The probability would be 1/52, since there are only 1 two of diamonds in all 52 cards.
Final answer. 1/52 or 1.92%
Answer:
13/52
Step-by-step explanation:
a standard 52-card deck has 13 diamond cards (1,2,3,4,5,6,7,8,9,10,J,Q,K)
P(diamond) = number of diamonds/number of cards in a deck = 13/52
A department store mails a customer satisfaction survey to people who make credit card purchases at the store. This month, 3521 people made credit card purchases. Surveys are mailed to 278 of these people, chosen at random, and 172 people return the survey form. Identify the population and the sample.
Answer:
The population is the population of 3521 people who made credit card purchases.
The sample is the 172 people who returned the survey form.
Step-by-step explanation:
Department mails customers satisfactions forms to those who make credit cards purchase at the store, totaling 3521 people. Thus, the population is the population of 3521 people who made credit card purchases.
Surveys are mailed to 278 of these people, chosen at random, and 172 people return the survey form.
Thus the sample, that is, those from whom the data will be taken and expanded to the rest of the population, is the 172 people who returned the survey form.
The population is all 3521 people who made credit card purchases.
The sample is the 172 people who returned the survey form.
. In Habib High School 275 of 300 students received a grade of A, while in Public Hall 120 out of 150 students received a grade of A. Which of the two schools has a better record?
The probability that Barry Bonds hits a home run on any given at-bat is 0.16, and each at-bat is independent.
Part A: What is the probability that the next home run will be on his fifth at-bat? (5 points)
Part B: What is the expected number of at-bats until the next home run? (5 points)
Answer:
a) 0.0797 = 7.97% probability that the next home run will be on his fifth at-bat.
b) The expected number of at-bats until the next home run is 6.25.
Step-by-step explanation:
For each at bat, there are two possible outcomes. Either it is a home run, or it is not. The probability of an at bat resulting in a home run is independent of any other at-bat, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability that Barry Bonds hits a home run on any given at-bat is 0.16
This means that [tex]p = 0.16[/tex]
Part A: What is the probability that the next home run will be on his fifth at-bat?
0 on his next 4(P(X = 0) when n = 4)
Home run on his 5th at-bat, with 0.16 probability. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.16)^{0}.(0.84)^{4} = 0.49787136 [/tex]
0.49787136 *0.16 = 0.0797.
0.0797 = 7.97% probability that the next home run will be on his fifth at-bat.
Part B: What is the expected number of at-bats until the next home run?
The expected number of trials for n successes is given by:
[tex]E = \frac{n}{p}[/tex]
In this question, [tex]n = 1, p = 0.16[/tex]. So
[tex]E = \frac{1}{0.16} = 6.25[/tex]
The expected number of at-bats until the next home run is 6.25.
Given the function R(x)=x+3/x−5, find the values of x that make the function greater than or equal to zero. Write the solution in interval notation.
Answer:
Step-by-step explanation:
[tex]R(x)=\frac{x+3}{x-5} \geq 0\\R(x)=0,gives~x+3=0,x=-3\\R(x)>0 ,if~both~numerator ~and~denominator~are~of~same~sign.\\let~x+3>0,x>-3\\and~x-5>0,x>5\\combining \\x>5\\\\again~let~x+3<0,x<-3\\x-5<0,x<5\\combining\\x<-3\\Hence~R(x)\geq 0\\if ~x \in ~[- \infty,-3]U(5,\infty)[/tex]
find all complex numbers z such that z^2=2i
please answer in a+bi
thank you
2 Answers:
z = 1 + i and z = -1 - i
========================================================
Explanation:
We want z to be a complex number in the form z = a+bi, where a,b are real numbers and [tex]i = \sqrt{-1}[/tex] is imaginary.
Let's plug that into the equation your teacher gave you
[tex]z^2 = 2i\\\\(a+bi)^2 = 2i\\\\(a+bi)(a+bi) = 2i\\\\a(a+bi)+bi(a+bi) = 2i\\\\a^2+abi+abi+b^2*i^2 = 2i\\\\a^2+2abi+b^2*(-1) = 2i\\\\a^2+2abi-b^2 = 2i\\\\(a^2-b^2)+2abi = 0+2i\\\\[/tex]
You could use the FOIL rule to take a shortcut. I'm deciding to be a bit more wordy to show a further breakdown how everything is multiplying out.
Notice that the real part a^2-b^2 must be 0 so that it matches the real part on the right hand side.
a^2-b^2 = 0
(a-b)(a+b) = 0 .... difference of squares rule
a-b = 0 or a+b = 0
a = b or a = -b
So whatever solution z = a+bi is, it must have either a = b or a = -b.
--------------------------------
If a = b, then the 2abi portion on the left side turns into 2a^2*i
Set this equal to 2i on the right hand side and isolate 'a'
[tex]2a^2*i = 2i\\\\2a^2 = 2\\\\a^2 = 1\\\\a = 1 \text{ or } a = -1\\\\[/tex]
So a = 1 leads to b = 1
Or a = -1 leads to b = -1
Two complex solutions so far are: z = 1 + i and z = -1 - i based on those two cases above.
--------------------------------
Now consider the case that a = -b
We'll effectively have the same steps as the previous section, but the equation to solve now is [tex]-2a^2*i = 2i\\\\[/tex]
The only difference is that negative is out front. You should find that it leads to a^2 = -1, but this has no solutions because we stated earlier that a,b were real numbers.
So if a = -b, then it concludes with a,b being nonreal numbers. Ultimately we rule out the case that a = -b is possible.
Put another way, note how -2a^2 is always negative which clashes with the idea that the right hand side is positive (ignore the 'i' portions). This contradiction means that no real values of 'a' will make the equation [tex]-2a^2*i = 2i\\\\[/tex] to be true.
--------------------------------
To wrap things up, we only have two solutions and they are
z = 1 + i and z = -1 - i
You can use a tool like WolframAlpha to confirm this.
Kenji simplifies 3^5 x 4^ 5and gets the result 12^10, but Darlene is not sure. Is Kenji correct? Justify your answer.
That's a question about exponentiation.
Answer:
Kenji is wrong because he does not aply the porperty correctly.
Step-by-step explanation:
A exponetiation has this form:
[tex]\boxed{a^b}[/tex]
a is the base
b is the power or exponent
To understand that situation it's important to know a property about exponentiation. When we have a multiplication with the same exponent and diferent bases, the result is the multiplication of the bases with the same exponent. Let's see this above, in mathematical language:
[tex]\boxed{a^b \cdot c^b = (a\cdot c) ^b}[/tex]
Examples:
[tex]2^3 \cdot 8^3 = (2 \cdot 8) ^3 = 16^3[/tex][tex]10^9 \cdot 23^9 = (10 \cdot 23) ^9 = 230^9[/tex]Now, we can say why Kenji is wrong. It's easy simplify [tex]3^5 \cdot 4^5[/tex]! We know that the result is [tex](3 \cdot 4) ^5 = 12^5[/tex], but Kenji multiplied the bases and added the exponents, that's why he is wrong.
I hope I've helped. ^^
Enjoy your studies! \o/
Find the missing pieces of the triangle round to the nearest tenth
Answer:
8√3
Step-by-step explanation:
Missing side,
√(19²-13³)
= 8√3
Answered by GAUTHMATH
For a two-tailed test with a sample size of 20 and a .20 level of significance, the t value is _____. Selected Answer: d. 1.328
Answer:
1.328
Step-by-step explanation:
Given :
Sample size, n = 20.
Degree of freedom, df = n - 1
df = 20 - 1 = 19
α = 0.2
Using the T-distribution calculator :
Since it is two - tailed:
Tα/2 ; 19 = T0.2/2 ; 19 = T0.1, 19 = 1.3277 = 1.328
Using a t-distribution calculator, it is found that the t-value is of t = 1.328.
How to find the critical value of the t-distribution?In a calculator, these following inputs are needed:
The number of degrees of freedom, which is one less than the sample size.The level of significance.Whether the test is one-tailed or two-tailed.In this problem, inputting the data given in a calculator, it is found that the t-value is of t = 1.328.
More can be learned about the t-distribution at https://brainly.com/question/13873630
Given the parabola below, find the endpoints of the latus rectum. (x-2)^2=-20(y+2)
Answer:
The endpoints of the latus rectum are [tex](12, -7)[/tex] and [tex](-8, -7)[/tex].
Step-by-step explanation:
A parabola with vertex at point [tex]C(x, y) = (h,k)[/tex] and whose axis of symmetry is parallel to the y-axis is defined by the following formula:
[tex](x-h)^{2} = 4\cdot p \cdot (y-k)[/tex] (1)
Where:
[tex]y[/tex] - Independent variable.
[tex]x[/tex] - Dependent variable.
[tex]p[/tex] - Distance from vertex to the focus.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex.
The coordinates of the focus are represented by:
[tex]F(x,y) = (h, k+p)[/tex] (2)
The latus rectum is a line segment parallel to the x-axis which contains the focus. If we know that [tex]h = 2[/tex], [tex]k = -2[/tex] and [tex]p = -5[/tex], then the latus rectum is between the following endpoints:
By (2):
[tex]F(x,y) = (2, -2-5)[/tex]
[tex]F(x,y) = (2,-7)[/tex]
By (1):
[tex](x-2)^{2} = -20\cdot (-7+2)[/tex]
[tex](x-2)^{2} = 100[/tex]
[tex]x - 2 = \pm 10[/tex]
There are two solutions:
[tex]x_{1} = 2 + 10[/tex]
[tex]x_{1} = 12[/tex]
[tex]x_{2} = 2-10[/tex]
[tex]x_{2} = -8[/tex]
Hence, the endpoints of the latus rectum are [tex](12, -7)[/tex] and [tex](-8, -7)[/tex].
HELP
Which of the lines below has a slope of 0?
Answer:
C has a zero slope
Step-by-step explanation:
A horizontal line has a slope of zero
A vertical line has an undefined slope
A positive slope goes up from left to right
A negative slope goes down from left to right
what is the length of a rectangular solid with a volume of 180 cu ft, if it is 9 ft high and 4ft wide?
Answer:
5 ft
Step-by-step explanation:
The formula for Volume is V=lwh, or Volume = length x width x height.
The equation would be:
[tex]180=l(4)(9)[/tex]
or
[tex]180=36l[/tex]
To find the answer, divide by 36.
[tex]\frac{180}{36} =\frac{36l}{36}[/tex]
[tex]5=l[/tex]
Let $f$ be a linear function for which $f(6)-f(2)=12$. What is $f(12)-f(2)?$ Please explain how you found your answer. Thank you!
========================================================
Explanation:
Since f(x) is linear, this means f(x) = mx+b
m = slopeb = y interceptLet's plug in x = 6
[tex]f(x) = mx+b\\f(6) = m*6+b\\f(6) = 6m+b[/tex]
Repeat for x = 2
[tex]f(x) = mx+b\\f(2) = m*2+b\\f(2) = 2m+b[/tex]
Now subtract the two function outputs
[tex]f(6)-f(2) = (6m+b)-(2m+b)\\f(6)-f(2) = 6m+b-2m-b\\f(6)-f(2) = 4m\\[/tex]
The b terms cancel out which is very handy.
Set this equal to 12, since f(6)-f(2) = 12, and solve for m
[tex]f(6)-f(2) = 12\\4m = 12\\m = 12/4\\m = 3\\[/tex]
So the slope of f(x) is m = 3
-------------------------------------------------------------------------
Next, plug in x = 12
[tex]f(x) = mx+b\\f(12) = m*12+b\\f(12) = 12m+b[/tex]
We can then say:
[tex]f(12)-f(2) = (12m+b)-(2m+b)\\f(12)-f(2) = 12m+b-2m-b\\f(12)-f(2) = 10m\\[/tex]
Lastly, we plug in m = 3
[tex]f(12)-f(2) = 10m\\f(12)-f(2) = 10*3\\f(12)-f(2) = 30\\[/tex]
what is the radius of a circle in it in if the area is 36m²?
A.0.339 m
B.3.39 m
C.78.5 m²
D.339 m
Answer:
B. 3.39 m
Step-by-step explanation:
r² = A/π
= 36/3.14
= 11.465
r = √11.465 = 3.39
Meg is 6 years older than Victor. Meg's age is 2 years less than five times Victor's age. The equations below model the relationship between Meg's age (m) and Victor's age (v):
m = v + 6
m = 5v − 2
Which is a possible correct method to find Meg's and Victor's ages?
Solve m + 6 = 5m − 2 to find the value of m.
Write the points where the graphs of the equations intersect the x axis.
Solve v + 6 = 5v − 2 to find the value of v.
Write the points where the graphs of the equations intersect the y axis.
Answer:
Option C
Step-by-step explanation:
Step 1: Find the correct method
Option A is incorrect because we don't have m + 6 and 5m - 2
Option B is incorrect because that wouldn't show us the correct value
Option C is correct, once we solve for v, we can plug in v and get the value of m. For example: v + 6 = 5v - 2 → v + 8 = 5v → 8 = 4v → 2 = v. Then we plug it into the other equation m = 2 + 6 → m = 8
Option D is incorrect because that wouldn't show us the correct value.
Answer: Option C
Please help 20 points an will give Brainiest to who ever is right
Answer:
horizontal expansion factor of 2
2^x =2(2)=4
2^4=2×2×2×2= 16
A supervisor records the repair cost for 17 randomly selected stereos. A sample mean of $66.34 and standard deviation of $15.22 are subsequently computed. Determine the 80% confidence interval for the mean repair cost for the stereos. Assume the population is approximately normal. Find the critical value that should be used in constructing the confidence interval.
A supervisor records the repair cost for 17 randomly selected stereos. A sample mean of $66.34 and standard deviation of $15.22 are subsequently computed. Determine the 80 % confidence interval for the mean repair cost for the stereos. Assume the population is approximately normal. Construct the 80% confidence interval.
Answer:
I AM VERY SORRY AARUSH KAPUSH
Step-by-step explanation:
The following expression gives an approximate value of the total average credit card debt in a U.S. household (in dollars) t years after 1995.
400t + 5750
Use this expression to predict what the total average credit card debt will be in the year 2025.
Answer: In the year 2025, the total average credit card debt for a U.S. household will be ------------ dollars.
Answer:
In 2025, t=30. so D=418*30+6000 = 18540
Linda leaves the school to go home. She walks 7 blocks south and then 9 blocks east. how far is Linda from her office?
A.8 blocks
B.11.5 blocks
C.20 blocks
D.14 blocks
Answer:
B. 11.5
Step-by-step explanation:
That missing length can be solved via the equation a^2+b^2=c^2, where the hypotenuse is c. We know A and B, which is 7 and 9.
7^2+9^2=130
sqrt 130 is 11.4017543
Here, you kinda have to break the rules of rounding to say that it is B.
There could be a more efficient route for resolving this answer, but this is the method that I was taught.
Bobby wants to bring popsicles to a summer barbecue. He decides to try a new recipe for pineapple-orange popsicles, so he makes a small batch with 1 cup of pineapple juice and 3 cups of orange juice to taste. He likes the combination, so he uses 3 cups of pineapple juice and 7 cups of orange juice to make a larger batch for the barbecue. Which batch of popsicles tastes more like oranges?
Answer:The first would taste more like oranges
Step-by-step explanation:
Find the solution(s) of the system of equations. y = x2 + 4x y + x2 = –4x Question 7 options: A) (–4, 0) and (0, 0) B) (0, 0) C) (–4, 0) and (4, 0) D) (0, 0) and (4, 0)
Answer:
Hello,
Answer A (-4,0) and (0,0)
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y&=&x^2+4x\\y+x^2&=&-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\y&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\x^2+4x&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}2*x^2+8*x&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}x(x+4)&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\[/tex]
[tex]\left\{\begin{array}{ccc}x&=&0 \\y&=&0\\\end{array} \right. \ or\ \left\{\begin{array}{ccc}x&=&-4 \\y&=&0\\\end{array} \right.[/tex]
Points B, A, and E are:
A. coplanar and non-collinear
B. collinear and coplanar
C. non-collinear and non-coplanar
D. collinear and collinear
Answer:
Option B.
Step-by-step explanation:
3 points are collinear if we can draw a line that connects the points.
And we know that any 2 or 3 points are always coplanar because we can find a plane such that the 2 or 3 points belong to it.
In the image we can see that B, A, and E are at the same y-value, thus these points are collinear, then the points define a line, and these are 3 points, thus we know that are coplanar.
Then points A, B, and E are collinear and coplanar.
The correct option is B.
T is the midpoint of pq where pt=3x-3 and tq=5x-7 find x
Answer: x = 2
Step-by-step explanation:
P-----------------------T----------------------Q
(3x-3) (5x-7)
Since T is the midpoint we know that PT and TQ are equal
Just solve the equation: 3x-3 = 5x-7
[tex]3x-3 = 5x-7[/tex]
now move the x to one side
[tex]-3 = 2x-7[/tex] (I subtracted the 3x)
then get the 2x by itself
[tex]4=2x[/tex]
lastly, divide by 2 to get x by itself
[tex]x=2\\[/tex]
A map has a scale in which 1.25 inches represents 250 miles.
How many miles does 1 inch represent?
Answer: 200 miles
Work Shown:
(1.25 inches)/(250 miles) = (1 inch)/(x miles)
(1.25)/(250) = 1/x
1.25x = 250*1 ..... cross multiplication
1.25x = 250
x = 250/(1.25)
x = 200 miles
PLEASE HELP ANSWER THISS!!! I NEED THIS PLEASE!!! AND NO LINKS EITHER PLSS!!
It doesn't change because to add fractions, you need a common denominator. To find it, they multiplied 1/3 by 2 to make 2/6, to add to the 3/6.
Which function is represented by the graph?
f(x) = −|x − 3| + 4
f(x) = −|x + 3| + 4
f(x) = −|x − 4| + 3
f(x) = −|x + 4| + 3
What are the zeroes of f(x) = x2 - X - 2?
x= -2,1
x = 2, -1
x= -2, -1
x = 2,1
Answer:
x=2 x=-1
Step-by-step explanation:
f(x) = x^2 - X - 2
0= x^2 -x-2
Factor
0 =(x-2)(x+1)
Using the zero product property
x-2 =0 x+1 =0
x=2 x=-1
Answer:
x=2, -1
Step-by-step explanation:
Hi there!
We want to find the zeros of this function: f(x)=x²-x-2
The zeros are the values of x that will make f(x)=0
So that means in order to find the zeros, set f(x) as 0
In that case,
x²-x-2=0
Now let's solve the quadratic equation
We can do it by factoring
-x is the sum of two numbers, while -2 is the product of those two same numbers
Now think: which two numbers add up to -1, but multiply to get -2?
Those numbers are -2 and 1
Now factor the polynomial by FOIL:
(x-2)(x+1)=0
Split and solve
x-2=0
x=2
x+1=0
x=-1
The zeros are x=2, -1
Hope this helps!
How many spaces does it move over
Answer:
The point at the bottom has to move over 2 to the left to be aligned with the point at the top however they will have a 3 space in between the 2 same for the point at the top, the top point moves over 2 to the right to be aligned with the bottom point, then they will have a 3 square space between each other.
Answer:Around 3 spaces between?
Step-by-step explanation:
By which number should (2/5)^-3 be multiplied to get (1/2)^4 as a product ?
Answer:
[tex]\frac{2}{5}^{-3}[/tex]×[tex]x=\frac{1}{2}^{4}[/tex]
[tex]x=\frac{2}{5} ^{3} \\[/tex]×[tex]\frac{1}{2}^{4}[/tex]
(negative in the exponent means reciprocal of the fraction)
x= [tex]\frac{1}{250}[/tex]
Brainliest please
Find RS. Can anyone help?
The segment XT splits the trapezoid exactly in half. The average of RS and Q will give us XT because of the properties of a trapezoid.
We find the area of a trapezoid by averaging the bases as well.
RS + Q / 2 = XT
RS + 26 / 2 = 22
RS + 26 = 44
RS = 18
Hope this helps!
In a random sample of 7 residents of the state of Montana, the mean waste recycled per person per day was 2.8 pounds with a standard deviation of 0.16 pounds. Determine the 90% confidence interval for the mean waste recycled per person per day for the population of Montana. Assume the population is approximately normal.
Answer:
The 90% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.68 and 2.92 pounds.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 7 - 1 = 6
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.9432.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.9432\frac{0.16}{\sqrt{7}} = 0.12[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 0.12 = 2.68 pounds.
The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.12 = 2.92 pounds.
The 90% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.68 and 2.92 pounds.
