The Equivalent measurements of a given quantity can be useful in a variety of situations, such as when you need to convert between different units of volume
2 1/2 gallons is equal to various measurements depending on the context, but here are a few common conversions:
- 10 pints: There are 2 pints in a quart, and 4 quarts in a gallon, so 2 1/2 gallons would be 2 x 4 + 2 = 10 pints.
- 20 cups: There are 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon, so 2 1/2 gallons would be 2 x 4 x 2 + 2 = 20 cups.
- 640 fluid ounces: There are 8 fluid ounces in a cup, 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon, so 2 1/2 gallons would be 4 x 2 x 2 x 8 x 2.5 = 640 fluid ounces.
Knowing the equivalent measurements of a given quantity can be useful in a variety of situations, such as when you need to convert between different units of volume, or when you need to mix ingredients in a recipe.
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3. Simplify
8/3y + 5y/4 - 5/8
for all permissible values of y.
Step 1: Find a common denominator.
The denominators are 3y, 4, and 8. The least common multiple (LCM) of these is 24y.
Step 2: Adjust each term to have a denominator of 24y.
To do this, we multiply the numerator and denominator of each term by the appropriate factor:
For the term 8/3y, multiply numerator and denominator by 8: (8/3y) * (8/8) = 64/24y.
For the term 5y/4, multiply numerator and denominator by 6y: (5y/4) * (6y/6y) = 30y^2/24y.
For the term 5/8, multiply numerator and denominator by 3: (5/8) * (3/3) = 15/24y.
Step 3: Combine the terms.
Now that all terms have a common denominator of 24y, we can add them together:
(64/24y) + (30y^2/24y) - (15/24y)
Step 4: Combine the numerators.
Add the numerators of the fractions:
(64 + 30y^2 - 15) / 24y
Step 5: Simplify the numerator.
Combine like terms in the numerator:
(49 + 30y^2) / 24y
Thus, the simplified expression is (49 + 30y^2) / 24y, considering all permissible values of y.
K
Use the survey results to find the probability that a respondent has a pet, given that the respondent has had a pet.
32% have a pet now and have had a pet.
68% do not have a pet now.
85% have had a pet.
15% do not have a pet now and have never had a pet.
The probability that the respondent has a pet given that the respondent has had a pet is
(Type an integer or decimal rounded to the nearest hundredth as needed.)
The probability that the respondent has a pet given that the respondent has had a pet is 32/85 or 0.38
How is this so?We are given the following results below;
32% have a pet now and have had a pet.638% do not have a pet now.815% have had a pet.195% do not have a pet now and have never had a pet.Let event B = respondent has a pet now
Now, Probability that the respondent has had a pet = P(A) = 0.88
Probability that the respondent has a pet now and has had a pet = 0.32
So, Probability that the respondent has a pet given that the respondent has had a pet is given by = P(B/A)
This conditional probability is solved as ;
P(B/A) = 32/85
= 0.3764705882
≈ 0.38
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Evaluate the step function for f(1.4).
The correct option is the first one, we need to round down to the nearest whole so we will get:
f(1.4) = 1
Which value does the function take when x = 1.4?Here we have the step function:
f(/x) = [x]
This function rounds down to the nearest whole any input we give (like you can see on the graph).
Then we have:
f(0) = 0
f(0.5) = 0
f(0.7) = 0
f(1.2) = 1
f(1.3) = 1
f(5.2) = 5
And so on.
With that in mind, if we evaluate in 1.4, then we round down to the nearest whole which is 1, then:
f(1.4) = 1
The correct option is the first one.
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Look at the box plots below. Which is a
true statement?
A. If you moved the students from the top
25% in Class 1 into Class 2, the Class 2
median would increase.
B. If you omitted the student(s) who did
no homework in Class 1, the IQR for
Class 1 would increase.
C. If you combined the data from both
classes onto one box plot, the range
would be 105.
D. If you combined the data from both
classes onto one box plot, the median
would be double the current median for
Class 1.
ANSWER ASAP PLEASE!! THANKS
Answer:
A. If you moved the students from the top 25% in Class 1 into Class 2, the Class 2 median would increase.
Step-by-step explanation:
You want to know the effect of changing or combining class data, given the box plots show two classes with the same median.
We can consider the choices:
A. C2 median would increaseThe medians of the two classes are the same. The maximum value of Class 1 is in the third quartile of Class 2, so the top 25% of Class 1 would be added to the data values currently in the 3rd quartile of Class 2.
In general, one might expect that adding data values above the median will raise the median. Whether this is actually true depends on the details of the distribution and the number of data points added.
It is probably true that the Class 2 median would increase.
B. C1 IQR would increaseThe students who did no homework in Class 1 are the reason for the whisker extending to 0. Removing those from the data set will increase the minimum, likely increasing the value of Q1. This will cause the IQR to be reduced, not increased.
C. Range to 105The range of the combined data sets will be the difference of the largest maximum (70) and the smallest minimum (0). The combined range will be 70, not 105.
D. MedianCombining two data sets with the same median will result in a set of data with the same median. The median will not change, as half the combined data will be above it, and half the combined data will be below it.
Choice A is the only one that makes sense.
<95141404393>
Using an equation of a line of fit can be helpful in many contexts. For example, a city planner could use data comparing time and population to predict the city’s population in 50 years.
What are some other real-world situations where an equation of a line of fit can be useful in making predictions?
Any situation where there is a relationship between two variables that can be modeled by a linear equation can benefit from the use of a line of fit to make predictions.
There are many other real-world situations where an equation of a line of fit can be useful in making predictions. For instance, a business owner could use data on sales and time to forecast future sales and plan inventory accordingly. A scientist could use data on temperature and precipitation to predict crop yields and plan agricultural strategies. An economist could use data on interest rates and inflation to forecast future economic trends and plan investment strategies. In general, any situation where there is a relationship between two variables that can be modeled by a linear equation can benefit from the use of a line of fit to make predictions.
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What conclusion can be determined from the dot plot below?
The conclusion that can be gotten from the dot plot is that the median is 10
what is a dot plot?A dot plot, also known as a dot chart or dot graph, is a simple type of data visualization that displays individual data points on a number line. It is a way to visually represent the distribution and frequency of a dataset.
In a dot plot, each data point is represented by a dot or a marker placed above the corresponding value on the number line. If there are multiple data points with the same value, the dots are stacked vertically above that value.
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Given the same change in coordinates, which line has a greater rate of change in
y− coordinates?
If you start at (0,0) and increase 2 units in the x-direction on both lines, Line B goes up 2 units in the y-direction, while Line A only goes up 1 unit in the y-direction.
Put another way, if you started at the origin and were walking up either line (pretend their two hills), your elevation on Line B increases more quickly because it's a steeper hill.
So Line B has a great rate of change. The rise compared to the run is greater.
Answer:
A, the line is shorter, therefore the result is faster. Hence - change for the greater!
But not necessarily when I’m terms of God Almighty. Change can take longer and God uses it for His glory all the meanwhile He’s teaching, loving and correcting people. That’s Gods endless unconditional love!
John 3:16!!
Step-by-step explanation:
30 points!
answer plss
Answer:
1890ml<10litres
1.72m=172cm
Step-by-step explanation:
10 x 1000 = 10000 ml which is greater than 1890 ml.
1.72 x 100 = 172 cm
A line has a slope of 0 and includes the points (3, t) and (5, -7). What is the value of t?
t =
Answer:
-7
(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)
Step-by-step explanation:
To find the value of t, we can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1)
Given that the slope of the line is 0, we have:
0 = (-7 - t) / (5 - 3)
To solve for t, we can cross-multiply:
0 * (5 - 3) = -7 - t
0 = -7 - t
To isolate t, we can add 7 to both sides:
7 = -t
Dividing both sides by -1, we get:
t = -7
Therefore, the value of t is -7.
Question
Which equation is correct?
Responses
39 × 3 = 30 + 9 × 3
39 × 3 = 30 + 9 × 3
39 × 3 = 300 × 3 + 9 × 3
39 × 3 = 300 × 3 + 9 × 3
39 × 3 = 30 × 3 + 9 × 3
39 × 3 = 30 × 3 + 9 × 3
39 × 3 = 30 × 3 + 9
The correct equation is:
39 × 3 = 30 × 3 + 9 × 3
This equation shows that multiplying 39 by 3 is equal to the sum of multiplying 30 by 3 and multiplying 9 by 3.
Therefore, the answer is:
39 × 3 = 30 × 3 + 9 × 3
A small rectangular prism has a length of 5 inches, a width of 4 inches, and a volume of 100 cubic inches. A large rectangular prism also has a length of 5 inches and a width of 4 inches, but its volume is 200 cubic inches.
How much taller is the large prism than the small prism?
Write your answer as a whole number or decimal. Do not round.
Answer:
The large prism is 5 inches taller than the small prism
Step-by-step explanation:
We know that the formula for volume of a rectangular prism is
V = lwh, where
V is the volume in cubic unitsl is the length,w is the width,and h is the heightStep 1: We're given the volume, length, and width for both rectangular prisms, but not the height. We can find the height of each rectangular prism by rewriting the volume formula in terms of h (i.e., isolate h), which gives us:
V / (lw) = h
Step 2: To find the height of the small prism, we plug in 100 for V, 5 for l, and 4 for w in the volume formula (in terms of h) and simplify:
100 / (5 * 4) = h
100 / 20 = h
5 inches = height
Optional Confirmation of Step 2:
We can check that our height is correct by plugging in 5 for h in the regular volume formula, with 100 for V, 5 for l, and 4 for w;
100 = 5 * 4 * 5
100 = 20 * 5
100 = 100
Step 3: To find the height of the large prism, we plug in 200 for V, 5 for l, and 4 for w in the volume formula (in terms of h) and simplify:
200 / (5 * 4) = h
200 / 20 = h
10 inches = height
Optional Confirmation of Step 3:
We can check that our height is correct by plugging in 5 for h in the regular volume formula, with 200 for V, 5 for l, and 4 for w;
200 = 5 * 4 * 10
200 = 20 * 10
200 = 200
Step 5:
We now know that the heights of the small and large prism are 5 inches and 10 inches respectivelyWe subtract the small prism's height (5 inches) from the large prism's height (10 inches)This will show how much taller is the large prism than the small prism:10 - 5 = 5 inches taller
You are interested in finding a 95% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 11 randomly selected physical therapy patients. Round answers to 3 decimal places where possible.
13 5 10 11 26 20 18 18 24 23 5
a. To compute the confidence interval use a
t
Correct distribution.
b. With 95% confidence the population mean number of visits per physical therapy patient is between
and
visits.
c. If many groups of 11 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About
percent of these confidence intervals will contain the true population mean number of visits per patient and about
percent will not contain the true population mean number of visits per patient.
For finding a 95% confidence interval:
a. To compute the confidence interval, use a t distribution with 10 degrees of freedom.b. With 95% confidence, the population mean number of visits per physical therapy patient is between 13.011 and 19.249 visits.c. About 95% of these confidence intervals will contain the true population mean number of visits per patient and about 5% will not contain the true population mean number of visits per patient.How to solve confidence interval?a) The sample mean is x = 16.13.
The sample standard deviation is s = 6.948.
The degrees of freedom are df = 10.
The critical value of t for a 95% confidence interval is t = 2.228.
The margin of error is ME = t × s/√n = 2.228(6.948)/√11 = 4.263.
The 95% confidence interval is x ± ME = 16.13 ± 4.263 = (11.867, 20.393).
b) The 95% confidence interval is (11.867, 20.393).
This means that we are 95% confident that the true population mean number of visits per physical therapy patient is between 11.867 and 20.393 visits.
c) This is because the confidence interval is a range of values that is likely to contain the true population mean. If many samples of the same size are taken from the same population, then about 95% of the confidence intervals from these samples will contain the true population mean.
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HELP PLEASE URGENT!!!!!! 50 Points question answer part a and part b from the image.
The proportion that shows the relationship is h/4 = 8/h
The values of a, h and b are a = 16√3, b = 16√6 and h = 4√2
Writing the proportion that shows the relationship between the lengthsFrom the question, we have the following parameters that can be used in our computation:
The similar triangles
Using the right triangle/altitude similarity theorem, we have
h/4 = 8/h
Calculating the values of a, h and b
In (a), we have
h/4 = 8/h
This means that
h² = 32
So, we have
h = 4√2
For the value of (a), we have
a² = h² + 4²
So, we have
a² = 32 + 4²
a² = 48
Evaluate
a = 16√3
Next, we have
b² = 32 + 8²
b² = 96
So, we have
b = 16√6
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Find the value of tan I rounded to the nearest
hundredth, if necessary.
39
I
K
15
36
Answer:
Set your calculator to degree mode.
[tex] {tan}^{ - 1} \frac{15}{36} = 22.62 \: degrees[/tex]
So angle I measures about 22.62°.
Before a chair manufacturer sells its beanbag chairs, they spot check a random sample of chairs on the production line. The table below shows the number of common problems found during one such spot check.
Common Problems
Frequency
Open seam
4
Cuts in upholstery
14
Understuffed
15
None
267
Total
300
If the manufacturer makes 1500 beanbag chairs per day, how many of those chairs would they expect to be understuffed?
They would expect 15 chairs to be understuffed.
They would expect 75 chairs to be understuffed.
They would expect 300 chairs to be understuffed.
They would expect 750 chairs to be understuffed.
75 chairs expected to be understaffed.
Given : number of common problems found during one such spot check. manufacturer makes 1500 beanbag chairs per day.
To Find : how many of those chairs would they expect to be understaffed?
Common Problems Frequency
Open seam 4
Cuts in upholstery 14
Understaffed 15
None 267
Total 300
Probability of understaffed = Understaffed / Total
= 15/300
= 1/20
manufacturer makes 1500 beanbag chairs per day,
Number of chairs expected to be understaffed = (1/20) x 1500 = 75
Hence 75 chairs expected to be understaffed.
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Maria plans to purchase a new work truck. The dealer requires a 10% down payment on the $47,000 vehicle. Maria will finance the rest of the cost with a fixed-rate amortized auto loan at 8.5% annual interest with monthly payments over 5 years. Complete the parts below. Do not round any intermediate computations. Round your final answers to the nearest cent if necessary. If necessary, refer to the list of financial formulas. (a) Find the required down payment. (b) Find the amount of the auto loan. (c) Find the monthly payment.
a) The required down payment = $4,700
b) The amount of the auto loan is = $42,300
c) The monthly payment is $864.97
Given data ,
Maria plans to purchase a new work truck. The dealer requires a 10% down payment on the $47,000 vehicle
Maria will finance the rest of the cost with a fixed-rate amortized auto loan at 8.5% annual interest with monthly payments over 5 years
(a)
The required down payment is 10% of $47,000, which is:
Down payment = 0.1 x $47,000 = $4,700
(b)
The amount of the auto loan is the total cost of the truck minus the down payment, which is:
Auto loan = $47,000 - $4,700 = $42,300
(c)
To find the monthly payment, we can use the formula for a fixed-rate amortized loan:
PMT = r(PV) / [1 - (1 + r)^(-n)]
where PMT is the monthly payment, r is the monthly interest rate (which is the annual interest rate divided by 12), PV is the present value of the loan (which is the auto loan amount), and n is the total number of payments (which is the number of years multiplied by 12).
Substituting the given values, we get:
r = 0.085 / 12 = 0.00708333 (monthly interest rate)
PV = $42,300
n = 5 x 12 = 60 (total number of payments)
PMT = 0.00708333($42,300) / [1 - (1 + 0.00708333)^(-60)] = $864.97
Hence , the monthly payment is $864.97
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let c = 800 +40x be the cost to manufacture x items. find the average cost per item to produce 90 items
Answer:
The average cost is 4400
Step-by-step explanation:
c=800+40x
where x=number of items
c=800+4x;when x=90
c=800+40(90)
c=800+3600
c=4400
Answer:
4400
Step-by-step explanation:
Match the given slope (m) and y-intercept (b) with the equation of the line in slope-intercept form.
To match a given slope (m) and y-intercept (b) with the equation of the line in slope-intercept form is y = (3/4)x - 5.
The formula y = mx + b,
where "m" stands for the slope and "b" for the y-intercept, is used to match a given slope (m) and y-intercept (b) with the equation of the line in slope-intercept form.
1. If m = 2 and b = 3, the slope-intercept form of the equation would be y = 2x + 3
2. With m = -1/2 and b = 4, the slope-intercept form of the equation would be: y = (-1/2)x + 4.
3. If m = 0 and b = 2, then the slope-intercept form of the equation is: y = 0x + 2 (or just y = 2).
4. With m = 3/4 and b = -5, the slope-intercept form of the equation is: y = (3/4)x - 5.
Therefore, The equation of the line in slope-intercept form is y = (3/4)x - 5, which may be used to match a given slope (m) and y-intercept (b) with it.
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m^(1/2) in root form
Answer:
[tex]\sqrt[2]{(m)^1}[/tex]
Step-by-step explanation:
denominator = the root number ___
numerator = to the power of ___
give the sum of 10+7_5+3
Answer:
17 and 8
Not sure what the underscore is for
Step-by-step explanation:
Answer:
17 and 8
Step-by-step explanation:
10+7 = 17 and 5+3 =8
PLEASE PLEASE HELP WILL MARK BRAINLIST!!!!!!!!!!!!
Answer:
The answer is y>-x+3
Step-by-step explanation:
slope=rise/run
(0,3),(3,0)
m=y2-y1/x2-x1
m=0-3/3-0
m=-3/3
m= -1
y=mx+b
y= -x+b
3=-(0)+b
b=3
y>-x+3
7
Select the correct answer.
Consider the function f(x) = 2* and the function g(x) shown below. How will the graph of g(x) differ from the graph of f(x)?
g(z) = 2 f(x) = 2(2³)
O A. The graph of g(x) is the graph of f(x) shifted up by a factor of 2.
The graph of g(x) is the graph of f(x) shifted to the right by a factor of 2.
The graph of g(x) is the graph of f(x) stretched vertically by a factor of 2.
D. The graph of g(x) is the graph of f(x) stretched horizontally by a factor of 2.
B.
C.
Reset
Next
The description of the difference between the graph of g(x) and f(x), based on the equation relating the functions is the option C.
C. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 2What is a function?A function is a definition or rule that maps an input on to an output.
The possible function, obtained from a similar function on the internet can be presented as follows;
f(x) = 2ˣ
g(x) = 2·f(x) = 2·(2ˣ)
Therefore;
The graph of g(x) can be obtained from the graph of f(x), by a transformation of vertical stretch by factor of 2 and the correct option therefore is option C.
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Select all ordered pairs that satisfy the function.
y = -4x - 3/4
a.) (1, 3 1/4)
b.) (-1, 3 1/4)
c.) (3, -12 3/4)
d.) (15 1/4, -4)
Answer:
(-1, 3 1/4) and (3, 12 3/4)
Step-by-step explanation:
These are the only two pairs that will work for the graph.
30 POINTS. Given ABC with coordinates A(-6,1), B(4,1), and C(4,-3). the ordered pair (9,y) is on the line ac. Enter the value of y for this ordered pair.
Answer:
The value of y is -5, so the ordered pair is (9, -5).
Step-by-step explanation:
To determine the value of y for the ordered pair (9, y) on the line AC, we first need to find the equation of the line AC.
To find the slope of the line AC, substitute the points A and C into the slope formula:
[tex]\textsf{Slope}\;(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{y_C-y_A}{x_C-x_A}=\dfrac{-3-1}{4-(-6)}=\dfrac{-4}{10}=-\dfrac{2}{5}[/tex]
To determine the equation of line AC, substitute the found slope and one of the points into the point-slope formula:
[tex]\begin{aligned}y-y_1&=m(x-x_1)\\\\y-1&=-\dfrac{2}{5}(x-(-6)\\\\y-1&=-\dfrac{2}{5}x-\dfrac{12}{5}\\\\y&=-\dfrac{2}{5}x-\dfrac{7}{5} \end{aligned}[/tex]
Now we have found the equation of the line AC, to determine the value of y for the ordered pair (9, y), substitute x = 9 into the equation:
[tex]\begin{aligned}y&=-\dfrac{2}{5}(9)-\dfrac{7}{5}\\\\&=-\dfrac{18}{5}-\dfrac{7}{5}\\\\&=\dfrac{-18-7}{5}\\\\&=\dfrac{-25}{5}\\\\&=-5\end{aligned}[/tex]
Therefore, the value of y for the ordered pair is y = -5.
So the ordered pair is (9, -5).
A survey of 2290 adults in a certain large country aged 18 and older conducted by a reputable polling organization found that 414 have donated blood in the past two years. Complete parts (a) through (c) below.
The estimated proportion of adults in the country who have donated blood in the past two years is approximately 0.1803 or 18.03%. the 95% confidence interval for the proportion of adults in the country who have donated blood in the past two years is approximately 0.1589 to 0.2017.
(a) Estimate the proportion of adults in the country who have donated blood in the past two years.
To estimate the proportion of adults who have donated blood, we divide the number of adults who have donated blood by the total number of adults surveyed.
Number of adults who have donated blood = 414
Total number of adults surveyed = 2290
Proportion of adults who have donated blood = Number of adults who have donated blood / Total number of adults surveyed
Proportion of adults who have donated blood = 414 / 2290
Proportion of adults who have donated blood ≈ 0.1803 (rounded to four decimal places)
Therefore, the estimated proportion of adults in the country who have donated blood in the past two years is approximately 0.1803 or 18.03% (rounded to two decimal places).
(b) Construct a 95% confidence interval for the proportion of adults in the country who have donated blood in the past two years.
To construct a confidence interval, we can use the formula for a proportion with a confidence level of 95%:
Confidence interval = Sample proportion ± Margin of error
Sample proportion = Proportion of adults who have donated blood = 0.1803 (from part a)
Margin of error = Z * √[(Sample proportion * (1 - Sample proportion)) / Sample size]
Z represents the critical value for a 95% confidence level. Since the sample size is large (n > 30), we can use the standard normal distribution and take Z = 1.96.
Sample size = Total number of adults surveyed = 2290
Margin of error = 1.96 * √[(0.1803 * (1 - 0.1803)) / 2290]
Calculating the margin of error:
Margin of error ≈ 1.96 * √[(0.1803 * 0.8197) / 2290]
Margin of error ≈ 0.0214 (rounded to four decimal places)
Confidence interval = 0.1803 ± 0.0214
Lower bound = 0.1803 - 0.0214 ≈ 0.1589 (rounded to four decimal places)
Upper bound = 0.1803 + 0.0214 ≈ 0.2017 (rounded to four decimal places)
Therefore, the 95% confidence interval for the proportion of adults in the country who have donated blood in the past two years is approximately 0.1589 to 0.2017 (or 15.89% to 20.17%, rounded to two decimal places).
(c) Interpret the confidence interval in the context of the problem.
The confidence interval provides a range of values within which we can be 95% confident that the true proportion of adults in the country who have donated blood lies. Based on the survey data, the estimated proportion is 18.03% (from part a). The 95% confidence interval for this proportion is approximately 15.89% to 20.17%.
This means that we are 95% confident that the true proportion of adults in the country who have donated blood in the past two years falls within this range. In other words, if we were to repeat the survey multiple times and construct confidence intervals, approximately 95% of those intervals would contain the true proportion.
Therefore, based on this survey, we can conclude that the proportion of adults who have donated blood in the past two years in the country is likely to be between 15.89% and 20.17%, with a confidence level of 95%.
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Which number line represents the solutions to |x+4| = 2?
Answer:
The number line has a closed circle at -2 and a closed circle at -6.
Step-by-step explanation:
|x+4| = 2
x + 4 = 2 or x + 4 = -2
x = -2 or x = -6
The number line has a closed circle at -2 and a closed circle at -6.
i need help with my work asap
The area of the figure is 225 ft²
How to determine the valueFrom the figure shown, we have that it is made up of a triangle and a rectangle.
Now, the formula for calculating the area of a triangle is expressed as;
A = 1/2bh
Such that;
b is the baseh is the heightSubstitute the values
Area = 1/2 × 10 × 15
Multiply the values
Area = 75 ft²
Area of the rectangle is;
Area = length × width
Area = 10(15)
Area = 150 ft²
Total area = 225 ft²
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NO LINKS!! URGENT HELP PLEASE!!!
Write a rule for the nth term of this arithmetic sequence. Then find a_20.
3. 8, 21, 34, 47, 60, . . .
4. 6, 2, -2, -6, -10, . . .
Answer:
3) an = 8 +13(n -1); a20 = 255
4) an = 6 -4(n -1); a20 = -70
Step-by-step explanation:
You want the rule and the 20th term for the arithmetic sequences ...
3) 8, 21, 34, ...
4) 6, 2, -2, ...
RuleThe n-th term of an arithmetic sequence is given in terms of the first term (a1) and the common difference (d) as ...
an = a1 +d(n -1)
3.The first term is 8. The common difference is 21 -8 = 13. The rule is ...
an = 8 +13(n -1)
The 20th term is ...
a20 = 8 +13(20 -1) = 255
4.The first term is 6. The common difference is 2 -6 = -4. The rule is ...
an = 6 -4(n -1)
The 20th term is ...
a20 = 6 -4(20 -1) = -70
#95141404393
Answer:
3. 255
4. -70
Step-by-step explanation:
3.
For the arithmetic sequence 8, 21, 34, 47, 60, ...
The common difference between consecutive terms is d =(21-8)= 13. Therefore, the nth term of the sequence can be expressed as:
[tex]\bold{a_n = a_1 + (n - 1) * d}[/tex]
where [tex]\bold{a_1}[/tex] is the first term of the sequence,
n is the term number, and d is the common difference.
Substituting [tex]a_1 = 8[/tex] and d = 13, we get:
[tex]a_n = 8 + (n - 1) * 13\\a_n = 13n - 5[/tex]
To find [tex]a_{20}[/tex], substitute n = 20 in the above formula:
[tex]a_{20} = 13(20) - 5\\a_{20}= 255[/tex]
4.
For the arithmetic sequence 6, 2, -2, -6, -10, ...
The common difference between consecutive terms is d =(2-6)= -4. Therefore, the nth term of the sequence can be expressed as:
[tex]\bold{a_n = a_1 + (n - 1) * d}[/tex]
where [tex]a_1[/tex] is the first term of the sequence,
n is the term number, and
d is a common difference.
Substituting [tex]a_1[/tex]= 6 and d = -4, we get:
[tex]a_n = 6 + (n - 1) * (-4)\\a_n = 10 - 4n[/tex]
To find [tex]a_{20}[/tex], substitute n = 20 in the above formula:
[tex]a_{20} = 10 - 4(20)\\a_{20}= -70[/tex]
I don’t get this question I need help
The result to the equation is x = 7.
To find the results of the equation √( 2x- 5) 4 = 1, we can break it step by step
Abate 4 from both sides of the equation
√( 2x- 5) = 1- 4
√( 2x- 5) = -3
Square both sides of the equation to exclude the square root
√( 2x- 5))² = (- 3)²
2x- 5 = 9
Add 5 to both sides of the equation
2x = 9 + 5
2x = 14
Divide both sides of the equation by 2
x = 14/2
x = 7
Thus, the result to the equation is x = 7.
Checking the extraneous result
Substituting x = 7 back into the original equation
√(2(7)-5)+4=1
√(14-5)+4=1
√9+4=1
3+4=1
7 = 1
This equation isn't true, which means that x = 7 is an extraneous result.
Learn more about Extraneous solution here:
https://brainly.com/question/28362830
#SPJ1
Need this ASAP please
Answer:
8 months
Step-by-step explanation:
[tex]4000=400(\frac{(1+.045)^{n}-1 }{.045})[/tex]
Do what's in parentheses.
[tex]4000=400(\frac{(1.045^{n}-1) }{.045})[/tex]
Multiply 400 by the numerator.
[tex]4000=(\frac{400(1.045^{n})-400 }{.045})[/tex]
Divide both sides by .045.
[tex]180=400(1.045)^{n}-400[/tex]
Add 400 to both sides.
[tex]580=400(1.045)^{n}[/tex]
Divide both sides by 400.
[tex]\frac{29}{20} =1.045^{n}[/tex]
Convert to logarithmic equation.
[tex]log_{1.045}\frac{29}{20}=n[/tex]
8.441=8 months
Hope this helps!!
