Solution
Step 1:
In a pack or deck of 52 playing cards, they are divided into 4 suits of 13 cards each i.e. spades ♠ hearts ♥, diamonds ♦, clubs ♣. Cards of Spades and clubs are black cards. Cards of hearts and diamonds are red cards. The card in each suit, are ace, king, queen, jack , 10, 9, 8, 7, 6, 5, 4, 3 and 2.
Step 2:
Total possible outcomes = 52
Total number of jacks = 4
Total number of red cards = 26
Step 3:
The probability of selecting Jack or a red card
[tex]\begin{gathered} \text{Probability of any event = }\frac{n\text{umber of required outcomes}}{n\text{umber of possible outcomes}} \\ =\text{ }\frac{4}{52}\text{ + }\frac{26}{52} \\ =\text{ }\frac{30}{52} \\ =\text{ }\frac{15}{26} \end{gathered}[/tex]Final answer
[tex]\frac{15}{26}[/tex]I need help with this problem it says to find the area of each shaded sector and round to the hundredth place
Answer:
1330.81 square feet
Explanation:
In the circle, there are two unshaded sectors with central angles 26° and 90°.
The sum of the central angles = 360°.
Therefore, the sum of the central angle of the shaded sectors will be:
[tex]360\degree-(26\degree+90\degree)=244\degree[/tex]The area of a sector is calculated using the formula:
[tex]A=\frac{\theta}{360\degree}\times\pi r^2\text{ where }\begin{cases}Central\; Angle,\theta=244\degree \\ Radius,r,HK=25ft\end{cases}[/tex]Substitute the values into the formula:
[tex]\begin{gathered} A=\frac{244}{360}\times\pi\times25^2 \\ =1330.8136 \\ \approx1330.81\; ft^2 \end{gathered}[/tex]The area of the shaded sector is 1330.81 square feet (rounded to the hundredth place).
Please someone can help me please #1
Complete the following Division
Quotient of 96, 55, 84 and 63 is 12, 11, 14 and 21 respectively
What is Division?
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
1) 96
Divisor = 8
96 / 8
= 12
Quotient = 12
2) 55
Divisor = 5
55 / 5
= 11
Quotient = 11
3) 84
Divisor = 6
84 / 6
= 14
Quotient = 14
4) 63
Divisor = 3
63 / 3
= 21
Quotient = 21
Hence , Quotient of 96, 55, 84 and 63 is 12, 11, 14 and 21 respectively
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Find the maximum and minimum values of the function g(theta) = 2theta - 4sin(theta) on the interval Big[0, pi 2 Bigg\
Hello there. To solve this question, we have to remember some properties about polar curves and determining maximum and minimum values.
In this case, we have the function in terms of the angle θ:
[tex]g(\theta)=2\theta-4\sin(\theta)[/tex]We want to determine its minimum and maximum values on the closed interval:
[tex]\left[0,\,\dfrac{\pi}{2}\right][/tex]We graph the function as follows:
Notice on the interval, it has a maximum value of 0.
We can determine its minimum value using derivatives, as follows:
[tex]g^{\prime}(\theta)=2-4\cos(\theta)[/tex]Setting it equal to zero, we obtain
[tex]\begin{gathered} 2-4\cos(\theta)=0 \\ \Rightarrow\cos(\theta)=\dfrac{1}{2} \\ \\ \Rightarrow\theta=\dfrac{\pi}{3} \end{gathered}[/tex]Taking its second derivative, we obtain
[tex]g^{\prime}^{\prime}(\theta)=4\sin(\theta)[/tex]And notice that when calculating it on this point, we get
[tex]g^{\prime}^{\prime}\left(\dfrac{\pi}{3}\right)=4\sin\left(\dfrac{\pi}{3}\right)=2\sqrt{3}[/tex]A positive value, hence it is a minimum point of the function.
Its minimum value is then given by
[tex]g\left(\dfrac{\pi}{3}\right)=2\cdot\dfrac{\pi}{3}-4\sin\left(\dfrac{\pi}{3}\right)=\dfrac{2\pi}{3}-2\sqrt{3}[/tex]Of course we cannot determine that 0 is a maximum value of this function using derivatives because it is a local maxima on a certain interval, and derivatives can only gives us this value when the slope of the tangent line is equal to zero.
Identify the constant of variation. 8y-7x=0
A direct variation between two variables "x" and "y" is given by the following formula:
y = kx
We can rewrite the given expression 8y-7x=0 to get an equation of the form y = kx like this:
8y - 7x = 0
8y - 7x + 7x = 0 + 7x
8y = 7x
8y/8 = 7x/8
y = 7/8x
The number that is being multiplied by x should be the constant of variation k, then in this case, the constant of variation equals 7/8
2.Find the range of thisquadratic function.1-3-2-11y = x2 + 2x-27А-1 < y< ooB- < y < oo
Okay, here we have this:
Considering that the range of a function is the complete set of all possible resulting values of the dependent variable (y), we can see in the graph of the function that:
The values of the variable "y" go from -1 to plus infinity, this mean that the range is:
-1≤y<∞
Finally we obtain that the correct option is the first option.
Find the vertex of the following equation: y = -5x² - 270x - 520
In order to find the vertex of this quadratic equation, first let's find the coefficients a, b and c from the standard form of the quadratic equation:
[tex]y=ax^2+bx+c[/tex]Comparing with the given equation, we have a = -5, b = -270 and c = -520.
Now, let's calculate the x-coordinate of the vertex using the formula below:
[tex]\begin{gathered} x_v=\frac{-b}{2a} \\ x_v=\frac{-(-270)}{2\cdot(-5)} \\ x_v=\frac{270}{-10} \\ x_v=-27 \end{gathered}[/tex]Using this value of x in the equation, we can find the y-coordinate of the vertex:
[tex]\begin{gathered} y_v=-5x^2_v-270x_v-520 \\ y_v=-5\cdot(-27)^2-270\cdot(-27)-520 \\ y_v=-5\cdot729+7290-520 \\ y_v=-3645+7290-520 \\ y_v=3125 \end{gathered}[/tex]Therefore the vertex is located at (-27, 3125).
One angle measures 140°, and another angle measures (5k + 85)°. If the angles are vertical angles, determine the value of k.
The value of k when one angle measures 140°, and another angle measures (5k + 85)° and if the angles are vertical angles is 11.
What is vertical angles?
Vertical angles are angles opposite each other where two lines cross.
Note: Vertical angles are equal.
To calculate the value of k, we use the principle of vertical angle
From the question,
140 = (5k+85)°Solve for k
5k = (140-85)5k = 55Divide both side by the coefficient of k (5)
5k/5 = 55/5k = 11Hence, the value of k is 11.
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A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 96 m long and 64 m wide. Find the area of the training field. Use the value 3.14 for n, and do not round your answer. Be sure to include the correct unit in your answer.
To find:
The area of the training field.
Solution:
The training field is made of two semicircles and a rectangle.
The length and width of the rectangle is 96 m and 64 m. So, the area of the rectangle is:
[tex]\begin{gathered} A=l\times w \\ =96\times64 \\ =6144\text{ m}^2 \end{gathered}[/tex]The diameter of the semicircle is 64 m. SO, the radius of the semicircle is 32 m.
The area of two semicircles is:
[tex]\begin{gathered} A=2\times\frac{1}{2}\pi r^2 \\ =3.14\times(32)^2 \\ =3.14\times1024 \\ =3215.36 \end{gathered}[/tex]So, the area of the training field is:
[tex]\begin{gathered} A=6144+3215.36 \\ =9359.36 \end{gathered}[/tex]Thus, the area of the training field is 9359.36 m^2.
Solve the problem. Use 3.14 as the approximate value of pie
The volume of a cylinder is calculated using the formula:
[tex]V=\pi r^2h[/tex]where r is the radius of the cylinder and h is the height.
From the question, we have the following parameters:
[tex]\begin{gathered} diameter=4.8 \\ \therefore \\ r=\frac{4.8}{2}=2.4 \\ and \\ h=6.66 \end{gathered}[/tex]Therefore, we c n calculae tehe volume of a cylinder to be:
[tex]\begin{gathered} V=3.14\times2.4^2\times6.66 \\ V=120.455424 \end{gathered}[/tex]For four cylinders, the combined volume will be:
[tex]\begin{gathered} V=120.455424\times4 \\ V=481.821696 \end{gathered}[/tex]The volume i 481 .82 cubic inches.
which expressions are equivalent to 9 divided by 0.3
Answer:
Step-by-step explanation:
So the answer would be 90 divided by 3 because all you have to do is multiply 0.3 times 10 and 9 times 10 simple hope this was understandable30 will be the expressions that are equivalent to 9 divided by 0.3.
What is an equivalent expression?In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in maths are those that hold true even when they appear to be distinct. However, both forms provide the same outcome when the values are entered into the formula.
An expression is equivalent even when both sides are multiplied or divided with the same non-zero value.
The expression 9 divided by 0.3 can be written as 9/0.3
The expression that will be equivalent will be determined as:
= 9/0.3
= 90/3
= 30
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Determine the z-intercepts of the parabola whose graph is given below.
The x-intercepts are the points where a curve intercepts the x-axis.
From the picture of the problem, we see that the curve intercepts the x-axis in two points:
Answer
The x-intercepts are at:
• x = -6 at (-6,0)
,• x = -2 at (-2,0)
Suppose you have $14,000 to invest Which of the two rates would yield the larger amount in 2 years 6% compounded monthly or 5.88% compounded continuously?
We were given a principal to invest ($14,000) in a timespan of 2 years, and we need to choose between applying it on an account that is compounded montlhy at a rate of 6%, and one that is compounded continuously at a rate of 5.88%. To solve this problem, we need to calculate the final amount on both situations, and compare them.
The expression used to calculate the amount compounded monthly is shown below:
[tex]A=P(1+\frac{r}{12})^{12\cdot t}[/tex]Where A is the final amount, P is the invested principal, r is the interest rate and t is the elapsed time.
The expression used to calculate the amount compounded continuously is shown below:
[tex]A=P\cdot e^{t\cdot r}[/tex]Where A is the final amount, P is the invested principal, r is the interest rate, t is the elapsed time, and "e" is the euler's number.
With the two expressions we can calculated the final amount on both situations, this is done below:
[tex]\begin{gathered} A_1=14000\cdot(1+\frac{0.06}{12})^{12\cdot2} \\ A_1=14000\cdot(1+0.005)^{24} \\ A_1=14000\cdot(1.005)^{24} \\ A_1=14000\cdot1.127159 \\ A_1=15780.237 \end{gathered}[/tex][tex]\begin{gathered} A_2=14000\cdot e^{0.0588\cdot2} \\ A_2=14000\cdot e^{0.1176} \\ A_2=14000\cdot1.124794 \\ A_2=15747.12 \end{gathered}[/tex]The first account, that is compounded monthly yields a return of $15780.24, while the second one that is compounded continuously yields a return of $15747.12, therefore the first account is the one that yield the larger amount in 2 years.
what property is used to solve this?
4x-3
x=2
4(2)-3
Please help me and I will give the pictures for the choices..
The first compound indequality is:
[tex]x>7\, and\, x<7[/tex]We can view this in the real line:
There is no number that can be both greater AND less than 7, which makes the correct answer "No solution".
The second is:
[tex]x<7\, or\, x>7[/tex]Now, we are not looking for intercetion, we are looking for the union of both. The firts inequality takes all number less than 7 and the second all that are greater than 7, so the only one that is not a solution is 7, which means the correct answer is "all real numbers except 7"
The third is:
[tex]x\ge7\, and\, x\le7[/tex]This is the same as the first one, but now the 7 is included in both:
So, there is only 7 that can be in both indequalitys, thus the correct answer is "one solution, 7".
The fourth is
[tex]x\le7\, or\, x\ge7[/tex]This is similar to the second, but now 7 is included, which means it is also a solution, thus the answer is "all real numbers".
Car Survey In a survey of 3,100 people who owned a certain type of car, 1,550 said they would buy that type of car again.
What percent of the people surveyed were satisfied with the car?
% of the people surveyed were satisfied with the car.
(Type a whole number.)
The percentage of people satisfied with car is 50.
What is percentage?
A number or ratio which can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it. There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of something, we mean that it is 50% of everything. As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any subject have been calculated in terms of percentages in academics. Ram, for instance, scored 78% on his exam.
To find the percentage We divide 1550 by 3100 and then multiply by 100
We get
[tex]\frac{1550}{3100}*100\\=50[/tex]
Hence the percentage of people satisfied with the car is 50%
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Find the area of a triangle with vertices at N(-4,2), A(3,2)and P(-1,-4).
The distance between points N and A is 7, and we can take that as the base of the tringle (up side down)
The distance between the base (NA) and the point P is 6, and we can take that as the height of the triangle
Area of a triangle = (Base x Height)/2
Area = (7 x 6)/2 = 42/2 = 21
Answer:
Area = 21
27–34: Describing Distributions. Consider the following distributions.-How many peaks would you expect the distribution to have? Explain.-Make a sketch of the distribution.-Would you expect the distribution to be symmetric, left-skewed, or right-skewed? Explain.-Would you expect the variation of the distribution to be small, moderate, or large? Explain.#29The annual snowfall amounts in 50 randomly selected American cities
Answer:
Step-by-step explanation:
A major record label has seen its annual profit decrease in recent years. In 2011, the label's profit was $128 million. By 2015, the label's profit had decreased by 30%.What was the record label company's profit in 2015? million dollars Suppose the record label wants to increase its profit to $128 million by 2017. By what percent must the label's profit increase from its 2015 value to reach $128 million within the next two years? %
the company's profit in 2015 was $89,600,000 (89.6 million dollars)
43%
Explanation:
Profit in 2011 = $128 million
Profit in 2015 decreased by 30%
% decrease = (old price - new price)/old price
old price = Profit in 2011 , new price = Profit in 2015
30% = (128,000,000 - new price)/128000000
[tex]\begin{gathered} 30percent=\text{ }\frac{128,000,000 -newprice}{128000000} \\ 0.30\text{ = }\frac{128,000,000-newprice}{128000000} \\ \text{cross multiply:} \\ 0.3(128,000,000)\text{ = }128,000,000-newprice \end{gathered}[/tex][tex]\begin{gathered} 38400000\text{ = }128,000,000-newprice \\ \text{subtract }38400000\text{ from both sides:} \\ 38400000-\text{ }38400000\text{ = }128,000,000-38400000-newprice \\ \text{0 = 89600000 }-newprice \\ newprice\text{ = 89600000 } \end{gathered}[/tex]Hence, the company's profit in 2015 was $89,600,000 (89.6 million dollars)
Percentage increase = (new price - old price)/old price
new price = 128million dollars , old price = 89.6 million dollars
% increase = [(128 - 89.6)in millions/(89.6) in millions] × 100
% increase = 38.4/89.6 × 100
% increase = 0.43 × 100
% increase = 43%
Hence, the label's profit must increase by 43% from its 2015 value to reach $128 million within the next two years
3: Select the correct equation for the given situation. Then, select the solution for that equation. Two research submarines start to rise vertically toward the ocean surface. The Tri-I sub is at 4,863 feet below sea level (or -4,863 feet) and is ascending 81.1 feet per minute. The Quad-II sub is at 3,645 feet below sea level (or -3,645 feet) and is ascending 76.9 feet per minute. If the ocean surface is at 0 feet, how many minutes (m) must elapse for the two submarines to reach the same depth? m = 290 minutes m = 145 minutes m = 53.8 minutes 4,863 - 76.9m = 3,645 - 81.1m O -4,863 + 81.1m = - 3,645 + 76.9m 0 - 4, 863 + 76.9m = -3, 645 + 81.1m – 4, 863 – 81.2m 2 – 3, 645 + 76.9m Om < 53.8 minutes
Unknown, the correct equation is:
- 4,863 + 81.1m = - 3,645 + 76.9m
And to solve for m, you use the standard form:
Like terms:
81.1m - 76.9m = -3,645 + 4,863
4.2m = 1,218
Answer:Nuts
Step-by-step explanation:
green on green
Can you please solve the last question… number 3! Thanks!
Let us break the shape into two triangles and solve for the unknowns.
The first triangle is shown below:
We will use the Pythagorean Theorem defined to be:
[tex]\begin{gathered} c^2=a^2+b^2 \\ where\text{ c is the hypotenuse and a and b are the other two sides} \end{gathered}[/tex]Therefore, we can relate the sides of the triangles as shown below:
[tex]25^2=y^2+16^2[/tex]Solving, we have:
[tex]\begin{gathered} y^2=25^2-16^2 \\ y^2=625-256 \\ y^2=369 \\ y=\sqrt{369} \\ y=19.2 \end{gathered}[/tex]Hence, we can have the second triangle to be:
Applying the Pythagorean Theorem, we have:
[tex]22^2=x^2+19.2^2[/tex]Solving, we have:
[tex]\begin{gathered} 484=x^2+369 \\ x^2=484-369 \\ x^2=115 \\ x=\sqrt{115} \\ x=10.7 \end{gathered}[/tex]The values of the unknowns are:
[tex]\begin{gathered} x=10.7 \\ y=19.2 \end{gathered}[/tex]A. Marvin worked 4 hours a day plus an additional 5-hour day for a total of 29 hours.B. Marvin worked 9 hours a day for a total of 29 hoursC. Marvin worked 4 hours one day plus an additional 5 hours for a total of 29 hours.D. Marvin worked 4 days plus 5 hours for a total of 29 hours.
Cost of a pen is two and half times the cost of a pencil. Express this situation as a
linear equation in two variables.
The equation to illustrate the cost of a pen is two and half times the cost of a pencil is C = 2.5p.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the cost of a pen is two and half times the cost of a pencil.
Let the pencil be represented as p.
Let the cost be represented as c.
The cost will be:
C = 2.5 × p
C = 2.5p
This illustrates the equation.
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OA.y> -22² +10z - 8OB. y<-2x² +102-8OC. y2-22² +10r - 8OD. y ≤-22² +10z - 8
Solution:
Using a graph plotter,
The correct answer that satisfies the graph is OPTION C.
Find the distance between the parallel lines. If necessary, round your answer to the nearest tenths.
The distance between the parallel lines is [tex]\frac{3}{5}}[/tex].
The given parallel lines are
[tex]y= $-$3x+4\\y= $-$3x+1[/tex]
We have to find the distance between the given parallel lines.
The formula is used to solve the distance between two parallel lines [tex]ax+by+c_{1}=0[/tex] and [tex]ax+by+c_{2}=0[/tex] is
[tex]d=|c_{2} $-$c_{1}|\frac{1}{\sqrt{a^{2}+b^{2}}}[/tex]
The first given line is [tex]y= $-$3x+4[/tex]
We can write that line as [tex]3x$-$y $-$4=0[/tex]
The second given line is [tex]y= $-$3x+1[/tex]
We can write that line as [tex]3x$-$y $-$1=0[/tex]
Comparing the both given parallel lines with the standard equation of line.
After comparing we get
[tex]a=3, b= $-$1, c_{1}= $-$4, c_{2}= $-$1[/tex]
Putting the value in the formula
[tex]d=|(-1) -(-4)|\frac{1}{\sqrt{(3)^{2}+(-4)^{2}}}\\d=|-1+4|\frac{1}{\sqrt{9+16}}\\d=|3|\frac{1}{\sqrt{25}}\\d=\frac{3}{5}}[/tex]
Hence, the distance between the parallel lines is [tex]\frac{3}{5}}[/tex].
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Does anyone know the answer to this?
The most appropriate choice for equation of line in slope intercept form will be given by
x + 2y = -16 is the required equation of line
What is equation of line in slope intercept form?
Equation of line in slope intercept form is given by y = mx + c
Where, m is the slope of the line and c is the y intercept of the line
The distance from the origin to the point where the line cuts the x axis is called x intercept
The distance from the origin to the point where the line cuts the y axis is called y intercept
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by
[tex]m=tan\theta[/tex]
If the line passes through ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex])
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Here,
The line passes through (0, -8) and (-2, -7)
Slope =
[tex]\frac{-7 -(-8)}{-2-0}\\-\frac{1}{2}[/tex]
The line passes through (0, -8)
Equation of line
[tex]y - (-8) = -\frac{1}{2}(x - 0)\\\\y + 8 = -\frac{1}{2}x\\2y + 16 = -x\\x + 2y = -16[/tex]
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f(x) = (x ^ 2 + 2x + 7) ^ 3 then
Answer
[tex]f^{\prime}(x)=6(x+1)(x^{2}+2x+7)^{2}[/tex][tex]f^{\prime}(1)=1200[/tex]Explanation
Given
[tex]f\mleft(x\mright)=(x^2+2x+7)^3[/tex]To find the derivative, we have to apply the chain rule:
[tex][u(x)^n]^{\prime}=n\cdot u(x)^{n-1}\cdot u^{\prime}(x)[/tex]Considering that in our case,
[tex]u(x)=x^2+2x+7[/tex][tex]u^{\prime}(x)=2x+2+0[/tex]and n = 3, then:
[tex]=3\cdot(x^2+2x+7)^{3-1}\cdot(2x+2)[/tex]Simplifying:
[tex]f^{\prime}(x)=3\cdot2(x+1)(x^2+2x+7)^2[/tex][tex]f^{\prime}(x)=6(x+1)(x^2+2x+7)^2[/tex]Finally, we have to replace 1 in each x in f'(x) to find f'(1):
[tex]f^{\prime}(1)=6((1)+1)((1)^2+2(1)+7)^2[/tex][tex]f^{\prime}(1)=6(1+1)(1+2+7)^2[/tex][tex]f^{\prime}(1)=6(2)(10)^2[/tex][tex]f^{\prime}(1)=6(2)(100)[/tex][tex]f^{\prime}(1)=12(100)[/tex][tex]f^{\prime}(1)=1200[/tex]why are whole numbers rational numbers?
Answer:
Step-by-step explanation:
A whole number can be written as a fraction that has a denominator of 1. So, the whole numbers 18, 3, and 234 can be written as the rational numbers 18/1, 3/1, and 234/1.
So, all whole numbers are rational numbers, but not all rational numbers are whole numbers.
Bob buys a vase for $15 and spends $2 per flower.
4) Write an equation to represent the cost of buying flowers.
If Bob buys a vase for $15 and spends $2 per flower, then the equation to represent the cost of buying flowers is 15+2x
The cost of flower vase = $15
The cost of each flower = $2
Consider the number of flowers as x
Then the linear equation that represents the cost of buying flowers = The cost of flower vase + The cost of each flower × x
Substitute the values in the equation
The equation that represents the cost of buying flowers = 15+2x
Hence, If Bob buys a vase for $15 and spends $2 per flower, then the equation to represent the cost of buying flowers is 15+2x
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Let S be the universal set, where: S = { 1 , 2 , 3 , ... , 18 , 19 , 20 } Let sets A and B be subsets of S , where: Set A = { 2 , 5 , 9 , 11 , 12 , 14 , 15 , 17 , 18 } Set B = { 4 , 7 , 8 , 9 , 10 , 12 , 15 , 17 , 18 , 19 , 20 } Find the following: LIST the elements in the set ( A ∪ B ): ( A ∪ B ) = { } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set ( A ∩ B ): ( A ∩ B ) = { } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE
The elements that are in ( A ∪ B ) = { 2, 4, 5, 7, 8, 9, 10 , 11, 12, 14, 15, 17, 18, 19, 20}
The elements of the set that are in ( A ∩ B ) = {9, 12, 15, 17, 18 }
What is a the union of a set?This is the term that is used to refer to all of the elements that are contained in a two or more sets which are a subset of the Universal set.
In this case, the union of the set is given as the elements in both A and B written together as { 2, 4, 5, 7, 8, 9, 10 , 11, 12, 14, 15, 17, 18, 19, 20}. All of these values are in A and B.
What is the intersection of a set?This is the term that is used to refer to all of the values that would appear in the two sets that are in the subset of the universal set.
Here we have the value of A ∩ B = {9, 12, 15, 17, 18 }
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Suppose you know students at school are, on average, 68 inches tall with a standard deviation of 4 inches. If you sample 36 students, what is the probability their average height is more than 70 inches?
Answer:
0.135% or 0.00135
Explanation:
• The population mean height = 68 inches
,• The population standard deviation = 4 inches
,• Sample Size, n = 36
First, find the sample standard deviation:
[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}=\frac{4}{\sqrt{36}}=\frac{4}{6}=\frac{2}{3}[/tex]Next, for X=70, find the z-score:
[tex]\begin{gathered} z-score=\frac{X-\mu}{\sigma_x} \\ z=\frac{70-68}{2\/3}=\frac{2}{2\/3}=3 \end{gathered}[/tex]Since we are looking for the probability that their average height is more than 70 inches, we need to find:
• P(X>70)=P(z>3)
Using the z-score table:
[tex]P(z>3)=0.0013499[/tex]The probability that their average height is more than 70 inches is 0.135%.
