The integral of \(\sqrt{x}\) is (2/3)\(x^{3/2}\) + C, where C is the constant of integration. The integral of 12√x is 8x^(3/2) + C.
a) To find the integral of \(\sqrt{x}\), we can use the power rule for integration. The power rule states that the integral of \(x^n\) with respect to x is (1/(n+1))\(x^{n+1}\) + C, where C is the constant of integration. In this case, n = 1/2, so the integral of \(\sqrt{x}\) is (1/(1/2 + 1))\(x^{1/2 + 1}\) + C, which simplifies to (2/3\()x^{3/2}\) + C.
b) To find the integral of 12\(\sqrt{x}\), we can apply a constant multiple rule for integration. This rule states that the integral of a constant multiple of a function is equal to the constant multiplied by the integral of the function. In this case, we have 12 times the integral of \(\sqrt{x}\). Using the result from part a), we can substitute the integral of \(\sqrt{x}\)as (2/3)\(x^{3/2}\) + C. Multiplying this by 12 gives us 12((2/3)\(x^{3/2}\)+ C), which simplifies to 8\(x^{3/2}\) + C.
Therefore, the integral of \(\sqrt{x}\) is (2/3)\(x^{3/2}\) + C, and the integral of 12 \(\sqrt{x}\) is 8\(x^{3/2}\) + C, where C represents the constant of integration.
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An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by the local dealer. The customer relations department will survey a random sample of customers and compute a 95% confidence interval for the proportion who are not satisfied.
(a) Past studies suggest that this proportion will be about 0.17. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015. (You will need a critical value accurate to at least 4 decimal places.) Sample size:
(b) Using the sample size above, when the sample is actually contacted, 25% of the sample say they are not satisfied. What is the margin of the error of the confidence interval? MoE:
The margin of error for the confidence interval is approximately 0.014, indicating that the estimate of the proportion of dissatisfied customers could be off by approximately plus or minus 0.014. This means that we can be 95% confident that the true proportion of dissatisfied customers falls within the range of the estimated proportion ± 0.014.
(a) To find the sample size needed to achieve a margin of error of about 0.015 with a 95% confidence level, we can use the formula for sample size calculation for proportions:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = sample size
Z = critical value (corresponding to the desired confidence level)
p = estimated proportion of the population
E = margin of error
In this case, the estimated proportion of dissatisfied customers is 0.17, and the desired margin of error is 0.015. Since we want a 95% confidence level, the critical value can be obtained from a standard normal distribution table. The critical value for a 95% confidence level is approximately 1.96.
Plugging these values into the formula, we have:
n = (1.96^2 * 0.17 * (1-0.17)) / 0.015^2
n ≈ 1901.63
Therefore, the sample size needed is approximately 1902.
(b) If 25% of the sample say they are not satisfied, we can calculate the margin of error using the following formula:
MoE = Z * sqrt((p * (1-p)) / n)
Where:
MoE = margin of error
Z = critical value (corresponding to the desired confidence level)
p = proportion of the sample
n = sample size
Using the same critical value of 1.96 for a 95% confidence level and plugging in the values:
MoE = 1.96 * sqrt((0.25 * (1-0.25)) / 1902)
MoE ≈ 0.014
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Solve for the indicated variable.
L = M - N for N
( 2 + 2i )^20=
(a) 2^20
(b) 2^30
(c) 2^20i
(d) -2^30
24
34
22i
-34
yup your welcome
(b) an experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. mendel claimed that the proportion of peas with yellow pods should be 25%. we want to know if these data are consistent with mendel's hypothesis. which statistical inference procedures should we use?
As per Mental hypothesis, the statistical inference procedures that we should use Chi-square test for goodness of fit.
Hypothesis
In probability, an idea or explanation that you then test through study and experimentation is known as hypothesis.
Given,
Here we have given that, an experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. Mendel claimed that the proportion of peas with yellow pods should be 25%. we want to know if these data are consistent with Mendel's hypothesis.
And we need to find in which statistical inference procedures should we use.
According to the definition of Chi-square test for goodness of fit, the claim is that the proportion of peas with yellow pods should be 25%. And then here the researcher wants to check that the experimental and observed counts of yellow offspring peas shows significant difference or not.
So, the statistical procedure used to study this case is Chi-square test for goodness of fit . Hence, option (1) is correct.
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How is field data aggregated? Number of failed parts Number of failures Hours of operation Maintenance time Mark for follow up Question 3 of \( 7 . \) Data collection extends over a large number of it
Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,
such as a day or a week. Number of Failed Parts: The number of parts that have failed over a given period of time, such as a day or a week. Hours of Operation: The amount of time that a machine or system was operational during a given period of time, such as a day or a week. Maintenance Time: The amount of time that was spent maintaining a machine or system during a given period of time, such as a day or a week.
Mark for Follow-Up: An indication of which issues need to be addressed or followed up on to prevent future failures or improve performance. Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,
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What is the value of x in the equation 6 +4x = 7
Answer:
x = - \(\frac{1}{4}\)
Step-by-step explanation:
Given
6 + 4x = 7 ( subtract 6 from both sides )
4x = 1 ( divide both sides by 4 )
x = \(\frac{1}{4}\)
Answer:
x = 1/4
Step-by-step explanation:
6 +4x = 7
collect terms
4x = 7 - 6
4x = 1
Divide both sides by 4
x = 1/4
Bye ! :-)
. a paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top). if water is poured into the cup at a rate of 2 cm3 ys, how fast is the water level rising when the water is 5 cm deep?
The water level is rising at a rate of 0.0764 cm per second.
Using implicit differentiation, it is found that the water level is rising at a rate of 0.0764 cm per second.
The volume of a cone of radius r and height h is given by:
V = πr²h/3
Applying implicit differentiation, the rate of change is given by:
dV/dt = 2πr/3 dr/dt + πr²/3 dh/dt
In this problem:
The radius is constant, thus dr/dt = 0
Height of 5 cm and radius of 3 cm, thus h = 5, r=3.
Water poured at a rate of 2 cm³/s, thus dV/dt = 2
Then
dV/dt = 2πr/3 dr/dt + πr²/3 dh/dt
2 = 25π/3 dh/dt
dh/dt = 6/25π
dh/dt = 0.0764
The water level is rising at a rate of 0.0764 cm per second.
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PLEASEEE HELLP. I NEED HELP PLS
Answer:
C
Step-by-step explanation:
Triangle = 180
100+62.7+18=180.7
180.7 is not a triangle
Answer:
C 100.3, 62.7, 18
Step-by-step explanation:
Angles inside of a triangle add up to 180 degrees
Option A
25+85+70=180
Option B
11.6+91+77.4=180
Option C
100.3+62.7+18=181
Option D
60+60+60=180
Option C is the answer as it is the only option that does not add up to 180 degrees
(a) We would like to know if Intel's stock and Southwest Airlines' stock have similar rates of return. To find out, we take a random sample of 50 days, and record Intel's and Southwest's stock on those same days.
Thus, to determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can use a statistical analysis of the daily rate of return for each stock over a 50-day period. However, the small sample size means that we must be cautious when interpreting the results.
To determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can conduct a statistical analysis using the sample data collected. The sample size of 50 days is relatively small, so we must be cautious when interpreting the results.
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A helicopter flies 665 feet above ground. What is the measure of the angle of depression from the helicopter to the girl’s line of sight? Round to the nearest degree. 23° 25° 65° 67°
Answer:
67°
Step-by-step explanation:
Given:
Height of helicopter from the ground, x = 665 feet
Distance from the helicopter to the girl's line of sight(opposite) = 665ft - 5 ft = 600 ft
Horizontal distance(adjacent) = 280 ft
To find the angle of depression, use the formula:
\( tan y = \frac{x}{y} \)
Solve for y:
\(y = tan^-^1 (\frac{x}{y})\)
\(y = tan^-^1 (\frac{660}{280}) = 67.01\)
Angle of depression = 67°
Answer:
67 degrees
Step-by-step explanation:
Find the missing probability. P(A)=15,P(A∪B)=1225,P(A∩B)=7100 ,P(B)=?
Answer:
p(B) = 8310Step-by-step explanation:
We will use the addition rule of probability of two events to solve the question. According to the rule given two events A and B;
p(A∪B) = p(A)+p(B) - p(A∩B) where;
A∪B is the union of the two sets A and B
A∩B is the intersection between two sets A and B
Given parameters
P(A)=15
P(A∪B)=1225
P(A∩B)=7100
Required
Probability of event B i.e P(B)
Using the expression above to calculate p(B), we will have;
p(A∪B) = p(A)+p(B) - p(A∩B)
1225 = 15+p(B)-7100
p(B) = 1225-15+7100
p(B) = 8310
Hence the missing probability p(B) is 8310.
Please help me with this question!
I need an explanation on how to get the answer!
Answer:
C - 136
Step-by-step explanation:
Something important to remember here is that whenever you replace a variable with something else, that something else needs to go in parentheses.
3(7)² - 2(7) + 3
Following PEMDAS, you need to take care of that exponent before anything else. While parentheses are included as coming first, that is referring to operations within parentheses, which we don't have here.
3(49) - 2(7) + 3
Multiplication is the next step...
147 - 14 + 3
And finally, addition and subtraction.
147 - 11
136
Answer:
136
Step-by-step explanation:
Since the question stated that x= 7 you simply substitute all x in the expression with 7 and it would look something like this
3 (7)^2 - 2 (7) +3
PLEASE BRAINLIEST
1. Si tengo el siguiente ejercicio x = 8+9*4+(32*2+5*4)+3*6 aplicando la jerarquía de operaciones, el resultado sería? a. 25 b. 45 c. 78 d. Ninguna de las anteriores
Answer:
Option D is correct.
The answer is none of the above.
x = 146
La opción D es correcta.
La respuesta es ninguna de las anteriores.
x = 146
Step-by-step explanation:
English Translation
If I have the following exercise x = 8 + 9 * 4 + (32 * 2 + 5 * 4) + 3 * 6 applying the hierarchy of operations, the result would be?
a. 25
b. 45
c. 78
d. None of the above
Solution
The hierarchy of operations includes BODMAS.
B - Brackets
O - Order
D - Division
M - Multiplication
A - Addition
S - Subtraction
x = 8 + 9 * 4 + (32 * 2 + 5 * 4) + 3 * 6
Solving the bracket first.
The multiplication in the bracket are first simplified to give
x = 8 + 9 * 4 + (64 + 20) + 3 * 6
Then further simplifying the bracket
x = 8 + 9 * 4 + (84) + 3 * 6
We then solve the multiplication outside the brackets
x = 8 + 36 + 84 + 18
We now sum all of this
x = 146
In Spanish/En Español
La jerarquía de operaciones incluye BODMAS.
B - Soportes
O - Orden
D - División
M - Multiplicación
A - Suma
S - Resta
x = 8 + 9 * 4 + (32 * 2 + 5 * 4) + 3 * 6
Resolver el soporte primero.
La multiplicación en el paréntesis se simplifica primero para dar
x = 8 + 9 * 4 + (64 + 20) + 3 * 6
Luego simplificando aún más el soporte
x = 8 + 9 * 4 + (84) + 3 * 6
Luego resolvemos la multiplicación fuera de los corchetes
x = 8 + 36 + 84 + 18
Ahora sumamos todo esto
x = 146
Hope this Helps!!!
¡¡¡Espero que esto ayude!!!
Cole deposits $500 into his savings account. The bank pays him 2% interest on the amount he has in his account. What expression would you
use to find the total Cole has in his account?
Answer:
500*2%=10
500+10=510
Step-by-step explanation:
is this correct? I'm not too sure how I'm supposed to do it
Answer:
Indeed it Correct, but am not quiet sure
How is the product of 4 and 2 shown using integer tiles? 4 positive tiles and 2 positive tiles. 4 negative tiles and 2 negative tiles. 4 sets of 2 positive tiles. 4 sets of 2 negative tiles. Plz i need help
Answer: 4 sets of 2 positive tiles.
Step-by-step explanation:
We have the product of 4 and 2.
We can represent this as:
4 is equivalent to 4 positive tiles.
if we multiplicate it by 2, then we must have 2 sets of 4 positive tiles.
Another example is using 2 positive tiles to represent the 2.
So when we multiply it by 4, we end with 4 sets of 2 positive tiles.
This is because the order of the factors does not change the product.
Then, from the given options, the correct one is:
4 sets of 2 positive tiles.
Answer:
C on edge 2021
Explanation:
4 groups of 2
[+] [+] [+] [+] [+] [+] [+] [+]
here, what do we do if it says y=-x or y=x
You plot the points on the graph first with a pencil. Draw the given line, in this case, it's y=-x.
From a point, you do rise and run to the line and reverse it on the other side of the line to get the points.
Refer the attached diagram, for easy method.
Hope it helps :)
A projectile fired at 5 m/s from a gun. If the horizontal component of the initial velocity is equal to 4 m/s. What is the value of the vertical component?
Answer:
\(the \: value \: of \: the \: vertical \: component \to : \\ (v_v) = 3m {s}^{ - 1} \\ \)
Step-by-step explanation:
\(let \: the \: velocity \: be \to \: v \\let \: the \: horizontal \: component \: be \to \: v_h \\ let \: the \: vertical \: component \: be \to \: v_v \\ applying \: the \: pythagorean \: rule \: of \: vectors \to : \\ {v}^{2} = {v_v}^{2} + {v_h}^{2} \\ {v_v}^{2} = {v}^{2} - {v_h}^{2} \\ {v_v}^{2} = {5}^{2} - {4}^{2} \\ v_v = \sqrt{(25 - 16)} \\ v_v = \sqrt{9} \\ \boxed{ v_v = 3 {ms}^{ - 1} }\)
PLEASE HELP DRAW WHERE THE DOT GO ON THE IMAGE PLEASE
Answer:
Step-by-step explanation:
What additional information is obtained from an ordinal scale compared to a nominal scale?
An ordinal scale provides more information than a nominal scale since values linked with an ordinal variable will be in natural order, whereas values connected with the nominal variable won't.
Types of Variables:Ordinal variables as well as nominal variables are the two categories of variables listed here. This sort of variable cannot be submitted to the same forms of statistical tests as interval and ratio variables, hence it is crucial to be able to recognize them accurately. Both of these variables fall within the qualitative category. This contrasts with interval as well as rate variables, both of which are categorized as quantitative.
An illustration of an ordinal variable is a Likert scale with words for mood (such as joyful, neutral, or sad). An illustration of a nominal variable is the names of cities in the Canadian province of Alberta.
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Rodrigo entrena para una maraton todos los dias sale a correr a una pista de 6 kilimetros de longitud,el lunes da dos vueltas,el martes da una vuelta y un medio,el miercoles da una vuelta y un tercio,el jueves da dos vueltas y dos quintos,el viernes da una vuelta y dos tercios,y el sabado dio dos vueltas y tres cuartos cuantos kilometros recorrio por dia
Answer:
11.65 km / day
Step-by-step explanation:
We can calculate the amount of daily kilometer in the following way
First day: 2 * 6 = 12 km
Second day: 1.5 * 6 = 9 km
Third day: 1.333 * 6 = 8 km
Fourth day: 2.4 * 6 = 14.4 km
Sixth day: 1.666 * 6 = 10 km
on Saturday: 2.75 * 6 = 16.5 km
the average per day
(12 + 9 + 8 + 14.4 + 10 +16.5) / 6 = 11.65
11.65 km/day
Suppose two cars depart from a four-way intersection at the same time, one heading north and the other heading west. The car heading north travels at the steady speed of 40 ft/sec and the car heading west travels at the steady speed of 64 ft/sec.
When are the two cars 1 mile apart? (Round your answer to one decimal place.)
answer in seconds
50.76922
after 50.8 seconds because
50.76922*40 +50.76922*64= 5279.99 which rounds to the admit if feet in a miles
i need severe help Plz
Answer:
-12
Step-by-step explanation:
Mark as Brainliest.
Because I am Indian and solving your question from India.
pls answer all the questions FOIL pre calc
Answer for Part I: x² - 3x - 10
Step-by-step explanation:
The FOIL method means to multiply the "First, Outside, Inside, and Last" in order of the terms. See attached for a visual and the work behind the answer.
Using this method, we end up with;
x² - 3x - 10
EEK! I WILL GIVE BRAINLIEST!
Answer:
The first one
Step-by-step explanation:
The left moat one (the fist one)
Step-by-step explanation:
what value of t would you use for the 99% confidence interval?
The value of t for a 99% confidence interval depends on the sample size. With larger sample sizes (typically >30), t approaches the value of Z (standard normal distribution critical value).
In statistical inference, the value of t used for constructing a confidence interval depends on the desired confidence level and the sample size. For a 99% confidence interval, the critical value of t can be determined from the t-distribution table or calculated using software.The value of t for a 99% confidence interval is based on the degrees of freedom, which is generally determined by the sample size minus one (n - 1) for an independent sample. The larger the sample size, the closer the t-distribution approaches the standard normal distribution. For large sample sizes (typically n > 30), the critical value of t becomes very close to the value of Z (the standard normal distribution critical value) for a 99% confidence level.
To calculate the specific value of t, you need to know the sample size (n) and the degrees of freedom (df = n - 1). With these values, you can consult a t-distribution table or use statistical software to find the appropriate critical value. For a 99% confidence interval, the value of t will be higher than the corresponding value for a lower confidence level such as 95% or 90%, allowing for a wider interval that captures the true population parameter with higher certainty.
Therefore, The value of t for a 99% confidence interval depends on the sample size. With larger sample sizes (typically >30), t approaches the value of Z (standard normal distribution critical value).
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concerning the eoq model, if demand or annual usage increases by 10 percent, then the eoq will ________.
If demand or annual usage increases by 10 percent, the Economic Order Quantity (EOQ) will increase. The EOQ model is used in inventory management to determine the optimal order quantity that minimizes total inventory costs.
The Economic Order Quantity (EOQ) is a model used in inventory management to determine the optimal order quantity that minimizes total inventory costs. It takes into account factors such as demand, holding costs, and ordering costs. When demand or annual usage increases by 10 percent, it means that more units are being consumed or sold within a given time period.
With an increase in demand, the EOQ will also increase. This is because the EOQ formula takes into consideration the trade-off between holding costs and ordering costs. Holding costs are the costs associated with holding inventory, such as warehousing and insurance, while ordering costs are the costs incurred when placing an order, such as administrative and transportation costs.
When demand increases, more units need to be ordered to meet the higher demand. This results in an increase in ordering costs, as more frequent orders will need to be placed. Consequently, the EOQ will increase to find the new optimal order quantity that balances the increased ordering costs with the holding costs.
In summary, if demand or annual usage increases by 10 percent, the EOQ will increase due to the need to order more frequently to meet the higher demand, resulting in increased ordering costs. This adjustment ensures that the inventory management system remains efficient and cost-effective.
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I don't know how to do this Solve the equation.
x3=−8
x=
Answer: -2 2/3 or -8/3
Solve with steps please.
Urgenttt
Type the correct answer in each box. Use numerals instead of words.
Consider the given circle with the shaded sector XY and central angle, 225°. The circumference of the circle is 30
units.
A circle with center C has two lines C X, and C Y drawn from the center of the circle to the circle wall such that the exterior angle of X C Y is 225 degrees.
Use the given information to complete the statements. Round any non-integer answers to the hundredths place.
The correct answer is Length of arc XY: 15.03 units.Area of shaded sector XY: 15.73 square units.
To complete the statements, we can use the properties of circles and the given information.
The length of the arc XY, denoted as "s," can be found using the formula:
s = (θ/360) * 2πr
where θ is the central angle in degrees and r is the radius of the circle.
Given that the central angle is 225° and the circumference of the circle is 30 units, we can solve for the radius (r):
Circumference = 2πr
30 = 2πr
r = 30 / (2π) ≈ 4.77 units (rounded to the hundredths place)
Now we can calculate the length of the arc XY:
s = (225/360) * 2π * 4.77 ≈ 15.03 units (rounded to the hundredths place)
Therefore, the length of the arc XY is approximately 15.03 units.
The area of the shaded sector XY, denoted as "A," can be found using the formula:
A = (θ/360) * πr²
Using the same values for θ and r as above, we can calculate the area:
A = (225/360) * π * (4.77)² ≈ 15.73 square units (rounded to the hundredths place)
Therefore, the area of the shaded sector XY is approximately 15.73 square units.
Note: Please double-check the formulas and calculations with the provided information to ensure accuracy.
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