Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. ex = 3 − 2x, (0, 1) The equation ex = 3 − 2x is equivalent to the equation f(x) = ex − 3 + 2x = 0. f(x) is continuous on the interval [0, 1], f(0) = _____, and f(1) = _____. Since f(0) < 0 < f(1) , there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation ex = 3 − 2x, in the interval (0, 1)
Answer:
[tex]f(0)=-2\\f(1)=e-1[/tex]
Step-by-step explanation:
According to intermediate value theorem, if a function is continuous on an interval [tex][a,b][/tex], and if [tex]k[/tex] is any number between [tex]f(a)[/tex] and [tex]f(b)[/tex], then there exists a value, [tex]x=m[/tex], where [tex]a<m<b[/tex], such that [tex]f(m)=k[/tex]
In the given question,
Intermediate Value Theorem is used to show that there is a root of the given equation in the specified interval.
Here,
[tex]f(x)=e^x-3+2x[/tex]
Put [tex]x=0[/tex]
[tex]f(0)=e^0-3+2(0)=1-3+0=-2[/tex]
Put [tex]x=1[/tex]
[tex]f(1)=e^1-3+2(1)=e-3+2=e-1[/tex]
Find atleast 5 numbers between 1/2 and 1/3.
Answer:
12.2 12.3 12.4 12.5
Step-by-step explanation:
m∠3 = 57. Find m∠1. (I'm just typing here to meet the 20 character min.)
Answer:
The correct answer is 57 degrees.
Step-by-step explanation:
To solve this problem, we must remember that vertical angles (angles that are across from each other) are congruent, which means that they have the same measure.
In the diagram, angle 3 and angle 1 are vertical angles, so we can conclude that they have the same measure.
Therefore, m<1 = m<3 = 57 degrees.
Hope this helps!
Keiran wants to save $56 for a gift for his mother’s birthday in 14 weeks. How much money must he save each week?
Please Solve Brainliest and 10 points!
Answer:
x=20°
Step-by-step explanation:
statements:1.) m<DOB = m<DOE + m<BOE (or m<EOB)
2.) m<DOB = 90°+x
3.) m<AOC = m<DOB
4.) 110° = 90° + x
5.) x = 20°
reasons:1.) given
2.) substitution
3.) vertical/reflexive
4.) substitution
5.) algebra
• Which expression is equivalent to 2(8n)
Answer:
It's B :) *the second one to the right*
Step-by-step explanation:
An expression is equivalent to given expression is 2×8n×8n×8n×8n. Therefore, option B is the correct answer.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is 2(8n)⁴.
Here, the equivalent expression is
2×8n×8n×8n×8n
= 2×4096n⁴
= 8192n⁴
Therefore, option B is the correct answer.
To learn more about an equivalent expression visit:
https://brainly.com/question/28170201.
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A food-protection agency counts the number of insect heads found per 100-gram batch of wheat flour. The researchers have 500 batches, and they want to know whether the frequency of insect heads in batches follows a distribution called a Poisson distribution. To generate the expected frequencies of batches with different numbers of insect heads under a Poisson distribution, they had to estimate the mean number of insect heads per batch from the data. The 500 batches included at least 5 batches having 0, 1, 2, 3, or 4 insect heads. No batches had more than four heads. Given this information, there are_____classes (k).
Answer:
The correct answer is k = 5.
Step-by-step explanation:
The Chi-square goodness of fit test would be used to determine whether the frequency of insect heads in batches follows a distribution called a Poisson distribution.
The hypothesis for the test can be defined as follows:
H₀: The frequency of insect heads in batches does not follows a Poisson distribution.
Hₐ: The frequency of insect heads in batches follows a Poisson distribution.
Assume that the significance level of the test is, α = 0.05.
The Chi-square test statistic is given by:
[tex]\chi^{2}=\sum\limits^{k}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
It is provided that the 500 batches included at least 5 batches having 0, 1, 2, 3, or 4 insect heads. No batches had more than four heads.
So, the number of classes or categories are, k = 5.
Thus, the correct answer is k = 5.
1. FRUITS Find the ratio of bananas to oranges in the graphic at the right. Write the
ratio in simplest form. Then explain its meaning.
Ratio:
Simplified Ratio:
Explanation:
so what is the answer?
Answer:
999kkk b8llion
Step-by-step explanation:
iiuugghhgvvjhhffffffffffffffggttgggg
Divide.
636-3
The quotient is
and the remainder is
Answer:
212
Step-by-step explanation:
3 goes into 6 = 2 times
3 goes into 3 = 1 time
3 goes into 6 = 2 times
2 → 1 → 2 = 212
15 men can dig a ditch in 10 days, how many day
Will 10men take working at the same rate
Answer:
If 10 men dig a ditch in 12 days .
Total man-days required to dig the ditch
= 10 men × 12 days
= 120 man-days
how long would 15 men take to dig it?
No of days required to finish the job by 15 men
= 120 men-days / 15 men
= 8 days
Answer: 8 days will be required to finish the job by 15 men
Step-by-step explanation:
Hope this helps u
Crown me as brainliest:)
The quanities x and y are proportional Find the constant of proportionality (r) in the equation y= rx
CORRECT ANSWER = BRAINLEIST
Answer:
5
Step-by-step explanation:
7*5=35
12*5=60
20*5=100
Find the point P that is 2/5 of the way from A to B on the directed line segment AB if A (-8, -2) and B (6, 19).
The location of the point P that is 2/5 of the way from A to B on the directed line segment AB if A(x, y) = (- 8, -2) and B(x, y) = (6, 19) is P(x, y) = (- 12/5, 32/5).
How to determine the location of a point within a line segment
By geometry we know that a line segment is generated from two distinct points set on a plane. The location of the point P within the line segment can be found by means of the following vectorial formula:
P(x, y) = A(x, y) + k · [B(x, y) - A(x, y)], 0 < k < 1 (1)
Where:
A(x, y) - Initial pointB(x, y) - Final pointk - Distance factorIf we know that A(x, y) = (- 8, - 2), B(x, y) = (6, 19) and k = 2/5, then the location of the point P is:
P(x, y) = (- 8, -2) + (2/5) · [(6, 19) - (- 8, -2)]
P(x, y) = (- 8, -2) + (2/5) · (14, 21)
P(x, y) = (- 12/5, 32/5)
The location of the point P that is 2/5 of the way from A to B on the directed line segment AB if A(x, y) = (- 8, -2) and B(x, y) = (6, 19) is P(x, y) = (- 12/5, 32/5).
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A process is normally distributed and in control, with known mean and variance, and the usual three-sigma limits are used on the control chart, so that the probability of a single point plotting outside the control limits when the process is in control is 0.0027. Suppose that this chart is being used in phase I and the averages from a set of m samples or subgroups from this process are plotted on this chart. What is the probability that at least one of the averages will plot outside the control limits when m = 5? Repeat these calculations for the cases where m = 10, m = 20, m = 30, and m = 50.
Required:
Discuss the results that you have obtained.
Answer:
The solution to the issue is outlined in the following portion of the summary.
Step-by-step explanation:
The given value is:
p = 0.0027
When m = 5,
⇒ [tex]P (x \geq 1) = 1 - P (x = 0)[/tex]
[tex]=1 - 5C0 (0.0027)^0 (1 - 0.0027)^5[/tex]
[tex]= 1 - 0.9866[/tex]
[tex]=0.0134[/tex]
When m = 10,
⇒ [tex]P (x \geq 1) = 1 - P (x = 0)[/tex]
[tex]=1 - 10C0 (0.0027)^0 (1 - 0.0027)^{10}[/tex]
[tex]=1 - 0.9733[/tex]
[tex]= 0.0267[/tex]
When m = 20,
⇒ [tex]P (x \geq 1) = 1 - P (x = 0)[/tex]
[tex]=1 - 20C0 (0.0027)^0 (1 - 0.0027)^{20}[/tex]
[tex]=1 - 0.9474[/tex]
[tex]=0.0526[/tex]
When m = 30,
⇒ [tex]P (x \geq 1) = 1 - P (x = 0)[/tex]
[tex]=1 - 30C0 (0.0027)^0 (1 - 0.0027)^{30}[/tex]
[tex]=1 - 0.9221[/tex]
[tex]=0.0779[/tex]
When m = 50,
⇒ [tex]P (x \geq 1) = 1 - P (x = 0)[/tex]
[tex]= 1 - 50C0 (0.0027)^0 (1 - 0.0027)^{50}[/tex]
[tex]= 1 - 0.8736[/tex]
[tex]=0.1264[/tex]
A survey of 120 college students is conducted and the results displayed below show that 80 students have a smartphone, 65 have a tablet, and 10 have neither. Fill in the empty table cells in the two-way frequency table.
Smartphone No Smartphone Total
Tablet 65
No Tablet 10
Total 80 120
What is the probability (rounded to the nearest whole percent) that a randomly selected college student has a tablet but not a smartphone? (4 points)
a
25%
b
30%
c
54%
d
38%
Answer:
the answer is 54 %
Step-by-step explanation:
divide 120/65=0.54, then since you're looking for the percent you multiply it by 100, and the answer would be 54%
NEED HELP WITH MATH! Will Give Brainliest! Image is below.
Answer:
2
Step-by-step explanation:
What number should be placed in the box to help complete the division calculation?
Long division setup showing an incomplete calculation. 17 is in the divisor, 2635 is in the dividend, and 1 hundreds and 5 tens is written in the quotient. 1700 is subtracted from 2635 to give 935. An unknown value represented by a box is being subtracted from 935.
Numerical Answers Expected!
Answer for Blank 1:
I WILL GIVE LOTS OF BRAINYS 20
PLEASE HELP I WILL DO ENEYTHING PLEASE
l. l. l_____. l. l__-__
l------- l l_____. l l. ____ l
l. l. l_____. l_____ l
Answer:
780
Step-by-step explanation:
17 is the divisor, while 2635 is the dividend. So that,
[tex]\frac{2635}{17}[/tex] = 155
The quotient = 155 = 1 hundreds, 5 tens and 5 units
Also,
2635 - 1700 = 935
Hence, let the unknown value be represented by x. Then;
935 - x
The answer of the subtraction should be equal to the quotient of the division.
935 - x = 155
935 - 155 = x
780 = x
Therefore the unknown value represented by a box is 780.
Answer:
780
Step-by-step explanation:
Given the probability that "she's up all night 'til the sun" OR "she's up all night for good fun" is 0.36, the probability that "she's up all night for good fun" is 0.41, and the probability that "she's up all night 'til the sun" is 0.36, what's the probability that "she's up all night 'til the sun" AND "she's up all night for good fun"?
Answer:
0.41
Step-by-step explanation:
S = "she's up all night 'til the sun"
F = "she's up all night for good fun"
P(S or F) = P(S) + P(F) − P(S and F)
0.36 = 0.36 + 0.41 − P(S and F)
P(S and F) = 0.41
Write each prime factorization using exponents.
1. 2×2×2×7
2. 2×3×3
3. 7×7×7×7
The manager of a restaurant determined that the odds against a customer ordering dessert are 11/12 . What is the probability of a customer ordering dessert?
Answer:
1 out of 12
Step-by-step explanation:
12-11=1
Please help!!!- Find the measure of the angle in bold.
Need help to figure out to solve this.
Answer:
x = 11
Step-by-step explanation:
3x + 7 = 13 (x = -2; x = 2; x = 5)
Answer:
(x=2)
Step-by-step explanation:
Answer:
x = 2
Step-by-step explanation:
3(-2) + 7 = 1....its not this one because when we plug in -2 for x we get 1 not 13.
3(2) + 7 = 13...its this one because when we plug in 2 for x we get 13.
3(5) + 7 = 22...its not this one because when we plug in 5 for x we get 22 not 13.
hope this helps
What is 86.929 rounded to the nearest tenth ?
Answer:
86.9
Step-by-step explanation:
This is because after the decimal point, it goes to the tenths place and then the thousands place, therefore, if you round it, it would be 86.9.
ax+6=15 a is a negative, what must be true about x?
Answer:
x= 9/a
Step-by-step explanation:
Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R^5? Why?
a. The matrix must have nothing pivot columns. If A had fewer pivot columns, then the equation A would have only the trivial solution.
b. The matrix must have nothing pivot columns. The statements "A has a pivot position in every row" and "the columns of A span " are logically equivalent.
c. The matrix must have nothing pivot columns. Otherwise, the equation A would have a free variable, in which case the columns of A would not span .
d. The columns of a 57 matrix cannot span because having more columns than rows makes the columns of the matrix dependent
Answer:
The answer is "Option B".
Step-by-step explanation:
In the given choices there is some mistake so, the correct choice can be defined in the attached file. please find it.
In the given question, If the column of [tex]5 \times 7[/tex] matrix, and the A span is equal to [tex]R^5[/tex], and then the value of A has a pivot in each row, that's why in each pivot its position in the different columns of A has the five pivot columns, that's why the choice B is correct.
How do you solve this? Without going into anything to complicated as this should be Year 10 maths
Given : ABCD is a square with each side 5cm .
To Find : The area of the shaded region .
Solution : On observing the figure we can see two quadrants , quadrant ADC & quadrant ABC .
If we join A to C , then it will be common for triangles ADC & ABC . And they will be congruent by SSS congruence condition.
Therefore the area of both quadrants will also be equal . Now we can find area of quadrant as ;
[tex]\large\boxed{\red{\bf Area_{quadrant}=\dfrac{\pi r^2}{4}}}[/tex]
Here radius will be equal to 5cm .
⇒ Area = πr² / 4 .
⇒ Area = π (5cm)² / 4 .
⇒ Area = 22/7 × 25 × 4 cm².
⇒ Area = 19.64 cm² .
So , total area of both quadrants = 39.28 cm² .
Also , area of square will be :
[tex]\large\boxed{\bf{\red{Area_{square}=(side)^2}}}[/tex]
⇒ Area = 5cm × 5cm .
⇒ Area = 25 cm².
Now , subtract area of one quadrant from the area of square = 25cm² - 19.64 cm² = 5.36 cm².
Similarly area of other white region = 5.36cm² .
And the areas sum will be = 5.36cm² × 2 = 10.72cm² .
Now , from the figure it's clear that ,
⇒ Area of unshaded region + Area of shaded region = 25cm².
⇒ 10.72cm² + ar( Shaded region ) = 25cm².
⇒ ar ( Shaded region ) = 25cm² - 10.72cm².
⇒ ar ( Shaded region ) = 14.28 cm².
Hence the area of shaded region is 14.28 cm².
[tex]\large\boxed{\red{\bf Answer = 14.28cm^2}}[/tex]
Please help me!!! ASAP!
Option C
Olivia paid $ 15683.28 after 8 years
14. Three years ago, Kyaw Kyaw was thrice as old as his
sister Zin Zin. After three years
Kyaw Kyaw will be twice as old as Zin Zin. What is the present age of Zin Zin?
Answer: Just a question what was the present age of Zin Zin three years ago will really help?? Thank You
Step-by-step explanation:
The inverse of a function is a function. True or False
Answer:
false
Step-by-step explanation:
Answer:
TrueStep-by-step explanation:
The inverse of a function may not always be a function! The original function must be a one-to-one function to guarantee that its inverse will also be a function.
If the graph does not pass the Horizontal Line Test, then the graphed function's inverse will not itself be a function
to multiply a decimal number by a 1,000 , move the decimal point four places to the right
Answer:
that is the answer
Step-by-step explanation:
Answer:
Step-by-step explanation:
whoop
A florist must make 5 identical
bridesmaid bouquets for a wedding. The budget is
$160, and each bouquet must have 12 flowers. Roses
cost $2.50 each, lilies cost $4 each, and irises cost
$2 each. The florist wants twice as many roses as the
other two types of flowers combined.
Answer:
A. 40x + 10y + 10z = $160
B. 8 Roses, 2 lilies and 2 irises
C.
1. 20x + 5y + 5z = $80
2. 4x + y + z = $16
3. 8x + 2y + 2z = $32
Step-by-step explanation:
Cost for each flower = $160/5 = $32
So we have $32 for each bouquet consisting of 12 flowers each.
Roses = x = $2.50 each
lilies = y = $4 each
irises = z = $2 each
8x + 2y + 2z = $32
8($2.50) + 2($4) + 2($2) = $32
$20 + $8 + $4 = $32
$32 = $32
a. Maximum budget is $160
40x + 10y + 10z = $160
40($2.50) + 10($4) + 10($2) = $160
$100 + $40 + $20 = $160
$160 = $160
b. From above
8x + 2y + 2z = $32
8 Roses, 2 lilies and 2 irises
c. No. There are other solutions If total cost is not limited
1. 20x + 5y + 5z
20($2.50) + 5($4) + 5($2)
$50 + $20 + $10
= $80
2. 4x + y + z
4($2.50) + $4 + $2
$10 + $4 + $2
= $16
3. 8x + 2y + 2z
8($2.50) + 2($4) + 2($2)
$20 + $8 + $4
= $32