Solve for the length of the unknown side in the following right triangle. (Side AC is the hypotenuse.)
Round your answer to two places, where applicable.
Side AB 3 Side BC 4 Side AC ?
Answer:
side AC is 5
Step-by-step explanation:
by using th pythagorean theorm you would square both sides add them together and the square root the sum to get you answer.
AB =3 BC=4
9+16=25
25 square root is 5
makeing AC=5
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s = 17.6 milligrams.
Required:
Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.
Answer:
CI ≈ (173.8 < μ < 196.2)
Step-by-step explanation:
We are told that laboratory tested twelve chicken eggs. Thus;
n = 12
Mean; x¯ = 185 mg
S.D; s = 17.6 mg
DF = n - 1 = 12 - 1 = 11
We have a 95% confidence level. Thus; α = 0.05
Since n < 30, we will use t-sample test.
Thus, from t-table attached at 95% Confidence level and DF = 11, we have;
t = 2.201
Thus,formula for Confidence interval is;
CI = (x¯ - t(s/√n)) < μ < (x¯ + t(s/√n))
CI = (185 - 2.201(17.6/√12)) < μ < (185 + 2.201(17.6/√12))
CI = (185 - 11.1825) < μ < (185 + 11.1825)
CI = (173.8175 < μ < 196.1825)
CI ≈ (173.8 < μ < 196.2)
A sample of 13 sheets of cardstock is randomly selected and the following thicknesses are measured in millimeters. Give a point estimate for the population standard deviation. Round your answer to three decimal places. 1.96,1.81,1.97,1.83,1.87,1.84,1.85,1.94,1.96,1.81,1.86,1.95,1.89
===============================================
Explanation:
Add up the values to get
1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54
Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.
So the mean is approximately 1.8876923
---------------------
Now make a spreadsheet as shown below
We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.
After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.
That sum is approximately 0.04403076924
Next, we divide that over n-1 = 13-1 = 12
0.04403076924 /12 = 0.00366923077
That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.
sqrt(0.00366923077) = 0.06057417576822
This rounds to 0.061 which is the final answer.
The sum of one and three times a number is -89. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
The equation is
B) Solve your equation in part [A] for
Answer:
A. 1 + 3x = -89
B. x = -30
Step-by-step explanation:
Let the unknown variable be x.
A. Translating the word problem into an algebraic expression, we have;
1 + 3x = -89
B. To solve for the unknown variable;
1 + 3x = -89
3x = -89 -1
3x = -90
x = -90/3
x = -30
Check:
1 + 3x = -89
Substituting the value of x;
1 + 3(-30) = -89
1 + (-90) = -89
1 - 90 = -89
-89 = -89
18 is 65% of what number
Answer:
65% of 27.69 is 18.
Step-by-step explanation:
Formula = Number x 100
Percent = 18 x 100
65 = 27.69
Following shows the steps on how to derive this formula
Step 1: If 65% of a number is 18, then what is 100% of that number? Setup the equation.
18
65% = Y
100%
Step 2: Solve for Y
Using cross multiplication of two fractions, we get
65Y = 18 x 100
65Y = 1800
Y = 1800
100 = 27.69
If an object of mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account is: c= mg/c (1- e^ -ct/m), where g is the acceleration due to gravity and c is a positive constant describing air resistance.
Required:
a. Calculate lim v
t→[infinity]
b. What is the meaning of this limit? (choose from the following options)
1. It is the time it takes the object to reach its maximum speed.
2. It is the speed the object reaches before it starts to slow down.
3. It is the time it takes the object to stop.
4. It is the speed the object approaches as time goes on.
Answer:
a. mg/c b. 4. It is the speed the object approaches as time goes on.
Step-by-step explanation:
a. Calculate lim v as t→[infinity]
Since v = mg/c(1 - e^ -ct/m)
[tex]\lim_{t \to \infty} v = \lim_{t \to \infty} (\frac{mg}{c}[1 - e^{-\frac{ct}{m} } ] )[/tex]
[tex]\lim_{t \to \infty} v =[/tex] mg/c(1 - e^(-c(∞)/m))
[tex]\lim_{t \to \infty} v =[/tex] mg/c(1 - e^(-∞/m))
[tex]\lim_{t \to \infty} v =[/tex] mg/c(1 - e^(-∞))
[tex]\lim_{t \to \infty} v =[/tex] mg/c(1 - 0)
[tex]\lim_{t \to \infty} v =[/tex] mg/c(1)
[tex]\lim_{t \to \infty} v =[/tex] mg/c
b. What is the meaning of this limit?
4. It is the speed the object approaches as time goes on.
This is because, since t → ∞ implies a long time after t = 0, the limit of v as t → ∞ implies the speed of the object after a long time. So, the limit of v as t → ∞ is the speed the object approaches as time goes on.
Eli had mini-golf scores of -3, -4, and -3. What was his total score for the three rounds?
Answer:-10
-3+-4+-3
-3-4=-7
-7+-3=-7-3
=-10
I need to know the answer please
Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.
g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]
Option C
Hope this helps!
Solve for x the find the measure of A
Answer:
84°
Step-by-step explanation:
the total angle in a straight line sum up to 180°
Write the polynomial in standard form. Then name the polynomial based on its degree and number of
terms.
y-7y3 + 15y9
Answer:
[tex]15y^9 - 7y^3 + y[/tex]
Nonic polynomial
Step-by-step explanation:
Given
[tex]y - 7y^3 + 15y^9[/tex]
Required
Write in standard form
The standard form of a polynomial is:
[tex]ay^n + by^{n-1} + ......... + k[/tex]
So, we have:
[tex]y - 7y^3 + 15y^9[/tex]
The standard form is:
[tex]15y^9 - 7y^3 + y[/tex]
And the name is: Nonic polynomial (because it has a degree of 9)
2. Approximately what is the ratio of customers
from Zone 1 to customers from Zone 3?
UA. 3:5
B. 3:2
OÇ. 2:1
D. 1:2
The ratio of customers from Zone 1 to from Zone 3 is 1 : 2
This question appears to be incomplete.
Please find attached the graph required to answer this question
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
The graph is in the image is a bar graph
A bar graph is a pictorial representation of data. The rectangles measure the length of the data
Looking at the graph, the interval is 100
Looking at the rectangle that represents zone 1, it appears to be halfway between 400 and 500. It is concluded that the number of customers in zone 1 is 450
Looking at the rectangle that represents zone 3, it appears to lie on 900.
It can be concluded that there are 900 customers in zone 3
the ratio of zone 1 to 3
450 : 900
to convert to its simplest form, divide both side of the ratio by 450
1 : 2
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F(x)=x+8;g(x)=x+2. Find f=g
Answer:
f(x) can not be equal to g(x)
Step-by-step explanation:
If the result is possible:
f(x) = g(x)
x + 8 = x + 2
x + 8 - (x + 2) = x + 2 - (x + 2)
6 = 0
Because 6 can't be equal to 0, so do f(x) can't be equal to g(x)
In one year the population of
Zebras in the park was 3400. In
the following year the population
reduced by 25%. What was the
size of the population after
reduction?
A hexagonal pyramid is located ontop of a hexagonal prism. How many faces are there?
A. 15
B. 24
C. 6
D. 13
Answer:
15
Step-by-step explanation:
The figure has total 15 faces, the correct option is A.
What is a Hexagon?A hexagon is a polygon with six sides.
A hexagonal pyramid has 8 faces
From (2 hexagonal base + 6 lateral surfaces)
A hexagonal prism has 7 faces
From ( A hexagonal base + 6 lateral faces)
Total faces the figure has is 8 +7 = 15
To know more about Hexagon
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Both before and after a recent earthquake, surveys were conducted asking voters which of the three candidates they planned on voting for in the upcoming city council election. Has there been a change since the earthquake? Use a level of significance of 0.05. Table shows the results of the survey. Has there been a change in the distribution of voter preferences since the earthquake?
Peter Alan Sui
Before 1838 418 1475
After 1420 329 1140
What is the chi-square test-statistic for this data?
χ2=_____.
Answer:
0.05547
Step-by-step explanation:
Given :
_____Peter __ Alan __ Sui__total
Before 1838 __ 418 ___1475 _3731
After _ 1420 __ 329 ___1140_2889
Total _3258 __ 747 __ 2615 _6620
The expected frequency = (Row total * column total) / N
N = grand total = 6620
Using calculator :
Expected values are :
1836.19 __ 421.006 __ 1473.8
1421.81 ___325.994__ 1141.2
χ² = Σ(Observed - Expected)² / Expected
χ² = (0.00177817 + 0.0214571 + 0.000974852 + 0.00229642 + 0.0277108 + 0.00125897)
χ² = 0.05547
The graph shows the distribution of the number of text messages young adults send per day. The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.
A graph titled daily text messaging has number of text on the x-axis, going from 8 to 248 in increments of 30. Data is distributed normally. The highest point of the curve is at 128.
What percentage of young adults send between 68 and 158 text messages per day?
34%
47.5%
81.5%
95%
This value is approximate.
====================================================
Explanation:
We have a normal distribution with these parameters
mu = 128 = population meansigma = 30 = population standard deviationThe goal is to find the area under the curve from x = 68 to x = 158, where x is the number of text messages sent per day. So effectively, we want to find P(68 < x < 158).
Let's convert the score x = 68 to its corresponding z score
z = (x-mu)/sigma
z = (68-128)/30
z = -60/30
z = -2
This tells us that the score x = 68 is exactly two standard deviations below the mean mu = 128.
Repeat for x = 158
z = (x-mu)/sigma
z = (158-128)/30
z = 30/30
z = 1
This value is exactly one standard deviation above the mean
-------------------------------------------
The problem of finding P(68 < x < 158) can be rephrased into P(-2 < z < 1)
We do this because we can then use the Empirical rule as shown in the diagram below.
We'll focus on the regions between z = -2 and z = 1. This consists of the blue 13.5% on the left, and the two pink 34% portions. So we will say 13.5% + 34% + 34% = 81.5%
Approximately 81.5% of the the population sends between 68 and 158 text messages per day. This value is approximate because the percentages listed in the Empirical rule below are approximate.
Answer:
C. 81.5%
Step-by-step explanation:
On a recent trip to the convenience Store you picked up 4 gallons of milk 4 bottles of water and 5 snack size bags of chips your total was $28.35 if a bottle of water cost twice as much as a bag of chips and a gallon of milk cost $2.10 more than a bottle of water how much does each item cost
Answer:
The milk cost $2.10 each the snacks cost $1.535 each the water cost $3.07 each
Step-by-step explanation:
I think Im right
A turboprop plane flying with the wind flew 1,200 mi in 4 h. Flying against the wind, the plane required 5 h to travel the same distance. Find the rate of the wind and the rate of the plane in calm air.
Answer:
30 and 270 respectively
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*4=1200 and (x-y)*5=1200. Solving it, we get x=270 and y=30
can earn 5 coins In my town, gas prices are always listed to the thousandths place. Since the smallest coin we have is the penny, we have to round them to the hundredths place. If the price of gas is $3.545, what will the price be when we round it to the hundredths place?
Answer:
$3.55
Step-by-step explanation:
1st number after 0 is tenths, 2nd is hundredths.
since the number after is 5, we round up
five sutracted from x is at most -21 translate the sentence into an inequality?
PLEASEEEE HELPPPP ASAPPPPPP
(x - 7)2 = x2 - 49
O True
O False
Answer:
False
Step-by-step explanation:
Amanufacturer of potato chips would like to know whether its bag filling machine works correctly at the 433 gram setting. It is believed that the machine is underfilling the bags. A 26 bag sample had a mean of 427 grams with a variance of 324. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?
Answer:
There is not enough evidence to support the claim that the bags are under filled.
Step-by-step explanation:
Given :
Population mean, μ = 433
Sample size, n = 26
xbar = 427
Variance, s² = 324 ; Standard deviation, s = √324 = 18
The hypothesis :
H0 : μ = 433
H0 : μ < 433
The test statistic :
(xbar - μ) ÷ (s/√(n))
(427 - 433) / (18 / √26)
-6 / 3.5300904
T = -1.70
The Pvalue :
df = 26-1 = 25 ; α = 0.05
Pvalue = 0.0508
Since Pvalue > α ; WE fail to reject the Null and conclude that there is not enough evidence to support the claim that the bags are underfilled
Which line segment has the same measure as ST?
RX
TX
SR
XS
Answer:
The answer is Line Segment SR.
50 money prize for solve
Answer:
-7.5
Alternatively,
-0.5(units^-1) + (-4(units^0)) + (-3(units))
Step-by-step explanation:
On graph, only clearly defined points:
1. x = -3 , y = 0
2. x = -3 , y = -8
3. x = 5 , y = -4
So for:
1. -3 = c ( + a×(0^2) + b×0)
And
2. -3 = a×((-8)^2) + b×(-8) + c = 64×a + (-8)×b + c
Since c = -3 ==> 64×a - 8×b = 0
Simplified ==> 8×a - b = 0 ==> b = 8×a
3. 5 = a×((-4)^2) + b×(-4) + c = 16×a + (-4)×b + c
Since c = -3 ==> 16×a - 4×b = 5 - (-3) = 8
Simplified ==> 4×a - b = 2
Since b = 8×a ==> 4×a - (8×a) = 2
Simplified ==> 2×a - 4×a = 1
==> -2×a = 1
==> a = -0.5
Since b = 8×a ==> b = 8×(-0.5) = -4
So...
c = -3
b = -4
a = -0.5
Then...
a + b + c = -0.5 - 4 - 3 = -7.5
Will mark brainliest
Plz solve on a paper or draw on the picture thx in advance
9514 1404 393
Answer:
the red angle has no specific value
Step-by-step explanation:
There is sufficient information here to specify all of the angles except the two unknown angles in the 70° (dark blue) triangle. Those two angles must total 110°, but that measure cannot be allocated between them based on the information in the diagram.
The attachments show that all of the given angle constraints can be met while the red angle may vary considerably. It can range through the interval (0°, 110°), but cannot be either of those end values.
Write the equation in slope-intercept form.
y+3 - 2(x-1)
Answer:
y = 2x - 5
Step-by-step explanation:
[tex]y+3=2(x-1)\\y+3=2x-2\\y+3-3=2x-2-3\\y=2x-5[/tex]
Political Stcibility
Answer:
Political stability is a variable of great importance in a country's evolution since, across time, it was identified as causing law level of economic growth, but also it was presented as a consequence of poor economic development.
Solve for y. 14y-6(y-3)=22
Answer:
y=0.5
Step-by-step explanation:
14y-6(y-3)=22
14y-6y+18=22
8y+18=22
8y=4
y=0.5
Then we check our work...
14(0.5)-6((0.5)-3)=22
7-6(-2.5)=22
7+15=22
7+15 does equal 22, so this solution is correct.
A postal worker can sort a day's worth of mail in 8 hours. With her
supervisor helping, it takes 3 hours. How long would it take the
supervisor working alone?
Answer:
6 hours.
Step-by-step explanation:
x = supervisor's hours alone
Since there are two people working together, you need to incorporate some kind of 2 in this problem.
If the postal worker was cloned, it would take 4 hours.
3 x 2 = 6.
