Answer:
0.03125 = 3.125% probability that the person flipped 5 heads
Step-by-step explanation:
For each coin, there are only two possible outcomes. Either it was heads, or it was tails. The result of a coin toss is independent of other coin tosses. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Five coins:
This means that n = 5.
Fair coin:
Equally as likely to be heads or tails, so p = 0.5.
What is the probability that the person flipped 5 heads?
This is P(X = 5).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]
0.03125 = 3.125% probability that the person flipped 5 heads
Please answer this correctly without making mistakes
Answer:
7
Step-by-step explanation:
hh
ht
th
tt
so it's a 1/4 chance
1/4 * 28 = 7
Answer:
7
Step-by-step explanation:
The probability of both coins landing on heads is:
1/2 × 1/2 = 1/4
Multiply by 28.
1/4 × 28
= 7
Jose can assemble 12 car parts in 40 minutes. How many minutes
would be needed to assemble 9 parts7
Answer:
12/40=0.3
0.3 car parts per minute
9 / 0.3 = 30 minutes
30 minutes for 9 parts
Hope this helps
Step-by-step explanation:
Jose required 30 minutes to assemble 9 parts.
Jose assemble 12 car parts in 40 minutes. Time consumed by jose to assemble 9 parts to be calculated.
In mathematics it deals with numbers of operations according to the statements.
Here,
40 minute = 12 parts
40/12 = 1 part
Time to assemble 9 parts: = 40/12 x 9
= 10/3 x 9
= 30
Thus, Jose required 30 minutes to assemble 9 parts.
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The heights of 10 year old children has a normal probability distribution with mean of 54.6 inches and standard deviation of 5.7 inches. What is the approximate probability that a randomly selected 10-year old child will be more than 51.75 inches tall? Group of answer choices 0.69 0.31 0.62 0.67 0.93
Answer:
a) 0.69
The probability that a randomly selected 10-year old child will be more than 51.75 inches tall
P(X>51.75 ) = 0.6915
Step-by-step explanation:
Step(i):-
Given mean of the Population = 54.6 inches
Given standard deviation of the Population = 5.7 inches
Let 'X' be the random variable of normal distribution
Let 'X' = 51.75 inches
[tex]Z = \frac{x-mean}{S.D} = \frac{51.75-54.6}{5.7} = -0.5[/tex]
Step(ii):-
The probability that a randomly selected 10-year old child will be more than 51.75 inches tall
P(X>51.75 ) = P(Z>-0.5)
= 1 - P( Z < -0.5)
= 1 - (0.5 - A(-0.5))
= 1 -0.5 + A(-0.5)
= 0.5 + A(0.5) (∵A(-0.5)= A(0.5)
= 0.5 +0.1915
= 0.6915
Conclusion:-
The probability that a randomly selected 10-year old child will be more than 51.75 inches tall
P(X>51.75 ) = 0.6915
Explain how to translate the statement into an equation. Use n for the variable. Thirteen less than a number is four EXPLAIN:
start here
Answer:
13-n=4
Subtract both sides by 13
-n=-9
n=9
Step-by-step explanation:
13 less means - and a number means n that you don’t know. is means = sign. And so we get the answer that I gave you. Thank you
Please answer this correctly
Answer:
I want to say 9 but im preety sure it's 6
Step-by-step explanation:
you have 54 times to pick it
you have 9 marbles,
54 divided by 9= 6
answer is 6
hope this helped:))))
have a grate dayy
Answer:
1
this is because I see only one marble present which is orange
PLEASE I NEED HELP ASAP
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
A 11 gram sample of a substance that's
used to treat thyroid disorders has a k-
value of 0.1247.
Enter the correct answer.
N = Noekt
DONE
No = initial mass (at time t = 0)
ĐOO
t?
N = mass at time t.
k = a positive constant that depends on
the substance itself and on the units
used to measure time
t = time, in days
Answer: 55.6 days
Step-by-step explanation:
[tex]P=P_oe^{kt}\\\\\bullet \quad P=\dfrac{1}{2}P_0\\\bullet \quad k=-0.1247\\\bullet \quad t = unknown\\\\\\\dfrac{1}{2}P_o=P_oe^{-0.1247t}\\\\\\\dfrac{1}{2}=e^{-0.1247t}\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=-0.1247t\\\\\\\dfrac{ln\dfrac{1}{2}}{-0.1247}= t\\\\\\\large\boxed{55.6=t}[/tex]
7th grade math I need help with this
Answer:
each bag of candy is $6.00
Step-by-step explanation:
1 bag would cost $6.00
1×$6.00=$6.00
6 bags × $6.00 = $36.00
Answer:
the constant of proportionally is 6
the prices of 6 bags of candy is 36
Step-by-step explanation:
to find the constant u divide 6 by 1 to find how they multiplying it by
the prices for six bags is 36 bc u can do 6 times 6 or look at the graph and see that it lands on 36
hope this helps
What is the conjugate?
2x2 + √3
Answer: 2x²-√3
Step-by-step explanation:
Another way to say the conjugate is the opposite. All you have to do is to change the sign in the binomial, which is 2x²+√3. When you change the sign, it becomes 2x²-√3.
4. The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Answer:
5in³Step-by-step explanation:
The question is in complete. Here is the complete question.
"The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Base of triangle = 1in
height of triangle = 5in"
Given the dimension of the triangular base of base 1 inch and height 5inches with the height of the pyramid to be 6inches, the volume of the triangular pyramid is expressed as [tex]V = \frac{1}{3}BH[/tex] where;\
B = Base area
H = Height of the pyramid
Base area B = area of the triangular base = [tex]\frac{1}{2}bh[/tex]
b = base of the triangle
h = height of the triangle
B = [tex]\frac{1}{2} * 5 * 1\\[/tex]
[tex]B = 2.5in^{2}[/tex]
Since H = 6inches
Volume of the triangular pyramid = [tex]\frac{1}{3} * 2.5 * 6\\[/tex]
[tex]V = 2.5*2\\V =5in^{3}[/tex]
Let f be the function that determines the area of a circle (in square cm) that has a radius of r cm. That is, f ( r ) represents the area of a circle (in square cm) that has a radius of r cm.Use function notation to complete the following tasks
a. Represent the area (in square cm) of a circle whose radius is 4 cm.
b. Represent how much the area (in square cm) of a circle increases by when its radius increases from 10.9 to 10.91 cm.
Answer:
(a)f(4) square cm.
(b)f(10.91)-f(10.9) Square centimeter.
Step-by-step explanation:
f(r)=the area of a circle (in square cm) that has a radius of r cm.
(a)Area (in square cm) of a circle whose radius is 4 cm.
Since r=4cm
Area of the circle = f(4) square cm.
(b) When the radius of the increases from 10.9 to 10.91 cm.
Area of the circle with a radius of 10.91 = f(10.91) square cm.Area of the circle with a radius of 10.9 = f(10.9) square cm.Change in the Area = f(10.91)-f(10.9) Square centimeter.
Mighty Casey hits two baseballs out of the park. The path of the first baseball can be described by the displacement (distance and direction) vector,
b1 = 100 i ^ + 10 j ^. The path of the second baseball can be described by the displacement vector b2 = 90 i ^ + (−20) j ^.
(a) How much farther did the first ball travel than the second? (Round your final answer to the nearest tenth.)
(b) How far are the baseballs apart? (Round your final answer to the nearest tenth.)
Answer:
a) 8.3 units of length
b) 31.6 units of length
Step-by-step explanation:
a) The distances traveled by each ball are given by:
[tex]d_1^2=100^2+10^2=10,100\\d_1=100.5\\\\d_2^2=90^2+(-20^2)=8,500\\d_2=92.2[/tex]
The diference between the distance traveled by both balls is:
[tex]d_1-d-2=100.5-92.2\\d_1-d_2=8.3[/tex]
The first ball traveled 8.3 units of length farther than the second ball.
b) The distance between both balls is:
[tex]d^2=(i_1-i_2)^2+(j_1-j_2)^2\\d^2=(100-90)^2+(10-(-20))^2\\d^2=1,000\\d=31.6[/tex]
The balls are 31.6 units of length apart.
Do all systems of linear inequalities have solutions? If not, write a system of inequalities that has no solution. What would the graph of a system of linear inequalities with no solution look like?
Answer: There are systems with no solutions, and the graphs may show two regions with no intersections (as you know, the solution set is in the intersection of the sets of solutions for each inequality)
Step-by-step explanation:
Ok, suppose that our system is:
y > x
and
y < x.
This system obviously does not have any solution, because y can not be larger and smaller than x at the same time.
The graph of y > x is where we shade all the region above the line y = x (the line is not included)
and the graph of y < x is where we sade all the region under the line y = x (the line is not included)
So we will look at a graph where we never have a region with the two shades overlapping (so we do not have a intersection in the sets of solutions), meaning that we have no solutions.
Which of the x-values are solutions to the following inequality? 17 > x Choose all answers that apply: (A) x = 7 (B) x = 12 (C) x = 17
Answer:
7 and 12
Step-by-step explanation:
7 and 12 are ok
17 is not
hope this helps
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The inequality is given below.
x < 17
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
More about the inequality link is given below.
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Write the expression 3*3*3*3*3 in exponential notation
Answer:
3^5
Step-by-step explanation:
becuase 3*3*3*3*3
Answer: 3^5 (3 to the power of 5)
Step-by-step explanation:
3 is multiplied by itself 5 times
To shorten the expression, exponential notation is used and it becomes 3^5, which essentially means three multiplied by itself 5 times
ex. 4^3 equals 4x4x4
In rhombus MNOP, mMNO = 24. What is the measure of PMO
Someone please help ASAP
Answer:
[tex]\boxed{\sf \ \ \ k = 1 \ \ \ }[/tex]
Step-by-step explanation:
hello,
saying that p-1 is a factor of [tex]p^4+p^2-p-k[/tex]
means that 1 is a root of this expression, so it comes
1+1-1-k=0
<=> 1-k=0
<=> k = 1
Which table shows the correct methods used to justify the solution steps?
3 (x minus 5) + 7 x = 65
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries division property of equality, combine like terms, distributive property, addition property of equality.
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries distributive property, combine like terms, addition property of equality, division property of equality.
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries distributive property, addition property of equality, combine like terms division property of equality.
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries division property of equality, combine like terms, addition property of equality, distributive property.
Answer:
B.
Step-by-step explanation:
The correct table that shows the justified solution steps is the second table.
The correct option is B.
The correct table that shows the justified solution steps is:
A 2-column table with 4 rows.
Column 1: Solution step
3x - 15 + 7x = 65
10x - 15 = 65
10x = 80
x = 8
Column 2: Method to Justify
Distributive property
Combine like terms
Addition property of equality
Division property of equality
In this table, the solution steps are correctly listed in the first column, showing the step-by-step process of solving the equation. The methods to justify each step are accurately provided in the second column, demonstrating the mathematical properties used at each stage.
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Which expression are equivalent to 4m-2+(-8m)
Answer:
combine 4m -8m to get -4m
[tex] - 4m - 2[/tex]
Answer:
− 4m-2
Step-by-step explanation:
Phil has $20,000, part of which he invests at 8% interest and the rest at 6%. If the total income from the two investments was $1460, how much did he invest at 6%?
Answer: 7000
Step-by-step explanation:
Let the amount invested in 8% account be P1 and the amount invested in 6% account be P2
. If the total amount invested is $20,000 then:
P1+P2=20,000. (Eq. 1)
The interest earned in one year from the 8% account is:
I1=0.08P1
and the interest earned in one year from the 6% account is:
I2=0.06P2
If the total interest earned is $1460, then:
I1+I2=1460
0.08P1+0.06P2=1460
(Eq. 2) From Eq. 1 :
P1=20000−P2
Substituting this into Eq. 2:
0.08 (20000−P2) + 0.06P2 = 1460
1600 − 0.08P2 + 0.06P2 = 1460
0.02P2 = 140
P2 = 140 / 0.02
P2 = 7000
Hence, he invested $7000 at the rate of 6%.
Evaluate f(x) = x2 + 1 for f(-1)
Answer: -1
Step-by-step explanation:
to calculate f(-1), you know that x = -1. so all you have to do is substitute:
f(-1) = (-1)2 + 1
f(-1) = -2 + 1
f(-1) = -1
Answer:
0
Step-by-step explanation:
5. A worker can do a piece of
piece of wook
in 14 days.
How much coook does he do ini day!
. How much work does he do in 7 days?
lijIt he works for 2 days and leaves,
how much work is left to finish it?
Answer:
therefore the left work of worker will be 6/7 part of work
Find the value of x for which line a is parallel to line b. 34 32 68 56
Answer
value of x is 34 degrees
Step-by-step explanation:
A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is:_______ a) 30 b) 100 c) 729 d) 1,000"
Answer: Option d.
Step-by-step explanation:
Ok, we have 3 urns.
Each urn can give a number between 0 and 9, so each urn has 10 options.
And as the urns are different, the outcome in the first urn does not affect the outcomes in the others, and the same happens for the outcome in the second urn, so the events are independent.
The total number of combinations is equal to the product of the number of options for each event (here each urn is one event)
then the number of combinations is:
C = 10*10*10 = 10^3 = 1000
Then the correct option is d.
Given a = 4 and b= -2, evaluate -Ib-al.
-2
-6
6
Express the number using scientific notation: 0.000000067
Select one:
O a. 67 x 10-7
O b. 6.7 x 10-7
O c. can not be written in scientific form
O d. 6.7 x 10 -8
Answer: D
Step-by-step explanation:
To express this number in scientific notation, we want to move the decimal so that it goes past the first nonzero integer. In this case, we would move it to the right 8 times.
6.7×10⁻⁸
The only reason why the 8 is negative is because when you write the scientific notation in standard form, you will need to move the decimal to the left in order to get 0.000000067. Negative means moving to the left. Therefore, 6.7×10⁻⁸ is our correct answer.
If log 5 = p and log 2=q then log 200 can be written in terms of p and q as?
Work Shown:
log(200) = log(2^3*5^2)
log(200) = log(2^3) + log(5^2)
log(200) = 3*log(2) + 2*log(5)
log(200) = 3*q + 2*p
log(200) = 2p + 3q
The log rules I used were
log(A*B) = log(A)+log(B)
log(A^B) = B*log(A)
The equivalent expression of log(200) is 2p + 3q
The logarithmic expression is given as:
[tex]\mathbf{log 200}[/tex]
Rewrite as:
[tex]\mathbf{log(200) = log (25 \times 8)}[/tex]
Express as exponents
[tex]\mathbf{log(200) = log (5^2 \times 2^3)}[/tex]
Split
[tex]\mathbf{log(200) = log (5^2) +log(2^3)}[/tex]
Apply law of logarithms
[tex]\mathbf{log(200) = 2log (5) +3log(2)}[/tex]
From the question;
log(5) = p and log(2) = q
So, we have:
[tex]\mathbf{log(200) = 2p +3q}[/tex]
Hence, the equivalent expression of log(200) is 2p + 3q
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Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level α. n = 12, α = 0.01
Answer:
[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]
And is distributed with n-2 degreed of freedom. df=n-2=12-2=10
The significance level is [tex]\alpha=0.01[/tex] and [tex]\alpha/2 = 0.005[/tex] and for this case we can find the critical values and we got:
[tex] t_{\alpha/2}= \pm 3.169[/tex]
Step-by-step explanation:
In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:
Null hypothesis: [tex]\rho =0[/tex]
Alternative hypothesis: [tex]\rho \neq 0[/tex]
The statistic to check the hypothesis is given by:
[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]
And is distributed with n-2 degreed of freedom. df=n-2=12-2=10
The significance level is [tex]\alpha=0.01[/tex] and [tex]\alpha/2 = 0.005[/tex] and for this case we can find the critical values and we got:
[tex] t_{\alpha/2}= \pm 3.169[/tex]
Write an equation in slope-intercept form for the line that passes through (4,5) and parallel to the to the line described by y=5x+10
Answer:
[tex]y = 5x-15[/tex]
Step-by-step explanation:
Parallel ⇒ So the slopes will definitely be equal
So,
Slope = m = 5
Now,
Point = (x,y) = (4,5)
So, x = 4, y = 5
Putting these in the slope intercept form to get b
[tex]y = mx +b \\[/tex]
5 = (5)(4) + b
5 = 20 + b
b = -20+5
b = -15
So, Putting m and b in the slope intercept form to get the required equation,
[tex]y = 5x-15[/tex]
What are the like terms in the algebraic expression? Negative a squared b + 6 a b minus 8 + 5 a squared b minus 6 a minus b Negative a squared b and negative 6 a Negative a squared b and 5 a squared b 6 a b and 5 a squared b 6 a b and negative 6 a
Answer:
The like terms are: [tex]a^{2}b,\ ab,\ \teaxt{and}\ a[/tex]
Step-by-step explanation:
The expression is:
[tex]-a^{2}b+6ab-8+5a^{2}b-6a-b-a^{2}b-6a-a^{2}b+5a^{2}b+6ab+5a^{2}b+6ab-6a[/tex]
Collect the like terms as follows:
[tex]-a^{2}b+6ab-8+5a^{2}b-6a-b-a^{2}b-6a-a^{2}b+5a^{2}b+6ab+5a^{2}b+6ab-6a[/tex]
[tex]=(-a^{2}b+5a^{2}b-a^{2}b-a^{2}b+5a^{2}b+5a^{2}b)+(6ab+6ab+6ab)-(6a-6a-6a)-b-8[/tex]
[tex]=12a^{2}b+18ab+18a-b-8[/tex]
Thus, the final expression is [tex]12a^{2}b+18ab+18a-b-8[/tex]
The like terms are: [tex]a^{2}b,\ ab,\ \teaxt{and}\ a[/tex].
Answer:
The CORRECT answer is B
Step-by-step explanation:
In a genetics experiment on peas, one sample of offspring contained 450 green peas and 371 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of three fourths that was expected?
Answer:
P(G) = 0.55
the probability of getting an offspring pea that is green. Is 0.55.
Is the result reasonably close to the value of three fourths that was expected?
No
Expected P(G)= three fourths = 3/4 = 0.75
Estimated P(G) = 0.55
Estimated P(G) is not reasonably close to 0.75
Step-by-step explanation:
Given;
Number of green peas offspring
G = 450
Number of yellow peas offspring
Y = 371
Total number of peas offspring
T = 450+371 = 821
the probability of getting an offspring pea that is green is;
P(G) = Number of green peas offspring/Total number of peas offspring
P(G) = G/T
Substituting the values;
P(G) = 450/821
P(G) = 0.548112058465
P(G) = 0.55
the probability of getting an offspring pea that is green. Is 0.55.
Is the result reasonably close to the value of three fourths that was expected?
No
Expected P(G)= three fourths = 3/4 = 0.75
Estimated P(G) = 0.55
Estimated P(G) is not reasonably close to 0.75