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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A researcher has collected the following sample data. The mean of the sample below is 5.
3 , 5 , 12 , 3 , 2
Find the coefficient of variation
Answer:
The coefficient of variation is 72.66%
Step-by-step explanation:
Data : 3 , 5 , 12 , 3 , 2
We are given that The mean of the sample is 5.
Formula of standard deviation =[tex]\sigma = \sqrt{\frac{\sum(x-\bar{x})^2}{n}[/tex]
Substitute the values :
[tex]\sigma = \sqrt{\frac{(3-5)^2+(5-5)^2+(12-5)^2+(3-5)^2+(2-5)^2}{5}}=3.633[/tex]
Coefficient of variation=[tex]\frac{\sigma}{\mu} \times 100=\frac{3.633}{5} \times 100 =72.66\%[/tex]
Hence The coefficient of variation is 72.66%
The coefficient of variation of the data set, 3 , 5 , 12 , 3 , 2, is: 72.7%
Recall:
Coefficient of variation = Standard deviation / mean x 100%Given, the following data:
3 , 5 , 12 , 3 , 2Mean is given as: 5We are not given the standard deviation.
First, find the standard deviation of the data set, using the formula, [tex]\mathbf{SD = \sqrt{\frac{\sum (x - \bar{x}) }{n} } }[/tex]
Thus:SD = [tex]\sqrt{\frac{66}{5} } = \sqrt{13.2}[/tex]
SD = 3.633
Next, find the coefficient of variation:
Cov. = 3.633/5 x 100 = 72.7%
Therefore, the coefficient of variation of the data set, 3 , 5 , 12 , 3 , 2, is: 72.7%
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You fill an aquarium with water. The water is 22 inches deep. The water evaporates at a rate of 2 inches per week. a. Write an equation that approximates the depth y of water in the aquarium c weeks after you fill it. b. After two weeks, you have not yet refilled the aquarium. What is the depth of the water?
The equation for water depth in the aquarium after evaporation is y = 22 - 2c.
a. Equation: The equation approximating the depth y of water in the aquarium c weeks after filling it is y = 22 - 2c.
b. Depth after Two Weeks: Substitute c = 2 into the equation, y = 22 - 2(2) = 18 inches.
What is the volume of the prism?
in.3.
I need help
Answer:
18
Step-by-step explanation:
Answer: V ≈ 18
Step-by-step explanation: To get the volume of a prism, we have to follow the method. We have to use V = L * H * W.
First, let's turn 2 [tex]\frac{1}{4}[/tex] into a decimal.
We must divide the numerator by the denominator using long division.
1 ÷ 4 = 0.25 = 2.25
Now, let's use V = L * H * W.
2.25 * 4 = 9 * 2 = 18
The volume is 18, I hope this helps!
The sum of 20.7 and a number is 50.5. Which equation could you use to solve the problem? What should you do to each side of the equation to isolate the variable? What is the solution of the equation?
Answer:
Which equation could you use to solve the problem?
✔ g + 20.7 = 50.5
What should you do to each side of the equation to isolate the variable?
✔ Subtract 20.7 from each side.
What is the solution of the equation?
✔ 29.8
Step-by-step explanation:
An equation that could be used to solve this word problem is 20.7 + x = 50.5.
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
In order to solve this word problem, we would assign a variable (x) to the unknown number and then translate the word problem into algebraic equation as follows:
20.7 + x = 50.5
Subtract 20.7 from each side:
20.7 - 20.7 + x = 50.5 - 20.7
x = 50.5 - 20.7
x = 29.8.
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Can someone help me ...
100 POINTS.
PLEASE PROVIDE STEPS
Step-by-step explanation:
12 ∫ (cot⁴(3x) csc²(3x)) dx
If u = cot(3x), then du = -3 csc²(3x) dx. So -⅓ du = csc²(3x) dx.
12 ∫ u⁴ (-⅓ du)
-4 ∫ u⁴ du
-⅘ u⁵ + C
Substituting back:
-⅘ cot⁵(3x) + C
Evaluate between x=0 and x=π/12. cot(0) is undefined, so the integral does not exist.
Answer:
12 ∫ (cot⁴(3x) csc²(3x)) dx
If u = cot(3x), then du = -3 csc²(3x) dx. So -⅓ du = csc²(3x) dx.
12 ∫ u⁴ (-⅓ du)
-4 ∫ u⁴ du
-⅘ u⁵ + C
Substituting back:
-⅘ cot⁵(3x) + C
Evaluate between x=0 and x=π/12. cot(0) is undefined, so the integral does not exist.
Step-by-step explanation:
On one day a Plumber Joe earned $80 on a plumbing job. Out of his earnings he spent $6.85 on tea and snacks, $5.50 on food and $21.40 on tools. Before reaching home that evening his boss sent Plumber Joe $22 on "cash app", which his boss said was a tip from his early morning plumbing job. How much did he save on that day?
Answer:
Joe saved 68.25
Step-by-step explanation:
Subtract 6.85 from 80, you get 73.15
Subtract 5.50 from 73.15 and you get 67.65.
Subtract 21.40 from 67.65 and you get 46.25.
Add 22 to that amount, you get 68.25.
P.S
Have an Amazing Day! I Hope this Helps and Good Luck!!
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Algal blooms can have negative effects on an ecosystem by dominating its phytoplankton communities. Gonyostomum semen is a nuisance alga infesting many parts of northern Europe. Could the overall biomass of G. semen be controlled by grazing zooplankton species? A research team examined the relationship between the net growth rate of G. semen and the number of Daphnia magna grazers introduced in test tubes. Net growth rate was computed by comparing the initial and final abundance of G. semen in the experiment, with a negative value indicative of a decrease in abundance. Here are the findings:Number of D. magna grazers 1 2 3 4 5 6Net growth rate of G. semen −1.9 −2.5 −2.2 −3.9 −4.1 −4.3Using the above information, software tells us that the least-squares slope is b = −0.5286 with standard error SEb = 0.1059.(a) What is the t statistic for testing H0: β = 0? (Round your answer to two decimal places.)t = (b) How many degrees of freedom does t have?df = Use this table to approximate the P-value of t against the one-sided alternative Ha: β > 0 (as the grazers would be expected to reduce algal growth).0.001 < P < 0.00250.0025 < P < 0.005 0.005 < P < 0.0100.010 < P < 0.0200.020 < P < 0.025(c) What do you conclude? (Use α = 0.05.)There is strong evidence that the population slope β is negative.There is not enough evidence to conclude that the population slope β is negative.
Answer:
Step-by-step explanation:
Hello!
To study if the biomass of Gonyostomum semen can be controlled by grazing zooplankton species the research team examined the relationship between:
Y: Net grow rate of G. semen in a test tube.
X: Number of D. magna grazers introduced in test tubes.
Since they are testing the relationship between two variables, i.e. how one variable affects the other, the researchers made a linear regression analysis and estimated the slope of the regression:
The point estimate of the slope: b= -0.5286
Standard deviation of the slope: Sb= 0.1059
n= 6 test tubes.
a)
For the hypotheses:
H₀: β = 0
H₁: β ≠ 0
The formula for the t-statistic is:
b)
The statistic has n-2 degrees of freedom.
So in this case you are working with a Student's t with 6-2= 4 degrees of freedom.
c)
Considering a one-sided alternative hypothesis H₁: β > 0, the calculated value of the statistic under the null hypothesis doesn't change, what change is the direction and size of the rejection region. In item a, the hypotheses had a two-tailed rejection region, for this item the rejection region is one-tailed to the right. This means that you'll reject at hight values of the statistic. The p-value is also one-tailed and you'll find it in the right tail of the distribution (That's why it's positive):
P(t₄≥4.99)= 1 - P(t₄<4.99)
Looking at the t-table. For this distribution, the value of 4.99 is between the t values that accumulate P(t₄<4.604)= 0.995 and P(t₄<7.173)= 0.999 of probability, so it will be between:
1 - 0.995= 0.005
and
1 - 0.999= 0.001
Using the given table and considering the value is closer to 4.064 than 7.173, the p-value will be approximate:
0.00025 < P < 0.005
The p-value is less than the significance level, α: 0.05, so the decision is to reject the null hypothesis. You can conclude that the population slope is not negative (β > 0)
⇒There is not enough evidence to conclude that the population slope β is negative.
I hope you have a SUPER day!
The answers are: a) The t statistic is approximately -4.99. b) the degrees of freedom are 4. c) There is strong evidence that the population slope β is negative.
(a) The t statistic for testing the null hypothesis H0: β = 0 is calculated using the formula:
t = (b - 0) / SEb
Where:
b = slope coefficient = -0.5286
SEb = standard error of the slope coefficient = 0.1059
Substitute the values into the formula:
t = (-0.5286 - 0) / 0.1059 ≈ -4.99
So, the t statistic is approximately -4.99.
(b) The degrees of freedom for the t statistic can be calculated using the formula:
df = n - 2
Where n is the number of data points, which is the number of observations (in this case, the number of Daphnia grazers), minus 2 for the two estimated coefficients (intercept and slope).
Given that there are 6 data points:
df = 6 - 2 = 4
So, the degrees of freedom are 4.
we see that the P-value falls between 0.001 and 0.0025. Therefore, we can approximate the P-value as:
0.001 < P < 0.0025
(c) Using α = 0.05 as the significance level, we compare the P-value to α. Since the P-value is less than α (0.0025 < 0.05), we reject the null hypothesis.
Therefore, the conclusion is: There is strong evidence that the population slope β is negative. In other words, based on the provided data and statistical analysis, it can be concluded that there is strong evidence that an increase in the number of Daphnia magna grazers is associated with a decrease in the net growth rate of Gonyostomum semen, indicating that the grazers are likely reducing the algal growth.
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Is 3 a solution for -3(x-7+2)=16? If not, find at least one solution
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
x= -1/3
Decimal Form:
x= -0.3 repeating
Brainliest?
Answer:wym by soulution?
Step-by-step explanation:
which of the functions below have period pi? check all that apply
The functions that actually have period pi are:
B. y = csc x
C. y = sec x
Let's understand what the period of a function is all about.
What is period of a function?Period of a function is known to be the distance that exists between the repetition of any function. In trigonometry, the length of a complete cycle is known as a period.
So, we can see that the functions that actually have period pi are y = csc x and y = sec x.
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Answer:
Step-by-step explanation:
each shape is divided into equal parts. select the shapes that show thirds. mark all that apply
Answer:
Triangle,Circle,Square, 3 cubes
Step-by-step explanation:
what is equivalent to 601/2
Answer:
as a mixed number: 300 1/2 (reduced or equivalent)
as a decimal: 300.5 (reduced or equivalent)
as a percentage: 30,050% (reduced or equivalent)
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
im smart
Which of the following choices is equivalent to 1 + 8(2x + 3)?
16x + 12
10x + 12
16x + 25
10x + 25
Answer:
16x + 25
Step-by-step explanation:
First, distribute the 8 to both numbers within the parenthesis.
1 + 16x + 24
Then, add similar terms together.
16x + 25
Final answer:
To simplify the expression 1 + 8(2x + 3), distribute the 8 across the terms inside the parentheses, leading to the equivalent expression 16x + 25 that is option C is correct.
Explanation:
To simplify 1 + 8(2x + 3), we distribute the 8:
1 + 8(2x) + 8(3)
1 + 16x + 24
16x + 25
What is the volume of a prism with base 32inches squared and height of 8
Answer:
V =256 in^3
Step-by-step explanation:
The volume of a prism is given by
V = Bh where B is the area of a base and h is the height
V = 32 * 8
V =256 in^3
A circle has a radius of 5. An arc of 162 degrees. What is the length of the arc?
Answer:
242
Step-by-step explanation:
Answer:
14.14 units
Step-by-step explanation:
Klan Academy- I checked and it was correct.
Determine whether the data described below are qualitative or quantitative and explain why. The postal codes of survey respondents Choose the correct answer below. A. The data are quantitative because they consist of counts or measurements. B. The data are quantitative because they don't measure or count anything. C. The data are qualitative because they don't measure or count anything. D. The data are qualitative because they consist of counts or measurements.
Answer:
C
Step-by-step explanation:
Postal code numbers are qualitative data because on these numbers, we can't perform any calculations.
The data are qualitative because they don't measure or count anything.
The correct option is C.
What is qualitative data?
Information that cannot be quantified, tallied, or simply stated using numbers is referred to as qualitative data.
Given:
The postal codes of survey respondents.
Here, no numbers are given.
Data visualization technologies like word clouds, idea maps, graph databases, timelines, and infographics are used to communicate the information that is gathered from text, audio, and visual sources.
And the data can not be calculated.
Therefore, Postal code numbers are qualitative data.
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Point A is at (3,-8) and point M is at (5,-2.5).
Point M is the midpoint of point A and point B.
What are the coordinates of point B?
Answer:
B(7, 3)
Step-by-step explanation:
The formula for the unknown endpoint is ...
B = 2M -A
B = 2(5, -2.5) -(3, -8) = (2·5 -3, 2(-2.5)+8)
B = (7, 3)
Answer:
b 7,3
Step-by-step explanation:
When calculating the successive discounts of 15% and 10% on a $100 item,
а. take 10% of $85
b. take 10% of $90
C. take 15% of $85
d. take 25% of $100
Answer:
A. Take 10% of $85
Step-by-step explanation:
Taking away 15% from $100 leaves you with $85 to take the second discount away from (10%)
For what values of x is x2-36=5x true?
A. -9 and -4
B. -4 and 9
C. 4 and -9
D. 9 and 4
Answer:
B. -4 and 9
Step-by-step explanation:
First, you want to get the equation to equal 0.
[tex]x^{2} - 36 = 5x[/tex] subtract 5x from both sides to make the equation equal to 0.
[tex]x^{2} -5x - 36 =0[/tex]
Now you are going to want to factor the equation
Find factors that add up to 5
[tex](x+4)(x-9)[/tex] I used 4 and 9 because they multiply to be 36, since 36 is negative that means that one of the numbers has to be negative. I made 9 negative because when you add 4 it equals 5.
Make both equations equal to 0
[tex]x+4=0[/tex]
[tex]-4[/tex] [tex]-4[/tex] subtract 4 from both sides to get x alone
[tex]x = -4[/tex]
[tex]x-9=0[/tex]
[tex]+9[/tex] [tex]+9[/tex] add 9 to both sides to get x alone
[tex]x=9[/tex]
Answer:
B. -4 and 9
Step-by-step explanation:
move the 5x over and factor to get (x-9)(x+4)=0, set both of the expressions equal to zero, and solve, pretty much you just fator and flip the signs. Hope this helps!
A group of 4 people share 1/2 pounds of almonds how many pounds of almonds does each person get choose an equation you can use to answer the question
Answer:
1/2 x 1/4=1/8
Step-by-step explanation:
For every truck a police officer encounters she writes down T, for every car C, for every van V, and for every vehicle that is not a car, truck or van O (for "other"). Estimate the probability that the next vehicle the police officer encounters is not a car, truck, or van.
T T T C V O O V C T T C C C C C C V O
Answer:
5 = T
8 = C
3 = V
3 = O
which means its other because it said it is not a car, truck or van so its other meaning O
O = other
Answer: O
Step-by-step explanation: Theirs really nothing to it just pay attention to the hint :)
Answer:
3/19
Step-by-step explanation:
Gradpoint
Which hypotheses are being tested by the chi-square test? The distribution of gender is different for the three different goals. The null hypothesis is that the most important goal is the same for each gender, and the alternative is that the means differ. The distribution of most important goals is different for men and women. The null hypothesis is that the most important goal and gender are independent, and the alternative is that they are dependent.
Answer:
The null hypothesis is that the most important goal and gender are independent, and the alternative is that they are dependent.
Step-by-step explanation:
Chi Square test is used to test relationship between categorical (nominal) variables of a population. Eg : Testing men & women for any attribute, lets say empathy
Null Hypothesis states that there is no relationship between the attribute & categorical variable, they are independent.Alternate Hypothesis states that there is relationship between the attribute & categorical variable, they are dependent.Eg : Null hypothesis states that there is no difference of empathy level in men & women. Alternate Hypothesis states that there is difference of empathy level in men & women.
A hotel installs smoke detectors with adjustable sensitivity in all public guest rooms. (a) State the null and alternative hypotheses. There is no fire There is a fire (b) Define Type I and II errors. A smoke detector sounds an alarm when there is no fire A smoke detector does not sound an alarm when there is a fire (c) In this case, which type of error has the more severe consequences
Answer:
(a) H₀: There is no fire vs. Hₐ: There is a fire.
(b) A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).
(c) In this case, type II error has the more severe consequences.
Step-by-step explanation:
It is provided that a hotel installs smoke detectors with adjustable sensitivity in all public guest rooms.
(a)
The hypothesis can be defined as follows:
H₀: There is no fire.
Hₐ: There is a fire.
(b)
A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).
In this case a type I error will be committed if we conclude that there is a fire and the smoke detector sounds an alarm, when in fact there is no fire.
In this case a type II error will be committed if we conclude that there is no fire and the smoke detector does not sounds an alarm, when in fact there is a fire.
(c)
In this case, type II error has the more severe consequences.
Concluding that there is no fire as the smoke detector did not sound an alarm, when in fact there is a fire, will cause casualties and is harmful for the health of the guests.
Guests would not be alert about the fire as there was not any alarm, and many may loose their lives because of this.
The null hypothesis is 'There is no fire', the alternative hypothesis is 'There is a fire'. A Type I error would be sounding an alarm when there is no fire (rejecting the null hypothesis when it is true), a Type II error would be not sounding an alarm when there is a fire (failing to reject the null hypothesis when it is false). The more severe consequence would be due to a Type II error, as it could result in unrecognized danger.
Explanation:In this scenario, the null hypothesis would be 'There is no fire' and the alternative hypothesis would be 'There is a fire'. In terms of type I and II errors, a Type I error would occur if the smoke detector sounded an alarm when there is no fire, or in other words, rejecting the null hypothesis when it is in fact true. A Type II error would occur if the smoke detector does not sound an alarm when there is a fire, meaning failing to reject the null hypothesis when it is in fact false.
Considering the consequences of these errors, a Type II error would be more severe in this scenario, as it could lead to a serious danger not being recognized, potentially resulting in damage or harm.
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One conveyor belt can move 1000 boxes in 9 minutes. Another can move 1000 boxes in 11 minutes. If another conveyor belt is added and all three are used, the boxes are moved in 3 minutes. How long would it take the third conveyor belt alone to do the same job?
Answer:
It would take 7.62 minutes for the third conveyor belt alone to do the same job
Step-by-step explanation:
The together rate is the sum of each separate rate.
In this question:
First conveyor: Rate of 1/9.
Second: Rate of 1/11.
Third: Rate of 1/x.
Total: 1/3
So
[tex]\frac{1}{9} + \frac{1}{11} + \frac{1}{x} = \frac{1}{3}[/tex]
[tex]\frac{11x + 9x + 99}{99x} = \frac{1}{3}[/tex]
[tex]\frac{20x + 99}{99x} = \frac{1}{3}[/tex]
[tex]3(20x + 99) = 99x[/tex]
[tex]60x + 297 = 99x[/tex]
[tex]39x = 297[/tex]
[tex]x = \frac{297}{39}[/tex]
[tex]x = 7.62[/tex]
It would take 7.62 minutes for the third conveyor belt alone to do the same job
In a random sample of 7 residents of the state of California, the mean waste recycled per person per day was 1.5 pounds with a standard deviation of 0.58 pounds. Determine the 99% confidence interval for the mean waste recycled per person per day for the population of California. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
CI(99%) = ( 0.93 , 2.07)
Therefore at 99% confidence interval (a,b) = ( 0.93 , 2.07)
Critical value z(at 99% confidence) = z(0.005) = 2.58
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean gain x = 1.5
Standard deviation r = 0.58
Number of samples n = 7
Confidence interval = 99%
Critical value z(at 99% confidence) = z((1-0.99)/2)
z(0.005) = 2.58
Substituting the values we have;
1.5+/-2.58(0.58/√7)
1.5+/-2.58(0.2192)
1.5+/-0.565536
1.5+/-0.57
= ( 0.93 , 2.07)
Therefore at 99% confidence interval (a,b) = ( 0.93 , 2.07)
"We keep tossing a fair coin n = 10^6 million times, write down the outcomes: it gives a Heads-and-Tails-sequence of length n. We call an integer i special, if the i, i + 1, i + 2, i + 3, . . . , i + 18-th elements of the sequence are all Heads. That is, we have a block of 19 consecutive Heads starting with the i-th element of the sequence. Let X denote the number of special integers i. What is the expected value of X? I also want the numerical value. 5. We rand
Answer:
Check the explanation
Step-by-step explanation:
Let [tex]X_{i}[/tex] be the indicator random variable that takes the value 1 if the ith coin is the first coin in a sequence of 19 consecutive heads.
For any sequence of length 19, the starting coin can be from toss i ,
such that i is between 1 and n - 19+1
Thus the number of such sequences is
Kindly check the attached image below for the step by step explanation to the question above.
Mary made $1,850 last month. A 25% deduction was subtracted from her pay. What was her deduction?
Answer:$462.50
Step-by-step explanation:multiply $1,850 by .25 to get your answear
Triangle ABC has vertices at A(-5, 4), B(4, 1), and C(1, -8). Choose the terms below which correctly describe this triangle:
Answer:
An ISOSCELES TRIANGLE
Step-by-step explanation:
Given a triangle ABC with vertices at A(-5, 4), B(4, 1), and C(1, -8), to know the type of triangle this is, we need to find the three sides of the triangles by taking the distance between the points.
Distance between two points is expressed as:
D = √(x2-x1)²+(y2-y1)²
For side |AB|:
A(-5, 4) and B(4, 1)
|AB| = √(4-(-5))²+(1-4)²
|AB| = √9²+3²
|AB| = √90
For side |BC|
B(4, 1), and C(1, -8)
|BC| =√(1-4)²+(-8-1)²
|BC| = √3²+9²
|BC| = √90
For side |AC|:
A(-5, 4) and C(1, -8).
|AC| = √(1-(-5))²+(-8-4)²
|AC| = √6²+12²
|AC| = √36+144
|AC| = √180
Based on the distances, it is seen that side AB and BC are equal which shows that two sides of the triangle are equal. A triangle that has two of its sides to be equal is known as an ISOSCELES TRIANGLE. Therefore the term that correctly describes the triangle is an isosceles triangle.
How many times can a 9/2 yard line be divided into 3- inch segment?
a.45 times
b.54 times
c.64 times
d.84 times
Answer:
54 times
Step-by-step explanation:
1 yard = 3 feet
[tex]9/2 * 3 = 27/2 ft = 13.5 ft[/tex]
1 ft = 12 inches
[tex]13.5*12=162[/tex] inches
162 / 3 = 54 times
B is the answer.
Find the sum of the first 10 terms if a(n) = n^2 - n +1
Answer:
The formula to find the sum of the first n terms of our sequence is n divided by 2 times the sum of twice the beginning term, a, and the product of d, the common difference, and n minus 1. The n stands for the number of terms we are adding together.