The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency
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Related Questions
A piggy bank contains the same number of quarters, nickels, and dimes. the coins total $4.40. how many of each type of coin does the piggy bank contain?
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The total sum of these coins is $4.40. So we can write:
n Nickles + n Dimes + n Quarters = 4.40
0.05n + 0.10n + 0.25n = 4.40
0.40n = 4.40
n = 11
So this means, there are 11 coins of each type.
Answer: 11 of each type
Step-by-step explanation:
Draw a box plot for the data:
135, 149, 156, 112, 134, 141, 154, 116, 134, 156
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We first order the data from least to greatest:
112, 116, 134, 134, 135, 141, 149, 154, 156, 156
We find the median (middle value). There are 10 data values, which puts the median between 135 and 141:
(135+141)/2 = 276/2 = 138
The Upper Quartile (UQ) is the median of the upper half of data, cut by the median. This is 154.
The Lower Quartile (LQ) is the median of the lower half of data, cut by the median. This is 134.
The middle line of the box is drawn at the median, 138. The left side of the box is at the LQ, 134. The right side of the box is at the UQ, 154. There is a whisker drawn from the right side to the highest value, 156. There is a whisker drawn from the left side to the smallest value, 112.
The solution is: The box plot is attached.
What is median?In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
We first order the data from least to greatest:
112, 116, 134, 134, 135, 141, 149, 154, 156, 156
We find the median (middle value). There are 10 data values, which puts the median between 135 and 141:
(135+141)/2 = 276/2 = 138
The Upper Quartile (UQ) is the median of the upper half of data, cut by the median. This is 154.
The Lower Quartile (LQ) is the median of the lower half of data, cut by the median. This is 134.
The middle line of the box is drawn at the median, 138. The left side of the box is at the LQ, 134. The right side of the box is at the UQ, 154. There is a whisker drawn from the right side to the highest value, 156. There is a whisker drawn from the left side to the smallest value, 112.
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Is the mean value theorem for integrals the same as the mean value thoerem for derivatives?
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Answer:
a^2 + b^2 =C^2
Step-by-step explanation:
Calculate cos theta where theta is the angle between u and v
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However, I can explain how to solve the problem so that you can determine the angle.
cos theta = side opposite of theta divided by the hypotenuse.
Reminder that the hypotenuse is the side NOT touching the 90° angle.
Hope this helps! If not, upload an image of the drawing.
You’re baking a circular cake for a party. Your cake can be any size you want. What will the radius of your cake be and how many slices will you be able to cut?
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This is a problem of geometry. Given that the cake is circular, the greater the cake the greater the radius of it. So, as shown in the figure 1, the radius will be the distance from the center to any extreme point of the circle.
How many slices will you be able to cut?
The total area of a circle is given by:
[tex]A= \pi r^{2}[/tex]
We need to fin how many slices will be cut, so let's calculate the area of the circular sector which can be obtained simply applying rule of three, so:
[tex]A_{cs}= \pi r^{2}( \frac{\theta}{2\pi})= \frac{r^{2}\theta}{2}[/tex]
Let's name n the number of slices, if we divide the total area by n this result, each area must equal, then:
[tex] \frac{\pi r^{2}}{n}=\frac{r^{2}\theta}{n}[/tex]
Finally, we will be able to cut:
[tex]n= \frac{2\pi}{\theta}[/tex] Slices
A students is taking a 5-question
a. True
b. False quiz and guesses at each question. find the probability that the student will get all questions correct. find the probability that the student will get no questions correct.
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It's too short. Write at least 20 characters to explain it well.
How many solutions are there for the system of equations shown on the graph?
No solution
One solution
Two solutions
Infinitely many solutions
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If the lines are parallel then No solution.
Answer:
D. Infinitely many solutions
Step-by-step explanation:
We have been given an image of two lines on coordinate plane. We are asked to find the number of solutions for our given lines.
Upon looking at our given graph, we can see that both lines are same. Since both lines coincide, therefore, each point on the line will be solution of our given lines.
Therefore, our given lines will have infinitely many solutions and option D is the correct choice.
help please, i don't understand it!!!!
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Substitute to S.A.
[tex]S.A.=4\pi r^2=4\pi\cdot\dfrac{3V}{4\pi r^2}=\dfrac{3V}{r}[/tex]
[tex]\dfrac{S.A.}{V}=\dfrac{4\pi r^2}{\frac{4}{3}\pi r^3}=\dfrac{3}{r}[/tex]
[tex]\dfrac{S.A.}{V}=1\to\dfrac{3}{r}=1\to r=3[/tex]
Answer: B
Mr. Hart is hanging a picture on a wall. the picture frame has a length of 13 inches and a width of 9 inches. how much wall space will the picture need?
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A=wl
So:
9*13=117
The area would be 117, the amount of wall space needed is 117.
Hope this helps:)
To determine the wall space needed for Mr. Hart's picture, calculate the area of the rectangle formed by the picture's dimensions: length (13 inches) times width (9 inches), resulting in 117 square inches of wall space.
The student's question about Mr. Hart hanging a picture on a wall involves calculating the wall space the picture will occupy. This is essentially a question about finding the area of a rectangle. To find the area, one must multiply the length by the width of the rectangle. In this case, the length of the picture frame is 13 inches and the width is 9 inches. The calculation will be:
Area = Length × Width
Area = 13 inches × 9 inches
Area = 117 square inches
Therefore, the picture will need 117 square inches of wall space.
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What is the sum of the polynomials?
A. 10x^2 - 9
B. 11x^2 - x - 9
C. 11x^2 + x - 1
D. 12x^2 - 1
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What is the interquartile range of this data? 6 7 8 9 Box-and whisker plot titled Temperatures in Celsius ranging from 12 to 48 with the five number summary from left to right 18, 25, 28, 33, and 42
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Hope this helps!
What is the interquartile range of this data? 6 7 8 9 Box-and whisker plot titled Temperatures in Celsius ranging from 12 to 48 with the five number summary from left to right 18, 25, 28, 33, and 42
Solution:
The problem is not clear.
But, considering data set is:
18,25,28,33,42
So, if we consider the data set, Interquartile Range is the difference of Quartile3-Quartile1
IQR=Q3-Q1
To find, Q1 and Q3. Let us find the median, or, Q2 first.
Median is the middle term of the data set.
So, Median, Q2=28
Q1 is the median of first half of the data set. That is, 18,25,28
So, Lower Quartile, Q1=25
Q3 is the median of second half of data set. That is, 28, 33,42
So, Upper Quartile, Q3=33
IQR=Q3-Q1
=33-25=8
Answer: IQR=8
If we consider data set: 6,7,8,9
Median, Q2=[tex] \frac{(7+8)}{2}=\frac{15}{2} [/tex]=7.5
Lower Quartile, Q1=6.25
Upper Quartile, Q2=8.75
IQR=Q3-Q1=8.75-6.25=2.5
IQR=2.5
For what value of a does (1/9)^a+1 = 81^a+1 x 27^2-a?
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Solution:
(1/9)^(a+1)=81^(a+1) x 27^(2-a), then the answer would be a=-3.
Answer:
-4
Step-by-step explanation:
Next time use the internet :)
Use double angle to rewrite 12sinxcosx
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To rewrite 12sinxcosx using the double angle formula, multiply by (1/2) and use the formula for sin(2x) to obtain the answer of 12sin(2x).
Explanation:To rewrite 12sin(x)cos(x) using the double angle formula, we need to know the formula for sin(2x) and cos(2x). The double angle formula for sine is sin(2x) = 2sin(x)cos(x), and for cosine it is cos(2x) = cos^2(x) - sin^2(x). Let's use these formulas to rewrite the expression:
12sin(x)cos(x) = 12 * (1/2) * 2sin(x)cos(x), since 1/2 is the value of cos^2(x) - sin^2(x).12 * (1/2) * 2sin(x)cos(x) = 6 * 2sin(x)cos(x).6 * 2sin(x)cos(x) = 12sin(2x). This is our final answer, using the double angle formula to rewrite the original expression.Learn more about double angle formula here:https://brainly.com/question/34830073
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Final answer:
The expression 12sinxcosx can be rewritten as 6sin(2x) by using the double angle formula for sine.
Explanation:
The expression 12sinxcosx can be rewritten using the double angle formula for sine, which is sin(2a) = 2sina ⋅ cosa. By comparing this to the given expression, we can see that it is in the form of the right-hand side of the double angle formula, where a is equivalent to x. Therefore, the expression can be rewritten as 6sin(2x). Such double angle formulae are available for other trigonometric ratios as well.
In a study of 38% of adults questioned reported that their health was excellent. a researcher wishes to study the health of people living close to a nuclear power plant. find the probability that when 11 adults are randomly selected, at most 3 are in excellent health
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The probability that when 12 adults are randomly selected, 3 or fewer are in excellent health is 0.947.
To find the probability that when 12 adults are randomly selected, 3 or fewer are in excellent health, we can use the binomial distribution formula.
The formula for the probability of getting exactly k successes in n trials, with a probability of success p, is:
P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))
In this case, n = 12, k = 3, and p = 0.38 (as 38% of adults reported excellent health).
So, the probability that 3 or fewer adults are in excellent health can be calculated as follows:
P(X <= 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
Let's calculate each term:
P(X = 0) = (12 choose 0) * (0.38^0) * (0.62^12) = 0.190P(X = 1) = (12 choose 1) * (0.38^1) * (0.62^11) = 0.342P(X = 2) = (12 choose 2) * (0.38^2) * (0.62^10) = 0.269P(X = 3) = (12 choose 3) * (0.38^3) * (0.62^9) = 0.146Adding up these probabilities:
P(X <= 3) = 0.190 + 0.342 + 0.269 + 0.146 = 0.947
Rounded to three decimal places, the probability that when 12 adults are randomly selected, 3 or fewer are in excellent health is 0.947.
The probable question may be:
In a study, 38% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 12 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 12 adults are randomly selected, 3 or fewer are in excellent health. Round to three decimal places.
On a map, the distance between two cities is 2.4 inches. the two cities are actually 768 miles apart. on this same map, what would be the distance between two cities in miles that are 4.8 inches apart on the map?
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Sara loves to go hiking this weekend she hiked 3 miles on Monday 4 miles on Tuesdays and 3 miles on Thursday .last week Sara hiked 8 miles. How many more miles did Sara hike this week than last week
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Last week: 8
Difference: 10 - 8 = 2
Sarah walked two more miles this week than last week.
Answer:
2 miles
Step-by-step explanation:
Sara loves to go hiking.
She hiked 3 miles on Monday 4 miles on Tuesdays and 3 miles on Thursday.
Last week Sara hiked 8 miles
This week sara hiked = Monday + Tuesday + Thursday
= 3 + 4 + 3
= 10 miles
Last week hiked = 8 miles
Difference in two week hiked by Sarah = 10 - 8
= 2 miles
So, Sarah hike 2 miles more than last week.
Which of the following is equivalent to C(16, 4)?
answer choices:
12!
C(16, 12)
C(15, 3)
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Answer- C(16,12)
C(n,r) = n! / r!* (n-r)!
So,
C(16,4) = 16!/ 4! * 12!
C(16,12) = !6!/ 12! * 4!
42) According to the 2000 Census the population of Canton was 7,720. Holly Spring's population was 3,200. Canton's population increases at a rate of 80 people a year and Holly Spring's population increases by 120 people a year. Which equation may be used to determine the number of years before the populations are equal?
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The diameter of Jupiter is 88,000 miles This is about 11.1 times the diameter of Earth What is the diameter of the earth
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linear sale factor=(diameter of Jupiter) /(diameter of earth)=11
thus:
diameter of earth=(diameter of Jupiter)/(linear scale factor)
=88000/11
=8000 miles
The diameter of earth is 8000 miles
Find the value of x.
The polygons are similar, but not necessarily drawn to scale.
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Cross multiply:
[tex]12x = 3 \times 40[/tex]
Evaluate RHS:
[tex]12x = 120[/tex]
Divide both sides by 12:
[tex]x = 10[/tex]
Answer:
[tex]x=10 units[/tex]
Step-by-step explanation:
Given: The polygons ABCD and JKLM are similar.
To find: The value of x.
Solution: Since, the given polygons are similar, therefore using the similarity condition, we have
[tex]\frac{AD}{JM}=\frac{CD}{LM}[/tex]
Substituting the given values, we get
[tex]\frac{12}{40}=\frac{3}{x}[/tex]
On cross multiplying, we get
[tex]\frac{3\times40}{12}=x[/tex]
[tex]x=10 units[/tex]
Therefore, the value of x is 10 units.
The real number 8.09 belongs to which set of numbers??
A-natural numbers
B-integers
C-irrational numbers
D-rational numbers
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Hope this helps!
8.09 can be rewritten as 8 9/100, which in turn can be rewritten as 809/100. This is the ratio of two integers. So, 8.09 is rational.
The slope of BY is -1/5, and BYllJE
What is the slope of JE?
-5
-1/5
1/5
5
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I hope this helped.
What is 6.8 rounded to the nearest ones place?
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6.8 is nearer to 7 than to 6. so, 6.8 ≈ 7
↓
|------|------|------|------|------|------|-----|------|------|------|
6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7
Answer: 7
In the circle below, radius mn = 1.4 m and mlmn = 52°. determine the length of arc ln. round your answer to the nearest tenth and use π = 3.14.
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Arc length=θ/360×π×d
θ=52
d=2×1.4=2.8 m
thus
Arc length will be:
52/360×3.14×2.8
=1.27 m
Answer:
1.27 is the answer
Step-by-step explanation:
PLEASE HELP. evaluate the radical 3√1000
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We can also do this by doing √9000 which is also 94.87
Simplify the expression below. 6n2 - 5n2 + 7n2
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18n^2
14. the number of deer spotted in a nature preserve each day over a two week period is listed below. 32 27 15 12 42 35 46 29 38 18 40 38 32 34
which frequency table represents the data ?
A. deer
10-19
20-29
30-39
40-49
frequency
3
3
5
4
B. Deer
10-19
20-29
30-39
40-49
frequency
3
2
5
4
c. deer
10-19
20-29
30-39
40-49
frequency
4
1
7
2
d. deer
10-19
20-29
30-39
40-49
frequency
3
2
6
3
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Simply put, The frequency of a particular data value is the number of times the data value occurs. A frequency table is constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies. I hope this helps with answering any further questions. Good luck!
Using Frequency table, Option: (d) is correct.
What is Frequency?Frequency refers to "the number of times an event or values occurs".
According to the question,
The number of deer spotted in preserve is
32,27,15,1,42,35,46,29,38,18,40,38,32,34
The number deer appear in the interval 10 - 19 is 3
The number deer appear in the interval 20 - 29 is 2
The number deer appear in the interval 30 - 39 is 6
The number deer appear in the interval 40 - 49 is 3
From the above data, we can form frequency table
Deer 10 - 19 20 - 29 30 - 39 40 - 49
Frequency 3 2 6 3
Hence, the answer is Option: (d)
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triston is baking specity bread for the school bake sale. she has 10 1/2 cups of flour. the recipe for 1 loaf of bread calls for 2 1/3 cups of flour. How many whole loaves of bread can she make.
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Triston can make 4 whole loaves of bread using her 10 1/2 cups of flour. This was determined by dividing the total flour available by the flour required per loaf. Fractional or partial loaves are not counted.
To determine how many whole loaves of bread Triston can make, we need to perform a simple division of the total amount of flour by the amount required for one loaf.
First, let's convert the mixed numbers to improper fractions:
10 1/2 cups of flour = 21/2 cups of flour2 1/3 cups of flour = 7/3 cups of flourNext, we will divide the total flour by the flour needed per loaf:
(21/2) ÷ (7/3) = (21/2) × (3/7) = (21 × 3) / (2 × 7) = 63/14 = 4.5 loaves
Since we can only make whole loaves, Triston can make 4 whole loaves of bread.
A fair coin is tossed three time sin succession. the set of equally likely outcomes is {hhh,hht,hth,thh,htt,tht,tth,ttt}. find the probabilty of getting exactly zero tails
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Now, there is only one of the eight outcomes that has zero tails.
Therefore the probability of getting zero tails after tossing a fair coin three times in succession is
[tex] \frac{1}{8} [/tex]
divide and simplify completely. 8x-8/x^2-1 * x + 1 / 6x^2 - 12x / 24 / x^2 - 4
A 32 / x(x + 2)(x - 2)^2
B x + 2 / 18x
C 32(x + 1) / x(x + 2)(x - 2)^2
D (x + 2)(x + 1) / 18x(x - 1)