (y + 4)2 = 110
D) (x − 5)2 + (y − 4)2 = 130
Answer:
D
Step-by-step explanation:
If (2,-7) and (8,15) is the end points of the diameter, they must be on the circle.
Here is a graph: search up https:// www . desmos. com /calculator/ yl9uiyhttps, sorry I couldn't put up a link cause of brainly. Type it in without spaces.
Answer:
D
Step-by-step explanation:
Stephen got a new job through an employment agency. The job pays $41,236 per year. The agency fee is 15% of the first 5 weeks pay.
How much will Stephen pay to the agency?
Answer:
$594.75
Step-by-step explanation:
Given
yearly salary of Stephen= $41,236
No of weeks in a year = 52
Therefore, one week salary of Stephen = $41,236/52 = $793
to get one week salary divide total salary by number of weeks
5 weeks salary of Stephen = 5*793 = $ 3,965
agency fees = 15% of Stephen's 5 week salary
(15/100)*($ 3,965) = $594.75
Therefore, Stephen has to pay $594.75 to the agency.
Where does the line y = 4x + 1 intersect the y-axis (the y-intercept)?
Answer:
(0,1)
Step-by-step explanation:
The equation for slope is y=mx+b.
The b value stands as the y - intercept.
Is 6cups of coffee for $8 and 9 cups of coffee for $12 proportional
Answer:
They are proportional
Step-by-step explanation:
Let's simplify the ratio of coffee to cost:
6:8 :: 3:4
9:12 :: 3:4
Both simplify to 3:4, so they are proportional
Answer:
Yes, proportional
Step-by-step explanation:
Price 'P' in dollars
No. of cups 'C'
P = kC
8 = 6k
k= 8/6
k = 4/3
12 = 9k
k = 12/9
k = 4/3
Same constant, so proportional
2 Points
is the term used to describe the study of motion.
Answer: Mechanics and Kinematics
Step-by-step explanation:
The study of motion with regard to the forces or energies that may be involved is called Mechanics
The study of motion without regard to the forces or energies that may be involved is called kinematics
8n+6<46
need answer asap!!!
Answer:
n < 5
Step-by-step explanation:
8n+6 < 46
1. subtract 6 from both sides
8n < 40
2. Divide both sides by 8
40/8 = 5
So n<5
Answer:
(explanation)
Step-by-step explanation:
[tex]8n + 6 < 46\\8n +6 (-6) < 46 - 6\\8n < 40\\\frac{8n}{8} <\frac{40}{8}\\ n < 5[/tex]
Find the measure of angle 1 when X= 96 and y=132
Help!?
Answer:
96 degrees
Step-by-step explanation:
A center angles degree measurement is the same as the ark it is on
Rewrite the equation in Ax+By=C form.
Use integers for A, B, and C.
y+6=-6(x+1)
Answer:
-6x+y=0
Step-by-step explanation:
y+6=-6(x+1)
y+6=-6x-6
-6x+y=0
On converting y + 6 = -6(x + 1) to Ax+By=C form, get 6x + y = -6 with A=6, B=1, and C=-6.
To rewrite the equation y + 6 = -6(x + 1) in the Ax+By=C form, where A, B, and C are integers, we need to distribute the -6 and then move all terms involving variables to one side of the equation and the constant term to the other side.
First, distribute the -6:
y + 6 = -6x - 6
Now, move the variable terms to one side by adding 6x to both sides:
6x + y + 6 = 0
Finally, subtract 6 from both sides to isolate the constant:
6x + y = -6
Now the equation is in the desired format with A=6, B=1, and C=-6.
Definition: To get the volume of a ______, multiply pi by the radius squared and then multiply by the height.
Answer:
Cylinder
explanation:
The formula for the volume of a cylinder is V=πr²h
To find the volume of a cylinder, the formula V = πr²h is used, where you multiply the square of the radius by π and then by the height, ensuring consistent units throughout.
Explanation:To get the volume of a cylinder, you need to use the formula V = πr²h, where V stands for volume, π is a mathematical constant approximately equal to 3.14159, r represents the radius of the cylinder's base, and h denotes the height of the cylinder. To calculate the volume, first square the radius, then multiply that by π, and finally multiply by the cylinder's height. For example, if a cylinder has a radius of 0.750 cm and a height of 5.25 cm, you would calculate the volume as follows: 3.142 × (0.750 cm)2 × 5.25 cm, which equals approximately 9.278 cm3. Remember to use consistent units throughout the calculation.
I need your help and fast
Answer:
copy
Step-by-step explanation:
just copy and paste your answers to google
MARKING AS BRAINLIST HELP ASAP
Answer:
42
Step-by-step explanation:
Because the circle is tangent to all sides, that makes the perimeter of the triangle equivalent to the sum of the numbers given, multiplied by 2.
(6+10+5)(2) = 42 inches
find x and y 5x=2y-5
Answer:
[tex]x = 2/5y - 1, y = 5/2x + 5/2[/tex]
Step-by-step explanation:
Step 1: Solve for x
[tex]5x / 5 = (2y - 5) / 5[/tex]
[tex]x = 2/5y - 1[/tex]
Step 2: Solve for y
[tex]5x + 5 = 2y - 5 + 5[/tex]
[tex](5x + 5) / 2 = 2y / 2[/tex]
[tex]5/2x + 5/2 = y[/tex]
Answer: [tex]x = 2/5y - 1, y = 5/2x + 5/2[/tex]
pauline uses 2/5 of a cup of sugar in each batch of cookies.Yesterday, pauline used 1 cup of sugar .How many batches of cookie did pauline make yesterday?
Answer:
Step-by-step explanation
two and a half batches?
Final answer:
Pauline used 1 cup of sugar and each batch of cookies requires 2/5 cup. By dividing 1 cup by 2/5 cup, we get 2.5 giving us ≈2 batches.
Explanation:
The question asks how many batches of cookies Pauline was able to make if she used 1 cup of sugar, with each batch requiring 2/5 of a cup of sugar. To find this, we can use a simple division process as our conversion factor. You divide the total amount of sugar used by the amount needed per batch.
Steps to calculate the number of batches:
Pauline uses 2/5 of a cup of sugar for each batch of cookies.
She used a total of 1 cup of sugar yesterday.
To find the number of batches made, divide the total amount of sugar by the amount per batch: 1 cup / (2/5 cup per batch) = 5/2 = 2.5 batches.
However, since you cannot make half a batch of cookies, Pauline must have made 2 batches.
Which linear function has a y-intercept at –3? On a coordinate plane, a line goes through points (negative 1.5, 0) and (0, 3). On a coordinate plane, a line goes through points (0, negative 1) and (2, 0). On a coordinate plane, a line goes through points (negative 2.5, 0) and (negative 2, negative 2). On a coordinate plane, a line goes through points (negative 3, 0) and (0, negative 3).
Answer:
(-3,0) and (0,-3)
Step-by-step explanation:
When you are looking for an intercept one of the coordinates is going to be 0.
The line or linear function which has a y-intercept at -3 will be that line that passes through (-3,0) and (0, -3).
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
F(x) = x is a line through the origin and is the parent linear function.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
A linear function has a single and unique constant slope.
In the given problem the line which intercepts y at -3 will be that line in which one y coordinate should be -3 since, it is coordinated with 0, -3) hence, it will be the correct answer.
For more about the linear function
https://brainly.com/question/21107621
#SPJ5
negative five divided by 5/7
Answer:
-7
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
-5 ÷ 5/7 = -7. the fives cancel each other out and you're left with -7.
|x+18| =1
please help show steps plz
Answer:
x=-17 and x=-19
Step-by-step explanation:
-17+18=1
-19+18=-1
|-1| =1
Answer:
-17 and -19
Step-by-step explanation:
Absolute value equations have two problems and two solutions unless the original answer equals a negative-then it would be no solution.
x + 18 =1 subtract 18 from both sides to get x by itself
x = 1-18
x= -17
x +18 = -1 subtract 18 from both sides to get x by itself
x= -1 -18
x= -19
Which of the following is an irrational number?
49
O
C. 1.333...
O
D.
22
7
Answer:
1.333...
Step-by-step explanation:
because irrational numbers can be repeating decimals, numbers that aren't perfect squares,and numbers that can not be in fraction form.
math question (picture linked)
Answer:
the graph that represents the inequality is f.
0 is greater than or equal to and it is going to the right
Answer:
F
Step-by-step explanation:
f means x is above or at 0 and 0 counts because it is a closed circle, if it was open it would not have a line underneath.
The sum of two numbers is 38. The smaller number is eight less than the larger number. What are the numbers?
Answer: 15 + 23 =38
So n + n + 8 = 38
which means n + n = 30
and since the n's are the same, you just cut the 30 in 2 equal pieces. 15 and 15.
So n = 15, n + 8 = 23
15 + 23 = 38 :)
what is the square root of r^64?
a. r^4
b. r^8
c. r^16
d. r^32
The Hernandez family is evenly splitting
7
liters of gasoline between their
4 cars.
How many liters of gasoline should each car get?
Answer:
1.75 liters
Step-by-step explanation:
7/4 = 1¾ or 1.75 liters