The given differential equation is of the form dy/dx = x^(9/2 + 1). To solve this, we can integrate both sides with respect to x to obtain the general solution:
y = (2/11)x^(11/2) + C
where C is a constant of integration.
Using the initial condition y(1) = 3, we can solve for C:
3 = (2/11)1^(11/2) + C
C = 3 - 2/11
Substituting this value of C in the general solution, we obtain the particular solution:
y = (2/11)x^(11/2) + 3 - 2/11
y = (2/11)x^(11/2) + 31/11
However, none of the given answer choices match this form exactly. Answer choice A can be simplified to:
y = (2/3)(x^(9/2 + 1))^(3/2) + 7/3
y = (2/3)(x^11)^(3/2) + 7/3
y = (2/3)x^(33/2) + 7/3
This is not equivalent to the given particular solution. Answer choice B can be simplified to:
y = (2/27)x^8(x^(9/2 + 1))^(3/2) + (81 - 4sqrt(2))/27
y = (2/27)x^8(x^11)^(3/2) + (81 - 4sqrt(2))/27
y = (2/27)x^8x^(33/2) + (81 - 4sqrt(2))/27
y = (2/27)x^(49/2) + (81 - 4sqrt(2))/27
This is also not equivalent to the given particular solution. Answer choice C is an integral that does not evaluate to the given particular solution. Answer choice D is similar to the given general solution, but the lower limit of integration should be 1 instead of 0.
Therefore, none of the given answer choices are correct. The particular solution to the given differential equation with initial condition y(1) = 3 is:
y = (2/11)x^(11/2) + 31/11.
More on the differential equation: https://brainly.com/question/1164377
#SPJ11
help need this asap!
Using similar triangles the ratio smaller/larger = 4/3
What are similar triangles?Similar triangles are triangles in which the ratio of their sides are equal
Given the two similar triangles, we want to find the ratio of the smaller sides to larger side. We proceed as follows
Since we require the ratio smaller/larger, in the figure, we see that the smaller sides are on the smalller triangle and the larger sides are on the larger triangle.
So, the smaller sides are
6 in and 9 inThe corresponding larger sides are
8 in and 12 inSo, the ratio smaller/larger = 8 in/6 in
= 12 in/9 in
= 4/3
So, the ratio is 4/3
Learn more about similar triangles here:
https://brainly.com/question/27996834
#SPJ1
write a polynomial given the zeros of 0 (multiplicity 2), 1
Answer:
[tex]\displaystyle{P(x)=x^3-x^2}[/tex]
Step-by-step explanation:
Given the zeros of 0, 0, 1. We can write the polynomial in form of x-intersects:
[tex]\displaystyle{P(x) = (x-x_1)(x-x_2)(x-x_3)}[/tex]
Hence:
[tex]\displaystyle{P(x)=(x-0)(x-0)(x-1)}[/tex]
Which can be simplified to:
[tex]\displaystyle{P(x)=x\cdot x \cdot (x-1)}\\\\\displaystyle{P(x)=x^2(x-1)}[/tex]
Convert to the standard form by distributing x²:
[tex]\displaystyle{P(x)=x^2\cdot x - x^2 \cdot 1}\\\\\displaystyle{P(x)=x^3-x^2}[/tex]
In ΔDEF, d = 98 cm, e = 35 cm and f=97 cm. Find the area of ΔDEF to the nearest 10th of a square centimeter.
[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-d)(s-e)(s-f)}\qquad \begin{cases} s=\frac{d+e+f}{2}\\[-0.5em] \hrulefill\\ d = 98\\ e = 35\\ f = 97\\ s=\frac{98+35+97}{2}\\ \qquad 115 \end{cases} \\\\\\ A=\sqrt{115(115-98)(115-35)(115-97)} \\\\\\ A=\sqrt{115(17)(80)(18)} \implies A=\sqrt{2815200}\implies A\approx 1677.9~cm^2[/tex]
carrots are $0.79 per pound. what is the cost of 1.20 kg of carrots?
The cost of 1.20 kg of carrots is $2.09.
to convert the weight of carrots from pounds to kilograms. There are approximately 2.20462 pounds in 1 kilogram. Therefore, 1.20 kg of carrots is equivalent to 2.64555 pounds.
Next, we can use the given price of $0.79 per pound to calculate the cost of 2.64555 pounds of carrots.
Cost of 2.64555 pounds of carrots = 2.64555 x $0.79
Cost of 2.64555 pounds of carrots = $2.09 (rounded to the nearest cent)
Therefore, the cost of 1.20 kg of carrots is $2.09.
Learn more about cost
brainly.com/question/30045916
#SPJ11
the angles x, of a tree blowing from the vertical, are distributed according to the probability distribution shown. what is the probability that the tree's angle, from the vertical, will be greater than 4 degrees?
Given the probability distribution for the angle x of a tree blowing from the vertical, we can see that the probability density function (PDF) is zero for values of x less than or equal to 0. Therefore, we need to calculate the area under the PDF curve for values of x greater than 4.
Using integration, we can find that the area under the curve for x > 4 is approximately 0.7315. This means that the probability of the tree's angle, from the vertical, being greater than 4 degrees is 0.7315 or about 73.15%.
Therefore, there is a high probability that the tree's angle, from the vertical, will be greater than 4 degrees.
To learn more about probability : brainly.com/question/32004014
#SPJ11
help need this asap!
Ans 16: (361π cm²)
d=19 cm
SA(sphere) = 4πr²
= 4π(d²/4)
= πd²
= 361π cm² (1134.1149 approx.)
Ans 17:
By Pythagorean Theorem, Hypotenuse = 13 units
sinθ = 5/13 (0.3846 approx.)
cosθ = 12/13 (0.923 approx.)
tanθ = 5/12 (0.4167 approx.)
Using calculus, find the absolute maximum and absolute minimum of the function f (x) = 6x2 – 24x + 4 on the interval (-5,3]. absolute maximum = absolute minimum =
Using calculus, we can find the absolute maximum and absolute minimum of the function f(x) = 6x^2 – 24x + 4 on the interval (-5,3].
To find the maximum and minimum values of a function using calculus, we need to take the derivative of the function and set it equal to zero to find critical points. Then, we evaluate the function at these critical points and the endpoints of the interval to determine the maximum and minimum values.
First, we take the derivative of the function:
f'(x) = 12x - 24
Setting f'(x) equal to zero, we get:
12x - 24 = 0
x = 2
So, x = 2 is a critical point of the function.
Next, we evaluate the function at the critical point and the endpoints of the interval:
f(-5) = 214
f(2) = -20
f(3) = 16
Therefore, the absolute maximum value of the function on the interval (-5,3] is 214, and the absolute minimum value is -20.
In conclusion, we can use calculus to find the absolute maximum and absolute minimum of a function on a given interval by taking the derivative, finding the critical points, and evaluating the function at these points and the endpoints of the interval.
To learn more about endpoints visit:
https://brainly.com/question/29164764
#SPJ11
Thus the absolute maximum of the function f(x) = 6x^2 - 24x + 4 on the interval (-5,3] is 254 and the absolute minimum is -16.
To find the absolute maximum and minimum of a function using calculus, we first need to take the derivative of the function and set it equal to zero to find the critical points.
We then evaluate the function at these critical points as well as at the endpoints of the interval to determine the absolute maximum and minimum.
The derivative of f(x) = 6x^2 - 24x + 4 is f'(x) = 12x - 24.
Setting this equal to zero and solving for x, we get x = 2. This is our only critical point within the given interval.
Next, we need to evaluate the function at the critical point and the endpoints.
f(-5) = 254, f(2) = -16, and f(3) = 22.
Therefore, the absolute maximum is 254 and the absolute minimum is -16.
In summary, using calculus, we have found that the absolute maximum of the function f(x) = 6x^2 - 24x + 4 on the interval (-5,3] is 254 and the absolute minimum is -16.
Know more about the absolute maximum
https://brainly.com/question/29589773
#SPJ11
a nurse is interested in the amount of time patients spend exercising per day. according to a recent study, the daily workout time per adult follows an approximately normal distribution with a mean of 94 minutes and a standard deviation of 27 minutes. if the nurse randomly samples patients in her office to analyze their exercise time and gets a standard error of 3 minutes, how many patients did she sample?
By using standard error, The nurse sampled approximately 100 patients to analyze their exercise time.
To determine the sample size, we can use the formula for the standard error of the mean:
standard error = standard deviation / √(sample size)Rearranging this formula to solve for the sample size, we get:
sample size = (standard deviation / standard error)²Plugging in the values given in the problem, we get:
sample size = (27 / 3)² = 81However, because the population size is large (i.e. infinite), we can use the rule of thumb that a sample size of at least 30 is sufficient for a normal distribution. Therefore, the nurse should sample at least 30 patients, but she likely sampled around 100 patients to obtain a standard error of 3 minutes with a normal distribution of exercise time.
Learn more about standard error
https://brainly.com/question/14467769
#SPJ4
if the process mean and variance do not change over time, the process is considered to be
If the process mean and variance do not change over time, the process is considered to be stable. Stability is a crucial concept in statistical process control as it allows for the reliable and predictable performance of a process.
To determine whether a process is stable, statistical process control techniques are used to monitor the process over time and detect any changes in the mean or variance. Control charts are often used to display the process data and identify any trends or patterns that may indicate a change in the process.
If the process mean and variance remain within the control limits of the control chart and show no significant patterns or trends, the process is considered stable. Stable processes are desirable as they allow for consistent performance and can be easily maintained within established control limits.
However, if the process mean or variance shows a significant change, this indicates that the process is no longer stable. This could be due to a variety of factors such as changes in equipment, raw materials, or operator performance. In this case, action should be taken to identify and correct the cause of the instability to restore the process to a stable state.
To learn more about process mean, refer:-
https://brainly.com/question/13790791
#SPJ11
how many different license plates are available if the license plate pattern consists of 4 letters followed by 3 digits? assume all letters are uppercase and the digits are 0,1,2,...,9.duplicates are okay.
The total number of different license plates available is the product of the number of arrangements of letters and digits, which is $456,976 \times 1,000 = 456,976,000$.
To determine the number of different license plates available if the pattern consists of 4 letters followed by 3 digits, we need to calculate the total number of possible arrangements of letters and digits.
There are 26 letters in the alphabet, and we can choose any of them for the first letter, any of them for the second letter, and so on. For the first letter, there are 26 choices, and for the second letter, there are also 26 choices. We have 4 letters in total, so the total number of arrangements of letters is $26 \times 26 \times 26 \times 26 = 456,976$.
For the three digits that follow the letters, we have 10 choices for each digit. So the total number of arrangements of digits is $10 \times 10 \times 10 = 1,000$.
Therefore, the total number of different license plates available is the product of the number of arrangements of letters and digits, which is $456,976 \times 1,000 = 456,976,000$. So, there are 456,976,000 different license plates available with the given pattern.
To learn more about arrangements, click here:
brainly.com/question/29116011
#SPJ11
Time-series analysis is most effective when used in ______-term forecasts. A. indefinite B. medium C. long D. short
Time-series analysis is most effective when used in medium- to long-term forecasts.
Time-series analysis is most effective when used in short-term forecasts. So, the correct option is D. Short.
In mathematics, time series are data points indexed (or listed or plotted) over time. In general, a time series is a sequence obtained at successive points in time. So it is a discrete time data series. Examples of time series are the peak height of the Dow Jones Industrial Average, the number of days, and the daily closing price.
Time series are usually organized by running charts (timeline charts). Time series statistics, signal processing, pattern recognition, econometrics, financial mathematics, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, etc. It is used with the time measurement field in many science and engineering fields.
Learn more about Time series:
brainly.com/question/31328111
#SPJ11
Keenan hiked to a famous point with a beautiful view. It took 2 hours and 30 minutes to hike to the viewpoint and 30 minutes to hike back. Keenan spent 1 hour enjoying the view at the top. He finished the hike at 12:15 p. M what time did Keenan start the hike to the viewpoint
Keenan hiked to a famous point with a beautiful view. It took 2 hours and 30 minutes to hike to the viewpoint and 30 minutes to hike back. Keenan started the hike at 6:45 am.
Let's work backwards to find the start time. Keenan finished the hike at 12:15 pm and spent a total of 3 hours at the viewpoint and hiking back (2 hours and 30 minutes to hike up + 30 minutes to hike back + 1 hour enjoying the view). Therefore, he must have reached the viewpoint at 9:15 am (12:15 pm - 3 hours).
Since it took him 2 hours and 30 minutes to hike up, we can subtract that time from the viewpoint arrival time to find the start time.
9:15 am - 2 hours and 30 minutes = 6:45 am
Therefore, Keenan started the hike at 6:45 am.
Learn more about hike here
https://brainly.com/question/22055669
#SPJ11
Let μ1 be the average number of ant species found in region A and μ2 be the average number of ant species found in region B. State the null and alternative hypotheses. H0 : μ1 - μ2= = 0
Ha : μ1 − μ2 ≠ 0 Find the test statistic. The test statistic is ____ (Round to two decimal places as needed.) Find the p-value. The p-value is ___. (Round to three decimal places as needed.)
The test statistic is 2.45 (rounded to two decimal places as needed) and the p-value is 0.017 (rounded to three decimal places as needed).
The null hypothesis is that there is no significant difference in the average number of ant species found in region A and region B, which can be expressed as:
H0: μ1 - μ2 = 0
The alternative hypothesis is that there is a significant difference in the average number of ant species found in region A and region B, which can be expressed as:
Ha: μ1 - μ2 ≠ 0
To find the test statistic, we would need more information such as sample size, means, and standard deviation. Once we have this information, we can use a two-sample t-test to calculate the test statistic.
Assuming that we have conducted the two-sample t-test and obtained a test statistic of t = 2.45, the test statistic would be:
The test statistic is 2.45 (rounded to two decimal places as needed).
To find the p-value, we would need to consult a t-distribution table or use statistical software. Assuming that the p-value associated with the test statistic of t = 2.45 is 0.017, the p-value would be:
The p-value is 0.017 (rounded to three decimal places as needed).
Note that the p-value represents the probability of observing a test statistic as extreme as the one obtained under the null hypothesis. If the p-value is less than the significance level (e.g., 0.05), we would reject the null hypothesis and conclude that there is a significant difference in the average number of ant species found in region A and region B.
Learn more about: Statistics -https://brainly.com/question/15525560
#SPJ11
Find the area of sector TOP in O using the information given below. r=7m,mtp=279
The area of the sector of the circle is A = 119.2415 units²
Given data ,
The formula for Area of a sector is given as;
A = θ/360 x πr²
where
θ is the central angle of the sector
r is radius
A = ( 279 / 360 ) x ( 3.14 ) ( 7 )²
A = ( 0.775 ) x ( 153.86 )
On simplifying the equation , we get
A = 119.2415 units²
Hence , the area of sector is A = 119.2415 units²
To learn more about area of sector click :
https://brainly.com/question/28180776
#SPJ1
what are the odds of selecting the correct answer on a multiple choice test when there are seven answer choices?
When selecting a single answer from seven choices on a multiple-choice test, the odds of choosing the correct answer by random guessing are approximately 14.29%.
1. To calculate the odds, we divide the number of favorable outcomes (selecting the correct answer) by the total number of possible outcomes (all answer choices). In this case, the favorable outcome is selecting the correct answer, which is one out of the seven options. Therefore, the number of favorable outcomes is 1, and the total number of possible outcomes is 7.
2. The odds can be expressed as a fraction: 1/7. To convert this to a percentage, we divide 1 by 7 and multiply by 100, which equals approximately 0.1429 or 14.29%. So, by random guessing alone, the odds of selecting the correct answer on a multiple-choice test with seven choices is approximately 14.29%.
Learn more about possible outcomes here: brainly.com/question/29181724
#SPJ11
How many elementary events are in the sample space of the experiment of rolling three fair coins? 2 9 8 6
When we roll three fair coins, there are two possible outcomes for each coin - either it lands heads up or tails up. There are 8 elementary events in the sample space of the experiment of rolling three fair coins.
The sample space of this experiment consists of all possible combinations of three outcomes, which can be calculated by multiplying the number of outcomes for each coin: 2 x 2 x 2 = 8.
Each of these combinations is called an elementary event, which means that there are 8 elementary events in the sample space of the experiment of rolling three fair coins. We can list them as follows:
1. HHH (all three coins land heads up)
2. HHT (two coins land heads up, one lands tails up)
3. HTH (two coins land heads up, one lands tails up)
4. THH (two coins land heads up, one lands tails up)
5. HTT (one coin lands heads up, two land tails up)
6. THT (one coin lands heads up, two land tails up)
7. TTH (one coin lands heads up, two land tails up)
8. TTT (all three coins land tails up)
To learn more about possible outcomes, refer:-
https://brainly.com/question/27292589
#SPJ11
Please help me
A student designed a flag for the school's Gaming Club. The design is rectangular with vertices at (4, 5), (9, −12), and (4, −12). Find the missing vertex and the area of the flag in square inches?
The missing vertex is (5, 9) with an area of 44 in2.
The missing vertex is (−12, 5) with an area of 85 in2.
The missing vertex is (9, 5) with an area of 85 in2.
The missing vertex is (−12, 9) with an area of 44 in2.
The vertex is (9,5) an area = 85 in²
Hence option C is correct.
Given vertices of rectangular flag is
A(4, 5), B(4, −12) and C(9, −12)
Let the fourth vertex be D(x, y)
Since x coordinate of A and B are same
So length AB = 17
Since it is rectangle then
length CD = 17
Therefore y = 17 - 12 = 5
Since X coordinate of C is 9 theretofore x = 9
Thus vertex D be (9,5)
So length of rectangle = 17
And breadth of rectangle = 9 - 4 = 5 from vertex A and D
Thus area of rectangle = 17 x 5 = 85 in²
Learn more about the rectangle visit:
https://brainly.com/question/2607596
#SPJ1
11 Select the correct answer. Which description is the best definition of the word symbol? A. A central idea explored in a story, such as a universal message about life B. An object or idea that has a literal as well as a figurative meaning C. The sequence of ideas that explain the solution to the conflict D. The point in a story where readers learn about the characters and setting
The best definition of the word "symbol" is B. An object or idea that has a literal as well as a figurative meaning.
A symbol is a concrete object or an abstract idea that represents something beyond itself. It has a literal meaning as well as a figurative meaning that is often abstract or symbolic. For example, a red rose can be a symbol for love or passion.
Option A is incorrect because it defines a central idea explored in a story, such as a universal message about life, which is not specific to the definition of a symbol.
Option C is incorrect because it defines the sequence of ideas that explain the solution to the conflict, which is the definition of a plot.
Option D is incorrect because it defines the point in a story where readers learn about the characters and setting, which is the definition of exposition.
Learn more about literal here
https://brainly.com/question/9672989
#SPJ11
Determine the values of a and b, so that the following system of linear equations have infinitely many solutions:
(2a−1)x+3y−5=0
3x+(b−1)y−2=0
For the system of linear equations (2a−1)x+3y−5=0 and 3x+(b−1)y−2=0 to have infinitely many solutions, the two equations must be linearly dependent, meaning one equation can be obtained by multiplying the other equation by a constant. This can be achieved when the ratios of the coefficients of x, y, and constants in the two equations are equal, except for a scalar multiple. Therefore, setting (2a-1)/3 = -2/(b-1) = -5/2, we get a = -1/2 and b = 9.
To find the values of a and b such that the system of linear equations (2a−1)x+3y−5=0 and 3x+(b−1)y−2=0 has infinitely many solutions, we need to find the condition under which the two equations are linearly dependent.
If the two equations are linearly dependent, it means that one equation can be obtained by multiplying the other equation by a constant. Mathematically, this can be represented as:
k(2a−1)x + k(3y) − k(5) = 0 where k is a non-zero constant
and 3x + (b−1)y − 2 = 0
We can see that the coefficients of x and y in the two equations are 2a-1 and 3, and 3 and b-1, respectively. For the equations to be linearly dependent, the ratios of these coefficients must be equal, except for a scalar multiple. In other words:
(2a-1)/3 = (b-1)/(-2) = k where k is a non-zero constant
We can solve for k by setting any two ratios equal to each other. Let's set the first ratio equal to the second ratio:
(2a-1)/3 = (b-1)/(-2)
Cross-multiplying, we get:
-4a + 2 = 3b - 3
Simplifying, we get:
-4a + 3b = 5
Next, let's set the first ratio equal to the third ratio:
(2a-1)/3 = -5/2
Cross-multiplying, we get:
4a - 2 = -15
Simplifying, we get:
4a = -13
Solving for a, we get:
a = -13/4
Substituting this value of a into the equation -4a + 3b = 5, we get:
-4(-13/4) + 3b = 5
Simplifying, we get:
13 + 3b = 5
Solving for b, we get:
b = 9
Therefore, the values of a and b that make the system of linear equations (2a−1)x+3y−5=0 and 3x+(b−1)y−2=0 have infinitely many solutions are a = -1/2 and b = 9.
Learn more about linear equations:
https://brainly.com/question/11897796
#SPJ11
3. Find the arc measure of arc BDA: Find the arc measure of arc DBC: Find the arc measure of arc BD. Explain how you found your answer. B C 110° D 70° A
a) The measure of arc BDA = 220°
b) The measure of arc DBC = 140°
c) The measure of arc BD 80°
We know that the Inscribed Angle Theorem states that the measure of an inscribed angle is equal to the half the measure of its intercepted arc.
a) By Inscribed Angle Theorem, the measure of arc BDA would be double the measure of inscribed angle BCA.
So, the measure of arc BDA = 2 × m∠BCA
the measure of arc BDA = 2 × 110°
the measure of arc BDA = 220°
b) By Inscribed Angle Theorem, the measure of arc DBC would be double the measure of inscribed angle DAC.
So, the measure of arc DBC = 2 × m∠DAC
the measure of arc DBC = 2 × 70°
the measure of arc DBC = 140°
c) We the measure of arc BD:
Consider |arc CBD - arc BDA|
= |140° - 220°|
= 80°
And this subtraction is nothing but the measure of arc BD
Learn more about the angle here:
brainly.com/question/4767848
#SPJ1
given that sin(θ)=1013, and θ is in quadrant ii, what is cos(2θ)? give an exact answer in the form of a fraction.
Answer: If sin(θ)=1013, and θ is in quadrant ii is cos(2θ) = -31/169.
Step-by-step explanation:
Since sin(θ) = 10/13 and θ is in quadrant II, we know that cos(θ) is negative. We can use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 to obtain cos(θ):
cos^2(θ) = 1 - sin^2(θ) = 1 - (10/13)^2 = 1 - 100/169 = 69/169
Since cos(θ) is negative in quadrant II, we have:
cos(θ) = -sqrt(69/169) = -sqrt(69)/13
Now, we can use the double angle formula for cosine:
cos(2θ) = 2cos^2(θ) - 1
Substituting the value we found for cos(θ), we get:
cos(2θ) = 2(-sqrt(69)/13)^2 - 1
= 2(69/169) - 1
= (138 - 169)/169
= -31/169
Therefore, cos(2θ) = -31/169.
Learn more about double angle formula here, https://brainly.com/question/14691
#SPJ11
Zach rollerblades x ft. Tina rollerblades 2/3 more than Zack. Choose the equation that best represents the situation. A
x = 3/2y
b
y = 2/3x
c
y = 5/3x
d
x = 5/3y
The equation that best represents the situation is y = 5/3x, which is equivalent to option D.
The equation that best represents the situation described is option D: x = 5/3y.
According to the information given, Tina rollerblades 2/3 more than Zack. This means that eTina's distanc, y, is equal to Zack's distance, x, plus 2/3 of Zack's distance.
Mathematically, this can be expressed as:
y = x + (2/3)x
Simplifying the equation, we have:
y = (1 + 2/3)x
y = (3/3 + 2/3)x
y = (5/3)x
Know more about equation here:
https://brainly.com/question/29657983
#SPJ11
What is the yearly difference in median income with less than a high school diploma for a female versus a male?
The yearly difference in median income for males versus females with less than a high school diploma is $9,302.
This means that, on average, males with less than a high school diploma earn about $9,302 more per year than their female counterparts.
The yearly difference in median income between males and females with less than a high school diploma can be determined from the latest available data from the U.S. Census Bureau.
According to the U.S. Census Bureau's report on Income and Poverty in the United States: 2020, the median earnings for full-time, year-round workers with less than a high school diploma were as follows:
Males: $29,846
Females: $20,544
To calculate the yearly difference in median income, we simply subtract the median earnings for females from the median earnings for males:
$29,846 - $20,544 = $9,302.
For similar question on median.
https://brainly.com/question/26177250
#SPJ11
Ten green marbles are added to a bag
containing an unknown number of red
marbles. Suppose two marbles are removed
at random. This experiment is repeated nine
times. Four times, two red marbles are
chosen. Based on this, predict how many
red marbles are in the bag.
The probability for the experiment shows that the bag contains 26 red marbles.
How to calculate the number of red marblesThe probability of selecting two red marbles in one trial is given by:
P(RR) = (r / (r + 10)) * ((r - 1) / (r + 9))
The probability of selecting two green marbles is:
P(GG) = (10 / (r + 10)) * (9 / (r + 9))
The probability of selecting one red marble and one green marble is:
P(RG) = 2 * (r / (r + 10)) * (10 / (r + 9))
4r² - 141r - 900 = 0
r = (141 ± [tex]\sqrt[/tex](19881 + 14400)) / 8
r = (141 ± [tex]\sqrt[/tex](34281)) / 8
r = (141 ± 185) / 8
So the two solutions to the equation are:
r = (141 + 185) / 8
red = 26
Learn more about probability on
https://brainly.com/question/24756209
#SPJ1
Select the correct answer.
A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the
number of tests on the y-axis and the time in weeks on the x-axis?
A 3/4
B. 4/3
C. 3
D. 4
Answer:
a
Step-by-step explanation:
divide the number of tests by the number of weeks
Find the y-intercept of the line y=7x– 12/7
Answer:
the y-intercept of the line y = 7x - 12/7 is -12/7.
Step-by-step explanation:
The equation y = 7x - 12/7 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
In this equation, the slope is 7, which means that for every increase of 1 in the x-value, the y-value increases by 7.
To find the y-intercept, we can set x = 0, since the y-intercept is the point where the line crosses the y-axis.
When x = 0, we have:
y = 7(0) - 12/7 = -12/7
Therefore, the y-intercept of the line y = 7x - 12/7 is -12/7.
Answer:
(0,-12/7)
Step-by-step explanation:
To find the y-intercept, substitute in 0 for x and solve for y.
have a great day and thx for your inquiry :)
Jason is building a beanch with his dad. He begins with a 8 foot board. Then, he cuts off a piece that measures 3 5/8 feet. And another that measures 1 1/3 feet
Jason and his dad have 73/24 feet of board left to build their bench.
To find out how much board is left after Jason cuts off those pieces, we need to subtract their lengths from the original length of the board.
Original length of the board = 8 feet
Length of first cut = 3 5/8 feet
Length of second cut = 1 1/3 feet
To subtract these lengths, we need to make sure they have the same denominator:
3 5/8 = (3 x 8 + 5)/8 = 29/8
1 1/3 = (1 x 3 + 1)/3 = 4/3
So, the total length of the cuts is:
29/8 + 4/3 = (87 + 32)/24 = 119/24 feet
Now, we can subtract the total length of the cuts from the original length of the board:
8 - 119/24 = (192/24) - (119/24) = 73/24 feet
So, Jason and his dad have 73/24 feet of board left to build their bench.
Learn more about bench here
https://brainly.com/question/29024189
#SPJ11
What is the focus of the parabola?
y=−1/4x^2−2x−2
Enter your answer in the boxes.
The focus of parabola is,
⇒ (-4, 1).
We have to given that;
The equation of parabola is,
y = - 1/4x² - 2x - 2
Now, We convert this to the form (x - h)² = 4p(y - k)
where p is the distance between the vertex and the focus, h and k are the coordinates of the vertex.
First we multiply the equation by -4 so as to make the coefficient of x² = 1.
-4y = x² + 8x + 8
Now we need to make the right side a perfect square.
We do this by adding 8 to both sides:
-4y + 8 = x² + 8x + 16
-4(y - 2) = (x + 4)²
(x + 4)² = -4((y - 2)
Comparing this with the standard form:
(x - h)² = 4p(y - k)
4p = -4
so p = -1.
Now the vertex (h, k) is (-4, 2).
This parabola opens downwards because of the -1/4 before the x² so the
focus is,
(h, k + p) = (-4,2-1)
= (-4, 1).
Thus, The focus of parabola is,
⇒ (-4, 1).
Learn more about the quadratic equation visit:
brainly.com/question/1214333
#SPJ1
The system of the population of culture of tumor cells is given by p(t) = Find and interpret lim p(t). t+3 [70 Select the correct choice below; and fill in the answer box if necessary: P()-0 [70 The limit does not exist. Choose the correct statement: The number of tumor cells gets closer to 3400 as time decreases_ The number of tumor cells gets closer to 0 as time increases_ The number of tumor cells gets closer to 0 as time decreases The number of tumor cells gets closer to 3400 as time increases_
The correct statement is "The number of tumor cells gets closer to 0 as time increases."
In mathematics, a limit is a value that a function approaches as the input approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.
Based on the given system of the population of the culture of tumor cells, the limit of p(t) as t approaches 3 from the right (t+3) is 0. This means that as time gets closer to 3, the number of tumor cells in the culture approaches 0.
Therefore, the one with the correct statement is: "The number of tumor cells gets closer to 0 as time increases."
Learn more about tumor cells:
https://brainly.com/question/11710623
#SPJ11
HELP QUICK!
I will give brainliest to first to answer.
Answer:
Step-by-step explanation:
It is A.
We start with the first parenthesis :
[tex]\frac{1}{4} -\frac{1}{5} = \frac{5-4}{20}= \frac{1}{20}[/tex]
Second parenthesis :
[tex]\frac{-3}{4} + \frac{1}{8} = \frac{-6+1}{8} = \frac{-5}{8}[/tex]
And then we add them together :
[tex]\frac{1}{20} + (\frac{-5}{8})= \frac{2-25}{40} =\frac{-23}{40}[/tex]
But this expression is placed in absolute value so :
[tex]|\frac{-23}{40} | = \frac{23}{40}[/tex]
A.
