Answer: false is correct
The statement is false; a value one standard deviation from the mean is more likely to occur than a value three standard deviations from the mean due to the Empirical Rule for normal distributions.
The statement is false. A value one standard deviation from the mean is more likely to occur than a value three standard deviations from the mean. According to the Empirical Rule, which applies to bell-shaped and symmetric distributions, about 68 percent of the data lies within one standard deviation of the mean, while more than 99 percent of the data is within three standard deviations. This means that as you move further away from the mean, the likelihood of occurrence decreases.
Find the coordinates of the midpoint of a segment having the given endpoints.
Q(0.3, 1.8), R(2.7, 3.9)
(1.5, 2.85)
O (1.05, 3.3)
(-1.2, -1.05)
O(-2.4, -2.1)
Answer:
[tex](1.5,2.85)[/tex]
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
we have the endpoints:
Q(0.3, 1.8), R(2.7, 3.9)
substitute in the formula
[tex]M(\frac{0.3+2.7}{2},\frac{1.8+3.9}{2})[/tex]
[tex]M(\frac{3}{2},\frac{5.7}{2})[/tex]
[tex]M(1.5,2.85)[/tex]
You randomly guess the answers on a multiple choice test each question has three choices what is the probability that you will guess the correct answer
Answer:
If the question is single answer correct then the answer is [tex]\frac{1}{3}[/tex] and if it's multiple options correct than the answer is [tex]\frac{1}{7}[/tex]
Step-by-step explanation:
There is a little ambiguity in the question, that whether one answer is correct or multiple options are correct, but let;s deal with both the cases.
Probability = [tex]\frac{TotalNo.OfFavourableOutcomes}{TotalOfNoOfOutcomes}[/tex]
Probability when one option is right=[tex]\frac{1}{3}[/tex]
If this is a question , where multiple options are right then the total no. of cases for it will be = TTT, TFF, FTF, FFT, TTF, TFT, FTT (FFF is not a valid case, because the question has to have at least one valid answer.)
Probability when more than one option can be right=[tex]\frac{1}{7}[/tex]
How can you use the values of a, b, and c to write a quadratic function in vertex form?
Answer:
y = a(x +b/(2a))^2 + (4ac -b^2)/(4a)
Step-by-step explanation:
We presume you're starting with ...
y = ax^2 +bx +c
As you would with numbers, factor the first two terms:
y = a(x^2 +b/a·x) +c
Add half the square of the x term inside and its opposite outside parentheses:
y = a(x^2 +(b/a)x + (b/(2a))^2) + c - a(b/(2a))^2
y = a(x +b/(2a))^2 +c -b^2/(4a)
You can combine the last two terms to a more familiar fraction:
y = a(x +b/(2a))^2 + (4ac -b^2)/(4a)
To write a quadratic function in vertex form, use the values of a, b, and c. Find the coordinates of the vertex using h = -b/2a and k = f(h).
Substitute the values into the vertex form.
To write a quadratic function in vertex form, you can use the values of a, b, and c.
The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k,
where (h, k) represents the coordinates of the vertex.
To find h and k, you can use the formulas h = -b/2a and k = f(h).
Once you have the values of h and k, you can substitute them into the vertex form to obtain the quadratic function in vertex form.
Learn more about quadratic function in vertex form here:
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For every integer k from 1 to 10, inclusive the "k"th term of a certain sequence is given by (−1)(k+1)∗(12k). If T is the sum of the first 10 terms in the sequence, then T isA. Greater than 2B. Between 1 and 2C. Between 1/2 and 1D. Between 1/4 and 1/2E. Less than 1/4
Answer:
Option D. is the correct option.
Step-by-step explanation:
In this question expression that represents the kth term of a certain sequence is not written properly.
The expression is [tex](-1)^{k+1}(\frac{1}{2^{k}})[/tex].
We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as [tex](-1)^{k+1}(\frac{1}{2^{k}})[/tex].
where k is from 1 to 10.
By the given expression sequence will be [tex]\frac{1}{2},\frac{(-1)}{4},\frac{1}{8}.......[/tex]
In this sequence first term "a" = [tex]\frac{1}{2}[/tex]
and common ratio in each successive term to the previous term is 'r' = [tex]\frac{\frac{(-1)}{4}}{\frac{1}{2} }[/tex]
r = [tex]-\frac{1}{2}[/tex]
Since the sequence is infinite and the formula to calculate the sum is represented by
[tex]S=\frac{a}{1-r}[/tex] [Here r is less than 1]
[tex]S=\frac{\frac{1}{2} }{1+\frac{1}{2}}[/tex]
[tex]S=\frac{\frac{1}{2}}{\frac{3}{2} }[/tex]
S = [tex]\frac{1}{3}[/tex]
Now we are sure that the sum of infinite terms is [tex]\frac{1}{3}[/tex].
Therefore, sum of 10 terms will not exceed [tex]\frac{1}{3}[/tex]
Now sum of first two terms = [tex]\frac{1}{2}-\frac{1}{4}=\frac{1}{4}[/tex]
Now we are sure that sum of first 10 terms lie between [tex]\frac{1}{4}[/tex] and [tex]\frac{1}{3}[/tex]
Since [tex]\frac{1}{2}>\frac{1}{3}[/tex]
Therefore, Sum of first 10 terms will lie between [tex]\frac{1}{4}[/tex] and [tex]\frac{1}{2}[/tex].
Option D will be the answer.
Charlie and his friend Jay went to the fair. They were having a sale and the admission was 25% off. The regular ticket price was $9.00 and the tax is 6%. What would Charlie's total be?
Answer:
The Total of Charlie's will be $7.16.
Step-by-step explanation:
Given:
Charlie and his friend Jay went to the fair. They were having a sale and the admission was 25% off.
Price of regular ticket = $9.00.
tax = 6%.
We need to find Charlie’s total.
So we will first find the price of regular ticket with 25% off.
25% percent of regular ticket = [tex]\frac{25}{100}\times 9 = \$2.25[/tex]
Discounted Price of regular ticket will be equal to Price of regular ticket minus Discounted amount.
Discounted Price of regular ticket = 9 - 2.25 = $6.75
Now, including tax :
Tax paid will be on discounted amount.
Hence Amount paid in tax = [tex]6\% \times 6.75= \frac{6}{100}\times 6.75 = \$0.405[/tex]
Total amount paid by charlie is equal to sum of Discounted Price of regular ticket and Amount paid in tax
Total Amount paid by charlie = [tex]6.75+0.405 =\$7.155 \approx \$7.16[/tex]
Therefore, the total of Charlie's will be $7.16.
determine the y-intercept of 5x-6y=10
Answer:
The y intercept of the equation is 10.
In this Circular Flow example the Money Supply is reduced as the Fed ___________ $20 billion of Treasury bonds and bills from/to the banking system..
Answer:
Deduct/subtract
Step-by-step explanation:
Federal Reserve board uses different methods to increase or decrease the currency in circulation. This methods are known as Monetary policy. The Central bank, at its discretion, can print more currency to increase the flow of currency in circulation
The Federal Reserve Board, which is the governing body that manages the Federal Reserve System, oversees all domestic monetary policy. The Fed"s job is to increase and decrease paper currency in circulation. This effort is to curb inflation and hyperinflation, stabilize the economy and create room for ease of doing business with the international community
The Fed can increase the money supply by lowering the reserve requirements for banks, which allows them to lend more money.
Also, by raising the banks' reserve requirements, the Fed can decrease the size of the money supply.
The Central bank modify short-term interest rates by lowering or increasing the discount rate that banks pay on short-term loans from the Fed.
Modifying Reserve Requirements : they can moderate the amount of money banks can hold.
The measure of central angle QRS is StartFraction 8 pi Over 9 EndFraction radians. What is the area of the shaded sector? 36Pi units squared 72Pi units squared 144Pi units squared 324Pi units squared
The question is missing the figure. So, it is attached below.
Answer:
Area of the shaded sector is 144π units squared.
Step-by-step explanation:
Given:
Central angle of the sector is, [tex]\theta=\frac{8\pi}{9}\ rad[/tex]
Radius of the circle is, [tex]R=18\ units[/tex]
We know that, area of a sector of a circle of radius 'R' and central angle [tex]\theta[/tex] is given as:
[tex]A=\frac{1}{2}R^2\theta[/tex]
Plug in [tex]\theta=\frac{8\pi}{9},R=18[/tex]. This gives,
[tex]A=\frac{1}{2}\times (18)^2\times \frac{8\pi}{9}\\\\A=(\frac{324\times 4}{9})\pi\\\\A=(36\times 4)\pi\\\\A=144\pi\ units^2[/tex]
Therefore, the area of the shaded sector is 144π units squared.
Answer: 144Pi units squared
Step-by-step explanation:
Researchers at Gallup were interested in whether there was a decrease in the proportion of nonretirees (in other words, people who are not yet retired) who did not believe that the U.S. Social Security program will be able to pay them a retirement benefit when they retire. In the summer of 2010, the Gallup poll found that 60% of nonretirees thought that Social Security would not be able to pay a benefit. Five years later in the summer of 2015, Gallup asked the same question to 1,282 nonretirees and found that 51% of respondents did not think that Social Security would be able to pay a retirement benefit by the time that they retire. We would like to test the hypothesis that in 2015 there is a lower proportion of nonretirees who do not think that Social Security will be able to pay them a benefit. A z-test for the population proportion showed that z = -4.29, p < 0.001.
Which of the following is the best conclusion based on the output?
A. We have extremely strong evidence to reject H0.
B. We have extremely strong evidence to reject Ha.
C. We have moderately strong evidence to reject H0.
D. There is a probability of 0 that H0 is correct.
E. There is a probability of 0 that Ha is correct.
Answer:
A. We have extremely strong evidence to reject H0.
Step-by-step explanation:
Let P be the proportion of non-retirees in 2015 who did not think that Social Security would be able to pay a retirement benefit by the time that they retire.
According to the data null and alternative hypotheses should be:
[tex]H_{0}[/tex]: P=0.60[tex]H_{a}[/tex]: P<0.60Test statistics is -4.29 and p-value of the statistics is p<0.001
At every significance levels higher than 0.001, we can reject the null hypothesis since p<0.001.
PLEASE HELP !!!
Give all angles of rotational symmetry less than 360°, listed from least to greatest.
The angles of rotational symmetry less than 360°, listed from least to greatest, are
°,
°,
°, and
°.
Answer: 60°, 72°, 90°, 120° and 180°
Step-by-step explanation:
To calculate the angle of rotational symmetry of a shape or polygon, you make use of this formula
[tex]\frac{360}{n} where n is the number of sides of the shape[/tex]
example for a Square with 4 sides. the angle of rotational symmetry is 360/4 =90°.
What is the simple interest earned on $3,672 at 4.5% for three years?
$459.72
$594.86
$518.36
$495.72
Answer: interest at the end of 3 years is $495.72
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T = 3 years
P = $3,672
R = 4.5%
Therefore
I = (3672 × 4.5 × 3)/100
I = 49572/100
I = 495.72
for which values of x and y is line p parallel to line q?
x=5, y=3
x=1, y=5
x=3, y=5
x=3, y=6
Answer:
x=3, y=5
Step-by-step explanation:
(16x+2) and (45x-5) are co-interior angles and they sum up to 180 degrees.
To find x
(16x+2)+(45x-5)=180
16x+45x-5+2=180
61x-3=180
61x=180+3
61x=183
x=3
(45x-5) and (26y) are corresponding angles so their values are equal
(45x-5)=(26y), x=3
(45 (3)-5)=(26y)
135-5=26y
130=26y
5=y
A fried chicken franchise finds that the demand equation for its new roast chicken product, "Roasted Rooster," is given by p = 45 / q 1.5
where p is the price (in dollars) per quarter-chicken serving and q is the number of quarter-chicken servings that can be sold per hour at this price.
1) Express q as a function of p.
2) Find the price elasticity of demand when the price is set at $4.00 per serving.
Answer:
1. [tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex]
2. [tex]E_d=-\dfrac{2}{3}[/tex]
Step-by-step explanation:
The given demand equation is
[tex]p=\dfrac{45}{q^{1.5}}[/tex]
where p is the price (in dollars) per quarter-chicken serving and q is the number of quarter-chicken servings that can be sold per hour at this price.
Part 1 :
We need to Express q as a function of p.
The given equation can be rewritten as
[tex]q^{1.5}=\dfrac{45}{p}[/tex]
Using the properties of exponent, we get
[tex]q=(\dfrac{45}{p})^{\frac{1}{1.5}}[/tex] [tex][\because x^n=a\Rightarrow x=a^{\frac{1}{n}}][/tex]
[tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex]
Therefore, the required equation is [tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex].
Part 2 :
[tex]q=(45)^{\frac{2}{3}}p^{-\frac{2}{3}}[/tex]
Differentiate q with respect to p.
[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(p^{-\frac{2}{3}-1}})[/tex]
[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(p^{-\frac{5}{3}})[/tex]
[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})[/tex]
Formula for price elasticity of demand is
[tex]E_d=\dfrac{dq}{dp}\times \dfrac{p}{q}[/tex]
[tex]E_d=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})\times \dfrac{p}{(45)^{\frac{2}{3}}p^{-\frac{2}{3}}}[/tex]
Cancel out common factors.
[tex]E_d=(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})\times \dfrac{p}{p^{-\frac{2}{3}}}[/tex]
Using the properties of exponents we get
[tex]E_d=-\dfrac{2}{3}(p^{-\frac{5}{3}+1-(-\frac{2}{3})})[/tex]
[tex]E_d=-\dfrac{2}{3}(p^{0})[/tex]
[tex]E_d=-\dfrac{2}{3}[/tex]
Therefore, the price elasticity of demand is -2/3.
To address the question, q as a function of p is q = (45/p)^(2/3), and the price elasticity of demand when p is $4 can be found by taking the derivative of q with respect to p and substituting the given values in the elasticity formula.
Explanation:The student has asked to express q as a function of p and to find the price elasticity of demand when the price is set at $4.00 per serving for a new roast chicken product. The given equation is p = 45 / q1.5.
To find q as a function of p, we rearrange the equation: q = (45/p)1/1.5 or q = (45/p)2/3.To find the price elasticity of demand, we use the formula Ed = (dq/dp) × (p/q). First, we calculate the derivative dq/dp of the function q(p), and then substitute p=4 to find Ed at that price.The derivative of q with respect to p is dq/dp = -2/3 × (45/p4/3). Substituting p=4, we get the quantity q = (45/4)2/3. Plugging these values into our elasticity formula gives us the price elasticity of demand at p=$4.00.
In your own words, describe what happens when a line is reflected across the x-axis.
Answer:
Every point in the line would get reflected about the x axis and we would get a new line.
Step-by-step explanation:
When you reflect a point about the x-axis , the x-coordinate of the image remains the same but the y - coordinate changes to its negative value.
Now a line is a collection of points and we have to find out what happens when we reflect a line about the x-axis.
Reflecting a line about the line is same as keeping a mirror along the x-axis and the image we see in the mirror is the same as the image we obtain in the mirror.
So every point in the line would get reflected about the x axis and we would get a new line.
Final answer:
Reflecting a line across the x-axis inverts the y-coordinates of all points on the line, while the x-coordinates remain unchanged; the reflected line appears flipped over the x-axis, preserving distance but potentially changing orientation.
Explanation:
When a line is reflected across the x-axis, each point on the original line is flipped vertically to a new position on the opposite side of the x-axis, maintaining the same distance from the x-axis. Essentially, every point's y-coordinate is multiplied by -1, causing the line to appear as a mirror image of itself with respect to the x-axis. This transformation preserves the shape and size of the original line but changes its orientation relative to the x-axis.
Thirty elves would like to build a skating ring so they can all use it at the same time. Santa tells them, they need at least 40 square feet for each skater, so no one will bump into each other. If they build a rectangular rink, what are the possible dimensions (length and width)for the rink?
Answer:
The Possible dimension of the ring could be;
20 ft × 60 ft
25 ft × 48 ft
30 ft × 40 ft
60 ft × 20 ft
48 ft × 25 ft
40 ft × 30 ft
Step-by-step explanation:
Given:
Number of skaters = 30
Area for each skater = 40 sq ft
We need to find the dimension of rectangular ring the are going to build.
Now we know that they building the skating ring such that they all can use at same time.
Hence if the all use at same time then we will find the total area first.
Total area can be calculated by multiplying Number of skaters with area required for each skaters.
Framing the equation we get;
Total area = [tex]30\times 40 = 1200 \ ft^2[/tex]
Hence The total area of the rectangular ring would be 1200 sq. ft.
Now we know that Total area is equal to product of length and width.
[tex]length\times width =1200ft^2[/tex]
1200 can be written as = 20 × 60, 25 × 48, 30 × 40,60 × 20,48 × 25,40 × 30
Hence the Possible dimension of the ring could be;
20 ft × 60 ft
25 ft × 48 ft
30 ft × 40 ft
60 ft × 20 ft
48 ft × 25 ft
40 ft × 30 ft
Let f(x) = x³+6x²+6x and let c be the number that satisfies the Mean Value Theorem for f on the interval [-6,0].Find the Mean Value Theorem.
Answer:
c = 0 or c = -4
Step-by-step explanation:
According to the Mean Value Theorem
[tex]f^{'}(c) = \frac{f(0) - f(-6)}{0 - (-6)} = \frac{0 - (-6)^3 - 6*(-6)^2 - 6*(-6)}{6} = 36 - 36 + 6 = 6[/tex]
By taking the first derivative of f
[tex]f^{'}(x) = 3x^2 + 12x + 6[/tex]
Since[tex]f^{'}(c) = 6[/tex]
We can solve for c
[tex]3c^2 + 12c + 6 = 6[/tex]
[tex]3c^2 + 12c = 0[/tex]
[tex]c(c + 4) = 0[/tex]
c = 0 or c = -4
The posterior lobe of the pituitary gland is NOT a true endocrine gland because ________. A it is unable to function as an endocrine tissue because it is actually part of the neural system due to its location B it is strictly a part of the neural system and has little or nothing to do with hormonal release C embryonically it was an endocrine tissue, but in the adult human it is no longer functional
Isn't this Anatomy and Physiology?
The local bike shop sells a bike and accessories package for $320 if the bike is worth 7 times more than the accessories,how much does the bike cost ?
What is the area of a right triangle with the given vertices? A(3,1) , B(5,4) , C(6,−1)
Answer:
[tex]\frac{13}{2}[/tex] square units
Step-by-step explanation:
We are given that vertices of a right triangle are A(3,1) ,B(5,4) and C(6,-1).
We have to find the area of triangle.
We know that area of triangle=[tex]\frac{1}{2}\mid (x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))\mid [/tex]
[tex]x_1=3,x_2=5,x_3=6[/tex]
[tex]y_1=1,y_2=4,y_3=-1[/tex]
Substitute the values in the formula then we get
Area of right triangle =[tex]\frac{1}{2}\mid (3(4+1)+5(-1-1)+6(1-4))\mid [/tex]
Area of right triangle =[tex]\frac{1}{2}\mid (15-10-18)\mid [/tex]
Area of right triangle =[tex]\frac{1}{2}\times 13=\frac{13}{2}[/tex] square units
The number of stamps that Kaye and Alberto had were in the ratio 5 : 3, respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7 : 5. As a result of this gift, Kaye had how many more stamps than Alberto?
A. 20
B. 30
C. 40
D. 60
E. 90
Answer:
D.
Step-by-step explanation:
Let the number of stamps Kaye had be k and that of Alberto be a. Then we know that are in a ratio of 5 to 3.
Hence, k : a = 5:3
or 3k = 5a
Then Kaye gave Alberto 10 of her stamp to make the ratio 7:5
k - 10/a + 10 = 7/5
Cross multiply:
5(k - 10) = 7(a + 10)
5k - 50 = 7a + 70
5k - 7a = 120
Let us now solve the last equation simultaneously with the equation 3k = 5a
5k - 7a = 120
3k - 5a = 0
Multiply equation 1 by 3 and equation 2 by 5
15k - 21a = 360
15k - 25a = 0
Subtract 1 from 2, 4a = 360
and thus a = 90
We know 3k = 5a
3k = 5 * 90
k = 450/3 = 150
Now if we subtract 90 from 150, this yields 60
Joe wants to purchase a new skateboard. He already has $40 and can save $20 each week from his job. Write a linear equation to represent the total amount he has after ‘w’ weeks.
A) T = 20 + 40w
B) T = 60w
C) T = 40 + 20 + w
D) T = 40 + 20w
Answer:
D
Step-by-step explanation:
Joe already has $40 and can save $20 each week. the total amount he can save in a given number of weeks is $20 multiplied by the that number of weeks which in this case is w so 20w. To find the total T of the amount he has after w weeks, you add the amount he already has to the amount saved. So the equation would be T=40+20w
Answer:
D) T = 40 + 20w
Step-by-step explanation:
Trust me! i had this on my test/ exam, and it was correct!!
i really hoped this helped! Have a wonderful day!
Molly is making Strawberry infused water for each ounce of strawberry juice she uses three times as many ounces of water she wants to make a total of 64 ounces of strawberry infused water
Answer:
The Total of 16 ounces of Strawberry juice and 48 ounces of water is used for making 64 ounces of Strawberry infused water.
Step-by-step explanation:
Let the amount of Strawberry juice in ounces be 'j'
Let the amount of water in ounce be 'w'
Given:
For each ounce of strawberry juice she uses three times as many ounces of water.
It means that amount of water in ounce is 3 times of amount of strawberry juice in ounce.
framing the equation we get;
[tex]w=3j[/tex]
Now we need how many ounces of strawberry juice and how many ounces of water does she need to make 64 ounces of strawberry infused water.
We know that Total Strawberry infused water is equal to sum of amount of Strawberry juice in ounces and the amount of water in ounces
Framing in equation form we get;
[tex]j+w=64[/tex]
But we know [tex]w=3j[/tex]
hence,
[tex]j+3j= 64\\\\4j=64\\\\j=\frac{64}{4} = 16 \ ounces[/tex]
Hence amount of Strawberry juice = 16 ounces
Amount of water = [tex]3j = 3\times16 =48 \ ounces[/tex]
Hence The Total of 16 ounces of Strawberry juice and 48 ounces of water is used for making 64 ounces of Strawberry infused water.
Graph the linear equation.
x = - 9
help in any way u can please
This is a vertical line that goes through all points with an x-coordinate of -9.
To graph it, I can give you a couple of points this line goes through so you can draw it more easily.
Points that are on line: (-9,0) and (-9,1)
After converting the following numbers into scientific notation, solve the problem. Show all results in scientific notation. 1,217 + (4.1 × 103) =_________.
Answer:
[tex]1217+(4.1\times 10^3)=5.317\times 10^3[/tex]
Step-by-step explanation:
Given : Expression [tex]1217+(4.1\times 10^3)[/tex]
To find : After converting the following numbers into scientific notation, solve the problem ?
Solution :
Expression [tex]1217+(4.1\times 10^3)[/tex]
Re-write 1217 by multiplying and divide by 1000 to convert into decimal,
[tex]=\frac{1217\times 1000}{1000}+(4.1\times 10^3)[/tex]
[tex]=1.217\times 10^3+(4.1\times 10^3)[/tex]
[tex]=(1.217+4.1)\times 10^3[/tex]
[tex]=5.317\times 10^3[/tex]
Therefore, in scientific notation [tex]1217+(4.1\times 10^3)=5.317\times 10^3[/tex]
Assume that the probability of any newborn baby being a boy is one half and that all births are independent. If a family has three children (no twins), what is the probability of the event that they are all boys?
Answer:
1/8
Step-by-step explanation:
P(B) = 1/2
Now we are considering that the three children are all boys. This means we are considering that the first is a boy, the second is a boy and the third too is a boy. This brings us to the situation BBB
That is a boy and a boy and another boy. In probability, the word and means we multiply the three.
Hence:
P(BBB) = P(B1) * P(B2) * P(B3) = 1/2 * 1/2 * 1/2 = 1/8 or 0.125
The probability of a three-child family having all boys, given that each birth is independently a boy with a probability of one half, is 1/8 or 0.125 (12.5%).
Explanation:The subject of your question is based in
probability
, a key concept in mathematics. Specifically, you're asking about the
probability of a family having three boys
, with the probability of any birth resulting in a boy being given as one half. As the question indicates that all births are independent, we're dealing with independent events in probability. The probability of independent events is calculated by multiplying the probabilities of each individual event. In this case, the probability of having a boy is one half (or 0.5), and we have three independent events (the births of the three children). Therefore, the probability of all three children being boys is (1/2) * (1/2) * (1/2), which simplifies to 1/8 or 0.125. So, assuming that all births are equally likely to result in a boy or a girl, the probability of a three-child family having all boys is 0.125, or 12.5%.
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Given ΔMNO, find the measure of ∠LMN.
Triangle MNO with segment LM forming a straight angle with segment MO and segment OP forming a straight angle with segment MO, the measure of angle NOP is 104 degrees, and segment MN and NO are marked congruent.
38°
52°
76°
104°
Answer:
104°
Step-by-step explanation:
Thinking process:
Let the triangle be:
ΔMNO
The angle be: ∠LMN.
From the description, NOP is 104°
If, segment MN and NO are marked congruent then the corresponding angle, ∠LMN is 104°
This property of congruency applies since the segments are equal.
Suppose the size of a population of mustard plants is 6,000. According to genetic drift theory, what is the probability that a newly-arisen mutation will become fixed in this population?
Answer:
1/12,000
Step-by-step explanation:
Data provided in the question:
Size of a population of mustard plants = 6,000
Now,
According to genetic drift theory
The probability that a newly-arisen mutation will become fixed is given using the formula
⇒ 1 ÷ [ 2 × Size of a population of mustard plants ]
⇒ 1 ÷ [ 2 ×6,000 ]
⇒ [ 1 ÷ 12,000 ]
Hence,
probability that a newly-arisen mutation will become fixed in this population is 1/12,000
It costs serine $30 to start a lemonade stand plus $0.50 per cup of lemonade. She sells cups of the lemonade for $1.25.How many cups of lemonade will serine need to break even?
Answer: it will need 40 cups of lemonade to break even
Step-by-step explanation:
Break even represents the point at which there is neither profit nor loss.
It costs serine $30 to start a lemonade stand plus $0.50 per cup of lemonade. Assuming that she made x cups of lemonade, the total cost of making x cups would be
30 + 0.5x
She sells each cup of the lemonade for $1.25 . Assuming that she sold x cups of lemonade, therefore, the total amount would be 1.25×x = 1.25x
To break even,
30 + 0.5x = 1.25x
1.25x - 0.5x = 30
0.75x = 30
x = 30/0.75
x = 40
PLEASE HELP IM TERRIBLE AT MATH!!!! WILL GIVE BRAINLIEST!!!
Divide 3x^2 + 4x − 4 by x + 2.
A. x − 2
B. x + 6
C. 3x − 2
D. 3x + 6
Answer:
It is C
Step-by-step explanation:
(3x-2)(x+2)
3x(x)+3x(2)-2(x)-2(2)
3x^2+6x-2x-4
3x^2+4x-4 <----------
(Im bad at explaining but that is right trust me :P)
Bryce has heard that gas appliances are cheaper to use and can lower utility costs. He is interested in purchasing a new gas stove for his kitchen to replace his electric stove. Assuming that the stove gets used one hour per day, use the following chart to determine how much Bryce will save each year in utility costs by purchasing the gas appliance.
Answer:
C. $29.20
Step-by-step explanation:
The difference between using an electric stove and a gas stove everyday is 13 cents - 5 cents= 8 cents.
Saving 8 cents everyday.
Therefore for a year, Bryce will save 8 cents × 365days = 2920 cents
Then 2920 cents = $(2920÷100)
=$29.20
Answer:
C. $29.20
Step-by-step explanation: