love this called sketch a graph of the polynomial function f(x)=x^3-6x^2+3x+10. Use it to complete the following:
• increasing
• positive
• decreasing
• negative
f is ____ on the intervals (-∞, 0.27) and (3.73, ∞).
f is ____ on the intervals (-1,2) and (5, ∞).
f is ____ on the intervals (-∞, -1) and (2,5).
Answers
Answer:
increasingpositivenegativeStep-by-step explanation:
You can actually answer this question without graphing the equation, but a graph confirms the answers.
__
A cubic with a positive leading coefficient will be negative and increasing on any interval* whose left end is -∞. Similarly, it will be positive and increasing on any interval whose right end is +∞.
The answer choices tell you ...
there are zeros at -1, 2, 5there are turning points at 0.27, 3.73The function is increasing up to the first turning point and after the second one.
The function is negative up to the first zero and between the last two.
f is increasing on the intervals (-∞, 0.27) and (3.73, ∞).f is positive on the intervals (-1,2) and (5, ∞).f is negative on the intervals (-∞, -1) and (2,5)._____
* We say "any interval" but we mean any interval whose boundary is a zero or turning point, and which properly describes an interval where the function is one of increasing, decreasing, positive, or negative.
To graph the polynomial function f(x) = x^3 - 6x^2 + 3x + 10, we need to find the x-intercepts, y-intercept, and determine the behavior of the graph. Then, using test points, we can determine the intervals where the function is increasing or decreasing, and where it is positive or negative.
Explanation:Graphing the Function f(x) = x3 - 6x2 + 3x + 10To graph the polynomial function f(x) = x3 - 6x2 + 3x + 10, we can start by finding the x-intercepts, y-intercept, and identifying the behavior of the graph. The x-intercepts are the points where the graph intersects the x-axis, and they can be found by setting f(x) = 0 and solving for x using factoring or other methods. The y-intercept is the point where the graph intersects the y-axis, and it can be found by evaluating f(0). Finally, to identify the behavior of the graph, we can examine the signs of the coefficients of the polynomial.
Step 1: Finding the x-interceptsTo find the x-intercepts, we set f(x) = 0:
x3 - 6x2 + 3x + 10 = 0
At this point, we can either try factoring the polynomial or use more advanced methods like synthetic division or the rational root theorem. Let's use a graphing calculator to find the approximate x-intercepts. From the calculator, we find that the x-intercepts are approximately x = -1.01, x = 1.25, and x = 6.76.
Step 2: Finding the y-interceptThe y-intercept is the point where the graph intersects the y-axis, which occurs when x = 0. We can find the y-intercept by evaluating f(0):
f(0) = 03 - 6(0)2 + 3(0) + 10 = 10
The y-intercept is (0, 10).
Step 3: Identifying the behavior of the graphBy examining the signs of the coefficients of the polynomial, we can determine the behavior of the graph.
For x3, the coefficient is positive, which means the graph will be “up” on the left side and “down” on the right side. For -6x2, the coefficient is negative, which means the graph will be “down” on the left side and “up” on the right side. The positive coefficient of 3x indicates that the graph will have a “upward” trend on both sides. Finally, the constant term 10 does not have an effect on the overall behavior of the graph.
Step 4: Sketching the graphBased on the information gathered, we can sketch the graph of the polynomial function f(x) = x3 - 6x2 + 3x + 10. By plotting the x-intercepts (-1.01, 0), (1.25, 0), and (6.76, 0) and the y-intercept (0, 10), and considering the behavior of the graph, we can roughly sketch the shape of the graph.
Based on the sketch of the graph, we can now identify the intervals where the function f(x) is increasing or decreasing, and where it is positive or negative. We can use test points within each interval to determine the sign of the function. For example, to determine the sign of f(x) within the interval (-∞, 0.27), we can choose a test point like x = -1. Plugging in this value, we find that f(-1) = -11. Since f(-1) is negative, we can conclude that f(x) is negative within the interval (-∞, 0.27). Similarly, we can choose test points in the other intervals to determine the signs of f(x) and complete the statement.
Summary:The graph of the polynomial function f(x) = x3 - 6x2 + 3x + 10 has x-intercepts at approximately x = -1.01, x = 1.25, x = 6.76, and a y-intercept at (0, 10). The graph has a certain behavior, with an upward trend on both sides. Using test points, we can determine that f(x) is negative on the intervals (-∞, 0.27) and (3.73, ∞), positive on the intervals (-1, 2) and (5, ∞), and positive on the intervals (-∞, -1) and (2, 5).
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Related Questions
Which of the following items are elements of a monthly checking account statement? I. A period (beginning date and ending date) II. A beginning balance and ending balance. III. A detailed list of debits and credits during the period.
Answers
Answer:
the answer is d.
Step-by-step explanation:
Monthly checking account statements include:
- A period
- A beginning balance and an ending balance
- A detailed list of debits and credits during the period
so it is d since it is all three.
While on vacation, Enzo sleeps 115% percent as long as he does while school is in session. He sleeps an average of s hours per day while he is on vacation.
Answers
The complete question is written below:
While on vacation, Enzo sleeps 115% as long as he does while school is in session. He sleeps an average of s hours per day while he is on vacation. Which of the following expressions could represent how many hours per day Enzo sleeps on average while school is in session?
A.1.15s
B.s/1.15
C.100/115s
D.17/20s
E.(1.15-0.15)s
Answer:
B. [tex]\dfrac{s}{1.15}[/tex]
Step-by-step explanation:
Let the hours per day slept while school is in session be [tex]x[/tex].
Given:
Hours slept per day on vacation = [tex]s[/tex]
Enzo sleeps 115% as long in vacation as he does in school. Therefore, as per question,
[tex]s=115\%\ of\ x\\\\s=\frac{115}{100}x\\\\s=1.15x\\\\x=\dfrac{s}{1.15}[/tex]
Hence, the number of hours Enzo sleeps while school is in session is given as:
[tex]x=\dfrac{s}{1.15}[/tex]
How many milligrams of zinc ions do the trout need to be exposed to in order for them to survive exactly one minute after exposure?
Answers
Answer:
1770
Step-by-step explanation:
No calculator is needed.
When you fill in the numbers, you get ...
1 = (x/1770)^(-0.8)
The only way the value will be 1 is if the fraction is 1:
x/1770 = 1
The only way the fraction will be 1 is x = 1770.
1770 mg Zn ions per liter will be lethal in 1 minute.
_____
Check
You know the answer will be slightly more than 1743 from your answer to the second part of the first question.
Need help ASAP! 6 responses, just need answers the cut off letters are W and Z z is on bottom W is on top
Answers
Answer:
a) ZY = 27
b) WY = √2×27 = 38.18
c) RX = √2×27 ÷ 2 = 19.09
d) m∠ WRZ = 90°
e) m∠ XYZ = 90°
f) m∠ ZWY = 45°
Step-by-step explanation:
Properties of a Square:
All the sides are equal.All the vertex angles are 90°.Diagonals are equal and bisect each other at right angle.Diagonal bisect the vertex angles 90° i.e 45° each.The measure of the diagonal is √2 times the length of the side.i.e [tex]d=\sqrt{2}\times side[/tex]We have [] WXYZ is a SQUARE with side = WZ = 27
Therefore By Applying the above Properties we will get the required Answers.
a) ZY = 27 .........{ From 1 above properties}
b) WY = √2×27 = 38.18 .......{ From 5 above properties}
c) RX = √2×27 ÷ 2 = 19.09 ...{ From 3 above properties}
d) m∠ WRZ = 90° ...........{ From 3 above properties}
e) m∠ XYZ = 90° .........{ From 2 above properties}
f) m∠ ZWY = 45° .........{ From 4 above properties}
I NEED URGENT HELP ASAP + BRAINLIEST
The table shows the amount of money made by a summer blockbuster in each of its fi...
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If you all could help him, that would be great! Thanks mates!
Answers
that's cool I saw what you did your a nice friend lol
Answer:
dam it
Step-by-step eddqowd23r43tttt5xplanation:
The diameter of a cylindrical construction pipe is 5 ft. If the pipe is 21 ft long, what is its volume?
Use the value 3.14 for it, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answers
Answer:
412 ft³
Step-by-step explanation:
Diameter = 5 ft
Radius = D/2 = 5/2 = 2.5 ft
Volume of a Cylinder = 2πr²*h
Plug in values
2(3.14)(2.5)^2*21 = 412.33 ft^3
Volume of the pipe is 412 cubic feet rounded to nearest whole number.
The volume of the cylindrical construction pipe is 330 cubic feet.
To find the volume of a cylindrical construction pipe, we can use the formula:
Volume = π * [tex](radius)^2[/tex] * height
Given that the diameter is 5 ft, the radius of the pipe is half of the diameter, which is 2.5 ft.
The height of the pipe is given as 21 ft.
Plugging these values into the volume formula:
Volume = 3.14 *[tex](2.5)^2[/tex] * 21 = 330 ft³
Therefore, the volume of the cylindrical construction pipe is 330 cubic feet.
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More on Areas. Farmer Jones, and his wife, Dr. Jones, both mathematicians, decide to build a fence in their field to keep the sheep safe. Being mathematicians, they decide that the fences are to be in the shape of the parabolas y=6x2 and y=x2+9. What is the area of the enclosed region?
Answers
The enclosed region has an area of zero.
Here, we have,
To find the area of the enclosed region between the two parabolas, we need to calculate the definite integral of the difference of the two functions over the interval where they intersect.
The two parabolas are given by:
y=6x²
y=x² + 9
To find the intersection points, we set the two equations equal to each other:
6x² =x² + 9
Now, let's solve for
6x² =x² + 9
=> 6x² - x² = 9
=> 5x² = 9
=> x² = 9/5
=> x = ±√9/5
Since we are looking for the area between the two curves, we only need to consider the positive x value:
x = √9/5
=> x = 3/√5
Now, the definite integral to find the area between the curves is given by:
[tex]A = \int\limits^b_a {(y_2 - y_1)} \, dx[/tex]
where [tex]y_2[/tex] and [tex]y_1[/tex] are the equations of the two curves, and a and b are the x-coordinates of the intersection points.
In this case,
[tex]y_2 = x^2+9 \\ y_1 = 6x^2[/tex]
So, the area A is:
A = [tex]\int\limits^\frac{3}{\sqrt{5} } _0 {(9-5x^2)} \, dx[/tex]
Now, integrate with respect to x:
[tex]A = [9x - \frac{5x^3}{3} ]^{\frac{3}{\sqrt{5} }}_0[/tex]
solving we get,
A = 0
The enclosed region has an area of zero.
This result may seem counterintuitive, but it means that the two parabolas intersect at a point and do not enclose any finite area between them.
Instead, they share a single point in the coordinate plane.
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The area of the fenced field, enclosed by the parabolas y=6x² and y=x²+9, can be found by integrating the difference of the two functions from their points of intersection, which are x=-3 and x=3.
Explanation:The subject of this question is Mathematics, more specifically it's an application of calculus. To find the area enclosed by two curves, we need to integrate the difference of the two functions from where they intersect. In this case, the two parabolas y=6x² and y=x²+9. To find the points of intersection X₁ and X₂, we make the two equations equal and solve for x, which gives us x= -3 and x=3.
Then we take the integral of (6x² - (x² + 9)) from -3 to 3. The result of this integral will give us the area between these two parabolas, which represents the area of the fenced field.
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which of the following rain-related losses WOULD be covered under this renters insurance policy?
a. Your laptop is ruined because you left your window open during a moderate rain shower
b. Your mattress is ruined because part of the apartment's roof blew off during a major rainstorm, creating
a stream of water landing directly on your bed
C. Your carpet is ruined because your roommate negligently left her wet boots, umbrella, and raincoat
sitting in a pile on the rug all afternoon
d. You lose a day's wages because a horrible rainstorm makes it impossible to get to your job
Answers
Answer:I think this is the nswer
Step-by-step explanation:
C. Your carpet is ruined because your roommate negligently left her wet boots, umbrella, and raincoat
sitting in a pile on the rug all afternoon
The statement of rain-related losses that WOULD be covered under this renters insurance policy is when your mattress is ruined because part of the apartment's roof blew off during a major rainstorm, creating a stream of water landing directly on your bed.
What is the renter's insurance policy?Basically, the renter's insurance is similar to the homeowner's insurance, but it is for people who rent or lease properties, such as houses and apartments. A renter's insurance refers to an insurance policy that can cover theft, water backup damage, certain natural disasters, bodily injuries and more in a rented property.
If we rent an apartment, home or even a dorm, the renter's insurance are more recommended for protecting your space and belongings in the event of a covered accident. Therefore, the Option B is correct.
Missing options "a. Your laptop is ruined because you left your window open during a moderate rain shower b. Your mattress is ruined because part of the apartment's roof blew off during a major rainstorm, creating a stream of water landing directly on your bed C. Your carpet is ruined because your roommate negligently left her wet boots, umbrella, and raincoat sitting in a pile on the rug all afternoon D. You lose a day's wages because a horrible rainstorm makes it impossible to get to your job"
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In a rural area, only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by "dowsing"—using a forked stick to indicate where the well should be drilled. You check with 80 of his customers and find that 27 have wells less than 100 feet deep. What do you conclude about his claim?
a) Write appropriate hypotheses.
b) Check the necessary assumptions.
c) Perform the mechanics of the test. What is the P-value?
d) Explain carefully what the P-value means in context. e) What’s your conclusion?
Answers
Answer:
Step-by-step explanation:
Given that in a rural area, only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less.
The sample size n = 80
no of wells less than 100 feet deep=27
Sample proportion = [tex]\frac{27}{80} =0.3375[/tex]
a) Create hypotheses as
[tex]H_0: p = 0.30\\H_a: p >0.30\\[/tex]
(Right tailed test)
p difference [tex]= 0.3375-0.30 = 0.0375[/tex]
Std error of p = [tex]\sqrt{\frac{0.3(0.7)}{80} } =0.0512[/tex]
b) Assumptions: Each trial is independent and np and nq >5
c) Z test can be used.
Z= p diff/std error = [tex]\frac{0.0375}{0.0512} =0.73[/tex]
p value = 0.233
d) p value is the probability for which null hypothesis is false.
e) Conclusion: Since p >0.05 we accept null hypothesis
there is no statistical evidence which support the claim that more than 30% are drilled.
Plz explain and prove the triangles congruence.
Answers
Answer:
[tex]\overline {JL} \cong \overline{MO}[/tex] is the only correct statement.
Step-by-step explanation:
When the two triangles are congruent then their Vertices are correspondence to each other. the correspondence of vertices are as
For, Δ JKL ≅ Δ MNO
J ↔ M
K ↔ N
L ↔ O
The true statement with respect to the correspondence are as
For, Δ JKL ≅ Δ MNO
∠JKL ≅ ∠MNO
∠JLK ≅ ∠MON
∠KJL ≅ ∠NMO
[tex]\overline {JL} \cong \overline{MO}[/tex]
[tex]\overline {KL} \cong \overline{NO}[/tex]
[tex]\overline {JK} \cong \overline{MN}[/tex]
These all are corresponding parts of congruent triangles (c.p.c.t).
Solve for (p).
17−2p=2p+5+2p
p= ?
Answers
The solution of p is given by the equation p = 2
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
17 - 2p = 2p + 5 + 2p be equation (1)
Adding 2p on both sides , we get
2p + 2p + 2p + 5 = 17
On simplifying , we get
6p + 5 = 17
Subtracting 5 on both sides , we get
6p = 17 - 5
6p = 12
Divide by 6 on both sides , we get
p = 12 / 6
p = 2
Therefore , the value of p is 2
Hence , the solution is p = 2
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On march 4 1999 the new england journal of medicine published a research article by Dr Douglas Jorenby and colleague comparing different treatments to help patients stop smoking.
Answers
Is this a question or a statement?
What are the coordinates of the circumcenter of the triangle ?
Answers
Answer:
A=(-1,3)
B=(5,3)
C=(5,-5)
Step-by-step explanation:
Answer:
The answer to your question is (2, -1)
Step-by-step explanation:
1.- Find half points
AB
Between A and B there are 6 units, then the half point is three units from point A to the right
(2, 3)
BC
Between B and C there are 8 units, then the half point is four units below the point B.
(5, -1)
AC
Xm = -1 + 5 / 2 = 4 / 2 = 2
Ym = 3 - 5 / 2 = - 2 / 2 = - 1
(2, -1)
2.- Find the equations of the mediatrices
AB
x = 2 because the line must be perpendicuar to AB
BC
y = - 1 because the line must be perpendicular to BC
AC
slope m =[tex]\frac{-5 - 3}{5 + 1}[/tex]
m = [tex]\frac{-8}{6}[/tex]
m = [tex]\frac{-4}{3}[/tex]
mediatrix AC
y + 1 = -4/3 (x -2)
3y + 3 = -4x + 8
4x + 3y = 8 - 3
4x + 3y = 5
3.- Find the circumcenter
When x = 2
4(2) + 3y = 5
8 + 3y =5
3y = 5 - 8
3y = -3
y = -3/3
y = -1
When y = -1
4x + 3(-1) = 5
4x - 3 = 5
4x = 5 + 3
4x = 8
x = 8/4
x = 2
Circumcenter (2, -1)
Suppose that F′(x)=f(x) and G′(x)=g(x). Which statements are true? A. If F and G differ by a constant, then f=g. B. If f and g differ by a constant, then F=G. C. If f=g, then F=G. D. None of the above
Answers
Answer: The correct option is
(A) If F and G differ by a constant, then f = g.
Step-by-step explanation: According to the given condition, we have
[tex]F'(x)=f(x)~~~\textup{and}~~~G'(x)=g(x).[/tex]
We are to select the correct statement.
Let F(x) = p(x) and G(x) = p(x) + c, c - constant.
Then, we get
[tex]F'(x)=p'(x)~~~\textup{and}~~~G'(x)=p'(x).[/tex]
Therefore,
[tex]F'(x)=G'(x)\\\\\Rightarrow f(x)=g(x)\\\\\Rightarrow f=g.[/tex]
Thus, if F and G differ by a constant, then f = g.
Option (A) is CORRECT.
A local news agency conducted a survey about unemployment by randomly dialing phone numbers until they had gathered responses from 1000 adults in their state. In the survey, 19% of those who responded said they were not currently employed. In reality, only 6% of the adults in the state were not currently employed at the time of the survey. Which of the following best explains the difference in the two percentages?
(a) The difference is due to sampling variability. We shouldn't expect the results of a random sample to match the truth about the population every time.
(b) The difference is due to response bias. Adults who are employed are likely to lie and say that they are unemployed.
(c) The difference is due to undercoverage bias. The survey included only adults and did not include teenagers who are eligible to work.
(d) The difference is due to nonresponse bias. Adults who are employed are less likely to be available for the sample than adults who are unemployed.
(e) The difference is due to voluntary response. Adults are able to volunteer as a member of the sample.
Answers
Answer:
Option d is right
Step-by-step explanation:
Given that a local news agency conducted a survey about unemployment by randomly dialing phone numbers until they had gathered responses from 1000 adults in their state. In the survey, 19% of those who responded said they were not currently employed. In reality, only 6% of the adults in the state were not currently employed at the time of the survey.
The reason more approporiate woul dbe
(d) The difference is due to nonresponse bias. Adults who are employed are less likely to be available for the sample than adults who are unemployed.
would be the correct option.
Adults who are employed will lie is absurd may be reverse true. Since survey done for adults, eligible teenagers also included. Voluntary response is also wrong as given 1000 persons selected.
The difference in percentages is due to sampling variability. Random sampling may not perfectly represent the population, resulting in differences in the percentages.
Explanation:The difference in percentages is best explained by (a) sampling variability. When conducting a survey, it is expected that there will be some variability between the sample results and the true population values. Even with random sampling, there is a chance that the sample may not perfectly represent the entire population. In this case, the survey respondents may not be an accurate reflection of the overall population, resulting in a difference in the percentages.
For example, if the survey happened to include a higher proportion of unemployed individuals in the sample, the percentage of unemployed respondents would be higher than the true population percentage.
Sampling variability is common in statistics and can be mitigated by increasing the sample size to reduce the margin of error.
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For a continuous random variable x, the height of the function at x is a. 0.50, since it is the middle value. b. a value less than zero. c. the probability at a given value of x. d. named the probability density function f(x).
Answers
Answer:
Answer is a continuous random variable x the height of the function named the probability density function f(x)
Step-by-step explanation:
A continuous random variable takes infinite number of possible values.
example include height , weight amount of sugar in an orange time required to run a mile.
Continues random variable named probability function f(x).
The height of a function at a certain value of x in the case of a continuous random variable represents the probability density at that point, not the actual probability. The area under the curve of the function between two points gives the actual probability that x falls between those points. The total probability (the total area under the curve) is always 1.
Explanation:For a continuous random variable x, the height of the function at a certain value of x is named the probability density function f(x) which describes the probabilities for continuous random variables. The value does not represent a direct probability but the density of probability around that point, and the area under the curve between two given points gives the probability that x would fall between those points. This is represented by the notation P(c < x < d), where c and d are the boundaries of the interval.
It is essential to note that for any specific value of a continuous random variable, the probability is always 0, represented as P( x = c )= 0, which means the height of the function at a particular x does not represent the exact probability at that point but just the density.
The total probability of a continuous random function is always 1, thus, the total area under the probability density function curve equals one. And the value of the function at any given point can be less or greater than 1 given the function's shape and range.
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[50+25 Points + The Brainliest]
If sin θ = 3/5, and lies in Quadrant II, what are the exact values of sin 2θ, cos 2θ , and tan 2θ ?
Thank you in advance!
Answers
Answer:
sin2θ = -24/25
cos2θ = 7/25
tan2θ = -24/7
Step-by-step explanation:
sinθ = 3/5
θ is in Quadrant II. So 2θ is in Quadrant III or IV. So sin2θ is negative. Nothing can be said about cos and tan yet.
sin135 = 0.707 > 3/5.
So θ > 135.
2θ lies in Quadrant IV. So cos2θ is positive and tan2θ is negative.
cosθ = √(1 - sin²θ)
= -4/5
sin2θ = 2sinθcosθ = 2x(3/5)x(-4/5) = -24/25
cos2θ = 1 - 2sin²θ = 1 - 2x(3/5)² = 7/25
tan2θ = sin2θ/cos2θ = -24/7
Please help me with this problem
Answers
Answer:
12
Step-by-step explanation:
The degree of the polynomial is 12, so the theorem tells you it has 12 zeros.
Answer:
[tex]\displaystyle 12[/tex]
Step-by-step explanation:
You base this off of the Leading Coefficient's degree.
I am joyous to assist you anytime.
A recipe for brownies calls for 2/3 Cup of chocolate chips for a batch of two dozen brownies. How many chocolate chips will be needed to make 18 brownies.
Answers
Answer:
6 cups
Step-by-step explanation:
[tex](18 \times \frac{2}{3} ) \div 2 = [/tex]
[tex]12 \div 2 = [/tex]
[tex]6[/tex]
Carol has two cats rover and Bobo. Rover eat three fourths of a can of cat food each day and bobo eat a half of a can of cat food each day. Cat food cost five dollars for three cans. It's is only sold in three can packs. How much does it cost carol for a sixty day supply of cat food for her two cats.
Answers
Answer: A sixty day supply of cat food for her two cats will cost her $125
Step-by-step explanation:
Carol has two cats Rover and Bobo.
Let x = the quantity of a can of fast food.
Rover eats three fourths of a can of cat food each day. This means that Rover eats 3x/4 each day. Bobo eats a half of a can of cat food each day. This means that bobo eats x/2 each day.
Cat food costs five dollars for three cans. This means that 3x = 5
Total number of cans consumed by both dogs in a day is 3x/4 + x/2 =5x/4
That means the cost per day would be
(5x/4 × 5)/3x = 25x/4 ×1/3x
= 25/12
It costs her $25/12 per day
To determine the cost for 60 days, we would multiply the cost per day by 60. It becomes
25/12 × 60 = $125
What is the angle in the picture below called?
A. a reflex angle
B. a straight angle
C. an acute angle
D. a right angle
Answers
Answer:
b
Step-by-step explanation:
Answer:straight angle
Step-by-step explanationbecause it’s straight
A grocer sells milk chocolate at $2.50 per pound, dark chocolate at $4.30 per pound, and dark chocolate with almonds at $5.50 per pound. He wants to make a mixture of 50 pounds of mixed chocolates to sell at $4.54 per pound. The mixture is to contain as many pounds of dark chocolate with almonds as milk chocolate and dark chocolate combined. How many pounds of each type must he use in this mixture?
Answers
To make a mixture of 50 pounds of chocolates with a price of $4.54 per pound, the grocer needs to use 12.5 pounds of milk chocolate, 12.5 pounds of dark chocolate, and 12.5 pounds of dark chocolate with almonds.
Explanation:Let's assume the grocer uses:
x pounds of milk chocolatey pounds of dark chocolatey pounds of dark chocolate with almondsGiven that the mixture needs to contain as many pounds of dark chocolate with almonds as milk chocolate and dark chocolate combined, we have the equation:
y = x + y
The total cost of the mixture is:
2.50x + 4.30y + 5.50y = 4.54 * 50
Simplifying the equation and solving the system of equations, we can find the values of x and y:
x = 12.5 pounds, y = 12.5 pounds
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Using the system of equations method, we use the given conditions to form three equations. By solving these equations, we can determine the quantities of each type of chocolate the grocer needs to use in their mixture.
Explanation:Identifying this problem as a system of equations problem, we can use three unknowns: M for milk chocolate, D for dark chocolate, and A for dark chocolate with almonds.
Given that he wants to make a 50-pound mixture, the first equation can be represented as M + D + A = 50.
The second equation is derived from the condition that the mixture should contain as many pounds of dark chocolate with almonds as milk chocolate and dark chocolate combined, which gives us: A = M + D.
The third equation is obtained by acknowledging that a weighted average of the mixture's component prices matches the price per pound of the mixture. That equation is 2.5M + 4.3D + 5.5A = 4.54*50.
Finally, by solving this system of equations, we can determine the quantities of each type of chocolate required.
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8.90 × 10^6 L has __ significant figures.
Answers
Answer:3 significant figures
Step-by-step explanation:got it right!!
A paper airplane was thrown from the top of a tall building, The height of the paper airplane above the ground can be found using the function y= -1.5x+60, where x is the time in seconds the airplane has been in the air.
Answers
Answer:
How many seconds did it take the paper airplane to reach the ground?
40 Seconds.
Step-by-step explanation:
When the paper airplane touches the ground is equivalent to having a height equal to zero (y=0). So replacing in the equation:
[tex]y= -1.5x+60\\0= -1.5x+60\\1.5x=60\\x=\frac{60}{1.5} \\x=40[/tex]
The function y= -1.5x+60 describes the downward trajectory of a paper airplane. The '-1.5' represents the falling speed per second, and '+60' represents the initial height. To find the paper airplane's height at any time, substitute the time into the equation.
Explanation:The question deals with the concept of linear equations and gravity, a physics concept represented in mathematical terms. The function y= -1.5x+60 describes the trajectory of a paper airplane thrown from a building. This function means that the height y of the airplane above the ground, after x seconds, decreases by 1.5m each second, starting from an initial height of 60m.
The coefficient -1.5 represents the speed of the plane, which is downwards due to negative sign. After each second, the paper airplane will be 1.5 m lower than it was the previous second. The '+60' means the paper airplane was initially 60m off the ground.
To use this function for any given time (x), simply substitute the time into the equation. For example, for 5 seconds (x=5), the height y would be -1.5*5+60 = -7.5 + 60 = 52.5m
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The top and bottom margins of a poster are 6 cm each, and the side margins are 4 cm each. If the area of the printed material on the poster is fixed at 384 square centimeters, the dimensions of the poster of the smallest area would be _____.
Answers
Answer:
The dimensions of the poster of the smallest area would be 24×36 cm.
Step-by-step explanation:
Let x and y be the width and height respectively of the printed area, which has fixed area.
If the area of the printed material on the poster is fixed at 384 square centimeters.
i.e. [tex]xy=384\ cm^2[/tex]
[tex]\Rightarrow y=\frac{384}{x}[/tex]
The top and bottom margins of a poster are 6 cm each is y+1.
The total width of the poster including 4 cm at sides is x+8.
The area of the total poster is [tex]A=(x+8)(y+12)[/tex]
Substitute the value of y,
[tex]A=(x+8)(\frac{384}{x}+12)[/tex]
[tex]A=384+12x+\frac{3072}{x}+96[/tex]
[tex]A=12x+\frac{3072}{x}+480[/tex]
Derivate w.r.t x,
[tex]A'=12-\frac{3072}{x^2}[/tex]
Put A'=0,
[tex]12-\frac{3072}{x^2}=0[/tex]
[tex]\frac{3072}{x^2}=12[/tex]
[tex]x^2=\frac{3072}{12}[/tex]
[tex]x^2=256[/tex]
[tex]x=16[/tex]
Derivate again w.r.t x,
[tex]A''=\frac{2(3072)}{x^3}[/tex] is positive for x>0,
A is concave up and x=16 is a minimum.
The corresponding y value is
[tex]y=\frac{384}{16}[/tex]
[tex]y=24[/tex]
The total poster width is x+8=16+8=24 cm
The total poster height is y+12=24+12=36 cm
Therefore, the dimensions of the poster of the smallest area would be 24×36 cm.
To find the dimensions of the poster with the smallest area, subtract the margin widths from the total dimensions. Set up and solve an equation to find the dimensions. The smallest area occurs when the expression 2x + 3y - 72 is minimized.
Explanation:To find the dimensions of the poster with the smallest area, we need to subtract the margin widths from the total dimensions. The top and bottom margins are 6 cm each, and the side margins are 4 cm each. Let the length of the printed material be x and the width be y. Then, the length of the poster is x + 2(6) = x + 12, and the width of the poster is y + 2(4) = y + 8. We know that the area of the printed material is fixed at 384 square centimeters, so we have the equation (x + 12)(y + 8) = 384. We can solve this equation to find the dimensions of the poster.
Expanding the equation, we get xy + 8x + 12y + 96 = 384. Rearranging the terms and isolating xy, we have xy = 384 - 8x - 12y - 96. Rearranging the terms again, we get xy = -8x - 12y + 288. Factoring out a -4, we have xy = -4(2x + 3y - 72). Now, we want to minimize the area of the poster, which means we want to minimize the value of xy. So, we need to minimize the expression 2x + 3y - 72 to find the minimum dimensions of the poster.
There are various methods to minimize this expression, such as using calculus or graphing techniques. Using calculus, we can take the partial derivatives of the expression with respect to x and y, set them equal to 0, and solve for x and y. However, since this is a high school level question, we can use a simpler method by observing that the expression 2x + 3y - 72 represents a straight line. The minimum value of this expression occurs at the point where the line intersects the x and y axes. So, to find the minimum dimensions of the poster, we can set 2x + 3y - 72 = 0 and solve for x and y. Solving this equation, we get x = 36 and y = 16. Therefore, the dimensions of the poster with the smallest area are 36 cm by 16 cm.
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A new school has opened in the area the school did not have yearbook before 2010. In 2010 there were 500 yearbooks sold . In 2014 there were 1000 yearbooks sold . Write the linear function that represents the number of yearbooks sold per year
Answers
Answer:
Step-by-step explanation:
The increase in the number of books sold each year follows an arithmetic progression, hence it is linear.
The formula for the nth term of an arithmetic progression is expressed as
Tn = a + (n - 1)d
Where
Tn is the nth term of the arithmetic sequence
a is the first term of the arithmetic sequence
n is the number of terms in the arithmetic sequence.
d is the common difference between consecutive terms in the arithmetic sequence.
From the information given,
a = 500 (number of books in the first year.
T5 = 1000 (the number of books at 2014 is)
n = 5 (number of terms from 2010 to 2014). Therefore
T5 = 1000 = 500 + (5 -1)d
1000 = 500 + 4d
4d = 500
d = 500/4 =125
The linear function that represents the number of yearbooks sold per year will be
T(n) = 500 + 125(n - 1)
The correct linear function that represents the number of yearbooks sold per year is [tex]\( f(t) = 100t + 500 \)[/tex], where [tex]\( t \)[/tex] is the number of years since 2010.
To determine the linear function, we need to find the slope (rate of change) and the y-intercept (initial value) of the function.
Given that in 2010, 500 yearbooks were sold, we can denote this point as (0, 500) since 0 years have passed since 2010. This gives us the y-intercept of the function.
Next, we look at the year 2014, where 1000 yearbooks were sold. This is 4 years after 2010, so we can denote this point as (4, 1000).
The slope of the line (m) is calculated by the change in the number of yearbooks sold divided by the change in time (years). So, we have:
[tex]\[ m = \frac{1000 - 500}{4 - 0} = \frac{500}{4} = 125 \][/tex]
This means that the number of yearbooks sold increases by 125 each year.
Now, we can write the linear function using the slope-intercept form [tex]\( f(t) = mt + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Substituting the values we have:
[tex]\[ f(t) = 125t + 500 \][/tex]
However, to make the function more general and to avoid dealing with fractions, we can express the slope as a multiple of 100. Since 125 is the same as [tex]\( \frac{5}{4} \times 100 \)[/tex], we can rewrite the function as:
[tex]\[ f(t) = \frac{5}{4} \times 100t + 500 \][/tex]
Simplifying this, we get:
[tex]\[ f(t) = 100t + 500 \][/tex]
This function represents the number of yearbooks sold each year, where [tex]\( t \)[/tex] is the number of years since 2010. For example, in 2011 (t=1), the function would predict [tex]\( f(1) = 100(1) + 500 = 600 \)[/tex] yearbooks sold.
Plz explain and prove the triangles congruence.
Answers
Answer:
ΔNAS≅ΔSEN by SSA axiom of congruency.
Step-by-step explanation:
Consider ΔNAS and ΔSEN,
NS=SN(Common ie . Both are the same side)
SA=NE( Given in the question that SA≅ NE)
∠SNA=∠NSE( Due to corresponding angle property where SE ║ NA)
Therefore, ΔNAS ≅ΔSEN by SSA axiom of congruency.
∴ NA≅SA by congruent parts of congruent Δ. Hence, proved.
At 4pm Charlie realizes he has half an hour to get to his grandmothers house for diner. If his grandmother lives 40 miles away how fast will Charlie have to drive to get there on time
Answers
Answer: Charlie have to drive at a speed of 80miles per hour in order to reach there on time.
Step-by-step explanation:
At 4pm Charlie realizes he has half an hour to get to his grandmothers house for diner. Knowing that the time he has left is 30 minutes and the distance to his grandmother's place is 40 miles, the only thing that he can control is his speed
Speed = distance travelled / time taken
40/0.5 = 80 miles per hour
En el borde superior de un vaso cilíndrico de cristal hay una gota de miel. En el punto diametralmente opuesto, se ha parado una mosca, como se muestra en la figura. Si la mosca avanza (sin volar) sobre el borde superior del vaso hasta la gota de miel, diga qué distancia tendría que recorrer. Considere que el diámetro del vaso es de 10 cm.
Answers
Answer
On the upper edge of a glass cylindrical glass there is a drop of honey. At the diametrically opposite point, a fly has stopped, as shown in the figure. If the fly advances (without flying) over the upper edge of the glass to the drop of honey, say how far it would have to travel. Consider that the diameter of the vessel is 10 cm.
Step-by-step explanation:
Earches related to bus traveled at an average rate of 60 miles per hour and then reduced its average rate to 40 miles per hour for the rest of the trip. If the 288 dash mile trip took 6 hours, determine how long the bus traveled at each rate.
Answers
Answer: the bus traveled 144 miles at a speed of 60 miles per hour and 144 miles at a speed of 40 miles per hour
Step-by-step explanation:
The bus traveled at an average rate of 60 miles per hour and then reduced its average rate to 40 miles per hour for the rest of the trip.
Let x miles = distance travelled at 60 miles per hour.
Let y miles = distance travelled at 40 miles per hour.
Total distance travelled = 288 miles.
Therefore,
x + y = 288 - - - - - - - 1
Total time spent in travelling 288 miles = 6 hours
Speed = distance /time
Time = distance / speed
Time spent when travelling x miles at a speed of 60 miles per hour = x/60
Time spent when travelling y miles at a speed of 40 miles per hour = y/40
Since total time is 6 hours, this means that
x/60 + y/40 = 6
(2x + 3y)/120 = 6
2x + 3y = 6 × 120 = 720 - - - - - - - 2
Substituting x = 288-y from equation 1 into equation 2, it becomes
2(288-y) + 3y= 720
576 - 2y + 3y = 720
- 2y + 3y = 720 - 576
y = 144 miles
x = 288 - y = 288-144
x = 144 miles