Answers
The explanation is shown below:
1. As you can see in the figure attached, the blue parabola has the function f(x)=x^2. This is the patern function. By definition, this is the most basic function of the quadratics functions.
2. The red parabola is shifted 2 units to the -y axis and is wider than the first one, by multiplying the variable x. Therefore. As you can see, the correct function that represents this parabola is the function of the option D
3. If you want to verify it, you can give values to x and plot each point on a graph.
a) F(x) is wider than G(x)
This can be obtained by multiplying the function by a value with magnitude less than 1.
b) F(x) is shifted down
This can be obtained by subtracting a number from the function value.
From the given option, only option D satisfies these conditions.
So, the correct answer is option D
Related Questions
Trevor just received a jar of mixed nuts containing 325 almonds, 250 pistachios, 75 cashews, and 350 pecans for his birthday. He's going to start randomly choosing some nuts from the jar, and he's not going to do anything that would favor him choosing any particular type of nut over another. Let's use this information to calculate some probabilities. (4 points: Part I - 1 point; Part II - 1 point; Part III - 1 point; Part IV - 1 point)
What is the probability that the first nut Trevor chooses is a pecan?
Part II: What is the probability that the first nut Trevor chooses is an almond or a cashew?
Answers
325 +250 +75 +350 = 1000
Part I.
The probability of choosing a pecan at random is
(# of pecans)/(total # of nuts) = 350/1000 = 0.35
Part II.
The probability of choosing an almond or cashew is
(# of almonds or cashews)/(total # of nuts) = (325 +75)/1000 = 0.40
Final answer:
The probability of choosing a pecan first is 35%, and choosing either an almond or a cashew first is 40%.
Explanation:
Probability Calculation in Combinatorics
The student's question involves calculating the probability of certain outcomes when choosing nuts from a jar. To answer Part I: the probability that the first nut Trevor chooses is a pecan, we'll need to divide the number of pecans (350) by the total number of nuts in the jar (1000). Therefore, the probability of choosing a pecan first is 350/1000 or 0.35 (35%).
For Part II, we calculate the probability of choosing either an almond or a cashew. The total of almonds and cashews is 325 almonds + 75 cashews = 400. So, the probability is 400/1000, which simplifies to 0.4 (40%).
A rectangle has a width of 8 centimeters and an area of 160 square centimeters a similar rectangle has an area of 250 square centimeters. What are the dimensions of the larger rectangle?
Answers
The dimensions of the lager rectangle are;
length = 25cm
width = 10cm
Similar shapes are shapes with equal corresponding angles and equal side ratio. This side ratio is called scale factor.
scale factor = √ area factor
area factor = area of new shape/ area of old shape
area factor = 250/160
= 25/16
scale factor = √25/√16 = 5/4
Therefore the width of the larger rectangle = 8 × 5/4 = 10cm
the length = 250/10 = 25 cm
Therefore the dimensions of the larger rectangle are;
length = 25cm
width = 10cm
Lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. a bank conducts interviews of job applicants with the use of the lie detector. there are 15 applicants who are interviewed.
a.assuming all 15 applicants tell the truth, what is the probability that the lie detector will conclude that all 15 are telling the truth?
b.assuming all 15 applicants tell the truth, what is the probability that the lie detector will conclude that at least one is lying?
c.what are the mean and standard deviation of the 15 applicants the lie detector concludes are lying?
d.what is the probability that the number of truthful applicants classified as liars is greater than the mean?
Answers
Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.
The case that the lie detector correctly determined that a selected person is saying the truth has a probability of 0.85
Thus p = 0.85
Thus, the probability that the lie detector will conclude that all 15 are telling the truth if all 15 applicants tell the truth is given by:
[tex]P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(15)={ ^{15}C_{15}(0.85)^{15}(0.15)^0} \\ \\ =1\times0.0874\times1=0.0874[/tex]
Part B:
Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.
The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.25
Thus p = 0.15
Thus, the probability that the lie detector will conclude that at least 1 is lying if all 15 applicants tell the truth is given by:
[tex]P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(X\geq1)=1-P(0) \\ \\ =1-{ ^{15}C_0(0.15)^0(0.85)^{15}} \\ \\ =1-1\times1\times0.0874=1-0.0874 \\ \\ =0.9126[/tex]
Part C:
Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.
The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15
The mean is given by:
[tex]\mu=npq \\ \\ =15\times0.15\times0.85 \\ \\ =1.9125[/tex]
Part D:
Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.
The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15
The probability that the number of truthful applicants classified as liars is greater than the mean is given by:
[tex]P(X\ \textgreater \ \mu)=P(X\ \textgreater \ 1.9125) \\ \\ 1-[P(0)+P(1)][/tex]
[tex]P(1)={ ^{15}C_1(0.15)^1(0.85)^{14}} \\ \\ =15\times0.15\times0.1028=0.2312[/tex]
An airliner travels 45 miles in 5 minutes. What is it’s speed in miles?
Answers
John paid 5% sales tax on his television, which cost $769 before taxes. What did the television cost in total?
Answers
$ 769 ---------> 100%
x --------------> 105%
From here, we clear the value of x.
We have then:
x = (105/100) * (769)
x = 807.45 $
Answer:
the television did cost 807.45 $ in total
F(x, y, z) = yz i + xz j + (xy + 18z) k c is the line segment from (1, 0, −1) to (5, 6, 1) (a) find a function f such that f = ∇f. f(x, y, z) = (b) use part (a) to evaluate c ∇f · dr along the given curve
c.
Answers
[tex]\displaystyle\int\frac{\partial f}{\partial x}\,\mathrm dx=\int yz\,\mathrm dx[/tex]
[tex]\implies f(x,y,z)=xyz+g(y,z)[/tex]
[tex]\dfrac{\partial f}{\partial y}=xz+\dfrac{\partial g}{\partial z}=xz[/tex]
[tex]\implies\dfrac{\partial g}{\partial z}=0[/tex]
[tex]\implies g(y,z)=h(z)[/tex]
[tex]\dfrac{\partial f}{\partial z}=xy+\dfrac{\mathrm dh}{\mathrm dz}=xy+18z[/tex]
[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=18z[/tex]
[tex]\implies h(z)=9z^2+C[/tex]
[tex]\implies f(x,y,z)=xyz+9z^2+C[/tex]
[tex]\implies\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f(5,6,1)-f(1,0,-1)=30[/tex]
Through anti-derivatives, we find a function f(x, y, z) in part (a) of the problem. We then use the fundamental theorem of line integrals in part (b) to evaluate the line integral of ∇f ∙ dr along a curve c, using the function f we found.
Explanation:This problem lies within the field of vector calculus, specifically dealing with gradient fields and line integrals. Part (a) requires us to find a function f(x, y, z) such that the gradient of f (∇f) is equal to the field F. Since ∇f yields the vector field (Fx, Fy, Fz), we find the anti-derivatives of each component of F to solve for f. For this particular function f, the anti-derivatives are 1/2 * yz^2 + C1 for Fx = yz, 1/2 * xz^2 + C2 for Fy = xz, and 1/2 * xy^2 + 9z^2 + C3 for Fz = xy + 18z. Therefore, the function that satisfies the requirement is 1/2 * yz^2 + 1/2 * xz^2 + 1/2 * xy^2 + 9z^2 + C, where C is a constant.
Part (b) then requires the evaluation of the line integral of ∇f ∙ dr along a curve c, from point (1,0,-1) to (5,6,1). According to the fundamental theorem of line integrals, if a vector field is conservative (as it is in this case because we found a function f such that F = ∇f), the line integral of a vector field F along a curve c from a to b is simply f(b) - f(a). Therefore, using the function f found in part a, you can substitute the coordinates of points a and b to find the solution to the line integral equation.
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Find the length of the arc shown in red, Leave your answer in terms of pi.
Answers
Answer:
The red arc has length (3/2) π
Step-by-step explanation:
* Lets revise some rules in the circle
- The measure of any arc = the measure of the central angle
subtended by this arc
- Equal central angles subtended by equal arcs
- The length of the arc is a part from the length of the circle,
it depends on the ratio between the measure of this arc
and the measure of the circle
- The measure of the circle = 360°
- The length of the circle = 2πr
* Lets solve our problem
∵ The measure of the arc = 30°
∴ The measure of its central angle 30°
∴ The central angle of the red arc = 30° by condition of
vertically opposite angles are equal in measures
∴ The measure of the red arc = 30°
- The ratio between measure the arc and the measure
of the circle is 30/360 = 1/12
∴ The arc is 1/12 from the circle
∴ The length of the arc is 1/12 from the length of the circle
∴ Length red arc = (1/12) × 2πr
∵ r = 9
∴ Length red arc = (1/12) × 2 × π × 9 = (3/2) π
* The red arc has length (3/2) π
NEED HELP WILL GIVE OUT BRAINLIEST AND POINTS
11. Find the area. The figure is not drawn to scale.
12. Find the area of the kite. The figure is not drawn to scale.
Answers
we know that
the area of the triangle is
A=b*h/2
in this problem
b=9
h=12
so
A=9*12/2-----> A=54 units²
the answer part 1) is
Area=54 units²
Part 2) Find the area of the kite
see the picture attached with letters to better understand the problem
we know that
The area of a Kite is half the product of the diagonals
step 1
find CB
applying Pythagoras Theorem
AB²=AC²+BC²------> BC²=AB²-AC²-----> BC²=5²-3²----> BC²=16
BC=4
so
the diagonals are
(10+4) and (3+3)---------> 14 and 6
Area=(1/2)*[14*6]----> Area=42 units²
the answer Part 2) is
the area of a kite is 42 units²
Let μ = 160 and σ = 16. find the z-score for the score, x = 150.
Answers
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
and evaluate.
z = (150 -160)/16 = -10/16
z = -5/8
The z-score for the score x=150 is -5/8 = -0.625.
Starting at home, ishaan traveled uphill to the grocery store for 121212 minutes at just 151515 mph. he then traveled back home along the same path downhill at a speed of 303030 mph. what is his average speed for the entire trip from home to the grocery store and back?
Answers
First of all we need to convert the time interval from minutes to hours, so:
[tex]121212min(\frac{1h}{60min}) = 2020.2h[/tex]
We know that the distance, speed and time are related as follows:
[tex]d = vt[/tex]
Thus, the distance covered from home to the grocery store is:
[tex]d = 151515(2020.2)=306090603mi[/tex]
So, the total distance covered for the entire trip from home to the grocery store and back is:
[tex]d_{t} = 2(306090603) = 612181206mi[/tex]
We need to the total time interval, that is:
[tex]t = t_{1} + t_{2} = 2020.2h + t_{2}[/tex]
So, it is necessary to find [tex]t_{2} [/tex] as:
[tex]t_{2} = \frac{306090603mi}{303030mph} = 1010.1h[/tex]
In this way:
[tex]t = 2020.2h + 1010.1h = 3030.3h [/tex]
Finally, his average speed for the entire trip from home to the grocery store and back is:
[tex]v_{a} = \frac{d_{t}}{t} = \frac{612181206mi}{3030.3h} = 202020,ph[/tex]
Answer: The average speed for the entire trip from home to the grocery store and back is 20 mph.
Step-by-step explanation:
Since we have given that
Ishan traveled uphill to the grocery store for 12 minutes at just 15 mph.
So, Time taken by him = 12 minutes
Speed = 15 mph
So, distance traveled = Speed × time
So, Distance becomes [tex]15\times \dfrac{12}{60}=\dfrac{180}{60}=3\ miles[/tex]
Again, he traveled back home along the same path downhill = 180 miles
Speed of covering downhill = 30 mph
so, Time taken [tex]\dfrac{Distance}{Speed}=\dfrac{3}{30}=\dfrac{1}{10}\ hours[/tex]
Since we know the formula for "Average speed ":
[tex]\dfrac{Total\ distance}{Total\ Time}\\\\\\=\dfrac{3+3}{\dfrac{12}{60}+\dfrac{1}{10}}\\\\\\=\dfrac{6}{\dfrac{1}{5}+\dfrac{1}{10}}\\\\\\=\dfrac{6\times 10}{2+1}\\\\\\=\dfrac{6\times 10}{3}\\\\\\=20\ mph[/tex]
Hence, the average speed for the entire trip from home to the grocery store and back is 20 mph.
You have the opportunity to lease space for your business with a fixed-rate lease. The property owner has proposed a five-year lease with a rent of $4,000 per month. How much is the rent per year? How much is the rent over the life of the lease?
Answers
400,000 + 80,000 + 4,000 + 50 + 9 Write the standard form of the number shown above.
Answers
400,000
80,000
4,000
59
--------------
484,059 (answer)
Short answer: 484,059
Why?
This equation shown is an expanded form of a number. 400k is the largest number, so that'd go first. 80k is the second largest, so that would go next to the largest number, 4. (400k) 4k is the third largest, so that'd go next to the first and second largest numbers, 48. (480k) Now, we have 484,000. Since there is no hundred, we put a zero there. Now, add a 59 at the end of the zero. Which gives us the number 484,059.
Hope this helped you! ♥
Is 28 cups greater or less than 14 Pints
Answers
28 cups is exactly equal to 14 pints. (There are 2 cups per pint.)
help with this question?
Answers
The appropriate choice is ...
c. continuous at every real number except x = 1.
Two students, Ann and Max, factored the trinomial 4x2 − 6x − 4. Ann factored it as 2(x − 2)(2x + 1) and Max factored it as (x − 2)(4x + 2). Indicate which student factored the trinomial completely and which student did not, and explain why.
Answers
Max did not. Max's second factor has terms with a common factor of 2 that can be removed.
QM Q9.) Write the standard form of the equation of the circle with the given center and radius.
Answers
The standard form of the equation of a circle with center (h, k) and radius r is:
(x - h)² + (y - k)² = r²
So we have h = 4 and k = 3 and r = √5
So we just need to add these numbers to where they belong.
(x - 4)² + (y - 3)² = (√5)²
(x - 4)² + (y - 3)² = 5
Let me know if you have questions about the answer. As always, it is my pleasure to help students like you!
What does same amount means?
Answers
I need help on this one please
Answers
Grace has one $10 bill and three $5 bills she spends 9.30 on a belt and $4.20 on snack how much money does grace have left
Answers
Amount spent = $9.30 + $4.20 = $13.50
Amount left = $25 - $13.50 = $11.50
Answer: $11.50
11.50
GIVE ME BRAINLIEST PLZZZZ
hey can some one look at this?
Answers
1 foot = 12 inches.
x feet = 60 inches.
1 foot * 60 inches = 12 * x divide by 12
60 / 12 = 5
So the person is at least 5 feet tall. The height you want is 5 feet 4 inches.
So add 4 inches to 5 feet.
or
Add 4 inches to 60 inches.
you get 64 inches.
There are 20 entries all together. 2 people are 64 inches tall.
P(64) = 2/20 = 1/10 = 0.1
Answer P(64) = 0.1
I would check all of this if I were you. I'm not sure I counted either one correctly.
Q #14 Solve the equation
Answers
The scalene triangle is a polygon with three sides, all of which are different.
As a consequence, their angles will also all be unequal. These, as in all triangles, add up to 180º (α + β + γ = 180º).
Answer:
Scalene
option 3
what problem does the model show?
Answers
1/2 is the fraction represents the diagram.
What is Fraction?A fraction represents a part of a whole.
Fractions are of three types.
Proper fraction, improper fraction and mixed fraction.
A proper fraction is a fraction which has its numerator value less than the denominator.
An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
A fraction represented with its quotient and remainder is a mixed fraction
In the diagram there are 8 boxes in whole, the number of boxes shaded are 4 out of 8.
4/8 is the fraction represents the diagram, 1/2 is another way of representing 4/8.
Hence, 1/2 is the fraction represents the diagram.
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Alex walked 1 mile in 15 minutes. Sally walked 3,520 yards in 24 minutes. In miles per hour, how much faster did Sally walk than Alex? (Note: 1 mile = 1,760 yards)
Answers
3520yards÷1760yards/mile=2 miles
From there we know:
Alex walked 1 mile for 15 mins and Sally walked 2mile in 24 mins
We need to convert these mileages to miles per hour
1mile/15mins*60mins/hour=4miles /hour
2mile/24mins*60mins/hour=5miles per hour
Alex walks at 4 miles per hour and Sally at 5 miles per hour
Sally walks 1 mile per hour faster than Alex
identify the type of conic section that has the equation 4x^2+25y^2=100 and identify its domain and range.
Answers
4x^2+25y^2=100
The range:
set y=0, and solve for x:
4x^2=100
x^2=25
x=+/-5
thus the domain is:
[-5,5]
Range:
set x=0 and solve for y:
25y^2=100
y^2=4
y=+/-2
thus the range is:
[-2,2]
The equation given represents an ellipse, a type of conic section. The domain of this particular conic section is -5 to 5, and its range is -2 to 2.
Explanation:The equation given represents an ellipse, which is one kind of conic section. The general form of the equation of an ellipse is[tex]x^2/a^2 + y^2/b^2 = 1,[/tex] where a and b are the lengths of the semi major and minor axes respectively. The equation you provided, [tex]4x^2+25y^2=100,[/tex]when arranged to fit into the general form of ellipse becomes [tex]x^2/25 + y^2/4 =1.[/tex] Thus, it is clear that the given equation represents an ellipse.
The domain of the function described by this elliptical equation includes all the x-values that the ellipse covers, and for this particular equation, is -5 to 5. The range includes all the y-values that the ellipse covers, which in this case is -2 to 2.
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If the typos are randomly distributed over the 10 pages, find the probability of having a single typo on each page
Answers
Of the 5th grade boys, 2/3 play sports. Of the boys who play sports, 1/4 play baseball. what fraction of the 5th grade boys play baseball?
Answers
2/3 * 1/4
2/12
Simplify:
1/6 of the 5th grade boys play baseball
How does an earthquake of magnitude 7.9 compare in intensity with an earthquake of magnitude of 3.7 on the Richter scale? The larger earthquake's intensity was nothing times as great as the smaller earthquake's intensity. (Round to the nearest whole number as needed.)
Answers
Answer:
15,849
Step-by-step explanation:
A magnitude 7.9 earthquake releases approximately 2.7 million times more energy than a 3.7 magnitude earthquake, as the Richter scale is logarithmic and represents a 32-fold increase in energy release for each unit increase in magnitude.
Explanation:The Richter scale is logarithmic, which means that each whole number increase represents a tenfold increase in amplitude and roughly a 32-fold increase in the energy released by an earthquake.
Therefore, when comparing a magnitude 7.9 earthquake to a magnitude 3.7 earthquake, there is a difference of 4.2 on the Richter scale.
This corresponds to a tenfold increase in amplitude 4.2 times, which would be 10 to the power of 4.2 in terms of amplitude.
However, if we consider the energy, which increases by a factor of 32 for each whole number increase, we're looking at 32 to the power of 4.2, which is approximately 2,704,156 times greater in terms of energy release.
To determine the intensity difference in a more simplified manner, taking the base-10 logarithm of the energy ratio is effective.
The simplified comparison tells us that the larger quake's intensity is about 2.7 million times greater than the smaller quake's intensity.
After rounding to the nearest whole number, we find that the intensity is 2,704,156 times as great.
Suppose x is a normal random variable with μ = 35 and σ = 10. find p(55.5 < x < 69.7).
Answers
Answer:
[tex]\boxed{\boxed{P(55.5 < X< 69.7)=0.01992}}[/tex]
Step-by-step explanation:
We know that,
[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]
where,
Z = z-score,
X = raw score,
μ = mean,
σ = standard deviation.
So,
[tex]=P(55.5 < X< 69.7)[/tex]
[tex]=P(55.5-35 < X-35< 69.7-35)[/tex]
[tex]=P(\dfrac{55.5-35}{10}< \dfrac{X-35}{10}< \dfrac{69.7-35}{10})[/tex]
[tex]=P(\dfrac{55.5-35}{10}< Z< \dfrac{69.7-35}{10})[/tex]
[tex]=P(2.05< Z<3.47)[/tex]
[tex]=P(Z<3.47)-P(Z<2.05)[/tex]
[tex]=0.99974-0.97982\\\\=0.01992[/tex]
What is the mean of 20, 37, 43, 54, 83, 102, 117, 160, 208?
Answers
PLZ HELP ASAP INSCRIBED SHAPES
Answers
It’s handy to remember that 5, 12, 13 is a pythagorean triple.
So, 13 is the radius.
Hope this helped!
The find the hypotenuse, simply use the following,
[tex] \sqrt{a { }^{2} + b ^{2} } [/tex]
Or the square root of one leg squared us the other leg squared.
I already know this to be a 5 - 12 - 13 right triangle and you can get 13 with the equation.
~~
Half of 13 is 6.5 meaning 6.5 is our radius.
~~
I hope that helps you out!!
Any more questions, please feel free to ask me and I will gladly help you out!!
~Zoey