Answer:
[tex]19.22\:<\:\mu\:<\:44.78[/tex]
Step-by-step explanation:
Tthe population is normally distributed and the sample size is [tex]n=22\:<\:30[/tex].
Since the population standard deviation [tex]\sigma[/tex] is unknown and the sample standard deviation [tex]s[/tex], must replace it, the t distribution must be used for the confidence interval.
Hence with degrees of freedom of 21, [tex]t_{\frac{\alpha}{2} }=3.527[/tex].(Read from the t distribution table)
The 98% confidence interval can be constructed using the formula:
[tex]\bar X-t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n} } )\:<\:\mu\:<\:\bar X+t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n} } )[/tex].
From the question the sample mean is [tex]\bar X=32[/tex]dollars and the sample standard deviation is [tex]s=17[/tex] dollars.
We substitute the values into the formula to get
[tex]32-3.527(\frac{17}{\sqrt{22} } )\:<\:\mu \:<\:32+3.527(\frac{17}{\sqrt{22} } )[/tex]
[tex]19.22\:<\:\mu\:<\:44.78[/tex]
Therefore, we can be 98% confident that the population mean is between is between 19.22 and 44.78 dollars.
A pizza restaurant charges for each pizza and adds a delivery fee. The cost (c), in dollars, to have any number of pizzas (p) delivered to a home is described by the equation c = 11p + 5.
Each pizza costs $5 and the delivery fee is $11
The cost of 11 pizzas is $16
Each pizza costs $11 and the delivery fee is $5
The cost of 5 pizzas is $11
Answer:
Each pizza costs $11 and the delivery fee is $5
Step-by-step explanation:
We assume you want an interpretation of the equation.
The total cost of an order is the sum of any fixed cost (such as a delivery fee) and the variable cost.
Here, the variable cost is the cost of some number of pizzas. It is proportional to the number of pizzas. In the equation, it is represented by 11p, where p is the number of pizzas. The cost of each pizza must be $11, since the cost of p pizzas is 11p.
The equation's two parts are a fixed cost of $5 and a variable cost of $11 per pizza. The best description is ...
Each pizza costs $11 and the delivery fee is $5
The cost (c) to have any number of pizzas (p) delivered is calculated using the equation c = 11p + 5. This implies that each pizza costs $11 and the delivery fee is $5.
Explanation:The question involves the concept of linear equations in mathematics. In this particular case, the equation is c = 11p + 5. This equation denotes the cost (c) of pizzas delivered where each pizza prices ($11 each) is multiplied by the number of pizzas (p) and then added to the delivery fee ($5). Therefore, the third option, 'Each pizza costs $11 and the delivery fee is $5' is the correct interpretation of the equation.
To find out the cost of any number of pizzas, you would substitute that number in for 'p' in the equation. For instance, the cost of 5 pizzas would be calculated as 5 * $11 + $5 = $60.
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In the triangles, and .
Which statement correctly compares and ?
and are the same length.
is longer than .
is shorter than .
is shorter than or the same length as .
Answer:
answer is B just got 100%
Step-by-step explanation:
Jace has consumed 1,500 calories so far today. He has also burned off 400 calories at the gym. He would like to keep his daily calorie total to 1,900 calories per day. How many calories does he have left to consume for the day? Is 1,100 a viable solution to this problem?
===================================
Yes; 1,100 is less than 1,500.
No; 1,100 is more than the 400 he burned off at the gym.
No; 1,100 will cause him to exceed 1,900.
Yes; 1,100 is less than 1,900
Answer:
No, it will cause him to exceed 1900.
Step-by-step explanation:
1,500 - 400 = 1,100 (his total after the gym)
1,100 + 1,100 exceeds 1,900. He wants to keep his total below 1,900, so this is not a viable solution.
Answer:
No; 1,100 will cause him to exceed 1,900.
Step-by-step explanation:
The rationale for this problem is basic.
Jace established a diet restricted to 1900kcal.
If he started 1500kcal and burned 400kcal in the gym, Jane's partial jump is 1100 calories.
Thus, it can still eat the total of 1900-100 = 800kcal.
Any value over 800kcal will exceed the tax threshold and will disrupt Jane's results.
To the nearest tenth the value of x that satisfies 2x = −2x + 11 is
Answer:
2.8 (from 2.75 because of rounding)
Step-by-step explanation:
2x = -2x + 11
Add 2x on both sides
4x = 11
Divide 4 on both sides
x = 11/4
x = 2.75
Round to nearest tenth
x is about 2.8
Please mark me for brainliest :D !! Thanks!
Answer:
x = 2.8
Step-by-step explanation:
2x = - 2x + 11 Add 2x to both sides.
2x+2x = -2x+2x + 11 Combine
4x = 11 Divide by 4
4x/4 = 11/4
x = 2 3/4
x = 2.75
Rounded to the 10th place, you would get 2.8
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. A survey with a two-point scale was conducted in an organization. It concluded that 85% of the respondents were unsatisfied with the career guidance they were provided. If 2,000 people participated in the survey, people were satisfied with the career guidance. Reset Next
Answer:
300 people were satisfied
Step-by-step explanation:
If 85% were unsatisfied, we assume the remaining 15% were satisfied. That percentage of 2000 is ...
0.15×2000 = 300
Answer:
300
Step-by-step explanation:
PLATO
To solve this system of equations by elimination, what operation could be used to eliminate the y-variable and find the value of x? 2x ? 4y = 6 ?3x + 3y = 9 A) add 3 times the second equation to 4 times the first equation B) add 4 times the second equation to 3 times the first equation C) subtract 3 times the second equation from 4 times the first equation D) subtract 4 times the second equation from 3 times the first equation
Step-by-step explanation:
4y=6 (first equation)
3x+3y=9(second equation)
we know if a=a, a+x=a+x,ax=ax
now we add 3 times
4y=6(=)12y=18
now add 4 times
12x+12y=36
now we can eliminate the y and will be
12x=18
x=1,5
2x=3
In order to avoid a training violation, 85% of your store's employees must complete diversity training by the end of the week. You have 142 employees at your store and 91 have currently completed the training. How many more employees must complete the training by the end of the week to avoid a training violation? 15 20 25 30 45
Multiply the number of total employees by 85%:
142 x 0.85 = 120.7, round to 121
121 total people need to complete the training.
Now subtract the number of people who already took the training:
121 - 91 = 20
20 more people need to take it.
Situation:
Find the age of the skull to the nearest year,
Enter the correct answer.
A hiker in Africa discovers a skull that
contains 32% of its original amount of C-
14.
DONE
N = Noekt
00000
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
K = 0.0001
t = time, in years
Answer:
11,394 years old
Step-by-step explanation:
The equation looks like this:
[tex]N=N_{0}e^{kt}[/tex]
The only thing left up to us is to decide what value should go in for N. Since we are told that 32% of the original amount is what the hiker finds, we are operating in percentages. Before any decomposition took place, the amount of skull was 100%. Filling in now we have:
[tex]100=32e^{.0001t}[/tex]
Divide both sides by 32 to get
[tex]3.125=e^{.0001t}[/tex]
In order to get that t out of the exponential position that it is currently in, we will take the natural log of both sides, since a natural log "undoes" an e (that is because the base of a natural log is e). Taking the ln of both sides and utilizing that rule for natural logs and e's gives us:
ln(3.125) = .0001t
Divide both sides by .0001 to get that
t = 11,394 years
Can mutually exclusive events have an intersection of events? Explain your answer
Answer:
no
Step-by-step explanation:
exclusive pertains to one, hence the phrase, exclusive.
Mutually exclusive events or disjoint events are two events that don’t have anything in common. Nothing in common means NO INTERSECTION.
Answer: No!
The results of a common standardized test used in psychology research is designed so that the population mean is 135 and the standard deviation is 30. A subject earns a score of 198. What is the z-score for this raw score?
z-score=
Answer:
2.1
Step-by-step explanation:
Mean+z score(Standard deviation)=raw score
Let the z score be z
135+z(30)=198
30z=63
z=2.1
The z-score is a measure of how many standard deviations a score is from the mean. In this case, where the test was designed with a mean of 135 and a standard deviation of 30, a score of 198 results in a z-score of 2.1.
Explanation:The z-score represents how many standard deviations an element is from the population mean. In this particular case, the results of a standardized test designed with a population mean of 135 and a standard deviation of 30 are given. A subject has a test score of 198.
To calculate the z-score, you use the formula: z = (X - μ) / σ. Where X is the score, μ is the mean, and σ is the standard deviation.
Substitute the given values into the formula:
z = (198 - 135) / 30
z = 2.1
So a test score of 198 would yield a z-score of 2.1.
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A coin is tossed and a single die is rolled. What is the probability that the coin shows heads and the die shows a 3 or a 4?
Answer:
1/6
Step-by-step explanation:
landing on heads is a 1/2% and landing on a 3 or 4 is a 1/3 then multiply together
Based on the model N(1154,81) describing steer weights, what are the cutoff values for
a) the highest 10% of the weights?
b) the lowest 20% of the weights?
c) the middle 40% of the weights?
Find the measure of angle ABC.
A. 124
B. 97
C. 56
D. 51
Answer D. 51
Step-by-step explanation:
Sum of the interior angles of a triangle is up to 180
.: 32+(2x-15) + (x-5) = 180
Group like terms
2x+x =180 - 32 + 15 + 5
When - and + sign cross equal sign it turns to the opposite
3x = 168
x= 168/3
.: X =56
Now put x = 56 in (x - 5)
Angle ABC = 51
Since BC is parallel to DE, triangles ABC and ADE are similar. What are the lengths of the unknown sides?
A. AC = 14 cm; CE = 8 cm
B. AC = 12 cm; CE = 7 cm
C. AC = 10 cm; CE = 5 cm
D. AC = 5 cm; CE = 10 cm
Answer:
C
Step-by-step explanation:
Step 1: find BC
Given Triangles ABC and ADE are similar,
[tex]\frac{AB}{AD}[/tex] = [tex]\frac{BC}{DE}[/tex]
BC = [tex]\frac{AB}{AD}[/tex] x DE
= [tex]\frac{8}{8 + 4}[/tex] x 9
= 6 cm
Step 2: use Pythagorean theorem to find AC and / or AE
Consider triangle ABC,
by Pythagorean theorem,
AB² + BC² = AC²
AC² = 6² + 8² = 100
AC = √100 = 10 (answer... we can see that C is the only one with AC=10.
Step 3: Verify.. even though we know that it is C because AC = 10, you can verify that the ansewer is correct by finding CE and confirming that CE=5
By using similar triangles ABC and ADE,
AC/AE = AB / AD
AE = AD/AB x AC = 12/8 x 10 = 15
CE = AE - AC = 15 - 10 = 5 (answer confirmed)
Which set of boxes containing tiles with the letters A, B, C, and D meet the following conditions?
In Box 1, P(A) > P(B)
In Box 2, P(B) + P(C) + P(D) = 1
In Box 3, P(D) = 2P(C)
Answer:
your choice is correct
Step-by-step explanation:
In your selected set of boxes, ...
Box 1 has p(A) = 2/6 > p(B) = 1/6
Box 2 contains only B, C, and D.
Box 3 has P(D) = 4/6 = 2*P(C) = 2*2/6
I DONT WANT TO FAIL!!!! PLEASE HELP ME WITH THE CORRECT ANSWER, WILL MARK AS BRAINLIEST!!!
What is the solution to the system of linear equations? {4x+3y=543x+9y=108 Enter your answer in the boxes.
Answer:
x = -24
y = 66
Step-by-step explanation:
12x+9y = 102
12x+16y = 432
---------------------
y = 66
4x + (66*3) = 102
198-102 = -96
-96 / 4 = -24
Answer:
solution is [tex](6,10)[/tex]
Step-by-step explanation:
[tex]4x+3y=54[/tex]
[tex]3x+9y=108[/tex]
WE use elimination method to solve for x and y
Multiply the first equation by [tex]-3[/tex]
[tex]-12x-9y=-162[/tex]
[tex]3x+9y=108[/tex]
Now add both the equations, we will get
[tex]-9x=-54[/tex]
Divide by [tex]-9[/tex] on both sides
[tex]x=6[/tex]
Now we plug in the x value in first equaiton and find out y
[tex]4x+3y=54[/tex]
[tex]4(6)+3y=54[/tex]
[tex]24+3y=54[/tex], subtract 24 on both sides
[tex]3y=30[/tex]
Divide both sides by 3
[tex]y=10[/tex]
So solution is [tex](6,10)[/tex]
Need help with a math question PLEASE HELP
Answer:
57%
Step-by-step explanation:
From the table you can state that:
the total number of students is 10,730the number of students receiving Finincial Aid is 6,101Use the definition of the probability
[tex]Pr=\dfrac{\text{The number of favorable outcomes}}{\text{The number of all possible outcomes}}[/tex]
So,
the number of favorable outcomes = 6,101the number of all possible outcomes = 10,730Hence, the probability is
[tex]Pr=\dfrac{6,101}{10,730}\approx 0.5685\approx 57\%[/tex]
sherrie is baking a pie for her family. she leaves the room and comes back to 35% of the pie having been eaten before she can put the topping on. how much 1 square inch strips of dough will she need for the top, now that a portion is missing? round your answer to the nearest while nimber.
Answer:
131
Step-by-step explanation:
We need to find the area of the top of the pie that is leftover. To do this, we use the formula for the area of a circle and multiply by 0.65 since that is how much of the pie is left.
A = 0.65π[tex]r^{2}[/tex] = 0.65π[tex]8^{2}[/tex] = 130.69025 [tex]in^{2}[/tex]
If each strip of dough is 1 square inch, the total strips of dough needed is 131.
The total strips of dough needed is 131 if Sherrie is baking a pie for her family. she leaves the room and comes back to 35% of the pie.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have:
Sherrie is baking a pie for her family. she leaves the room and comes back to 35% of the pie having been eaten before she can put the topping on.
Area of circle:
A = 0.65πr² = 0.65π(8)²
A = 130.69025 square inches ≈ 131 square inches
If each strip of dough is 1 square inch
The total strips of dough needed = 131/1 = 131
Thus, the total strips of dough needed is 131 if Sherrie is baking a pie for her family. she leaves the room and comes back to 35% of the pie.
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please Simplify 3^2x3^3
Answer:
[tex]243[/tex]
Step-by-step explanation:
[tex]3^2*3^3 = 9 * 27[/tex]
[tex]9 * 27 = 243[/tex]
Answer:
243
Step-by-step explanation:
[tex]3^2*3^3[/tex]
To solve your equation, employ the use of PEMDAS.
According to PEMDAS, exponents come before multiplication, so we can simply the 3 squared and the 3 cubed first.
3 squared is the same as 3 x 3, which is 9.
3 cubed is the same as 3 x 3 x 3, which is 27.
Thus, our new equation is
[tex]9*27[/tex]
Simply do the multiplication and you have your simplified answer.
[tex]9*27=243[/tex]
How to find the legs of a right triangle with only the hypotenuse?
Let x = legs of right triangle.
The set up would be:
x^2 + x^2 = (hypotenuse)^2
Understand?
To find the legs of a right triangle with only the hypotenuse known, the Pythagorean theorem is used. Without extra information like an angle or one leg length, it's impossible to find the specific leg lengths due to the infinite possibilities of right triangle configurations with the same hypotenuse length.
The question involves finding the lengths of the legs of a right triangle when only the length of the hypotenuse is known. Utilizing the Pythagorean theorem, which states that in a right triangle the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), expressed as a² + b² = c². To find the lengths of the legs (a and b) given the hypotenuse (c), one needs additional information such as the angle of the triangle or the length of one of the legs.
Without such information, it is not possible to determine the specific lengths of the legs because there are infinitely many right triangles with different sets of leg lengths that could have the same hypotenuse length. Therefore, to address this problem, one might use trigonometry if any angle is known, or apply other relevant context or given data.
A square prism has a height of 15 centimeters and a volume of 960 cubic centimeters. What is the measure of the width of the square base
Answer:
8
Step-by-step explanation:
Because if you do 15•8•8 then it equals 960 and the formula for volume is l•w•h
What is the surface area of the regular pyramid below
Answer:
C. 864 units²Step-by-step explanation:
We have the square in the base and four triangles on the lateral surface.
The formula of an area of a square:
[tex]A_{\square}=a^2[/tex]
a - side lenght
We have a = 16. Substitute:
[tex]A_{\square}=16^2=256[/tex]
The formula of an area of a triangle:
[tex]A_{\triangle}=\dfrac{bh}{2}[/tex]
b - base
h - height
We have b = 16 and h = 19. Substitute:
[tex]A_{\triangle}=\dfrac{(16)(19)}{2}=152[/tex]
The Surface Area:
[tex]S.A.=A_{\square}+4_{\triangle}[/tex]
Substitute:
[tex]S.A.=256+4(152)=256+608=864[/tex]
Answer: it C. 864 units²
Step-by-step explanation: I just did it
Problem: an old book listed that 72 turkeys were bought for $\$\square.\square\square$ each, at a total cost of $\$\square 67.9\square.$ what was the cost of each turkey, if each $\square$ stands for a digit that was unreadable in the old book
Answer:
72 turkeys were bought at $5.11 each for a total cost of $367.92.
Step-by-step explanation:
Trial and error isn't so difficult for this problem. The final price will be an even number of cents. Without those pennies added, the price per turkey must be below an integer number of cents, but within 1/8 cent of that integer number.
167.90/72 = 2.3319... (too high)267.90/72 = 3.7208... (too high)367.90/72 = 5.1097... good candidate467.90/72 = 6.4986... (too low)567.90/72 = 7.8875 (too low)667.90/72 = 9.2763... (too low)For higher first digits of the total cost, the per-turkey cost is more than 3 digits.
For our "good candidate", the per-turkey cost will be $5.11, so the total bill will be $5.11×72 = $367.92 . . . . matches the required digits.
Five friends are going to the theater. They have purchased a row of five seats with an aisle on either end. James doesn't want to sit next to Jill Betty and Herb are dating and want to sit next to each other Bob must sit on an aisle Provide a seating order that conforms to the above rules. An example of an invalid seating order is: James, Betty, Herb, Bob, Jill The above arrangement is invalid because: Bob is not sitting on an aisle. Specify the seating order as the names separated by s (as in the above example). Please be sure to spell the names correctly, including capitalization.
Answer:
Bob, Jill, Betty, Herb, James
Final answer:
A valid seating arrangement for the five friends is either Bob, Betty, Herb, James, Jill, or Jill, James, Herb, Betty, Bob. Each arrangement adheres to all given conditions: Bob is on an aisle, Betty and Herb are seated together, and James is not sitting next to Jill.
Explanation:
To solve the seating problem for the five friends going to the theater, we must adhere to the conditions: Bob must sit on an aisle, James cannot sit next to Jill, and Betty and Herb want to sit next to each other. Bearing in mind that there's an aisle on either side of the row of five seats, we can begin by placing Bob on an aisle seat since he must sit on one. This can either be the first seat on the left or the right. Since James doesn't want to sit next to Jill, we can't place Jill next to Bob if we sit James on the other end to maximize distance between them. Betty and Herb must sit together, which can only happen in the three seats left in the middle.
Here is a seating arrangement that satisfies all conditions: Bob, Betty, Herb, James, Jill. In this arrangement, Bob is on an aisle, Betty and Herb are seated together, and James is not sitting next to Jill.
Alternatively, if we place Bob on the other aisle, we get: Jill, James, Herb, Betty, Bob. Again, all conditions are met. Bob is on an aisle, Betty and Herb are sitting together, and James is not sitting next to Jill.
please help asap will mark brainlest
Answer: -79, 21, 46, 80
Step-by-step explanation:
-79, 21, 46, 80
79 is a negative number making it the smallest. After -79 just order the numbers in the consecutive order of how you count.
Hope this helped!
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PLEASE HELP ASAP I WILL MARK BRAINLIEST!! If measures 65°, what is the measure of WZ?
Answer:
180-65=115
Step-by-step explanation:
Straight line always measures 180 degrees, take 180 and subtract 65 thats your answer.
Answer:
115 dude
Step-by-step explanation:
you just substract 65 with 180 and then you get 115
Please help me with this last part. The other parts are fine.
These percentiles on small data sets are confusing. We have 8 data points. So the median is the average of the 4th and 5th.
The upper quartile, 75th percentile, is between the 6th and 7th data point of the 8. I calculated its index as (8-1)*.75=6.25. One definition of upper quartile has us just pick the next one up, 36 here. Another definition has us interpolate. Since 6.25 = (3/4) 6 + (1/4) 7 we take (3/4) 33 + (1/4) 36 = 33.75 as a 75th percentile. It's hard for me to choose without knowing what you were taught.
Need help with a math question
Answer:
0.000032,0.00000.64
Step-by-step explanation:
For this case, it can be observed that the sequence is performed by multiplying each term by 0.2:
We have to:
[tex]0.1 * 0.2 = 0.02\\0.02 * 0.2 = 0.004\\0.004 * 0.2 = 0.0008\\0.0008 * 0.2 = 0.00016\\0.00016 * 0.2 = 0.000032\\0.000032 * 0.2 = 0.0000064[/tex]
Answer:
The next terms are:
[tex]0.000032\\0.0000064[/tex]
A musician begins performing concerts. His first concert had 500 people attending. The musician says that if attendance grows by 5% every concert, there will be 650 people at his third concert. Explain why the musician's prediction is incorrect.
Answer:551.25
Step-by-step explanation:
500 x .05 =25+500= 525 which is the second concert. Multiply that by .05 which is 26.25, add that to 525 to get 551.25 which is not 650.
A cricketer has a mean 58 runs in nine innings.Find out how many runs are to be scoredin the 10th inningd to raise the mean scroce to 61.
Answer:
88
Step-by-step explanation:
Nine innings have a mean of 58 runs, and the tenth inning will have x runs. So the overall mean is:
μ = (9×58 + x) / 10
We want the mean to be 61, so:
61 = (9×58 + x) / 10
610 = 522 + x
x = 88
The cricketer must score 88 runs to raise the mean to 61.