SOLUTION:
Case: Probability
Given:
Number of TV Graphic magazines = 6
Number of News time magazines = 8
Total number of magazines on the stand = 14.
*two customers purchased a magazine*
Required: find the probability that one each magazine was purchased
Method:
[tex]\begin{gathered} Pr\left(one\text{ magazine each}\right? \\ =\text{ }\frac{^{n1}C_{x1}\times^{n2}C_{x2}}{^nC_x} \\ n1=\text{ number of TV graphic magazines} \\ x1=\text{ number of TV graphic magazines selected} \\ n2=\text{ number of News time magazines} \\ x2=\text{ number of News time magazines selected} \\ n=\text{ total number of magazines selected} \\ x=\text{ total number sslected} \end{gathered}[/tex][tex]\begin{gathered} \frac{^{n1}C_{x1}\times^{n2}C_{x2}}{^nC_x} \\ \frac{^6C_1\times^8C_1}{^{^14}C_2} \\ \frac{6\times8}{91} \\ \frac{48}{91} \end{gathered}[/tex]Final answer:
The probability that one each magazine was purchased is 48/91
7(1 - 6p) need help please
Find 7•(1-6p)
First eliminate parenthesis
Apply distributive law
a•(b+c) = ab + ac
Then
7•(1-6p) = 7•1 - 7•6p
. = 7 -42p
ANSWER IS
7 - 42p
An archaeologist finds dinosaur bones 100 miles East and 200 miles North of his office. He finds whale bones 100 miles East and 300 miles South of his office. Graph and label these two points. How far apart are they?
Let's draw a picture of our problem:
where the red point (100 East, 200 Norh) represents the place where Archaeologist found the dinosaur. The blue point (100 East, 300 South) represents the place where Arcaeologist found the whale bones. Additionally, the green point (0,0) represents Arcaeologist's offfice.
write the equation for each sentence below.a) (p) is the product of 7 to the sum of 3 and 9 b) The difference of (T) and 24 is 9 more than 34
(p) is the product of 7 to the sum of 3 and 9
This means we take the sum of "3" and "9" and multiply it with the variable "p". The expression is shown below
[tex]\begin{gathered} p\times(3+9) \\ =p\times12 \\ =12p \end{gathered}[/tex](b)The difference of (T) and 24 is 9 more than 34
The difference of T and 24 means T - 24
is 9 more than 34 means 34 + 9
Writing it together:
[tex]\begin{gathered} T-24=34+9 \\ T-24=43 \end{gathered}[/tex]Marco wants to take a taxi cab ride if the cost to ride is 7.00 with the cost per m is 0.25 per mile and mr. o can only spend 30 write linear inequality that model
Each ride has a fixed cost of 7 and a cost that increases proportionally to the distance travelled of 0.25 per mile. Therefore the total cost of the ride is:
[tex]\text{ cost(x)}=0.25\cdot x+7[/tex]Where "x" is the distance in miles. Marco can only spend 30 on his ride, therefore the cost must be less or equal to that value.
[tex]\begin{gathered} \text{ cost(x)}\leq30 \\ 0.25\cdot x+7\leq30 \end{gathered}[/tex]We can solve the linear equation by isolating the "x" variable on the left side.
[tex]\begin{gathered} 0.25\cdot x\leq30-7 \\ 0.25\cdot x\leq23 \\ x\leq\frac{23}{0.25} \\ x\leq92 \end{gathered}[/tex]Marco's travel must be shorter or equal to 92 miles.
Jerry and Steve each had 24 candy bars to sell. Jerry sold 50% of his candy bars. Steve sold of his candy 6 bars. What fraction of the total candy bars did Jerry and Steve sell together?
Jerry and Steve each had 24 candy bars, that is, the total candy bars are 48:
If Jerry sold 50% of his candy bars, it means that he sold one half of the total, then, he sold 12 bars.
Steve sold 6 candy bars.
Then, they both sold 12 + 6 = 18 candy bars together.
The fraction of the total candy bars is then:
18/48 = 9/24 = 3/8
Which point is a solution to the system of inequalities below?A. (1,2)B. (4,7)C. (0,3)D. (-1,1)
For this problem we have the following two inequalities given:
[tex]x+2y\ge4\text{, y}-2x<0[/tex]And we want to find the point of solution to the system of inequalities and for this case we can work with equations
[tex]x+2y=\text{4 (1) }[/tex][tex]y-2x=\text{ 0 (2)}[/tex]If we solve for x from equation (1) we got:
[tex]x=\text{ 4}-2y\text{ (3)}[/tex]And replacing equation (3) into equation (2) we got:
[tex]y-2(4-2y)=\text{ 5y}-8=\text{ 0}\rightarrow y=\text{ }\frac{8}{5}=\text{ 1.6}[/tex]And solving for x we got:
[tex]x=\text{ 4}-(2\cdot1.6)\text{ = 0.8}[/tex]So then the intersection point between the two lines is (0.8,1.6). If we analyze all the possible options we have this:
(1,2)
How do you solve an area of a rectangle with fractions
Given the figure, we can deduce the following information:
Perimeter = 65 in.
length = n
width = 11 2/4 in. = 23/2 in.
To determine the value of n, we use the formula:
[tex]P=2(l+w)[/tex]where:
P= Perimeter
l=length
w=width
We plug in what we know:
[tex]\begin{gathered} P=2(l+w) \\ 65=2(n+11\frac{2}{4}) \\ \text{Simplify and rearrange} \\ 65=2(n+\frac{23}{2}) \\ \frac{65}{2}=n+\frac{23}{2} \\ n=\frac{65}{2}-\frac{23}{2} \\ n=\frac{65-23}{2} \\ n=\frac{42}{2} \\ \text{Calculate} \\ n=21 \end{gathered}[/tex]Therefore, the value of n is 21 in.
Linda Davis agreed to lend money to Alex Luciano at a special interest rate of 7% per year, on the condition that he borrow enough that would pay her $500 in interest over a four-year period. What was the minimum amount Alex could borrow?
It is given that,
[tex]\begin{gathered} Rate(R)\text{ = 7\%} \\ I\text{ = \% 500} \\ T\text{ =3 years} \end{gathered}[/tex]Interest is given by the formula,
[tex]I\text{ = }\frac{PRT}{100}[/tex]Substituting the value in the formula,
[tex]\begin{gathered} 500\text{ = }\frac{P\times7\times4}{100} \\ 50000\text{ = 28P} \\ P\text{ = }\frac{50000}{28} \\ P\text{ = 1785.71 } \end{gathered}[/tex]Thus the minimum amount to be borrowed is $ 1785.71.
A motivational speaker charges $5 for an adult's ticket and $2 for a child's ticket. For one event, he sold 785 tickets for $3280. How many adult tickets were sold? a) 785 b) 570 c) 215 d) 58
Answer:
the number of adult ticket sold is 570
[tex]x=570[/tex]Explanation:
Let x represent the number of adult ticket and y represent the number of child's ticket.
Given that he charges $5 for an adult's ticket and $2 for a child's ticket.
For one event, he sold 785 tickets.
So, we have;
[tex]x+y=785\text{ -----1}[/tex]he sold 785 tickets for $3280.
Then;
[tex]5x+2y=3280\text{ ------2}[/tex]let us solve by substitution.
make y the subject of formula in equation 1 and substitute to equation 2;
[tex]y=785-x[/tex]substituting to equation 2;
[tex]\begin{gathered} 5x+2y=3280 \\ 5x+2(785-x)=3280 \\ 5x+1570-2x=3280 \\ 5x-2x=3280-1570 \\ 3x=1710 \\ x=\frac{1710}{3} \\ x=570 \end{gathered}[/tex]Therefore, since x represent the number of adult tickets sold, then the number of adult ticket sold is 570
[tex]x=570[/tex]Write a sine function that has an amplitude of 5, a midline of 4 and a period of 3/2
Note that in any sine function :
[tex]y=A\sin (B(x+C))+D[/tex]Amplitude = A
Verical Shift or midline = D
Period = (2π)/B
Horizontal or Phase Shift = C
From the given,
since we dont have any horizontal shift, C = 0.
Amplitude = 5, so A = 5
Midline = 4, so D = 4
and
Period = 3/2, so equating it to (2 π)/B
[tex]\frac{3}{2}=\frac{2\pi}{B}[/tex][tex]B=\frac{4\pi}{3}[/tex]Now, substituting the values obtained, the sine function will be :
[tex]y=5\sin (\frac{4\pi}{3}x)+4[/tex]Tamara's monthly budget shows$490.00 in fixed expenses, $529.50in variable expenses, and anexpected income of $1,250.00.1. Why doesn't Tamara's budgetbalance?
She has an expected income of $1250.
The total expenses are $490 + $529.50 = $1019.50.
She has a superavit that she can save. This amount is $1250 - $1019.50 = $230.50.
Answer: the budget balance does not balance because the income is greater than the expenses.
Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.04 and a standard deviation of 1.53. Using the empirical rule, whatpercentage of American women have shoe sizes that are less than 11.1? Please do not round your answer.
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution.
So we have
So we can apply the rule to obtain
A bag of 11 marbles contains 7 marbles with red on them, 6 with blue on them, 6 with green on them, and 3 with red and green on them. What is the probability that a randomly chosen marble has either green or red on it? Note that these events are not mutually exclusive. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
In the case of two not mutually exclusive events, we have that, given events A and B,
[tex]P(A\lor B)=P(A)+P(B)-P(A\cap B)[/tex]Notice that if we only include the first two contributions, we would count the intersection of the two events twice; therefore, we must subtract the probability of its intersection once.
In our case,
[tex]P(R\lor G)=\frac{7}{11}+\frac{6}{11}-\frac{3}{11}=\frac{10}{11}[/tex]Therefore, the answer is 10/11.
fresh flowers charges $1.50 per flower and a $10 delivery fee. beautiful bouquets does not change a delivery fee but charges $4.00 per flower. which equation would allow you to find the number of flowers that would make the cost the same.1.50+ 10x=41.50x+10=41.50x + 10=4x1.50+ 10x=4
Step 1 : Let's review the information provided to us to answer the question correctly:
Fresh flower price = $ 1.50
Delivery = $ 10
Bouquets per flower = $ 4.00
Step 2:
Let x to represent the number of flowers, either fresh or in bouquet
what is 6 3/8 written as a demcimal
Answer:
The solution is 6,375
Step-by-step explanation:
[tex] \sf 6 \frac{3}{8} \\ \\ = \sf \frac{6 \times 8 + 3}{8} \\ \\ \sf \frac{48 + 3}{8} \\ \\ = \sf \frac{51}{8} \\ \\ = \sf 51 \div 8 \\ \\ = \sf6.375[/tex]
in a popular restaurant on a Saturday night three out of every four customers are female. how many customers y are there for x number of total customers
Let y be the number of female customers in the restaurant. Since we know that 3 out of 4 customers are females and that x is the total number of customers, this means that:
[tex]y=\frac{3}{4}x[/tex]A sample of 34 customers was taken at a local computer store. The customers were asked the prices of the computers they had bought. The data are summarized in the following table. Find the mean price for the sample. Round your answer to the nearest dollar
To find the mean we will sum the prices (total price, including repeated values) and divide by the total number of computers, then
[tex]m=\frac{14\cdot1400+11\cdot800+3\cdot2600+6\cdot1500}{34}[/tex]Using a calculator
[tex]\begin{gathered} m=\frac{45200}{34} \\ \end{gathered}[/tex]Do the division (use a calculator)
[tex]\begin{gathered} m=\frac{45200}{34} \\ \\ m=1329.41 \end{gathered}[/tex]The mean price is 1329.41
which domain restrictions apply to the rational expression? 14-2x / x^2-7x
The domain restrictions that apply on the given rational expression are that x can neither be 0 nor 7.
We are given the rational expression:-
[tex]\frac{(14-2x)}{(x^2-7x)}[/tex]
We have to find the domain restrictions that apply on the given expression.
We know that in a fraction, denominator cannot be 0, or else it will make the fraction indefinite.
Hence, by putting the denominator as 0, we will get the domain restrictions of the expression.
[tex]x^2-7x=0[/tex]
x(x - 7) = 0
x = 0 and 7
Hence, the domain restrictions that apply on the given rational expression are that x can neither be 0 nor 7.
To learn more about fraction, here:-
https://brainly.com/question/10354322
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During a class election the ratio of students who voted for candidate A compared tocandidate B was 7: 4. If candidate A received 21 votes, what is the combined amount ofvotes candidate A and candidate B received?
Given: Ratio of students that voted for A compared to B is 7:4
A recieved 21 votes so let B recieve x votes.
So as the given ratios,
[tex]\frac{7}{4}=\frac{21}{x}[/tex][tex]x=\frac{21\times4}{7}=12[/tex]Hence, combined votes received by candidate A and B is 12+21=33
Please help!Which equation best represents the relationship between x and y in the graph?A. y = -3/4x - 3B. y = -4/3x - 3C. y = -3/4x - 4D. y = -4/3x - 4
Recall that the equation of a line in slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept of the line.
The y-intercept is the point where the line intersects the y-axis.
From the graph, we can see that the line intersects the y-axis at y = -3
So, the y-intercept is -3
The slope of the line is given by
[tex]m=\frac{\text{rise}}{\text{run}}=\frac{-3}{4}[/tex]The rise is the vertical distance between the two points on the line.
The run is the horizontal distance between the two points on the line.
So, the equation of the line is
[tex]y=-\frac{3}{4}x-3[/tex]Therefore, option A is the correct answer.
in art class, Rafi made 5 clay bowls to send to family members. the bowls are fragile, so Rafi bought a roll of bubble wrap to protect them. he used a total of 11 feet of bubble wrap to wrap the bowls. how much bubble wrap did Rafi use for each bowl?
Number of bowls: 5
Bubble wrap = 11 feet
To find how many bubble wrap he used for each bowl, divide the bubble graph length by the number of bowls.
11 / 5 = 2.2
2.2 feet for each bowl
A rectangular piece of metal is 25 in longer than it is wide Squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an openbox. If the volume of the box is 1530 in. What were the original dimensions of the piece of metal?What is the original width? ____in
Given:-
A rectangular piece of metal is 25 in longer than it is wide Squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1530 in.
To find the original width.
The formula for volume of the box is,
[tex]v=l\times b\times h[/tex]The volume given is 1530.
Also we have,
[tex]L=W+25,H=5[/tex]Substiutiting the values. we get,
[tex]\left(W+15\right)*W-10*5=1530[/tex]Divide both sides by 5,
[tex]\left(W+15\right)*W-10=306[/tex]So,
[tex]w^2+5w-150=306[/tex]So now we get,
[tex]w^2+5w-456=0[/tex]Now we solve the quadratic equation,
[tex]\begin{gathered} w=\frac{-5\pm\sqrt{5^2-4\cdot\:1\cdot\left(-456\right)}}{2\cdot\:1} \\ w=\frac{-5\pm\:43}{2\cdot\:1} \\ w=19,-24 \end{gathered}[/tex]So now we skip the negative value and take the positve value 19.
So the required value is 19.
what is 20/5*(3.8)=?
Given:
[tex]\frac{20}{5}\cdot3.8=\text{?}[/tex]first, we will find the result of dividing 20 by 5, then multiply the result by 3.8
so, the answer will be as follows:
[tex]\begin{gathered} \frac{20}{5}\cdot3.8 \\ \\ =4\cdot3.8=15.2 \end{gathered}[/tex]So, the answer will be 15.2
Type the correct answer in each box.In this figure, sin ZQOP=cos ZRand cosZROQ sin 2
From the given figure, we have:
[tex]\begin{gathered} \sinSimilarly,[tex]\begin{gathered} \cosFind WX.Write your answer as an integer or as a decimal rounded to the nearest tenth.WX = ____
The give figure is of a triangle WXY right angled at X.
From the figure, WY=10 and
Using trigonometric property in the triangle,
[tex]\cos \theta=\frac{\text{adjacent side}}{\text{hypotenuse}}[/tex][tex]\begin{gathered} \cos Find WX by solving the above equation.[tex]\begin{gathered} WX=10\times\cos 44^{\circ} \\ =7.2 \end{gathered}[/tex]Therefore, WX=7.2.
-14x +P = Qx + 18find the values of P and Q the equation has infinite solutions
To have infinite solutions, both sides of the equation must be equal, we have to end with a statement that is true no matter what:
-14x+P = Qx+18
-14x = Qx
So, Q must be -14
-14x = -14x
For the next term
P = 18
So:
-14x+18 =-14x+18
Values:
P =18
Q=-14
Fill in the missing number to complete the pattern.18, 12, _ , 0
The given pattern starts with an 18, then we have a 12, we can go from 18 to 12 by subtracting 6 from the initial number. By subtracting 6 from 12, we get the number that goes on the right side of 12, that is:
12 - 6 = 6
Then, fill the missing number with a 6.
18, 12, 6, 0
The recycling center processed 36,000 pounds of recyclable materials. How many tons of recyclable materials are processed? A 18 TonC 72,000 TonB 38,000 TonD 180 Ton
We were told that the recycling center processed 36,000 pounds of recyclable materials. We would convert from pounds to tonnes. Recall,
1 tonne = 2000 pounds
Thus, x tonnes = 36000 pounds
By cross multiplying, we have
2000x = 36000
x = 36000/2000
x = 18
18 tons of recyclable materials were processed
using your place value vocabulary, describe the place value pattern you see occur in these four problems.10 × $8 = $8010 × $0.80 = 8.00$5.40 ÷ 10 = $0.54$0.60 ÷ 10 = $0.60
The place value of 8 on multiply by 10 becomes tens
The place value of the 8 in 0.80 by multiply with 10 becomes ones
Teh place of 5 on dividing with 10 becomes tenths
The place of 6 from 0.60 on divide by 10 becomes tenths
Hello can you assist me please i need to solo e and Identity sine cosine or tangent and identify opposite hypnose or adjeact.Number 11.
Given the Right Triangle shown in the exercise, you need to use the following Trigonometric Function in order to find the measure of "x":
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]In this case, you can identify that:
[tex]\begin{gathered} \alpha=21° \\ opposite=x \\ adjacent=18 \end{gathered}[/tex]Then, by substituting values and solving for "x", you get:
[tex]\begin{gathered} tan(21\text{\degree})=\frac{x}{18} \\ \\ 18\cdot tan(21\text{\degree})=x \end{gathered}[/tex][tex]x\approx6.9[/tex]Hence, the answer is:
[tex]x\approx6.9[/tex]