Let f(x)=6x and g(x)=x+4 what’s the smallest number that’s in the domain of F(G)
Answers
Answer:
(-4) will be the smallest value.
Step-by-step explanation:
Two functions have been given in this question,
f(x) = [tex]\sqrt{6x}[/tex] and g(x) = x + 4
Then the composite function (fog)(x) will be,
(fog)(x) = f[g(x)]
f[g(x)] = [tex]\sqrt{6(x+4)}[/tex]
Since this function is defined for (x + 4) ≥ 0
(x + 4) - 4 ≥ 0 - 4
x ≥ -4
Domain of this function : [-4 ∞)
Therefore, the smallest number in the domain or smallest value for 'x' should be (-4).
Related Questions
Find all x in set of real numbers R Superscript 4 that are mapped into the zero vector by the transformation Bold x maps to Upper A Bold x for the given matrix A.
Answers
Answer:
[tex]x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right][/tex]
Step-by-step explanation:
According to the given situation, The computation of all x in a set of a real number is shown below:
First we have to determine the [tex]\bar x[/tex] so that [tex]A \bar x = 0[/tex]
[tex]\left[\begin{array}{cccc}1&-3&5&-5\\0&1&-3&5\\2&-4&4&-4\end{array}\right][/tex]
Now the augmented matrix is
[tex]\left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\2&-4&4&-4\ |\ 0\end{array}\right][/tex]
After this, we decrease this to reduce the formation of the row echelon
[tex]R_3 = R_3 -2R_1 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&2&-6&6\ |\ 0\end{array}\right][/tex]
[tex]R_3 = R_3 -2R_2 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right][/tex]
[tex]R_2 = 4R_2 +5R_3 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&4&-12&0\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right][/tex]
[tex]R_2 = \frac{R_2}{4}, R_3 = \frac{R_3}{-4} \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&1\ |\ 0\end{array}\right][/tex]
[tex]R_1 = R_1 +3 R_2 \rightarrow \left[\begin{array}{cccc}1&0&-4&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right][/tex]
[tex]R_1 = R_1 +5 R_3 \rightarrow \left[\begin{array}{cccc}1&0&-4&0\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right][/tex]
[tex]= x_1 - 4x_3 = 0\\\\x_1 = 4x_3\\\\x_2 - 3x_3 = 0\\\\ x_2 = 3x_3\\\\x_4 = 0[/tex]
[tex]x = \left[\begin{array}{c}4x_3&3x_3&x_3\\0\end{array}\right] \\\\ x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right][/tex]
By applying the above matrix, we can easily reach an answer
when a stone falls freely, the time taken to hit the ground varies as the square root of the distance fallen. If it takes four seconds th fall 78.4m, find how long would it takefor a stone to fall 500m
Answers
Answer:
The stone would take approximately 10.107 seconds to fall 500 meters.
Step-by-step explanation:
According to the statement of the problem, the following relationship of direct proportionality is built:
[tex]t \propto y^{1/2}[/tex]
[tex]t = k\cdot t^{1/2}[/tex]
Where:
[tex]t[/tex] - Time spent by the stone, measured in seconds.
[tex]y[/tex] - Height change experimented by the stone, measured in meters.
[tex]k[/tex] - Proportionality constant, measured in [tex]\frac{s}{m^{1/2}}[/tex].
First, the proportionality constant is determined by clearing the respective variable and replacing all known variables:
[tex]k = \frac{t}{y^{1/2}}[/tex]
If [tex]t = 4\,s[/tex] and [tex]y=78.4\,m[/tex], then:
[tex]k = \frac{4\,s}{(78.4\,m)^{1/2}}[/tex]
[tex]k \approx 0.452\,\frac{s}{m^{1/2}}[/tex]
Then, the expression is [tex]t = 0.452\cdot y^{1/2}[/tex]. Finally, if [tex]y = 500\,m[/tex], then the time is:
[tex]t = 0.452\cdot (500\,m)^{1/2}[/tex]
[tex]t \approx 10.107\,s[/tex]
The stone would take approximately 10.107 seconds to fall 500 meters.
Construct a frequency distribution and a frequency histogram for the given data set using the indicated number of classes. Describe any patterns.
Number of classes: 8
Data set: Reaction times (in milliseconds) of 30 adult females to an auditory stimulus.
430 386 352 301 450 291 429 467 454 385 380
373 386 307 321 336 310 413 306 357 514 443
442 326 508 424 386 429 412 418
Answers
Answer:
The histogram for the data is attached below.
Step-by-step explanation:
Arrange the data in ascending order as follows:
S = {291 , 301 , 306 , 307 , 310 , 321 , 326 , 336 , 352 , 357 , 373 , 380 , 385 , 386 , 386 , 386 , 412 , 413 , 418 , 424 , 429 , 429 , 430 , 442 , 443 , 450 , 454 , 467 , 508 , 514}
Compute the range:
[tex]Range=Max.-Min.\\=514-291\\=223[/tex]
Compute the class width:
[tex]Class\ Width =\frac{Range}{No.\ of\ classes}=\frac{223}{8}=27.875\approx 28[/tex]
The classes are as follows:
290 - 318
319 - 347
348 - 376
377 - 405
406 - 434
435 - 463
464 - 492
493 - 521
Compute the frequency distribution as follows:
Class Interval Frequency
290 - 318 5
319 - 347 3
348 - 376 3
377 - 405 5
406 - 434 7
435 - 463 4
464 - 492 1
493 - 521 2
The histogram for the data is attached below.
2.35=11x Equals What
Answers
Answer:
x=0.2136
Step-by-step explanation:
Answer:
x=0.214 rounded to the thousandths
Step-by-step explanation:
2.35=11x
divide each side by 11 to isolate the x
x=0.214 rounded to the thousandths
Identify an equation in point-slope form for the line perpendicular to
y= - 1/3x - 6 that passes through (-1,5).
O A. y + 1 = 3(x - 5)
O B. y + 5 = 1/3(x - 1)
O C. y - 5 = 3(x + 1)
O D. y - 5 = - 1/3(x + 1)
Answers
Answer:
hope you get it....sorry for any mistake calculations
find the coordinates of Q' after a reflection across parallel lines; first across the line y= -2 and then across the x-axis
Answers
Answer: new Q = (-4, 5)
Step-by-step explanation:
Given: Q = (-4, 1)
Reflected across y = -2:
Q is 3 units above y = -2 so a reflection is 3 units below y = -2 --> Q' = (-4, -5)
Reflected across x-axis:
Q' is 5 units below x-axis so a reflection is 5 units above x-axis --> Q'' = (-4, 5)
Find the value of a A.130 B.86 C.58 D.65
Answers
Answer:
Option (B)
Step-by-step explanation:
If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.
Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]
a + c = 172°
Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.
Therefore, a = c
⇒ a = c = 86°
Therefore, a = 86°
Option (B) will be the answer.
Determine the t critical value(s) that will capture the desired t-curve area in each of the following cases.
a. Central area = 0.95, df = 10
b. Central area = 0.95, df = 20
c. Central area = 0.99, df = 20
d. Central area = 0.99, df = 60
e. Upper-tail area = 0.01, df = 30
f. Lower-tail area = 0.025, df = 5
Answers
Answer:
a) Central area = 0.95, df = 10 t = (-2.228, 2.228)
(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)
(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)
(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)
(e) Upper-tail area = 0.01, df = 30 t= 2.457
(f) Lower-tail area = 0.025, df = 5 t= -2.571
Step-by-step explanation:
In this question, we are to determine the t critical value that will capture the t-curve area in the cases below;
We can use the t-table for this by using the appropriate confidence interval with the corresponding degree of freedom.
The following are the answers obtained from the table;
a) Central area = 0.95, df = 10 t = (-2.228, 2.228)
(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)
(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)
(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)
(e) Upper-tail area = 0.01, df = 30 t= 2.457
(f) Lower-tail area = 0.025, df = 5 t= -2.571
Player A finished first in a tournament at a golf club with a score of −9, or nine strokes under par. Tied for 46th place was player B, with a score of +9, or 9 strokes over par. What was the difference in scores between Player A and Player B?
Answers
Answer:
18
Step-by-step explanation:
since you want the difference in scores, you want to take the absolute value of the difference
9 - (-9) = 9+9 = 18
The difference in scores between Player A and Player B is 18.
How do we calculate the difference?The difference between two numbers is found by subtracting the smaller number from the greater number.
How do we solve the given question?We are informed that Player A finished first in a tournament at a golf club with a score of −9 or nine strokes under par. Tied for 46th place was player B, with a score of +9, or 9 strokes over par.
We are asked for the difference in scores between Player A and Player B.
The score of Player A = -9.
The score of Player B = 9
Since Player B's score > Player A's score,
To calculate the difference in their scores, we subtract player A's score from player B's score.
∴ Difference = 9 - (-9)
or, Difference = 9 + 9
Difference = 18.
∴ The difference in scores between Player A and Player B is 18.
Learn more about the difference at
https://brainly.com/question/25421984
#SPJ2
What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of 1/3 . A.x - 3y - 7 = 0 B.x - 3y + 7 = 0 C.3x - y - 7 = 0
Answers
Answer:
The answer is option A
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
Equation of the line using point (1 , - 2) and slope 1/3 is
y + 2 = 1/3( x - 1)
Multiply through by 3
That's
3y + 6 = x - 1
Simplify
x - 3y - 1 - 6 = 0
We have the final answer as
x - 3y - 7 = 0Hope this helps you
Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 ft high
Answers
Answer:
0.0526ft/minStep-by-step explanation:
Since the gravel being dumped is in the shape of a cone, we will use the formula for calculating the volume of a cone.
Volume of a cone V = πr²h/3
If the diameter and the height are equal, then r = h
V = πh²h/3
V = πh³/3
If the gravel is being dumped from a conveyor belt at a rate of 20 ft³/min, then dV/dt = 20ft³/min
Using chain rule to get the expression for dV/dt;
dV/dt = dV/dh * dh/dt
From the formula above, dV/dh = 3πh²/3
dV/dh = πh²
dV/dt = πh²dh/dt
20 = πh²dh/dt
To calculate how fast the height of the pile is increasing when the pile is 11 ft high, we will substitute h = 11 into the resulting expression and solve for dh/dt.
20 = π(11)²dh/dt
20 = 121πdh/dt
dh/dt = 20/121π
dh/dt = 20/380.133
dh/dt = 0.0526ft/min
This means that the height of the pile is increasing at 0.0526ft/min
At a deli counter, there are sandwiches with meat and vegetarian sandwiches. Kira is at the counter buying sandwiches for a picnic. In how many ways can she choose sandwiches if fewer than must be vegetarian sandwiches
Answers
Answer:
The number ways to choose between meat and vegetarian sandwiches can be computed using computation technique.
Step-by-step explanation:
There are two types of sandwiches available at the deli counter. The possibility of combinations can be found by computation technique of statistic. It is assumed that order does not matter and sandwiches will be selected at random. The sandwiches can be arranged in any order and number ways can be found by 2Cn.
Construct the confidence interval for the population mean mu. c = 0.90, x = 16.9, s = 9.0, and n = 45. A 90% confidence interval for mu is:______.
Answers
Answer:
The 90% confidence interval for population mean is [tex]14.7 < \mu < 19.1[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 16.9[/tex]
The confidence level is [tex]C = 0.90[/tex]
The sample size is [tex]n = 45[/tex]
The standard deviation
Now given that the confidence level is 0.90 the level of significance is mathematically evaluated as
[tex]\alpha = 1-0.90[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the standardized normal distribution table. The values is [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
The reason we are obtaining critical values for [tex]\frac{\alpha }{2}[/tex] instead of that of [tex]\alpha[/tex] is because [tex]\alpha[/tex] represents the area under the normal curve where the confidence level 1 - [tex]\alpha[/tex] (90%) did not cover which include both the left and right tail while [tex]\frac{\alpha }{2}[/tex] is just considering the area of one tail which is what we required calculate the margin of error
Generally the margin of error is mathematically evaluated as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 1.645* \frac{ 9 }{\sqrt{45} }[/tex]
[tex]MOE = 2.207[/tex]
The 90% confidence level interval is mathematically represented as
[tex]\= x - MOE < \mu < \= x + MOE[/tex]
substituting values
[tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]
[tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]
[tex]14.7 < \mu < 19.1[/tex]
amanda teaches the art of quilling to 4 students. These students each teach art of quilling to 4 other students. If this process continues for 5 generation after amanda, BLANK people other than amanda will know the art of qiulling
Answers
Answer:
1024
Step-by-step explanation:
4 * 4 * 4 * 4 * 4
Use the Chain Rule to find ∂z/∂s and ∂z/∂t. (Enter your answer only in terms of s and t. Please use * for multiplication between all factors.)
z = x8y9, x = s cos(t), y = s sin(t)
∂z/∂s =
∂z/∂t =
Answers
Answer:
Step-by-step explanation:
Using chain rule to find the partial deriviative of z with respect to s and t i.e ∂z/∂s and ∂z/∂t, we will use the following formula since it is composite in nature;
∂z/∂s = ∂z/∂x*∂x/∂s + ∂z/∂y*∂y/∂s
Given the following relationships z = x⁸y⁹, x = s cos(t), y = s sin(t)
∂z/∂x = 8x⁷y⁹, ∂x/∂s = cos(t), ∂z/∂y = 9x⁸y⁸ and ∂y/∂s = sin(t)
On substitution;
∂z/∂s = 8x⁷y⁹(cos(t)) + 9x⁸y⁸ sin(t)
∂z/∂s = 8(scost)⁷(s sint)⁹(cos(t)) + 9(s cost)⁸(s sint)⁸ sin(t)
∂z/∂s = (8s⁷cos⁸t)s⁹sin⁹t + (9s⁸cos⁸t)s⁸sin⁹t
∂z/∂s = 8s¹⁶cos⁸tsin⁹t + 9s¹⁶cos⁸tsin⁹t
∂z/∂s = 17s¹⁶cos⁸tsin⁹t
∂z/∂t = ∂z/∂x*∂x/∂t + ∂z/∂y*∂y/∂t
∂x/∂t = -s sin(t) and ∂y/∂t = s cos(t)
∂z/∂t = 8x⁷y⁹*(-s sint) + 9x⁸y⁸* (s cos(t))
∂z/∂t = 8(scost)⁷(s sint)⁹(-s sint) + 9(s cost)⁸(s sint)⁸(s cos(t))
∂z/∂t = -8s¹⁷cos⁷tsin¹⁰t + 9s¹⁷cos⁹tsin⁸t
∂z/∂t = -s¹⁷cos⁷tsin⁸t(8sin²t-9cos²t)
Simplify the expression . 39*x / 13
Answers
Answer:
3x
Step-by-step explanation:
39*x / 13
39/13 * x
3*x
3x
Answer:
3x
Step-by-step explanation:
We are given the expression:
39*x /13
We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.
(39*x /13) / (13/13)
(39x/13) / 1
3x / 1
When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.
3x
The expression 39*x/13 can be simplified to 3x
A table of values of a linear function is shown below. Find the output when the input is N. Type your answer in the space provide
Answers
Answer:
[tex] -3n - 7 [/tex]
Step-by-step explanation:
Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.
Using the slope-intercept formula, y = mx + b, let's find the equation.
Where,
m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]
[tex] m = \frac{-13 + 10}{1} [/tex]
[tex] m = \frac{-3}{1} [/tex]
[tex] m = -3 [/tex]
Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept
[tex] y = mx + b [/tex]
[tex] -10 = -3(1) + b [/tex]
[tex] -10 = -3 + b [/tex]
Add 3 to both sides:
[tex] -10 + 3 = -3 + b + 3 [/tex]
[tex] -7 = b [/tex]
[tex] b = -7 [/tex]
The equation of the given linear function can be written as:
[tex] y = -3x - 7 [/tex]
Or
[tex] f(x) = -3x - 7 [/tex]
Therefore, if the input is n, the output would be:
[tex] f(n) = -3n - 7 [/tex]
6th grade math help me, please :))
Answers
Answer:
[tex]\sf a) \ 2.5\\b) \ 7.5[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{250}{100}[/tex]
[tex]\sf Express \ as \ a \ decimal.[/tex]
[tex]=2.5[/tex]
[tex]\sf Multiply \ 3\% \ with \ 250.[/tex]
[tex]\displaystyle 250 \times \frac{3}{100}[/tex]
[tex]\displaystyle \frac{750}{100}=7.5[/tex]
At what point does the line
Y = -1/2 X + 2 intercept the Y-axis?
A. - 1
B. -1/2
C. 1
D. 2
E. -2
Answers
Answer:
D. 2
Step-by-step explanation:
The y-intercept is when the graph crosses the y-axis when x = 0. In that case, simply plug in x as 0:
y = -1/2(0) + 2
y = 2
Therefore, the graph crosses the y-axis at 2.
Answer:
D
Step-by-step explanation:
our equation is y= [tex]\frac{-1}{2}[/tex] x +2
-1/2 is the slope 2 is the y-interceptso the answer is 2
if we want to verify our answer we can follow these steps
the y-intercept is given by calculating the image of 0
y= -1/2*0+2 = 2so it's right
he numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set. 2, 10, 15, 3, 13, 9, 14, 7, 2, 9 The range is nothing.
Answers
Answer:
Range = 13
Mean = 8.4
Variance= 21.24
Standard deviation= 4.61
Step-by-step explanation:
2, 10, 15, 3, 13, 9, 14, 7, 2, 9
For the range
Let the set of data be arranged inn ascending order
Range= higehest value- lowest value
Range = 15-2
Range= 13
For the mean
Mean = (2+2+3+7+9+9+10+13+14+15)/10
Mean = 84/10
Mean = 8.4
For variance
Variance=((2-8.4)²+(2-8.4)²+(3-8.4)²+(7-8.4)²+(9-8.4)²+(9-8.4)²+(10-8.4)²+(13-8.4)²+(14-8.4)²+(15-8.4)²)/10
Variance= (40.96+40.96+29.16+1.96+0.36+0.36+2.56+21.16+31.36+43.56)/10
Variance= 212.4/10
Variance= 21.24
Standard deviation= √variance
Standard deviation= √21.24
Standard deviation= 4.609
Approximately = 4.61
A club is holding a raffle. Ten thousand
tickets have been sold for $2 each. There
will be a 1st prize of $3000, 3 second prizes
of $1000 each, 5 third prizes of $500 each
and 20 consolation prizes of $100 each.
Find the expected winnings of a single ticket.
Answers
Answer: Other answer is incorrect. It’s asking for the expected winnings of a single ticket. The answer is -.95
Step-by-step explanation:
1/10,000
3/10,000
5/10,000
20/10,000
9971/10,000
-
2998
998
498
98
-2
-
2998+2994+2490+1960-1992 =
-9500/10000 = -.95
About 5% of the population has a particular genetic mutation. 500 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 500.
Answers
Answer:
4.87
Step-by-step explanation:
According to the given situation, for calculation of standard deviation for the number of people first we need to calculate the variance which is shown below:-
Variance is
[tex]np(1 - p)\\\\ = 500\times (0.05)\times (1 - 0.05)[/tex]
After solving the above equation we will get
= 23.75
Now the standard deviation is
[tex]= \sqrt{\sigma} \\\\ = \sqrt{23.75}[/tex]
= 4.873397172
or
= 4.87
Therefore for computing the standard variation we simply applied the above formula.
I need help with this problem.
Answers
________________________Alike______________________
→ Both of the lines are proportional meaning they go through the origin.
→ Both of the lines have a positive slope meaning the slope goes towards the top right corner.
__________________________________________________
_____________________Difference_____________________
→ The 2 lines have different slopes, the first one has a slope of 1/3x whereas the 2nd one has a slope of 3x.
→ The points that create the lines are totally different, no two points are the same.
__________________________________________________
(a) Plot the following function ona Karnaugh map.(Do not expand to minterm form before plotting.)
F(A,B,C,D)=A‘B’+CD’+ABC +A’B’CD’+ABCD’
(b) Find the minimum sum of products.
(c) Find the minimum product of sums
Answers
Answer:
a) the K-map is in the attachment
f = Σm(0,1,2,3,6,10,14,15)
b) from the k-map, the minimum sum of products is
F = A'B' + CD' + ABC
c) the minimum product of sums is
F = (B' + C)(A' + C)(A+ B' +D')(A' + B + D')
Step-by-step explanation:
A Karnaugh map (K-map) is a pictorial framework used to limit the Boolean expressions without utilizing Boolean algebra theorems and equation controls.
a) the given function is f(A,B,C,D)=A‘B’+CD’+ABC +A’B’CD’+ABCD’
expanding the function as four variable terms
f(A,B,C,D)=A‘B’+CD’+ABC +A’B’CD’+ABCD’
= A'B'(C + C')(D + D')+(A + A')(B + B")CD' + ABC(D + D') + A'B'CD' + ABCD'
= A'B'CD + A'B'CD' + A'B'C'D' + ABCD' +AB'CD' + A'BCD' + A'B'CD' + ABCD +ABCD' + A'B'CD' + ABCD'
=A'B'CD + A'B'CD' + A'B'C'D + A'B'C'D' + ABCD' + AB'CD' + A'BCD' +ABCD
f = Σm(0,1,2,3,6,10,14,15)
note: diagram is in the attachment
b) the minterms for the minimum sum of product are
f = Σm(0,1,2,3,6,10,14,15)
simplifying the K-map(done in the attachment)
from the k-map, the minimum sum of products is
F = A'B' + CD' + ABC
c) the maxterms for the minimum product of sums are
f = ПM(4,5,7,8,9,11,12,13)
plot the K-map to find minimum product of sums(done in the attachment)
the minimum product of sums is
F = (B' + C)(A' + C)(A+ B' +D')(A' + B + D')
Lengths of pregnancies (in humans) have a mean of 267.6 days and a standard deviation of 15.4 days. A woman tracked her pregnancy and found it to be 309 days. Find the z score for 309 days. Is such a length unusual?
Answers
Answer:
The z-score is [tex]z = 2.65[/tex]
The length of days is not unusual
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 267.6 \ days[/tex]
The standard deviation is [tex]\sigma = 15.4 \ days[/tex]
The value considered is [tex]x = 309 \ days[/tex]
The z-score is mathematically represented as
[tex]z = \frac{x - \mu}{\sigma }[/tex]
[tex]z = \frac{309 - 267.6}{15.6 }[/tex]
[tex]z = 2.65[/tex]
Now given that the z-score is not greater than 3 then we can say that the length of days is not unusual
(reference khan academy)
Please HELP best answer will receive a BRAINLIEST. Given the probability density function f ( x ) = 1/3 over the interval [ 4 , 7 ] , find the expected value, the mean, the variance and the standard deviation.
Answers
Answer:
[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]
[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]
[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]
And the variance for this case would be:
[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]
And the standard deviation is:
[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]
Step-by-step explanation:
For this case we have the following probability density function
[tex] f(x)= \frac{1}{3}, 4 \leq x \leq 7[/tex]
And for this case we can find the expected value with this formula:
[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]
[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]
[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]
And the variance for this case would be:
[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]
And the standard deviation is:
[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]
Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. 2 4 6 8 10 amount of sugar (mg) 180 182 184 186 188 190 192 194 Frequency What is the sample size for this data set?
Answers
Answer:
The sample size is 30.
Step-by-step explanation:
The sample size of a histogram can be calculated by summing up all the frequencies of all the occurrences in the data set
From the question the frequency is given as
Frequency = 2 4 6 8 10
The sample size n =
2 + 4 + 6 + 8 + 10
= 30
Therefore the sample size n of the data set = 30
How do you make a table of value for the following equation? 3x=y
Answers
Answer:
Step-by-step explanation:
y= 3x
x y
0 0
1 3
2 6
3 9
-1 -3
-2 -6
Evan wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Evan has 1000 feet of fencing, you can find the dimensions that maximize the area of the enclosure. a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write an function for the area A of the enclosure in terms of w . (HINT first write two equations with w and l and A . Solve for l in one equation and substitute for l in the other). A(w) = ___________ b) What width would maximize the area? w = __________ c) What is the maximum area? A = _________ square feet
Answers
Answer: A. A=(1000-2w)*w B. 250 feet
C. 125 000 square feet
Step-by-step explanation:
The area of rectangular is A=l*w (1)
From another hand the length of the fence is 2*w+l=1000 (2)
L is not multiplied by 2, because the opposite side of the l is the barn,- we don't need in fence on that side.
Express l from (2):
l=1000-2w
Substitude l in (1) by 1000-2w
A=(1000-2w)*w (3) ( Part A. is done !)
Part B.
To find the width w (Wmax) that corresponds to max of area A we have to dind the roots of equation (1000-2w)w=0 ( we get it from (3))
w1=0 1000-2*w2=0
w2=500
Wmax= (w1+w2)/2=(0+500)/2=250 feet
The width that maximize area A is Wmax=250 feet
Part C. Using (3) and the value of Wmax=250 we can write the following:
A(Wmax)=250*(1000-2*250)=250*500=125 000 square feets
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Answers
Answer:
acute isosceles triangle
vertex angle, y = 44.0 degrees. (smallest angle)
Step-by-step explanation:
If the sides are in the ratio 4:4:3,
two of the sides have equal lengths, so it is an isosceles triangle.
Also, the sum of square of the two shorter sides is greater than the square of the longest side, so it is an acute triangle.
To find the smallest angle, we draw the perpendicular bisector of the base (side length 3) and form two right triangles.
The base angle x is given by the ratio
cos(x) = 1.5/4 = 3/8
Consequently the base angle is arccos(3/8) = 68.0 degrees.
The vertex angle equals twice the complement of 68.0
vertex angle, y = 2 (90-68.0) = 44.0 degrees. (smallest angle)