The graph of g(x) will be the same as the graph of f(x) shifted vertically downwards by 5 units because k=-5 represents a vertical shift, not a horizontal one. There is no horizontal shift involved.
When considering the functions [tex]f(x)=2^x[/tex]and g(x)=f(x)+k, with k=-5, we look at how the graph of g(x) compares to the graph of f(x).
Since the value of k is negative, it implies that a constant is being subtracted from the function f(x). This means that the graph of g(x) will not be shifted horizontally, but rather vertically downwards by 5 units.
Therefore, option c is the correct answer: the graph is not shifted horizontally from the graph of f(x).
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)
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.)
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.
An airliner travels 45 miles in 5 minutes. What is it’s speed in miles?
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.
Stocks are units of ownership in a company. The stock market is a place where stocks are bought and sold. When you buy a stock, you own a part of the company. If the company’s profits go up, the stock value goes up. If the profits fall, so does the value of the stock. Stock prices rise and fall every day. Last week, Isabelle bought stock in a toy company. Since then, the price of the stock had a change of -3 dollars. What is the absolute value of -3?
Answer:
The absolute value is three!
Step-by-step explanation:
have a nice day/night!
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?
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.
QM Q9.) Write the standard form of the equation of the circle with the given center and radius.
If the typos are randomly distributed over the 10 pages, find the probability of having a single typo on each page
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?
What is the mean of 20, 37, 43, 54, 83, 102, 117, 160, 208?
400,000 + 80,000 + 4,000 + 50 + 9 Write the standard form of the number shown above.
identify the type of conic section that has the equation 4x^2+25y^2=100 and identify its domain and range.
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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help with this question?
Matt has $550 in his savings account. He is eager to know how much interest the bank will pay him for the whole year. He knows that the bank pays a 3 percent interest rate. He sits down with a pen, paper, and calculator to find out the simple interest
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?
Let μ = 160 and σ = 16. find the z-score for the score, x = 150.
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.
PLZ HELP ASAP INSCRIBED SHAPES
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?
What does same amount means?
Is 28 cups greater or less than 14 Pints
hey can some one look at this?
John paid 5% sales tax on his television, which cost $769 before taxes. What did the television cost in total?
what problem does the model show?
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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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
I need help on this one please
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?
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%).
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.
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.
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
Suppose x is a normal random variable with μ = 35 and σ = 10. find p(55.5 < x < 69.7).
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]