Answer:
a. Mean: 9.5.
Standard deviation: 2.18.
b. The critical value for signficantly low girl births is 5.14.
The critical value for signficantly high girl births is 13.86.
Step-by-step explanation:
a) If we take a sample of 19 births, all with individual probability of 0.5, we have a random binomial variable with n=19 and p=0.5.
This random variable will have mean and standard deviation calculated as:
\(\mu=n\cdot p=19\cdot0.5=9.5\\\\\sigma=\sqrt{np(1-p)}=\sqrt{19\cdot0.5\cdpot0.5}=\sqrt{4.75}=2.18\)
b) Range rule of thumb: The standard deviation is approximately a quarter of the range, difference between the maximum and minimum value.
The range rule of thumb tells us that the expected minimum and maximum value are 2 standards deviation below or above, respectively, from the mean.
Then, the extreme expected values are:
\(Min=\mu-2\sigma=9.5-2\cdot2.18=9.5-4.36=5.14\\\\Max=\mu+2\sigma=9.5+2\cdot2.18=9.5+4.36=13.86\)
The critical value for signficantly low girl births is 5.14.
The critical value for signficantly high girl births is 13.86.
The likelihood of having a girl child is its probability
The mean and the standard deviation are 9.5 and 2.18, respectively.The values separating the significantly low and high results are 5.14 and 13.86, respectively.The given parameters are:
\(\mathbf{n = 19}\) --- sample size
\(\mathbf{p = 0.5}\) --- the probability of a girl child
(a) Mean and standard deviation
The mean is calculated as:
\(\mathbf{Mean = np}\)
So, we have:
\(\mathbf{\bar x= 19 \times 0.5}\)
\(\mathbf{\bar x = 9.5}\)
The standard deviation is:
\(\mathbf{SD = \sqrt{np(1 - p)}}\)
So, we have:
\(\mathbf{\sigma= \sqrt{19 \times 0.5 \times (1 - 0.5)}}\)
\(\mathbf{\sigma= \sqrt{4.75}}\)
\(\mathbf{\sigma= 2.18}\)
Hence, the mean and the standard deviation are 9.5 and 2.18, respectively.
(b) The values separating the significantly low and high results
Using the range rule of thumb, we have:
\(\mathbf{Low = \bar x - 2\sigma}\)
\(\mathbf{High = \bar x + 2\sigma}\)
So, we have:
\(\mathbf{Low= 9.5 - 2 \times 2.18 = 5.14}\)
\(\mathbf{High= 9.5 + 2 \times 2.18 = 13.86}\)
Hence, the values separating the significantly low and high results are 5.14 and 13.86, respectively.
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Evaluate. 4^3⋅(100÷25)−5^0
\(4 {}^{3} .(100 \div 25) - 5 {}^{0} \)
Solution\( {4}^{3} \times (100 \div 25) - {5}^{0} \\ \\ = 64 \times 4 - 1 \\ \\ = 256 - 1 \\ \\ = 255\)
\( \fbox \red{Hope This Helps }\)
Answer:
255
Step-by-step explanation:
1) Simplify 100 ÷ 25 to 4.
4³ × 4 - 5⁰
2) Use Rule of Zero: x⁰=1
4³ × 4 - 1
3) Use Product Rule
4⁴ - 1
4) Simplify 4⁴ to 256
256 - 1
5) Simplify
255
PLEASE HELP!
A poll is given, showing 45% are in favor of a new building project.
If 4 people are chosen at random, what is the probability that exactly 3 of them favor the new building project?
The probability that exactly 3 out of 4 people chosen at random favor the new building project is 0.2904.
This problem can be solved using the binomial probability formula. Let X be the number of people who favor the new building project out of the 4 chosen at random. Then X follows a binomial distribution with parameters n = 4 and p = 0.45.
The probability of having exactly k people who favor the new building project out of 4 is given by:
P(X = k) = (4 choose k) * \(0.45^{k}\) * \(0.55^{4-k}\)
where (4 choose k) is the binomial coefficient.
To find the probability that exactly 3 of the 4 people favor the new building project, we substitute k = 3 in the above formula and evaluate:
P(X = 3) = (4 choose 3) * \(0.45^{3}\) * \(0.55^{1}\)
= 0.290384375
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the phone company charges $33 for having a smartphone plus $9.95 a month for 2gb. IF mark has only $146.43 to spend on a phone, how many months can he have the phone? inequalities
The number of months Mark can have the phone is given by the equation
A = 11.4 months
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of months be represented as = A
Now , the equation is
Now , the total amount with Mark = $ 146.43
The initial amount for the smartphone = $ 33
The amount per month for 2GB is = $ 9.95
So , the amount for A months = $ 9.95 ( A )
So , the equation will be
Initial amount for the smartphone + the amount for A months = total amount with Mark
Substituting the values in the equation , we get
33 + 9.95 ( A ) = 146.43 be equation (1)
On simplifying the equation , we get
Subtracting 33 on both sides of the equation , we get
9.95 ( A ) = 113.43
Divide by 9.95 on both sides of the equation , we get
A = 11.4 months
Therefore , the value of A is 11.4 months
Hence , the number of months is 11.4 months
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A rectangular block has a length of 8 inches, a width of 3.5 inches, and a height of 2 inches. Four blocks are stacked to create a tower. What is the volume of the tower? O A. 56 in 3 O B. 140 in 3 O C. 280 in O D. 336 in
The volume of the tower is 224 in³, which is not listed among the given options.
To find the volume of the rectangular block, we need to multiply its length, width, and height. Therefore, the volume of the single block is:
8 x 3.5 x 2 = 56 cubic inches.
Since we are stacking four blocks to create a tower, we need to multiply the volume of a single block by 4.
Thus, the volume of the tower is:
56 x 4 = 224 cubic inches.
The volume of a rectangular block can be found using the formula,
V = length × width × height.
In this case, the length is 8 inches, the width is 3.5 inches, and the height is 2 inches.
V = 8 × 3.5 × 2 V
= 28 × 2 V
= 56 in³
Now that we know the volume of one block, we can find the volume of the tower created by stacking four blocks. Tower volume = block volume × number of blocks Tower volume = 56 in³ × 4 Tower volume = 224 in³
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An apple falls off a tree from a height of $36$36 feet.
a. What does the function $h(t)=-16t^2+36$h(t)=−16t2+36 represent in this situation?
BoldItalicUnderlineBullet listNumbered listSuperscriptSubscriptTable
0 / 10000 Word Limit0 words written of 10000 allowed
Question 2
b. Find and interpret the domain of h$h$h in this situation.
BoldItalicUnderlineBullet listNumbered listClear formattingSuperscriptSubscript
a)The term 1-16t²represents the effect of gravity on the apple, which causes it to fall with increasing speed. The constant term 36 represents the initial height of the apple
b)Interpreting the domain, we can say that h(t) makes sense only for non-negative values of t. In other words, we can use the function h(t)to find the height of the apple at any time t a
what is gravity ?
Gravity is a fundamental force of nature that causes objects with mass to attract each other. It is the force that keeps planets in orbit around stars, and stars in orbit around the center of their galaxies.
In the given question,
a. The function h(t)=-16t²+36 represents the height of an apple above the ground at time t after falling off a tree. The term1 -16t² represents the effect of gravity on the apple, which causes it to fall with increasing speed. The constant term 36 represents the initial height of the apple when it fell off the tree.
b. The domain of h(t) in this situation is the set of all possible values of t that make sense in the context of the problem. Since h(t) represents the height of the apple at time t after it fell off the tree, the domain of h(t)is the set of all non-negative real numbers, or [0,\infty) This is because time cannot be negative, and the apple cannot fall for an infinite amount of time.
Interpreting the domain, we can say that h(t)makes sense only for non-negative values of t. In other words, we can use the function h(t) to find the height of the apple at any time t after it fell off the tree, as long as t is non-negative..
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PLEASE HELP (0.1)^5 simplified
Answer:
0.1^5=0.00001
Step-by-step explanation:
\(0.1^5\\0.1^5=0.00001\)
Plz show work. Need help fast please please.
Step-by-step explanation:
10:
\( \sqrt{50} = \sqrt{2 \times 25} = \sqrt{2} \times \sqrt{25} = \: 2 \times \sqrt{5} \)
11:
\( \sqrt{88} = \sqrt{4 \times 22} = \sqrt{4} \times \sqrt{22} = \: \: \: \: \: 2 \times \sqrt{22} \)
12:
\( \sqrt[3]{54} = \sqrt[3]{ {3}^{3} \times 2} = \sqrt[3]{ {3}^{3} } \times \sqrt[3]{2} = \: \: \: \: \: 3 \times \sqrt[3]{2} \)
Determine if the equation given in slope-intercept form represents the graph. If the equation is correct support your reasoning with why it is correct. If the equation is incorrect, give the correct slope-intercept form equation explaining how you determined it.
The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.
The graph is given in the question.
As per the given line, we take two points (0, 4) and (5, 8)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 0, y₁ = 4
x₂ = 5, y₂ = 8
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 4 = (8 - 4)/(5-0 )[x -0]
⇒ y - 4 = (4/5)x
⇒ y = (4/5)x + 4
The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.
So, the equation of the line would be y = (4/5)x + 4.
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Use PEMDAS to answer the question.
Answer:
im gonna guess your talking about the "your turn" part
Step-by-step explanation:
exponents first
2*2*2
10+8*2
10+16
26
Answer: 26
Step-by-step explanation:
First you do 2 to the power of three and that is 8.
Then 8 * 2 = 16
Finally 16 + 10 = 26
Please give brainliest
Approximate -10 + √30 to the nearest tenth.
O-5.5
O-4.5
04.5
O5.5
Answer:
(b) -4.5
Step-by-step explanation:
Choosing the correct answer here is not the same as knowing what the correct value is.
EstimateYou know that √30 < √100 = 10, so the sum must be negative. That is, 10 subtracted from a positive number less than 10 will give a negative result.
You know that 25 < 30 < 36, so √25 < √30 <√36. That is, √30 will be between 5 and 6. If we say √30 ≈ 5.5, then the sum is ...
-10 +√30 ≈ -10 +5.5 = -4.5
__
Additional comment
Of course, a calculator can tell you the value to the desired precision.
Select all of the following expressions that require
use of the distributive property to simplify.
√5(-√2)
√√5(√√7-√√2)
(√5 + √2)(-√7)
(3√5)(-7√2)
0 0 0
15.08
The options given are correct formulas and should use the distributive law √5(√7-√2) for simplicity.
(√5+√2)(-√7)
distribution characteristics
Given integers A, B, and C. According to the distributive law,
A(B + C) = AB + AC
From the formula we can see that A is distributed over B and C.
Therefore, the sum of the coefficients and terms must be in the parentheses of the distribution properties. Based on the options given, the correct formulas that should use the distribution characteristics for simplicity are √5(√7-√2) and
(√5+√2)(-√7)
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(5x + 2) 6x
Solve for x and y
X =
y =
Answer:
x = 8
y = 138
Step-by-step explanation:
Three friends got the prize money worth $105,000. The first friend would get twice the amount of the third friend's portion. The third friend would get twice the amount of the second friend's portion. Determine the amount that each friend would receive.
Answer:
Step-by-step explanation:
The first friend would get $60,000
The second friend would get $15,000
The third friend would get $30,000
Create a factorable polynomial with a GCF of 6. Rewrite that polynomial in two
other equivalent forms. Explain how each form was created. (10 points)
Polynomial: 6x^3 + 12x^2 - 18x
Form 1: 6(x^3 + 2x^2 - 3x)
Explanation: This form was created by factoring out the GCF of 6 from each term in the polynomial.
Form 2: 6x(x^2 + 2x - 3)
Explanation: This form was created by factoring out the GCF of 6x from each term in the polynomial.
In both forms, the GCF of 6 allows us to factor out common factors and simplify the polynomial expression while preserving its original meaning.
To create a factorable polynomial with a greatest common factor (GCF) of 6, we can start by considering the common factors of the terms. Let's construct a polynomial:
Polynomial: 6x^3 + 12x^2 - 18x
To rewrite this polynomial in two other equivalent forms, we can factor out the GCF from each term and simplify.
Form 1: 6(x^3 + 2x^2 - 3x)
In this form, we factored out the GCF of 6 from each term: 6x^3/6 = x^3, 12x^2/6 = 2x^2, and -18x/6 = -3x.
Form 2: 6x(x^2 + 2x - 3)
In this form, we factored out the GCF of 6x from each term: 6x^3/6x = x^2, 12x^2/6x = 2x, and -18x/6x = -3.
We created each form by identifying the common factors in the polynomial and factoring them out. This process allows us to rewrite the polynomial in equivalent forms that emphasize different aspects.
In Form 1, we factored out the GCF of 6, leaving the remaining polynomial inside the parentheses. This form highlights the fact that the polynomial can be written as the product of the GCF and the remaining terms.
In Form 2, we factored out the GCF of 6x, again leaving the remaining polynomial inside the parentheses. This form emphasizes the fact that the polynomial can be written as the product of the GCF and another factor, in this case, x.
By rewriting the polynomial in these two forms, we have created equivalent expressions that emphasize the presence of the GCF and demonstrate the polynomial's factorability.
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simplify:(-7/10)-2/5=
Answer:
-11/10
-1.1
Step-by-step explanation:
Answer: 7/25
I hope this helps, and Happy Holidays! :)
collect like terms
-3b cubed subtract 2b cubed
Answer: -5b cubed
Step-by-step explanation:
What's the best definition of the word "ratio?"
Answer:
Compare
Step-by-step explanation:
Or relation I believe so...
Answer:
In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3). Equal quotients correspond to equal ratios.
HOPE YOU UNDERSTAND!!!Can someone please explain this to me please?
Will give brainly if you actually answer the question.
Answer: 50 weeks
Step-by-step explanation: If John already has $100 in his bank account and needs $850. You subtract $100 from $850 and get $750. To get how many weeks he needs to get 850, you divide 750 by 15 since john is making 15 per week. 750 divided by 15 equals 50 weeks. So the answer will be 50 weeks till he gets $850.
Answer:
Step-by-step explanation:
850 = 100 + 15x
850 - 100 = 100 + 15x - 100
750 = 15x
x = 750/15
x = 50 weeks
What is one way to add up 3-digit numbers?
Answer:
do it like step by step down below
Step-by-step explanation:
123
+ 240
+ 300
= 663
With lining them up
Step-by-step explanation:
Say you have 357 + 872
You would position your numbers so that they line up then you add the numbers that line up with each other, if your number is 10 or more you need to carry the first didgit over above the next row if your number was 14 you would carry the 1 over above the next row then you would add that number to the multiplicated 2 other numbers.
357
+ 872
_________
14. Simon earned 400sh as a for goods sold what Commission 15,000 worth so, 600 could be his varnings for a total sale of 7,000
His total earnings for a total sale of 7,000 could be 1450sh
How to determine his earnings for a total sale of 7,000.From the question, we have the following parameters that can be used in our computation:
Salary = 400
Commission = 15%
using the above as a guide, we have the following:
Total earnings = 400 + 15% * Total sales
So, we have
Total earnings = 400 + 15% * 7000
Evaluate
Total earnings = 1450
Hence, the total earnings is 1450
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Question
Simon earned 400sh weekly for goods sold and a commission of 15%
What could be his earnings for a total sale of 7,000.
PLZ HELP I WILL GIVE BRAINLIEST:
Find the average rate of change for the function f(x)= 3^x + 25
Using the intervals of x=2 to x=6.
PLZ SHOW WORK !
The average rate of change for the function f(x)= 3^x + 25 using the intervals of x=2 to x=6 is 6.75
The function is given as:
f(x) = 3^x + 25
The interval is given as:
x = 2 to 6
Start by calculating f(2) and f(6)
f(2) = 3^2 + 25 = 34
f(6) = 6^2 + 25 = 61
The average rate of change is then calculated as:
\(m = \frac{f(6) - f(2)}{6 -2}\)
This gives
\(m = \frac{61 - 34}{6 -2}\)
\(m = \frac{27}{4}\)
m = 6.75
Hence, the average rate of change is 6.75
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A traingular window pane has a base of 30 inches and a height of 24 inches. What is the area of the window pane?
The area of a triangle is
\(\text{area}=\frac{1}{2}bh\)where
b = base =30 inches
h = height = 24 iches
\(\begin{gathered} \text{area}=\frac{1}{2}\times30\times24 \\ \text{area}=\frac{720}{2} \\ \text{area}=360inches^2 \end{gathered}\)3x+12y=-8 show ur work
Here is the attached image for the answer. If you write it in in slope-intercept form, y=mx+b. You will get the answer below in the attached image.
Can anyone answer this?
Answer:
Ayo its Jose is the only one who was trying to get me to do the thank you usa for the support of the joy luck club the story is about a mother that lost every thing in China and whent to America to start a new life but she make her daughter do something that she don't want to be ninja in and she is not sending her
find the slope of a line perpendicular to the line whose equation is2x+3y=-3 . Fully simply your answer.
3/2 is a slope of a line perpendicular to the line whose equation of
2x+3y=-3 .
What is meant by perpendicular ?One specific example of the more broad mathematical concept of orthogonality is the concept of perpendicularity, which is the orthogonality of traditional geometric objects.
As a result, in higher mathematics, the term "perpendicular" is occasionally used to represent considerably more intricate geometric orthogonality criteria, like the relationship between a surface and its normal vector.
If two lines cross at a right angle, they are said to be perpendicular to one another.
A first line is explicitly said to be perpendicular to a second line if the two lines meet and the straight angle on one side of the first line is cut by the second line into two congruent angles at the point of junction.
This can be done by rearranging the equation into the slope intercept form.
2x +3y = -3
3y = -2x -3
y = -2/3x - 1
Thus, the slope of the given line is -2/3.
The slope of the perpendicular line is the negative reciprocal of the given line.
Slope of perpendicular line = 3/2
The slope-intercept form was:
(i) The reciprocal of m is 1/m.
(ii) The negative reciprocal of m is -1/m.
Negative reciprocal of -2/3
= -1 ÷ (- 2/3)
= -1 × (-3/2)
= 3/2
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Make (a) as the subject S = 3t + at2
the answer is ( a=st2-3t )
you deal one friend a card at random. Then you deal a second friend a card at random. What is the possibility that both friends got diamonds?
Answer:
0.0588
Step-by-step explanation:
There are 52 cards total in a pack of cards.
There are 13 diamond cards in a pack of card
When the first card is dealt, it is NOT replaced. When the second card is dealt, it is NOT replaced
In probability:
AND = multiplication
OR = addition
Probability = \(\frac{Total number of diamond cards}{Total number of cards}\)
Probability that both friends for diamonds:
First card is DIAMONDS AND second card is DIAMONDS:
= \(\frac{13}{52}\)×\(\frac{12}{51}\)
= \(\frac{156}{2652}\)
= 0.0588 (Rounded off to 3 significant figures)
Question:A study of several cities show positive correlation between 2% of people biking to work and 2% of people spending their vacation time at home. Which statement is most likely true? A. Correlation implies causation,therefore, vacationing at home makes people want to ride thief bike.B. Correlation does not imply causation,therefore,the correlation is due to a third variable: cost of milkC. Correlation does not imply causation,therefore,the correlation is due to a third varabile: cost of gas
The study shows positive correlation between 2% of people biking to work and 2% of people spending their vacation time at home .
I’ll give brainliest
Answer:
A=115.6
Step-by-step explanation:
Hey There!
So the first step is to find the formula for area of a trapezoid
\(A = \frac{1}{2} h(b1 +b2)\)
h = height
b1 = base 1
b2 = base 2
now all we do its plug in the values
\(A=\frac{1}{2} 6.8(28.3+5.7)\)
\(6.8x26.3=192.44\\5.7x6.8=38.76\\38.76+192.44=231.2\\\frac{231.2}{2} =115.6\\A=115.6\)
Hope this helps!!
If the length of a cube is 2cm then find the surface area of the cube?
Given:
Length of a cube is 2 cm
To Find:
Surface area of the cube
Solution:
A cube consists of 6 faces.
The area of each face = side x side
So, the total surface area of a cube = 6 x
side x side
Let a be the length of the given cube
: Surface area of a cube = 6a square
a = 2 cm (Given)
Surface area of cube = 6 x 22 =(6 x 4) = 24 cm square.
Hence, the surface area of the given
cube is 24cm square.
Hope it helps!