H_0: mu=10, H_a: mu not equal 10. n=25, sigma-3, sample mean xbar =11. The Z-value is 1.67. Option B
How to calculate the Z-valueTo calculate the Z-value, we can use the formula:
Z = (xbar - mu) / (sigma / sqrt(n))
Where xbar is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.
Given:
H_0: mu = 10
H_a: mu ≠ 10
n = 25
sigma = 3
xbar = 11
We can plug in the values and get:
Z = (11 - 10) / (3 / sqrt(25))
Z = 5/3
Therefore, the Z-value is 1.67.
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Jose is a middle-aged professor who wants to retire early and start his own coaching classes. He decides to invest his savings and use the returns to fund his business venture.
That sounds like a smart plan! Before investing his savings, Jose should do some research to determine the best investment strategy for his goals.
What is research?
He will need to consider factors such as his risk tolerance, the potential return on investment, and the length of time he has to invest. Once he has identified an investment strategy that aligns with his goals, he should start investing his savings.
Over time, as his investments generate returns, he can use these returns to fund his business venture. It is important for Jose to regularly monitor his investments and adjust his strategy as needed to ensure that he is on track to achieve his goals. With careful planning and a well-executed investment strategy, Jose can achieve his goal of retiring early and starting his own coaching classes.
What is an investment ?
An investment refers to the purchase of an asset with the goal of generating income, capital appreciation, or both. The asset could be anything of value, such as stocks, bonds, real estate, commodities, or mutual funds. Investors typically make an investment with the expectation of earning a return on their investment over a period of time.
The return could be in the form of interest, dividends, or capital gains, depending on the type of investment. Investors may choose to invest in different types of assets based on their investment goals, risk tolerance, and investment horizon. The process of investing involves conducting research, analyzing market trends, and making informed decisions based on the available information.
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Complete question is: Jose is a middle-aged professor who wants to retire early and start his own coaching classes. He decides to invest his savings and use the returns to fund his business venture. Before investing his savings, Jose should do some research to determine the best investment strategy for his goals.
23. 3 kg आलु र 2 kg प्याजको जम्मा मुल्य रु 240 आलुको दरमा 20% से वृद्धि र प्याजको दरमा 10% से कमी हुँदा 5kg आलु र 7 kg प्याजको जम्मा मुल्य रु 618 पर्न आउँछ भने 1 kg प्याजको मुल्य, 1 kg आलुको मुल्यभन्दा कति प्रतिशतले बढी वा कम हुन्छ ? पत्ता लगाउनुहोस् | The toptal cost of 3kg potato and 2 kg onion is Rs. 240. If the rate of potato increases by 20% and the rate of onion decreases by 10%, the total cost of 5 kg potato and 7 kg onion will be Rs. 618. By what percent the cost of 1 kg onion is more
Step-by-step explanation:
Here , the eqn is given as,
Let 1 kg onion cost Rs. y and 1kg potato cost Rs. y then,
3x + 2y= 240....eqn i
The When rate of potato increases by 20 percent,
New rate of unit kg potato becomes,
[tex]x \: + \: 20\% \: of \: x[/tex]
i.e. Rs.6x/5
And when price of onion decreases by 10% ,
New unit price is ,
[tex]y - 10\% \: of \: y[/tex]
i.e. Rs.9y/10
Now the second eqn becomes ,
20x + 21y= 2060
By using elimination method we get x= Rs 40 and y= Rs.60
Finally, we have to find percent change i.e
{(cost of 1kg onion - cost of 1kg potato)/ cost of 1kg potato}x 100%
This gives the ans as 50%
In parallelogram MNPQ if
m
∠
�
�
�
=
13
5
∘
m∠PQM=135
∘
find
m
∠
�
�
�
m∠MNP.
We can conclude that m∠MNP has a measure of 0 degrees in parallelogram MNPQ.
What is a parallelogram?A parallelogram is a four-sided geometric shape in which opposite sides are parallel and congruent (equal in length) to each other. It is a special case of a quadrilateral, which is any four-sided polygon.
In the given question,
Since opposite angles in a parallelogram are equal, we know that:
m∠MNP = m∠QMN
We also know that the sum of the interior angles of a triangle is 180 degrees. Therefore, we can find the measure of angle MQN as follows:
m∠MQN = 180 - m∠PQM = 180 - 135 = 45 degrees
Now, we can use the fact that the opposite angles in a parallelogram are equal to find the measure of angle QMN:
m∠QMN = m∠PQM = 135 degrees
Finally, we can use the fact that the angles in a triangle add up to 180 degrees to find the measure of angle MNP:
m∠MNP = 180 - m∠MQN - m∠QMN
= 180 - 45 - 135
= 180 - 180
= 0 degrees
Therefore, we can conclude that m∠MNP has a measure of 0 degrees. This means that the sides MN and PQ are parallel and do not intersect, so angle MNP does not exist.
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Giving out brainliest to the correct answer!
The nth derivative of g at x = 0 is given by g(n) (0) = (-1)n (n − 1)!
for n ≥ 1.
n+3
What is the coefficient for the term containing 4 in the Maclaurin series
of g?
Choose 1 answer:
1/28
6/7
1/7
3/28
Answer: 1/7
Step-by-step explanation:
d d x ( ∑ n = 0 ∞ c n ( x − a ) n ) = c 1 + 2 c 2 ( a − a ) + 3 c 3 ( a − a ) 2 + ⋯ = c 1/7
UV is tangent to ⨀T. What is
Step-by-step explanation:
if we extend the line VT to reach also the opposite side of the circle, we see that this line cuts the circle in half.
the whole arc angle of a half-circle is 360/2 = 180°.
now we can use the exterior angle rule :
the vertex angle (V) = 1/2 × difference of the angles of the intersected arcs.
the intersected arcs are
shorter = angle at T : the arc from U to the circle intersection with the line VT.
longer : the arc from U to the circle intersection with the extended line VT.
shorter + longer = 180°
longer = 180 - shorter
30 = 1/2 × ((180 - shorter) - shorter) =
= 1/2 × (180 - 2×shorter) = 90 - shorter
-60 = -shorter
shorter = 60°
the angle at T = 60°.
Suppose the weights of sumo wrestlers are normally distributed with a mean of 330lbs and a standard deviation of 15lbs. An up and coming competitor wants to defeat wrestlers whose weights are in the top 10%. What is the minimum weight of the sumo wrestlers at the highest weight of the league? Round your answer to the nearest whole number, if necessary.
I have to figure out how to use Excel's NORM.INV() function to solve this.
Answer: To use Excel's NORM.INV() function to solve this problem, we can follow these steps:
Determine the z-score corresponding to the top 10% of the distribution. We can use the NORM.INV() function to find this value. Since we want the top 10%, we'll use a probability of 0.9 and a mean of 330lbs and a standard deviation of 15lbs. In Excel, we can use the formula:
=NORM.INV(0.9,330,15,TRUE)
This gives us a z-score of 1.281552.
Once we have the z-score, we can use the formula for a normal distribution to find the corresponding weight. The formula is:
z = (x - μ) / σ
where z is the z-score, x is the weight we're trying to find, μ is the mean weight (330lbs), and σ is the standard deviation (15lbs).
Rearranging this formula to solve for x, we get:
x = z * σ + μ
Substituting in the values we know, we get:
x = 1.281552 * 15 + 330
This gives us a weight of approximately 349lbs.
Therefore, the minimum weight of the sumo wrestlers at the highest weight of the league is about 349lbs, rounded to the nearest whole number.
Step-by-step explanation:
For the function f(x) = 2 (x − 1), find ƒ−¹(x).
Answer:
To find ƒ⁻¹(x), we need to solve for x in terms of ƒ⁻¹(x).
So, we start with the equation:
x = 2 (ƒ⁻¹(x) - 1)
We isolate ƒ⁻¹(x) by dividing both sides by 2 and adding 1 to both sides:
ƒ⁻¹(x) = (x/2) + 1
Therefore, the inverse of the given function f(x) is:
ƒ⁻¹(x) = (x/2) + 1
I don’t understand please help ?
For the given functions f(x) and g(x), the inverse functions of f and g are:
a. f(g(x)) = x; g(f(x)) = x
ƒ and g are inverses of each other.
b. (g(x)) = x; g(f(x)) = x
ƒ and g are inverses of each other
What are the inverse functions of f and g?The inverse functions of the functions f(x) and g(x),are determined as follows;
a. f(x) = 2x, g(x) = x/2
f(g(x)) = f(x/2)
f(g(x)) = 2(x/2)
f(g(x)) = x
g(f(x)) = g(2x)
g(f(x)) = (2x)/2
g(f(x)) = x
Since f(g(x)) = g(f(x)) = x, ƒ and g are inverses of each other.
b. f(x) = 2x + 1, g(x) = (x -1)/2
f(g(x)) = f((x-1)/2)
f(g(x)) = 2((x-1)/2) + 1
f(g(x)) = x - 1 + 1
f(g(x)) = x
g(f(x)) = g(2x + 1)
g(f(x)) = ((2x + 1) - 1)/2
g(f(x)) = 2x/2
g(f(x)) = x
Since f(g(x)) = g(f(x)) = x, ƒ and g are inverses of each other.
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An equilateral triangle is inscribed in a
circle with center O. The triangle is ther
rotated 30° to obtain another equilateral
triangle inscribed in the circle.
Jom kuivad
5. What is m/AOC? ala
120
6. Prove that the diameter through B is
perpendicular to the diameter through C.
Since the triangle was rotated by 30 degrees, the angle AOA' is 30 degrees, as is the angle A'OC. Thus, m/AOC is equal to 60 degrees. To demonstrate that BD is perpendicular to CD, OB = OC, angles AOB and COA are both 60 degrees, and angles BOD and COD are both 60 degrees. BD and CD are both perpendicular to the diameter through A.
What is an equilateral triangle?A triangle is said to be equilateral if all three of its sides are the same length and all three of its angles are exactly 60 degrees. It has three regular sides and is a polygon. When dividing an equilateral triangle into two congruent 30-60-90 triangles, the altitude, median, and angle bisector from any vertex are also the same line.
5. Let's identify the circle's intersection points as the equilateral triangle's A, B, and C. All angles in a triangle that is equilateral are 60 degrees. Point A will change locations when the triangle is rotated by 30 degrees; let's designate this new position A'. Since O is the centre of the circle, the angle AOC remains at 60 degrees. Since the triangle has been turned by 30 degrees, the angle AOA' is 30 degrees, as is the angle A'OC. Thus, m/AOC is equal to 60 degrees.
6. The center of the circle is O, and D is the point where the diameter through B intersects the diameter through C. To demonstrate that BD is perpendicular to CD, the center of the circle, OB = OC, and angles AOB and COA are both 60 degrees, so angle BOC is 120 degrees. Angle BOD is a right angle, and angle OBD is half of angle BOC, so it is 60 degrees. Angle COD is also a right angle, and angle OCD is half of angle BOC, so it is also 60 degrees. Since angles OBD and OCD are both 60 degrees, and they are angles in a triangle, the third angle (angle BDC) must also be 60 degrees.
Therefore, triangle BDC is equilateral, and BD = CD. Since BD and CD are both perpendicular to the diameter through A, BD is perpendicular to CD.
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The volume of this cube is 64 cubic meters. What is the value of y?
y =
meters
Answer:
y = 4 meters
Step-by-step explanation:
to find a volume of a cube you do (y × y) y
so if Y equals 4 then it would look like this:
(4 × 4)4 which = 64
What scale factor was used to dilate point D? D(-1,-1)-D'(4,4)
Answer:
Step-by-step explanation:
scale factor is -4
D(-1 , -1) and if you divide either the x coordinate or the y coordinate by
4 - you get negative four which is the scale factor.
For what numbers x, -2π≤ x ≤ 2π, does the graph of y = sec x have vertical asymptotes.?
The graph of y = sec(x) will have vertical asymptotes at these three values of x.
Define vertical asymptotesVertical asymptotes are vertical lines on a graph where a function approaches either positive or negative infinity as the independent variable approaches a certain value.
The secant function, y = sec(x), is defined as the reciprocal of the cosine function:
sec(x) = 1/cos(x)
The cosine function has vertical asymptotes at x = (2n + 1)π/2 for any integer n, since cosine is undefined at these points (division by zero). Therefore, the secant function will have vertical asymptotes at the same points, since dividing 1 by a very small number (close to zero) results in a very large number (tending towards infinity).
So, the values of x in the interval -2π ≤ x ≤ 2π that will cause the secant function to have vertical asymptotes are:
x = (2n + 1)π/2, where n is an integer
For n = -2, we have x = -5π/2, which is outside the interval, so we can ignore it.
For n = -1, we have x = -π/2
For n = 0, we have x = π/2
For n = 1, we have x = 3π/2
For n = 2, we have x = 5π/2, which is also outside the interval.
Therefore, the values of x in the interval -2π ≤ x ≤ 2π that will cause the secant function to have vertical asymptotes are:
x = -π/2, π/2, 3π/2
So, the graph of y = sec(x) will have vertical asymptotes at these three values of x.
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Please help me describe how to simplify this expression.
we have successfully simplified the expression x⁵-x³ into x³(x + 1)(x - 1). This can be useful for further algebraic manipulation or simplification in larger expressions.
How to simplify?
To simplify the expression x⁵-x³, we can factor it using the distributive property of multiplication. First, we can factor out x³ from both terms:
x⁵ - x³ = x³(x² - 1)
Now, we can further simplify by recognizing that x² - 1 is a difference of squares, which can be factored into (x + 1)(x - 1). So, we have:
x⁵ - x³ = x³(x² - 1) = x³(x + 1)(x - 1)
This is the fully simplified form of the expression. We can also expand the expression to verify that it is equivalent to the original expression:
x³(x + 1)(x - 1) = (x³ * x) + (x³ * -1) + (x³ * 1) + (x³ * -1) = x⁴ - x³ + x³ - x³ = x⁴ - x³
So, we have successfully simplified the expression x⁵-x³ into x³(x + 1)(x - 1). This can be useful for further algebraic manipulation or simplification in larger expressions.
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Please help me to get my homework completed so that we don’t have to worry anymore and we can go back home tomorrow morning if we want to
Answer:
45.32
Step-by-step explanation:
Emilie has a drawer full of color for ribbons the probability of randomly selecting a green ribbon is 84% which of the following describes the likelihood of selecting a green ribbon
When the probability of an event is high, we can say that the likelihood of that event occurring is also high. Conversely, when the probability of an event is low, the likelihood of that event occurring is also low.
What is probability?
In mathematics, probability is a measure of the likelihood that an event will occur. It is a way of quantifying the uncertainty or randomness associated with an event or set of events. The probability of an event is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. For example, the probability of flipping a fair coin and getting heads is 0.5, or 50%, since there are two equally likely outcomes (heads or tails) and getting heads is one of them. Probability theory is a fundamental branch of mathematics that has applications in many areas, including statistics, finance, engineering, and computer science, among others.
Here,
The likelihood of selecting a green ribbon from Emilie's drawer is high, since the probability of randomly selecting a green ribbon is 84%. This means that out of all the ribbons in the drawer, 84% of them are green.
Another way to interpret this is that if Emilie were to randomly select a ribbon from her drawer without looking, there is an 84% chance that the ribbon she selects will be green.
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Correct question is "Emilie has a drawer full of color for ribbons the probability of randomly selecting a green ribbon is 84% which describes the likelihood by the example of selecting a green ribbon".
uno de los catetos del triangulo rectángulo mide 77cm y la hipotenusa excede al otro cateto en 49 cm.
CALCULA LA HIPOTENUSA
La hipotenusa mide 137 cm.
Podemos utilizar el teorema de Pitágoras para resolver este problema, que establece que en un triángulo rectángulo, el cuadrado de la hipotenusa es igual a la suma de los cuadrados de los catetos.
Sea "a" la medida del otro cateto, entonces:
a² + 77² = (a+49)²
Desarrollando los cuadrados y simplificando, tenemos:
a² + 5929 = a²+ 98a + 2401
Restando a ambos lados a², obtenemos:
5929 = 98a + 2401
Restando 2401 a ambos lados, obtenemos:
3528 = 98a
Dividiendo por 98, obtenemos:
a = 36
Por lo tanto, el otro cateto mide 36 cm, y la hipotenusa se puede calcular utilizando el teorema de Pitágoras:
h² = a² + b²
h2 = 36² + 77²
h² = 12996 + 5929
h² = 18925
Tomando la raíz cuadrada en ambos lados, obtenemos:
h = 137
Por lo tanto, la hipotenusa mide 137 cm.
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A blue balloon usually costs $0.34. Today it is on sale for $0.16. If Francesca buys a balloon today, how much will she save?
Answer:18 cents.
Step-by-step explanation: I did the math.
Hope this helps <3
She will save $0.18
To find the answer, you use the amount of what it usually costs and subtract the sale price to get the amount she saves.
$0.34 - $0.16 = $0.18
Solve the system by substitution if you get a decimal round to the nearest hundred
Answer:
(-1.29, 8.29) or (9.29,-2.29)
Step-by-step explanation:
Find what y equals in terms of x for both equations.
Set those two equations equal to each other (Because y=y)
Solve for x (you may need to use the quadratic formula for this step)
Plug the value(s) of x into the original equation to find y.
1. Julio Carson has a brick home with a replacement value of $100,000. It
is insured for 80% of the replacement value and is in an area that has been
designated fire protection class.
a. Find the amount
of the insurance.
b. Find the annual premium
a) The amount of the insurance or the sum assured by Julia Carson on his brick home is $80,000.
b) The annual premium is $5,148.00.
What is the sum assured?The sum assured represents the fixed amount that the insurance company pays to Julio Carson (the policyholder) if the unpredictable event, such as fire, occurs and damages his brick home.
The purpose of the payment is to reimburse Julio not for the costs incurred but according to the risks undertaken and it is a fixed sum of money unlike the sum insured, which reimburses to cover the costs incurred.
Replacement value of the brick home = $100,000
Sum insured = 80%
= $80,000 ($100,000 x 80%)
b) Annual premium:Monthly premium = $429
Number of insured years = 10 years
Annual premium = $5,148 ($429 x 12)
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triangle fun has vertices located at f(-2,-3), u (4,-2), and n (1,2), find the slope of UN. show your work
[tex]U(\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad N(\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{4}}} \implies \cfrac{2 +2}{-3} \implies \cfrac{ 4 }{ -3 } \implies - \cfrac{4 }{ 3 }[/tex]
The money spent, M , purchasing burritos at a particular fast food restaurant varies directly with the number of burritos purchased, B . When 4 burritos are purchased, $18 is spent. How much money is spent if 20 burritos are purchased?
Camila returns to work part time after
her accident. She could have
maintained all of her benefits without
working. What do you think this says
about Camila and her personal
investment in her human capital?
Camila's decision to return to work part-time instead of relying solely on her benefits reflects her personal investment in her human capital. By continuing to work, she is not only earning a salary but also investing in herself and her future career prospects.
How to solve the problem?
Camila's decision to return to work part-time after her accident instead of maintaining all her benefits without working shows that she values her human capital and is invested in it. Human capital refers to the skills, knowledge, and abilities that individuals possess, which are gained through education, training, and experience. By choosing to work, Camila is not only earning a salary, but she is also developing and enhancing her skills, knowledge, and abilities, thereby increasing her human capital.
Furthermore, Camila's decision to return to work part-time also shows that she has a strong work ethic and is committed to her career. She understands the importance of staying active in the workforce, even if it means working part-time, to maintain her professional network and stay up-to-date with industry developments. This commitment to her career and her willingness to work despite her physical limitations is a testament to her determination and resilience.
Overall, Camila's decision to return to work part-time instead of relying solely on her benefits reflects her personal investment in her human capital. By continuing to work, she is not only earning a salary but also investing in herself and her future career prospects.
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1. The quality control manager at a light-bulb factory needs to estimate the mean life of a new type of light-bulb. The population standard deviation is assumed to be 39 hours. A random sample of 30 light-bulbs shows a sample mean life of 400 hours. Construct and explain a 95% confidence interval estimate of the population mean life of the new light-bulb.
2. In a random sample of 360 men, 18, or older, 165 were married. Construct and explain a 99% confidence interval estimate of the true population proportion of married men, 18 or older.
3. A survey of first-time home buyers found that the sample mean annual income was $47,000. Assume that the survey used a sample of 26 first-time home buyers and that the sample standard deviation was $1,050. Compute and explain a 95% confidence interval estimate of the population mean.
4. For problem #1 above, what size sample would be needed to achieve a margin of error of 20 hours or less?
1. The 95% confident that the true population mean is 64.97 and 435.03 hours. 2. The 99% confident is between 0.407 and 0.500. 3. The 95% estimate of the mean is (45,424, 48,576). 4. Sample size is 91.27.
What is central limit theorem?A fundamental idea in statistics known as the central limit theorem (CLT) argues that, under specific circumstances, the sampling distribution of the mean of a random sample from any population tends to resemble a normal distribution as the sample size rises.
1. For 95% confidence interval we have:
CI = x ± z*(σ/√n)
Substituting the values:
CI = 400 ± 1.96*(39/√30) = (364.97, 435.03)
2. For 99% confidence interval we have:
CI = p-cap ± z*(√(p - cap(1- p-cap)/n))
Substituting the values:
CI = 165/360 ± 2.58*(√((165/360)*(195/360)/360)) = (0.407, 0.500)
Hence, we can be 99% confident that the true population proportion of married men, 18 or older, is between 0.407 and 0.500.
3. 95% estimate of the mean:
CI = x ± t*(s/√n)
Substituting the values:
CI = 47,000 ± 2.064*(1,050/√26) = (45,424, 48,576)
4. For sample size:
CI = 47,000 ± 2.064*(1,050/√26) = (45,424, 48,576)
Substitute the values:
n = (1.96*39 / 20)^2 = 91.27
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=
A rectangular parking lot has a length that is 4 yards
greater than the width. The area of the parking lot is 192
square yards. Find the length and the width.
Answer:
4√3
Step-by-step explanation:
length > width
If width = y
length =4y
Length × width = area
y × 4y = 192
4 y^2 = 192
y^2 = 48
y = 4 √3
2
A tire is sold at a discount of 10%. It is sold for $45. Find the usual price of the tire.
Answer:
Step-by-step explanation:
50$ (Sorry for the mistake, it’s a little hard for me to give such assignments, if the translator would translate correctly, then there would be no mistake, sorry again)
Answer:
Step-by-step explanation:
A tire is sold at a discount of 10%. It is sold for $45. Find the usual price of the tire.
from the question you understand that $45 is 90% of the original price (100%-10%=90%), so we divide 45 by 90 and multiply by 100 and we find the original price
45 : 90 x 100 =
0.5 x 100 =
50$
----------------------------
50$ - 10% = 45
The radius of a circle is 1. What is the length of an arc that subtends an angle of
6radians?
Answer:
pi/6
Step-by-step explanation:
the full arc of the circle is the circumference = 2pi×r.
since r = 1, we get circumference = 2pi.
the full arc of 2pi is for 360° or 2pi radians (hence the definition).
an angle given in radians for the norm circle with radius = 1 IS therefore already the arc length for that angle.
for 2pi the arc length is 2pi.
for pi/6 the arc length is ... pi/6.
70 adults with gum disease were asked the number of
times per week they used to floss before their
diagnoses. The (incomplete) results are shown below:
(frequency of 6, relative frequency of 4, and cumulative frequency of 5 are blank)
# of
times
floss
per
week
0
1
2
3
4
5
Frequency
6
7
4
11
15
11
6
7
Relative
Frequency
6
0.1571
0.2143
0.1571
0.0857
0.1
Cumulative
Frequency
0.1429
64
0.0857
70
a. Complete the table (Use 4 decimal places when
applicable)
4
15
30
41
47
b. What is the cumulative relative frequency for
flossing 3 times per week?
%
Answer:
a. To complete the table:
# of times floss per week Frequency Relative Frequency Cumulative Frequency
0 6 0.0857 6
1 7 0.1 13
2 4 0.0571 17
3 11 0.1571 28
4 15 0.2143 43
5 11 0.1571 54
6 6 0.0857 60
7 7 0.1 67
Step-by-step explanation:
b. To find the cumulative relative frequency for flossing 3 times per week, we need to add up the relative frequencies for all values of flossing less than or equal to 3.
Cumulative relative frequency for flossing 3 times per week:
= relative frequency for flossing 0 times per week + relative frequency for flossing 1 time per week + relative frequency for flossing 2 times per week + relative frequency for flossing 3 times per week
= 0.0857 + 0.1 + 0.0571 + 0.1571
= 0.4
Therefore, the cumulative relative frequency for flossing 3 times per week is 40%.
Evaluate the definite integral.
[tex]\int\limits^7_0 {e^{x}sin(x) } \, dx[/tex]
To solve the integral [tex]\rm\int_0^7 e^x \sin(x) dx\\[/tex], we can use integration by parts. Let u = sin(x) and dv = [tex]\rm e^x[/tex] dx, then we have:
[tex]\begin{align} \rm\int \rm e^x \sin(x) dx &= \rm-e^x \cos(x) + \rm\int e^x \cos(x) dx \\&= \rm -e^x \cos(x) + e^x \sin(x) - \int e^x \sin(x) dx\end{align}[/tex]
Rearranging, we get:
[tex] \begin{align}2 \rm \int e^x \sin(x) dx &= \rm e^x (\sin(x) - \cos(x)) \bigg|^7_0 \\& \rm= e^7 (\sin(7) - \cos(7)) - 1\end{align}[/tex]
Dividing both sides by 2, we get:
[tex] \rm\int_0^7 e^x \sin(x) dx = \frac{e^7 (\sin(7) - \cos(7)) - 1}{2} \\ [/tex]
Therefore, the value of the integral is
[tex] \rm \boxed{ \rm\frac{e^7 (\sin(7) - \cos(7)) - 1}{2}}[/tex]
The function g is related to one of the parent functions
g(x) = −(x − 2)^3
a.) Identify the parent function f.
b.) Use function notation to write g in terms of f.
a. f(x) = x³
b. g(x) = -f(x-2)
Answer:
a) parent: f(x) = x³
b) g(x) = -f(x -2)
Step-by-step explanation:
You want the parent function and the given function written in terms of the parent function for g(x) = -(x -2)³.
a) Parent functionThe parent function is the function that remains after scale factors and translations are removed. In general, a transformed function will look like ...
g(x) = c·f((x-a)/b) +d
which scales the function f(x) horizontally by a factor of b, vertically by a factor of c, and translates the result by (a, d).
Here, we recognize that ...
g(x) = -(x -2)³
has c = -1, a = 2, b = 1, d = 0
and the parent function is ...
f(x) = x³
b) g in terms of fUsing the values for a, b, c, d that we recognized above, we have ...
g(x) = -f(x -2)
__
Additional comment
When scale factors are negative, they reflect the function over the relevant axis. Here, the negative vertical scale factor reflects the function vertically over the x-axis. The translation is 2 units to the right.
given: MATH is a parallelogram
prove: MT bisects AH
Answer:
Step-by-step explanation:
In a parallelogram, opposite sides are parallel and equal.
MA // HT & AH is transversal.
∠MAG ≅ ∠GHT {Alternate interior angles are equal} --Angle
MA = HT {MATH is a parallelogram} ---> Side
MA // HT & MT is transversal.
∠AMG ≅ ∠HTG {Alternate interior angles area equal} ---->Angle
ΔMGA ≅ ΔTGH { Angle side angle congruent}
AG = HG {CPCT}
MT bisects AH