Answers
Answer:
33 yd
Step-by-step explanation:
To find the area of a triangle, you can follow the formula:
(base x height) / 2
By putting this formula into context, you can substitute the values of the terms with the information provided in the problem:
(base x height) / 2
(11 yd x 6 yd) / 2
66 yd / 2
33 yd
Related Questions
plz answer this asap
Answers
Answer:
100 inches square
Step-by-step explanation:
The surface is a trapezoid
Area = ½ × (sum of // sides) × height
= ½ × (5+15) × 10
= ½ × 20 × 10
= 100 in²
Is the mean age at which American children learn to walk less than 15 months? A study of 40 American children found a mean walking age of = 13.2 months. If the population of all American children has mean age μ until they begin to walk and standard deviation σ, which of the following null and alternative hypotheses should we test to answer this question? H 0 : μ ≥ 13.2 vs. Ha : μ < 13.2 H 0 : μ = 13.2 vs. H a : μ ≠ 13.2 H 0 : μ = 15 vs. H a : μ ≠ 15 H 0 : μ ≥ 15 vs. Ha : μ < 15
Answers
Answer:
We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.
Null hypothesis: [tex]\mu \geq 15[/tex]
Alternative hypothesis: [tex]\mu <15[/tex]
And for this case the best answer would be:
H 0 : μ ≥ 15 vs. Ha : μ < 15
Step-by-step explanation:
We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.
Null hypothesis: [tex]\mu \geq 15[/tex]
Alternative hypothesis: [tex]\mu <15[/tex]
And for this case the best answer would be:
H 0 : μ ≥ 15 vs. Ha : μ < 15
And the data given from the sample is:
[tex]\bar X = 13.2[/tex] represent the sample mean
[tex]\sigma[/tex] represent the population deviation
[tex] n = 40[/tex] represent the sample size
And the statistic would be given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
What is the combined weight of all the kittens? Weight of kittens: 1/4 pound: 3 kittens. 3/8 pound: 2 kittens. 1/2 pound: 4 kittens. 5/8 pound: 4 kittens
Answers
Answer:
6 pounds
Step-by-step explanation:
1/4 times 3 = 3/4
3/8 times 2: 6/8 = 3/4
1/2 times 4: 4/2 = 2
5/8 times 4: 20/8 = 2 1/2
3/4 + 3/4 = 6/4 = 1 1/2
2 + 2 1/2 + 1 1/2 = 6 pounds
Suppose that $77,000 is invested at 5 1/2% interest, compounded quarterly.
a) Find the function for the amount to which the investment grows after t years.
b) Find the amount of money in the account at t=0,3, 6, and 10 years.
Answers
Answer:
a) [tex]A(t) = 77000(1.01375)^{4t}[/tex]
b)
The amount of money in the account at t = 0 years is $77,000.
The amount of money in the account at t = 3 years is $90,711.
The amount of money in the account at t = 6 years is $106,864.
The amount of money in the account at t = 10 years is $132,961.
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
Suppose that $77,000 is invested at 5 1/2% interest, compounded quarterly.
This means that, respectively, [tex]P = 77000, r = 0.055, n = 4[/tex]
a) Find the function for the amount to which the investment grows after t years.
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 77000(1 + \frac{0.055}{4})^{4t}[/tex]
[tex]A(t) = 77000(1.01375)^{4t}[/tex]
b) Find the amount of money in the account at t=0,3, 6, and 10 years.
[tex]A(0) = 77000(1.01375)^{4*0} = 77000[/tex]
The amount of money in the account at t = 0 years is $77,000.
[tex]A(3) = 77000(1.01375)^{4*3} = 90711[/tex]
The amount of money in the account at t = 3 years is $90,711.
[tex]A(6) = 77000(1.01375)^{4*6} = 106864[/tex]
The amount of money in the account at t = 6 years is $106,864.
[tex]A(10) = 77000(1.01375)^{4*10} = 132961[/tex]
The amount of money in the account at t = 10 years is $132,961.
The function for the investment after t years is [tex]A = 77000(1 + 0.055/4)^{(4t).[/tex] To find the amount in the account at different times, trigger this function with the desired time intervals.
Explanation:The subject of the questions is about compound interest which belongs to the finance section of Mathematics.
To solve problems related to compound interest, a simple formula can be used: [tex]A = P(1 + r/n)^{(nt)[/tex] where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is time the money is invested for in years.
a) First, identify the variables from the question:[tex]P = $77000, r = 5.5/100 = 0.055[/tex](convert the percentage to a decimal), n = 4 (since interest is compounded quarterly).
We can now plug these values into our formula to determine the function: [tex]A = 77000(1 + 0.055/4)^{(4t).[/tex]
b) To find the amount of money in the account at different time intervals, plug the specified values for t into the function. For t = 0, 3, 6, 10 years, simply replace t in A with each of these time intervals and calculate the resulting A.
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Solve the two-step equation and identify the steps.
1.4x + 6.1 = -7.9
1. The first step is to
2. The second step is to
sides.
v on both sides.
von both
The solution is x =
ASAP
Answers
Answer:
1. The first step is to subtract 6.1 on both sides.
2. The second step is to divide by 1.4 on both sides.
3. The solution is x = -10
Step-by-step explanation:
I just finished the Egdenuity Assignment
The steps will be
The first step is to subtract 6.1 on both sides.The second step is to divide by 1.4 on both sides.The solution is x = -10How to solve linear equation of one variable?Step-1: we have to balance each side by simplifing the equation
Step-2: add/substract constant term on both side of the equation to separate variable and constant term on both side
Step-3: divide the coefficient of the variable on both side to make the coefficient of the variable 1.
So according to asked question,
1.4x+6.1=-7.9
Step 1: subtract 6.1 on both sides.
1.4x+6.1-6.1=-7.9-6.1
⇒1.4x=-14
Step 2: divide by 1.4 on both of the sides.
1.4x/1.4=-14/1.4
⇒x=-10
Therefore,
The steps will be
The first step is to subtract 6.1 on both of the sides.The second step is to divide by 1.4 on both of the sides.The solution is x = -10.Learn more about linear equation of one variable
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Exhibit 5-11 The random variable x is the number of occurrences of an event over an interval of 10 minutes. It can be assumed the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is 5.3. Refer to Exhibit 5-11. The expected value of the random variable x is
Answers
Answer:
The expected value of the random variable x is [tex]E(x) = 5.3[/tex]
Step-by-step explanation:
From the question we are told that
The number of occurance is x
The interval for the x occurance of the event is [tex]t = 10 minutes[/tex]
Generally the expected value is the same as the mean so the expected value the random variable x is
[tex]E(x) = 5.3[/tex]
What is the value of x in the equation 2(6х+4)- 6+ 2х = 3(4х+3) + 12
оооо
Answers
Answer:X= 19/2
Step-by-step explanation:
First to answers gets marked brainliest
Drag the tiles to the correct boxes to complete the pairs. Match each event to the probability of its occurrence. the probability of getting a six when a six-sided die is rolled the probability of randomly picking a vanilla-scented candle from a set of 3 vanilla-scented candles, 8 rose-scented candles, and 10 lavender-scented candles the probability of selecting a girl named Maria to be line leader from a class of 32 girls in which 4 students are named Maria the probability of getting an even number when a six-sided die is rolled
Answers
1/2 : the probability of getting an even number when a six-sided die is rolled.
1/6 : the probability of getting a six when a six-sided die is rolled.
1/7 : the probability of randomly picking a vanilla-scented candle from a set of 3 vanilla-scented candles, 8 rose-scented candles, and 10 lavender-scented candles.
1/8 : the probability of selecting a girl named Maria to be line leader from a class of 32 girls in which 4 students are named Maria.
g In American roulette, the wheel has the 38 numbers, 00, 0, 1, 2, ..., 34, 35, and 36, marked on equally spaced slots. If a player bets $1 on a number and wins, then the player keeps the dollar and receives an additional $35. Otherwise, the dollar is lost. Calculate the expected value for the player to play one time. Round to the nearest cent.
Answers
The expected value for the player to play one time in American roulette is -$0.05. This suggests that, on average, the player can expect to lose $0.05 every time they play the game.
Explanation:The expected value for the player to play one time in American roulette can be calculated by multiplying the probability of winning by the amount the player wins and subtracting the probability of losing. In this case, the probability of winning is 1/38, since there is one winning number out of the 38 possibilities. The amount the player wins is $35. The probability of losing is 37/38, since there are 37 losing numbers out of the 38 possibilities. Using these values, the expected value can be calculated as follows:
Expected value = (1/38 * $35) - (37/38 * $1) = -$0.0526
Rounded to the nearest cent, the expected value is -$0.05. This means that, on average, the player can expect to lose $0.05 every time they play the game.
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The expected value for a player betting on a single number in American roulette is approximately -$0.03, indicating an average loss of 3 cents per play.
The question asks for the calculation of the expected value for a player betting on a single number in American roulette.
To find the expected value, we consider the winnings and the probability of winning.
In American roulette, there are 38 equally spaced slots with the numbers 00, 0, and 1 through 36, which means the probability of winning for a player when betting on a specific number is 1/38, and the probability of losing is 37/38.
The payoff for a win is $35 plus the return of the original $1 bet, for a total of $36. If the bet is lost, the player loses their $1 bet.
Using these payouts and their associated probabilities, we can calculate the expected value (EV) as follows:
→ EV = (Probability of Winning) × (Winning Amount) + (Probability of Losing) × (Loss Amount)
→ EV = (1/38) × $36 - (37/38) × $1
To calculate the exact value:
→ EV = (1/38) × 36 - (37/38) × 1
→ EV ≈ 0.9474 - 0.9737
→ EV ≈ -$0.0263
When rounding to the nearest cent, the expected value is approximately -$0.03. This means, on average, the player will lose about 3 cents per play.
A container contains balls numbered from 1 to 55. A ball is drawn randomly. What is the probability that the first ball is number 9 and the second ball is number 41?
Answers
Answer:
1/55 * 1/55 = 1/3025
Step-by-step explanation:
The probability of 2 consecutive events is:
P(A and B) = P(A) * P(B) - where P(something) is the probability of it
so:
P(picking 9) = 1 possibility out of 55 total, so 1/55
P(picking 41) = 1 possibility out of 55 total, so 1/55
Finally:
P(9 and 41) = 1/55 * 1/55 = 1/3025
The probability of drawing a specific number (e.g. 9) from 55 balls is 1/55. After one ball is drawn, the probability of drawing another specific number (e.g. 41) is 1/54. The total probability of these events happening in sequence is (1/55) * (1/54).
Explanation:This problem falls under the category of probability. Probability is a mathematical way of expressing the likelihood of an event happening, using numbers from 0 (impossible) to 1 (certain).
In this case, the total number of balls is 55. Since the ball is drawn randomly, the probability of drawing any specific number (such as 9) on the first draw is 1/55. Similarly, after the first ball is drawn, there are now 54 balls left in the container, but we're again interested in drawing a specific number (41), so the probability for the second draw is also 1/54.
Our task is to find the joint probability of both these events happening - drawing the 9 first and then the 41. To do that, we multiply the probabilities of the individual events, which means the final answer will be (1/55) * (1/54).
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Is 9/10 greater than 3/20
Answers
Answer:
Yes.
Step-by-step explanation:
9/10 is equal to 18/20, which is evidently greater than 3/20.
-3+(-4) • 5 + 10???? I need help!!!
Answers
Answer:
-13
Step-by-step explanation:
used a calculator ._.
The operator of a beachfront hotel in a tropical island wishes to select a new paint for the hotel’s exterior walls. Three different paints are applied to sample pieces of plywood, then exposed to a heat lamp and sprayed continuously with salt water until the paint begins to peel. Five plywood samples are used for testing each paint. The hours needed in order for the paint to begin to peel are listed below: • Paint A: 25, 27, 28, 28, and 30 hours. • Paint B: 23, 28, 30, 31, and 32 hours. • Paint C: 30, 31, 33, 33, and 37 hours. The hotel operator believes that there is no fundamental difference in longevity/endurance between the three types of paint. Do you agree or disagree? Perform ANOVA to justify your answer.
Answers
Find the given attachment for complete answer and solution
The yearly tuition at lewis college is set at $13,494 for the year maria will graduate, which is a 568% increase from 1995 when her mother graduated from there. How much was tuition when her mother graduated? Round your answer to the nearest dollar
Answers
Answer:
$2375.70
Step-by-step explanation:
5.68x=13,494
x=2375.70
Determine Whether the triangle with the given side lengths is a right triangle
6,8,10
Right Triangle
Not A Right Triangle
Answers
Answer:
Yes, right triangle
Step-by-step explanation:
Since it is a right triangle, we can use Pythagorean Theorem.
a^2+b^2=c^2
a and b are the legs, or shorter sides, and c is the hypotenuse, or the longest side.
We have 3 side lengths: 6, 8 and 10
6 and 8 are the shorter legs, so they are a and b.
10 is the longest leg, so it is c
Substitute the values into the equation, and see if it is true.
6^2+8^2=10^2
Evaluate the exponents
36+64=100
100=100
Since this is a true statement, these sides can make a right triangle.
Find the circumference of a circle with a diameter of 100 feet. Use 3.14 for it (pi).
Answers
Answer: 314
Step-by-step explanation:
3.14 * 100= 314
Answer:
314 feet
Step-by-step explanation:
Circumference of a circle is 2pi*r
Radius = 100/2
Circumference = 2*3.14*50 = 314 feet
A country's balance of payments is divided up into three categories, the
current account, capital account and financial account. The current account
mainly measures
A) the flow of credit.
B) the flow of goods and services.
c) purchases and sales of nonfinancial assets.
D) purchases of sales of stocks and bonds and other financial assets.
Answers
Answer:
B) the flow of goods and services
Step-by-step explanation:
Balance of payments (BOP) is a statement of all transactions made between one country and the rest of the world at a particular period of time. It is also called balance of international payment. BoP is divided into current and capital account.
1. The current account: This is account of country's net trade in goods and services, net earnings on cross-border investments, and its net transfer payments. The current account measures the flow of goods and services.
2. The capital account: This is a country's imports and exports of capital and foreign aid. It can also be called financial account.
The sum of all transactions recorded in the balance of payments should be zero.
Balance of payment deficit is when a country's import is higher than its export.
Balance of payment surplus is when a country's export is greater than its import.
several years ago wolves were reintroduced in to a national park in north carolina in north carolina. Researchers have monitored the populations over the last severals years and the per capita growth rate of the population is .5. If the current population size is 100, what equation would you use to determine how large the population will be in ten years
Answers
Answer: [tex]5766.503\ \text{wolves}[/tex]
Step-by-step explanation:
Given
Current Population of wolves is [tex]P_o=100[/tex]
If the growth rate is [tex]=0.5[/tex]
So the population in next year is
[tex]P_1=100+100\times 0.5[/tex]
[tex]P_1=100(1+0.5)[/tex]
similarly [tex]P_2=100(1+0.5)^2[/tex]
So population after n years is [tex]P_n=P_o(1+r)^n[/tex]
Population after 10 years is
[tex]P_{10}=100(1+0.5)^{10}[/tex]
[tex]P_{10}=5766.503\ \text{wolves}[/tex]
Chase and his brother like to play basketball. About a month ago they decided to keep track of how many games they have each won. As of today, Chase has won 18 out of 30 games against his brother
How many games would Chase have to win in a row in order to have a 75% winning record? Chase would have to win _________ games in a row to have a 75% winning record. How many games would Chase have to win in a row in order to have a 90% winning record? Chase would have to win _________ games in a row to have a 90% winning record. Is Chase able to reach a 100% winning record? Chase (is or isn’t) able to reach a 100% winning record because ________________.
Suppose that after reaching a winning record of 90 in part 2, Chase has a losing streak. How many games in a row would Chase have to lose in order to drop down to a winning record below 55% again?
Chase would have to lose _______ games in order to drop down to a winning
Answers
Answer:
Step-by-step explanation:
As of today, Chase has won 18 out of 30 games against his brother. The percentage of games that he has won as of today is
18/30 × 100 = 60%
In order to get 75% wins, let the number of games would be x. Then
(18 + x)/(30 + x) × 100 = 75
100(18 + x) = 75(30 + x)
1800 + 100x = 2250 + 75x
100x - 75x = 2250 - 1800
25x = 450
x = 450/25 = 18
chase has to win 18 games in a row.
In order to get 90% wins, let the number of games would be y. Then
(18 + x)/(30 + x) × 100 = 90
100(18 + x) = 90(30 + x)
1800 + 100x = 2700 + 75x
100x - 75x = 2700 - 1800
25x = 900
x = 900/25 = 36
chase has to win 36 games in a row in order to have a 90% winning record.
(18 + x)/(30 + x) × 100 = 100
100(1800 + x) = 100(30 + x)
1800 + 100x = 3000 + 100x
100x - 100x = 3000 - 1800
Therefore, it is impossible to for chase to reach a 100% winning record because he has already had some losses.
2) for a wining record of 90, the total number of games played is
30 + 36 = 66 games and the total number of wins was 18 + 36 = 54
In order to get 55% losses, let the number of games would be z. Then
(54 + z)/(66 + z) × 100 = 55
100(54 + z) = 55(66 + z)
5400 + 100z = 3630 + 55z
100z - 55z = 3630 - 5400
45z = - 1770
z = - 1770/45 = - 40
chase has to lose 40 games in a row in order to drop down to a winning record below 55% again.
Chase would need to win 6 more games for a 75% win record, 108 more games for a 90% win record. He could never achieve a 100% win record due to past losses. If he reached a 90% win record and then lost, he would need to lose 20 games to drop below a 55% record.
Explanation:To calculate how many games Chase needs to win to achieve a 75% winning record, a solution is needed for the equation (18 + x) / (30 + x) = 0.75, where x represents the additional games won. The solution is x = 6. Therefore, Chase must win an additional 6 games without losing to reach a 75% win record.
For a 90% winning record, we solve the equation (18 + x) / (30 + x) = 0.9. The solution is x = 108. Therefore, Chase must win an additional 108 games without losing to reach a 90% winning record.
Chase is unable to reach a 100% winning record because he has already lost some games and it isn't possible to change those past results.
In the event that Chase reaches a 90% winning record and then begins to lose, we need to find out the number of games he would need to lose to drop to a win rate below 55%. We can solve this by calculating the equation (126) / (138 + y) = 0.55, where y is the lost games. Solving for y, we get y = 20, so Chase would have to lose 20 games in a row.
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(3 + 5) * 2Y = (5 * 8) - (2 * 4). What does Y equal?
Answers
Answer:
pretty sure y should equal 15
The solution of the linear equation (3 + 5) × 2Y = (5 × 8) - (2 × 4) will be 2.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given below.
(3 + 5) × 2Y = (5 × 8) - (2 × 4)
Simplify the equation, then the value of the variable y will be
8 × 2Y = 40 - 8
16Y = 32
Y = 32 / 16
Y = 2
The solution of the linear equation (3 + 5) × 2Y = (5 × 8) - (2 × 4) will be 2.
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A trampoline has a diameter of 10ft. What is it’s area ?
Answers
Answer: 78.5 feet squared for short answer
Step-by-step explanation:
If the diameter is 10 feet, then the radius is half of that, or 5 feet. feet squared is the EXACT answer, and we surely didn't need a calulator for this one. However, a real world answer is probably more appropriate if you were trying to measure the area. So the area of our trampoline is about 78.5 feet squared.
Answer:
78.54 square feet
Step-by-step explanation:
The formula to find the area of a circle is πr², and since we know the diameter is 10 ft we know the radius is 5 feet, so π5²=78.54
The average age of online consumers a few years ago was 24.1 years. As older individuals gain confidence with the Internet, it is believed that the average age has increased. We would like to test this belief. Answer parts a) through e) below. a) Write the appropriate hypotheses. Choose the correct answer below. A. Upper H 0 : mugreater than24.1 years Upper H Subscript Upper A Baseline : muequals24.1 years B. Upper H 0 : muless than24.1 years Upper H Subscript Upper A Baseline : muequals24.1 years C. Upper H 0 : muequals24.1 years Upper H Subscript Upper A Baseline : mugreater than24.1 years D. Upper H 0 : muequals24.1 years Upper H Subscript Upper A Baseline : muless than24.1 years
Answers
Answer:
The correct option is (C).
Step-by-step explanation:
A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.
It is a hypothesis of no difference.
It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.
Whereas the alternative hypothesis is a contradicting statement tot he null hypothesis. It is denoted by Hₐ.
In this case we need to test whether the average age of online consumers has increased or not.
From previous data we know that the average age of online consumers a few years ago was 24.1 years.
A one-sample mean test can be used to determine whether the mean age has increased or not.
The hypothesis for the test can be defined as follows:
H₀: The average age of online consumers is 24.1 years, i.e. μ = 24.1.
Hₐ: The average age of online consumers is more than 24.1 years, i.e. μ > 24.1.
Thus, the correct option is (C).
So much dance class is 3 miles away from her home her music class is 12 miles away from her home right now equation that shows the number of times farther so with music class is from her home then the dance class from her home
Answers
The music class is 4 times farther from her home than the dance class.
Explanation:To find the number of times farther the music class is from her home than the dance class, we first need to determine the distance of each class from her home. The dance class is 3 miles away, and the music class is 12 miles away. To get the ratio of these distances, we divide the distance to the music class by the distance to the dance class. Therefore, the equation that represents the number of times farther the music class is from her home is:
12 miles / 3 miles = 4
So, the music class is 4 times farther from her home than the dance class.
An ice cream machine produced 52 ice creams per minute. After reconditioning, its speed increased to 65 ice creams per minute. By what percent did the speed of the machine increase?
Answers
Answer:25 %
Step-by-step explanation:
Given
Earlier machine was producing 52 ice cream per minute and
Now it is Producing 65 ice creams per minute
So percentage increase of the machine [tex]=\frac{\text{final-Initial}}{\text{Initial}}\times 100[/tex]
[tex]=\frac{65-52}{52}\times 100[/tex]
[tex]=\frac{13}{52}\times 100[/tex]
[tex]=\frac{1}{4}\times 100=25\ \%[/tex]
So there is increase of 25 % in speed
given U=-7i - 5j and V= -6i - 4j find U + V
Answers
Answer:
u+v= -13i-9j
Step-by-step explanation:
u=-7i - 5j and v= -6i - 4j
u+v=-7i-5j+(-6i-4j)=-7i-5j-6i-4j
u+v=-13i-9j
Answer:
U + V= i-9j
Step-by-step explanation:
hello :
U=-7i - 5j and V= -6i - 4j so : U + V=(7i-6i)+(-5j-4j)
U + V= i-9j
En una granja hay 500 animales. Si hay el triple de vacas que de ovejas, ¿ cuantas animales hay de cada especie
Answers
Answer:
Hay 375 vacas y 125 ovejas
Step-by-step explanation:
Para resolver este problema simplemente tenemos que plantear una igualdad entre vacas y ovejas
b = oveja
v = vaca
v = 3b
b + v = 500
reemplazamos la b por (3v) en la segunda ecuacion
b + v = 500
b + 3b = 500
4b = 500
b = 500/4
b = 125
reemplazamos este valor en la primer ecuacion
v = 3b
v = 3(125)
v = 375
Hay 375 vacas y 125 ovejas
A toy car can go 5 mph. How long would it take to go 7 miles?
Answers
Answer:
by the way what grade are you in? If you are more than 7th grade can you help me? https://brainly.com/question/16233847
35 mph
Step-by-step explanation:
7 times 5
which type of graph would you use to show the number of water bottles sold at four different stores and water bottles come in packs of 20
Answers
Answer:
pictograph
Step-by-step explanation:
i got it right :) so yeah trust me
Which number line models the expression 1/8-(-3/4)
Answers
The number line to model the expression 1/8 - (-3/4) would start at 1/8, and move 6/8 steps to the right to reach 7/8 because subtracting a negative is the same as adding a positive.
Explanation:To solve the mathematical expression 1/8 - (-3/4), we need to understand that subtracting a negative number is equivalent to adding a positive number. Hence, we rewrite the expression as 1/8 + 3/4.
Before you can add these two fractions, they must have a common denominator. The least common denominator (LCD) for 8 and 4 is 8, so we rewrite 3/4 as 6/8 to match the denominator of 1/8.
Now, you can add 1/8 + 6/8 to get 7/8.
A number line that models this expression would start at 1/8 and go forward 6/8 (equivalent to 3/4) steps to end at 7/8.
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To model the expression 1/8 - (-3/4) on a number line, you would first convert the expression to 1/8 + 3/4 by changing the minus negative to a plus. Then, find a common denominator and add the fractions to get 7/8. This result is represented on a number line by starting at 1/8 and moving right to reach 7/8.
Explanation:To model the expression 1/8 - (-3/4) on a number line, we need to understand that subtracting a negative is the same as adding its positive counterpart. Therefore, the expression simplifies to 1/8 + 3/4. To add these fractions together, they must have a common denominator. The least common denominator for 8 and 4 is 8. So, we convert 3/4 to 6/8, since 3 multiplied by 2 gives us 6, and 4 multiplied by 2 gives us 8. Adding 1/8 to 6/8 gives us 7/8.
On a number line, we would start at the point representing 1/8 and then move to the right by 6/8 (which represents 3/4) to arrive at 7/8. This portrays the answer to our initial expression, 1/8 - (-3/4) = 7/8.
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A high-profile consulting company chooses its new entry-level employees from a pool of recent college graduates using a five-step interview process. Unfortunately, there are usually more candidates who complete the interview process than the number of new positions that are available. As a result, cumulative GPA is used as a tie-breaker. GPAs for the successful interviewees are Normally distributed, with a mean of 3.3 and a standard deviation of 0.4. What percent of candidates have a GPA above 3.9?
Answers
Answer:
Only 0.0668 of the candidates, or 6.68%, have a GPA above 3.9.
Step-by-step explanation:
The GPA, according to the question, is a random variable normally distributed. A normal distribution is determined by its parameters. These parameters are the population mean, [tex] \\ \mu[/tex], and the population standard deviation, [tex] \\ \sigma[/tex]. The normal distribution for GPA has a [tex] \\ \mu = 3.3[/tex], and [tex] \\ \sigma = 0.4[/tex].
To find probabilities related to normally distributed data, we can use the standard normal distribution. To use it, we first need to find the corresponding standardized score or z-score for the value we want to obtain the probability. This value, in this case, is x = 3.9. The related z-score or standardized value is given by the formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
A z-score tells us the distance from the mean in standard deviations units. A negative value indicates that the value is below the mean. A positive value is, conversely, above the mean.
And we already have all the necessary data to use [1].
Thus
[tex] \\ z = \frac{3.9 - 3.3}{0.4}[/tex]
[tex] \\ z = \frac{0.6}{0.4}[/tex]
[tex] \\ z = 1.5[/tex]
This value for z tells us that the "equivalent" raw score, x = 3.9, is above the mean, and it is at 1.5 standard deviations units from the population mean.
We can find the probabilities for standardized values in the cumulative standard normal table, available on the Internet or in Statistic books (we can also use statistical packages or even spreadsheets).
To use the cumulative standard normal table, we have the z-score as an entry. With this value, we find the z column on this table, and, since it is z = 1.5, we only need to select the first column (which has two decimal places, that is, .00). Then, the cumulative probability for P(z<1.50) = 0.9332.
However, we are asked for the percent of candidates that have a GPA above 3.9 (z-score = 1.50). This probability is the complement of P(z<1.50) or 1 - P(z<1.50). Mathematically
[tex] \\ P(z<3.9) + P(z>3.9) = 1[/tex]
[tex] \\ P(z<1.50) + P(z>1.50) = 1[/tex] (standardized)
[tex] \\ P(z>1.50) = 1 - P(z<1.50)[/tex]
[tex] \\ P(z>1.50) = 1 - 0.9332[/tex]
[tex] \\ P(z>1.50) = 0.0668[/tex]
That is, only 0.0668 of the candidates, or 6.68%, have a GPA above 3.9.
We can see this probability in the graph below.