Determine the total number of marble in the bag.
[tex]\begin{gathered} n(T)=7+3+5 \\ =15 \end{gathered}[/tex]Determine the probability for first three marbles be red.
[tex]\begin{gathered} P(R=3)=\frac{^7C_3^{}}{^{15}C_3} \\ =\frac{35}{455} \\ =\frac{7}{91} \end{gathered}[/tex]The probability for first three marble is not to be red is equal to one minus the probability for the first three marble be red.
[tex]\begin{gathered} P(R\ne3)=1-P(R=3) \\ =1-\frac{7}{91} \\ =\frac{91-7}{91} \\ =\frac{84}{91} \\ =\frac{12}{13} \end{gathered}[/tex]So answer is 12/13.
A door to playhouse is 50 inches tall.Which of the following is another measure eaqual to the height?A.4 ft 2 in.B.4 ft 1 in.C.4 ft 1/2 in.D.5 ft
Dereo, this is the solution:
All we need to do is to convert inches to feet, as follows:
Let's recall that:
12 inches = 1 feet
In consequence,
50 inches = 50/12 feet
50 inches = 4 feet + 2 inches
The correct answer is A.
Consider the following functions.Step 3 of 4: Find (f g)(-1). Simplify your answer.Answerf(x) = x² + 6 and g(x) = -x +5(-2)-1)=
Solving for (f•g)(-1)
[tex]\begin{gathered} (f\cdot g)(x)=f(x)\cdot g(x) \\ (f\cdot g)(x)=(x^2+6)\cdot(-x+5) \\ (f\operatorname{\cdot}g)(-1)=((-1)^2+6)\operatorname{\cdot}(-(-1)+5) \\ (f\operatorname{\cdot}g)(-1)=(1+6)\cdot(1+5) \\ (f\operatorname{\cdot}g)(-1)=7\cdot6 \\ \\ \text{Therefore, }(f\operatorname{\cdot}g)(-1)=42 \end{gathered}[/tex]What is the area of this figure?5 in5 in12 in23 in18 in17 in
The area of the figure is 331 square inches
Explanation:The area of the shape can be obtained by:
Treating the shape as a rectangle with side lengths 23 in and 17 in
Finding the area of the rectangle
Finding the area of the small portion cut, which is a rectangle with side lengths 5 in and 12 in.
Subtracting the area of the small portion from the area of the big rectangle.
Area of the big rectangle = 23 * 17 = 391 in^2
Area of the small portion = 5 * 12 = 60 in^2
Area of the shape = 391 - 60 = 331 in^2
Identify the parent function of f(x) = -×^2+2
The given function is
[tex]f(x)=-x^2+2[/tex]The parent function refers to the simplest function possible.
Hence, the parent function is[tex]f(x)=x^2[/tex]Study the data given,Below are the weights of 6 randomly selectedblack bears and 6 randomly selected grizzly bearsliving on a wildlife refuge.Which type of bear had morevariation in weight?Black Bear Weights (lbs): 102, 151, 248, 342,453, 498A. Black BearsMean: 299MAD: 132B. Grizzly BearsC. Both showed the same amount ofvariation in weightHaven't learned this yet.Grizzly Bear Weights (lbs): 294, 302, 347, 422,553, 596Mean: 419MAD: 104 2/3
The mean absolute deviation (MAD) is a statistical measure of how much the different data points "move away" from the mean of the data set. In this case the weights of the bears have been given, the mean has been calculated and the MAD is derived by deducting each data point from the mean. The MAD has been given already by the way. Some data points fall below the mean while some are above it. but whatever the difference is, you'll have to take the "absolute value" that is positive value only. For example, the mean weight of the black bears is 299, and the weight of the first black bear is 102, that gives you adifference of 197. note that the result should be negative 197 (-197) but we are interested in the absolute values only.
Same way you find the absolute deviation for the other data points and you have, 197, 148, 51, 43, 154, and 199. Sum up these numbers and divide by the number of observed data (number of black bears) and you have 792 divided by 6 which gives you 132. This means the mean absolute deviation of the observed data is 132 as compared to the mean which is 299.
If you compare the MAD of the black bears with that of the grizzly bears, you would see that the MAD of the grizzly bears is more varied, because 104 2/3 moves further away from 419 than the MAD of the black bears which is 132 moving away from 299.
I have a calculus question about linear approximation. It is a doozie. High school, 12th grade senior AP Calculus. Math, not physics.
To get the linear approximation, we follow the equation below:
[tex]y=f(a)+f^{\prime}(a)(x-a)[/tex]where "a" is the given value of x and f'(a) is the slope of the function at a given value of "a".
In the given equation, the given value of "a" or x is 5.
Let's now solve for the linear approximation. Here are the steps:
1. Solve for f(a) by replacing the x-variable in the given function with 5.
[tex]f(5)=5^5[/tex][tex]f(a)=3125[/tex]The value of f(a) is 3125.
2. Solve for the first derivative of f(x) using the power rule.
[tex]f(x)=x^5\Rightarrow f^{\prime}(x)=5x^4[/tex]The first derivative is equal to 5x⁴.
3. Replace the "x" variable in the first derivative with 5 and solve.
[tex]f^{\prime}(5)=5(5)^4[/tex][tex]f^{\prime}(5)=5(625)[/tex][tex]f^{\prime}(5)=3125[/tex]The value of the first derivative at x = 5 is also 3,125.
4. Using the linear approximation formula above, let's now replace f(a) with 3125 and f'(a) with 3125 as well since those are the calculated value in steps 1 and 3. Replace "a' with 5 too.
[tex]y=3125+3125(x-5)[/tex][tex]y=3125+3125(x-5)[/tex]5. Simplify the equation above.
[tex]y=3125+3125x-15625[/tex][tex]y=3125x-12500[/tex]Hence, the equation of the tangent line to f(x) at x = 5 is y = 3,125x - 12500 where the slope m is 3,125 and the y-intercept b is -12,500.
Now, to find our approximation for 4.7⁵, replace the "x" variable in the equation of the tangent line with 4.7 and solve.
[tex]y=3,125x-12,500[/tex][tex]y=3,125(4.7)-12,500[/tex][tex]y=14,687.5-12,500[/tex][tex]y=2187.5[/tex]
Using the approximated linear equation, the approximated value of 4.7^5 is 2, 187.5.
pls help with this. just the answer
Answer:
Step-by-step explanation:
“y” should be the first step of the system.
Solve for y:2x – 3y = 5
y = (2x-5)/3
Explanation:
[tex]\begin{gathered} 2x\text{ - 3y = 5} \\ To\text{ solve for y, we need to make y the subject of formula} \end{gathered}[/tex][tex]\begin{gathered} \text{Let's take every other thing not attached to y to the right side of the equation:} \\ -3y\text{ = 5 - 2x} \\ To\text{ make y stand alone, we will divide through by -3} \\ \frac{-3y}{-3}=\text{ }\frac{5-2x}{-3} \\ y\text{ = }\frac{-(5-2x)}{3}\text{ or }\frac{-5\text{ +2x}}{3}\text{ } \\ y\text{ = }\frac{2x\text{ -5}}{3} \end{gathered}[/tex]Which statement describes a key feature of the function g if g(x) =f(x)-7
The graph of the function f(x)=e^x is given.
To determine the function g(x),
g(x)=f(x)-7.
Then the graph of function g(x) is
Then from the graph above , the horizontal asymptote is y=-7.
Hence the correct option is D.
Solve the compound an equality. Write the solution in interval notation.
Step 1: Write the two inequalities equations
[tex]4u\text{ + 1 }\leq\text{ -3 -2u }\ge\text{ 10}[/tex]Step 2: Solve the two inequalities separately
[tex]\begin{gathered} 4u\text{ + 1 }\leq\text{ -3} \\ 4u\text{ }\leq\text{ -3 -1 } \\ 4u\text{ }\leq\text{ -4} \\ u\text{ }\leq\text{ }\frac{-4}{4} \\ u\text{ }\leq\text{ -1} \end{gathered}[/tex][tex]\begin{gathered} -2u\text{ }\ge\text{ 10} \\ \text{When you divide inequalities by -2, the sign will change} \\ \frac{-2u}{-2}\text{ }\leq\text{ }\frac{10}{-2} \\ u\text{ }\leq\text{ -5} \end{gathered}[/tex]
Final answer
[tex](-\infty,\text{ -5\rbrack}[/tex]Or
[tex]\lbrack\text{ x }\leq\text{ -5\rbrack or ( -}\infty,\text{ -5)}[/tex]find the following numbers
We have the numbers 5, 11, 8, 8 7, 4, 10, 9, 7, 7, 6 and we have to calculate its mean.
To calculate the mean of a group of numbers we have to sum them all and then divide by the number of items we have added.
In this case we have 11 elements, so the mean can be calculated as:
[tex]M=\frac{5+11+8+8+7+4+10+9+7+7+6}{11}=\frac{82}{11}\approx7.45[/tex]The mean of this group of numbers is 7.45 periodic.
The school that Imani goes to is selling tickets to a spring musical. On the first day of ticketsales the school sold 6 senior citizen tickets and 8 child tickets for a total of $122. The schooltook in $167 on the second day by selling 9 senior citizen tickets and 8 child tickets. WriteaSOE and solve it to find the price of a senior citizen ticket and the price of a child ticket
Define the system of equations to solve the problem
Take x as the price of a senior citizen ticket and y as the price of a child ticket
[tex]\begin{gathered} 6x+8y=122 \\ 9x+8y=167 \end{gathered}[/tex]Solve the system
[tex]\begin{gathered} 6x+8y=122 \\ 8y=122-6x \\ 9x+8y=167 \\ 8y=167-9x \end{gathered}[/tex][tex]\begin{gathered} 122-6x=167-9x \\ 9x-6x=167-122 \\ 3x=45 \\ x=\frac{45}{3} \\ x=15 \end{gathered}[/tex][tex]\begin{gathered} 8y=122-6x \\ y=\frac{122-6x}{8} \\ y=\frac{122-6\cdot15}{8} \\ y=\frac{122-90}{8} \\ y=\frac{32}{8} \\ y=4 \end{gathered}[/tex]The price of a senior citizen ticket is $15 and for child is $4
More and more people are purchasing food from farmers' markets. As a consequence, a market researcher predicts that the number of farmers' markets will increase by 5% each year. If there are 7,700 farmers' markets this year, how many will there be in 5 years?
Given:
A market researcher predicts that the number of farmers' markets will increase by 5% each year
There are 7,700 farmers' markets this year
we will the number of farmers' markets after 5 years
So, we will use the following formula:
[tex]A=P\cdot(1+r)^t[/tex]We will calculate (A) when P = 7700, r = 5% and t = 5
so,
[tex]A=7700\cdot(1+\frac{5}{100})^5=7700\cdot1.05^5=9827.368[/tex]Rounding to the nearest whole number
so, the answer will be 9827
Suppose z varies directly with x and inversely with the square of y. If z = 18 when I = 6 and y = 2, what is z when I 7 and y = 7? Z =
It is given that z varies directly with x and inversely with the square of y so it follows:
[tex]z=k\frac{x}{y^2}[/tex]It is also given that z=18 when x=6 and y=2 so it follows:
[tex]\begin{gathered} 18=k\frac{6}{2^2} \\ k=\frac{18\times4}{6} \\ k=12 \end{gathered}[/tex]So the equation of variation becomes:
[tex]z=12\frac{x}{y^2}[/tex]Therefore the value of z when x=7 and y=7 is given by:
[tex]\begin{gathered} z=\frac{12\times7}{7^2} \\ z=\frac{12}{7} \\ z\approx1.7143 \end{gathered}[/tex]Hence the value of z is 12/7 or 1.7143.
Match the appropriate graph to each equation. t(x)= 1/x+3t(x) = -1/x +3
The graph of the function is attached below.
[tex]t(x)=\frac{1}{x+3}[/tex]This matches with the 3rd graph.
Part B
The graph of the function is attached below
[tex]t(x)=-\frac{1}{x}+3[/tex]This matches with the 2nd graph.
Need help. The ps5 cost 610 dollars And Be gets 100 dollars every week
Let x be the number of weeks after Mohammed started to save up. Since he receives $100 every week, then, after x weeks, he would receive 100x dollars.
Since he already had $50 at the beginning, then, the total amount of money y that he has saved after x weeks, is:
[tex]y=100x+50[/tex]Since the cost of the PS5 is $610, then, set y=610 and solve for x to find the number of weeks that he will need to save money:
[tex]\begin{gathered} y=610 \\ \Rightarrow610=100x+50 \\ \Rightarrow610-50=100x \\ \Rightarrow560=100x \\ \Rightarrow\frac{560}{100}=x \\ \Rightarrow x=5.6 \end{gathered}[/tex]He will need to save for at least 5.6 weeks. Nevertheless, he only receives money once a week and 5 weeks won't be enough for buying the PS5. Then, he needs to save for 6 weeks.
In 2018 the scores of students on the May SAT had a normal distribution with mean u = 1450 and a standard deviation of o = 120.a. What is the probability that a single student randomly chosen from all those taking the test scores 1500 or higher?b. If a sample of 50 students is taken from the population, what is the probability that the sample mean score of these students is 1470 or higher?
From the question,
[tex]\begin{gathered} \mu\text{ = 1450, } \\ \sigma\text{ = 120} \end{gathered}[/tex]a. We are to find the probability that a single student randomly chosen from all those taking the test scores 1500 or higher?
we will do this using
[tex]\begin{gathered} P(x<\text{ z) such that } \\ z\text{ = }\frac{x\text{ -}\mu}{\sigma} \end{gathered}[/tex]From the question, x = 1500.
Therefore
[tex]\begin{gathered} z\text{ =}\frac{1500\text{ - 1450}}{120} \\ z\text{ = }\frac{50}{120} \\ z\text{ = 0.417} \end{gathered}[/tex]applying z - test
[tex]\begin{gathered} P(xThus, the probability that a single student is randomly chosen from all those taking the test scores 1500 or higher is approximately 34%b. From the question
[tex]\begin{gathered} n\text{ = 50, }^{}\text{ }\mu\text{ = 1450} \\ \bar{x}\text{ = 1470},\text{ }\sigma\text{ = 120} \end{gathered}[/tex]we will be using
[tex]\begin{gathered} z\text{ = }\frac{\bar{x}\text{ - }\mu}{\frac{\sigma}{\sqrt[]{n}}} \\ \end{gathered}[/tex]inserting values
[tex]\begin{gathered} z\text{ = }\frac{1470\text{ - 1450}}{\frac{120}{\sqrt[]{50}}} \\ z\text{ = }20\text{ }\times\frac{\sqrt[]{50}}{120} \\ z\text{ = }\frac{\sqrt[]{50}}{6} \\ z\text{ = 1.18} \end{gathered}[/tex]Applying z-test
[tex]\begin{gathered} P(xHence,
The probability that the sample mean score of these students is 1470 or higher is approximately 12%
I don't understandDescribe in words and by using function notation
f(x) = 2(x +3)^2 + 1
1. Scale f(x) by 1/2 ==> (1/2) f(x) = (x + 3)^2 + 1
2. Reflect f(x) through x axis ==> -(x+3)^2 + 1
3. Shirt f(x) to the right by 5 units ==> -(x + 3)^2 - 4
4. Shift f(x) down by 5 units ==> -(x - 2) - 4 = g(x)
Vector performed an experiment at a local farm to determine if the addition of bananas to his biomass cow menure recipe helps produce more or less energy. Me collected random samples of menure and benenes from the farm, prepared 15 bottles each of both matures, and placed oballeen on top of each bottle. Alter two weeks, he measured the circumference of each balloon in centimeters: the bigger the balloon grew, the more energy that was produced. The results of the experiment are displayed in the box plots below. Which description most accurately summarizes the sample results? 10. 11. 13. 13. 14. 15. 15. 15. 18. 18. 19 20. 22. 25. 26 22.22.26 29 30 31 36. 36 38. 39. 43 46. 46. 49. 50 MORE CONSISTENT LESS S OUT THE Autor behind ONE CON nece MORE
Notice the smaller range and values of the experiment with cow manure (smaller box diagram and also located at smaller values of total energy.
The banana mixture clearly generates a wider box diagram (so less consistent) and also located at higher values (to the right).
Therefore, the answer we choose is the last one (bottom right) that says that the cow manure data is more consistent than the other one, and also, since the mashed banana data is so much higher, combined with the previous will clearly give larger amounts of biogas.
Please select the bottom right option.
The engine in a airplane has a power curve approximated by x2 270 y = + 14 15000 44 where I is the RPin and y is the horsepower generated. - At what RPM is the engine putting out maximum horsepower?. Round your answer to three decimal places. RPM What is the maximum horsepower? Round your answer to three decimal places.
A)For this question, we will use the first and second derivative criteria. First, we compute the first and second derivative of the given function:
[tex]\begin{gathered} \frac{dy}{dx}=-\frac{2x}{15000}+\frac{27}{44} \\ \frac{d^{2}y}{dx^{2}}=-\frac{2}{15000} \end{gathered}[/tex]Setting the first derivative equal to zero and solving for x we get:
[tex]\begin{gathered} -\frac{2x}{15000}+\frac{27}{44}=0 \\ \frac{2x}{15000}=\frac{27}{44} \\ x=\frac{27(15000)}{44(2)}=4602.273 \end{gathered}[/tex]Evaluating the first second derivative at x=4602.273 we get a negative number, therefore the function has a maximum value at x=4602.273. At 4602.273 RPM the engine puts out its maximum horsepower.
B) Now, to compute the maximum horsepower we evaluate the given function at x=4602.273:
[tex]\begin{gathered} y=-\frac{(4602.273)^{2}}{15000}+\frac{27}{44}(4602.273)-14 \\ y=1398.061 \end{gathered}[/tex]Therefore, the maximum horsepower is 1398.061.
Prove that these 3 equations are the same. There is more than one way to do this. Show in multipleways for a higher score.y = (x + 5)(x + 1)y = (x + 3)^2 - 4y = x^2 + 6x + 5
For the first equation:
y = (x + 5)(x + 1)
apply distribution property:
y = (x + 5)(x) + (x + 5)(1)
y = x·x + 5·x + x·1 + 5·1
y = x² + 5x + x + 5
y = x² + 6x + 5
For the second equation:
y = (x + 3)² - 4
use the fact that (a + b)² = a² + 2ab + b², for the term (x + 3)², then, you have:
y = x² + 2·x·3 + 3² - 4
y = x² + 6x + 9 - 4
y = x² + 6x + 5
The third equation is already in the convenient form.
Then, you can notice that all three equations are the same equations.
this composed figure is made up of three similar shapes what is the area of the figure
Given data:
The given figure is shown.
The area of the composite figure is,
[tex]\begin{gathered} A=(10\text{ cm)}\times(5\text{ cm)+}(3\text{ cm)(6 cm)+}\frac{1}{2}(3\text{ cm)(4 cm)} \\ =50cm^2+18cm^2+6cm^2 \\ =74cm^2 \end{gathered}[/tex]Thus, the area of the composite figure is 74 square-cm.
please help me please please please please please please please please please please please please please please
EXPLANATION
The Area of a square shape is:
Area= side*side = s^2
If we have that:
Area = 121 yd^2, then:
121=s^2
Isolating s:
[tex]s=\sqrt[]{121}=11\text{ ---> The answer is 11}[/tex]Calculate the sum of interior angles of a 6 sided polygon
The sum of interior angles of a polygon can be calculated using the formula below.
[tex]\begin{gathered} S\text{ = }(n-2)\times180^0 \\ \text{Where; } \\ S\text{ = sum of interior angles of the polygon } \\ n\text{ = number of sides of the polygon} \end{gathered}[/tex]For the given question the polygon is 6 sided, so;
[tex]n\text{ = 6}[/tex]Substituting the value of n into the formula, we have;
[tex]\begin{gathered} S\text{ = (6-2)}\times180^0 \\ S\text{ = 4}\times180^0 \\ S=720^0 \end{gathered}[/tex]Therefore, the sum of interior angles of a 6 sided polygon is 720 degree
[tex]S=720^0[/tex]2. Two baseball players were up to bat. Consider the parabolic paths of their two hits, represented in thegraph at right. One hit covers a horizontal distance of 4 feet and reaches a maximum height of 20 feet.The other hit covers a horizontal distance of 6 feet, but only reaches a maximum height of 9 feet.
Explanation:
The equation of parabola can be founded using the following equation:
[tex]y=a(x-h)^2+k[/tex]Where the point (h, k) is the vertex. So, if the hit covers a horizontal distance of 4 feet and reaches a maximum height of 20 feet, we can say that the vertex will be located at (2, 20) because the maximum height of 20 ft is reached when the horizontal distance is half of the maximum horizontal distance 4 ft.
So, the equation for the first hit is:
[tex]undefined[/tex]Over 12 hours, the water in Julia's pool drained a total of 534.72 liters. It drained the same number of liters each hour. Write an equation to represent the change in the number of liters of water in Julia's pool each hour.
Answer:
the pool lost 44.56 liters per hour
Step-by-step explanation:
Find the percent of change and classify as a percent increase or decrease. Round to the nearest tenth of a percent when necessary. A $39 watch is now on clearance for $17.50.
The percent of increase or decrease = change/original x 100%
Since the original price of the watch is $39
Since its price now is $17.50, then
The change of the price = 39 - 17.50 = 21.50 dollars
The percentage of decrease = 21.50/39 x 100%
The percentage of decrease = 55.1282
Round it to the nearest tenth
The percentage of decrease is 55.1%
Construct a truth table of the following statement. Jack will not play or Chris is hurtUse the symbolic representationp: Jack will playr: Chris is hurt
ANSWER and EXPLANATION
We want to construct a truth table for the following statement:
Jack will not play or Chris is hurt
where p: Jack will play; r: Chris is hurt
"Jack will not play" will be represented by -p.
This implies that "Jack will not play or Chris is hurt" will be represented by - p v r.
Let us now construct the truth table:
That is the truth table for the statement.
Determine whether the ordered pair is a solution of linear equation.Y = x - 1/2, ( -5, -2 ) A- yes it is a solution B- no it is not a solution
The ordered pair is (- 5, - 2)
This means that when x = - 5, y = - 2
To determine if the ordered pair is a solution of the linear equation, We would substitute the values into the equation. If we substitute x = - 5 into the equation and y gives us - 2, then it is a solution.
Therefore,
y = - 5 - 1/2 = - 5 - 0.5
y = - 5.5
Since it is not - 2, then the answer is B
B- no it is not a solution
ed pai
Given that tan A= 5/12 and tan B= -4/3 such that A is an acute angle and B is an obtuse angle find the value of,a) tan (A-45°)b) tan (B+360°)
Solve for tan(A-45°).
Recall that tan(45°) = 1
[tex]\begin{gathered} \tan (A-45\degree)=\frac{\tan A-\tan B}{1+\tan A\tan B} \\ \tan (A-45\degree)=\frac{\frac{5}{12}-1}{1+(\frac{5}{12})(1)} \\ \tan (A-45\degree)=\frac{-\frac{7}{12}}{1+\frac{5}{12}} \\ \tan (A-45\degree)=\frac{-\frac{7}{12}}{\frac{17}{12}} \\ \tan (A-45\degree)=-\frac{7}{17} \end{gathered}[/tex]Therefore, tan(A-45°) = -7/17.
Solve for tan(B+360°)
Recall that tan(360°) = 0
[tex]\begin{gathered} \tan (B+360\degree)=\frac{\tan A+\tan B}{1-\tan A\tan B} \\ \tan (B+360\degree)=\frac{\frac{5}{12}+0}{1-(\frac{5}{12})(0)} \\ \tan (B+360\degree)=\frac{\frac{5}{12}}{1-\frac{5}{12}} \\ \tan (B+360\degree)=\frac{\frac{5}{12}}{\frac{7}{12}} \\ \tan (B+360\degree)=\frac{5}{7} \end{gathered}[/tex]Therefore, tan(B+360°) = 5/7.