Answer:
The expected number of boys a family might have is 2.5.
Step-by-step explanation:
Let X denote the number of boys in a family with 5 children.
The probability of a boy is, p = 0.50.
The child can either be a by or a girl independently.
The random variable X follows a binomial distribution with parameters n = 5 and p = 0.50.
The probability mass function is:
[tex]p_{X}(x)={5\choose x}(0.50)^{x}(1-0.50)^{5-x};\ x=0,1,2...5[/tex]
Compute the expected number of boys a family might have as follows:
[tex]E(X)=\sum x\cdot p_{X}(x)[/tex]
x p (x) x · p (x)
0 [tex]p(0)={5\choose 0}(0.50)^{0}(1-0.50)^{5-0}=0.03125[/tex] [tex]0\times 0.03125=0[/tex]
1 [tex]p(1)={5\choose 1}(0.50)^{1}(1-0.50)^{5-1}=0.15625[/tex] [tex]1\times 0.15625=0.15625[/tex]
2 [tex]p(2)={5\choose 2}(0.50)^{2}(1-0.50)^{5-2}=0.3125[/tex] [tex]2\times 0.3125=0.625[/tex]
3 [tex]p(3)={5\choose 3}(0.50)^{3}(1-0.50)^{5-3}=0.3125[/tex] [tex]3\times 0.3125=0.9375[/tex]
4 [tex]p(4)={5\choose 4}(0.50)^{4}(1-0.50)^{5-4}=0.15625[/tex] [tex]4\times 0.15625=0.625[/tex]
5 [tex]p(5)={5\choose 5}(0.50)^{5}(1-0.50)^{5-5}=0.03125[/tex] [tex]5\times 0.03125=0.15625[/tex]
Then,
[tex]E(X)=\sum x\cdot p_{X}(x)[/tex]
[tex]=0+0.15625+0.625+0.9375+0.625+0.15625\\\\=2.5[/tex]
Thus, the expected number of boys a family might have is 2.5.
f(x) = |3x+5| + 6
g(x) =7
find (f+g) (x)
Answer:
(f + g)(x) = |3x + 5| + 13
Step-by-step explanation:
Given
f(x) = |3x + 5| + 6
g(x) = 7
Required
Find (f + g)(x)
In functions
(f + g)(x) = f(x) + g(x)
Meaning that, we simply add the given functions together
So, we have that:
(f + g)(x) = |3x + 5| + 6 + 7
(f + g)(x) = |3x + 5| + 13
Hence, (f + g)(x) when calculated equals |3x + 5| + 13
anyone smart enough to do this?
Answer:
8 tan 50 deg
Step-by-step explanation:
m<A = 50 deg
tan A = x/8
x = 8 tan 50 deg
Answer: C 8 tan 50 deg
An 80-member committee voted on whether to send a certain bill to the governing board. One-fourth voted in favor, 2/5 voted against, and the rest abstained. How many abstained?
Answer:
Let's understand the concept:-Here the committee consists of 80membersFor finding the abstained we need to find first How many voted in favour and in against Required Answer :-The number of members =80
One fourth voted in favour So first find how many voted in favour[tex]{:}\longmapsto [/tex][tex]\sf {\dfrac{1}{{\bcancel {4}}}}×{\bcancel {80}} [/tex]
[tex]{:}\longmapsto [/tex][tex]\sf 20[/tex]
20 members voted in favour Again two fifth voted against Find how many voted against[tex]{:}\longmapsto [/tex][tex]\sf {\dfrac {2}{5}}×80 [/tex]
[tex]{:}\longmapsto [/tex][tex]\sf {\dfrac {160}{5}}[/tex]
[tex]{:}\longmapsto [/tex][tex]\sf 32 [/tex]
32 members voted against Now ,Rest members stayed abstained So we need to substract all voted members from the whole committee to get rest[tex]{:}\longmapsto [/tex][tex]\sf 80-(32+20)[/tex]
[tex]{:}\longmapsto [/tex][tex]\sf 80-52 [/tex]
[tex]{:}\longmapsto [/tex][tex]\sf 28 [/tex]
[tex]\therefore[/tex] 28 members stay abstained.
there are two equivalent fractions that have a least common denominator of 14. the sum of both of the denominators is 56. the sum of both of the numerators is 12. the smaller numerator is over the smaller denominator. what are these two equivalent fractions brainly
Answer:
11+2=
Step-by-step explanation:
The cable railway was driven by a 8 foot diameter drum that turned 13 revolutions per minute. Find the linear velocity of the cable.
Answer:
The linear velocity of the cable ≅ 327 feet per minute.
Step-by-step explanation:
Given that the diameter of the drum = 8 feet
Radius of the drum = [tex]\frac{diameter}{2}[/tex]
= [tex]\frac{8}{2}[/tex]
= 4 feet
Radius of the drum = 4 feet
1 revolution = circumference of the drum
circumference of the drum = 2[tex]\pi[/tex]r
where r is the radius.
So that;
circumference of the drum = 2 x [tex]\frac{22}{7}[/tex] x 4
= [tex]\frac{176}{7}[/tex]
= 25.143
circumference of the drum = 25.143 feet
The linear velocity of the cable = (13 x 25.143) feet per minute
= 326.859 feet per minute
The linear velocity of the cable ≅ 327 feet per minute.
URGENT. Find f(3) if
f(x)=x^3 + 2x^2-x-1
Answer:
41
Step-by-step explanation:
Jus replace x with 3 and put it in a calculator.
If Jeff hikes 1/2 a distance in 1/4 an hour how fast can he walk in 1/2 an hour?
Answer:
2/4? i think....
idrk sry :(
Step-by-step explanation:
For 1-4 which congruence postulate or theorem could be used to prove that the triangles are congruent
Answer:
Theorem 4.6 Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
Step-by-step explanation:
A labtop has ablisted price of $739.98 befire tax. If the sales tax rate is 8.75%, find the total cost of the labtop with sales tax included.
A potting mixture contains 12.0% peat moss and 6.00% vermiculite. How much peat moss and how much vermiculite must be added to 100lb of this mixture to produce a new mixture having 15.0% peat and 15.0% vermiculite?
Answer:
Answer is 3% more peat and 9% more vermiculite.
Step-by-step explanation:
The weight of the initial potting mixture is not given, but the percentage amounts of peat moss & vermiculite are given.
The weight of the new potting mixture is 100lb.
For the new mixture to have 15% peat and 15% vermiculite,
The amount of peat that must be added is 3% of the peat in the initial mixture.
Hint: subtract 12 from 15. Retain the percentage sign.
The amount of vermiculite that must be added is 9% of the vermiculite in the initial mixture.
Hint: subtract 6 from 15. Retain the percentage sign, as that is the scale of measurement here.
IQ scores (as measured by the Stanford-Binet intelligence test) in a certain country are normally distributed with a mean of 95 and a standard deviation of 18. Find the approximate number of people in the country (assuming a total population of 323,000,000) with an IQ higher than 126. (Round your answer to the nearest hundred thousand.)
Answer:
13,797,339 people
Step-by-step explanation:
Given that μ = 95 and σ = 18
The total number of population is N = 323,000,000
Now, we calculate the probability that IQ is higher than 126
P(X>126) = 1 - P[Z ≤ 126 - 95 / 18]
P(X>126) = 1 - P[Z ≤ 1.72]
P(X>126) = 1 - [ NORMSDIST(1.72)] Using MS Excel
P(X>126) = 1 - 0.957283779
P(X>126) = 0.042716221
Hence, the required probability is 0.042716221
Now, we calculate the approximate number of people in the county with an IQ higher than 126
Number of people = P(X>128) * N
Number of people = 0.042716221 * 323,000,000
Number of people = 13797339.383
Number of people = 13,797,339
Therefore, the approximate number of people in the country with an IQ higher than 126 is 13,797,339 in population
There are 13800000 people in the country with an IQ higher than 126
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation[/tex]
Given that μ = 95, σ = 18;
For x > 126:
[tex]z=\frac{126-95}{18} =1.72[/tex]
From the normal distribution table, P(z > 1.72) = 1 - P(z < 1.72) = 1 - 0.9573 = 0.0427
For a total population of 323,000,000:
Number of people in the country = 0.0427 * 323,000,000 = 13800000
Hence there are 13800000 people in the country with an IQ higher than 126
Find out more at: https://brainly.com/question/15016913
A movie theater sold 1,096 tickets on Friday. On Saturday, it sold 4 times as many tickets as on Friday. How many tickets did the movie theater sell on Saturday? A. 4,096 B. 4,364 C. 4,384 D. 4,416
Answer:C.4,384
Step-by-step explanation:
1,096 × 4 = 4,384
This is why the answer is C.4,384.
what are the first four multiples of the number 6
Answer:
6,12,18,24
Step-by-step explanation:
Help meee I don’t understand
True or false:
FGH is a right triangle
Answer:
False
Step-by-step explanation:
Suppose |FG| is hypotenuse
the sum of square length of side legs must be equal to square of hypotenuse
(√63)^2 + 6^2 = 10^2
63 + 36 = 100
99 is not equal to 100 therefore the given triangle is not a right triangle.
Select the correct answer how many solutions for x dose the following equation have 2(x+4)-1=2x+7
Answer:
every number is correct.
Step-by-step explanation:
2 (x + 4) - 1 = 2x + 7
2x + 8 - 1 = 2x + 7
2x + 7 = 2x + 7
- 7 - 7
2x = 2x
/2 /2
x = x
Per 100 grams, an apple has 5 mg of magnesium whereas a banana has 27 mg, an apple has 6 mg of calcium where a banana has 5 mg, and an apple has 11 mg of phosphorus where a banana has 22 mg. Now, consider the vectors v1 = 2 4 5 6 11 3 5 and v2 = 2 4 27 5 22 3 5. (a) Give a physical interpretation of these two vectors, i.e. write a sentence explaining what these vectors represent in the real-world context described. (b) Give a physical interpretation of the linear combination 4v1 + 2v2. (c) Give a physical interpretation of the span of these two vectors. (What has to be true about the weights of the vectors in this situation.)
Answer:
hello your question lacks some vital information attached below is the complete question
answer :
a) consuming some amount of apple ( x ) and (y) amount of banana will determine the amount of magnesium, calcium and phosphorous you will be getting
b) 74mg of magnesium is consumed
34 mg of calcium consumed
88 mg of phosphorous consumed
c) The span of the two vectors will intercept for any value of X and Y ( whole number values ) and this indicates
The amount of magnesium, calcium and phosphorous consumed is finite and a whole number
Step-by-step explanation:
Given :
per 100 grams, apple has 5 mg of magnesium
per 100 grams , a banana has 27 mg
also an apple has 6 mg of calcium while a banana has 5 mg
An apple has 11 mg of phosphorous while a banana has 22 mg
attached below is the detailed solution
A) Give a physical interpretation of the vectors is that
consuming some amount of apple ( x ) and (y) amount of banana will determine the amount of magnesium, calcium and phosphorous you will be getting
B) Physical interpretation of linear combination : 4v1 + 2v2
Detailed solution attached below
= 74mg of magnesium is consumed
34 mg of calcium consumed
88 mg of phosphorous consumed
C) The span of the two vectors will intercept for any value of X and Y ( whole number values ) and this indicates
The amount of magnesium, calcium and phosphorous consumed is finite and a whole number
Mayzie's Masks has a monthly demand of 250 masks. It costs $100 to place an order
and the holding cost is 20% of the cost of a mask, which is $30. What is the total
cost?
Answer:
$951
Step-by-step explanation:
EOQ = Sqroot{(2*Annual Demand*Ordering cost)/Holding cost}
= Sqroot{(2*250*12*100)/(0.2*30)}
= 317 Units Approximately
Total Holding cost = Average Inventory * Holding cost per unit
= (EOQ/2)*Holding cost per unit
= (317/2)*(0.2*30)
= $951
So by knowing the holding cost and the percentage that it represents, we want to find the total cost of the masks. We will find that the cost is $150.
We know that the holding cost is 20% of the cost of a single mask, so if the cost of a mask is C, the holding cost is:
(20%/100%)*C = 0.2*C
And we know that this is equal to $30, so we get:
0.2*C = $30
Now we can solve this for C, the total cost of a mask:
C = $30/0.2 = $150.
If you want to learn more, you can read:
https://brainly.com/question/14094934
3) 4 hours worked for $12; 7 hours worked for $28
O yes
no
Answer:
no cuz if u work for 4 hours and get $12 then if u work for 7 hours u get $21
Step-by-step explanation:
A camera has listed a price of $687.99 before tax. If the sales tax rate is 9.25% find the total cost of the camera with sales tax
Answer:
$ 751.63
Step-by-step explanation:
1) To find 9.25% of $687.99, multiply both of them. 687.99 x 0.0925 = 63.64
2) Add the previous number to the original price of the camera, 687.99 + 63.64 = $751.63
Which of the shows the correct sums that would be found when clustering is used to find the answer to the problem 41 x 22?
820 + 82 = 912
800 + 2 = 802
820 + 82 = 902
820 + 80 = 900
If four out of ten people vote, then in a town with two hundred thousand people, how many will not vote?
Answer:50000
Step-by-step explanation:
help me i’m stuck on thus question
Answer:
2•8n•8n•8n•8n
Step-by-step explanation:
8n is it's own separate number so the other three would not work
The perimeter of a triangle is 37 cm. The lengths of its sides are x cm, x + 3 cm, and x + 7 cm. What is the length, in cm, of the longest
side of the triangle?
Answer:
x + (x +3) + (x +7) = 37
3x = 27
x = 9
Longest side = x + 7 = 16 cm
Step-by-step explanation:
Answer:
16cm
Step-by-step explanation:
x + x + 3 + x + 7 = 37 (make all sides equal 37)
3x + 10 = 37 (Add x's and coefficiants together)
-10 -10 (subtract 10 from each side)
3x = 27 (divide 27 by 3)
x = 9 (answer)
x, x + 3, x + 7 (finding longest length)
9, 9 + 3, 9 + 7 (Substitute 9 for x)
9cm, 12cm, 16cm (add each together)
16cm (answer)
I need help pls i don't know the answer to these words
Answer:
a parallel line: is coplanar lines that never interact
a skew: is lines that are not on the same plane and never intersect
an interior angle: is interior lines that lie on the same side of transversal
an exterior angle: is a line that lies between parallel lines that are cut by transversal
a consecutive interior angle: is a line that lies on the same side both parallel lines and the transversal
a corresponding angle: lies in the region not between parallel lines that are cut by transversal
a tranversal: is a line that interacts 2 or more coplanar lines at 2 different points
Have a great day love!
Step-by-step explanation:
A park shaped like a rectangle. The diagram shows the how the park is split into a sports field and a playground. Let x represent the length in meters of the sports field. Write an expression to represent the area of the park as the sum of the areas of the sports field and the playground.
Answer:
20x + 310
Step-by-step explanation:
step 2 is 20(x + 15.5)
What is the distance along the unit circle between any two successive 8th roots of 1?
Answer:
C.) pi/4
Step-by-step explanation:
Edg 2020, answered the question and got it right :)
Given the rotation in the image below, solve for the values of x and y,
HELPPPP
Answer:
x = 5
y = 4
Step-by-step explanation:
Since, rotation of a figure is a rigid transformation.
In a rigid transformation shape and size of the figure remains unchanged, that means image and pre-image are always congruent.
By the property of congruent triangles,
x = 5
3y = x + 7
3y = 5 + 7
3y = 12
y = 4
A piece of cardboard measures 10 in. by 15 in. Two equal squares are removed from the corners of a 10-in. side as shown in the figure. Two equal rectangles are removed from the other corners so that the tabs can be folded to form a rectangular box with a lid.
(a) Write a formula V(x) for the volume of the box.
(b) Find the domain of V for the problem situation.
(c) Use ANALYTICAL method (my teacher said don't graph) to find the maximum volume and the value of x that gives it.
SEE IMAGE!!!
Answer:
[tex]V(x) = 66.02\ \text{in}^3 \ \vert \ _x_=_1_._9_6[/tex]
Step-by-step explanation:
Part (a)The volume of a rectangular prism is found using the formula: V = lwh.
In order to write a formula in terms of the variable x, we need to write expressions for the length, width, and height of the rectangle.
We can say the length is the bottom of the base of the prism. To find this value, we can subtract x and x from 15 and divide this by 2, since there are two equal rectangles (base and lid).
Length: [tex]\frac{15-2x}{2} =7.5-x[/tex]We can say the width is the side of the base of the prism. To find this value, we can subtract 2x from 10.
Width: [tex]10-2x[/tex]The height of the prism can be x, which is the labeled length of the rectangle next to the base and lid.
Height: [tex]x[/tex]Now we are able to write a formula for volume in terms of x.
[tex]V(x)=(7.5-x)(10-2x)(x)[/tex] [tex]V(x)=x(75-25x+2x^2)[/tex] [tex]V(x)=75x-25x^2+2x^3[/tex] Part (b)The domain of the volume is where x > 0, 2x < 10, and 2x < 15.
This is because our expressions for length ([tex]\frac{15-2x}{2}[/tex]), width (10-2x), and height (x) cannot go below 0, because you cannot have a negative value for measurement - realistically.
Therefore, if we take into account all of these restrictions on x, the domain is where 0 < x < 5.
x cannot be > 5 since that would not satisfy 2x < 10.
The domain of V for this problem situation is D: (0, 5).
Part (c)In order to find the maximum volume of the rectangular prism using our formula we derived, we can use the idea of optimization in calculus.
Start by taking the derivative of V(x).
[tex]V'(x)=75-50x+6x^2[/tex]Set the derivative equal to 0. This gives us the critical point(s) in order to determine the extreme values of the function, aka where the max and min occur.
[tex]0=75-50x+6x^2[/tex] [tex]0=6x^2-50x+75[/tex]Solve for x by using the quadratic formula.
[tex]x=\frac{-(-50)\pm\sqrt{(-50)^2-4(6)(75)} }{2(6)}[/tex] [tex]x=\frac{50\pm\sqrt{2500-1800}}{12}[/tex] [tex]x=\frac{50\pm\sqrt{700} }{12}[/tex]Input this into your calculator and you should get:
[tex]x=6.37, \ 1.96[/tex]We are going to use x = 1.96 since 6.37 is NOT in the domain of V(x).
[tex]\boxed{x=1.96}[/tex]Now, since this value of x is going to give the maximum volume of this rectangular prism, or cardboard box, we can plug it back into the V(x) equation for volume to determine the maximum volume of the box.
[tex]V(1.96)=75(1.96)-25(1.96)^2+2(1.96)^3[/tex] [tex]V(1.96) = 66.02\ \text{in}^3 \ \vert \ _x_=_1_._9_6[/tex]The maximum volume of the cardboard box is 66.02 in³ and the value of x that gives this is 1.96.
PLEASE HELPPP MEEEEE
Step-by-step explanation:
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