Use the parabola tool to graph the quadratic function f (x) = 2x2 - 4x + 6.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
The vertex of the parabola f(x) = 2x^2 - 4x + 6 is (1, 4)
How to graph the parabola?The function is given as:
f(x) = 2x^2 - 4x + 6
Differentiate the function
f'(x) = 4x - 4
Set to 0
4x -4 =0
So, we have:
4x = 4
Divide by 4
x = 1
Substitute x = 1 in f(x) = 2x^2 - 4x + 6
f(1) = 2(1)^2 - 4(1) + 6
This gives
f(1) = 4
This means that the vertex is (1, 4)
Next, we set x = 0.
So, we have:
f(0) = 2(0)^2 - 4(0) + 6
This gives
f(0) = 6
This means that the parabola passes through the point (0, 6)
See attachment for the parabola
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3 m 3 m 3 m 3m 7 m Find the surface area of the object.
Answer:
123 m²
Step-by-step explanation:
Surface area of the object = surface area of the bigger rectangular prism + (surface area of the smaller rectangular prism - area of the smaller rectangular prism base)
Surface area of the bigger rectangular prism:
L = 7 m
W = 3 m
H = 3 m
S.A = 2(LW + WH + LH)
S.A = 2(7*3 + 3*3 + 7*3)
S.A = 102 m²
Surface area of the smaller rectangular prism:
L = 3 m
W = 3 m
H = 1 m
S.A = 2(LW + WH + LH)
S.A = 2(3*3 + 3*1 + 3*1)
S.A = 30 m²
Area of the base of the smaller rectangular prism = L*W
L = 3 m
W = 3 m
Area = 3*3 = 9 m²
Surface area of the object = 102 + (30 - 9)
= 102 + 21
= 123 m²
You want to have 80000 college fund in 12 years. How much will you have to deposit now under the scenario below. Assume that you make no deposits into the account after the initial deposit.
An APR of 7.5% compounded daily
9514 1404 393
Answer:
$32,528.58
Step-by-step explanation:
For simplicity, we'll assume each year has 365 days.
The future value A of principal amount P at rate r compounded daily for t years is ...
A = P(1 +r/365)^(365t))
We want P when A = 80,000, r = 0.075, and t = 12.
P = A/(1 +r/365)^(365t)
P = $80000/(1+0.075/365)^(365·12) ≈ $32,528.58
You will have to deposit about $32,528.58.
These dot plots show the heights (in feet) from a sample of two different types of elephants Asian Elephants . 5 10 11 12 14 15 16 17 18 19 20 Height at the shoulder ift) African Elephants Helghut the shoulder It) What are the differences between the centers and spreads of these distributions? Select two choices: one for the centers and one for the spreads. A. Spreads. The heights of the Asian elephants are more spread out ( B. Centers: The Asian elephants have a lower median height than the African elephants c. Centers. The Asian elephants have a greater median height than the African elephants 1 D. Spreads The heights of the African elephants are more spread will give brainliest just help
Answer:
B - Centers: The Asian elephants have a lower median height than the African elephants
D - Spreads: The heights of the African elephants are more spread out
Step-by-step explanation:
On analyzing the dot plots, we find that the heights of the African elephants are more spread out and the Asian elephants have a lower median height than African elephants.
What is median?
Median is a statistical measure that determines the middle value of a dataset listed in ascending order. The measure divides the lower half from the higher half of the dataset.
Median of height of Asian elephants = 8 ft
Median of height of African elephants = 11 ft
This implies that the Asian elephants have a lower median height than African elephants.
What is spread of data?Spread describes the variation of the data. One of the measures of spread is range.
Range of height of Asian elephants = 4ft
Range of height of African elephants = 10ft
This implies that the height of African elephants are more spread out.
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Make r the subject of x= e + r/d
Step-by-step explanation:
X=e+r/d
swap both sides
e+r/d=x
subtract e from both sides
e-e+r/d=x-e
r/d=x-e
multiply d to both sides
d×r/d=x-e×d
r=x-e×d
PLEASEE GIVE AN EXPLANATION TO THIS
Answer:
C.
Step-by-step explanation:
The numbers in the front will be the first number and the ones behind it will be the second number.
So the numbers are 79,82,82,83,86,90,91,93,94 and 97
Then you want to add the lowest number and the greatest number which is 79 and 97
equals to 176
Question #7
Correct answer is B
Explain or show steps
Refer to the diagram below. We have the following points
A = base of the streetlampB = base of the personC = tip of the person's shadowD = top of the streetlampE = head of the personThe shadow extends from point B to point C. If we let x be the the horizontal distance from the lamp to the person, then dx/dt represents the speed at which the person is walking away from the lamp. In this case, dx/dt = 4 feet per second.
Let y be the length of the shadow. We can use similar triangles and proportions to help find what y is equal to in terms of x
AD/BE = AC/BC
15/6 = (x+y)/y
15y = 6(x+y)
15y = 6x+6y
15y-6y = 6x
9y = 6x
y = 6x/9
y = 2x/3
y = (2/3)*x
The length of the shadow is 2/3 that of the distance from the person to the lamp.
Now apply the derivative to both sides to compute dy/dt, which represents how fast the shadow is changing.
y = (2/3)x
dy/dt = d/dt[ (2/3)x ]
dy/dt = (2/3)*d/dt[ x ]
dy/dt = (2/3)*dx/dt
dy/dt = (2/3)*4
dy/dt = 2.667
The rate in which the shadow is lengthening is approximately 2.667 ft per second.
What is the slope of the following equation?
y = -5x -2
In ΔBCD, the measure of ∠D=90°, CB = 85, DC = 77, and BD = 36. What is the value of the cosine of ∠B to the nearest hundredth?
Answer:
cosB = 0.91
Step-by-step explanation:
Draw a picuture!
cosB = adj/hyp
cosB = DC / CB
cosB = 77 / 85
cosB = 0.91
In ΔBCD, the measure of ∠D=90°, CB = 85, DC = 77, and BD = 36. The value of the cosine of ∠B to the nearest hundredth, cos B = 0.91.
What are trigonometric identities?The trigonometric ratio can be defined in terms of ratios of perpendicular, bases, and hypotenuse.
These are defined only in right-angled triangles (triangles whose one angle is of 90 degree measure).
Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
In ΔBCD, the measure of ∠D=90°, CB = 85, DC = 77, and BD = 36.
We know that
cos B = adj/hyp
cos B = DC / CB
cos B = 77 / 85
cos B = 0.91
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(PLEASE HELP) (NO SPAM) Complete the special right tringale:
What is the length of (BD)?
What is the length of (BC)?
Answer:
Step-by-step explanation:
BD is opposite the 30° angle. The sine of 30° is 0.5. The sin of an angle in a right triangle is opposite/hypotenuse so BD = sin 30°x8.
Now you have two known lengths The third can be found by applying the Pythagorean theorem: BC²+BD²=CD², from which you can establish a numerical value for BC.
A point (-20, 48 ) is on the terminal side of angle 8. Find the exact value of sin 0.
A. 5/13
B. -5/13
C. -12/13
D. 12/13
Answer:
D. 12/13
Step-by-step explanation:
Hyp = √( (-20)² + 48² )
Hyp = 52
Sin = opp/hyp
sin = 48/52 = 12/13
The value of trigonometric ratio Sinθ = 12/13.
Hence option D is correct.
According to the given point
The base of the triangle be = -20
Perpendicular of triangle = 48
We know that the Pythagoras theorem for a right-angled triangle:
(Hypotenuse)²= (Perpendicular)² + (Base)²
Therefore,
Hypotenuse = √( (-20)² + 48² )
Hypotenuse = 52
Since we know that,
Sinθ = opposite side of θ /hypotenuse
= 48/52
= 12/13
Hence,
Sinθ = 12/13
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The complete question is:
A point (-20, 48 ) is on the terminal side of angle θ .
Find the exact value of Sinθ.
A. 5/13
B. -5/13
C. -12/13
D. 12/13
A manufacturer of cases for sound equipment requires drilling holes for metal screws. The drill bits wear out and must be replaced; there is expense not only in the cost of the bits but also for lost production. Engineers varied the rotation speed of the drill and measured the life- time y of four bits at each of five speeds.
Speed Lifetime
60 4.6
60 3.8
60 4.9
60 4.5
80 4.7
80 5.8
80 5.5
80 5.4
100 5
100 4.5
100 3.2
100 4.8
120 4.1
120 4.5
120 4
120 3.8
140 3.6
140 3
140 3.5
140 3.4
1. Create a scatterplot of the data. Does there appear to be a relation? Does it appear to be linear?
2. Regardless fit a simple linear regression model to the data. What can you say about the fit of the model to the data?
3. Is there any evident outlier
. Remove this observation and fit the regression model again. Is it improving the model f?
Answer:
There seems to be m linear relation between te data.
Negative relationships between variables.
Step-by-step explanation:
Speed(X)
60
60
60
60
80
80
80
80
100
100
100
100
120
120
120
120
140
140
140
140
Lifetime (Y) :
4.6
3.8
4.9
4.5
4.7
5.8
5.5
5.4
5
4.5
3.2
4.8
4.1
4.5
4
3.8
3.6
3
3.5
3.4
The linear regression equation obtained by fitting the data using a regression model is :
ŷ = -0.017X + 6.03
From the regression plot, the relationship between the two variables, speed and lifetime is negative, that is an increase in one variable will lead to a corresponding decrease in the other.
Tan(43)=1347/x
Can someone help please
the answer is ssmsmsmsmsmememememeememekekeke
Answer:
Step-by-step explanation:
tan(43) = 1347/x
Multiply by x to bring it to the other side.
x*tan(43) = 1347
Divide by tan(43) to get x by itself.
x = 1347/tan(43)
Use the tan and cot relationship.
x = 1347 * cot(43)
Multiply.
x ≈ 1444.5
On a regional map, the scale shows that 2 cm on the map = 10 actual miles. The actual distance from Forest Hills to Plainville is 74 miles. How far apart are these cities on the map?
A.)5 cm
B.)7.4 cm
C.)8 cm
D).14.8 cm
Answer:
D
Step-by-step explanation:
if every 2 cm on the map=10 miles, I can use my basic knowledge to find out how many cm will equal 70, in this case I can multiply 7 on both sides to find out how many cm on the map will equal 70, so 2(7)cm=10(7)mi will result as 14cm=70mi. Even though the answer seems pretty clear I can round my answer closer to 2 or I can double check by dividing 74 by 10=7.4 times the 2 cm which gets me 14.8.
Listed below are annual data for various years. The data are weights(metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using alpha (Ī±) =0.05 Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Select all TRUE statements for the above hypothesis test from those given below.
Lemon_Imports_(x) Crash_Fatality_Rate_(y)
230 15.8
264 15.6
359 15.5
482 15.3
531 14.9
Reqiured:
a. What are the null and alternative hypotheses?
b. Construct a scatterplot.
c. The linear correlation coefficient r is: ________
d. The test statistic t is :__________
e. The P-value is :___________
Answer:
R = - 0.9453
T = - 5.019
Pvalue = 0.212
Step-by-step explanation:
Given the data:
Lemon_Imports_(x)
230
264
359
482
531
Crash_Fatality_Rate_(y):
15.8
15.6
15.5
15.3
14.9
The Correlation Coefficient, R using a correlation Coefficient calculator is - 0.9453 ; this depicts a strong negative correlation between the dependent and independent variable.
The test statistic, T :
T = r / √(1 - r²) / (n - 2)
T = -0.9453/ √(1 - (-0.9453)²) / (5 - 2)
T = - 0.9453 / 0.1883329
T = - 5.019
The Pvalue using a Pearson Pvalue calculator ;
df = n - 1 = 5 - 2 = 3 ; r = - 0.9453
Pvalue = 0.212
Someone help me with this pls ty :) Math. No Fake answers please!!!
Answer:
-1 , 5 for the original figure and 7, 2 for the final figure
Step-by-step explanation:
Self Explanatory
If you want explanation, comment on this answer and I will tell you
Hassan surveyed 120 of the students in his school about their favorite color. 114 students said their favorite color was purple. What percentage of the surveyed students said their favorite color was purple?
Answer:
95%
Step-by-step explanation:
A surveyor is 100 feet from a building. He finds the angle of elevation to the top of the building is 23 degrees. If the surveyor’s eyelevel is 5.3 feet above the ground, find the height of the building.
Answer:
47.7 ft
Step-by-step explanation:
tan= o/a
tan(23)= x/100
x=100/tan(23)
x= 42.4
42.4 + 5.3 = 47.7
Answer:
m∠B = 15°
and
h ≈ 31.28 ft
Step-by-step explanation:
only if it's on edge 2021. this showed up when I put in the question, so imma just assume there are others here like me.
Sierra walks her dog Pepper twice a day. Her evening walk is two and a half times as far as her morning walk. At the end of the week, she tells her mom, “I walked pepper for 30 miles this week! How long is her morning walk?
Answer:
(30*2)/49
Step-by-step explanation:
let her morning walk distance be x
her evening distance walk =2 1/2 x
= 5x/2
her daily walk distance =5x/2+x
= 5x/2+2x/2=7x/2
her weekly walk distace= 7x/2*7=49x/2=30miles
x= (30*2)/49
Given that ux=$6 calculate o x •round your answer to two decimal places
Answer:
[tex]\sigma_x = 0.57[/tex]
Step-by-step explanation:
Given
[tex]\mu_x = 6[/tex]
See attachment
Required
Calculate [tex]\sigma_x[/tex]
This is calculated as:
[tex]\sigma_x = \sqrt{Var(x)}[/tex]
Where
[tex]Var(x) =\sum (x - \mu_x)^2 * P(x)[/tex]
So, we have:
[tex]Var(x) =(0 - 0.4)^2 * 0.64 + (1 - 0.4)^2 * 0.32 + (2 - 0.4)^2 * 0.04[/tex]
Using a calculator
[tex]Var(x) =0.32[/tex]
[tex]\sigma_x = \sqrt{Var(x)[/tex]
[tex]\sigma_x = \sqrt{0.32[/tex]
[tex]\sigma_x = 0.57[/tex] --- approximated
Jenelle invested $17000 in two mutual funds. Fund A earned 4% profit during the first year, while Fund B suffered a 1.5% loss. If she received a total of $460 profit, how much had she invested in each mutual fund?
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
Jenelle put $13,000 in Fund A mutual fund and $ 4,000 in Fund B mutual fund.
Step-by-step explanation:
As soon as Jenelle invested $ 17000 in two mutual funds: Fund A, which earned a 4% profit during the first year; and Fund B, which suffered a 1.5% loss, if she received a total of $ 460 profit, to know how much had she invested in each mutual fund, the following calculation must be done:
17000 x 0.04 - 0 x 0.015 = 680
15000 x 0.04 - 2000 x 0.015 = 570
13000 x 0.04 - 4000 x 0.015 = 460
Therefore, Jenelle put $ 13,000 in Fund A mutual fund and $ 4,000 in Fund B mutual fund.
Final question NO LINKS
Fake answers will be reported
Bots will be reported
Good answers that are right and perfect will get brainly extra points five stars thanks and a blessing
This is final and FINAL.
6. 24
7. 40
8. 16
9. 10
10. 18
11. 36
12. 24
13. 22
I haven't done these kinds of problems in a while so sorry if any of them are wrong :(
Have a good day :)
Find the value of x.
43°
X
x = [?]°
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute.a. What is the mean or expected number of customers that will arrive in a five-minute period?b. Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period.c. Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur?
Answer:
a) 2
b)
0.1353 = 13.53% probability that exactly 0 customers will arrive during a five-minute period.
0.2707 = 27.07% probability that exactly 1 customer will arrive during a five-minute period.
0.2707 = 27.07% probability that exactly 2 customers will arrive during a five-minute period.
0.1805 = 18.05% probability that exactly 3 customers will arrive during a five-minute period.
c) 0.1428 = 14.28% probability that delays will occur
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
a. What is the mean or expected number of customers that will arrive in a five-minute period?
0.4 customers per minute, so for five minutes, this is [tex]\mu = 5*0.4 = 2[/tex]
b. Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period.
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
0.1353 = 13.53% probability that exactly 0 customers will arrive during a five-minute period.
[tex]P(X = 1) = \frac{e^{-2}*2^{1}}{(1)!} = 0.2707[/tex]
0.2707 = 27.07% probability that exactly 1 customer will arrive during a five-minute period.
[tex]P(X = 2) = \frac{e^{-2}*2^{2}}{(2)!} = 0.2707[/tex]
0.2707 = 27.07% probability that exactly 2 customers will arrive during a five-minute period.
[tex]P(X =3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1805[/tex]
0.1805 = 18.05% probability that exactly 3 customers will arrive during a five-minute period.
c. Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur?
This is:
[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]
In which:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1353 + 0.2707 + 0.2707 + 0.1805 = 0.8572[/tex]
[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8572 = 0.1428[/tex]
0.1428 = 14.28% probability that delays will occur
Use the following function rule to find f(1).
f(x) = 5(8)x+ 4
f(1) =
Answer:
on the pic
Step-by-step explanation:
substitute the x with 1
Answer:
f(1)=44
Step-by-step explanation:
Wherever you see x, you will replace it with 1
so, 5(8)1+4
(40)1+4
40+4
=44
A. B,D,A,E,C
B. B,C,D,A,E
C. C,D,A,B,E
D. C,A,D,B,E
9514 1404 393
Answer:
C. C,D,A,B,E
Step-by-step explanation:
The first set of coordinates, (-3, 4) and (3, 4) are on the horizontal line y=4. The distance between them is the difference of their x-values: 3 -(-3) = 6. This is the third distance on the list, so 'A' will be 3rd in the sequence of matching.
Choices A and C have 'A' listed 3rd.
__
The second set of coordinates (-5, 3) and (-5, 11) are on the vertical line x=-5. The distance between them is the difference of their y-values: 11 -3 = 8. This is the 4th distance on the list, so 'B' will be 4th in the sequence of matching.
Choice C has 'B' listed 4th.
The appropriate sequence of matching is ...
C, D, A, B, E
_____
Additional comment
In this problem, as in most multiple-choice problems, it isn't necessary to find the complete answer. It is only necessary to find enough of the answer to determine the correct choice among those offered. You do need to know enough about how to work the problem to be able to tell a correct choice from an incorrect one. Knowing the required relationships is useful; slogging through the arithmetic is often not necessary.
Answer:
C. C,D,A,B,E
Step-by-step explanation:
Find the length of side x in simplest radical form with a rational denominator
60°
3
30
X
Answer: 5/2
Explanation:
According to 30-60-90 triangle rule:
The side opposite of 30 degree is equal to half of the hypotenuse and the hypotenuse here is 5 so therefore x = 5/2
Consider the intersecting lines shown. Which of the following statements could you prove based on this?
A. ∠w ≅ ∠z
B. m∠x + m∠z = 180°
C. ∠x ≅ ∠z
D. m∠w + m∠y = 90°
Answer:
c
Step-by-step explanation:
trust
At the Dr. Kim's office, 4 out of
every 5 patients treated had the
flu. If Dr. Kim treated 25 patients,
how many of them had the flu?
Answer:
20 patients
Step-by-step explanation:
4/5 of 25 is 20
what is
1 1/4 + 2/14
Answer:
1.39285714286
Step-by-step explanation:
[tex]1\frac{1}{3} + 2\frac{1}{4} = \frac{3*1+1}{3} + \frac{4*2+1}{4} = \frac{4}{3} + \frac{9}{4} = \frac{4*4}{3*4} + \frac{9*3}{4*3} = \frac{16}{12} + \frac{27}{12} = \frac{16+27}{12}=\frac{23}{12} = 1\frac{11}{12}[/tex]