Answer:2^(31-1)
Step-by-step explanation:
a box contains 5 white balls and 6 black balls. two balls are drawn out of the box at random. what is the probability that they both are white?
The probability of getting 2 white balls is 2/11.
What is probability?
The ratio of good outcomes to all possible outcomes of an event is known as the probability. It has a range from 0 to 1.
Probability(Event) = Favorable Outcomes / Total Outcomes
Main body:
total balls = 5+6 =11
1st try:
P(white balls) = 5/11
2nd try:
as there is no replacement,
no. of white balls = 4
total balls =10
P( white ball) = 4/10
Now multiplying both the result = (5/11)*(4/10)
P( WHITE BALLS) = 2/11
Hence answer is 2/11.
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suppose is a property such that , , are all true, for each integer , if is true, then is true. must it follow that is true for every integer ? if yes, explain why; if no, give a counterexample.
The answer is no, and the below explanation is given with a counter-example.
What is meant by an integer?An integer is a number that includes both negative and positive numbers, including zero. It has no decimal or fractional parts. Here are a few examples of integers: -5, 0, 1, 5, 8, 97, and 3,043
P(n) is a condition that is true for P(0), P(1), and P(2), but P(3k) is true when P(k) is true for all numbers k0.
P(n) is thus not always true for all nonnegative integers n because 4 is not a multiple of 3.
For example, consider the property P(n): "n is 0 or 1, or n is a multiple of 3." Then P(0), P(1), and P(2) are trivially true, however, P(3k) is true for all numbers k because 3k is a multiple of 3. However, P(4) is false because 4 is not a multiple of 3.
As a result, no.
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The complete question is:
"Suppose P(n) is a property such that 1. P(0), P(1), P(2) are all true, 2. for all integers k≥0, if P(k) is true, then P(3k) is true. Must it follow that P(n) is true for all integers n≥0?
If yes, explain why; if no, give a counterexample".
if the mean of a group of samples is 135 with a standard deviation of 45, what is the probability that a number would be less than 170?
Answer: C / .33
Step-by-step explanation:
What is 18% more than 61
Answer: I think the answer is 71.98
Step-by-step explanation:
100pts
Jesus planted tomatoes and peppers in his garden. All together, he planted a dozen plants. If he planted three times as many peppers as tomatoes, how many peppers did he plant?
Answer:
9 peppers
Step-by-step explanation:
A dozen is 12
so 3t + t = 12
4t=12 /3
t=3
He planted 9 peppers
Answer:
tomatoes are T so T3 is how many peppers he planted.
PS: if you are looking for a direct question you need to give the number of tomatoes or peppers.
Step-by-step explanation:
Or Lelie climb a 10-meter tower to ride a traight water lide. After landing in the plah pool, he walk 24 meter back to the bae of the tower. How far did he travel in all?
The total distance traveled by him is 60 ft
In this question, apply the Pythagorean relationship
Let's assume, the climbing, sliding and walking back to the base form a right-angle triangle
The tower height = the height of the triangle, h=10f
The sliding lane= the hypotenuse of the triangle=?
The distance covered to the base= base of the triangle=24f
Applying the relation ;
a²+b²=c²
10²+24²=c²
100+576=c²
676=c²
[tex]\sqrt{626}[/tex]=c
26=c
Distance traveled in all=26+24+10=60 feet
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. melitta found out that if she walks really fast during her morning exercise, she can cover 2 1/4 miles in 3/4 of an hour. how fast is she walking in miles per hour?
Melitta found out that if she walks really fast during her morning exercise, she can cover 2 1/4 miles in 3/4 of an hour.
Mellita is walking with a coverage of 2.8 miles per hour. We simply need to know how far she covers in an hour to calculate her walking speed in miles per hour.
Time taken to complete 2~1/4 miles is 3/4 of an hour. This is the time she can beat, so we have to find for the remaining 1/4th half of 2~1/4 miles i.e
Miles she can cover in 1/4 of hour = 1/4 * 2~1/4
= 1/4 * 9/4
= 9/16 miles.
Now, Add this to the miles that she can cover, i.e 2~1/4
= 2~1/4 + 9/16
= 9/4 + 9/16
= (36+9)/16
= 45/16
= 2.8 miles.
Hence, Melitta can walk 2.8 miles per hour.
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What is the angle of elevation if a ramp with a height of 1 meter and a horizontal length of 3 meters?
The angle of elevation is 18. 43 degrees
What is angle of elevation?Angle of elevation can be described as an angle formed between a horizontal line and the line of sight above the line.
From the information given, we have that;
Length of opposite side = 1 meterLength of adjacent side = 3 metersAngle of elevation = θUsing the tangent identity, we have;
tan θ = opposite/ adjacent
tan θ = 1/ 3
Divide the values
tan θ =0. 3333
Find the tan inverse of the value to determine θ
θ = tan^-1(0. 3333)
θ = 18. 43 degrees
Hence, the value is 18. 43 degrees
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Write two equations that are equivalent to 3(x-4)= 18+2x-11
The equivalent equation of the given equation 3(x-4) = 18+2x-11 is given by,
x=19.
Given the mathematical equation is,
3(x-4) = 18+2x-11
Evaluating the equation we get,
3x-12 = 18+2x-11
3x-2x = 18-11+12, separating the variable and numbers
x = 19
Hence the equivalent equation of the given equation is x=19.
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The table shows the amounts of storage in y (gigabytes) on a music playing device when there are x songs on the device. a. Write an equation that models the amount of storage left as a function of the number of songs. b. Interpret the slope and y-intercept of the line of fit.
Using linear regression, it is found that:
a) The equation is: y = -0.00408x + 16.
b) The interpretation of each coefficient is:
Slope: Each music takes up 0.00308 GB of space in the device.Intercept: The capacity of the device is of 16 GB.How to obtain the linear regression equation?The linear regression equation is obtained inserting the points given on the table at the end of the answer in a linear regression calculator.
Then the equation will have the following format of a linear function:
y = mx + b.
In which the coefficients are as follows:
Slope m: amount taken by a single music.Intercept b: initial capacity of the storage device.The points are given as follows:
(0, 16), (242, 14.8), (519, 14.1), (698, 13.5), (825, 12.7), (1009, 11.6).
Using the calculator, the equation is:
y = -0.00408x + 16.
Missing InformationThe problem is given by the image at the end of the answer.
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To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total of n times and the mean of the weighings is computed. Suppose the scale readings are normally distributed with unknown mean and standard deviation g. How large should n be so that a 95% confidence interval for has a margin of error of ± 0. 0008?.
600 large should n be so that a 95% confidence interval for has a margin of error of ± 0. 0008.
Given:
standard deviation σ = 0.01
margin of error e = 0.0008
For 95% confidence interval:
z value = 1.96
we know that:
e = z * σ/[tex]\sqrt{n}[/tex]
0.0008 = 1.96*0.01/[tex]\sqrt{n}[/tex]
0.0008 = 0.0196/[tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex] = 0.0196/0.0008
= 24.5
n = 24.5^2
n = 600.25
Therefore 600 large should n be so that a 95% confidence interval for has a margin of error of ± 0. 0008.
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What expression is equivalent to -2(3x + 5y)
The expression equivalent to the given expression -2(3x + 5y) is
y = 3x / 5How to find the expression equivalent to the given expressiongiven that
-2(3x + 5y)
expanding the parenthesis
-6x - 10y = 0
10y = 6x
y = 6x/10
y = 3x / 5
we can conclude that y = 3x/5 is equivalent to -2(3x + 5y)
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Which triangle congruence postulate or theorem proves that these triangles are congruent?
There are ΔABC and ΔXYZ triangles that are congruent due to the SAS congruence postulate.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
As per the given question,
In ΔABC and ΔXYZ,
Side BC = Side YZ
m∠C = m∠Z
Side AC = Side XZ
According to SAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.
Thus, both triangles are congruent.
Hence, there are ΔABC and ΔXYZ triangles congruent due to the SAS congruence postulate.
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true or false: the p-value is the probability of obtaining a test statistic as extreme or more extreme than observed assuming the null hypothesis is true.
The given statement is false.
What is statistic?Statistics is a science concerned with developing and studying methods of collecting, analyzing, interpreting, and presenting empirical data. Statistical research is applicable to virtually all scientific disciplines, and research challenges in various scientific disciplines motivate the development of new statistical methods and theories. Statisticians use a variety of mathematical and computational tools to develop methods and study the theory behind methods.
In light of the question -The given statement is false: A p-value is the probability of obtaining a sample statistic less extreme than the one observed under the assumption that the statement in the null hypothesis is true.
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An experimenter would like to construct a 99% confidence interval with a width at most 0. 5 for the average resistance of a segment of copper cable of a certain length. If the experimenter knows that the standard deviation of such resistances is 1. 55. How big a sample should the experimenter take from the population? what happens if the standard deviation and the width of the confidence interval are both doubled?.
A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.
In the given question,
The confidence level = 99%
Given width = 0.5
Standard deviation of resistance([tex]\sigma[/tex])= 1.55
We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.
The formula to find the a big sample that should the experimenter take from the population is
Margin of error(ME) [tex]=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}[/tex]
So n [tex]=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2[/tex]
where n=sample size
We firstly find the value of ME and [tex]z_{\alpha /2}[/tex].
Firstly finding the value of ME.
ME=Width/2
ME=0.5/2
ME=0.25
Now finding the value of [tex]z_{\alpha /2}[/tex].
Te given interval is 99%=99/100=0.99
The value of [tex]\alpha[/tex] =1−0.99
The value of [tex]\alpha[/tex] =0.01
Then the value of [tex]\alpha /2[/tex] = 0.01/2 = 0.005
From the standard table of z
[tex]z_{0.005}[/tex] =2.58
Now putting in the value in formula of sample size.
n[tex]=(2.58\times\frac{1.55}{0.25})^2[/tex]
Simplifying
n=(3.999/0.25)^2
n=(15.996)^2
n=255.87
n≈256
Hence, the sample that the experimenter take from the population is 256.
Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.
The new values,
Standard deviation of resistance([tex]\sigma[/tex])= 2×1.55
Standard deviation of resistance([tex]\sigma[/tex])= 3.1
width = 2×0.5
width = 1
Now the value of ME.
ME=1/2
ME=0.5
The z value is remain same.
Now putting in the value in formula of sample size.
n[tex]=(2.58\times\frac{3.1}{0.5})^2[/tex]
Simplifying
n=(7.998/0.5)^2
n=(15.996)^2
n=255.87
n≈256
Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.
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HELP PLS
A bird was sitting 2 meters from the base of an oak tree and flew 6 meters to reach the top of the tree. How tall is the tree?
THIS NEEDS PYTHAGOREM THEORAM
Answer: I don't know if I'm 100% spot on but I belive it may be 6.32.
There are calculators for this online, try get home (unless it's a test) and use them.
A bisector which divides the line segment into two parts
The perpendicular bisector is a line that bisects the line segment into two equal halves and forms a right angle with the line segment.
What is a Perpendicular bisector?
A line that divides another line segment into two equal halves by intersecting it perpendicularly is known as a perpendicular bisector. A rule, compass, and pencil can be used to draw a perpendicular bisector. When two lines cross at right angles or 90 degrees, they are said to be perpendicular to one another. A line that splits a line into two equally sized parts is known as a bisector. A line segment's perpendicular bisector suggests that it meets the segment at a 90-degree angle and splits it into two equal halves.
So, In the given question, We can say that A bisector that divides the line segment into two parts is called a perpendicular bisector;
We can also, find the proof of it: as: It divides AB into two equal halves or bisects it. It makes right angles with (or is perpendicular to) AB.
Every point in the perpendicular bisector is equidistant from points A and B.A ruler and compass are needed. The process for creating a line segment's perpendicular bisector is as follows:
Draw the first segment of the line PQ.
Step 2: Set the compass to a length that is a little longer than half of PQ's length.
Draw arcs above and below the line by positioning the compass pointer at point P in step 3.
Step 4: Set the compass pointer at point Q while maintaining the same length. Draw two arcs above and below the line, in the same manner, maintaining the compass's pointer at Q.
Hence, The perpendicular bisector is a line that bisects the line segment into two equal halves and forms a right angle with the line segment
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Find the area of the triangle if the perimeter of the triangle is 144 ft.
Answer:
I think it is 671
Step-by-step explanation:
The 2 sides are the same length because of those dashes on them so 61 + 61 = 122.
144 - 122 = 22 which is the base
Area is "Base times height divided by two"
The height is 61
so the area is (22 x 61) / 2
22 x 61 = 1,342
1,342 divided by 2 is 671
I think this is right, im sorry if it is wrong.
give formular for the area of the square?
Answer:
area = base x height
Step-by-step explanation:
You multiply the base of the square and the height of the square and you get the area of it.
please help ty i struggle with angles so
The area of a rectangle with length of 4 ft. and width of 9 ft. is 36 ft²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The area of a figure is the amount of space occupied in a two dimensional shape or object.
The area of a rectangle is the product of its length and width. Hence:
Area = length * width
From the diagram:
Area = 4 ft. * 9 ft. = 36 ft²
The area is 36 ft²
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Answer:
Perimeter: 26 ft
Step-by-step explanation:
To find perimeter, you add all the side measurements together.
Since the left side (4 ft) is congruent to the right, the right side is also 4 ft. Add both and you get 8 ft.
Since the bottom side (9 ft) is congruent to the top, the top side is also 9 ft. Add both and you get 18 ft.
8 + 18 = 26
So the perimeter is 26 ft.
Given the points (-4,r) and (-8,3) find the value of r that results in a slope of -10
Answer:
r = -37
Step-by-step explanation:
Step 1: Write out what is known
Points are (-4,r) and (-8,3)Slope = m = -10[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]Step 2: Set up an equation to solve for r
[tex]m=\frac{3-r}{-8-(-4)} =-10[/tex]Step 3: Solve for r
[tex]\frac{3-r}{-8-(-4)} =-10\\[/tex][tex]\frac{3-r}{-8+4} =-10[/tex][tex]\frac{3-r}{-4} =-10[/tex][tex](-4)\frac{3-r}{-4} =-10(-4)[/tex][tex]3-r=40[/tex][tex]-r=37[/tex][tex]r=-37[/tex]Please provide an explanation please
Step-by-step explanation:
First we need to write down something
X*x+8*x+6*x=240msquares
X2+14x=240
X2+14x-240=0
So now we use discriminant formula
196-4(1*240)=-44
-14-+(root of 44)
_____________. = answer
2
1. (9x+3y) +(-7x)
2. (8m-6n) + (7m)
Answer:
1. 2x + 3y
2. 15m -6n
Step-by-step explanation:
Combine like terms.
Answer:
1) 2x+3y
2) 15m-6n
Step-by-step explanation:
Lets first simplify 1.
1) open parentheses
9x+3y-7x
2)combine like terms
2x+3y
Simplify 2.
1) open parentheses
8m-6n+7m
2) combine like terms
15m-6n
Hailey is making floral centerpieces for a wedding. Each centerpiece has 17 flowers. She has 430 flowers for the project. She estimates that she can make between 20 and 30 complete centerpieces. Is her estimate reasonable? Use your knowledge of place value and division to explain the reasonableness of her answer.
Hailey's estimation is reasonable, because she can make 25 centerpieces using 430 flowers
Number of flowers in each centerpieces = 17 flowers
The total number of flowers that she has = 430 flowers
She estimates that she can make between 20 and 30 complete centerpieces
Number of centerpieces that she can make = The total number of flowers that she has / Number of flowers in each centerpieces
Substitute the values in the equation
Here we have to use division
Number of centerpieces that she can make = 430 / 17
= 25.29
≈ 25 centerpieces
Hence, Hailey's estimation is reasonable, because she can make 25 centerpieces using 430 flowers
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8m plus 20 minus 6m minus m plus seven
Step-by-step explanation:
8m + 20 - 6m - m + 7
We combine 8m and -6m to get 2m. Now we combine 2m and -m to get m.
This gives us:
m + 20 + 7.
We combine 20 and 7 to get 27.
This gives us the answer of
m + 27
the scale on a map is stated as 1: 100 000 on the map jennifer estimates that the distance to her destination is 8cm is shes correct in her estimate ,how many kilometers are there to her destination
By using unitary method it is obtained that Jennifer is at a distance of 8 km to her destination
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here unitary method is used
The scale on a map is stated as 1: 100 000
So 1 cm on the map is equivalent to 100000 cm on the ground
8 cm on the map is equivalent to 100000 [tex]\times[/tex] 8 cm on the ground
8 cm on the map is equivalent to 800000 cm on the ground
8 cm on the map is equivalent to [tex]\frac{800000}{1000 \times 100}[/tex] km on the ground
8 cm on the map is equivalent to 8 km on the ground
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The sampling distribution of the sample mean will always have the same _________ as the original distribution.
The sampling distribution of the sample mean will always have the same the mean of the original non-normal distribution, as the original distribution.
What is distribution?
Each of these samples contains a mean, and if we add up all of the means, we can construct a probability distribution that explains the distribution of the means. As long as we have sufficient samples, as will be discussed later, this distribution is always normal and is referred to as the sampling distribution of the sample mean.
Since the sample mean's sampling distribution is normal, we can naturally calculate the distribution's mean and standard deviation and utilise that information to analyse probability questions.
Here, The sample variance is equal to the population variance divided by the sample size if the population is infinite and the sampling is random, or if the population is finite but we are sampling with replacement.
So we need to use the mean of non-normal distribution.
Hence the answer will be the mean of the original non-normal distribution.
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Create and solve a story problem that would use this equation: y=5x+3 Be sure to define x, y, the constant, the coefficient and the variable.
The problem and solution are:
(a) I have $3, and I get $5 every month as my pocket money. How much money will I have after 6 months?
(b) The person will have $33 after 6 months.
What is the slope-intercept form of a line?The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.
The given equation is y = 5x + 3.
(a) Problem: I have $3, and I get $5 every month as my pocket money. How much money will I have after 6 months?
(b) Solution: The person gets $5 every month, therefore, he will have $5x after x month.
The person has $3 initially, therefore, the total money he will have after x month is:
y = 5x + 3
To find how much money will the person have after 6 months, substitute x=6 into the above equation:
y = 5(6) + 3
y = 30 + 3
y = 33
The person will have $33 after 6 months.
Hence, the problem and solution are:
(a) I have $3, and I get $5 every month as my pocket money. How much money will I have after 6 months?
(b) The person will have $33 after 6 months.
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What is the awnser. Thank you
Answer:
Henry is correct
Step-by-step explanation:
add 4 to each sides of the equation
2x=16
Divide each side of the equation by 2
X=8
2x - 4 = 12
add 4 to both sides:
2x - 4 + 4 = 12 + 4
2x = 16
divide both sides by 2:
2x/2 = 16/2
x = 8
so Henry is correct.
Can sb help me find the final balance
The final balance after 1 year with initial value $1000 if the interest is compounded quarterly will be $1215.5
What is compound interest?
Compound interest is computed as interest on the initial principal plus any accrued interest from prior periods. The power of compound interest is the creation of "interest on interest."
We are given that she initially invested $1000 and that she get 5% and interest is compounded quaterly.
After 3 months the interest will be
I = 1000*(5/100)
I = 50
So the total amount becomes
$1050 after 3 months
Now after 3 months again 5% interest will be credited
Hence the amount becomes
I1 = 1050*(5/100)
I1 = 52.5
Hence the total amount becomes
1102.5 after 6 months
After 9 months the interest will be
I2 = 1102.5*(5/100)
I2 = 55.12
Hence the total amount becomes
$1157.62 after 9 months
After 1 years the interest will be
I3 = 1157.62*(5/100)
I3 = 57.88
Hence the total amount becomes $1215.5
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