Answer: 4/25
Step-by-step explanation:
Please help with this question!!?
Answer:
6 seconds
Step-by-step explanation:
The ball will hit the ground when its height is 0, so you can plug this into the equation to find your answer.
-16t^2+96t=0
Factoring out -16t, you get:
-16t(t-6), meaning that the solutions are 0 and 6 seconds. Since 0 is the starting point, the answer is 6 seconds. Hope this helps!
According to the Bureau of Labor Statistics it takes an average of 22 weeks for someone over 55 to find a new job. Assume that the probability distribution is normal and that the standard deviation is two weeks. What is the probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job
Answer:
The probability that eight workers over the age of 55 will take an average of more than 20 weeks to find a job is 0.9977 or 99.77%
Step-by-step explanation:
Average time to find a new job for someone over 55 years = μ = 22 weeks
Standard deviation = σ = 2 weeks
We have to find the probability that if 8 workers are selected at random what will be the probability that it will take them more than 20 weeks to find a job. So, this means that the sample size is n = 8.
Since, the distribution is normal and we have the value of population standard deviation, we will use the z-distribution to find the desired probability. For this, first we need to convert the value (20 weeks) to its equivalent z-score. The formula to calculate the z-score is:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
x = 20, converted to z-score will be:
[tex]z=\frac{20-22}{\frac{2}{\sqrt{8}}}=-2.83[/tex]
Thus, probability of time being greater than 20 weeks is equivalent to probability of z score being greater than - 2.83.
i.e.
P( X > 20 ) = P( z > -2.83 )
Using the z-table we can find this probability:
P( z > -2.83 ) = 1 - P( z < -2.83)
= 1 - 0.0023
= 0.9977
Since, P( X > 20 ) = P( z > -2.83 ), we can conclude that:
The probability that eight workers over the age of 55 will take an average of more than 20 weeks to find a job is 0.9977 or 99.77%
The probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job is approximately 99.77%.
To solve this problem, we need to use the concepts of the sampling distribution of the sample mean and the properties of the normal distribution. Here are the steps to find the probability that the average time for eight workers over the age of 55 to find a job is more than 20 weeks:
Step 1: Understand the given data
- Mean time[tex](\(\mu\))[/tex] = 22 weeks
- Standard deviation [tex](\(\sigma\))[/tex] = 2 weeks
- Sample size [tex](\(n\))[/tex] = 8 workers
Step 2: Define the sampling distribution of the sample meanThe sample mean [tex]\(\bar{X}\)[/tex] for a sample of size (n) from a normal distribution with mean [tex]\(\mu\)[/tex] and standard deviation [tex]\(\sigma\)[/tex] is itself normally distributed with:
- Mean:[tex]\(\mu_{\bar{X}} = \mu\)[/tex]
- Standard deviation: [tex]\(\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}\)[/tex]
Calculate the standard deviation of the sample mean:
[tex]\[\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}} = \frac{2}{\sqrt{8}} = \frac{2}{2.828} \approx 0.707\][/tex]
Step 3: Convert the problem to a standard normal distribution (Z)We want to find the probability that the sample mean [tex]\(\bar{X}\)[/tex] is greater than 20 weeks. First, we convert this to a Z-score:
[tex]\[Z = \frac{\bar{X} - \mu_{\bar{X}}}{\sigma_{\bar{X}}}\][/tex]
Calculate the Z-score for [tex]\(\bar{X} = 20\)[/tex] weeks:
[tex]\[Z = \frac{20 - 22}{0.707} = \frac{-2}{0.707} \approx -2.83\][/tex]
Step 4: Find the probability corresponding to the Z-scoreUsing standard normal distribution tables or a Z-score calculator, we find the probability that (Z) is less than -2.83.
The cumulative probability for (Z = -2.83) is approximately 0.0023. This represents the probability that the sample mean is less than 20 weeks. However, we want the probability that the sample mean is more than 20 weeks:
[tex]\[P(\bar{X} > 20) = 1 - P(\bar{X} \leq 20) = 1 - 0.0023 = 0.9977\][/tex]
Step 5: ConclusionThe probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job is approximately 0.9977, or 99.77%.
Therefore, we can conclude that there is a very high probability (99.77%) that the average time for these eight workers to find a job is more than 20 weeks.
Item 6
Simplify the expression.
p^5⋅p^2
Answer:
p^7
Step-by-step explanation:
p^5⋅p^2 = p ^(5+2) = p^7
Josh has a drawer full of unmatched socks. There are 3 purple socks, 2 blue socks, 6 black socks, 4 brown socks, 5 yellow socks. If he reaches in his drawer, what is the probability of him drawing out a purple sock?Immersive Reader (9 Points) 1/5 2/5 3/5 3/20
Answer:
3/20
Step-by-step explanation:
because there is only 3 purple socks out of 20 socks total
A 95% confidence interval for the proportion of students achieving a reading achievement score that is above the standard set by the teachers for a population of third grade students is (0.43, 0.49).
The margin of error of this interval is:
Group of answer choices
0.05
0.03
0.06
None of the above
The ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. If the first number in the ratio is 10, what is the second number?
Answer:
The second number is 40
Step-by-Step:
There is a pattern in the ratio table: you need to multiply the first number by 4, and the answer is the second number. So if the first number is 10, you will need to multiply that by 4 to get the second number. So the second number is 40
A manager wants to determine the number of containers to use for incoming parts for a kanban system to be installed next month. The process will have a usage rate of 83 pieces per hour. Because the process is new, the manager has assigned an inefficiency factor of .18. Each container holds 53 pieces and it takes an average of 80 minutes to complete a cycle. How many containers should be used? (Round up your answer to the next whole number.) Number of containers As the system improves, will more or fewer containers be required? More Fewer
Answer:
2 containers should be used
As the system improves, neither more or fewer containers be required
Step-by-step explanation:
According to the given data we have the following:
D=83 pieces per hour.
T=80 minutes=1.33 hour
X=0.18
C=53
In order to calculate how many containers should be used we would have to use the following formula:
Number of containers=DT(1+X)
C
Number of containers=(83)(1.33)(1+0.18)
53
Number of containers=2.45=2
2 containers should be used.
As the system improves, neither more or fewer containers be required
The volume of a cube is given by the expression s to the power of 3, and its surface area is given by the expression 6s to the power of 2, where s is the length of the cube’s side. What is the volume of a cube with a side length of 5 inches?
Answer:
The volume of the cube would be 125in³
Step-by-step explanation:
The volume of a cube is s³ (side). 5 x 5 x 5 = 125.
Two candidates ran for class president. The candidate that won received 80% of the 290 total votes. How many votes did the winning candidate receive?
Answer:
232 total votes
Step-by-step explanation:
change 80% to a decimal.... .8 and then multiply that by 290
Answer:
232
Step-by-step explanation:
80% of 290 is 232
290-232 is 58
20% of 290 is 58
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Step 2 of 2 : Suppose a sample of 1291 tenth graders is drawn. Of the students sampled, 1098 read above the eighth grade level. Using the data, construct the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.
Answer:
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.13, 0.168).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
1291 tenth graders, 1098 read above the eighth grade level.
1291 - 1098 = 193 read at or below this level.
We want the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.
So [tex]n = 1291, \pi = \frac{193}{1291} = 0.149[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 - 1.96\sqrt{\frac{0.149*0.851}{1291}} = 0.13[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 - 1.96\sqrt{\frac{0.149*0.851}{1291}} = 0.168[/tex]
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.13, 0.168).
5x+9=24 solve the equation
Answer:
x=3
Step-by-step explanation:
24-9
15/5
3
x=3
Answer:
x = 3
Step-by-step explanation:
3 * 5 + 9 =24
A study was conducted to measure the effectiveness of a diet program that claims to help manage weight. Subjects were randomly selected to participate. Before beginning the program, each participant was given a score based on his or her fitness level. After six months of following the diet, each participant received another score. The study wanted to test whether there was a difference between before and after scores. What is the correct alternative hypothesis for this analysis?
a. μ≠0
b. μd≠0
c. p1≠p2
Answer:
x=test value before , y = test value after
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_y- \mu_x = 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x \neq 0[/tex]
If we define the difference as [tex] d = y_i-x_i[/tex] we convert the system of hypothesis:
Null hypothesis: [tex]\mu_d = 0[/tex]
Alternative hypothesis: [tex]\mu_d \neq 0[/tex]
Step-by-step explanation:
Previous concepts
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation
x=test value before , y = test value after
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_y- \mu_x = 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x \neq 0[/tex]
If we define the difference as [tex] d = y_i-x_i[/tex] we convert the system of hypothesis:
Null hypothesis: [tex]\mu_d = 0[/tex]
Alternative hypothesis: [tex]\mu_d \neq 0[/tex]
45 POINTS! NEED HELP QUESTION IS A IMAGE.
A portion of the Quadratic Formula proof is shown. Fill in the missing statement.
Statements Reasons
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative 4 times a times c all over 4 times a squared plus b squared over 4 a squared Find a common denominator on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation
the quantity x plus b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Rewrite the perfect square trinomial on the left side of the equation as a binomial squared
? Take the square root of both sides of the equation
x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c end quantity, all over 4 times a squared
x plus b over 2 times a all squared equals plus or minus b squared minus 4 times a times c, all over 4 times a squared all squared
the square root of x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared
x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared
Answer:
Take the square root of each side
D (x+b/2a) =±sqrt( (b^2-4ac)/ 4a^2)
Step-by-step explanation:
We have
(x+b/2a) ^2 = (b^2-4ac)/ 4a^2
We need to take the square root of each side to continue to isolate x
(x+b/2a) =±sqrt( (b^2-4ac)/ 4a^2)
Answer:
Option 3
Step-by-step explanation:
[x + b/2a]² = (b² - 4ac)/4a²
Taking square root both sides, you get this:
x + b/2a = +/- sqrt(b² - 4ac)/2a
Remember we're trying to make x the subject,
So does get rid of the square by applying square root both sides
The population of a certain species of fish has a growth rate of 2.2% per year. It is estimated that the the current population is 350,000. Estimate the number of years it will take the fish population to reach 1,000,000. Round your answer to the nearest tenth.
We have been given that the population of a certain species of fish has a growth rate of 2.2% per year. It is estimated that the the current population is 350,000.
We are asked to find the time it will take the fish population to reach 1,000,000.
We will use exponential growth formula to solve our given problem.
An exponential growth function is in form [tex]y=a\cdot (1+r)^x[/tex], where,
y = Final amount,
a = Initial amount,
r = Growth rate in decimal form,
x = Time
[tex]2.2\%=\frac{2.2}{100}=0.022[/tex]
[tex]y=350,000\cdot (1+0.022)^x[/tex]
To find the time for the fish population to reach 1,000,000, we will substitute [tex]x=1,000,000[/tex] in our equation as:
[tex]1,000,000=350,000\cdot (1+0.022)^x[/tex]
[tex]1,000,000=350,000\cdot (1.022)^x[/tex]
[tex]\frac{1,000,000}{350,000}=\frac{350,000\cdot (1.022)^x}{350,000}[/tex]
[tex]2.8571428571428571=(1.022)^x[/tex]
Now we will take natural log on both sides:
[tex]\text{ln}(2.8571428571428571)=\text{ln}((1.022)^x)[/tex]
[tex]\text{ln}(2.8571428571428571)=x\cdot \text{ln}(1.022)[/tex]
[tex]x=\frac{\text{ln}(2.8571428571428571)}{\text{ln}(1.022)}[/tex]
[tex]x=\frac{1.0498221244986776733}{0.0217614917815127}[/tex]
[tex]x=48.2421947[/tex]
Upon rounding to nearest tenth, we will get:
[tex]x\approx 48.2[/tex]
Therefore, it will take approximately 48.2 years for the fish population to reach 1,000,000.
Answer:
47.7
Step-by-step explanation:
right answer
a whole number is squared. the result is between 200 and 260. the number is between?
Final answer:
The whole number squared resulting in a number between 200 and 260 must have the original whole number between 15 and 16.
Explanation:
If a whole number is squared and the result is between 200 and 260, we must determine which whole numbers will yield a square within that range. We find the square roots of both 200 and 260 to identify the range of whole number bases. The square root of 200 is approximately 14.14, and the square root of 260 is approximately 16.12. Therefore, the number must be greater than 14 but less than or equal to 16 because squaring whole numbers greater than 16 gives results exceeding 260. Hence, the number is between 15 and 16.
When Aubree goes bowling, her scores are normally distributed with a mean of 190 and a standard deviation of 14. Using the empirical rule, what percentage of the games that Aubree bowls does she score between 148 and 232?
Answer:
By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 190
Standard deviation = 14
Using the empirical rule, what percentage of the games that Aubree bowls does she score between 148 and 232?
148 = 190 - 3*14
So 148 is 3 standard deviations below the mean.
232 = 190 + 3*14
So 232 is 3 standard deviations above the mean
By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232
Alton High School sold adult and student tickets for a school play. Of the 128 tickets sold, 84 were student tickets. What percent of the total tickets sold, rounded to the nearest percent, were adult tickets?
Answer:
66%Step-by-step explanation:
84/128=.65625
.65625x100=65.625=66%
Final answer:
To calculate the percentage of adult tickets sold for the school play, subtract the student tickets from the total tickets sold to find the number of adult tickets (44), and then divide by the total number of tickets and multiply by 100 to get the percentage, which is approximately 34%.
Explanation:
The question asks us to find what percent of the total tickets sold at a school play were adult tickets. Alton High School sold a total of 128 tickets, of which 84 were student tickets. To calculate the number of adult tickets, we subtract the number of student tickets from the total number of tickets: 128 - 84 = 44 adult tickets.
Next, we calculate the percent of adult tickets out of the total tickets sold by using the formula:
Percent = (Number of adult tickets / Total number of tickets) imes 100
Plugging in our numbers, we get:
Percent = (44 / 128) imes 100
Percent = 0.34375 imes 100
Percent ≈ 34%
Rounded to the nearest percent, we find that approximately 34% of the tickets sold were for adults.
What is a difference of squares that has a factor of x+8?
Answer:
x^2 - 64
Step-by-step explanation:
A difference of squares is a special product in the form (a^2 - b^2)..their factored form is (a - b)(a + b)..
Thus here a = x and b = 8, thus if x + 8 is a factor, then x - 8 is also a factor..
(x + 8)(x - 8) <-- expand this out using difference of squares rules..
= (x)^2 - (8)^2
= x^2 - 64 <-- answer...
You could also expand that using FOIL (FOIL - first, outer, inner, last)..
(x + 8)(x - 8)
= (x)(x) + (x)(-8) + (8)(x) + (8)(-8)
= x^2 - 8x + 8x - 64 <-- the -8x and 8x cancels out..leaving you with..
= x^2 - 64
The difference of squares that has a factor of x+8 is x² - 64.
What is Algebraic Identity?An algebraic identity is an equality that holds for any values of its variables.
For example, the identity ( x + y )² = x² + 2xy + y²
(x+y)² = x² + 2xy + y²
(x+y)²=x²+2xy+y² holds for all values of x and y.
As, Difference of two squares
x² - y² = (x - y)(x + 8)
So, for difference of squares that has (x -8) as one of the factor.
The other factor is (x + 8)
So, we can write
(x - 8)(x + 8) = x² - 8²
= x² - 64.
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Scientists measure how much water and debris flows past a river station at different time of the year. The water and debris are called discharge. the table show the average discharge at a research station on a certain river in 2 months. How many more quarts of discharge per second are there in march than February? How many quarts of discharge per second were recorded in march and February. There are blank more quarts per second in march and February
Answer:
2664
Step-by-step explanation:
(2285gallons - 1619gallons) =
666 gallons * 4quarts(in a gallon) =
2664 Quarts
Suppose that $4000 is deposited at 2% compounded quarterly. How much money will be in the account at the end of 6 years?
Answer:
$4,508.64
Step-by-step explanation:
The compound interest formula can answer this for you.
A = P(1 +r/n)^(nt)
where A is the account balance, P is the principal invested (4000), r is the annual interest rate (.02), n is the number of times per year interest is compounded (4), and t is the number of years (6).
Putting the given values into the formula, doing the arithmetic tells us ...
A = $4000(1 +.02/4)^(4·6) = $4000·1.005^24 ≈ $4,508.64
There will be $4,508.64 in the account at the end of 6 years.
A probability experiment is conducted in which the sample space of the experiment is
Upper S equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSetS={7,8,9,10,11,12,13,14,15,16,17,18}.
Let event
Upper E equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 EndSetE={7,8,9,10,11,12}.
Assume each outcome is equally likely. List the outcomes in
Upper E Superscript cEc.
Find
?P(Upper E Superscript cEc?).
The outcomes in
Upper E Superscript cEc
are
StartSet nothing EndSet{}.
?(Use a comma to separate answers as? needed.)
?P(Upper E Superscript cEc?)equals=nothing
?(Type an integer or a simplified? fraction.)
Answer:
a) Eᶜ = {13,14,15,16,17,18}
The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet
b) P(Eᶜ) = (1/2) = 0.5
P(Upper E Superscript c) = (1/2) equals 0.5
Step-by-step explanation:
The set that represents the universal set with all the sample spaces is set S and is given by
Upper S equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet
S = {7,8,9,10,11,12,13,14,15,16,17,18}
Upper E equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 EndSet
Event E = {7,8,9,10,11,12}
a) Find Eᶜ
Eᶜ is the complement of event E; it includes all the outcomes in the universal set, S, that are not in the event E
Eᶜ = {13,14,15,16,17,18}
The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet
b) P(Upper E Superscript c) = P(Eᶜ)
= n(Eᶜ) ÷ n(S)
Each outcome is equally likely, hence,
n(Eᶜ) = number of outcomes in the event Eᶜ = 6
n(S) = number of outcomes in the set S = 12
P(Eᶜ) = (6/12) = (1/2) = 0.5
Hope this Helps!!!
Given a polynomial f(x), if (x + 2) is a factor, what else must be true? f(0) = 2 f(0) = −2 f(2) = 0 f(−2) = 0
Answer:
f(-2) = 0
Step-by-step explanation:
If x + 2 is a factor, then f(x) = 0 when x + 2 = 0.
x + 2 = 0
x = -2
f(-2) = 0
For the polynomial, f(0) = 2 and f(-2) = 0.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given x+2 is a factor,
And values of x from the options are x = 0, -2 and 2.
We will put the values of x to the factor,
f(0) = 0 +2 = 2
f(-2) = -2 +2 = 0
f(2) = 4
Therefore from the result only two options satisfy the factor and those are f(0) = 2 and f(-2) = 0.
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Which statement correctly compares the ratios?
The ratio 9 to 12 is greater than 4 to 6.
The ratio 9 to 12 is less than 4 to 6.
O The ratio 9 to 12 is equal to 4 to 6.
The ratios cannot be compared.
HIERE
Answer:
its 9 to 12 is greater than 4 to 6.
Step-by-step explanation:
As per the given question, the correct option is the ratio 9 to 12 is greater than 4 to 6.
Explanation:In comparing the ratios 9 to 12 and 4 to 6, we first need to simplify both ratios. The ratio 9 to 12 can be simplified by dividing both numbers by their greatest common divisor, which is 3. This gives us a simplified ratio of 3 to 4.
Similarly, the ratio 4 to 6 can be simplified by dividing both numbers by their greatest common divisor, which is 2, giving us a simplified ratio of 2 to 3.
If we convert both ratios to decimals by dividing the first number by the second in each pair, we'll find that 9/12 = 0.75 and 4/6 = 0.67, which shows that the first ratio is greater. Therefore, we find that the correct statement is the ratio 9 to 12 is greater than 4 to 6.
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Jason is entering a weight
lifting contest. Currently, his
maximum bench press weight is
105 pounds. If he increases the
weight by 7 pounds each week,
What is the maximum weight
he be able to bench press
after 13 weeks?
Answer:
196
Step-by-step explanation:
7 x 13 = 91 + 105
HELP ASAP PLEASE
What type of graph would have the title, "Daily Low Temperatures Last Week"?
a. stem-and-leaf plot
b. line graph
c. bar graph
d. line plot
Answer:
line graph
Step-by-step explanation:
Find the area of a sector of a circle whose radius is 7 cm and whose central angle is 45
degrees. Use pi = 3.14.
Answer:
The area of a sector of a circle = 19.2325
Step-by-step explanation:
Explanation:-
Given θ be the measure of angle and radius of circle
The area of a sector of a circle (see diagram)
[tex]A = \frac{theta}{360} \pi r^{2}[/tex]
Given the radius of circle 'r' = 7cm and given angle θ = 45°
The area of a sector of a circle
[tex]A = \frac{45}{360} \pi( 7)^{2}[/tex]
Use pi =3.14
[tex]A = \frac{45X 3.14( 7)^{2}}{360}[/tex]
A = 19.2325
Final answer:-
The area of a sector of a circle = 19.2325
What is the vertex of the graph of the function f(x) = 2(x − 2)2 + 3? Enter your answer in the boxes.
Answer:
The vertex of the function is at (2,3).
Step-by-step explanation:
I graphed the equation on the graph below.
If this answer is correct, please make me Brainliest!
The vertex of the graph of the function [tex]f(x)=2(x-2)^2+3[/tex] is at (2, 3). This is obtained by comparing the given function of the graph with the vertex form function of a parabola.
What is the vertex of a parabola?The vertex of a parabola is the point of intersection of the parabola and its line of symmetry.For a parabola whose equation is given in the standard form [tex]y=ax^2+bx+c[/tex], then the vertex will be the minimum of the graph if a>o and the maximum of the graph if a<0.The vertex form of a parabola is [tex]y=a(x-h)^2+k[/tex]. Where (h, k) is said to be the vertex of the graph.Finding the vertex:Given that the function of the graph is [tex]f(x)=2(x-2)^2+3[/tex].
We have the vertex form as [tex]y=a(x-h)^2+k[/tex]
So, the graph shows a parabola for the given equation.
On comparing the given equation with the vertex form,
f(x)=y, a=2, h=2, and k=3.
Then, (h, k)=(2, 3)
It is shown in the graph below.
Therefore, the vertex of the graph is at the point (2, 3).
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Marcela took out a $600 discount loan with a 4% annual interest rate over a period of 8 months. How much money does marcela get from the bank when she receives the loan? Round to the nearest dollar.
Answer:
Step-by-step explanation:
4 % of 600 over 8 months is 16
600-16=584
On Saturday, Cannor drives 62 1/4 miles each hour. If he travels 4 hours, how many miles does he travel altogether?
Final answer:
To find the total distance Cannor travels, multiply his hourly distance of 62 1/4 miles by the total travel time of 4 hours, resulting in 249 miles.
Explanation:
The question asks about calculating the total distance traveled by Cannor on Saturday. Since Cannor drives 62 1/4 miles each hour and travels for 4 hours, we can find the total distance by multiplying the number of miles driven in an hour by the number of hours traveled.
To calculate this, convert 62 1/4 to an improper fraction which is 249/4 and multiply it by 4 (the number of hours):
Total Distance = (249/4 miles/hour) × 4 hours
When we do the multiplication, the hours unit cancels out and we get:
Total Distance = 249 miles
This calculation shows how far Cannor will travel altogether if he maintains his speed for the entire duration of his trip.
A new postsurgical treatment was compared with a standard treatment. Eight subjects received the new treatment, while eight others (the controls) received the standard treatment. The recovery times, in days, are given below.
New Treatment Standard
12 18
13 23
15 24
19 30
20 32
21 35
24 39
Can you conclude that the mean recovery time for those receiving the new treatment differs from the mean for those receiving the standard treatment.
Answer:
1323
Step-by-step explanation: