Use the binomial theorem:
[tex](1+1)^{16}=\displaystyle\sum_{k=0}^{16}\binom{16}k1^{16-k}1^k[/tex]
So
[tex]\dbinom{16}0+\dbinom{16}1+\cdots+\dbinom{16}{16}=\boxed{2^{16}}[/tex]
More generally,
[tex]\displaystyle\sum_{k=0}^n\binom nk=2^n[/tex]
Which equation represents a population of 250 animals that decreases at an annual rate of 21%
Answer:
y= 250( 1-0.21)^x
Step-by-step explanation:
This represents exponential decay
The equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
What is an exponential function?The mathematical expression f(x)=[tex]e^t[/tex] denotes the exponential function. The term typically refers to the positive-valued function of a real variable, unless otherwise specified.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
It is given that a population of 250 animals is decreasing at an annual rate of 21%.
p = a x b[tex].^t[/tex]
p = a x (1+r)[tex].^t[/tex]
p = 250 x (1+(-0.21))[tex].^t[/tex]
p = 250(0.79)[tex].^t[/tex]
Note that r = -0.21 is negative to indicate we have exponential decay.
Hence, the equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
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What is the equation of the parabola with focus (1, -3) and directrix y = 22
A. y - 4x^2 +8x-21
B. y=2/3×^2-4/3×+7/6
C. y =-1/10×^2+1/5×-3/5
D. y=-3×^2+2x-2
Answer:22
Step-by-step explanation:
Answer:
Hola que tal
Step-by-step explanation:
C(t) = 2t^4 – 8t^3 +6t^2 Find the t-intercept?
Answer:
0
Step-by-step explanation:
The t-intercept here is what's khown as the x-intercept wich is given by C(t)=0
● C(t) = 2t^4-8t^3+6t^2
● 0 = 2t^4-8t^3+6t^2
Factor using t
● t(2t^3-8t^2+6t^1) = 0
Wich means that t=0
There were 3 squirrels and 18 acorns on Josh’s back porch. What was the ratio of squirrels to acorns? Enter your answer in reduced form. (100 points!!)
Answer:
1:6
Step-by-step explanation:
Answer:
Step-by-step explanation:
1:6
I need help with this one!
Answer:
[tex]\tan A=\frac{10}{24}=\frac{5}{12}[/tex]
Step-by-step explanation:
The easiest way to remember sine, cosine, and tangent ratios is to use SOH-CAH-TOA as an acronym.
SOH - Sine: Opposite over hypotenuse
CAH - Cosine: Adjacent over hypotenuse
TOA - Tangent: Opposite over adjacent
Note that these are referring to the position of the sides relative to the angle you are looking at. In this case, that is angle A. Since it's tangent, we have:
[tex]\tan A=\frac{10}{24}=\frac{5}{12}[/tex]
Circle A has center of (4,6) and a radius of 5, and circle B has a center of (1,0) and a radius of 15. What steps will help show that circle A is similar to circle B? Dilate circle Dilate circle A by a scale factor of 3. translate Circle A using the rule (x - 3, y + 6). Rotate circle A 180° about the center. reflect circle A over the y-axis.
The answer is A. Dilate circle A by a scale factor of 3
I took the test :)
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the functions given below. VIEW FILE ATTACHED
Answer: see below
Step-by-step explanation:
[tex]P(x)=\dfrac{2}{3x-1}\qquad \qquad Q(x)=\dfrac{6}{-3x+2}\\[/tex]
P(x) ÷ Q(x)
[tex]\dfrac{2}{3x-1}\div \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\times \dfrac{-3x+2}{6}\\\\\\=\large\boxed{\dfrac{-3x+2}{3(3x-1)}}[/tex]
P(x) + Q(x)
[tex]\dfrac{2}{3x-1}+ \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)+ \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)+6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4+18x-6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{12x-2}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{2(6x-1)}{(3x-1)(-3x+2)}}[/tex]
P(x) - Q(x)
[tex]\dfrac{2}{3x-1}- \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)- \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)-6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4-18x+6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-24x+10}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{-2(12x-5)}{(3x-1)(-3x+2)}}[/tex]
P(x) · Q(x)
[tex]\dfrac{2}{3x-1}\times \dfrac{6}{-3x+2}\\\\\\=\large\boxed{\dfrac{12}{(3x-1)(-3x+2)}}[/tex]
Which of the following is true? |−8| < 6 |−6| < |−8| |8| < |−6| |−6| < −8
Answer: The second choice
Step-by-step explanation:
Absolute value is the distance a number is from 0 on the number line. Thus, the absolute value of -8 is 8, which is greater than the absolute value of -6, or 6.
Hope it helps <3
Answer:
Step-by-step explanation:
the second option, |-6| < |-8|.
|2x-19| = 4x + 1 helppp
Answer:
x = 9
Step-by-step explanation:
Well to find x we need to use the commutative property which is the moving of numbers and variables to either side of the equation,
|2x - 19| = 4x + 1
-2x to both sides
|-19| = 2x + 1
Absolute value of -19 is 19
19 = 2x + 1
-1 to both sides
18 = 2x
Divide 2 to both sides
x = 9
Thus,
x is 9.
Hope this helps :)
The value of x is -10 when the equation is |2x-19| = 4x + 1
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is |2x-19| = 4x + 1
Mod of two times of x minus nineteen equal to four times of x plus one.
|2x-19| = 4x + 1
2x-19=4x+1
Now add 19 on both sides
2x=4x+20
Subtract 4x on both sides
-2x=20
Divide both sides by 2
x=-10
Hence, the value of x is -10 when the equation is |2x-19| = 4x + 1
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Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. nequals=5353, pequals=0.30.3, and Xequals=20
Answer and Step-by-step explanation: P(X) calculated by the binomial probability formula is:
P(X) = [tex]\left[\begin{array}{ccc}n\\X\end{array}\right][/tex].[tex]p^{x}.(1-p)^{n-x}[/tex]
P(20) = [tex]\left[\begin{array}{ccc}53\\20\end{array}\right] .(0.3)^{20}.(1-0.3)^{33}[/tex]
P(20) = [tex]\frac{53!}{33!.20!}.3.5.10^{-11}.7.7.10^{-6}[/tex]
P(20) = 0.0552
To determine whether the normal distribution can be used to estimate this probability, both n.p and n.(1-p) must be greater than 5:
n . p = 53*0.3 = 15.9
n.(1-p) = 53(1-0.3) = 37.1
Since both ARE greater than 5, normal distribution can be used.
To approximate:
mean = n . p = 15.9
standard deviation = [tex]\sqrt{n.p.(1-p)}[/tex] = 3.34
Find the z-score:
z = [tex]\frac{x - mean}{sd}[/tex] = [tex]\frac{20-15.9}{3.34} = 1.23[/tex]
z-score = 0.8907
Comparing values:
0.8907 - 0.0552 = 0.8355
Express 0.325 as a percentage
Answer:
32.5%
Step-by-step explanation:
0.325 x 100%=32.5%
Help Please! Solve this problem without the law of cosines.
Answer:A
Step-by-step explanation:
a. What is the area and circumference of circle P? Explain how you calculated this answer. b. If the arc measure of arc COD is 100 degrees and the arc measure of arc BSA is 60 degrees, what is the angle measure of angle CRB ? Explain how you calculated this answer.
Answer:
a) 9*π or approx 28.26
b) ∡CRB=100°
Step-by-step explanation:
As known for secants crossing each other inside the circle is coorect the following:
BR*RD=AR*RC
=> 3*RD=4*4.5
RD=6
The diameter of the circle with center P is BD=BR+RD=3+6=9
So the radius of the circle is D/2=9/2=4.5
As known the circumference of any circle can be calculated as
C=2*π*r , where r is the circle's radius
So C=2*4.5*π=9*π= approx 3.14*9=28.26
b) ∡CRB=∡ARD= (arcBC+arcAD), where arcBC and arcAD smaller arcs
BD is the circle's diameter, so arc BD=180°
So arcBC=180°-arcCOD=180°-100°=80°
Similarly arcBD=180°
arcAD=180°-arcBSA=180°-60°=120°
∡CRB= (80°+120°)/2=100°
What is the reciprocal of (17h)/(46j)?
Answer:
I dont give the answer right away so you read what i write and fully understand :D
Step-by-step explanation:
The reciprocal of something is basically when you flip something over. Since 17h/46j is a fraction, the reciprocal is 46j/17h. Remember, a number times the reciprocal is always equal to one.
Answer:
46j over 17h
Step-by-step explanation:
a reciprocal fraction is formed by flipping the fraction around
for example:
2/3
reciprocal= 3/2 or 1.5
HOPE THIS HELPS!!! :)
Explain how to write an equivalent expression using the
associative property.
2+(11 + y)
Answer:
2+(11+y)=(2+11)+y=11+(2+y)
Answer:
Sample Response: The associative property allows you to keep the order of the terms and change the position of the parentheses. So you can rewrite the terms in the same order and then move the parentheses so that the 2 + 11 is now inside. The equivalent expression is (2 + 11) + y.
Step-by-step explanation:
E d g e n u i t y
Find the number of possible outcomes Five books need to be placed on a shelf. You randomly arrange the books on the shelf from left to right.
Answer:
120
Step-by-step explanation:
Let's say you put them on the shelf one by one, from left to right.
You can pick 1 of the 5 for the first position.
5
Now you have 4 books left. You pick one out of those 4 for the second position.
5 * 4
There are 3 choices left for the 3rd position.
5 * 4 * 3
2 left for the 4th position.
5 * 4 * 3 * 2
Finally, there is one book left for the 5th position.
5 * 4 * 3 * 2 * 1
Now we multiply:
5 * 4 * 3 * 2 * 1 = 120
From past records it is known that 10% of items from a production
line are defective. If two items are selected at random, what is the
probability that only one is defective?
Answer: 0.18
Step-by-step explanation:
P(1 unit is defective)= C2 1* P^1*Q^1
C2 1= 2!/(1!*(2-1)!)=2
P=0.1 - probability that items from a production line are defective
Q=1-0.1=0.9 - probability that items from a production line are functional.
P(1 unit is defective)= 2*0.1*0.9=0.18
How many 4-digit numbers divisible by 5, all of the digits of which are even, are there?
Answer:
There are a total of 100 numbers!!
Step-by-step explanation:
Basically you have to do
4*5*5*1 because there are 4 even numbers 2,4,6,8 that can be in the beginning of a number, 5 even numbers 0,2,4,6,8 that can be in the middle and only 1 number at the end that will make it divisible by 5 which is zero.
Hope this helps!!!
Simplify the expression:
(4k – 4) + ( –9k – 5)
Answer:
The answer is
- 5k - 9Step-by-step explanation:
(4k – 4) + ( –9k – 5)
Remove the bracket and simplify
That's
4k - 4 + - 9k - 5
4k - 4 - 9k - 5
Group like terms
4k - 9k - 4 - 5
We have the final answer as
- 5k - 9
Hope this helps you
We can use FOIL to solve:
(4k - 4) + (-9k - 5)
(4k * -9k) + (4k * -5) + (-4 * -9k) + (-4 * -5)
-36k - 20k + 36k + 20
-20k + 20
Best of Luck!
Samuel filled the glasses shown below completely with water. The total amount of water that Samuel poured into the glasses is 60 cubic centimeters. What is the height of glass 1? Round your answer to the nearest tenth. (Use π = 3.14.) Note that all measurements are in centimeters and images are not drawn to scale. A cylinder with width 4 and height unknown is labeled glass 1, and a cone with height 6 and width 5 is labeled glass 2. 0.2 centimeter 1.7 centimeters 3.9 centimeters 5.6 centimeters
Answer:
1.7
Step-by-step explanation:
1. Find the volume of Glass 2 (volume of a cone = 1/3πr² ·h)
1/3 · 3.14 · 2.5² · 6 = 39.25 cm³
2. Subtract the volume of Glass 2 from the amount of water poured
60 - 39.25 = 20.75 cm³
3. Set up the equation for Glass A using x for the height being solved for (volume of a cylinder = πr² · h)
3.14 · 2² · x = 20.75
12.56x = 20.75
4. Solve for x by dividing both sides by 12.56 (round to the nearest tenth)
x = 1.7
The answer should be 1.7
a political candidate has asked you to conduct a poll to determine what percentage of people support her. if the candidate only wants a 8% margin of error at a 95% cnofidence level, what size of sample is needed
Answer:
The sample needed is [tex]n =150[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.08[/tex]
The confidence level is [tex]C = 95 \% = 0.95[/tex]
Given that the confidence level is 95% the level of significance is mathematically represented as
[tex]\alpha = 1 - 0.95[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the z-table , the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because
[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval ( [tex]1-\alpha[/tex] ) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error
The sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p[1-\r p][/tex]
Here [tex]\r p[/tex] is sample proportion of people that supported her and we will assume this to be 50% = 0.5
So
[tex]n = [\frac{1.96}{ 0.08} ]^2 * [0.5 (1- 0.5)][/tex]
[tex]n =150[/tex]
The average flight time from Seattle (SEA) to New York (JFK) is 4.3 hours. The distance between them is 2421 miles. The average flight time going the other way, JFK to SEA is 5.5 hours. The difference is due to the jet stream. Translate this situation to a system of equations and find the average speed of the jet and the average speed of the jet stream.
Answer:
Speed of the jet is 563.02 miles/hr
Speed of the jet stream is 122.83 miles/hr
Step-by-step explanation:
The average time for going from Seattle to New York is 4.3 hours
The distance between these places is 2421 miles
The average time for going back (impaired by jet stream) is 5.5 hours
If we designate the speed of the jet = v
and the speed of the jet stream = u
then on the return trip, the relative speed of the jet = v - u
Also, recall that distance = speed x time
For the going trip, the distance covered by the jet = 4.3 x v = 2421 miles
For the return trip, the distance covered by the jet = 5.5 x (v - u) = 2421 miles
= 5.5(v - u)
these translate into the following equation written below
4.3v = 2421 ....equation 1
5.5(v - u) = 2421 ....equation 2
solving, equation 1, we'll have
4.3v = 2421
v = 2421/4.3 = 563.02 miles/hr this is the speed of the jet
substituting the value of v into equation 2, we'll have
5.5(v - u) = 2421
5.5(563.02 - u) = 2421
3096.61 - 5.5u = 2421
3096.61 - 2421 = 5.5u
675.61 = 5.5u
u = 675.61/5.5
u = 122.83 miles/hr this is the speed of the jet stream
Determine which of the following statements is true. A: If V is a 6-dimensional vector space, then any set of exactly 6 elements in V is automatically a basis for V. B: If there exists a set that spans V, then dim V = 3. C: If H is a subspace of a finite-dimensional vector space V, then dim H ≤ dim V
Answer:
A. This statement A is false.
B. This statement A is false.
C. This statement is true .
Step-by-step explanation:
Determine which of the following statements is true.
From the statements we are being given , we are to determine if the statements are valid to be true or invalid to be false.
SO;
A: If V is a 6-dimensional vector space, then any set of exactly 6 elements in V is automatically a basis for V
This statement A is false.
This is because any set of exactly 6 elements in V is linearly independent vectors of V . Hence, it can't be automatically a basis for V
B. If there exists a set that spans V, then dim V = 3
The statement B is false.
If there exists a set , let say [tex]v_1 ...v_3[/tex], then any set of n vector (i.e number of elements forms the basis of V) spans V. ∴ dim V < 3
C. If H is a subspace of a finite-dimensional vector space V then dim H ≤ dim V is a correct option.
This statement is true .
We all know that in a given vector space there is always a basis, it is equally important to understand that there is a cardinality for every basis that exist ,hence the dimension of a vector space is uniquely defined.
SO,
If H is a subspace of a finite-dimensional vector space V then dim H ≤ dim V is a correct option.
PLEASE HELP
Speed of pulley A = 400 r.p.m.
Speed of pulley B =
A:100
B:200
C:1600
Speed of pulley C =
A:100
B:1600
C:200
Speed of pulley D =
A:100
B:40
C:160
see attachment a=400 rpm b and c = 200 rpm d = 40 rpm
Answer:
pulley B 200, pulley C 200, pulley D 160
Please help me with this!
Answer:
5:1
Step-by-step explanation:
20/4= 5
1*5 = 5
5:1 ratio
Hope this helps!
among the following, an incorrect statement is a) the volume of the hollow sphere =4/3π (r^3—r^3), where r is the radius of the outer sphere and r is the radius of the inner sphere. b) the volume of the hemisphere of radius(r) is 2πr^3 c) the surface area sphere = 4πr^2 d) the surface area of a spherical shell = 4π (r^2—r^2), where r = external radius and r= internal radius
please can someone say which one is incorrect
Answer:
fncjcnj jcj jcj jcj jd. d. c. dn. d. c. c. x. c. c. c.
What the answer fast
Answer:
when we add all the angles.
=58+94+15=167
so it's a 180..
180_167
=13
round to nearest tenth.
=10..
The shape in the figure is constructed from several identical squares. If the side of each square is 1 unit, what is the area and the perimeter of the shape?
Answer:
Area = 7 square units
Perimeter = 14 units
Step-by-step explanation:
The figure shown above consists of 7 squares, each having a side length of 1 unit.
==>Area of shape = area of 1 square × 7
Area of shape = s² × 7.
Where, s = side length = 1 unit
Area of shape = 1² × 7
= 1 × 7
Area = 7 square units
==>Perimeter of shape:
The perimeter of the shape is the sum of all the external sides of the 7 squares that form along the boundary of the shape. Check the attachment to see each side length that makes up the length of the entire boundary.
Perimeter of shape = 1 + 1 + 1 + ½ + ½ + 1 + 1 + ½ + 1½ + 1 + 4 + 1 = 14 units.
A weather balloon holds 2,000 cubic meters of helium. The density of helium is 0.1765 kilograms per cubic meter. How many kilograms of helium does the balloon contain? Only enter a numerical value in the answer blank.
Answer:
353 kg
Step-by-step explanation:
So you want to find the number of kg by finding the answer through the density formula. To do this you take the formula of Density, which is [tex]D=\frac{m}{v}[/tex]. Now you substitute D for the density of 0.1765, and v for the volume, which is 2000, to then get [tex]0.1765=\frac{m}{2000}[/tex]. Now you solve for m. To do this you multiply each side by 2000. This brings you with [tex]353=m[/tex] after multiplying 0.1765 and 2000. Hope this helps!
The mass of the helium that the balloon contain will be 353 kilograms.
What is density?Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.
The mass and density relation is given as
Mass = density × volume
A weather balloon holds 2,000 cubic meters of helium.
The density of helium is 0.1765 kilograms per cubic meter.
The mass of the helium that the balloon contain will be
Mass = 0.1765 × 2000
Mass = 353 kilograms
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thirteen less than the total of a number and eleven. Translate into variable expression. And also simply.
Answer: Required variable expression. [tex]x-13=11[/tex]
The value of x is 24.
Step-by-step explanation:
Let x be the number.
Given statement: "thirteen less than the total of a number and eleven."
Expression for "thirteen less than the total of a number" = [tex]x-13[/tex]
Now , the complete expression will be : [tex]x-13=11[/tex]
To simplify, we add 13 on both the sides , we get
[tex]x-13+13=11+13\\\\\Rightarrow\ x= 24[/tex]
Hence, the value of x is 24.