Using the t-distribution, as we have the standard deviation for the sample, it is found that the 98% confidence interval for the true mean age of Summer Olympians since the 1980 Olympics is (20.6, 24.8). It means that we are 98% sure that the true age of all Olympians is between these two values.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.In this problem, with the help of a t-distribution calculator, with a two-tailed significance level of 0.02 and 24 - 1 = 23 degrees of freedom, the parameters are:
[tex]\overline{x} = 22.7, s = 4.15, n = 24, t = 2.5[/tex]
Then, the interval is:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 22.7 - 2.5\frac{4.15}{\sqrt{24}} = 20.6[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 22.7 + 2.5\frac{4.15}{\sqrt{24}} = 24.8[/tex]
The 98% confidence interval for the true mean age of Summer Olympians since the 1980 Olympics is (20.6, 24.8). It means that we are 98% sure that the true age of all Olympians is between these two values.
More can be learned about the t-distribution at https://brainly.com/question/16162795
i need help 5/9 = /45 fractions
Answer:
5/9 = 25/45
Step-by-step explanation
multiply 5/9 by 5/5 this will turn it into 25/45
5x5=25
5x9=45
Find the length of the missing side of the right triangle. 15 C 36
The value of c in the missing triangle is 39
Right angle triangle:A right angle triangle is a triangle that has one of its angle as 90 degrees.The side c can be found using Pythagoras theorem.
Therefore,
c² = a² + b²
c² = 36² + 15²
c² = 1296 + 225
c = √1521
c = 39
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Victoria used 1.5 m of red ribbon and 240cm of blue ribbon to make a flower. How much
ribbon did she use in total?
Quadrilateral ABCD ~ quadrilateral JKLM. What is the
length of LM?
Step-by-step explanation:
just ratio and need to identify which lines are pairs.
2. If the raffle has 200 tickets total, then
about how many tickets will be in the dining out
raffle?
If the raffle has 200 tickets total, then about 50 tickets will be in the dining out raffle.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the diagram:
Percentage of dinner out = 65% - 40% = 25%
For 200 total tickets:
Number of dinning out raffle = 25% of 200 = 0.25 * 200 = 50 ticket
If the raffle has 200 tickets total, then about 50 tickets will be in the dining out raffle.
Find out more on equation at: https://brainly.com/question/2972832
If you have a 91.66% A and you have an exam worth 100 points what would your final grade be if u didn’t do so well on the exam?
Answer:
%70.83
Step-by-step explanation:
91.66 + 50 = 141.66
141.66÷2=70.83
Six more than the product of seven and a number is 55.
Answer:
7
Step-by-step explanation:
6 + 7x = 55
7x = 55 - 6
7x = 49
x = 49/7
therefore x = 7
1.10 friends are at a party and they decided the party was boring and decided to go to a
club in two different cars. One of the friends, Susan, has an SUV that can carry 7
passengers. So, Susan can take 6 more of the 9 friends with her. How many
different groups of 6 people are possible from the 9 remaining friends?
Using the combination formula, it is found that 84 different groups of 6 people are possible from the 9 remaining friends.
The order in which the friends are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 6 friends are chosen from a set of 9, hence:
[tex]C_{9,6} = \frac{9!}{6!3!} = 84[/tex]
84 different groups of 6 people are possible from the 9 remaining friends.
More can be learned about the combination formula at https://brainly.com/question/25821700
Answer:
this wrong
Step-by-step explanation:
sorry this is the picture
Answer:
ok so use the degrees
Step-by-step explanation:
x should be 8 + 17 and then multiply the 110 degrees by 8 + 17
Answer:
x = 6
The marked angle is 110°
Step-by-step explanation:
See how there are 8 angles in this type of image. The angles either are EQUAL, or they ADD UP TO 180°. It's just two numbers for the degrees of these angles. Four of them are the same and the other four are the same.
In your question the 8 + 17x = 110°
Solve.
Subtract 8.
17x = 102
Divide by 17.
x = 6
If your question says find the measure of the angle it is 110°, if you are to find x, then x = 6.
Jfyi, four of these angles are 110°. The other four are 70°.
If log, 7 -3 what is the value of x?
A. 21
B. 3V7
C. 37
D. 343
Answer:
B
Step-by-step explanation:
logₓ 7 = 3
x³ = 7
Take cube root both sides
[tex]x= \sqrt[3]{7}[/tex]
you take out a mortgage for 350,000$ at 4% compounded monthly your payment is 1671$ write a recursive formula
Answer:
Not sure if this is right but it might be something like
350,000-4%+1671m
or
3500,000-4%y/1671m
Step-by-step explanation:
The numbers we know are 350,000 4% and 1671 per month
350,000 is the full mortgage
4% is the APR or annual percentage rate like interest
and we know the monthly for the mortgage is 1671 per month
5. 26 = y + x
y = x
6. y = 2x + 7
y=-3x - 23
Solve each system of equations by substitution
Answer:
5.step 1
26=y+x
y=x
26=x+x
26=2x
then x=13
6.substitute y with the given equation equal to y the equate them with the first one and collect like terms the find x
if f(x) = 5x 1 and g(x)= x3 what is (g f)(0)?
Answer:
f(x)= -5x+1 and g(x)=x^3,
(g • f)(0)= g(f(0))
but f(0) = -5 (0)+1 = 1
(g • f)(0)= g(1) = 1^3 = 1
Step-by-step explanation:
hope this helps
Answer:
-1
Step-by-step explanation:
f(x) = 5x - 1
g(x) = x³
f(0) = 5(0) - 1
= -1
g(-1) = (-1)³
= -1
Enter the polynomial function with the least degree and a leading coefficient of 1 that has the given
zeros.
3i, 2, and -2
Answer:
±4i, ±3
p(x) = A(x - 4i)(x + 4i)(x - 3)(x + 3), with A = 1.
Step-by-step explanation:
±4i, ±3
p(x) = A(x - 4i)(x + 4i)(x - 3)(x + 3), with A = 1.
FedEx charges $14 per package plus $0.20 per
ounce. Write and solve for an equation that can be
used to find the weight of the package that costs
$19.40 to ship?
Answer:
19.40-14=5.40
5.40÷0.20=ounces
Hope this helps!!!
Answer:
27 ounces
Step-by-step explanation:
$14 package original charging fee
+ .20x27 = 5.40
14 + 5.4 = 19.4
$19.4
Ages Number of students 15-18 7 19-22 7 23-26 7 27-30 9 31-34 9 35-38 2 Find the relative frequency for the class with lower class limit 23 Relative Frequency
Answer:
14
Step-by-step explanation:
Relative Frequency = [tex]\frac{Frequency*100}{Total Frequency}[/tex]
Frequency for the class with lower class is 23 =7
Total Frequency= 7+7+7+9+9+9+2=50
Relative Frequency = [tex]\frac{7*100}{50}[/tex] = 14
The relative frequency for lower class limit 23 is 14
The perimeter of a rectangular garden is 262 m.
If the width of the garden is 54 m, what is its length?
Step-by-step explanation:
154 is my answer thank you
what is the range for the possible side lengths AB of ABC.
Answer:
adg
Step-by-step explanation:
adg is the range for the side lengths AB of ABC
Hope it's help
20+20+???
a. 80
b. 20
c .40
d. 100
Answer:
its C 40
Step-by-step explanation:
What is the volume of a cylinder , whose base diameter us of 20cm and height of 5cm.
[tex]\boxed{\tt \pink{Given:}}[/tex]
[tex]\red\star[/tex]Diameter of base of a cylinder = 20 cm.
[tex]\red\star[/tex]Height of cylinder = 5cm.
[tex]\\\\[/tex]
[tex]\boxed{\tt \pink{To~Find:}}[/tex]
[tex]\red\star[/tex]Volume of Cylinder.
[tex]\\\\[/tex]
[tex]\boxed{\tt \pink{Solution}}[/tex]
To find volume of Cylinder first we should know radius of Cylinder. We can get radius by diameter using this formula:-
[tex]\boxed{\rm Diameter = 2 radius}[/tex]
[tex]\\\\[/tex]
[tex]\hookrightarrow\sf Diameter = 2 radius[/tex]
[tex]\\[/tex]
[tex]\hookrightarrow\sf 20= 2 radius[/tex]
[tex]\\[/tex]
[tex]\hookrightarrow\sf \dfrac{20}{2}= radius[/tex]
[tex]\\[/tex]
[tex]\hookrightarrow\sf \dfrac{2\times10}{2}= radius[/tex]
[tex]\\[/tex]
[tex]\hookrightarrow \sf \dfrac{\cancel2\times10}{\cancel2}= radius[/tex]
[tex]\\[/tex]
[tex]\hookrightarrow \sf \dfrac{1\times10}{1}= radius[/tex]
[tex]\\[/tex]
[tex]\hookrightarrow \sf 10= radius[/tex]
[tex]\\[/tex]
[tex]\hookrightarrow \bf radius = \pmb{\blue{10 cm}}[/tex]
[tex]\\\\[/tex]
Now Finally Let's find volume of Cylinder.
we know:-
[tex]\boxed{\rm Volume ~ of ~ Cylinder = \pi radius^2 \times height}[/tex]
[tex]\\\\[/tex]
So:-
[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \pi radius^2\times height\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \pi (10)^2\times 5\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \pi 10\times10\times5\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \pi 100\times5\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \pi\times 500\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \dfrac{22}{7}\times 500\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \dfrac{11000}{7}\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow\bf Volume ~of ~Cylinder =\pmb{\blue{1,571.4~cm}}\\[/tex]
KNOW MORE:-[tex]\begin{gathered}\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc}\small\underline{\sf{\pmb{ \gray{More \: Formulae}}}} \\ \\ \bigstar \: \bold{CSA_{(cylinder)} = 2\pi \: rh}\\ \\\bigstar \: \bold{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bold{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bold{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar\: \bold{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bold{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bold{Volume_{(cube)} ={(side)}^{3} }\\ \\ \bigstar \: \bold{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bold{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\\bigstar \: \bold{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bold{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bold{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}\end{gathered}[/tex]
pls answer ASAP Plss
Buddy it's actually Isosceles Triangle because of the symbols used in the diagram
is this true 8ft equals 3 yards
Answer:
No
Step-by-step explanation:
1 yard = 3 feet, so 3 yards = 9 feet
Hope this helps :)
Part A. Dario purchased a party size sub, and he decides to share it with three of his friends. so he cuts the sub into four equal pieces. however another one of his friends also showed up, and they are now five people in total now that the sun will be shared equally among five people will each person get more or less sub briefly state why do you think so. Part B. Dario decide to take each one of the four pieces and shared equally among the five of them first he divides one piece into five equal parts in shares it then the next one and so on what fraction of the party say sub did each person get after all the parts were shared out explain your reasoning
Answer: 4/6 = 2/32/3 = 2/3
Step-by-step explanation: hope this help
Valerie drives 400 meters up a hill that makes an angle of 20° with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered?
Answer:
482.96 meters, Hope that helped
Let f(x) = x + 1 and g(x) = 1/x The graph of (fog)(x) is shown below. What is the range of (fog)(x)?
Answer:
Range is [tex]\{y|y\neq 1\}[/tex]
Step-by-step explanation:
[tex]f(x)=x+1\\g(x)=\frac{1}{x}\\ \\(f\circ g)(x)=f(g(x))=f(\frac{1}{x})=\frac{1}{x}+1[/tex]
Thus, the range of the composite function is [tex]\{y|y\neq 1\}[/tex], indicated by the horizontal asymptote.
Find the value of in the isosceles triangle shown below.
A x= √5
B x= √13
C x= √49
D x= √12
Answer:
B
Step-by-step explanation:
The height of 3 cut the base in half and perpendicular to the base, so
[tex]x = \sqrt{(4/2)^2 + 3^2}= \sqrt{13|[/tex]
That is B
In the diagram, △ABC∼△DEF. Find the value of x.
Given -
△ABC ∼ △DEF
To find -
the value of x.
Solution -
If △ABC ∼ △DEF then,
[tex]\frac{AB}{DE} =\frac{BC}{EF}[/tex]
➡ [tex]x=\frac{\cancel{12}^4}{\cancel{3}_1}\times2[/tex]
➡ [tex]x=4\times2[/tex]
➡ [tex]x=8[/tex]
Hence, the value of x is equal to 8.
Find the mean of the distribution class 1-3 3-5 5-7 7-9. frequency 9 22 27 17
Answer:
Hope this helps you
Step-by-step explanation:
Mean= [tex]\frac{404}{75} = 5.386666666666667[/tex]
Therefore, the mean of the given distribution =5.39 or 3.4
If you did not understand anything you can ask in the comments
Find the value of x.
х
x = [?]
Give your answer in simplest form.
Answer:
x = [12]
Step-by-step explanation:
=> [tex] \frac{x}{6} = \frac{6}{3} [/tex]
=> x = 2 × 6
=> x = 12
A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 70 pounds. The truck is transporting 60 large boxes and 55 small boxes. If the truck is carrying a total of 4050 pounds in boxes, how much does each type of box weigh?
Answer:
the large boxes weigh 40 pounds and the smaller boxes weigh 30 pounds
Step-by-step explanation:
define variables:
b is the weight of large boxes and s is the weight of small boxes. you can create two equations to represent what you know:
b + s = 70 (the weight of one large box and one small box is 70 pounds)
60b+ 55s = 4050 (the total weight of the 60 large boxes and the 55 small boxes is 4050)
then by making one of the equations equal to a variable, you can use substitution to solve.
s = 70 - b
so 60b + 55s = 4050 now becomes:
60b + 55(70 - b) = 4050, and next you solve for b
60b + 3850 - 55b = 4050
5b = 200
b = 40.
now you know that the large boxes weigh 40 pounds. to solve for the small box weight, you plug in b in either equation. i am going to choose the first once since it's fewer steps
b + s = 70 -> 40 + s = 70
s = 30
and now you know that the smaller boxes weigh 30 pounds.