Answer: upper bound = 89.36 and lower bound = 94.64
Step-by-step explanation:
Confidence interval for mean : [tex]\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}[/tex], where [tex]\overline{x}[/tex] = sample mean , n= sample size , z* = two-tailed critical value, [tex]\sigma[/tex]= population standard deviation
As per given , we have
[tex]\overline{x}[/tex] = 92
n = 55
[tex]\sigma[/tex]= 10
Critical value for 95% confidence interval = 1.96
Required confidence interval : [tex]92\pm (1.96)\dfrac{10}{\sqrt{55}}[/tex]
[tex]92\pm (1.96)(1.3484)\approx92\pm2.64\\\\= (92-2.64,\ 92+2.64)\\\\=(89.36,\ 94.64)[/tex]
Hence, for 95% confidence interval for the mean IQ of primary school students:
upper bound = 89.36 and lower bound = 94.64
Magan owns a small business selling bagels. He knows that in the last week 39
customers paid cash, 9 customers used a debit card, and 59 customers used a credit
card.
Based on these results, express the probability that the next customer will pay with a
debit card as a fraction in simplest form.
Using it's concept, it is found that there is a [tex]p = \frac{9}{107}[/tex] probability that the next customer will pay with a debit card.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there were 39 + 9 + 59 = 107 purchases, of which 9 were paid with debid cards, hence:
[tex]p = \frac{9}{107}[/tex]
There is a [tex]p = \frac{9}{107}[/tex] probability that the next customer will pay with a debit card.
More can be learned about probabilities at https://brainly.com/question/14398287
Answer: 9/107
Step-by-step explanation:
A recipe calls for a total of 3 cups flour and sugar. If the recipe calls for a cup of sugar, how much flour is needed?
o 3 te cups
3 cups
4 cups
3 cups
5
12 cup
3
13 cups
Answer:
3 cups
Step-by-step explanation:
The same amount of each is needed if I read that correctly.
Answer:
C) 3 5/12
Step-by-step explanation:
which is the right one???
Ston:A
ep-by-step explnswer:
anati
Hannah has a bag that contains orange chews, lemon chews, and lime chews. She performs an experiment. Hannah randomly removes a chew from the bag, records the result, and returns the chew to the bag. Hannah performs the experiment 74 times. The results are shown below:
An orange chew was selected 39 times.
A lemon chew was selected 17 times.
A lime chew was selected 18 times.
Based on these results, express the probability that the next chew Hannah removes from the bag will be orange chew as a decimal to the nearest hundredth.
Based on these results, probability that the next chew Hannah removes from the bag will be orange chew is 0.53.
What is the probability of picking an orange chew?Probability determines how likely it is that event would occur. The probability that an event would occur lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
The probability of picking an orange chew = 39 / 74 = 0.53
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5kg of food is £45 jim buys 3kg how much does it cost
Marissa Palmer's charge account statement showed a previous balance of $142.55, a finance charge of $2.82, new purchases of $56.22 and $30.28, and a payment of $80.00. What is her new balance?
Answer:
Marissa Palmer owes $26.77
Step-by-step explanation:
142.55
- 2.82
56.22
30.28
80.00
____________
-26.77
there are 36 pupils in mr. castro mathematics class mr. castro wants to seperate the class into equal group for doing an activity. what are the five diffrent ways that the teacher can do to the group he class?
Answer:
He can use the factors of 36 to determine the number of groups he can divide the class into such that they are equal.
The Factors (excluding 1) are;
2, 3, 4, 6, 9, 12, 18
Using these therefore he can divide them;
Into 3 groups each with 12 people.Into 4 groups each with 9 people.Into 6 groups each with 6 people. Into 9 groups each with 4 people. Into 12 groups each with 3 people.one digit even prime numbers
a.finite b. infinite
Answer:
a
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
hope this helps
i took this test
What kind of solution is x+3=2x-18
Step-by-step explanation:
x + 3 = 2x - 18- x = - 21x = 21This is your answer.Suppose that your younger sister is applying for entrance to college and has taken the SATs. She scored at the 85th percentile on the verbal section of the test and at the 96th percentile on the math section of the test. Because you have been studying statistics, she asks you for an interpretation of these values. What would you tell her?
I would tell her that out of all the people who took the verbal section, ___% scored higher than she did and ___ % scored at or below her score. For the math section, ___ % of those who took the exam scored at or below her score and ____ % scored higher than she did.
Answer:
See below
Step-by-step explanation:
Score at the 85th percentile on the verbal section of the testScore at the 96th percentile on the math section of the testBased on this info filling in the gaps
I would tell her that out of all the people who took the verbal section, _15__% scored higher than she did and _85__ % scored at or below her score. For the math section, _96_ % of those who took the exam scored at or below her score and _4_ % scored higher than she did.Which statement correctly describes the expression 19 · 3?
Answer:
Both factors are positive, so the product will be positive.
Step-by-step explanation:
no option available here so I hope
(Both factors are positive, so the product will be positive.)
bcz 19 · 3 are positive factors nd there product will be also postive
[tex] \bold {19 \times 3 = 57}[/tex]
All the best!
Every conditional has two parts. The part following "IF" is the ____ and the part following "THEN" is the ____.
Answer:
hypothesis is the answer for the fist blank
Step-by-step explanation:
5 - (x + 5) > -2(x+4)
Answer:
5-(1+5)= -1
-2(1+4)=-10
Step-by-step explanation:
Answer:
x>16
Step-by-step explanation:
5-(x+5) cancels out to just x
Use a net to find the surface area of the right triangular prism shown:
(I’ll give you 50 points)
The surface area of the right triangular prism is 270 sq ft
Total surface ara of the prismThe total surface area of the prism is the sum of all the area of its faces
For the two triangles
A = 2(0.5bh)
A = bh
A = 7 * 12 = 84 sq.ft
For the two rectangles
A = 2lw
A = 2(6*12)
A = 2 * 72 = 144 sq.ft
For the third triangle;
Area 6ft * 7ft
Area = 42 sq.feet
Taking the sum of the areas
TSA = 84 + 144 + 42
TSA = 270 sq ft
Hence the surface area of the right triangular prism is 270 sq ft
Learn more on surface area of prism here; https://brainly.com/question/1297098
NO LINKS!!!
Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Don't use a calculator. This is NOT MULTIPLE CHOICE!!
a. sin (405°)
b. cot (390°)
c. cos (33π/4)
d. sec (17π/4)
c.
[tex]\\ \rm\rightarrowtail sin(405)[/tex]
[tex]\\ \rm\rightarrowtail sin(360+45)[/tex]
[tex]\\ \rm\rightarrowtail sin45[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{1}{\sqrt{3}}[/tex]
#2
[tex]\\ \rm\rightarrowtail cot(390)[/tex]
[tex]\\ \rm\rightarrowtail cot(360+30)[/tex]
[tex]\\ \rm\rightarrowtail cot30[/tex]
[tex]\\ \rm\rightarrowtail \sqrt{3}[/tex]
#3
[tex]\\ \rm\rightarrowtail cos(33\pi/4)[/tex]
[tex]\\ \rm\rightarrowtail cos(8\pi+\pi/4)[/tex]
[tex]\\ \rm\rightarrowtail cos\pi/4[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{1}{\sqrt{2}}[/tex]
#4
[tex]\\ \rm\rightarrowtail sec(17\pi/4)[/tex]
[tex]\\ \rm\rightarrowtail sec(4\pi +\dfrac{\pi}{4})[/tex]
[tex]\\ \rm\rightarrowtail sec\dfrac{\pi}{4}[/tex]
[tex]\\ \rm\rightarrowtail \sqrt{2}[/tex]
Answer:
[tex]\sin(405)=\dfrac{\sqrt{2}}{2}[/tex]
[tex]\cot(390)=\sqrt{3}[/tex]
[tex]\cos\left(\dfrac{33}{4}\pi\right)=\dfrac{\sqrt{2}}{2}[/tex]
[tex]\sec\left(\dfrac{17}{4}\pi\right)=\sqrt{2}[/tex]
Step-by-step explanation:
Trig identities used:
[tex]\sin(A\pm B)=\sin A \cos B \pm \cos A \sin B[/tex]
[tex]\cos(A \pm B)=\cosA \cos B \mp \sin A \sin B[/tex]
[tex]\tan(A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}[/tex]
[tex]\cot A=\dfrac{1}{\tan A}[/tex]
[tex]\sec A=\dfrac{1}{\cos A}[/tex]
Standard trig angles
[tex]\sin(0 \pm 360n)=\sin(0 \pm 2 \pi n)=0\\\\\cos(0 \pm 360n)=\cos(0 \pm 2 \pi n)=1\\\\\tan(0 \pm 180n)=0\\\\\sin(45 \pm 360n)=\sin(\frac14 \pi \pm 2\pi n)=\dfrac{\sqrt{2}}{2}\\\\\cos(45 \pm 360n)=\cos(\frac14 \pi \pm 2\pi n)=\dfrac{\sqrt{2}}{2}\\\\\tan(30 \pm 180n)=\dfrac{\sqrt{3}}{3}[/tex]
Question a
[tex]\sin (405) = \sin (360 + 45)[/tex]
[tex]= \sin(360)\cos(45) + \cos(360)\sin(45)[/tex]
[tex]=0 \cdot \dfrac{\sqrt{2}}{2}+1 \cdot \dfrac{\sqrt{2}}{2}[/tex]
[tex]=\dfrac{\sqrt{2}}{2}[/tex]
Question b
[tex]\cot(390)=\dfrac{1}{\tan(390)}[/tex]
[tex]=\dfrac{1}{\tan(360+30)}\\\\[/tex]
[tex]=\dfrac{1-\tan(360) \tan(30)}{\tan(360)+\tan(30)}[/tex]
[tex]=\dfrac{1-0 \cdot \frac{\sqrt{3}}{3}}{0+\frac{\sqrt{3}}{3}}[/tex]
[tex]=\dfrac{1}{\frac{\sqrt{3}}{3}}[/tex]
[tex]=\sqrt{3}[/tex]
Question c
[tex]\cos\left(\dfrac{33}{4}\pi\right)=\cos(8\pi+\frac14\pi)[/tex]
[tex]=\cos(8\pi)\cos(\frac14\pi)}-\sin(8\pi)\sin(\frac14\pi)}[/tex]
[tex]=1 \cdot \dfrac{\sqrt{2}}{2}-0 \cdot \dfrac{\sqrt{2}}{2}[/tex]
[tex]=\dfrac{\sqrt{2}}{2}[/tex]
Question d
[tex]\sec\left(\dfrac{17}{4}\pi\right)=\dfrac{1}{\cos(4\pi+\frac14\pi)}[/tex]
[tex]=\dfrac{1}{\cos(4\pi)\cos(\frac14\pi)-\sin(4\pi)\sin(\frac14\pi)}}[/tex]
[tex]=\dfrac{1}{1 \cdot \dfrac{\sqrt{2}}{2} -0 \cdot \dfrac{\sqrt{2}}{2}}[/tex]
[tex]=\dfrac{1}{\dfrac{\sqrt{2}}{2} }[/tex]
[tex]=\sqrt{2}[/tex]
Belle bought an aquarium priced at $90. Shipping and handling cost an additional 10% of the price. What was the total cost of the aquarium, including shipping and handling?
1
Caleb finishes breakfast at 7:15 AM. Tell
what time he started breakfast if it took
the given number of minutes.
a. 10 minutes
b. 15 minutes
C. 20 minutes
d. 25 minutes
e. 26 minutes
Beth won 53 pieces of gum playing basketball at her school's game night. Later, she gave two to each of her friends. She only has 3 remaining. How many friends does she have?
What is the mean of this data set?
{14, 7, 2, 8, 3}
Enter your answer as a decimal in the box.
Answer:
Mean = 6.8
Step-by-step explanation:
Given data set :-
{14, 7, 2, 8, 3}
To find :-
Mean
Solving :-
Take sum of given data and divide by number of data pieces.
=> 14 + 7 + 2 + 8 + 3 / 5
=> 34 / 5
=> 6.8
Solution :-
Mean = 6.8
Given set of data :
{ 14,7,2,8,3 }To find :
Mean = ?Solution :
[tex] \qquad \sf \to \: mean = \frac{sum \: of \: observations}{total \: no. \: of \: observations} [/tex]
Total number of observations = 5[tex] \qquad \tt\longmapsto\: mean = \frac{14 + 7 + 2 + 8 + 3}{5}[/tex]
[tex] \qquad \tt\longmapsto\: mean = \frac{34}{5}[/tex]
[tex] \qquad \tt\longmapsto\: mean = 6.8[/tex]
[tex]-(a+b)+a[/tex]
Its so hard please help me quickly
Answer:
-b
Step-by-step explanation:
❖ Step 1: Apply distributive property.
[tex](-1)(a) + (-1)(b)+a[/tex] [tex]-a-b+a[/tex]❖ Step 2: Combine like terms.
[tex](-a+a)+(-b)[/tex] [tex]-b[/tex]Therefore, the answer is -b.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
In the game of Pick-A-Ball, there are 10 colored balls: 2 red, 4 white, and 4 blue. The balls have been placed into a small bucket, and the bucket has been shaken thoroughly. You will be asked to reach into the bucket without looking and select 2 balls. Because the bucket has been shaken thoroughly, you can assume that each individual ball is selected at random with equal likelihood of being chosen. It is common in games of chance to be rewarded for obtaining unlikely results. For example, in the game of poker, hands that are less likely to occur tend to trump hands that are more likely to occur. That same concept applies in this game. It costs $10 to play Pick-A-Ball, and your prize is the reciprocal of the probability of obtaining your exact sequence of results, expressed in dollars. For example, if the probability of obtaining your exact sequence of results is 0.10, your prize is 1/0.10
Required:
What is the probability of selecting the color of ball that you just selected?
Answer:
The probability of selecting the color of ball that you just selected(a red ball) is [tex]P(r) = \frac{2}{10}[/tex]
Step-by-step explanation:
From the question we are told that
The total number of colored balls is n = 10
The number of red balls is r = 2 red
The number of white ball is w = 4
The number of blue balls is b = 4
The number of balls to be selected is N = 2 balls
The cost of playing picking a ball is c = $10
The winnings is [tex]k = \$ P(A)[/tex]
Here P(A) is the probability of obtaining the exact sequence of result and from the question it is P(A) = 0.10
Generally my price according to the question is
[tex]k = \frac{0.10 }{10}[/tex]
=> [tex]k = 0.01 [/tex]
Let assume we selected a red ball
Generally the probability of selecting a red ball is mathematically represented as
[tex]P(r) = \frac{2}{10}[/tex]
(a lot of points) just show work please: 18x^2y^2−24xy^2+36y^2
Answer:
[tex]6y^2(3x^2-4x+6)[/tex]
Step-by-step explanation:
I'm assuming that you wanted us to factor the equation.
[tex]18x^2y^2 - 24xy^2+36y^2\\= 6y^2(3x^2-4x+6)[/tex]
The function within the parentheses doesn't factor anymore. Hope this is what you needed!
7 Jamila has a large toy box and a small toy box The large box is 120 cm long and 90 cm high. Each length of the small box is one-sixth the length of the large box
Write the length and height of the small box. Show your working
LENGTH of small box: .......cm
HEIGHT of small box: ......cm
Answer:
length = 20 cm
height = 15 cm
Step-by-step explanation:
Large Toy Box
length = 120 cmheight = 90 cmGiven:
Each length of the small toy box is one sixth of the corresponding lengths of the large toy box.Therefore, to calculate the length and height of the small toy box, multiply the length and height of the large toy box by one sixth:
[tex]\sf length=120 \times \dfrac16=\dfrac{120 \times 1}{6}=\dfrac{120}{6}=20 \ cm[/tex]
[tex]\sf height=90 \times \dfrac16=\dfrac{90 \times 1}{6}=\dfrac{90}{6}=15 \ cm[/tex]
Therefore,
length = 20 cmheight = 15 cmAnswer:
length = 20 cm , height = 15 cm
Step-by-step explanation:
calculate [tex]\frac{1}{6}[/tex] of the dimensions by dividing the large box dimensions by 6
length of small box = 120 cm ÷ 6 = 20 cm
height of small box = 90 ÷ 6 = 15 cm
Finding the surface area of a right triangular prism
Answer:
The formula that is used to calculate the surface area of a triangular prism is, Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh; where 'b' is the bottom edge of the base triangle, 'h' is the height of the base triangle, L is the length of the prism and S1, S2 and S3 ...
Can someone help me how to solve this please
200/50*17/2*5/17*50
Answer:
500
Step-By-Step Explanation:
200/50 = 4
4 * 17 = 68
68 / 2 = 34
34 x 5 = 170
170 / 17 = 10
10 x 50 = 500
Jake joins a soccer club. There is a registration fee of $35 dollars and a charge of $60 a month. If m is the number of months that Jake plays in the club and c is the total amount he pays, write an equation to represent the relationship between c and m.
60m + 35 = c
hope that helps :)
The volume of two spheres are in the ratio 27:125. What is the ratio of their areas?
The volume of two spheres are in the ratio 27:125. The ratio of their areas is 9:25
If the volume of two spheres are in the ratio 27:125, then the ratio of their areas is 9:25.
How to compute the above ratioThe ratio of the volumes of two spheres is equal to the ratio of the cubes of their radii.
Therefore, if the volume ratio is 27:125, the radius ratio would be the cube root of that, which is 3:5.
The surface area of a sphere is given by the formula A = 4πr², where A is the surface area and r is the radius.
Since the radius ratio is 3:5, the ratio of their surface areas would be (3/5)² : 1², which simplifies to 9:25.
Therefore, the ratio of the surface areas of the two spheres is 9:25.
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I need to find the length
Answer:
5.5
Step-by-step explanation:
I need help with questions 4-9 please and thank you
Answer:im not sure but i thinkk its like this
Step-by-step explanation:
You use the distributive property so
4. 16
5. 18
in numbre six you multuply 6x5 and 5x5 then you add it and its 55
6.55
7.6
8.39
9.17
when sunayana leaves for school the temperature is 12 degree celcius. By midday it is 26 degree celcius. How many degree has the temperature risen?
Answer:
14 degree
Step-by-step explanation:
First you will substrate 26 from 12 and the final result is 14