Answer:
The answer is "Option b".
Step-by-step explanation:
The significant variance shows that the numbers in the set are far from the mean and far from each other as well. Alternatively, a little variation implies the reverse. The variance value of 0, on either hand, shows that all values inside a set of numbers are the same. If you need yet another test, use a greater sample variance as the numerator of the test statistic to avoid having to reference tables of the F distribution that primary device from of the lower tail.
A plank 6m long leans against a vertical wall so that the foot of the plank is 4m away from the wall. A lizard climbs 2m up the plank. Calculate the horizontal distance between the lizard and the wall.
Answer: [tex]\dfrac{8}{3}\ m[/tex]
Step-by-step explanation:
Given
Length of the plank is [tex]6\ m[/tex]
Foot of the flank is [tex]4\ m[/tex] away from the wall
Lizard climbs 2 m up the wall
from the figure, the two triangles are similar
[tex]\therefore \dfrac{2}{6}=\dfrac{x}{4}\\\\\Rightarrow x=4\times \dfrac{2}{6}\\\\\Rightarrow x=\dfrac{4}{3}\ m[/tex]
So, the distance from the wall is
[tex]\Rightarrow 4-x\\\\\Rightarrow 4-\dfrac{4}{3}\\\\\Rightarrow \dfrac{8}{3}\ m[/tex]
20) solve:
[tex] {8}^{2} + 2 = [/tex]
21) solve:
[tex]4(2x + 5y = [/tex]
22) simplify the expression
[tex]4( {2}^{2} + 30) - 4 = [/tex]
A game involves correctly choosing the 5 correct numbers from 1 through 18 that are randomly drawn. What is the probability that a person wins the game, if they enter a) once? b) 7 times with a different choice each time?
Answer:
[tex]=\frac{1}{8568}\ = .00011\\\ =\frac{7}{8568} = .00081[/tex]
Step-by-step explanation:
[tex]5/18\cdot \:4/17\cdot \:3/16\cdot \:2/15\cdot \:1/14=\frac{1}{8568}[/tex]
A sample of 50 observations is taken from an infinite population. The sampling distribution of : a.is approximately normal because of the central limit theorem. b.cannot be determined. c.is approximately normal because is always approximately normally distributed. d.is approximately normal because the sample size is small in comparison to the population size.
Answer:
a.is approximately normal because of the central limit theorem.
Step-by-step explanation:
The central limit theorem states that if we have a population with mean μ and standard deviation σ and we take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
For any distribution if the number of samples n ≥ 30, the sample distribution will be approximately normal.
Since in our question, the sample of observations is 50, n = 50.
Since 50 > 30, then our sample distribution will be approximately normal because of the central limit theorem.
So, a is the answer.
The perimeter of a rectangle is 56 feet and
its area is 192 square feet. What are the
dimensions of the rectangle?
Answer:
Step-by-step explanation:
P = 2(L + W)
Area = L*W
Area = 192
(L + W)*2 = 56
L+W = 28
L = 28 - W
W*(28 - W) = 192
28W - w^2 = 92
-w^2 + 28w - 192 = 0
w^2 - 28w + 192 = 0
This factors into
(w - 12)(w - 16) = 0
w - 12 = 0
w = 12
L = 28 - 12 = 16
PLEASE HELP IM TRYING TO FINISH THIS BY NEXT MONDAY AND IVE BEEN STUCK ON THIS
Answer:
Step-by-step explanation:
Choice A is the only one that is applicable.
Answer:
A. F(x) has 1 relative minimum and maximum.
Step-by-step explanation:
[tex]{ \bf{F(x) = 2 {x}^{3} - 2 {x}^{2} + 1 }}[/tex]
As x and F(x) tend to positive and negative infinity:
[tex]{ \sf{x→ \infin : f(x) = \infin}} \\ { \sf{x→ {}^{ - } \infin : f(x) → {}^{ - } \infin}}[/tex]
❎So, B and C are excluded.
Roots of the polynomial:
[tex]{ \sf{f(x) = 2 {x}^{3} - 2 {x}^{2} + 1}} \\ { \sf{f(x) = - 0.6 \: \: and \: \: 0.8}}[/tex]
❎, D is also excluded.
✔, A
What is the volume?
9 ft
4 ft
2 ft
HELPPPP
Answer:
72?
Step-by-step explanation:
V=whl=4 x 2 x9=72
Guys please help me solve this I’m struggling
Answer:
[tex]Max\ z = 1[/tex]
[tex]Min\ z = -9[/tex]
Step-by-step explanation:
Given
[tex]z = 4x + 5y[/tex]
[tex]x \ge -1[/tex]
[tex]y \le 2x +3[/tex]
[tex]y \le -1[/tex]
Required
The maximum and minimum of z
To do this, we make use of the graphical method
See attachment for graphs of
[tex]x \ge -1[/tex]
[tex]y \le 2x +3[/tex]
[tex]y \le -1[/tex]
The corner points of the function are:
[tex](x,y) = (-1,1)[/tex]
[tex](x,y) = (-1,0)[/tex]
[tex](x,y) = (-1,-1)[/tex]
We have:
[tex]z = 4x + 5y[/tex]
Calculate z with the above values
[tex]z = 4(-1) + 5(1) = 1[/tex]
[tex]z = 4(-1) + 5(0) = -4[/tex]
[tex]z = 4(-1) + 5(-1) = -9[/tex]
So, we have:
[tex]Max\ z = 1[/tex]
[tex]Min\ z = -9[/tex]
A box contains a yellow ball, an orange ball, a green ball, and a blue ball. Billy randomly selects 4 balls from the box (with replacement). What is the expected value for the number of distinct colored balls Billy will select?
Answer:
[tex]Expected = 0.09375[/tex]
Step-by-step explanation:
Given
[tex]Balls = 4[/tex]
[tex]n = 4[/tex] --- selection
Required
The expected distinct colored balls
The probability of selecting one of the 4 balls is:
[tex]P = \frac{1}{4}[/tex]
The probability of selecting different balls in each selection is:
[tex]Pr = (\frac{1}{4})^n[/tex]
Substitute 4 for n
[tex]Pr = (\frac{1}{4})^4[/tex]
[tex]Pr = \frac{1}{256}[/tex]
The number of arrangement of the 4 balls is:
[tex]Arrangement = 4![/tex]
So, we have:
[tex]Arrangement = 4*3*2*1[/tex]
[tex]Arrangement = 24[/tex]
The expected number of distinct color is:
[tex]Expected = Arrangement * Pr[/tex]
[tex]Expected = 24 * \frac{1}{256}[/tex]
[tex]Expected = \frac{3}{32}[/tex]
[tex]Expected = 0.09375[/tex]
What is (0,6] n (6,8]?
Answer:
(6) the letter n : intersection which means the number you will find at the first bracket and has the same number at the other bracket
need help asap pls !
Answer:
L={∅}
Step-by-step explanation:
#What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x?
Discriminant = b2 – 4ac
–8
4
8
16
Answer:
16
Step-by-step explanation:
the quadratic equation –3 = –x2 + 2x can be changed into :
x²-2x-3= 0
a=1, b= -2 , and c = -3
so, the discriminant = (-2)²-4(1)(-3)
= 4 + 12 = 16
Help anyone can help me do the question,I will mark brainlest.
Answer:
a) 30
b)600pi
Step-by-step explanation:
For the first questions, since the arc is 240°, the area of the sector and circumference will be 240/360 or 2/3 of the total of the circles'. Therefore 125.6 x 3/2 is the circumference, which is 188.4. When we divide this by 6.28, we get 30
Now, since the area is pi r^2 where we know that r=30, we get 900pi as the area of the whole thing, however since the sector is 2/3 of the whole circle, 2/3 x 900pi = 600pi
using appropriate properties , find 7/5 × 5/12 − 3/12 × 7/5 − 1/15
Answer:
[tex] \frac{1}{6} [/tex]
Step-by-step explanation:
[tex] \frac{7}{5} \times \frac{5}{12} - \frac{3}{12} \times \frac{7}{5} - \frac{1}{15} = \frac{7}{5} ( \frac{5}{12} - \frac{3}{12} ) - \frac{1}{15} = \frac{7}{5} \times \frac{1}{6} - \frac{1}{15} = \frac{7}{30} - \frac{2}{30} = \frac{5}{30} = \frac{1}{6} [/tex]
find the missing segment in the image below
Answer:
3
Step-by-step explanation:
Intercept theorem
DE // CB ⇒ [tex]\frac{AD}{AC} = \frac{AE}{AB}[/tex]
⇒ [tex]\frac{6}{6+?} =\frac{4}{4+2}[/tex]
⇒ ? = 3
Mr. Ellington has a total of 32 students in his class , The ratio of girls to boys is 3:5, how many girls are in Mr . Ellington's class ?
Add the ratio: 3 + 5 = 8
Divide total students by that:
32/8 = 4
The ratio for girls is 3, multiply the 4 by 3:
4 x 3 = 12
There are 12 girls
Answer:
12
Step-by-step explanation:
If the ratio of girls to boys is 3:5, that means that for every 8 total students, 3 would be girls and 5 would be boys. Therefore 3/8 of the students are girls and 5/8 are boys. If 3/8 are girls, then:
[tex]\frac{3}{8}[/tex] of 32
= [tex]\frac{3}{8} * 32[/tex]
[tex]=\frac{3 * 32}{8} \\= \frac{96}{8} \\= 12[/tex]
There are 12 girls.
Which composite function can be used to find the
force of the object based on its volume?
The density of titanium is 4.5 g/cm3. A titanium object
is accelerating at a rate of 800 cm/s2. The mass of
the object can be modeled by the function m(v) =
4.5v, where v is the volume in cubic centimeters.
Additionally, the force of the object can be found
using the function F(m) = 800m.
A. F(m(v)) = 177.8V
B. F(m(v)) = 795.5v
C. F(m(v)) = 804.5v
D. F(m(V)) = 3,600V
Given:
The mass function is:
[tex]m(v)=4.5v[/tex]
where v is the volume in cubic centimeters.
The force function is:
[tex]F(m)=800m[/tex]
To find:
The composite function can be used to find the force of the object based on its volume.
Solution:
The composite function can be used to find the force of the object based on its volume is:
[tex]F(m(v))=F(4.5v)[/tex] [tex][\because m(v)=4.5v][/tex]
[tex]F(m(v))=800(4.5v)[/tex] [tex][\because F(m)=800m][/tex]
[tex]F(m(v))=3600v[/tex]
Therefore, the correct option is D.
Answer: F(m(v)) = 3,600v
Step-by-step explanation:DDDD
There is 10% salt solution and a 30% salt solution. How much of each is needed to make 10L mixture that is 25% salt solution?
Answer:
2.5L of 10% salt solution and 7.5L of the 30% salt solution
Step-by-step explanation:
let the amount of L in the 10% solution be 'x'
let the amount of L in the 30% solution be '10-x'
* because they add up to a total of 10L
10%(x) + 30%(10-x) = 25%(10)
0.1x + 3 - 0.3x = 2.5
-0.2x = -0.5
x = 2.5
x =2.5
10-x = 7.5
2.5 of 10% solution and 7.5% of 30% solution
A person walks away from a pulley pulling a rope slung over it. The rope is being held at a height 10 feet below the pulley. Suppose that the weight at the opposite end of the rope is rising at 4 feet per second. At what rate is the person walking when s/he is 20 feet from being directly under the pulley
The image of this question is missing and so i have attached it.
Answer:
dd/dt = 4.47 ft/s
Step-by-step explanation:
From the image attached, let's denote the following;
d = horizontal distance beneath pulley
h = height of pulley
l = diagonal from the pulley to the head of the person
v = velocity of rope rising
Using pythagoras theorem;
l² = d² + h²
Differentiating with respect to time and considering h = c^(te) gives;
2l(dl/dt) = 2d(dd/dt)
We are given;
d = 20 ft
h = 10 ft
v = 4 ft/s
We know that velocity in this case is change in diagonal distance with time. Thus;
v = dl/dt = 4 ft/s
From earlier, we saw that;
2l(dl/dt) = 2d(dd/dt)
Thus, reducing it gives
(dl/dt)(l/d) = dd/dt
Now, l² = d² + h²
l = √(d² + h²)
Also, v = dl/dt = 4
Thus;
4(√(d² + h²))/d = dd/dt
4(√(20² + 10²))/20 = dd/dt
dd/dt = 4.47 ft/s
Rhombus LMNO is shown with its diagonals.
Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. All sides are congruent.
Angle MNO measures 112°. What is the measure of angle LMN?
Answer:
hope this help
Step-by-step explanation:
Answer:
90
51
10
Step-by-step explanation:
Independent Practice
Find the first, fourth, and eighth terms of the sequence.
an=0.5 · 3n−1a subscript n baseline equals 0.5 times 3 superscript n minus 1 baseline
A.
0.667; 4.5; 364.5
B.
3; 0.375; 0.0234375
C.
0.5; 13.5; 1093.5
D.
0.5; 121.5; 280.5
Answer:
C.
0.5; 13.5; 1093.5
Step-by-step explanation:
Good Afternoon I am really stuck on this question whoever solves it I will give them brainliest with no unacceptable question thank you so much!
Answer:
Card picked=2
P(factors of 28)={1,2,4,7,14,28}
total cards=4
in percentage=4 x 20 + 20
80+20=100
Therefore 2 in percentage will be
2 x 20 + 20
=40+20=60%
Find the sum of the second multiple of 9 and the fifth multiple of 6.
Answer:
48
Step-by-step explanation:
9,18
6,12,18,24,30
18 + 30 = 48
Match the answers……………..
9 in 8956 = 900
9 in 95675 = 90000
9 = 9 in 124569
9 in 68795 = 90
90000 = 9 in 2549652.........
hope it helps...
Value of the boat after 3 years?
after each year it's 83% of it's value from last year (100%-17%=83%)
the function in 19000 * (0.83) ^x
3 will be filled in for x
19000 * (0.83) ^3= 10863.953
$10863.95
Answer:
$10,863.95
Step-by-step explanation:
y = 19,000[tex](.83)^{t}[/tex]
y = 19,000[tex](.83)^{3}[/tex]
y =$10,863.95
Pls help me ! L need help here
Answer:
H. 40 inches
Step-by-step explanation:
On Wednesday, he is 40 inches taller. ... That would make 5 days of growth, for 100 inches. But this is only 3 days therefore he would grow 40 inches taller
Please help me fast
Answer:
864
Step-by-step explanation:
A=6a^2=6·12^2=864
Answer:
864 in^2
Step-by-step explanation:
2(144+144+144) = 2(432) = 864 in^2.
Hope this helped!
You order CDs for $14.25 each and the website charges $4.50 for each shipment.
The expression $14.25p + $4.50 represents the cost of p CDs. Find the total cost for
ordering 4 CDs.
Answer:
$61.50
Step-by-step explanation:
14.25(4) + 4.50
= 57.00 + 4.50
= 61.50
The tens digits of a certain two-digit number is 1/3 of the units digit. When the digits are reversed, the new number exceed twice the original number by 2 more than the sum of the digits. Find the original number.
Answer:
The orginal number is 26.
Step-by-step explanation:
So the units digit can be 3 6 or 9
The tens digit can be 1 2 or 3
So the original number can be 13
31 = 2*13+ (1+3) + 2
31 =? 26 + 4 + 2
This doesn't work. The right side is 32
26
62 = 2*26 + 8 + 2
62 = 52 + 8 + 2
This is your answer.
3 and 9 won't work because 39 is odd and so is 93. The result has to be even.
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