The probability that when a couple has two children, at least one of them is a boy is 0.75.
Based on the information given, the sample space will be (BB, BG, GB, GG)
where,
B = Boy
G = Girl
Therefore, based on the sample space given, at least a boy occurs in 3 places out of 4. This will be 3/4 = 0.75.
In conclusion, the correct option is 0.75.
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The probability of a couple having at least one boy when they have two children is 75%, as three out of four possible outcomes include at least one boy. These outcomes are two boys, a boy then a girl, and a girl then a boy.
Explanation:The subject of the question is probability which is a branch of mathematics. In order to find the probability that when a couple has two children, at least one of them is a boy, we need to analyze possible outcomes. The couple could have two boys (BB), a boy and a girl (BG), a girl and a boy (GB), or two girls (GG). Hence, the total unique outcomes are 4 (BB, BG, GB, GG).
Considering at least one boy, the possible outcomes could be BB, BG, GB, which are 3 possibilities. Finally, the probability is given as the ratio of favorable outcomes to the total number of outcomes. So the probability of having at least one boy is 3/4 or 75%.
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tim earns $150 a week plus $15.50 for each desk he assembles. write an inequality to represent how many desks he needs to assemble to make $400 in one week.
x = number of desks needed to make
equation: 150 +15.50x >= 400
solution:
150 +15.50x >=400
15.50x = 250
x = 250/15.50 = 16.129
he needs to assemble 17 desks
15.50*17 = 263.50 +150 = $413.50
david kalb started a pet-walking business , he charges $20 to walk one dog, twice a day. He walks six dogs five days a week for four customers. He walks three dogs seven days a week for three other customers. How much money does David get from his customers each week? If his weekly expenses are $350, what is the profit?
Answer:
David earns $1,020 a week, and his weekly profit is $670.
Step-by-step explanation:
Since David walks six dogs per day, and each dog is $20, he earns a total of $120 per day from those six dogs. Also, knowing that he walks the six dogs five days a week, he earns $600 from walking the six dogs for five days per week alone. Using this same logic for the three dogs he walks seven days a week, we can conclude that he gets $60 from walking those three dogs. Knowing he walks those three dogs seven days a week, he gets $420 from walking those three dogs. Combining the totals gives us $1,020, the amount of money he earns per week. Since his weekly expenses are $350, we subtract that from $1,020 to get his weekly profit: $670.
The polynomial equation x^3-4x^2+2x+10=x^2-5x-3 has complex roots 3+2i What is the other root? Use a graphing calculator and a system of equations.
a –3
b –1
c 3
d 10
Answer:
The correct option is b.
Step-by-step explanation:
The given expression is
[tex]x^3-4x^2+2x+10=x^2-5x-3[/tex]
Simplify the equation.
[tex]x^3-4x^2+2x+10-x^2+5x+3=0[/tex]
[tex]x^3-5x^2+7x+13=0[/tex]
It is given that 3+2i is a root of the equation and (x-3-2i) is a factor.
By complex conjugate root theorem if a+ib is a root of an equation then a-ib must be the root of the equation.
It means 3-2i is a root of the equation and (x-3+2i) is a factor.
[tex](x-3-2i)(x-3+2i)=(x-3)^2-(2i)^2=x^2-6x+9+4=x^2-6x+13[/tex]
Divide [tex]x^3-5x^2+7x+13=0[/tex] by [tex]x^2-6x+13[/tex], to find the remaining factor.
By the long division method, the quotient is (x+1) and remainder is 0. It means (x+1) is a remaining factor of the given equation. Equate each factor equal to 0, to find the remaining roots.
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
Therefore the correct option is b.
A wallet contains 23 bills. All the bills are $1 bills and $5 bills. There are 7 more $1 bills than 5 bills. How much money does the wallet contain
Final answer:
The wallet contains a total of $55, given that there are 8 $5 bills and 15 $1 bills.
Explanation:
The student's question involves determining the total amount of money in a wallet given a specific mix of $1 bills and $5 bills. According to the information provided, there are 23 bills in total, with 7 more $1 bills than $5 bills.
Let's denote the number of $5 bills as x. Therefore, there are x + 7 $1 bills. The total number of bills is the sum of the number of $1 bills and the number of $5 bills, which gives us the equation:
x + (x + 7) = 23
Solving the equation for x will give us the number of $5 bills:
2x + 7 = 23
2x = 23 - 7
2x = 16
x = 8
Now, since there are 8 $5 bills, and 7 more $1 bills than $5 bills, we have:
Number of $1 bills = 8 + 7 = 15
Thus, the total amount of money in the wallet is:
($5 × 8) + ($1 × 15) = $40 + $15 = $55
Therefore, the wallet contains $55.
Write an equation in point-slope form of the line having the given slope that contains the given point. y= 3 4 ,(5 1 3 ,2 7 8 )
How many six-letter passwords are there that use only lowercase letters with no letter repeated?
Find the original price of a pair of shoes if the sale price is $44 after a 60% discount.
Final answer:
To find the original price of a pair of shoes after a 60% discount, divide the sale price by (1 minus the discount percentage). The original price of the pair of shoes is $110.
Explanation:
To find the original price of a pair of shoes after a 60% discount, we can use the formula:
Original price = Sale price / (1 - Discount percentage)
Substituting the given values:
Original price = $44 / (1 - 0.60)
Original price = $44 / 0.40
Original price = $110
Therefore, the original price of the pair of shoes was $110.
Final answer:
To determine the original price before a discount, subtract the discount percentage from 1, convert it to a decimal, and divide the sale price by this number. In this case, the original price for the shoes before a 60% discount, resulting in a $44 sale price, is $110.
Explanation:
To find the original price of an item before a discount, you can use the following steps:
First, understand that the sale price is the price after the discount has been applied to the original price.Express the discount as a decimal. A 60% discount is 0.60 when expressed as a decimal.Since the sale price reflects the remaining percentage after the discount, you subtract the discount decimal from 1 to find the multiplier for the original price. That is, 1 - 0.60 = 0.40.Divide the sale price by this multiplier to get the original price. So, $44 divided by 0.40 equals $110.Therefore, the original price of the shoes was $110 before the 60% discount was applied.
1.8 as a fraction????
Which is bigger 4 kilometers or 4400 meters?
Devon Price is a clerk typist. His annual salary is 18,720. What is his biweekly salary?
Answer:
Biweekly salary is $ 720.
Step-by-step explanation:
Given,
Annual salary = 18,720,
Number of weeks in a year = 52,
Thus, the number of bi weeks in a year = [tex]\frac{52}{2}[/tex] = 26,
Hence, the biweekly salary = [tex]\frac{\text{annual salary}}{\text{Number of bi weeks in a year }}[/tex]
[tex]=\frac{18720}{26}=\$ 720[/tex]
operations absolute value
|4 - 9| =
|4| -9 =
John Tucker is interested in purchasing stock. He wants to determine the costs.
Answer: a0 =$97.5 ; a1 =$87.96 ; a2=$282.48; a3=$1,722.5 ; a4=$1,553.96 ; a5=$4,990.48
Step-by-step explanation:
Hi, to solve this problem we have to multiply each total by the commission in decimal form (6 / 100= 0.06).
So:
$1625 x 0.06 = $97.5
$1,466 x 0.06 =$87.96
$4,708 x 0.06 =$282.48
And finally, to obtain the total costs we have to add to each total the commission of the total.
$1625 + $97.5 = $1,722.5
$1,466 +$87.96 = $1,553.96
$4,708 +$282.48 = $4,990.48
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The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 80% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 120 pints of a mixture that is 80% pure fruit juice?
The amount that results when $4,000 is compounded at 6% annually over seven years.
Find the area of a circle with a diameter of 10 units. Round answer to the nearest hundredth of a square unit.
Answer:
Step-by-step explanation:
The area of a circle is given by A = π*r²
If diameter is 10 units, the radius is 5, so:
A = π * 5² = 78,54units²
Deniz had a full gallon of milk. She poured out 4 cups of milk. There are 16 cups in 1 gallon. About what percent of the original volume is left?
Answer:
75% of the original volume is left.
Step-by-step explanation:
Deniz had a full gallon of milk, or 16 cups of milk, and then she poured out 4 cups of milk. That is:
[tex]\\ A_{full-gallon} = \frac{16}{16}[/tex] cups of milk, since [tex]\\ \frac{16}{16} = 1[/tex] or [tex]\\ 1 * 100\% = 100\%[/tex] of the original volume.Deniz poured out 4 cups of milk from the 16 available (or [tex]\\ \frac{4}{16}[/tex]).Then,
The total left is:
[tex]\\ Total_{left} = \frac{16}{16} - \frac{4}{16} = \frac{12}{16} = \frac{3}{4}[/tex], since we are dealing here with fractions with the same denominator.
In other words, [tex]\\ \frac{3}{4} = 0.75[/tex] is the amount of milk left in the container.
In terms of percentage, [tex]\\ \frac{3}{4} = 0.75[/tex] is equivalent to [tex]\\ 0.75*100\% = 75\%[/tex] of the original volume, because Deniz poured out [tex]\\ \frac{4}{16} = \frac{1}{4} = 0.25[/tex] or [tex]\\ 0.25*100\% = 25\%[/tex] from the original volume.
So, Deniz left 75% of the original volume of milk after pouring out 25% of it.
This can be represented in the graph below.
Answer:
75%
Step-by-step explanation:
Find the plane containing the points S, X, and V. Which statement is true?
Point Y is noncoplanar with points S, X, and V.
Point U is coplanar with points S, X, and V.
Point Z is coplanar with points S, X, and V.
Point C is coplanar with points S, X, and V.
The point-slope form of the equation of the line with slope 7 passing through the point (4, 6) is
Write an equation of the line passing through the point A(−6, 5)that is parallel to the line
y = 1/2 x−7.
The length of the side of a square is 8 radical 12 in. What is the area of the square?
2/3 is what percent of 1/4?
To determine what percent 2/3 is of 1/4, convert both fractions to percent form, where 1/4 is 25%. Converting 2/3 to a percent gives approximately 66.67%, and dividing this by 25% gives 266.68%. Thus, 2/3 is 266.68% of 1/4.
To find out what percent 2/3 is of 1/4, you first need to express the fractions in a way that allows comparison. A standard way of expressing a fraction as a percent involves having a denominator of 100. Since you know 1/4 equals 25 percent, you can use this as a basis for comparison with 2/3.
To convert 2/3 to a decimal, divide the numerator by the denominator: 2 divided by 3 equals approximately 0.6667. To then convert that decimal to a percent, multiply by 100, getting approximately 66.67 percent. To find what percent 2/3 is of 1/4, divide 66.67 by the percent value of 1/4, which is 25, and then multiply by 100 to get the percentage. This gives you (66.67 / 25) x 100 = 266.68 percent. So, 2/3 is 266.68 percent of 1/4.
Evaluate. 12+4⋅3−15 Enter your answer in the box.
Answer:
I think it is 9 because I know u multiply at the start plus I used a calculator and got 9 so if it is not my calculator it broke
In Saudi Arabia it takes 20 kursh to equal 1 riyal.
a. Write the two unit multipliers implied by this relationship.
b. Use one of the unit multipliers to convert 16,000 kursh to riyals.
help
The problem is about converting between two units of currency from kursh to riyals. The two unit multipliers from this scenario are: 1 riyal equals 20 kursh and 1 kursh equals 1/20 riyal. The conversion from 16,000 kursh to riyals would be 800 riyals.
Explanation:The question is about converting between two units of currency, specifically from kursh to riyals based on the exchange rate provided. It's a classic problem in unit conversion.
a. The two unit multipliers implied by this relationship are:
1 riyal = 20 kursh 1/20 riyal = 1 kursh
b. To convert 16,000 kursh to riyals, you would use the first unit multiplier. Given that 1 riyal equals 20 kursh, you simply divide the amount in kursh by 20 to get the equivalent amount in riyals. So, 16000 kursh ÷ 20 = 800 riyals.
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There were 91 books on a shelf. Twenty-eight of the books were nonfiction, 13 of the books were poetry books, and the rest were fiction books. How many books were fiction?
The sum of two numbers is 47 and the difference is 1 . what are the numbers?
Write an equation in point-slope form of the line having the given slope that contains the given point. m=34m=34, (36,24)
Scores on a test have a mean of 70 and q3 is 83. the scores have a distribution that is approximately normal. find p90. (you will need to first find the standard deviation.)
a. 94.84
b. 85.08
c. 85.31
d. 83.7
The value corresponding to the 90th percentile (p90) is 94.84. Option A is correct.
To find the value corresponding to the 90th percentile (p90), we first need to find the standard deviation of the scores.
We know that the third quartile (Q3) is 83, which corresponds to the 75th percentile (p75). Since the distribution is approximately normal, we can use the properties of the normal distribution to find the standard deviation.
In a standard normal distribution, the value corresponding to the p75 is approximately 0.6745 standard deviations above the mean. So, we can set up the following equation:
70 + 0.6745 * standard deviation = 83
Now, solve for the standard deviation:
standard deviation = (83 - 70) / 0.6745 ≈ 19.3047
Next, to find the value corresponding to the p90, we use the properties of the normal distribution again. The value corresponding to the p90 is approximately 1.2816 standard deviations above the mean.
Now, calculate p90:
p90 = 70 + 1.2816 * standard deviation
≈ 70 + 1.2816 * 19.3047
≈ 94.84
Rounding to two decimal places, we get p90 ≈ 94.84. So, the answer is (a) 94.84.
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To find p90 in a normally distributed set of scores, we need to find the standard deviation. Using the mean and q3, we can find the IQR and estimate the standard deviation. Finally, we can use the standard deviation to find the value corresponding to the 90th percentile.
Explanation:To find the value of p90 in a normally distributed set of scores, we need to first find the standard deviation of the scores. We know that the mean is 70 and q3 (the third quartile) is 83. Using the formula for the interquartile range (IQR = q3 - q1), we can calculate the value of q1. Subtracting q1 from q3 gives us the IQR. Since the distribution is approximately normal, we can assume that the IQR is approximately 1.35 times the standard deviation. Dividing the IQR by 1.35 gives us the standard deviation. Finally, we can use the standard deviation to find the z-score corresponding to the 90th percentile and then find the corresponding value in the original distribution using the mean and standard deviation. The correct answer is option (a) 94.84.
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Given triangle XP’s is congruent to triangle dnf, find the values of x and y.
x = 3
y = 15
Let's establish the proportion below to find the value of x and y
XP / DN = XS / DF = PS / NF
Since only 2 sides of XPS is given, then
4y - 3 = 5717x + 3 = 54Therefore,
4y = 60
y = 60 / 4
y = 15
17x = 57
x = 57 / 17
x = 3
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180=2x+y which equation is used to find x
The value of x would be equal to (180-y)/2
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
To solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
We are given the equation as- 180=2x+y
Now solving;
180=2x+y
180=2x+y
180-y=2x
(180-y)/2=x
x = (180-y)/2
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What happened to the glass blower who inhaled