6. You draw one card from a standard deck.(a) What is the probability that you do not select a diamond? (b) What is the probability that you do not select a face card? (c) What is the probability that you do not select an Ace? (d) What is the probability that you do not select a Jack or a King?
Answers
a.
We have 13 diamond cards.
The total of cards in a standard deck is 52
P(not a diamond) = 1 - P(Diamond)
= 1 - 13/52
= 3/4
b.
There are 12 faces cards
P(not a face card) = 1- P(face card)
= 1 - 12/52
= 10/13
c.
There are 4 ace cards
P(not an Ace) = 1-P(Ace)
= 1 - 4/52
= 12/13
d.
We have 4 jack cards and 4 king cards. 4+4 =8 j and k cards
P(not j or k) = 1 - P(j or k)
=1 - 8/52
= 44/52
Related Questions
#4 There is 3/4 pound of paper clips to share equally with 5 employees. What amount of paperclips will each employee receive? (total = how many in each group = groups)
Answers
the total amount of paper clip is 3/4 pound
if 3/4 pound is to be shared equally with 5 employee
then 3/4 is divided by 5
when you change the division to multiplication 5/1 becomes 1/5
[tex]\frac{3}{4}\times\frac{1}{5}\text{ = }\frac{3\times1}{4\times5}=\text{ }\frac{3}{20}[/tex]so each of the 5 employee receives 3/20 pound of the paper clips
Find an equation of the ellipse that has center (-2,4), a minor axis of length 12, and a vertex at (5, 4).
Answers
Given:
The centre of the ellipse = (-2,4),
A minor axis length a= 12 ,
And distence from the vertex(5,4) to centre ,
[tex]\begin{gathered} b=\sqrt[]{(5-(-2))^2+(4-4)^2} \\ =\sqrt[]{(5+2)^2+0} \\ =\sqrt[]{7^2} \\ =7 \end{gathered}[/tex]The equation of ellipse is ,
[tex]\begin{gathered} \frac{(x-(-2))^2}{7^2}+\frac{(y-4)^2}{12^2}=1 \\ \frac{(x+2)^2}{49}+\frac{(y-4)^2}{144}=1 \\ \end{gathered}[/tex]Fracciones inversas racionales
Answers
Given the function;
[tex]undefined[/tex]A crew averages 50 ft.² per hour. Their next job totals 1500 Square feet. How many hours will the next job take them?
Answers
Given: A crew averages 50 ft.² per hour. Their next job totals 1500 Square feet.
Required: How many hours will the next job take them.
Explnation:
We can find the hours using unitary method.
50 square feet are averaged in = 1 hour
1 square feet is averaged in = 1/50 hour
1500 square feet is averaged in =(1/50)1500 hours
[tex]\frac{1}{50}\times1500=30[/tex]So, 1500 square feet is averaged in 30 hours.
Final Answer: The next job will take 30 hours.
Which point lies on the graph of y=2(1/2^x?
Answers
the points that lies on the graph of the function is C because we get that
[tex]18=2\cdot(\frac{1}{3})^{-2}[/tex]Determine how much money she expects to take in at the end of the first week with her 12 chickens. Justify your response.
Answers
Answer: She would have $23.34 at the end of first week
EXPLANATION
The total number of chickens = 12
Let A represent the Americana chicken
Let D represent the delware chicken
Since, there are total of 12 chickens
Therefore, the algebraic expression can be represented mathematically as follows
A + D = 12 ------------------ equation 1
Each Americana chicken is sold for $3.75
Each Delware chicken is sold for $2.50
The total 12 chickens is purchased at $35
3.75 x A + 2.50 x D = 35
3.75A + 2.5D = 35 --------------- equation 2
The two equations can be solved simultaneously using substitution method
A + D = 12
3.75A + 2.5D = 35
Make A the subject of the formula in equation 1
A = 12 - D
Put A = 12 -D in equation 2
3.75(12 - D) + 2.5D = 35
Open the parenthesis
45 - 3.75D + 2.5D = 35
Collect the like terms
-3.75D + 2.5D = 35 - 45
-1.25D = -10
Divide both sides by -1.25
-1.25D/-1.25 = -10/-1.25
D = 10/1.25
D = 8 chickens
To find A, put the value of D in equation 1
A + D = 12
A + 8 = 12
A = 12 - 8
A = 4 chickens
Therefore, we have 8 Delware chickens and 4 Americana chickens
Part B
Determine how much money she expects to take at the end of first week
The americana chicken lay 2 eggs per day
Since, we have 4 americana chickens
Each chicken lays 2 eggs
4 x 2 = 8 eggs
The 4 chickens lay 8 eggs in one day
7 days = 1 week
in one week, they would laid 8 x 7
= 56 eggs
Therefore, Americana chickens would laid 56 eggs in one week
The Delware chicken lay 1 egg per day
We have a total of 8 Delware chickens
Total eggs laid in a day = 8 x 1
= 8 eggs
In one week = 8 x 7
= 56 eggs
Therefore, Delaware chickens would also laid 56 eggs in one week
The total number of eggs laid in one week = 56 + 56
Total eggs = 112 eggs
She do sell per dozen for $2.50
1 dozen = 12 eggs
The total eggs laid = 9 dozens 4 eggs
9 dozens of eggs = 9 x 2.50
9 dozens = $22.50
If 12 eggs is sold at $2.50
Then 1 egg will be sold at what
12 = 2.50
1 = x
cross multiply
x * 12 = 2.50 * 1
12x = 2.50
Divide both sides by 12
12x/12 = 2.50/12
x = 2.50/12
x = $0.21
Therefore one egg is sold for $0.21
For the remaining 4 eggs
0.21 x 4 = $0.84
Total money she will be expecting is = 22.50 + 0.84
= $23.34
Therefore, she would have $23.34 at the end of first week
John has been driving at 60 miles an hour for 3 hours how many miles has he traveled so far If the total distance to his destination is 240 miles how much father must John dry
Answers
John has been driving 60 miles an hour for 3 hours
The total distance to his destination is 240 miles
Since, D = R x T
Where, D = distance
R = rate
T = time
Since he drives 60 miles an hour, Then rate = 60/1
Rate = 60 miles/hour
From D= R x T
R = 60
T = 3
D = 60 x 3
D = 180 miles
John has traveled 180 miles for 3 hours.
Since his total destination is 240 miles
To calculate how much farther he needs to drive
Remaining distance = Total distance - Distance traveled in 3 hours
Remaining distance = 240 - 180
= 60 miles
John needs to travel 60 miles further before he can reach his final destination.
Two parallel lines are cut by a transversal, as shown below.x + 403xWhat is the solution when solved for x, and why?=10, because alternate interior angles are equal Therefore, c +40 = 3.= 20, because alternate interior angles are equal. Therefore 240 = 30x= 35, because alternate interior angles are supplemental. Therefore, t.40 3.0 = 180.I=80, because alternate interior angles are supplemental. Therefore, o+ 40 + 30 = 180.
Answers
we have:
[tex]x+40=3x[/tex]because they are alternate angles, i.e., they have equal measure, then solve for x:
[tex]\begin{gathered} x+40-x=3x-x \\ 40=2x \\ \frac{40}{2}=\frac{2x}{2} \\ x=20 \end{gathered}[/tex]therefore answer is the second one
The four sequential sides of a quadrilateral have lengths a = 3.1, b = 6.9, c = 9.6, and d = 10.6 (all measured in yards). The angle between the two smallest sides is a = 112°. What is the area of this figure?I got 58.72 but there saying that wrong
Answers
Step 1
see the figure below to better understand the problem
Step 2
Applying the law of sines
Find out the area of triangle ABC
[tex]\begin{gathered} A=\frac{1}{2}(3.1)(6.9)sin(112^o) \\ A=9.916\text{ yd}^2 \end{gathered}[/tex]Step 3
Applying the law of cosines
Find out the length of the side AC
[tex]\begin{gathered} AC^2=3.1^2+6.9^2-2(3.1)(6.9(cos112^o) \\ AC=8.6\text{ m} \end{gathered}[/tex]Step 4
Applying the law of cosines
Find out the measure of angle D
[tex]AC^2=AD^2+DC^2-2(AD)(DC)cosD[/tex]substitute given values
[tex]\begin{gathered} 8.6^2=10.6^2+9.6^2-2(10.6)(9.6)cosD \\ solve\text{ for cosD} \\ cosD=\frac{10.6^2+9.6^2-8.6^2}{2(10.6)(9.6)} \\ \\ angle\text{ D}=50.1^o \end{gathered}[/tex]Step 5
Applying the law of sines
Find out the area of the triangle ADC
[tex]\begin{gathered} A=\frac{1}{2}(10.6)(9.6)sin(50.1^o) \\ \\ A=39.03\text{ yd}^2 \end{gathered}[/tex]The area of the quadrilateral is equal to
[tex]\begin{gathered} A=9.92+39.03 \\ A=48.95\text{ yd}^2 \end{gathered}[/tex]The area is 48.95 square yards (rounded to two decimal places)Mr Scher's Homeroom - Me Sanchez Recorded the transportation methods that the students in his homeroom use to get home from school Use this data to answer the questions below wat percent of the students w Mar Sancheridas are bunden? F 40% G 67% H 12 J 30%
Answers
The percentage of students in Mr Sanchez class that are bus riders can be calculated below
number of student that are bus rider = 12
Total number of student = 12 + 8 + 4 + 6 = 30
Therefore, the percentage is
[tex]\begin{gathered} \text{ \% bus rider=}\frac{12}{30}\times100 \\ \\ \text{ \% bus rider}=\frac{1200}{30} \\ \text{ \% bus rider}=\text{ 40\%} \end{gathered}[/tex]Allison earns $6,500 per month at her job as a principal. the chart below shows the percentages of her budget how much does Allison pay for her Credit cards
Answers
to calculate the amount that she pays for her credit cards, we need to multiply the percentage given in the chart and what she earns per month
[tex]6500\cdot0.046=299[/tex]so she pays $299 for her credits cards
Find the quotient of 4 1/8 and 2 1/5
Answers
Given
[tex]4\frac{1}{8}\text{ and 2}\frac{1}{5}[/tex]Find
Quotient
Explanation
Now to find quotient , we need to divide these numbers
[tex]\begin{gathered} 4\frac{1}{8}\div2\frac{1}{5} \\ \\ \frac{4\times8+1}{8}\div\frac{2\times5+1}{5} \\ \\ \frac{33}{8}\div\frac{11}{5} \\ \\ \frac{33}{8}\times\frac{5}{11} \\ \frac{15}{8} \\ \\ 1\frac{7}{8} \end{gathered}[/tex]Final Answer
Therefore , the quotient is 1 .
Area (you must include units) Round to the tenths, as needed.
Answers
Okay, here we have this:
Considering the provided information, we are going to calculate the requested area, so we obtain the following:
Then to calculate the area of the circle we will substitute in the following formula:
A = πr^2
A = π(16.1 cm)^2
A = π(16.1 cm)^2
A = 269.21 π cm^2
A ≈ 814.3 cm^2
Finally we obtin that the area of the circle is approximately 814.3 cm^2.
5. Un atleta está realizando una maratón de 7 km. En estos momentos ha recorrido 60 metros ¿Cuántos metros le quedan por recorrer? I 1000
Answers
1km = 1000 metros
7km = 7 x 1000 = 7,000 metros
Si ya recorrio 60 metros:
7,000-60 = 6940 metros
Le quedan 6940 metros por recorrer
Maddox correctly compared the value of the digits in 422.44. Which comparison could he have made? The value of the tens digit is 10 times as much as the value of the tenths digit.The value of the hundredths digit is 10 times as much as the value of the tenths digit. The value of the hundreds digit is 10 times as much as the value of the hundredths digit.The value of the ones digit is 1/10 of the value of the tens digit
Answers
We have number 422.44.
Then, we can evaluate each comparison. In the last comparison, we have that:
The value of the one-digit is 1/10 of the value of the tens digit.
Then, we have that:
In the ones, 2 represents 2.
In the tens 2 represents 20.
Therefore, the ones are:
[tex]\frac{2}{20}=\frac{1}{10}[/tex]Thus, the answer must be the last option:
The value of the one-digit is 1/10 of the value of the tens digit.
The following question has two parts. First, answer part A. Then, answer part B. Part A: “If you share 7 apples equally with 3 people, then there are 2 1/3…”. First, complete this sentence. Then, briefly explain what the whole number 2, the denominator 3, and the numerator 1 mean in this problem. Part B: The expression 1 divided by 1/4 is given. Give a real-life application to explain this explanation and then simplify it.
Answers
Part A
7 apples are shared amongst 3 persons, we have:
[tex]\begin{gathered} =\frac{7}{3} \\ =2\frac{1}{3} \end{gathered}[/tex]The number "2" implies that everyone gets 2 apples each
The number "1" implies that after everyone had picked their apples, that's what was left
The number "3" represents the number of persons amongst whom the apples were shared
Part B
For example, you bought a pizza of 4 slices for yourself. You actually bought 1 pizza but in real-time, you have 4 pieces of pizza to yourself
[tex]\begin{gathered} 1\div\frac{1}{4} \\ =\frac{1}{\frac{1}{4}}=\frac{1}{0.25} \\ =4 \\ \\ \therefore1\div\frac{1}{4}=4 \end{gathered}[/tex]Which number line shows the solution to the inequality 9x - 4
Answers
We have the inequalty:
[tex]9x-4<5[/tex]We can isolate x:
[tex]\begin{gathered} 9x-4<5 \\ 9x<5+4 \\ x<\frac{9}{9} \\ x<1 \end{gathered}[/tex]So, the solution is the number less than 1 but not 1. In the number line this is represent by a empty circle (or white). In the options we have the representation is option B, all the number less than 1 but not 1.
Question 28 of 49Which of the following objects is best described by the term line segment?A. The point where two sides of a triangle meetB. The perimeter of a triangleOC. One side of a triangleD. The angle formed by two sides of a triangleSURMIT
Answers
A line segment is a piece o part of a line that has two endpoints.
Then, from the given options the one that best describes a line segment is: One side of a triangle
Answer: C
Solving rational equationsWhich step is the error.SOLVE FOR APlease explain step by step
Answers
To find the error, we repeat the steps correctly:
i)
[tex]b=\frac{1}{2}\cdot\sqrt[]{a-1}[/tex]ii) We pass the 2 dividing on the right, multiplicating at the left:
[tex]2b=\cdot\sqrt[]{a-1}[/tex]iii) We take the square on both sides:
[tex]\begin{gathered} (2b)^2=(\sqrt[]{a-1})^2 \\ 2^2b^2=a-1 \\ 4b^2=a-1 \end{gathered}[/tex]iv) Finally we pass the -1 on the right as +1 to the left:
[tex]4b^2+1=a[/tex]Answer
Comparing the steps, we see that the error was in step III, the square of 2b is 4b², not 2b².
Convert: 480 fluid ounces =quarts
Answers
1) The first thing to do is to consider that there is a relation between 1 fluid ounce and its equivalence to quarts.
[tex]1\:fl\:oz=0.03125\:qt[/tex]2) Based on that, we can set a proportion between fluid ounces and quarts to find either approximately or exactly how many quarts correspond to that.
[tex]\begin{gathered} fl\:oz\:-----quarts \\ 1\:\:\:\:\:\:\:\:\:\:0.03125 \\ 480\:\:\:\:\:\:\:\;x \\ \\ x=480\times0.03125 \\ \\ x=15\:qt \\ \end{gathered}[/tex]That is the answer.
The square root of a number is 6. What equation represents this situation? 0 20 = 6 sx = 6 O = 6 O x2 = 6
Answers
Looking at the options given, let the number be x
Given that the square root of x is 6, the expression would be
[tex]\sqrt[]{x}\text{ = 6}[/tex]The correct option is the second one
15. Your class rank in 2018 was 78 out of 456 students. In 2019 your class rank was 67 outof 501 students.a. In which year did you have the higher percentile ranking.b. If you had the data on the cumulative GPA of each student at the end of thespring semester in 2018, which measure of average would be the mostmeaningful – mean, median, mode? Explain.
Answers
The rankings are:
2018: 78 out of 456
2019: 67 out of 501
The rank and the percentile are related by:
[tex]P=\frac{i\cdot n}{100}[/tex]Where P is the position in the ranking, i is the percentile "type", and n is the number of students.
a)
Using the previous formula:
[tex]\begin{gathered} 2018\colon78=\frac{i\cdot456}{100}\Rightarrow i=\frac{78\cdot100}{456}=17.1\text{\%} \\ 2019\colon67=\frac{i\cdot501}{100}\Rightarrow i=\frac{67\cdot100}{501}=13.4\text{\%} \end{gathered}[/tex]Since in this case the lower the rank, the higher the number. For example, rank 18 is higher than rank 400. Then, in this case, we use the complement to find the real percentile rank:
[tex]\begin{gathered} 2018\colon100\text{\% }-17.1\text{\% }=82.9\text{\%} \\ 2019\colon100\text{\% }-13.4\text{\% }=86.6\text{\%} \end{gathered}[/tex]Then, the higher percentile ranking corresponds to 2019.
b)
If we have the cumulative GPA (grade point average), the mode is just the highest frequency of the distribution. The median is just the measure of cumulative GPA such that:
"50% of the students have a cumulative GPA of (median) or less"
The mean is just the average of all the distribution. Since the cumulative GPA is a measure that goes from 0 to 5, we can say that its distribution is somewhat normal, so the most meaningful measure of a normal distribution is the mean.
A cookie factory uses 1 2/5 barrels of oatmeal in each batch of cookies. The factory used8 2/5 barrels of oatmeal yesterday. How many batches of cookies did the factory make?Write your answer as a fraction or as a whole or mixed number.
Answers
We know that the cookie factory uses 1 2/5 barrels of oatmeal in each batch of cookies. And, the factory used
8 2/5 barrels of oatmeal yesterday.
In order to find how many batches of cookies the factory made we must divide the barrels of oatmeal used yesterday by the barrels of oatmeal that are used in each batch of cookies
First, we must convert mixed numbers in fractions
[tex]1\frac{2}{5}=\frac{1\cdot5+2}{5}=\frac{7}{5}[/tex][tex]8\frac{2}{5}=\frac{8\cdot5+2}{5}=\frac{42}{5}[/tex]Then, we must divide them
[tex]\frac{\frac{42}{5}}{\frac{7}{5}}=\frac{42}{7}=6[/tex]Finally, the factory make 6 batches.
FIND THE TOTAL AREA UNDER THE CURVE FOR THE FOLLOWING:A. TO THE LEFT OF Z=2.26B. TO THE RIGHT OF Z= -1.82C. BETWEEN Z= -1.35 AN Z= 0.37
Answers
Part A:
According to the normal table, the area to the left of Z = 2.26 is A(Z <= 2.26) = 0.5 + 0.4881 = 0.9881
Part B:
According to the normal table, the area to the right of Z = -1.82 is given by A( Z >= -1.82) = 0.5 + 0.4656 = 0.9656
Part C:
According to the normal table, the area to the left of Z = 0.37 is given by A(Z <= 0.37) = 0.5 + 0.1443 = 0.6443, and the area on the left of Z = -1.35 is given by A(Z <= -1.35) = 0.5 - 0.4115 = 0.0885.
Therefore, we have: A(-1.35 <= Z <= 0.37) = 0.6443 - 0.0885 = 0.5558
In Fig. 12.8, PQRS is a parallelogram, HSR isa straight line and HPQ = 90°. If|HQ| = 10 cm and |PQ| = 6 cm, what is thearea of the parallelogram?
Answers
Answer
48 cm²
Step-by-step explanation
First, we need to calculate the height of the parallelogram, segment HP. Applying the Pythagorean theorem to triangle HPQ, we get:
[tex]\begin{gathered} HQ^2=HP^2+PQ^2 \\ \text{ Substituting with HQ = 10 cm, and PQ = 6 cm, and solving for HP:} \\ 10^2=HP^2+6^2 \\ 100=HP^2+36 \\ 100-36=HP^2 \\ 64=HP^2 \\ \sqrt{64}=HP \\ HP=8\text{ cm} \end{gathered}[/tex]The area of a parallelogram is calculated as follows:
[tex]A=base\times height[/tex]In this case, the height is HP = 8 cm, and the base is PQ = 6 cm. Then the area of parallelogram PQRS is:
[tex]\begin{gathered} A=HP\times PQ \\ A=8\times6 \\ A=48\text{ cm}^2 \end{gathered}[/tex]
on Friday from 5 p.m. to 11 p.m. the temperature changed on average of -1.25 Fahrenheit each hour what it what number represents the total change in temperature in degrees Fahrenheit from 5 p.m. to 11 p.m.
Answers
We need to find the number of hours that passed from 5 p.m to 11 p.m and the multiply the number of hours by the average change in temperature which is -1.25.
Change in hours:
From 5 pm to 11 pm the change in hours is:
[tex]11-5=6\text{hours}[/tex]Change in temperature:
The average change per hour is -1.25 F. So to find the total change in those 6 hours, we need to multiply 6 by -1.25, we get the following:
[tex]6(-1.25)=-7.5[/tex]Answer: -7.5 Fahrenheit
Question 1: 11 ptsBased on results from recent track meets, Denita has a 68% chance of getting a medal in the 100 meter dash. Estimate the probability that Denita will get a medalin at least 5 of the next 10 races. Use the random number table, and make at least 10 trials for your simulation. Express your answer as a percent.
Answers
According to the binomial distribution of probability
[tex]P(k;n,p)=P(X=k)=(nbinomialk)p^k(1-p)^{n-k}[/tex]In our case,
[tex]n=10,p=68\text{percent}=0.68[/tex]Therefore,
[tex]P(k\ge5)=\sum ^{10}_{k=5}(10binomialk)(0.68)^k(1-0.68)^{10-k}[/tex]Thus,
[tex]\Rightarrow P(k\ge5)=(10binomial5)(0.68)^5(0.32)^5+(10binomial6)(0.68)^6(0.32)^4+(10binomial7)(0.68)^7(0.32)^3+(10binomial8)(0.68)^8(0.32)^2+(10binomial9)(0.68)^9(0.32)^1+(10binomial10)(0.68)^{10}(0.32)^0[/tex]After calculations, we reach the following result
[tex]\Rightarrow P(k\ge5)=0.9362\ldots[/tex]Then, the probability of Denita winning a medal in at least 5 of the next 10 races is, approximately 93.63%. The close option is 100%
Which answer correctly shows the graph of f(x)=x2+5x−1 and its inverse relation?
Answers
Given the function:
[tex]f(x)=x^2+5x-1[/tex]Let's select the answer for the graph of the function and its inverse.
Let's find random points on the function.
When x = 0:
[tex]f(0)=0^2+5(0)-1=-1[/tex]When x = -6:
[tex]f(-6)=-6^2+5(-6)-1=36-30-1=5[/tex]Thus, we have the points:
(x, y) ==> (0, -1) and (-6, 5)
Now, the inverse of this function will contain the points:
(x, y) ==> (-1, 0) and (5, -6)
Where f(x) is the blue function.
From the graphs shown, the graph which contains the points for f(x) = (0, -1) and (-6, 5) and g(x) = (-1, 0) and (5, -6) is the first graph.
Therefore, the correct graph which shows the f(x) and its inverse is:
aIn a class of students, the following data table summarizes the gender of the studentsand whether they have an A in the class. What is the probability that a student is amale given that they have an A?Female MaleHas an A42Does not have an A167-
Answers
Solution
We have the following info given:
Female Male
Has an A 4 2
Dos not have an A 16 7
And we want to find the probability that a student is a male given that they have an A?
We can create this notation:
M= student is male
A= student have an A
So we want this: P(M|A) and we can use the following formula using the conditional probability rule:
[tex]P(M|A)=\frac{P(\text{MandA)}}{P(A)}[/tex]And we can find the probabilities:
P(M and A) = 2/29
P(A)= 9/29
And replacing we got:
[tex]P(M|A)=\frac{\frac{2}{29}}{\frac{9}{29}}=\frac{2}{9}[/tex]uhh .. im stuck and this is area model ..
Answers
Solution
for this case we can do the following multiplicating the two terms
[tex]7x(5x^2)+7x(9x)+7x(6)+4(5x^2)+4(9x)+4(6)[/tex]If we multiply we got:
[tex]35x^3+63x^2+42x+20x^2+36x+24[/tex]And if we simplify we got:
[tex]35x^3+73x^2+78x+24[/tex]x 5x^2 9x 6
7x 35x^2 63x^2 42x
4 20x^2 36x 24