Answer:
6 / 51
Step-by-step explanation:
It is false.
Reason:
The probability of picking a black card at first is:
26 / 52 = 1/2
There are now 25 black cards and 51 cards in total.
The probability of picking another black card, if there's no replacement is now:
25 / 51
Now, there are 24 black cards and 50 cards left in total.
The probability of picking a black card without replacement now becomes:
24 / 50 = 12 / 25
Hence, the probability of picking three black cards without replacement is:
1/2 * 25/51 * 12 / 25 = 300 / 2550
In simplest form, it is 6 / 51
In science class, Emily's 1-liter beaker contains 0.3 liter of water. Ali's beaker conatains 0.8 liter water, and Katies beaker contains 0.63 liter of water. who can pour all of her water into Emily's beaker without going over 1 liter.Ali or Katie?
Answer:
Step-by-step explanation:
KATIE
PLEASE HURRY In order to solve the system of equations below, Juana multiplies each equation by a constant to eliminate the y terms.
4x-3y = 1
5x+4y=9
What are the resulting equations?
16x-12y - 4
15x+12y - 27
16x-12y=-4
15x+12y = 27
16x-12y=-4
15x-12y = 27
Answer:
16x -12y = 4
15x +12y = 27
Step-by-step explanation:
4x-3y = 1
5x+4y=9
We will use elimination to remove y from both equations.
We can multiply the first equation by 4
16x -12y = 4
and multiply the second equation by 3
15x +12y = 27
This will eliminate y from the system of equations, leaving only x as a variable.
Answer:
16x - 12y = 4
15x + 12y = 27
Step-by-step explanation:
In order to eliminate the y terms, the equations must be manipulated in order to make the coefficient of the y-term equal 0 when the equations are added.
In this case, we are trying to make one equation with -3y and another equation with 4y result in a single equation with 0y.
We can do this by multiplying the first equation by 4 and the second equation by 3 to result in -12y and 12y. When these are added, the sum is 0y.
4 * (4x - 3y = 1) = 16x - 12y = 4
3 * (5x + 4y = 9) = 15x + 12y = 27
The resulting equations are
16x - 12y = 4
15x + 12y = 27
Read the sentences below. Choose the correct option to show which sentence uses a colon correctly.
a) We’ve chosen two cities to visit London: and Paris.
b) We’ve chosen: two cities to visit London and Paris.
c) We’ve chosen two cities: to visit London and Paris.
d) We’ve chosen two cities to visit: London and Paris.
Answer:
d
Step-by-step explanation:
colons are used to list
Some couples planning a new family would prefer at least one child of each sex. The probability that a couple’s first child is a boy is 0.512. In the absence of technological intervention, the probability that their second child is a boy is independent of the sex of their first child, and so remains 0.512. Imagine that you are helping a new couple with their planning. If the couple plans to have only two children:
(a) What is the probability of getting one child of each sex? [5]
(b) What is the probability that at least one girl is born? [5]
(c) What is the probability that at least one boy is born? [5] and
(d) What is the probability that both children are the same sex? [5]
Answer: .250
Step-by-step explanation:
When will n(A∩B)=0? Explain and give an example.
Answer:
Two sets are called disjoint if they have no elements in common. For example:
The sets S = { 2, 4, 6, 8 } and T = { 1, 3, 5, 7 } are disjoint.
Another way to define disjoint sets is to say that their intersection is the empty set,
Two sets A and B are disjoint if A ∩ B = 0.
In the example above,
S ∩ T = ∅ because no number lies in both sets.
Step-by-step explanation:
When two sets A and B having no common items then n(A∩B) = 0.
What are disjoint sets?In mathematics, two sets are said to be disjoint sets if they have no element in common.
Let there be two sets A and B,
A = {a, b, c, d}
B = {e, f, g, h}
Therefore intersection of A ad B we get,
A∩B = {0}
Thus, the number of elements in n(A∩B) is 0.
⇒ n(A∩B) = 0
Thus, when two sets A and B having no common items then n(A∩B) = 0.
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You are interested in conducting a survey at your school to determine if gender or ethnicity is related to perceptions about educational opportunity. The school has 1,800 students but you only have resources to interview 100. The student body is approximately equally divided between males and females. Twelve percent of the school's population is Asian American, 8% is African American, 10% is Native American, and 70% is Caucasian. You are interested in being able to generalize the results of your survey to the entire student body. Describe a technique for obtaining a sample of size 100 that would have a reasonable chance of producing results that could be generalized to the entire school. Suppose you sent the surveys out to classes and asked the students to complete them and return them to the main office. Would the returns be likely to be biased in any direction? If so, why? In what direction? Suppose you decide to conduct the survey by personal interview. Members of the student council, all of whom happen to be Caucasian, will conduct personal interviews with the selected students. One of the survey questions reads, "Do you agree or disagree with the following statement: All students, regardless of ethnicity, have equal opportunity to become part of student government." What potential bias is present in this question?
Answers
We can use cluster sampling here. In this case, the population is divided into sampling units or clusters, for example, zone within educational or geographical areas. Having divided the population into clusters, we can use simple random sampling to select the clusters to be examined. Consider Asian American as one cluster, African american as another cluster and so on. According to the size of the cluster randomly select individuals from each cluster for a total of 100 individuals.
Generally there would be bias in accordance to the differnce in ethnicity. Also if the selected students are in a younger, then the teachers opnion would play a very big role there.
The question itself is a source of bias and it seems to give an idea to the students to think in these lines. The question can be better worded to get a correct answer. Even if there is equal opportunity, some students may read the question and give a negative answer.
Twelve bears eat five pounds of honey in one day. At the same rate, how many pounds of honey will 20 bears eat in three days?
Answer:
25
Step-by-step explanation:
3 more than the cube of a number.
Answer:
x³+3
Step-by-step explanation:
Answer:
x³+3
Step-by-step explanation:
x³+3
The depth of water at the end of a pier varies with the tides. The low tides occur on a particular day at 2:00 a.m. and 2:00 p.m. with a depth of 1.1 m. The high tides occur at 8:00 a.m. and 8:00 p.m. with a depth of 5.3 m. A large boat needs at least 3 m of water to be safely secured at the end of the pier. What is the first time in the morning that is it safe for the boat to be tied to the pier
Answer:
4:42 a.m.
Step-by-step explanation:
The earliest low tide occurs by 2:00 a.m. and the earliest high tide occurs by 8:00 a.m.
Between these hours, 6 hours elapsed.
The lowest point is 1.1 m and increases steadily to 5.3 m.
Let us take 2:00 a.m. as the zeroth hour, and 8:00 a.m. as the 6th hour, we can safely interpolate as below,
0 = 1.1 m
x = 3 m
6 = 5.3 m
we solve as [tex]\frac{x - 0}{6 - 0}[/tex] = [tex]\frac{3 - 1.1}{5.3 - 1.1}[/tex]
[tex]\frac{x}{6}[/tex] = [tex]\frac{1.9}{4.2}[/tex]
4.2x = 11.4
x = 2.71 hours from 2:00 a.m.
= 2 hrs + (0.71 x 60)min = 2 hrs 42.6 min
the time will approximately be by 4:42 a.m.
what is one and two thirds divided by four fifths
Answer:
2 and 1/12
Step-by-step explanation:
pls mrk brainliest
Answer: 25/12
Step-by-step explanation: One and two thirds is equal to 5/3, so now all you have to do is divide 5/3 by 4/5. To divide fractions you multiply the first fraction to the reciprocal of the second fraction. The reciprocal simply means to switch the numerator with the denominator. Multiply 5/3 by 5/4. To multiply fractions you need to multiply straight across. 5 times 5 is 25 and 3 times 4 is 12, so the answer is 25/12.
The population of Wyoming is about ? Times the population of Colorado
Heating oil is to be poured at the constant rate of 4.5 gallons per minute into a 400-gallon tank that already contains 115 gallons of heating oil. What fraction of the tank's total capacity will be full in 30 minutes?
Answer:
5/8
Step-by-step explanation:
The volume after 30 minutes is:
(4.5 gal/min) (30 min) + 115 gal = 250 gal
The fraction of total capacity is:
250 gal / 400 gal = 5/8
The fraction of the tank's total capacity will be full in 30 minutes will be 5 / 8.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Heating oil is to be poured at the constant rate of 4.5 gallons (17.03 l) per minute into a 400-gallon tank that already contains 115 gallons (435.32 l) of heating oil.
Then the fraction of the tank's total capacity will be full in 30 minutes will be
The amount of oil in the tank after 30 minutes. Then we have
Amount of oil in the tank = 115 + 4.5 x 30
Amount of oil in the tank = 115 + 135
Amount of oil in the tank = 250 gallons (946.35 l)
Then the fraction of the tank's total capacity will be full in 30 minutes will be
⇒ 250 / 400
⇒ 5 / 8
Thus, the fraction of the tank's total capacity will be full in 30 minutes will be 5 / 8.
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Gary drew a rectangle with a perimeter of 12 inches. Then he tried to draw a square with a pe
of 12 inches
Select the dimensions of the rectangle drawing.
1 inch by 5 inches
12 inches by 5 inches
5 inches by 3 inches
12 inches by 1 inch
Select the dimensions of the square drawing.
5 inches by 5 inches
1 inch by 1 inch
3 inches by 3 inches
12 inches by 12 inches
Answer:
A. 1 inch by 5 inches
B. 3 inches by 3 inches
Step-by-step explanation:
The perimeter of a rectangle is the sum of the sides of the rectangle. The perimeter of a rectangle can be represented mathematically as
perimeter of a rectangle = 2l + 2w
where
l = length
w = width
perimeter = 12 inches
perimeter of a rectangle = 2l + 2w
12 = 2(l + w)
divide both sides by 2
l + w = 12/2
l + w = 6
Base on the option the dimension can only be 1 inches by 5 inches because the sum can give 6.
Square
The perimeter of the square is 12 inches.
perimeter of a square = 4l
where
l = length
12 = 4l
divide both sides by 4
l = 12/4
l = 3 inches
The length should be 3 inches by 3 inches.
Tyler attempts 240 free throws in 60 minutes. How many free throws did he attempt per minute?
4
40
180
300
Answer:
its A aka 4
Step-by-step explanation:
What is
2 1/8 - 1 7/8=?
Answer:
1/4
Step-by-step explanation:
2 1/8 - 1 7/8
Borrow 1 from the 2 in the form of 8/8
1 + 8/8+1/8 - 1 7/8
1 9/8 - 1 7/8
2/8
Simplify
1/4
Answer: 1/4
Step-by-step explanation:
To subtract mixed fractions, you need to first trun them into improper fractions.
[tex]2\frac{1}{8} =\frac{17}{8}[/tex]
[tex]1\frac{7}{8} =\frac{15}{8}[/tex]
[tex]\frac{17}{8} -\frac{15}{8} =\frac{2}{8} =\frac{1}{4}[/tex]
Can someone tell me what 58-(1/4)^2 is
Answer:
57.9375
Step-by-step explanation:
Answer:
The answer above this is correct
An equation of an ellipse is given. x2 16 + y2 25 = 1 (a) Find the vertices, foci, and eccentricity of the ellipse. vertex (x, y) = 0,−5 (smaller y-value) vertex (x, y) = 0,5 (larger y-value) focus (x, y) = 0,−3 (smaller y-value) focus (x, y) = 0,3 (larger y-value) eccentricity 3 5 (b) Determine the length of the major axis.
Answer:
(a)
The vertices are at (0,-5) and (0,5).The coordinates of the foci are (0,-3) and (0,3).Eccentricity=3/5(b)Length of the major axis=10
Step-by-step explanation:
When the major axis of an ellipse is parallel to the y-axis.The standard form of the equation of an ellipse is given as:
[tex]\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1[/tex]
Given the equation:
[tex]\dfrac{x^2}{16}+\dfrac{y^2}{25}=1[/tex]
(I)The coordinates of the vertices are [tex](0, \pm a)[/tex]
[tex]a^2=25\\a^2=5^2\\a=5[/tex]
Therefore, the vertices are at (0,-5) and (0,5).
(II)The coordinates of the foci are [tex](0, \pm c)$ where c^2=a^2-b^2[/tex]
[tex]c^2=a^2-b^2\\c^2=25-16\\c^2=9\\c=3[/tex]
The coordinates of the foci are (0,-3) and (0,3).
(III)Eccentricity
This is the ratio of the distance c between the center of the ellipse and each focus to the length of the semi major axis.
Simply put, Eccentricity =c/a
Eccentricity=3/5
(b)Length of the major axis
The length of the major axis=2a
=2(5)=10.
Find the area of a circle with a radius of
3
3start color purple, 3, end color purple.
Either enter an exact answer in terms of
π
πpi or use
3.14
3.143, point, 14 for
π
πpi and enter your answer as a decimal.
Answer: The area is 9π unit squared ( in terms of π)
Step-by-step explanation:
From the equation for area of a circle, A = πr²
Where A is the area of the circle
r is the radius of the circle
From the question, the radius, r of the circle is 3
r = 3
Therefore, the Area of the circle is given by
A = π × (3)²
A = π×3×3
A = 9π unit squared ( in terms of π)
Hence, the area is 9π unit squared
OR
Since π is given as 3.14
Then,
A = 3.14 × (3)²
A = 3.14 × 3 × 3
A = 28.26 unit squared
Hence, Area is 28.26 unit squared (in decimal)
Using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches? Round to the nearest tenth.
Answer:
4.5 inches
Step-by-step explanation:
Put the given values in the volume formula and solve for width:
V = LHW
138.24 = (3.2)(9.6)W
138.24/30.72 = W = 4.5
The width of the prism is 4.5 inches.
Suppose tortilla chips cost 22.5 cents per ounce. If a bag costs $3.07, how many ounces are in the bag of chips? Round your answer to the nearest hundredth, if necessary.
Answer:
13.64 ounces
Step-by-step explanation:
Cost per ounce = $0.225
Cost per bag = $3.07
The number of ounces in a bag of chips is given by the cost per bag divided by the cost per ounce:
[tex]n=\frac{3.07}{0.225}\\ n=13.64\ ounces[/tex]
There are 13.64 ounces in a bag of chips.
Find the center and radius of the circle x2+y2=16
Answer:
The standard form of the equation of a circle is
(
x
−
a
)
2
+
(
y
−
b
)
2
=
r
2
where (a,b) are the coords of the centre and r , the radius.
x
2
+
y
2
=
16
is in this form
with a = b = 0 and r = 4
hence this circle has centre at the origin (0,0) and radius 4
The intercepts will therefore be (± 4,0) and (0, ± 4 )
A researcher wants to investigate whether there is a relationship between annual company profit ($) and median annual salary paid by the company ($). The researcher collects data on a random sample of companies and after analyzing the data finds the p-value to be 0.56. Which of the following is an appropriate conclusion based on this p-value?A. There is a 56% chance that there is no relationship between annual company profit and median annual salary paid by the company.
B. There is a relationship between annual company profit and median annual salary paid by the company, and the corresponding value of the correlation coefficient is r = 0.56.
C. There is no relationship between annual company profit and median annual salary paid by the company.
D. There is not convincing evidence of a relationship between annual company profit and median annual salary paid by the company.
Answer:
D. There is not convincing evidence of a relationship between annual company profit and median annual salary paid by the company.
Step-by-step explanation:
In this hypothesis test, the null hypothesis usually states that there is no relationship between the two variables in study.
In opposite, the claim that is being tested is the speculative hypothesis: that there is a significant relationship between both variables.
The researcher takes a sample and the P-value indicates the probability of getting that sample by pure chance if the null hypothesis is true.
Then, a very small P-value, below the significance level, indicates that the sample is very unusual if the null hypothesis is true, what gives evidence to reject the null hypothesis.
In this case, a P-value of 0.56 indicates that the sample is not unusual if the null hypothesis is true, so it gives no support to the claim that the null hypothesis is false and that there exists a relationship between the two variables in study.
D. There is not convincing evidence of a relationship between annual company profit and a median annual salary paid by the company.
An appropriate conclusion based on this p-value is that there is not convincing evidence of a relationship between annual company profit and the median annual salary paid by the company. The researcher takes a sample, and if the null hypothesis is true, the P-value indicates the probability of taking this sample purely by chance. A very small P-value below the significance level indicates that the sample is very abnormal if the null hypothesis is true. This indicates that the null hypothesis needs to be rejected. In this case, a P-value of 0.56 indicates that the sample is not uncommon if the null hypothesis is true. Therefore, the claim that the null hypothesis is false and that the two variables under investigation are related is not supported.Thus, the correct answer is D.
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Find the value of the function sin 460
Answer:
Sin(460 radians)= .97054
sin(460 degrees)= 0.98480775301
Step-by-step explanation:
I'm not sure where you are from, but usually you are allowed to use a calculator. (At least I was when I took Algebra 2/Trig in 6th grade.)
You never specified radians or degrees so I will answer both.
sin(460 radians)= .97054
sin(460 degrees)= 0.98480775301
If you are not allowed to use a calc, then I suggest looking at unit circle videos on Khan Academy.
What is the lowest value of the range of the function shown on the graph? 0 3
Answer:
-2
Step-by-step explanation:
Edge 2020
Answer: B. -2
Step-by-step explanation: On Edge!!!!!
Eric’s average income for the first 4 months of the year is $1,450.25, what must be his average income for the remaining 8 months so that his average income for the year is $1,780.75?
A study conducted at a certain college shows that 54% of the school's graduates move to a different state after graduating. Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.
Answer:
99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they move to a different state, or they do not. The probability of a graduate moving to a different state is independent of other graduates. So we use the binomial probability distribution 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.
54% of the school's graduates move to a different state after graduating.
This means that [tex]p = 0.54[/tex]
7 randomly selected graduates
This means that [tex]n = 7[/tex]
Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.
Either none moves, or at least one does. The sum of the probabilities of these events is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]. Then
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{7,0}.(0.54)^{0}.(0.46)^{7} = 0.0044[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0044 = 0.9956[/tex]
99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.
A company is planning to manufacture snowboards. The fixed costs are $ 100$100 per day and total costs are $55005500 per day at a daily output of 20 boards. A. Assuming that the total cost per day, C(x), is linearly related to the total output per day, x, write an equation for the cost function.
Answer:
The equation for total cost function is
C(x)=100+270x
Step-by-step explanation:
Variable cost per per board =total cost per day-fixed cost per day/daily output
total cost per day is $5,500
fixed cost per day is $100
20 boards are produced per day
variable cost per board=($5,500-$100)/20=$270 per day
Total cost C(x)=fixed cost per day+ variable per board*number of daily output
Since daily output is represented also by x ,total cost function is given thus:
C(x)=100+270x
The equation for total cost function is C(x)=100+270x
The calculation is as follows:Variable cost per board =total cost per day-fixed cost per day ÷ daily output
Here
total cost per day is $5,500
fixed cost per day is $100
20 boards are produced per day
So,
variable cost per board=($5,500-$100) ÷20
=$270 per day
Now the equation is
C(x)=100+270x
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The data below are the frequency of cremation burials found in 17 archaeological sites. a. Obtain the mean, median, and mode of these data. b. Which measure of center do you think works best here? 85 67 45 47 524 32 31 272 2141 45 390 28 86 424 59 256 143 a. The mean is 275. (Round to one decimal place as needed.) The median is nothing. (Round to one decimal place as needed.) Select the correct choice below and fill in any answer boxes within your choice. A. The mode is nothing. (Round to one decimal place as needed.) B. There is no mode. b. Which measure of center works best here?
Answer:
(a) The mean of the data is 275.
(b) The median of the data is 85.
(c) The mode of the data is 45.
(d) The measure of center that works best here will be median.
Step-by-step explanation:
We are given below the frequency of cremation burials found in 17 archaeological sites. Arranging those in ascending order we get;
28, 31, 32, 45, 45, 47, 59, 67, 85, 86, 143, 256, 272, 390, 424, 524, 2141.
(a) The formula for calculating mean for the above data is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{28+ 31+ 32+ 45+ 45+ 47+ 59+ 67+ 85+ 86+ 143+ 256+ 272+ 390+ 424+ 524+ 2141}{17}[/tex]
= [tex]\frac{4675}{17}[/tex] = 275
So, the mean of the data is 275.
(b) Since, the number of observations (n) in our data is odd (i.e. n = 17) , so the formula for calculating median is given by;
Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]
= [tex](\frac{17+1}{2} )^{th} \text{ obs.}[/tex]
= [tex](\frac{18}{2} )^{th} \text{ obs.}[/tex]
= [tex]9^{th} \text{ obs.}[/tex] = 85
So, the median of the data is 85.
(c) Mode is that value in our data which appears maximum number of times in our data.
So, after observing our data we can see that only number 45 is appearing maximum number of times (2 times) and all other numbers are appearing only once.
So, the mode of the data is 45.
(d) The measure of center that works best here will be median because there are outliers in our data (means extreme values) and mean gets affected by the outliers.
So, the best measure would be median as it represents the middle most value of our data.
How are you suppose to simplify a^-n ?
Answer:
1/a^n
Step-by-step explanation:
To simplify, you remove the negative by "flipping" what side it is on.
a^-n/1 -> 1/a^n
Answer:
[tex]\frac{1}{a^n}[/tex]
Step-by-step explanation:
[tex]a^{-n}[/tex]
You would apply exponent rule which is [tex]a^{-b}=\frac{1}{a^b}[/tex]:
[tex]=\frac{1}{a^n}[/tex]
#18 *
C) Assessment Practice
18. Last month you spent $30. This month you spent 140% of what you spent
last month. Set up a proportion to model this situation. How much did you
spend this month?
Your answer
Answer: You spent $42 this month.
Step-by-step explanation:
[tex]\frac{x}{30} = \frac{140}{100}[/tex] solve by cross product
100x = 4200
x= 42
