Find the third order maclaurin polynomial. Use it to estimate the value of sqrt1.3
Answers
You can use the well-known binomial series,
[tex]\displaystyle (1+x)^\alpha = \sum_{k=0}^\infty \binom \alpha k x^k[/tex]
where
[tex]\dbinom \alpha k = \dfrac{\alpha(\alpha-1)(\alpha-2)\cdots(\alpha-(k-1))}{k!} \text{ and } \dbinom \alpha0 = 1[/tex]
Let [tex]\alpha=\frac12[/tex] and replace [tex]x[/tex] with [tex]3x[/tex]; then the series expansion is
[tex]\displaystyle (1+3x)^{1/2} = \sum_{k=0}^\infty \binom{\frac12}k (3x)^k[/tex]
and the first 4 terms in the expansion are
[tex]\sqrt{1+3x} \approx 1 + \dfrac{\frac12}{1!}(3x) + \dfrac{\frac12\cdot\left(-\frac12\right)}{2!}(3x)^2 + \dfrac{\frac12\cdot\left(-\frac12\right)\cdot\left(-\frac32\right)}{3!}(3x)^3[/tex]
which simplify to
[tex]\sqrt{1+3x} \approx \boxed{1 + \dfrac32 x - \dfrac98 x^2 + \dfrac{27}{16} x^3}[/tex]
You can also use the standard Maclaurin coefficient derivation by differentiating [tex]f[/tex] a few times.
[tex]f(x) = (1+3x)^{1/2} \implies f(0) = 1[/tex]
[tex]f'(x) = \dfrac32 (1+3x)^{-1/2} \implies f'(0) = \dfrac32[/tex]
[tex]f''(x) = -\dfrac94 (1+3x)^{-3/2} \implies f''(0) = -\dfrac94[/tex]
[tex]f'''(x) = \dfrac{81}8 (1+3x)^{-5/2} \implies f'''(0) = \dfrac{81}8[/tex]
Then the 3rd order Maclaurin polynomial is the same as before,
[tex]\sqrt{1+3x} \approx f(0) + \dfrac{f'(0)}{1!} x + \dfrac{f''(0)}{2!} x^2 + \dfrac{f'''(0)}{3!} x^3 = 1 + \dfrac32 x - \dfrac98 x^2 + \dfrac{27}{16} x^3[/tex]
Now,
[tex]\sqrt{1.3} = \sqrt{1+3x} \bigg|_{x=\frac1{10}} \\\\ ~~~~~~~~ \approx 1 + \dfrac32 \left(\dfrac1{10}\right) - \dfrac98 \left(\dfrac1{10}\right)^2 + \dfrac{27}{16} \left(\dfrac1{10}\right)^3 \\\\ ~~~~~~~~ = \dfrac{18,247}{16,000} \approx \boxed{1.14044}[/tex]
Compare to the actual value which is closer to 1.14018.
[tex]\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}[/tex] is the maclaurin polynomial and estimate value of [tex]\sqrt{1.3}[/tex] is 1.14. This can be obtained by using the formula to find the maclaurin polynomial.
Find the third order maclaurin polynomial:Given the polynomial,
[tex]f(x)=\sqrt{1+3x}=(1+3x)^{\frac{1}{2} }[/tex]
The formula to find the maclaurin polynomial,
[tex]f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}[/tex]
Next we have to find f'(x), f''(x) and f'''(x),
[tex]f'(x) = \frac{3}{2}(1+3x)^{-\frac{1}{2} }[/tex] [tex]f''(x) =-\frac{9}{4}(1+3x)^{-\frac{3}{2} }[/tex][tex]f'''(x) = \frac{81}{8}(1+3x)^{-\frac{5}{2} }[/tex]By putting x = 0 , we get,
[tex]f(0)=(1+3(0))^{\frac{1}{2} }=1[/tex] [tex]f'(0) = \frac{3}{2}(1+3(0))^{-\frac{1}{2} }=\frac{3}{2}[/tex][tex]f''(0) =-\frac{9}{4}(1+3(0))^{-\frac{3}{2} }=-\frac{9}{4}[/tex][tex]f'''(0) = \frac{81}{8}(1+3(0))^{-\frac{5}{2} }=\frac{81}{8}[/tex]Therefore the maclaurin polynomial by using the formula will be,
[tex]\sqrt{1+3x}=f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}[/tex]
[tex]\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}[/tex]
To find the value of [tex]\sqrt{1.3}[/tex] we can use the maclaurin polynomial,
[tex]\sqrt{1.3}[/tex] is [tex]\sqrt{1+3x}[/tex] with x = 1/10,
[tex]\sqrt{1+3(1/10)}=1+\frac{3}{2} (1/10)-\frac{9}{8} (1/10)^{2} + \frac{81}{8}(1/10)^{3}[/tex]
[tex]\sqrt{1+3(1/10)}=\frac{18247}{16000} = 1.14[/tex]
Hence [tex]\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}[/tex] is the maclaurin polynomial and estimate value of [tex]\sqrt{1.3}[/tex] is 1.14.
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Related Questions
A quadrilateral must be a parallelogram if one pair of opposite sides is: a. congruent and the other pair is parallel b. congruent and parallel c. parallel d. congruent
Answers
Answer:
b
Step-by-step explanation:
the opposite sides of a parallelogram are parallel and congruent
thus option b is the correct one
There are an average of 45 buffalos for every 125 acres in the Canadian wilderness. How many buffalos are there in 150 acres?
Answers
Answer:
there are 54 buffalos in 150 acres
Step-by-step explanation:
1. determine the rate of buffalos per acres
45 buffalos per 125 acres =
45 / 125 =
0.36 buffalos per 1 acre
now we know the rate of buffalos per 1 acre, we can multiply it by the required amount of acres (in this case 150)
buffalos per 1 acre x total acres = total buffalos per total acres
0.36 x 150 = 54 buffalos
therefore, there are 54 buffalos per 150 acres.
hope this helps :)
A car is known to be 88% likely to pass inspection at a certain motor vehicle agency inspection office. what is the probability that at least 90 cars pass inspection if a random sample of 100 cars is taken at this motor vehicle agency inspection office?
Answers
Using the normal distribution, there is a 0.3228 = 32.28% probability that at least 90 cars pass inspection.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution are given by:
n = 100, p = 0.88.
Hence the mean and the standard deviation for the approximation are:
[tex]\mu = np = 100 \times 0.88 = 88[/tex][tex]\sigma = \sqrt{np(1-p)} = \sqrt{100 \times 0.88 \times 0.12} = 3.25[/tex]The probability that at least 90 cars pass inspection, using continuity correction, is P(X > 89.5), which is one subtracted by the p-value of Z when X = 89.5, hence:
Z = (89.5 - 88)/3.25
Z = 0.46
Z = 0.46 has a p-value of 0.6772.
1 - 0.6772 = 0.3228.
0.3228 = 32.28% probability that at least 90 cars pass inspection.
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Sami cuts out a rectangle that has a perimeter of 48 inches and a length of 13 inches.
Answers
Answer:
Width is 11 inches
Step-by-step explanation:
I am not sure what the question is. I think you might be looking for the width length. The perimeter is the distance around a rectangle. If the whole distance around is 48. We have 2 lengths and 2 widths. They tell us that the length is 13. We have two lengths so the lengths add up to 26. We can subtract that from 48 and that leaves us with 22 (48-26) This is the total for the 2 widths. Since the 2 widths are the same length we divide that number by 2 to get 11.
11 + 11+ 13 + 13 = 48
At the break-even point of 2000 units, variable costs are $45000, and fixed costs are $35000. how much is the selling price per unit? $40. 00 $17. 50 $22. 50 $5. 0
Answers
Answer:
$40/unit?
Step-by-step explanation:
I'll assume the the fixed and variable costs are for 2000 units.
Fixed Costs = $35,000
Variable Costs = $45,000
Tota Costs = $80,000
The selling price can be anything. Free and we lose $80,000; $40 each, net profit of $0; $100 each for a net profit of $120,000.
In the absence of any infoprmation regarding selling price (e.g., 50% profit margin), I'd select the $40/unit selling price since that is breakeven.
Find the surface area of the composite figure.
4 cm
13 cm
3 cm
4 cm
SA =
12 cm
[?] cm²
5 cm
3 cm
Answers
With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.
What is the surface area of a truncated prism?
The surface area of the truncated prism is the sum of the areas of its six faces, which are combinations of the areas of rectangles and right triangles. Then, we proceed to determine the surface area:
A = (12 cm) · (4 cm) + 2 · (3 cm) · (4 cm) + 2 · (12 cm) · (3 cm) + 2 · 0.5 · (12 cm) · (5 cm) + (5 cm) · (4 cm) + (13 cm) · (4 cm)
A = 48 cm² + 24 cm² + 72 cm² + 60 cm² + 20 cm² + 52 cm²
A = 276 cm²
With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.
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PLEASE HELP ME ASAP!! IM BEING TIMED!! Amria decided to help her mother bake muffins. She measured 300 mL of milk in a measuring cup. Then, she put 6 squares of chocolate in the cup. After she added the chocolate, the level in the measuring cup rose to 380 mL. What was the volume of the chocolate?
Answers
The volume of the total chocolate is 80 ml, where as the volume of each chocolate is 13.33 ml.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the volume of each chocolate. Hence:
6 * volume of each chocolate = (380 - 300) ml
6x = 80
Divide both sides of the equation by 6:
x = 13.33 ml
The volume of the total chocolate is 80 ml, where as the volume of each chocolate is 13.33 ml.
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Help me ASAP WILL MARK YOU BRAINLIEST!!
Answers
There are 7 ones on the left and only 2 on the right. The two sides need to be even, or balanced.
7 = 2 + r
r = 5
Hope this helps!
A jar contains 5 orange marbles, 3 black marbles, and 6 brown marbles. event a = drawing a brown marble on the first draw event b = drawing an orange marble on the second draw if two marbles are drawn from the jar, one after the other and not replaced, what is p(b|a) expressed in simplest form?
Answers
The probability of event A and event B IS 15/91.
What is the probability?
Probability determines the odds that a random event would occur. The odds lie between 0 and 1.
The probability of event A = number of brown marbles / total number of marbles
= 6/14
The probability of event B = number of orange marbles / total number of marbles -1
= 5/13
P(A and B) =6/14 x 5/13
= 30/182
= 15/91
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Answer:
B.) 5/13
Step-by-step explanation:
15/3=5
91/7=13
5/13
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Question 2(Multiple Choice Worth 2 points)
Based on the graphs of the equations y = -2x + 3 and y=x²-x + 1, the solutions are located at points?
Answers
Based on the given graphs and their equations, the solutions will be located at points (-2, 7) and (0, 1).
Where are solutions located?To find the solution to y = -2x+ 3, assume that x is a certain number then solve for y.
Given the options, we can assume that x = -2. Solution is:
= -2(-2) + 3
= 4 + 3
y = 7
Solution point is (-2, 7)
The second equation can be solved by equating x to 0:
y = 0² - 0 + 1
y = 1
Solution point is:
= (0, 1)
In conclusion, the solution points are (-2, 7) and (0,1).
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Jacy has a collection of 140 coins worth $19.00. she has only nickels, dimes, and quarters. the difference in the number of dimes and the number of quarters is 10. using matrices, how many nickels are in jacy’s collection?
Answers
She has 38 nickels
N as the number of nickels, D as the number of dimes, and Q as the number of quarters.
She has 140 coins in total, so we can writen:
N + D + Q = 140.
And the total value is $19.00
Then we have:
N*0.05 + D*0.10 + Q*0.25 = 19
And "The difference in the number of dimes and the number of quarters is 10."
D - Q = 10.
So we have a system of 3 equations and 3 variables:
N + D + Q = 140
N*0.05 + D*0.10 + Q*0.25 = 19
D - Q = 10.
First, let's isolate one of the variables in the third equation, i will isolate D.
D = 10 + Q.
Now we can replace this in the other two equations:
N + (10 + Q) + Q = 140
N*0.05 + (10 + Q)*0.10 + Q*0.25 = 19.
Now we can isolate Q in the first equation:
N + 10 + 2*Q = 140
2*Q = 140 - 10 - N
Q = 130/2 - N/2. = 65 - N/2
Now we can replace this in the other equation:
N*0.05 + 10*0.10 + Q*(0.10 + 0.25) = 19
N*0.05 + 10*0.10 + (65 - N/2)*( 0.35) = 19
Now we can find the number of nickels.
N*0.05 + 1 + 22.75 - N*0.175 = 19
23.75 - N*(0.175 - 0.05) = 19
23.75 - 19 = N*0.125
4.75/0.125 = N
38 = N
She has 38 nickels
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Suppose we roll one fair six-sided die, and flip six coins. what is the probability that the number of heads is equal to the number showing on the die?
Answers
The probability that the number of heads is equal to the number showing on the die is [tex]\frac{21}{128}[/tex] .
According to the question
we roll one fair six-sided die, and flip six coins
i.e
The Total Outcomes is the product of the sample spaces for the dice and the coins.
sample spaces for the dice = 6
sample spaces for the coins = 2⁶
S = 6.2⁶
S = 384
Now, The probability is
Therefore, the Favorable Outcomes
Consider the number of ways to get each total of heads from 1 to 6.
= 2⁶-1 (as TTT is excluded )
= 63
The probability that the number of heads is equal to the number showing on the die
As
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Probability(Event) = Favorable Outcomes/Total Outcomes
By substituting the values in the formula
Probability(Event) = [tex]\frac{63}{384}[/tex]
Probability(Event) = [tex]\frac{21}{128}[/tex]
Hence, the probability that the number of heads is equal to the number showing on the die is [tex]\frac{21}{128}[/tex]
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.
Find the value of x for which ABCD must be a parallelogram.
Answers
The value of x that would make ABCD a parallelogram is x = 5
How to find the interior angle of a parallelograms?A parallelogram, opposite sides are equal and parallel, which means opposite interior angles are equal.
Opposite sides of a parallelogram are congruent and parallel
Therefore,
5x - 3 = 14x - 48
subtract 5x from both sides
5x - 5x - 3 = 14x - 5x - 48
-3 = 9x - 48
add 48 to both sides
-3 + 48 = 9x - 48 + 48
45 = 9x
x = 45 / 9
x = 5
Therefore, the value of x that would make ABCD a parallelogram is x = 5
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A teacher prepares a test. She gives 5 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices.
Answers
The total number of ways in which 4 questions can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336
How to find probability combinations?We are given;
Total number of objective questions = 5 questions
Number of choices of first 2 questions = 3 choices
Number of choices of last 3 questions = 4 choices
Number of ways of answering the first 2 questions = 3 * 3 = 9 ways
Number of ways of answering the last 3 questions = 4 * 4 * 4 = 64 ways
Total number of ways of answering the five questions = 9 * 64 = 576 ways
Now, she has to answer only 4 which means it can be either 2 of the first and 2 of the last of 1 of the first and 3 of the last.
Thus, total number of ways of answering 4 questions if it is fist 2 and last 2 = 9 * 16 = 144
Total number of ways of answering 4 questions if 1 of the first and 3 of the last = 3 * 64 = 192
The total number of ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336
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A cell's expected frequency is: Group of answer choices the number of people in the cell's row multiplied by the number of people in the column the number of people in its column divided by the total number of people, divided by the row proportion the number of people in its row multiplied by the number in its column divided by the total number of people the number of people in the cell's row divided by the number of people in the column
Answers
A cell's expected frequency can be defined as the number of people in its row divided by the total number of people, multiplied by the number in its column and is therefore denoted as option C.
What is Frequency?This is defined as the number of occurrences of a repeating which takes place per unit time.It also helps to measure how frequent something occurs when counted or observed and is also used in the calculation of the different types of statistical data present or given.
This type of frequency is theoretical and are values which will most likely be in an experiment. it is calculated by multiplying the number in its column by the number of people in the row and dividing by the total number of people in this context.
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algebra Expression •x minus x
Answers
The answer is 0.
The expression in algebraic form is :
x - x0We know subtracting a term from its equivalent term will be 0.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
“[tex]\textsf{x minus x}[/tex]”
[tex]\huge\textbf{Simplifying it: }[/tex]
[tex]\textsf{x minus x}[/tex]
[tex]\mathsf{= x - x}[/tex]
[tex]\mathsf{= 1x - 1x}[/tex]
[tex]\mathsf{= 0x}[/tex]
[tex]\mathsf{= 0}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak 0}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
need help with number 9 pls
Answers
Answer:
i) a = 2, b = - 3, c =-6
Step-by-step explanation:
4x² - 12x + 3
4x² - 6x - 6x + 9 - 6
(2x - 3)(2x - 3) - 6
(2x - 3)² - 6
(2x + (- 3) )² - 6
In form of (ax + b)² - 6
a = 2, b = - 3, c =-6
What are the solutions to the system of equations? {−x+y=4y+12=x2+x
Answers
Answer: (-4, 0) and (4, 8)
Step-by-step explanation:
Looking at the graph, we can see where the line passes the parabola and can tell the solutions are (-4, 0) and (4, 8)
tan 45- cos ~ 60° = x. Sin 45. ta
Answers
The trigonometric values we require :
[tex]\begin{tabular}{c | l}trigonometric value & numerical value \\\cline{1-2}tan 45^{o}& 1 \\cos 60^{o} & 0.5 \\sin 45^{o} & 1 \div \sqrt{2}\end{tabular}[/tex]
Now, let's solve for x.
tan 45° - cos 60° = x (sin 45°)
[tex]\mathrm {1 - \frac{1}{2} = x (\frac{1}{\sqrt{2}})}[/tex]
[tex]\mathrm {\frac{1}{2} = \frac{x}{\sqrt{2}}}[/tex]
[tex]\mathrm {x = \frac{\sqrt{2}}{2}}[/tex]
[tex]\mathrm {x = \frac{1}{\sqrt{2}}}[/tex]
The value of x is 1/√2.
I hope it helped you solve the problem
Good luck on your studies!
How would I solve this, converting the left side to a square root? -16 = r^3
Answers
[tex]-16=r^3\implies \sqrt[3]{-16}=\sqrt[3]{r^3}\implies \sqrt[3]{-16}=r\implies \sqrt[3]{-2^4}=r \\\\\\ \sqrt[3]{(-2)^3\cdot 2^1}=r\implies -2\sqrt[3]{2^1}=r\implies -2\sqrt[3]{2}=r[/tex]
What is the radius of the sector of the circle below, if the area is 30.39 m^2 and the central angle < AOB measures 43 °. (round answer to the nearest whole meter)
Answers
Answer:
a. 9m
Step-by-step explanation:
Pi = 3.14 = 22/7
formula :
Area of a Sector of a Circle = (central angle)/360 * πr² =
(central angle)/360 * πr² = Area of a Sector of a Circle
43/360 * Pi * r^2 = 30.39
r^2 = (30.39 * 360) / (Pi * 43)
r^2 = (30.39 * 360) / (22/7 * 43)
r = √ (30.39 * 360 * 7) / (22 * 43)
r = √76582.8/946
r = √80.9543340381
8.99746264444 which is roughly
9
The radius of the sector will be 9m. The correct option is A.
What is the arc length of the circle?The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc segment by simulating it as a network of connected line segments.
The radius will be calculated as below:-
Area of a Sector of a Circle = (central angle)/360 * πr² =
(Ф)/360 * πr² = Area of a Sector of a Circle
43/360 * Pi * r²= 30.39
r² = (30.39 * 360) / (Pi x 43)
r²= (30.39 x 360) / (22/7 x 43)
r = √ (30.39 x 360 x 7) / (22 x 43)
r = √76582.8/946
r = √80.9543340381
r = 9
Therefore, the radius of the sector will be 9m. The correct option is A.
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Which simplified fraction is equal to 0.53 with bar?
StartFraction 24 Over 45 EndFraction
StartFraction 8 Over 15 EndFraction
StartFraction 48 Over 90 EndFraction
StartFraction 5 Over 9 EndFraction
Answers
I assume that 0.53 with a bar means the decimal fraction in which 3 is repeating.
24/45, 8/15, and 48/90 all result in the same decimal value. Thus, we are simply looking for the one that is fully simplified.
The correct answer is 8/15.
Hope this helps!
Which function is positive for the entire interval [-3, -2]?
Answers
Answer:
A function that is positive in the entire interval [-3, -2] is -x2 - 5x - 5.
Answer:
The second function (second graph and choice)
Step-by-step explanation:
If you look at the second function you will see that within the closed interval [-3,-2] the graph y values are positive
First choice is incorrect since at x = -2 the y value is negative
Third choice incorrect since at x = -2, y value is negative
Fourth choice incorrect since y value is negative for x = -2
Use the following recipe to answer questions 1 through 4:
Pumpkin- 1.2 kg
Chicken stock- 1.5L
Sugar- 5 mL
Yogurt- 0.25 L
1)what would be the best u.s standard unit in which to measure the pumpkin?
2) To measure the stock?
3) to measure the sugar?
4) to measure the yogurt?
Answers
#1
The unit is pounds
1kg=2.2lbs1.2kg=1.2(2.2)=2.64lbs#2
The unit must be pintSo
1L=2pints(Approx)1.5L=1.5(2)=3pints#3
We shall use cups
1mL=0.004cups5ml=0.020=0.02cups#4
We should use pints
1L=2pints0.25L=2/4=1/2=0.5pintsAnswer:
1. pounds (lb)
2. pints (pt)
3. teaspoon (tsp)
4. cups (c)
Step-by-step explanation:
US Standard UnitsLiquid
Fluid Ounces (fl oz)Cups (c)Pints (pt)Quarts (qt)Gallons (gal)128 fl oz = 16 cups = 8 pints = 4 quarts = 1 gallon
Mass
Ounces (oz)Pounds (lb)Tons (short ton)32000 ounces = 2000 pounds = 1 ton
Solutions1. The best US standard unit in which to measure pumpkin with a mass of 1.2 kg would be pounds (lb).
⇒ 1 kg ≈ 2.205 lb
⇒ 1.2 kg ≈ 1.2 × 2.205 = 2.65 lb
2. The best US standard unit in which to measure stock with a volume of 1.5 L would be pints (pt).
⇒ 1 L ≈ 2.133 pt
⇒ 1.5 L ≈ 1.5 × 2.113 = 3.17 pt
3. The best US standard unit in which to measure sugar of 5 mL would be teaspoon (tsp).
⇒ 5 mL = 5 g ≈ 1 teaspoon
4. The best US standard unit in which to measure yogurt with a volume of 0.25 L would be cups (c).
⇒ 1 L ≈ 4.167 c
⇒ 0.25 L ≈ 0.25 × 4.167 = 1.04 c
How much is 8000% + 80% =
Answers
Answer:
8000/100+80/100=80+0.8=80.8
Step-by-step explanation:
hope this helps (❁´◡`❁)
50 POINTS !! Charlotte has a map of the village. The scale on the map is such that 1cm represents 25m.
a) On the map, the church is 7cm from the village store. What is the real distance from the church to the village store?
b) Charlotte calculates her car is parked approximately half a kilometer from the church. On the map, how many cm would represent this distance?
Answers
Answer:
a) 175 m
b) 20 cm
Explanation:
scaled size → actual size
1 cm represents 25 m
a)
In the scaled size on the map, the distance from church to village is 7 cm.
Then actual size,
1 cm → 25 m
7 cm → (25 × 7) m
7 cm → 175 m
b)
half a kilometer = 0.5 km = 500 m
Then scaled size,
25 meter → 1 cm
500 meter → 500/25 cm = 20 cm
please give the right answer and i will mark you brainlyist
Answers
Considering the given box plots, we have that:
Class A has the higher IQR.Class A has the highest test score.Class B has the higher median.Class B has the smaller range.What is a box plot?It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.
The smallest value.The first quartile.The median.The third quartile.The highest value.Hence, for class A, we have that:
The smallest value is 62.The first quartile is 65.The median is of 70.The third quartile is 79.The highest value is of 86.Then:
The IQR is of 79 - 65 = 14.The range is of 86 - 62 = 24.Hence, for class B, we have that:
The smallest value is 68.The first quartile is 70.The median is of 74.The third quartile is 77.The highest value is of 79.Then:
The IQR is of 77 - 70 = 7.The range is of 79 - 68 = 11.Hence the correct options are given as follows:
Class A has the higher IQR.Class A has the highest test score.Class B has the higher median.Class B has the smaller range.More can be learned about box plots at https://brainly.com/question/27721471
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The given figure is a solid object formed by a cylinder and a hemisphere. If the total length of that solid object is 64 cm and length of the cylinder is 50 cm, find the total surface area of the solid object.
Answers
The total surface area of the solid object is 2660.925 square cm the answer is 2660.925 square cm.
What is a cylinder?In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the volume of the cylinder is given by:
[tex]\rm V = \pi r^2 h[/tex]
The surface area of the
= surface area of half sphere + surface area of the cylinder - surface area
of one circular base
The radius r = (64-50)/2 = 7 cm
= (1/2)[4π(7)²] + 2π(7)(50) + 2π(7)² - π(7)²
= (1/2)[615.75] + 2506.99 - 153.94
= 307.875 + 2506.99 - 153.94
= 2660.925 square cm
Thus, the total surface area of the solid object is 2660.925 square cm the answer is 2660.925 square cm.
Learn more about the cylinder here:
brainly.com/question/3216899
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Students in 7th grade took a standardized math test that they also took in 5th grade. The results are shown on the dot plot, with the most recent data shown first.
Find and compare the medians.
7th-grade median:
5th-grade median:
What is the relationship between the medians?
Answers
Using the median concept, it is found that:
The 5th-grade median is of 13.The 7th-grade median is of 17.The relationship is that 7th grade students have a higher median than 5th grade students.What is the median of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
Researching the problem on the internet, we have that there are 21 5th grade students. It is an odd number, hence the median is the 11th element, as (21 + 1)/2 = 11. Looking at the dot plot, the median is of 13.
There are 23 5th grade students. It is an odd number, hence the median is the 12th element, as (23 + 1)/2 = 12. Looking at the dot plot, the median is of 17.
The relationship is that 7th grade students have a higher median than 5th grade students.
More can be learned about the median of a data-set at https://brainly.com/question/17110151
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Victor spent 1/2 of his salary on rent, 1/4 of the remainder on food and saved \mbox{Sh 1500). How much was his salary?
Answers
Nag basa nito walang jõwa
