Answer:
The answer is 2pix3 or [tex]2\pi x^3\\[/tex]
Step-by-step explanation:
This problem brothers on the mensuration of solid shapes, a cylinder.
we know that the expression for the volume of a cylinder is
[tex]volume= \pi r^2h\\[/tex]
let the radius r of the base be= x
and the height h of the cylinder be = 2x
we can now solve the expression that represents the volume of the cylinder, in cubic units.
[tex]volume= \pi *x^2*2x\\volume= \pi *2x^3\\\\volume= 2\pi x^3\\[/tex]
Question 2 of 10
2 Points
What is the sum of the rational expressions below?
2x+3/3x+x/x+1
Answer:
5x^2+5x+3/3x^2+3x
Step-by-step explanation:
In an aquarium, there are 4 large fish and 16 small fish. Half of the small fish are blue. One fish is selected at random. Find the probability that it is a small, blue fish. Write your answer as a fraction in simplest form.
Answer:
2/5
Step-by-step explanation:
There are 20 fish, 8 of which are small and blue. Therefore, the probability of randomly selecting a small blue fish is 8/20 = 2/5.
Complete the following subtraction exercises.
10 – 2 =
14 – 6 =
15 – 9 =
17 – 8 =
13 – 5 =
11 – 8 =
20 – 8 =
16 – 7 =
12 – 9 =
21 – 9 =
11 – 6 =
5 – 5 =
4 – 0 =
16 – 8 =
10 – 5 =
18 – 7 =
13 – 8 =
12 – 4 =
Answer:
Below
Step-by-step explanation:
8,8,6,9,8,3,12,9,3,12,5,0,4,8,5,11,5,8. Answers are in order from the first to the last
EASY question will rate brainliest no explanation neccesary
Answer: choice A
Step-by-step explanation:
the shaded parts add up to 4wholes and 1/4
or 17/4=4 1/4
find the slope of the line that passes through the points (5,1) and (-4,1)
Answer:
B. 0
Step-by-step explanation:
To find slope, use [tex]m = \frac{y2 - y1}{x2 - x1}[/tex] to find m in y = mx + b. Your m is always your slope.
Minimize
z = 20x1 + 32x2 + 40x3,
subject to
3x1 + x2 + 6x3 ≥ 9
x1 + x2 ≥ 9
4x2 + x3 ≥ 12
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.
solve for x1, x2, x3 and z
Answer:
Step-by-step explanation:
1. constraints with "[tex]\geq[/tex]" we should subtract surplus variable S1, S2, S3 and add artificial variable A1, A2, A3
Hence Z = 20 x1 + 32x2 + 40x3 + 0S1 + 0S2 + 0S3 + MA1 + MA2 + MA3
subject to
[tex]3x_1 +x_2+6x_3-S_1+A_1=9[/tex]
[tex]x_1+x_2-S_2+A_2=9[/tex]
[tex]4x_2+x_3-S_3+A_3=12[/tex]
and [tex]x_1,x_2,x_3,S_1,S_2,S_3,A_1,A_2,A_3\geq 0[/tex]
18x-5x=13+20 what is the answer
Answer:
3.3
Step-by-step explanation:
18x-5x=13+20
13x=33
x=2.5
Robin read somewhere that adding salt to water while heating it will raise the temperature of
the water causing it to boil faster. To test this claim, she filled 30 identical pots with one quart
of water. She randomly selected 15 of the pots and added 1 teaspoon of salt. She then placed
each pot on identical burners set to the highest setting. She measured the water temperature
In each pot after 5 minutes.
Is Robin's research method an example of an observational study experiment, or
simulation?
b
If Robin does find that there is a difference between the water temperatures in the pots
with salt compared to those without can she conclude that the salt caused the
difference in temperature?
Answer:
a. An experiment
b. No
Step-by-step explanation:
a. Robin's research method can be concluded to be an experiment because she has a testable group (pots of water with salt) and a control group (pots of water without salt).
2. Based on this alone, she cannot conclude that the salt caused the
difference in temperature because she has not set some appropriate conditions which are to be met for this test.
Your local school board wants to determine the proportion of people who plan on voting for the school levy in the upcoming election. They conduct a random phone poll, where they contact 150 individuals and ask them whether or not they plan on voting for the levy. Of these 150 respondents, 78 people say they plan on voting for the levy. The school board wants to determine whether or not the data supports the idea that more than 50% of people plan on voting for the levy. Conduct a hypothesis test at the 0.10 significance level to test this claim.
Answer:
There is not enough evidence to conclude that the data supports the idea that more than 50% of people plan on voting for the levy
Step-by-step explanation:
Sample size, n = 150
Number of people that plan on voting for the levy, X = 78
Proportion of people that plan on voting for the levy:
[tex]\bar{p} = X/n\\\bar{p} = 78/150\\\bar{p} = 0.52[/tex]
The study is to determine whether or not the data supports the idea that more than 50%(0.5) of people plan on voting for the levy
The null and alternative hypotheses are:
[tex]H_0: p \leq 0.5\\H_a: p > 0.5[/tex]
Calculate the test statistics:
[tex]t_s = \frac{\bar{p} - p}{\sqrt{\frac{p(1-p)}{n} } } \\t_s = \frac{0.52-0.5}{\sqrt{\frac{0.5(1-0.5)}{150} } } \\t_s = 0.49[/tex]
For a test statistic [tex]t_s = 0.49[/tex], the p-value = 0.3121
The significance value, [tex]\alpha = 0.10[/tex]
Since the p-value(0.3121) is greater than α(0.10), the null hypothesis [tex]H_0[/tex] will be accepted.
This means that there is not enough evidence to conclude that the data supports the idea that more than 50% of people plan on voting for the levy
What is the area of a rectangle that is 4 1/2 cm long and 2 5/9 cm wide? Solution: Answer: What is the area of a square that has a side of 4 3/5 cm?
Answer:
1) 23/2
2) 529/25
Step-by-step explanation:
Transformation:
[tex]4\frac{1}{2} = \frac{(2*4) + 1}{2} = \frac{9}{2}[/tex]
[tex]2\frac{5}{9} = \frac{(9*2) + 5}{9} = \frac{23}{9}[/tex]
A = [tex]\frac{9}{2} * \frac{23}{9} = \frac{23}{2}[/tex]
-----------------------------
Transformation:
[tex]4\frac{3}{5} = \frac{(5*4) + 3}{5} = \frac{23}{5}[/tex]
A = [tex](\frac{23}{5})^{2} = \frac{529}{25}[/tex]
If your good at maths help me
Answer:
6n+1
Step-by-step explanation:
first term=13-6=7
nth term=7+(n-1)6=7+6n-6=6n+1
Answer:
aₙ= 6n +1
Step-by-step explanation:
Second term a₂= 13
Common difference d= 6
Then first term
a₁= 13 -6= 7nth term:
aₙ= a₁ + (n-1)daₙ= 7 + (n-1)*6= 7+6n -6 = 6n +1aₙ= 6n +1A student is getting ready to take an important oral examination and is concerned about the possibility of having an "on" day or an "off" day. He figures that if he has an on day, then each of his examiners will pass him, independently of one another, with probability 0.8, whereas if he has an off day, this probability will be reduced to 0.4. Suppose that the student will pass the examination if a majority of the examiners pass him. If the student believes that he is twice as likely to have an off day as he is to have an on day, should he request an examination with 3 examiners or with 5 examiners?
Answer:
The students should request an examination with 5 examiners.
Step-by-step explanation:
Let X denote the event that the student has an “on” day, and let Y denote the
denote the event that he passes the examination. Then,
[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]
The events ([tex]Y|X[/tex]) follows a Binomial distribution with probability of success 0.80 and the events ([tex]Y|X^{c}[/tex]) follows a Binomial distribution with probability of success 0.40.
It is provided that the student believes that he is twice as likely to have an off day as he is to have an on day. Then,
[tex]P(X)=2\cdot P(X^{c})[/tex]
Then,
[tex]P(X)+P(X^{c})=1[/tex]
⇒
[tex]2P(X^{c})+P(X^{c})=1\\\\3P(X^{c})=1\\\\P(X^{c})=\frac{1}{3}[/tex]
Then,
[tex]P(X)=1-P(X^{c})\\=1-\frac{1}{3}\\=\frac{2}{3}[/tex]
Compute the probability that the students passes if request an examination with 3 examiners as follows:
[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]
[tex]=[\sum\limits^{3}_{x=2}{{3\choose x}(0.80)^{x}(1-0.80)^{3-x}}]\times\frac{2}{3}+[\sum\limits^{3}_{x=2}{{3\choose x}(0.40)^{3}(1-0.40)^{3-x}}]\times\frac{1}{3}[/tex]
[tex]=0.715[/tex]
The probability that the students passes if request an examination with 3 examiners is 0.715.
Compute the probability that the students passes if request an examination with 5 examiners as follows:
[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]
[tex]=[\sum\limits^{5}_{x=3}{{5\choose x}(0.80)^{x}(1-0.80)^{5-x}}]\times\frac{2}{3}+[\sum\limits^{5}_{x=3}{{5\choose x}(0.40)^{x}(1-0.40)^{5-x}}]\times\frac{1}{3}[/tex]
[tex]=0.734[/tex]
The probability that the students passes if request an examination with 5 examiners is 0.734.
As the probability of passing is more in case of 5 examiners, the students should request an examination with 5 examiners.
Please help! Correct answer only, please! Determine the value of the following if it is possible. If it is not possible, explain. A. B. C. D.
Answer: C
Step-by-step explanation:
Multiply the number outside of the matrix to EVERY value inside that matrix.
Addition and subtraction of matrices is very simple - just add (or subtract) the values of each matrix that have the same designation.
[tex]X\left[\begin{array}{cc}a&b\\c&d\end{array}\right] +Y\left[\begin{array}{cc}e&f\\g&h\end{array}\right]=\left[\begin{array}{cc}X(a)+Y(e)&X(b)+Y(f)\\X(c)+Y(g)&X(d)+Y(h)\end{array}\right]\\\\\\\\\\-3\left[\begin{array}{cc}2&7\\8&-6\end{array}\right] +2\left[\begin{array}{cc}0&1\\4&-2\end{array}\right]\\\\\\=\left[\begin{array}{cc}-3(2)+2(0)&-3(7)+2(1)\\-3(8)+2(4)&-3(-6)+2(-2)\end{array}\right] \\\\\\=\left[\begin{array}{cc}-6&-19\\-16&14\end{array}\right][/tex]
Write a sine function that has a midline of 2, an amplitude of 4 and a period of 11.
Answer:
y = 4 sin(2π/11 x) + 2
Step-by-step explanation:
y = A sin(2π/T x + B) + C
where A is the amplitude,
T is the period,
B is the phase shift,
and C is the midline.
A = 4, T = 11, and C = 2. We'll assume B = 0.
y = 4 sin(2π/11 x) + 2
The sine function with the desired characteristics is given by:
[tex]y = 2\sin{\left(\frac{2\pi}{11}\right)} + 2[/tex]
The standard sine function is given by:
[tex]y = A\sin{Bx} + C[/tex]
The amplitude is 2A.The period is [tex]\frac{2\pi}{B}[/tex].The midline is C.In this problem:
Midline of 2, thus [tex]C = 2[/tex].Amplitude of 4, thus [tex]2A = 4 \rightarrow A = 2[/tex].Period of 11, thus [tex]\frac{2\pi}{B} = 11 \rightarrow B = \frac{2\pi}{11}[/tex]Then, the equation for the sine function is:
[tex]y = 2\sin{\left(\frac{2\pi}{11}\right)} + 2[/tex]
A similar problem is given at https://brainly.com/question/18055768
laura quiere cubrir con papel china una puesta como la que se muestran el dibujo cuánto centímetros cuadrados tendrá que cubrir con papeles llena
Answer:
El área a cubrir es de 4800 cm^2.
Step-by-step explanation:
La pregunta está incompleta:
Laura quiere cubrir con papel de china una puerta como la que se muestra en el dibujo cuánto es centímetros cuadrados. Las medidas son 80 cm de largo y 60 cm de ancho.
Tenemos que calcular el área que representa la puerta, cuyos lados son 80 cm y 60 cm.
El área A se calcula multiplicando ambos lados:
[tex]A=80\,cm\cdot60\,cm=4800\,cm^2[/tex]
please please solve for x
Answer:
Step-by-step explanation:
Discover the area of a circle with a diameter of 17 feet ?
Answer: A≈226.98 ft²
Step-by-step explanation:
The formula for area of a circle is A=πr². The formula doesn't include diameter , but we can certainly find the radius from the diameter.
d=2r
17=2r
r=17/2=8.5 ft
Now that we have the radius, we can plug it in to area formula.
A=πr²
A=π(8.5ft)²
A=π72.25ft²
A≈226.98 ft²
Area of a circle: A = πr²
Get the radius by dividing the diameter by 2.
17 / 2 = 8.5
Now, solve with the given values.
A = π(8.5)²
A = 72.25π
A = 226.865
Therefore, the area is 226.865ft³
Best of Luck!
Round 5 to the nearest ten.Enter your answer in the box below.
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]05[/tex]
If the units place is higher than 5, then add 1 to the tens place.
For the polynomial below, what is the coefficient of the term with the power of 3?
A.0
B.1
C.6
D.5
Answer:
Option B
Step-by-step explanation:
x^3
Coefficient = 1
Option B
Answer:
B = 1
Step-by-step explanation:
this is becus we don't write 1 as a coefficient it's there but in an invisible form
anyone who make the one visible is considered an amateur
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer:
2 is the answer
Step-by-step explanation:
area=1/2*base*height
as height = 2*base and area =4 it comes
1/2*2*base*base=4
so base *base=4
so base = 2
Brian flips a fair coin 3 times. What is the probability of getting exactly 2 tails?
Answer:
3/8
Step-by-step explanation:
The possible outcomes
TTT TTH THT THH HHH HHT HTH HTT = 8 outcomes
There are TTH THT HTT 3 with exactly two tails
P ( exactly 2 tails) = 3/8
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
The outcomes you are looking for are either HTT, THT, or TTH.
The possibility to toss tails or heads is 0.5. Thus the possibility to throw T and then H and then H is:
[tex]\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}[/tex]
We have three ways of getting 2 tails, the possibility of throwing exactly two tails in three tosses is:
[tex]\frac{1}{8} + \frac{1}{8} + \frac{1}{8} = \frac{3}{8}[/tex]
0.375 is the probability of getting exactly 2 tails in 3 tosses.
{0 tails}={HHH}
{1 tails}={TTH, THT, HTT}
{2 tails}={HTT, TTH, THT}
{3 tails}={TTT}
There are 3 cases with getting two tails out of 8 possible outcomes.
Use the given data to construct a box plot and identify the 5-number summary. Eleven different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings (mmHg) are listed below.
{ 130, 135, 140, 120, 130, 130, 144, 143, 140, 130, 150 }
Answer:
[tex] Min =120, Max= 150[/tex]
The first quartile can be calculated with this data:
130, 135, 140, 120, 130, 130
And the middle value is:
[tex] Q_1 = \frac{140+120}{2}=130[/tex]
The median is the value in the 6th position from the dataset ordered and we got:
[tex] Median= 135[/tex]
The third quartile can be calculated with this data:
135 140 140 143 144 150
And the middle value is:
[tex] Q_3 = \frac{140+143}{2}=141.5[/tex]
The five number summary for this case:
Min. 1st Qu. Median Mean 3rd Qu. Max.
120.0 130.0 135.0 135.6 141.5 150.0
The boxplot is on the figure attached
Step-by-step explanation:
We have the following data given:
130, 135, 140, 120, 130, 130, 144, 143, 140, 130, 150
If we sort the values on increasing order we got:
120 130 130 130 130 135 140 140 143 144 150
The minimum and maximum are:
[tex] Min =120, Max= 150[/tex]
The first quartile can be calculated with this data:
130, 135, 140, 120, 130, 130
And the middle value is:
[tex] Q_1 = \frac{140+120}{2}=130[/tex]
The median is the value in the 6th position from the dataset ordered and we got:
[tex] Median= 135[/tex]
The third quartile can be calculated with this data:
135 140 140 143 144 150
And the middle value is:
[tex] Q_3 = \frac{140+143}{2}=141.5[/tex]
The five number summary for this case:
Min. 1st Qu. Median Mean 3rd Qu. Max.
120.0 130.0 135.0 135.6 141.5 150.0
The boxplot is on the figure attached
Consider the scatterplot above. Write a sentence explaining the meaning of the value of the slope for this linear model. The is an average of per year .
Answer:
Slope: The percent that voted falls by 0.1271 units per year.
Step-by-step explanation:
The slope of a regression line represent the average rate of change in the dependent variable (y) based upon the changes in the independent variable (x).
In this case the regression equation provided is:
y = -0.1271 x + 307.53
The slope of the line is -0.1271.
The dependent variable is the percent that voted and the independent variable is the year.
The slope of -0.1271 indicates that every year, on average, the percent that voted decreases by 0.1271 units.
Or the percent that voted falls by 0.1271 units per year.
Order the numbers from greatest to least.
4. 234,358; 23,208; 23,098
Answer:
23,098; 23,208 ; 234,358
Step-by-step explanation:
Hope this helps
How do you solve this problem? population proportion is to be estimated from a sample of 400 with a sample proportion of 0.1. Approximate the 95% confidence interval of the population proportion
Answer:
(0.0706, 0.1294)
Step-by-step explanation:
Confidence interval of a proportion is:
CI = p ± CV × SE
where p is the proportion,
CV is the critical value (z score or t score),
and SE is the standard error.
The sample is large enough to estimate as normal. For 95% confidence level, CV = z = 1.96.
Standard error for a proportion is:
SE = √(pq/n)
SE = √(0.1 × 0.9 / 400)
SE = 0.015
The confidence interval is:
CI = 0.1 ± (1.96)(0.015)
CI = (0.0706, 0.1294)
Round as needed.
Simplify the expression. (-3 + 6i)(-3 + 5i)
Answer:
11i-6
Step-by-step explanation:
Answer:
11i-6
Step-by-step explanation:
(-3+6i)(-3+5i)
combine like terms (-3)+(-3)=-6
6i+5i=11i
A game is played using one die. If the die is rolled and shows 1, the player wins $5. If the die shows any number other than 1, the player wins nothing. If there is a $1 charge to play the game, what is the game’s expected value?
Answer:
1/5
Step-by-step explanation:
i had a similar question
For each roll you start with paying 2 dollars and you only with 10 dollars one out of 6 rolls (on average).
So the cost for one play is 2 dollars and your win is 10/6.
Value is -2+10/6=-1/3 dollars
So you lose 1/3 dollars on average with each game
since you have no limited rolls u put 1/5
this from another question but both same just different numbers
Autism is a serious and lifelong disability that is characterized by a severely decreased ability to engage in communication and social interaction. In 1998 citizens in a New Jersey town were concerned about the number of children diagnosed with autism, and a study was undertaken to establish the prevalence in the community. Data from the study are reported below:
Numbers of Children Diagnosed with Autistic Disorder
Age Category (y) Diagnosed with Autistic Disorder Number of Children in Population
3-5 19 3479
6-10 17 5417
Required:
a. Calculate the prevalence rate of autism for these children for the two age categories.
b. Convert the prevalence rate to a rate per 1,000
Answer:
a. Calculate the prevalence rate of autism for these children for the two age categories.
3-5: prevalence rate = 0.55%6-10: prevalence rate = 0.31%b. Convert the prevalence rate to a rate per 1,000
3-5: prevalence rate = 5.5 per thousand6-10: prevalence rate = 3.1 pér thousandStep-by-step explanation:
Generally prevalence is calculated using the following formula:
(number of people with autism / number of people measured) x 100%
age category
3-5: prevalence rate = (19/3,479) x 100% = 0.55%
6-10: prevalence rate = (17/5,417) x 100% = 0.31%
if you want to convert to a rate per 1,000, allyou need to do is multiply by 1,000 instead of 100
3-5: prevalence rate = (19/3,479) x 1,000 = 5.5
6-10: prevalence rate = (17/5,417) x 1,000 = 3.1
The graph of a linear function is a _______
The graph of a linear function is a straight line.
a boat operator in a boat can travel 15m/sec in still water he tries to cross a river which is flowing at 5 m/sec south. A) what is the resultant velocity of the boat? B) The takes exactly 55 seconds to cross the river in the resulting velocity, how many meters did the boat travel?
Answer:
a) 15.8 ms-1
b)869 m
Step-by-step explanation:
We have to obtain the resultant velocity by the Pythagorean theory;
R^2= V1^2 + V2^2
Where
R= resultant velocity of the boat
V1= velocity of the boat
V2= velocity of the flowing river
Thus;
R= √V1^2 + V2^2
R= √15^2 + 5^2
R= √225 + 25
R= √250
R= 15.8 ms-1
B) from
v= s/t
Where
v= velocity (resultant velocity in this case)
s= distance
t= time (55 secs)
s= vt
s= 15.8×55
s= 869 m