Answer:
Step-by-step explanation:
Hello,
[tex]f(g(x))=\dfrac{8}{x^2}+4[/tex]
So if we take
[tex]f(x)=\dfrac{8}{x}+4 \ \ and \\\\g(x)=x^2\\ \\f(g(x))=\dfrac{8}{g(x)}+4=\dfrac{8}{x^2}+4[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
5/3 x 6/7 real quick plz
Answer:
10/7 or 1 3/7. I hope this helps,
Step-by-step explanation:
A point (x,y) is a distance of 6 units from the x-axis. It is a distance of 5 units from the point (8,3). It is a distance [tex]\sqrt{n}[/tex] from the origin. Given that x<8, what is n?
Answer: n = 52
Step-by-step explanation:
when we have two vectors (x,y) and (a,b) the distance between the vectors is:
D = √( (x - a)^2 + (y - b)^2)
now, we know that:
1) the distance between (x, y ) and the x-axis is 6 units.
The nearest point to (x, y) in the x-axis is the point (x, 0) so we have:
D = 6 = √( (x - x)^2 + (y - 0)^2) = √y^2
so y can be 6 or -6.
So we know that y = 6, and now we can write our point as (x, +-6)
2) The distance between our point and (8, 3) is 5 units:
D = √( (x - 8)^2 + (y - 3)^2) = 5.
And we know that the distance from the origin, (n, n) is:
D = √n = √(x^2 + y^2}
n = x^2 + y^2
Now, we should start with:
√( (x - 8)^2 + (y - 3)^2) = 5
first suppose that y = -6, then:
√( (x - 8)^2 + (-6 - 3)^2) = √( (x - 8)^2 + (-9)^2) = 5.
√( (x - 8)^2 + 81) = 5.
Then we must have that:
and we know that √25 = 5
so (x-8)^2 + 81 = 25
this can never happen, so we can discard y = -6
Now the second case, if y = 6,
√( (x - 8)^2 + (6 - 3)^2) = 5.
√( (x - 8)^2 + (3)^2) = 5.
√( (x - 8)^2 + 9) = 5.
here:
(x - 8)^2 + 9 = 25
(x - 8)^2 = 16
(x - 8) = √16 = +-4
So again we have two cases:
if x - 8 = 4, then:
x = 4 + 8 = 12
but we must have x < 8, so this can be discarded.
now, if x - 8 = -4 then:
x = -4 + 8 = 4, this is an acceptable answer, then our point is (4, 6)
And we have:
n = 4^2 + 6^2 = 16 + 36 = 52
A house m by m is surrounded by a walkway m wide. 27 9 1.8 a) Find the area of the region covered by the house and the walkway. b) Find the area of the walkway.
Answer:
A. 385.56 square meters.
B. 142.56 square meters.
Step-by-step explanation:
A house 27m by 9m is surrounded by a walkway 1.8m wide.
a) Find the area of the region covered by the house and the walkway.
b) Find the area of the walkway.
Let
Length of the house=l=27m
Width of the house=w=9m
Wideness of the walkway=x=1.8m
Area of the region covered by the house and the walkway
=( L + 2*x) * (w + 2*x)
= (27+2*1.8)*(9+2*1.8)
=(27+3.6)*(9+3.6)
=(30.6)*(12.6)
=385.56 square meters.
b) Area of the walkway
= (L + 2*x)*(w + 2*x) - l*w
= (27+2*1.8)*(9+2*1.8) - 27*9
=(27+3.6)*(9+3.6) - 243
=(30.6)*(12.6) - 243
=385.56 - 243
=142.56 square meters.
A. f(x) = -x^2 - x - 4
B. f(x) = -x^2 + 4
C. f(x) = x^2 + 3x + 4
D. f(x) = x^2 + 4
Answer:
B: -x^2 + 4
Step-by-step explanation:
If the equation was [tex]f(x)=x^2[/tex], then the vertex would be at 0, and the "U" would be facing straight up. Here, the "U" is upside down, so that means the "x^2" would have to be a negative number ([tex]-x^2[/tex]) to get the upside-down "U". Then, we could see that the vertex is at positive 4, so that means that the parabola moved up 4 units, so the equation should end in +4.
Our answer is:
B: -x^2 + 4
Time spent using e-mail per session is normally distributed with a mean = to 8 minutes and standard deviation = 2minutes. If a random samples of 36 sessions were selected, the computed sample standard deviation would be
a. 0.25
b. 0.3333
c. 0.42
d. 0.48
Answer:
The correct option is (b) 0.3333.
Step-by-step explanation:
The standard deviation of the sampling distribution of sample mean [tex](\bar x)[/tex] is known as the standard error [tex](\sigma_{\bar x})[/tex].
The standard error is given as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=8\\\\\sigma=2\\\\n=36[/tex]
Compute the standard deviation of the sample mean as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=\frac{2}{\sqrt{36}}\\\\=\frac{2}{6}\\\\=\frac{1}{3}\\\\=0.3333[/tex]
Thus, the standard deviation of the sample mean is 0.3333.
Diane has a rectangular poster that is 20 centimeters long and 15 centimeters wide. What is the area of the poster in square meters? Do not round your answer. Be sure to include the correct unit in your answer.
Answer:
0.03 square meters
Step-by-step explanation:
1. convert 20 cm, 15 cm into m by dividing the number by 100 then you got 0.2 m and 0.15 m respectively
2. calculate the area by multiply 2 numbers together
0.2 × 0.15 = 0.03 square meter
=
Graphing an integer function and finding its range for a given...
The function h is defined as follows for the domain given.
h(x) = 2 -2x, domain = {-3, -2, 1, 5}
Write the range of h using set notation. Then graph h.
Answer:
Step-by-step explanation:
● h(x) = 2-2x
The domain is {-3,-2,1,5}
● h(-3) = 2-2×(-3) = 2+6 = 8
● h(-2) = 2 -2×(-2) = 2+4 = 6
● h(1) = 2-2×1 = 2-2 = 0
● h(5) = 2-2×5 = 2-10 = -8
The range is {-8,0,6,8}
help help help help help help
Answer:
75 yards long and 90 yards wide.
Step-by-step explanation:
Let's first find the perimeter of the main rectangle:
100x2 + 65x2 =
330
_________________________________________
Next we need to find two numbers that match:
75 and 90
75x2 + 90x2 =
330
_________________________________________
75x90 is 6750 (More Area)
100x60 is 6500 (Less Area)
Theresa bought 2 pineapples for $6. She wants to find the constant of proportionality in terms of dollars per pineapple. She modeled this proportional relationship on a number line diagram, as shown.
Part B
How much would 4 pineapples cost?
The yellow bar is the total cost of 2 pineapples. The black line in the middle of the yellow splits it equally in half and is located at the 3.
The constant bod proportionality would be 3, which means each pineapple cost $3
Answer:
first of all, brainly better not delete my answer again. (the answer is 3)
Step-by-step explanation:
you have to multiply to find the number of pineapples. but unlike me i did skip count and write down my number's and I tried to find "what number skips until it ends to 6?'' i found 3 as my answer! 3,6,9,12,15,18,21 etc..
The scale on a scale drawing is 1 : 30. What should you do with each measurement on the drawing to get the actual dimensions? Provide an example of a drawing that uses this scale. Include both the original and new dimensions.
Answer:
see below
Step-by-step explanation:
For the first question, you should multiply the scale dimension by 30 to get the actual dimension. This is because the scale is 1:30 where the scale dimension is the 1 and the actual dimension is 30, so therefore, the scale dimension is 1/30th of the actual dimension, so to get the actual dimension, we can multiply the scale dimension by 30. I'm not totally sure how to attach pictures from my phone on my computer (sorry) but an example of a drawing could be two rectangles, the first (this is the scale drawing) having dimensions of 1 by 2 units and the second (this is the actual drawing) having dimensions of 30 by 60 units. I hope this helps!
Please help with this
The shape has 11 sides.
Using the angle formula for polygons:
The sum of all the interior angles is:
11-2 x 180 = 9 x 180 = 1,620 degrees.
For one angle divide the total by number of sides:
1620 / 11 = 147.27 which rounds to 147.2
The answer is D.
please help me out! <3
Answer:
[tex]-1 \frac{3}{4}[/tex]
Step-by-step explanation:
Using this number line, we can plot our original number - [tex]\frac{3}{4}[/tex] (see picture attached)
Adding a negative is the same thing as subtracting - so we are subtracting [tex]2\frac{1}{2}[/tex] from [tex]\frac{3}{4}[/tex].
To subtract this, we can break up [tex]2\frac{1}{2}[/tex] into 3 parts: 1, 1, and [tex]\frac{1}{2}[/tex]. We can subtract each of these from the current number and see where we land up. (again see picture)
We land up at [tex]-1 \frac{3}{4}[/tex].
Hope this helped!
Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family. His dad tells him that he can check by using the inequality 2f < 223, where f is the time skied in seconds for each person. Plug the values for the time skied by each person into the inequality to find the answer.
Lori 55
Vanessa 265
Devon 172
Celia 112
Arnold 356
Answer:
Kelvin did not skied without falling more than twice as long as anyone else in his family.
Step-by-step explanation:
The inequality representing the event where Kelvin skied without falling more than twice as long as anyone else in his family is:
[tex]2f<223[/tex]
Here 223 is the time for Kelvin.
Check for Lori as follows:[tex]2f<223[/tex]
[tex]2\times 55=110<223[/tex]
Kelvin skied without falling more than twice as long as Lori.
Check for Vanessa as follows:[tex]2f<223[/tex]
[tex]2\times 265=530>223[/tex]
Kelvin skied without falling less than twice as long as Vanessa.
Check for Devon as follows:[tex]2f<223[/tex]
[tex]2\times 172=344>223[/tex]
Kelvin skied without falling less than twice as long as Devon.
Check for Celia as follows:[tex]2f<223[/tex]
[tex]2\times 112=224>223[/tex]
Kelvin skied without falling less than twice as long as Celia.
Check for Arnold as follows:[tex]2f<223[/tex]
[tex]2\times 356=712>223[/tex]
Kelvin skied without falling less than twice as long as Arnold.
Thus, Kelvin did not skied without falling more than twice as long as anyone else in his family.
Answer:
Yes, Kevin skied 2x as long as Lori.
Step-by-step explanation:
Kevin's time was 223 seconds; Lori's time was 110 seconds.
110^2 = 220 or 110 multiplied by 2 equals 220 or 110 x 2 = 220 or
110 * 2 = 220
Thus, Kevin indeed, skied twice as long as Lori.
PLZ HLEP QUICK!!! Which of the following is an arithmetic sequence? -2, 4, -6, 8, ... -8, -6, -4, -2, ... 2, 4, 8, 16, ...
Answer:
-8, -6, -4, -2, ...
Step-by-step explanation:
-8, -6, -4, -2, ... is an arithmetic sequence: each new term is obtained by adding 2 to the previous term.
Answer:
-8, -6, -4, -2
Step-by-step explanation:
"An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence."
two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 109 feet, and ball 2 is dropped from a height of 260 feet. Use the function f(t) -16t^2+h to determine the current height, f(t), of a ball from a height h, over given time t.
When does ball 1 reach the ground? Round to the nearest hundredth
Answer: 5.22 seconds
Step-by-step explanation:
t represents time and y represents the height.
Since we want to know when the ball hits the ground, find t when y = 0
Ball 1 starts at a height of 109 --> h = 109
0 = -16t² + 109
16t² = 109
[tex]t^2=\dfrac{109}{16}\\[/tex]
[tex]t=\sqrt{\dfrac{109}{16}}[/tex]
[tex]t=\dfrac{\sqrt{109}}{2}[/tex]
t = 5.22
=> H = 109
=> 0 = -16t² + 109
=> 16t² = 109
=> t² = 109/16
=> t = 109/2
=> t = 5.22 sec
Therefore, 5.22 second is the answer.
What do we use mathematical induction for?
proving statements!
it's the very definition of it
Graph the function f(x) = 18(0.8)
[tex]f(x)=18(0.8)=14.4[/tex]
is a constant function, so it will be a straight line parallel to x axis and passing through y axis at $14.4$
a wolf population of 850 wolves is increasing by 7% each year. Find the wolf population after 7 years
Answer:
1,267 wolvesStep-by-step explanation:
Initial population of wolf = 850 wolves
If the wolves increases by 7% each year, yearly increment will be 7% of 850
= 7/100 * 850
= 7*8.5
= 59.5 wolves.
This shows that the wolves increases by 59.5 each year.
After 7 years, increment will be equivalent to 59.5 * 7 = 416.5
The wolf population after 7 years = Initial population + Increment after 7 years
= 850 + 416.5
= 1266.5
≈ 1267 wolves
Hence the population of the wolves after 7 years is approximately 1,267 wolves
Complete the table for the given rule. Rule: y = x + 3. X ? Y 4. X ? Y 8. X ? Y 5
Answer:
X 1 for Y 4
X 5 for Y 8
X 2 for Y 5
Step-by-step explanation:
We can substitute the values of Y in the formula and then subtract three from both sides.
How many solutions does the system have? x+2y=2 2x+4y=−8
Answer:
Step-by-step explanation:
x + 2y = 2
2x + 4y = -8
-2x - 4y = -4
2x + 4y = -8
0 not equal to -12
no solution
Should I read Fruit's Basket? I need something to keep me busy.
Answer: Yes
Explanation: Yes because, sometimes you need to do stuff to get things of your head
1. What is sin(A)?
1
T
2
2. What is
tan(B)?
5
3
4
13
12
이
3. What is
cos(C)?
5
3
B
5
6
4. What is
cos(D)?
7
AddP
Answer:
Sin A=0.6
Tan B = 1.3333
Cos C= 0.9231
Cos C= 0.3846
Step-by-step explanation:
For sin A
Sin A= opposite/hypotenuse
Sin A= 3/5
Sin A=0.6
For Tan B
Tan B = opposite/adjacent
Tan B = 4/3
Tan B = 1.3333
For cos C
Cos C = adjacent/hypotenuse
Cos C= 12/13
Cos C= 0.9231
For Cos D
Cos D= adjacent/hypotenuse
Cos C = 5/13
Cos C= 0.3846
Michael records the height of 1000 people. This data is a normal distribution and the sample mean was 0.75. Identify the margin of error for this data set.
Answer:
0.0284Step-by-step explanation:
The formula for calculating the Margin of error of a dataset is expressed as;
Margin of error = [tex]Z*\sqrt{\frac{p(1-p)}{n} } \\\\[/tex] where;
Z is the z-score of 95% confidence interval = 1.96
p is the sample proportion/mean = 0.75
n is the sample size = total number of people = 1000
Note that when the confidence interval is not given, it is always safe to use 95% confidence.
Substituting this values into the formula we have;
[tex]ME = 1.96*\sqrt{\frac{0.7(1-0.7)}{1000} } \\\\ME = 1.96*\sqrt{\frac{0.7(0.3)}{1000} } \\\\ME = 1.96*\sqrt{0.00021} } \\\\ME = 1.96*0.01449\\\\ME = 0.0284[/tex]
Hence the margin error for the dataset is 0.0284
What is the rise over run for the slope -11/9
Answer: 11 down and 9 right
Step-by-step explanation:
Slope IS rise over run where the top number of the fraction (numerator) determines the vertical distance --> positive is up, negative is down
and the bottom number of the fraction (denominator) determines the horizontal distance --> positive is right, negative is left.
Given slope = -11/9
the numerator is -11 so the "rise" is DOWN 11 units
the denominator is 9 so the "run" is RIGHT 9 units
According to the Census Bureau, 3.34 people reside in the typical American household. A sample of 26 households in Arizona retirement communities showed the mean number of residents per household was 2.70 residents. The standard deviation of this sample was 1.17 residents. At the .10 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.34 persons?
(a) State the null hypothesis and the alternate hypothesis. (Round your answer to 2 decimal places.)
H0: ? ?
H1: ? <
(b)
State the decision rule for .10 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Reject H0 if t <
(c)
Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Value of the test statistic
(d)
Is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.34 persons?
H0. Mean number of residents less than 3.34 persons.
Answer:
Step-by-step explanation:
Given that:
Mean = 3.34
sample size = 26
sample mean = 2.7
standard deviation = 1.17
level of significance = 0.10
The null hypothesis and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o: \mu \geq 3.34} \\ \\ \mathtt{H_1: \mu < 3.34}[/tex]
degree of freedom = n - 1
degree of freedom = 26 -1
degree of freedom = 25
level of significance = 0.10
Since the alternative hypothesis contains <, then the test is left tailed
[tex]\mathtt{t_{\alpha, df} = t_{0.10, 25}}[/tex]
[tex]\mathtt{t_{0.10, 25}}[/tex] = - 1.316
The rejection region therefore consist of all values smaller than - 1.316, therefore ; reject [tex]H_o[/tex] if t < -1.316
The test statistics can be computed as follows:
[tex]t = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \dfrac{2.7 - 3.34}{\dfrac{1.17}{\sqrt{26}}}[/tex]
[tex]t = \dfrac{-0.64}{\dfrac{1.17}{5.099}}[/tex]
t = - 2.789
Decision Rule: To reject the null hypothesis if the t test lies in the rejection region or less than the rejection region.
Conclusion: We reject the null hypothesis since t = (- 2.789) < -1.316. Then we conclude that the mean number of residents in the retirement community household is less than 3.34 persons.
A 160-lb man carries a 5-lb can of paint up a helical staircase that encircles a silo with radius 20 ft. If the silo is 90 ft high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top
Weight of man and paint = 160 + 5 = 165 total pounds.
Gravitational force is independent of the path taken so we can ignore the radius of the silo.
Work done = total weight x height
The problem says he climbs to the top so overall height is 90 feet
Work = 165 lbs x 90 ft = 14,850 ft-lbs
Mario invested $5100 at 13%
to be compounded daily. What will be the value of Mario's investment in 2 years? Round your answer to the nearest cent, if necessary. Note: 365 days in a year and 30 days in a month.
Answer:
Amount = $6614 and 19 cent
Step-by-step explanation:
Formula for compound interest is
A= p(1+r/n)^(nt)
Compounded daily
So n= 365*2= 730
T= 2
r= 0.13
P= 5100
A= p(1+r/n)^(nt)
A= 5100(1+0.13/730)^(730*2)
A= 5100(1+1.78082*10^-4)^(1460)
A= 5100(1.000178082)^1460
A= 5100(1.2969)
A= 6614.19
Amount = $6614 and 19 cent
For the given data value, find the standard score and the percentile. A data value 0.6 standard deviations above the mean.
Answer:
The z-score is [tex]z = 0.6[/tex]
The percentile is [tex]p(Z < 0.6) = 72.57\%[/tex]
Step-by-step explanation:
From the question we are told that
The data value is 0.6 standard deviations above the mean i.e [tex]x = \mu + 0.6 \sigma[/tex]
Where [tex]\mu[/tex] is the population mean and [tex]\sigma[/tex] is the standard deviation
Generally the z-score is mathematically represented as
[tex]z = \frac{x - \mu }{\sigma }[/tex]
=> [tex]z = \frac{(\mu + 0.6\sigma ) - \mu }{\sigma }[/tex]
=> [tex]z = 0.6[/tex]
The percentile is obtained from the z-table and the value is
[tex]p(Z < 0.6) = 0.7257[/tex]
=> [tex]p(Z < 0.6) = 72.57\%[/tex]
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Write the perimeter of the triangle as a
simplified expression.
3y + 5
бу
Y-4
Answer:
10y+1
Step-by-step explanation:
The perimeter is the three sides added together
3y+5+6y+y-4=
10y+1
Answer:
[tex]\huge\boxed{P_\triangle=10y+1}[/tex]
Step-by-step explanation:
The formula of a perimeter of a triangle:
[tex]P_\triangle=a+b+c[/tex]
We have:
[tex]a=3y+5,\ b=6y,\ c=y-4[/tex]
Substitute:
[tex]P_\triangle=(3y+5)+(6y)+(y-4)=3y+5+6y+y-4[/tex]
Combine like terms:
[tex]P_\triangle=(3y+6y+y)+(5-4)=10y+1[/tex]
