different outcomes have at least heads 2048, 165, 2036, 1816,
1. total number of different outcomes for 11 times toss
=2048
2. exactly 8 heads can be found by combination ( exactly n heads possiblity can be found by 11Cn
= 165
3. number of outcomes with atleast 2 heads can be found by subtracting number of outcomes with with 0 and 1 heads from total number of outcomes
= total number of outcomes - outcomes with 0 heads - outcomes with 1 heads
= 2036
4. number of outcomes with atmost 7 heads can be found by subtracting number of outcomes with 8, 9, 10, 11 heads from total number of outcomes
= total number of outcomes - outcomes with 8 heads - outcomes with 9 heads - outcomes with 10 heads -outcomes with 11 heads
=1816
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mass of a banana and can of cola
The mass of a banana is about C. 150 g.
A can of cola would be around A. 300 ml.
What is the mass of a banana ?From the options, the best estimate for the mass of a banana is 150 g. This is because 1. 5 kg is much too heavy for a single banana which makes 15 kg ridiculously heavy. 15 g would be too light however as this is the mass of about 6 pennies.
What is the quantity of a can of cola ?There are several quantities for a can of cola, and they are all in 100s of milliliteters. The most likely quantity of a can of cola from the options is therefore 300 ml.
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what is separate the population into non overlapping groups and then obtain a simple random sample from each group is called?
"Stratified Sampling" is the process of dividing the population into non-overlapping groups and taking a simple random sample out of each category.
Explain about the Stratified Sampling?Differentiated stratified sampling. By employing a characteristic to divide the population, we can then obtain a proportional randomized sample of each group.
The population is divided into non-overlapping groups, or strata, and a proportional simple randomized sample is taken from each stratum to create a stratified sample. Each group's members ought to have some things in common. Once the strata have been established, we must decide how many people will be chosen from each stratum. Here, proportionality of the chosen number is crucial.Thus, "Stratified Sampling" is the process of dividing the population into non-overlapping groups and taking a simple random sample out of each category.
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Practice
1.
Three students wrote expressions for this diagram.
Explain or show why they are each correct.
Yolanda: 16 ÷8=2
Riku: 16 ÷ 2=8
Mariana: 8x2 = 16
All three expressions are correct based on the properties of arithmetic operations.
How to explain the expressionYolanda wrote 16 ÷ 8 = 2, which means she is finding how many times 8 fits into 16. The answer is 2, meaning 16 is divided into 8 equal parts and each part has a value of 2.
Riku wrote 16 ÷ 2 = 8, which means he is finding how many times 2 fits into 16. The answer is 8, meaning 16 is divided into 2 equal parts and each part has a value of 8.
Mariana wrote 8 x 2 = 16, which means she is finding the product of 8 and 2. The answer is 16, meaning 8 multiplied by 2 gives a total of 16.
All three expressions are correct.
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the amount of taxes a city collects is proportional to the population of the city. in 2005 the population was million and it had increased to million by 2017. if billion dollars in taxes were collected in 2005, how much was collected in 2017?
If billion dollars in taxes were collected in 2005, then 30 billion was collected in 2017.
In 2005 the population was 2 million and it had increased to 3 million by 2017.
If 20 billion dollars in taxes were collected in 2005 then we have to determine how much tax was collected in 2017.
The amount of taxes of the city is proportion to the population of that city.
Tax(T) = kP(Population)
where k is a constant.
In 2005 Population = 2 millions and T = 20 billion. So
20 = 2k
Divide by 2 on both side, we get
k = 10
In 2017 Population = 3 millions and k = 10. So the tax collection in 2017 is:
t = 10 × 3
t = 30 billion
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The complete question is:
The amount of taxes a city collects is proportional to the population of the city. In 2005 the population was 2 million and it had increased to 3 million by 2017. If 20 billion dollars in taxes were collected in 2005 how much was collected in 2017? billion dollars help?
Deandre's dog ate 8 cans of dog food this week. Each can contained 47.6 grams of protein. How much protein was this in all
Answer:
Step-by-step explanation:
380.8 grams
Answer:
Step-by-step explanation:
380.8
5.060 x 10 3rd power /km
Answer:
Step-by-step explanation:
charge it paigon
The level of significance in hypothesis testing is the probability of?
The level of significance in hypothesis testing is the probability of obtaining a result that is at least as extreme as the observed result, assuming that the null hypothesis is true, and is usually denoted by the symbol α (alpha).
In hypothesis testing, the level of significance is the probability of obtaining a result that is at least as extreme as the observed result, assuming that the null hypothesis is true. It is also known as the p-value and is usually denoted by the symbol α (alpha). The formula for calculating the level of significance is:
α = P (Statistic ≥ Observed Statistic | H0 is true)
For example, suppose we are testing a hypothesis that the mean height of all people in a population is 160cm. We select a sample of 50 people and measure the mean height to be 162cm. Assuming the null hypothesis is true, the level of significance is calculated as follows:
α = P (Statistic ≥ 162 | H0 is true)
This p-value measures the probability of obtaining a result that is at least as extreme as the observed result (162cm), if the null hypothesis is true. If this p-value is less than the predetermined significance level (usually 0.05 or 0.01), then the null hypothesis is rejected and we accept the alternative hypothesis.
The level of significance in hypothesis testing is the probability of obtaining a result that is at least as extreme as the observed result, assuming that the null hypothesis is true, and is usually denoted by the symbol α (alpha).
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An account with an initial balance of $2,000.00 and a 2.80% interest rate has a balance of $2,056.72 at the end of one year. What is the effective annual yield?
The effective annual yield (EAY) is 2.83%
How the answer was obtainedThe effective annual yield (EAY) is the true annual interest rate that an investor earns after taking into account the effect of compounding. To calculate the EAY, you need to find the interest rate that will make the formula (1 + r/n)^n = final balance/initial balance hold true, where r is the interest rate and n is the number of times compounding occurs in a year.
Given the initial balance of $2,000 and a final balance of $2,056.72 after one year, we can use the following formula to calculate the EAY:
(1 + r/n)^n = $2,056.72/$2,000
Since the interest rate is given as 2.80%, and the number of times compounding occurs in a year is not given, we'll have to assume n. A common assumption for n is 12, which represents monthly compounding. Plugging in the numbers, we have:
(1 + 0.028/12)^12 = $2,056.72/$2,000
Solving for r, we get:
r = 12 * (($2,056.72/$2,000)^(1/12) - 1)
r = 2.83%
So the effective annual yield (EAY) is 2.83%.
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the histogram below presents the compressive strengths of a sample of concrete blocks hardened for 28 days. one rectangle from the histogram is missing. what is its height?
The missing rectangle has a relative frequency of 0.15, and this is the same as the height.
Let us define what a frequency and relative frequency are
The frequency of a datum is the number of times a given item (datum) appears in the data set.
While the relative frequency is the fraction or proportion of times taken from the whole in which an item/datum occurs.
So, from the image I uploaded, the relative frequency column represents the height of the histogram. Let the height of the missing rectangle be x.
Therefore the heights of the rectangles written from left to right are 0.05, 0.1, 0.15, x, 0.25, 0.2, and 0.1.
From the definition of relative frequency, the total sum of relative frequency is 1, if represented as decimals or fractions it can either be expressed in percentage, or decimal (fractions). In this question, it is represented in decimal, and the sum of all the relative frequency is 1.
0.05 + 0.1 + 0.15 + x + 0.25 + 0.2 + 0.1 = 1 ;
0.85+ x =1
Therefore, x = 1 - 0.85= 0.15
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What is a residual? What does it mean when a residual is positive? Choose the correct answer below. A. A residual is the difference between an observed value of the response variable y and the value of the corresponding explanatory variable x. If it is positive, then the response variable is greater than the explanatory variable. B. A residual is the difference between an observed value of the response variable y and the average value of the response variable. If it is positive, then the response variable is greater than the mean. C. A residual is the difference between an observed value of the response variable y and the predicted value of y. If it is positive, then the observed value is greater than the predicted value. D. A residual is a data point that does not fit the pattern of the rest of the data. If it is positive, then the data point should still be included in the data set.
(C) The difference between an actual and expected value for the response variable y is known as a residual. If it is positive, the observed value is greater than the expected value.
What is residual?The discrepancy between a response variable's observed value and its expected value as predicted by the regression line.
A residual is a discrepancy between an observed and expected value for the response variable y.
In the event that it is positive, the observed value exceeds the expected value.
The information that was ignored throughout the (first) cycle of the modeling is contained in the residuals, which serve as a significant source of information.
They must thus divulge something to us.
It is possible to describe the residual plot to the students as a kind of magnifier for the modeling procedure.
Therefore, (C) the difference between an actual and expected value for the response variable y is known as a residual. If it is positive, the observed value is greater than the expected value.
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An angle measures 4.2° more than the measure of its complementary angle. What is the measure of each angle?
Answer:
Step-by-step explanation:
If 2 angles are complementary, they are equal to 90 degrees. So, lets say that the measure of the first angle is x, and the measure of the second angle is y.
Since x measures 4.2 degrees more than its complementary angle (y), we can say that x - 4.2 = y
And, since they are complementary angles, x+y = 90.
We can now use a system of equations to solve. Since we know y = x-4.2, we can substitute y with x-4.2, making the equation x + x - 4.2 =90.
Simplify:
x+x-4.2=90
2x -4.2 =90
2x = 94.2
x= 47.1
Since y=x-4.2, we can now find y.
y = x-4.2
y= (47.1)-4.2
y=42.9
So, the measure of the angles is 47.1° and 42.9°.
Hope this helps!
ou have an ordinary deck of 52 well-shuffled cards. you remove the cards one at a time until you get an ace. let the random variable x denote the number of cards removed. what is the probability mass function of x? make sure to specify where x can take values. recall that there are four aces in a standard 52-card deck.
The probability mass function of x is p(x) = 4/52 * (48/51)^(x-1) * (1/51)^(52-x) for x = 1, 2, ..., 52.
x indicates the number of cards removed
that means
x = 1, 2, ..., 52
The probability of picking an ace is
P(ace) = 4/52
that means:
P(Ace') = 48/51 ----- Cards are selected without replacement
If x Ace is chosen, remaining cards are 52 - x
Using the above as a guide, it looks like this:
For x = 1, 2, ..., 52, PMF = 4/52 * (48/51)^(x-1) * (1/51)^(52-x).
ABOUT PROBABILITYProbability is the magnitude of the chance (likelihood) of something events will occur. Based on the definition of probability, there are the important things are the magnitude of the opportunity and the event will occur.
The probability that an event will occur is between 0 and with 1. If an event has a chance of happening 0, then this event is definitely not going to happen. If an event has chance will occur 1, then the event will definitely occur. With thus it can be concluded that the smaller the probability of an event (the closer the probability is to 0), the smaller the chance of the event
it will happen.
Conversely, the greater the probability of an event (the closer the probability is to 1), the greater the chance of the event it will happen.
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a toll booth has 12 cars waiting to go through. in how many different ways can the first five cars go through, if the order in which the pass distinguishes one set of five from another?
There are 95,040 different ways for the first five cars to go through the toll booth.
The first car can be chosen in 12 ways. After the first car has been chosen, the second car can be chosen in 11 ways. This process continues, so the third car can be chosen in 10 ways, the fourth car can be chosen in 9 ways, and the fifth car can be chosen in 8 ways.
So the total number of ways to choose the first five cars is as follows:
12 x 11 x 10 x 9 x 8 = 95,040
Therefore, there are 95,040 different ways for the first five cars to go through the toll booth.
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what is 4/5x12 i need help please its so hard to do it
The simplification of the given fraction above would be = 9⅘
What is a fraction?A fraction is defined as the part of a whole value which is represented in the form of a numerator and a denominator.
The given fraction that requires simplification is as follows:
= 4/5 × 12
= 48/5
= 9⅘
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A linear function is shown on the graph. A linear function beginning with an open circle at negative 4 comma negative 1 and ending with a closed circle at 6 comma 4. What is the domain of the function? {x | −4 < x < 6} {x | −4 < x ≤ 6} {y | −1 < y < 4} {y | −1 < y ≤ 4}
Any x-value in the range of -4 to 6 (not including 6) is included in the domain of the linear function.
What is linear function?I linear function is a mathematical expression involving variable that when craft create is straight line linear function are used to model relationship between two variable such is cost and revenue price in demand in distance and time linear function can also be used to solve equation and the specialily useful for predicting future outcomes.
The domain of the linear function is {x | −4 < x < 6}, which means that the x-values of the function are all real numbers greater than -4 and less than 6. This means that any x-value in the range of -4 to 6 (not including 6) is included in the domain of the linear function.
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a rectangle with area 1800 sq m is 3 times as long as it is wide. what is the sum of the diagonals? round to the nearest tenth.
The sum of the diagonals is 60, rounded to the nearest tenth.
Let's call the width of the rectangle "w". Then the length is 3 times the width or 3w. The area of the rectangle is 1800 square meters, so:
w * 3w = 1800
w^2 * 3 = 1800
w^2 = 600
w = √600 = √(600^(1/2)) = √(600^(1/2)) = 6 √(10^(1/2))
So the width is 6 √(10^(1/2)) and the length is 3 * 6 √(10^(1/2)) = 18 √(10^(1/2)).
The sum of the diagonals is the square root of the sum of the squares of the lengths of the two sides, so:
d = √(w^2 + (3w)^2)
d = √(w^2 + 9w^2)
d = √(10w^2)
d = √(10 * w^2)
d = √(10 * (6 √(10^(1/2)))^2)
d = √(10 * (6^2 * (10^(1/2)))^2)
d = √(10 * (36 * 10))
d = √(10 * 360)
d = √3600
d = 60
So the sum of the diagonals is 60, rounded to the nearest tenth.
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what is -3/4 to the power of 3
Answer:
it is 2 minus six
2-6
Step-by-step explanation:
hdgeheksdiddh
Answer:
-27/64
Step-by-step explanation:
Exact form
-27/64
Decimal Form
-0.421875
a cycle shop gave away 5000 miniature cycles and bumper stickers. the cycles cost 0.62 each and the bumper stickers cost 0.52 each. the cycle shop spent $2798 on the gifts. how many of each gift did they buy>
The cycle shop gave away 1980 miniature cycles and 5000 - 1980 = 3020 bumper stickers.
Let's call the number of miniature cycles given away "x". The number of bumper stickers given away would then be 5000 - x.
The cost of the cycles is 0.62x, and the cost of the bumper stickers is 0.52 (5000 - x).
So we can write an equation to represent the total cost:
0.62x + 0.52 (5000 - x) = 2798
Expanding the second term:
0.62x + 2600 - 0.52x = 2798
Combining like terms:
0.10x = 198
Finally, solving for x:
x = 1980
So the cycle shop gave away 1980 miniature cycles and 5000 - 1980 = 3020 bumper stickers.
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Carter drove 210 miles in 7 hours. If he drove at a constant rate, how far did he travel each hour?
Answer: 30 miles
Step-by-step explanation:
We are given a constant rate of 210 miles in 7 hours. Since we are trying to find how far Carter travelled in 1 hour, we can set up a proportion.
[tex]\frac{210}{7} =\frac{x }{1}[/tex] [cross multiply]
[tex]210=7x[/tex] [divide both sides by 7]
[tex]x=30[/tex]
Therefore, Carter travelled 30 miles in one hour.
(4.6x10^6)(1.1x10^7)
Answer:
[tex]5.06*10^{13}[/tex]
Step-by-step explanation:
[tex](4.6*10^6)(1.1*10^7)=(4.6*1.1)(10^6*10^7)=5.06*10^{13}[/tex]
at his school's spring carnival, bryant is in charge of the balloon-launcher contest. in this contest, each team builds a catapult to launch water balloons at a target. bryant gives a bucket of 14 water balloons to each team in the contest. in all, he gives out 70 water balloons.which equation can you use to find the number of teams t in the contest?
The equation 70 = 14t can be used to find the number of teams in the contest. By solving this equation, we found that there were 5 teams in the contest.
70 = 14t
To find the number of teams in the contest, we can use the equation 70 = 14t. This equation states that the total number of water balloons, 70, is equal to the number of teams, t, multiplied by the number of balloons each team gets, 14.
To solve this equation, we can divide both sides of the equation by 14. This will give us the equation t = 70/14. We can then simplify this equation by dividing 70 by 14. This gives us t = 5. This means that there are 5 teams in the contest.
Therefore, the equation 70 = 14t can be used to find the number of teams in the contest. By solving this equation, we found that there were 5 teams in the contest.
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please help me in this duty
P(30)=3, If Ms. Crowley has 30 students in her class, she must buy 3 packs of red paper mate flair pens.
P(0)=0, and if she has 0 students, she does not need to buy any pens.
To find the number of packs of pens Ms. Crowley must buy, we need to divide the number of students by the number of pens in each pack and then round up to the nearest whole number.
This is because if Ms. Crowley has 30 students, for example, and each pack contains 12 pens, then 30 ÷ 12 = 2.5, which means she needs 3 packs of pens to ensure that every student has a pen.
Using this calculation, we can find the number of packs of pens Ms. Crowley must buy for each number of students:
P(30) = ceil(30 ÷ 12) = ceil(2.5) = 3
P(0) = ceil(0 ÷ 12) = ceil(0) = 0
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CAN SOMEONE PLS HELP MEE
Answer:
[tex]4\sqrt{3} - 4i = \boxed{\left(8, \dfrac{\pi}{6}\right)}[/tex]
Step-by-step explanation:
Given complex number is:
To plot this on polar coordinates use the fact that a complex number of the form [tex]z=x+yi[/tex] can be converted to polar form [tex](r, \theta)[/tex] using the relationship
[tex]r = \sqrt{x^2 +y^2) }\\\mathrm{and}\\\theta = cos^{-1}\left(\dfrac{x}{r}}\right)[/tex]
Comparing [tex]4\sqrt{3} - 4i[/tex] and [tex]z=x+yi[/tex]
we see that
[tex]r = \sqrt{(4\sqrt{3})^2 + (-4)^2}\\\\r = \sqrt{48 + 16}\\\\\\r = \sqrt{64} = 8\\\\\theta = cos^{-1} \left(\dfrac{4\sqrt{3}}{8}\right)[/tex]
[tex]\theta = \cos^{-1} \left(\dfrac{\sqrt{3}}{2}\right) = 30^\circ = \dfrac{\pi}{6} \;radians[/tex]
So in polar coordinates,
[tex]4\sqrt{3} - 4i = \left(8, \dfrac{\pi}{6}\right)[/tex]
Lindsay and Lorraine are trying to match the jump rope world record. Together, they need to jump 48 times in a row. Lindsay has gotten 14 jumps in a row and Lorraine has gotten 13. Write an equation and show your work to determine how many more jumps they need to complete. Use the variable j to represent the unknown number of jumps.
Together, Lindsay and Lorraine needs to jump 21 more jumps in a row.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum.
Number of jumps got by Lindsay = 14
Number of jumps got by Lorraine = 13
Total number of jumps gotten by both = 27
Let j be the number of jumps they need to jump more.
j = 48 - 27
j = 21
Hence 21 more jumps would be needed.
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pls help plssssss
it would really help
The length of side AC rounded to 1 decimal place is 17.3 cm.
What is the length of side AC?The figure on the image is a right triangle.
From the image;
Angle B = 68 degreesOpposite to angle B = AC = ?Adjacent to angle B = AB = 7cmusing the trigonometric ratio, we determine the length of side AC.
Tangent = Opposite / Adjacent
tan( 68 ) = AC / 7
AC = tan( 68 ) × 7
AC = 17.3 cm
Therefore, side AC has a length of 17.3 cm.
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how do i solve this asap
Answer:
Step-by-step explanation:
when there is a plus before a negative, ignore it, the negative makes it irrelavant.
-4-3=-7
-4y-7
Find the length of YB
Answer:
YB = 11.2
Step-by-step explanation:
Δ AYZ and Δ ABCare similar by the AA postulate
then the ratios of corresponding sides are in proportion , that is
[tex]\frac{AY}{AB}[/tex] = [tex]\frac{AZ}{AC}[/tex] ( substitute values )
[tex]\frac{7}{7+YB}[/tex] = [tex]\frac{15}{15+24}[/tex] = [tex]\frac{15}{39}[/tex] ( cross- multiply )
15(7 + YB) = 7 × 39 = 273 ( divide both sides by 15 )
7 + YB = 18.2 ( subtract 7 from both sides )
YB = 11.2
The length of YB would be; 11.2
We know that proportion is a fraction of a total amount, and the measures are related using a rule of three.
Since Δ AYZ and Δ ABC are similar by the AA postulate
Then the ratios of corresponding sides are in proportion , that is
AY/AB = AZ/AC
cross- multiply ;
15(7 + YB) = 7 × 39 = 273
7 + YB = 18.2
Hence, YB = 11.2
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the points on the graph below show the total cost for different numbers of tickets to a concert. as shown, 1 ticket costs $20, 2 tickets cost $40, 3 tickets cost $60, and 4 tickets cost $80. what is the slope of the dashed line on the graph? responses 120 1 20 1 20 12 1 2 1 2 2 2 20
The slope of the dashed line on the graph is 1 (rise/run). This can be determined by dividing the difference in the cost of tickets (20) by the difference in the number of tickets (1).
The slope of the dashed line on the graph is 1. To determine the slope, you need to divide the rise (difference in the cost of tickets) by the run (difference in the number of tickets). In this case, the difference in the cost of tickets is 20 (from $20 for 1 ticket to $40 for 2 tickets). The difference in the number of tickets is 1 (from 1 ticket to 2 tickets). Therefore, the slope of the dashed line on the graph is 1 (20/1). This means that the cost of tickets increases by $20 for every additional ticket purchased. For example, if you purchase 3 tickets, the total cost will be $60 (3 tickets x $20 = $60). If you purchase 4 tickets, the total cost will be $80 (4 tickets x $20 = $80).
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A certain bacteria has a half-life of every 1.5 hours. If you start with 600 bacteria cells, how many will you have left after 6 hours?
Please include an explanation if you can!!!
The number of bacteria that is left is 38
How to determine the bacteria's leftThe half-life is the time it takes for half of the bacteria to reduce
The time is given as 1.5 hours
After 1.5 hours:
The number will have gone through 6 / 1.5 = 4 half-lives.
So, the number of bacteria cells after 6 hours will be 600 * (1/2)^4
Evaluate
600 * (1/2)^4 = 600 / 16 = 37.5
Approximate
600 * (1/2)^4 = 600 / 16 = 378
Since the number of bacteria cells is 37.
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An investor deposited $7,590 in a savings account 10 years ago that earns simple annual interest. today, the account balance is $11,916.30. what is the simple interest rate?
To find the simple interest rate, you can use the following formula:
Simple interest rate = (ending balance - starting balance) / (starting balance * number of years)
In this case, the starting balance is $7,590, the ending balance is $11,916.30, and the number of years is 10. Plugging in these values, we have:
Simple interest rate = ($11,916.30 - $7,590) / ($7,590 * 10)
= ($4,326.30) / ($7,590 * 10)
= $4,326.30 / $75,900
= 0.057 or 5.7%.
Therefore, the simple interest rate is 5.7%.
Answer:
Suppose an investor invested $7,590 in a savings account with basic yearly interest 10 years ago. The account currently has a balance of $11,916.30. 5.7% is the basic interest rate.
Why do we call something "interesting"?
You must pay interest on money you borrow, and you must add interest to money you lend. The most typical approach to display interest is as a percentage of the annualized principal amount of a loan. This ratio represents the interest rate on the loan.
What is meant by an interest example?
By examining the rate, a person can figure out exactly how much interest they will accrue or pay on a loan. For example, if a $100 loan had a nominal interest rate, there would be a $6 interest fee.of 6% ($100 X 0.06). Despite an increase in loan size, the rate doesn't change. Even if the loan amount were increased to$1,000, the borrower would still be expected to pay 6% of the total.
Step-by-step explanation: