Answer:
The angle of the slice is 63.64 degrees
Step-by-step explanation:
Here in this question, we are concerned with calculating the angle of the slice.
What we should know are as follows;
1. A pizza is a perfect circular shape
2. A 12-inch pizza means the diameter of the pizza is 12 inches and consequently its radius will be 12/2 = 6 inches
3. A slice of a pizza represents a sector of the circle( a sector is part of a circle bounded by 2 radii and an arc)
Mathematically, to calculate the angle of the slice, we simply use the formula for the area of a sector.
Area of sector = theta/360 * pi * r^2
where Area of sector = 20 square inches
theta is the center angle we are looking for
r is the radius of the pizza which is 6 inches
Plugging these values into the area of sector equation, we have
20 = theta/360 * 22/7 * 6^2
20 = theta/10 * 22/7
22 theta = 10 * 20 * 7
theta = 1400/22
theta = 63.64 degrees which is approximately 64 degrees to the nearest degree
Can somebody explain how trigonometric form polar equations are divided/multiplied?
Answer:
Attachment 1 : Option C
Attachment 2 : Option A
Step-by-step explanation:
( 1 ) Expressing the product of z1 and z2 would be as follows,
[tex]14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right][/tex]
Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,
cos(π / 5) = [tex]\frac{\sqrt{5}+1}{4}[/tex],
sin(π / 5) = [tex]\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}[/tex]
cos(3π / 2) = 0,
sin(3π / 2) = - 1
Let's substitute those values in our expression,
[tex]14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right][/tex]
And now simplify the expression,
[tex]14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)[/tex]
The exact value of [tex]14\sqrt{5-\sqrt{5}}[/tex] = [tex]23.27510\dots[/tex] and [tex](-7\sqrt{10}-7\sqrt{2}\right))[/tex] = [tex]-32.03543\dots[/tex] Therefore we have the expression [tex]23.27510 - 32.03543i[/tex], which is close to option c. As you can see they approximated the solution.
( 2 ) Here we will apply the following trivial identities,
cos(π / 3) = [tex]\frac{1}{2}[/tex],
sin(π / 3) = [tex]\frac{\sqrt{3}}{2}[/tex],
cos(- π / 6) = [tex]\frac{\sqrt{3}}{2}[/tex],
sin(- π / 6) = [tex]-\frac{1}{2}[/tex]
Substitute into the following expression, representing the quotient of the given values of z1 and z2,
[tex]15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right][/tex] ⇒
[tex]15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right][/tex]
The simplified expression will be the following,
[tex]i\frac{5\sqrt{2}}{2}[/tex] or in other words [tex]\frac{5\sqrt{2}}{2}i[/tex] or [tex]\frac{5i\sqrt{2}}{2}[/tex]
The solution will be option a, as you can see.
In cooking class, Shivani measures a stick
of butter. It is 13 centimeters long, 3
centimeters wide, and 3 centimeters tall. What
is the volume of the stick of butter?
Answer:
117 cm³
Step-by-step explanation:
To find the volume of a rectangular prism, we can simply multiply the length, width and height so the answer is 13 * 3 * 3 = 117 cm³.
Answer:
117 cubic centimeters
Step-by-step explanation:
Assuming that the stick of butter is a perfect rectangular prism, we can calculate the volume by simply multiplying the length, width, and the height as modeled by the volume equation:
V = LWH
For this, the L = 13cm, W = 3cm, and H = 3cm
So our volume in cubic centimeters will be:
V = LWH
V = (13cm) * (3cm) * (3cm)
V = (13cm) * (9cm^2)
V = 117 cm^3
So the volume of the stick of butter is 117 cubic centimeters.
Cheers.
In how many years will
The Compounds interest
onRs. 14,000 be Rs. 4, 634 at 10%
p.a?
Answer:
3 years
Step-by-step explanation:
A = P(1 + r)^t
A = I + P
A = 14,000 + 4,634 = 18,634
18,634 = 14,000(1 + 0.1)^t
18,634/14,000 = 1.1^t
log (18,634/14,000) = log 1.1^t
log (18,634/14,000) = t * log 1.1
t = [log (18,634/14000)]/(log 1.1)
t = 3
PLZ HELP THANKS! Find the equation of the line passing through the pair points (-8,6) (-9,-9). The equation of the line in the form is Ax+By=C.
Answer:
The answer is
15x - y = - 126Step-by-step explanation:
To find the equation of the line we must first find the slope (m)
[tex]m = \frac{y2 - y1 }{x2 - x1} [/tex]
So the slope of the line using points
(-8,6) (-9,-9) is
[tex]m = \frac{ - 9 - 6}{ - 9 + 8} = \frac{ - 15}{ - 1} = 15[/tex]
So the equation of the line using point (-8,6) and slope 15 is
y - 6 = 15( x + 8)
y - 6 = 15x + 120
Writing the equation in the form
Ax+By=C
We have
15x - y = -120-6
The final answer is
15x - y = - 126Hope this helps you
According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a random sample of 15 households, what is the probability that fewer than 13 have vcrs?
Answer:
The probability is [tex]P(x < 13) = 0.8732[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.70
The sample size is [tex]n = 15[/tex]
Generally the distribution of U.S. households have vcrs follow a binomial distribution given that there are only two outcome (household having vcrs or household not having vcrs )
The probability of failure is mathematically evaluated as
[tex]q = 1- p[/tex]
substituting values
[tex]q = 1- 0.70[/tex]
[tex]q = 0.30[/tex]
The probability that fewer than 13 have vcrs is mathematically represented as
[tex]P(x < 13) = 1- [P(13) + P(14) + P(15)][/tex]
=> [tex]P(x < 13) = 1-[( \left 15 } \atop {}} \right. C_{13} *p^{13}* q^{15-13})+ (\left 15 } \atop {}} \right. C_{14} *p^{14}* q^{15-14}) +( \left 15 } \atop {}} \right. C_{15} *p^{15}* q^{15-15}) ][/tex]
Here [tex]\left 15 } \atop {}} \right. C_{13}[/tex] means 15 combination 13 and the value is 105 (obtained from calculator)
Here [tex]\left 15 } \atop {}} \right. C_{14}[/tex] means 15 combination 14 and the value is 15 (obtained from calculator)
Here [tex]\left 15 } \atop {}} \right. C_{15}[/tex] means 15 combination 15 and the value is 1 (obtained from calculator)
So
[tex]P(x < 13) = 1-[(105 *p^{13}* q^{2})+ (15 *p^{14}* q^{1}) +(1*p^{15}* q^{0}) ][/tex]
substituting values
[tex]P(x < 13) = 1-[(105 *(0.70)^{13}* (0.30)^{2})+ (15 *(0.70)^{14}* (0.30)^{1}) +(1*(0.70)^{15}* (0.30)^{0}) ][/tex]
[tex]P(x < 13) = 0.8732[/tex]
Convert the following:
How many kilometers are in 1 mile? (Hint: Use the answer from the previous problem)
1 mile is equivalent to
ao kilometers (rounded to the nearest hundredth)
Answer: 1.609344 kilometers.
Step-by-step explanation:
A mile is an English Unit that is used to measure the length of a linear surface.
Even though the kilometre has replaced it to a large extent as the standard measure of length, it is still the main unit of measurement for distances in the United States, the United Kingdom, Liberia and UK and US oversees territories.
Miles are longer than kilometres as a kilometer is equivalent to only 0.621371 miles.
1 mile is therefore;
= 1/0.621371
= 1.609344 kilometers.
When x=5 what would the value of expression
Answer:
46
Step-by-step explanation:
6 more than the product of 8 and a number x
6 more means 6+
product of 8 and a number x means 8x
6+8x
when x=5
6+8(5)=6+40=46
Cesium-137 has a half-life of about 30 years. A) Find the annual decay rate and round final result to 4 decimal places. B) Find the continuous decay rate and round final result to 4 decimal places. C) How long will it take for a 10 gram sample to decay to 1 gram? Round to nearest year and interpret your result with a complete sentence. D) Complete this statement: as x goes to infinity, y goes to ___.
Answer:
0.02280.0231100 years0Step-by-step explanation:
The exponential equation for the fraction remaining after x years can be written as ...
y = (1/2)^(x/30)
A) For x=1, the fraction remaining is ...
y = (1/2)^(1/30) ≈ 0.97716 = 1 - 0.0228
Of the original amount, 0.0228 decays each year.
__
B) The continuous decay rate is the natural log of the growth factor, so is ...
ln(0.97716) = -0.0231
The continuous decay rate is 0.0231 of the present amount (per year).
__
C) For y=.10 (1/10 of the original amount) we find x to be ...
.1 = .5^(x/30)
ln(.1) = (x/30)ln(.5) . . . . . take the natural log
30ln(0.1)/ln(0.5) = x ≈ 100 . . . years
It will take 100 years for a 10-gram sample to decay to 1 gram.
__
D) As x goes to infinity, y goes to zero.
_____
The relationship between growth rate and growth factor is ...
growth factor = 1 + growth rate
When the growth rate is negative, it is called a decay rate.
Use the Pythagorean theorem to find the length of the hypotenuse in the triangle shown below.4,3
Answer:
5
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + 3^2 = c^2
16 + 9 = c^2
25 = c^2
c = 5
Answer:
5Step-by-step explanation:
[tex]Hypotenuse = ?\\Opposite = 4\\Adjacent = 3\\\\Pythagoras \: Theorem ;\\\\Hypotenuse^2 =Opposite^2+Adjacent ^2\\\\Hypotenuse^2 = 4^2 +3^2\\\\Hypotenuse^2 = 16+9\\\\Hypotenuse^2 = 25\\\\\sqrt{Hypotenuse^2}=\sqrt{25} \\Hypotenuse = 5[/tex]
the product of two consecutive positive integer is 306
Answer:
[tex]\Large \boxed{\sf 17 \ and \ 18}[/tex]
Step-by-step explanation:
The product means multiplication.
There are two positive consecutive integers.
Let the first positive consecutive integer be x.
Let the second positive consecutive integer be x+1.
[tex](x) \times (x+1) =306[/tex]
Solve for x.
Expand brackets.
[tex]x^2 +x =306[/tex]
Subtract 306 from both sides.
[tex]x^2 +x -306=306-306[/tex]
[tex]x^2 +x -306=0[/tex]
Factor left side of the equation.
[tex](x-17)(x+18)=0[/tex]
Set factors equal to 0.
[tex]x-17=0[/tex]
[tex]x=17[/tex]
[tex]x+18=0[/tex]
[tex]x=-18[/tex]
The value of x cannot be negative.
Substitute x=17 for the second consecutive positive integer.
[tex](17)+1[/tex]
[tex]18[/tex]
The two integers are 17 and 18.
The product of two consecutive positive integers is 306.
We need to find the integers
solution : Let two consecutive numbers are x and (x + 1)
A/C to question,
product of x and (x + 1) = 306
⇒x(x + 1) = 306
⇒x² + x - 306 = 0
⇒ x² + 18x - 17x - 306 = 0
⇒x(x + 18) - 17(x + 18) = 0
⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18
so x = 17 and (x +1) = 18
Therefore the numbers are 17 and 18.
Hope it helped u if yes mark me BRAINLIEST
TYSM!
Which expression is equal to 7 times the sum of a number and 4
Answer:
7(n + 4)
Step-by-step explanation:
Represent the number by n. Then the verbal expression becomes
7(n + 4).
Jesse bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jesse bought?
Pattern A: 0, 5, 10, 15, 20,... Pattern B: 0, 20, 40, 60, 80,... Which statement is true about the relationship between the corresponding terms of Pattern A and Pattern B? A. The terms in Pattern B is 4 times the corresponding terms in Pattern A. B. The terms in Pattern A is 1/2 times the corresponding terms in Pattern B. C. The terms in Pattern B is 20 more than the corresponding terms in Pattern A. D. The terms in Pattern A is 5 more than the corresponding terms in Pattern B.
Answer:
Option 1: The terms in Pattern B is 4 times the corresponding terms of Pattern A
Step-by-step explanation:
Answer:
Pattern B has more then pattern A so option 2
Step-by-step explanation:
Question 36 of 40
The distance of a line bound by two points is defined as
L?
O A. a line segment
B. a ray
O
c. a plane
O D. a vertex
SUBMI
Answer:
A. a line segment
Step-by-step explanation:
a ray is directing in one dxn, and has no end pointa plane is a closed, so more than 2 points a vertex is a single point itselfHow to find probability from cumulative frequency graph
Answer:
find the difference of points on the graph
Step-by-step explanation:
The cumulative frequency graph (CDF) represents the integral of the probability distribution function (PDF). You find the probability that X is in some interval by subtracting the value of the CDF at the low end of the interval from the CDF value at the high end of the interval.
p(a < x < b) = cdf(b) -cdf(a)
John painted his most famous work, in his country, in 1930 on composition board with perimeter 101.14 in. If the rectangular painting is 5.43 in. taller than it is wide, find the dimensions of the painting.
Answer:
22.57 x 28
Step-by-step explanation:
10.86 + 4x = 101.14
-10.86 -10.86
4x = 90.28
/4 /4
x = 22.57
5.43 + 22.57 = 28
22.57
Find the volume of the cylinder. Round your answer to the nearest tenth.
Answer:
716.75 m^3
Step-by-step explanation:
Volume of a cylinder:
=> PI x R^2 x H
H = Height
R = Radius
=> PI x 3.9^2 x 15
=> PI x 15.21 x 15
=> PI x 228.15
=> 228.15 PI
or
=> 228.15 x 3.14159
=> 716.75 m^3
On a coordinate plane, a line goes through (negative 3, 3) and (negative 2, 1). A point is at (4, 1). What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (4, 1)? y − 1 = −2(x − 4) y – 1 = Negative one-half(x – 4) y – 1 = One-half(x – 4) y − 1 = 2(x − 4)
Answer:
y - 1 = -2(x - 4).
Step-by-step explanation:
First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).
(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.
The line will be parallel to the given line, so the slope is the same.
Now that we have a point and the slope, we can construct an equation in point-slope form.
y1 = 1, x1 = 4, and m = -2.
y - 1 = -2(x - 4).
Hope this helps!
The slope of the line passing parallel to the given line and passes through the point (4, 1) is y = -2x + 9
The equation of a straight line is given by:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
The slope of the line passing through the points (-3,3) and (-2,1) is:
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{1-3}{-2-(-3)} \\\\m=-2[/tex]
Since both lines are parallel, hence they have the same slope (-2). The line passes through (4,1). The equation is:
[tex]y-y_1=m(x-x_1)\\\\y-1=-2(x-4)\\\\y=-2x+9[/tex]
Find out more at: https://brainly.com/question/18880408
To apply Central Limit Theorem on sample proportions in One Sample Proportion test, the sample size and the population proportion under null hypothesis need to satisfy certain conditions. Which of the following scenarios meet the requirement?
A. The sample size is 50 and the population proportion under null hypothesis is 25%.
B. The sample size is 70 and the population proportion under null hypothesis is 90%.
C. The sample size is 50 and the population proportion under null hypothesis is 15%.
D. The sample size is 200 and the population proportion under null hypothesis is 4%.
Answer:
The sample size is 50 and population proportion under null hypothesis is 25% ( A ) meets the requirement
Step-by-step explanation:
when applying the central limit theorem on sample proportions in one sample proportion test .The conditions needed to be satisfied are np > 10, and n( 1-p ) > 10
A) sample size ( n ) = 50
population proportion = 25%
np = 50 * 0.25 = 12.5 which is > 10 ( 1st condition met )
n( 1 - p ) = 50( 1 - 0.25 ) = 37.5 which is > 10 ( second condition met )
B ) sample size (n) = 70
population proportion = 90%
np = 70*0.9 = 63 which is > 10 ( 1st condition met )
n(1-p) = 70 ( 1 - 0.9 ) = 7 which is < 10 ( second condition not met )
C) sample size ( n ) = 50
population proportion = 15% = 0.15
np = 50 * 0.15 = 7.5 which is < 10 ( 1st condition not met )
n ( 1 - p ) = 50 ( 1 - 0.15 ) = 50 * 0.85 = 42.5 which is > 10 ( second condition met )
D) sample size ( n ) = 200
population proportion = 4% = 0.04
np = 200 * 0.04 = 8 which is < 10 ( 1st condition not met )
n ( 1 - p ) = 200 ( 1 - 0.04 ) = 192 which is > 10 ( second condition met )
hence : The sample size of 50 with population proportion under null hypothesis of 25% meets the requirement
Evaluate
1+5.3
2
please answer quickly
Answer:
1+5.3=6.3
Step-by-step explanation:
not sure what your asking for with the 2
explain what your looking for with the 2 and maybe we can help you further
(I have to do it the way I did it because the 2 in the question is confusing)
Answer:
For expression 1 + 5.32: 6.32
For expression 1 + 5.3 × 2: 11.6
Step-by-step explanation:
If the expression is 1 + 5.32:
Add 1 to 5.32: 1 + 5.32 = 6.32If the expression is 1 + 5.3 × 2:
5.3 × 2 = 10.6Plug in 10.6: 1 + 10.61 + 10.6 = 11.6
A box is 90 cm long. Which of these is closest to the length of this box in feet?{1 inch= 2.54cm} (1 point)
Answer:
2.952755906 ft
Step-by-step explanation:
We need to convert 90 cm to inches
90 cm * 1 inch / 2.54 cm =35.43307087 inches
Now convert inches to ft
12 inches = 1ft
35.43307087 inches * 1 ft/ 12 inches =2.952755906 ft
Given that −4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x)=x4−2x3+x2−32x−240
Answer:
[tex]\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }[/tex]
Step-by-step explanation:
Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).
[tex]\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}[/tex]
The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.
[tex]f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240[/tex]
We identify the coefficients for the like terms, it comes
a = -2 and 16a = -32 (which is equivalent). So, we can write in [tex]\mathbb{R}[/tex].
[tex]\\f(x)=(x^2+16)(x^2-2x-15)[/tex]
The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.
[tex]f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}[/tex]
And we can write in [tex]\mathbb{C}[/tex]
[tex]f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Tanθ - cosecθ secθ (1-2 cos²θ) = cotθ
Answer:
I thinksomething is wrong.
I'm getting another proving it's-tan thita.
I hope this is the one you are searching for..
The base of a triangle is 4 cm greater than the
height. The area is 30 cm. Find the height and
the length of the base
h
The height of the triangle is
The base of the triangle is
Answer:
Step-by-step explanation:
Formula for area of a triangle:
Height x Base /2
Base (b) = h +4
Height = h
h + 4 x h /2 = 30cm
=> h +4 x h = 60
=> h+4h =60
=> 5h = 60
=> h = 12
Height = 12
Base = 12 +4 = 16
Which equation is equivalent to 3[x + 3(4x – 5)] = 15x – 24?15x – 15 = 15x – 2415x – 5 = 15x – 2439x – 45 = 15x – 2439x – 15 = 15x – 24?
Answer:
3[x + 3(4x – 5)] = (39x-15)
Step-by-step explanation:
The given expression is : 3[x + 3(4x – 5)]
We need to find the equivalent expression for this given expression. We need to simplify it. Firstly, open the brackets. So,
[tex]3[x + 3(4x -5)]=3[x+12x-15][/tex]
Again open the brackets,
[tex]3[x+12x-15]=3x+36x-45[/tex]
Now adding numbers having variables together. So,
[tex]3[x + 3(4x - 5)]=39x-15[/tex]
So, the equivalent expression of 3[x + 3(4x – 5)] is (39x-15).
the length of a mathematical text book the is approximately 18.34cm and its width is 11.75 calculate ?
the approximate perimeter of the front cover?
the approximate area of the front cover of the book?
Answer:
Perimeter=60.18cm
Area=215.495cm^2
Step-by-step explanation:
Given:
Length of book=18.34cm
Breadth=11.75cm
Solution:
Perimeter=2(l +b)
P=2(18.34+11.75)
P=2 x 30.09
P=60.18cm
Area=l x b
A=18.34 x 11.75
A=215.495 cm^2
Thank you!
) A random sample of size 36 is selected from a normally distributed population with a mean of 16 and a standard deviation of 3. What is the probability that the sample mean is somewhere between 15.8 and 16.2
Answer:
The probability is 0.31084
Step-by-step explanation:
We can calculate this probability using the z-score route.
Mathematically;
z = (x-mean)/SD/√n
Where the mean = 16, SD = 3 and n = 36
For 15.8, we have;
z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4
For 16.2, we have
z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4
So the probability we want to calculate is;
P(-0.4<z<0.4)
We can get this using the standard normal distribution table;
So we have;
P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)
= 0.31084
The domain of the following relation has how many elements?
[(1/2, 3.14/6), (1/2, 3.14/4), (1/2, 3.14/3), (1/2,3.14/2)]
a. 0
b. 1
c. 4
Answer:
b. 1
Step-by-step explanation:
All first coordinates are 1/2.
Answer: b. 1
Evaluate. log (down)2 256 . Write a conclusion statement.
[tex] \Large{ \boxed{ \bf{ \color{blue}{Solution:}}}}[/tex]
By using the fact that,
When,
[tex] \large{ \sf{ {a}^{x} =b}}[/tex]
Then, With logarithm base a of a number b:
[tex] \large{ \sf{ log_{a}(b) = x}}[/tex]
☃️So, Let's solve ths question....
To FinD:
[tex] \large{ \sf{log_{2}(256) }}[/tex]
Let it be x,
[tex] \large{ \sf{ \longrightarrow{ log_{2}(256) = x}}}[/tex]
Proceeding further,
[tex] \large{ \sf{ \longrightarrow \: {2}^{x} = 256}}[/tex]
[tex] \large{ \sf{ \longrightarrow \: {2}^{x} = {2}^{8} }}[/tex]
Then, We have same base 2, So
[tex] \large{ \sf{ \longrightarrow \: x = 8}}[/tex]
Or,
➙ log₂(256) = log₁₀(256) / log₁₀(2)
➙ log₂(256) = 2.40823996531 / 0.301029995664
➙ log₂(256) = 8
☕️ Hence, solved !!
━━━━━━━━━━━━━━━━━━━━
Answer:
256
Step-by-step explanation:
log 256 can most easily be found by rewriting 256 as a power of 2:
2
2^5 * 2^3 = 32*8 = 256, so 2^ (5 + 3) = 2^8.
Then we have:
log 256
2 2 = 256
Alternatively, write:
log (down)2 256 = log (down)2 2^8 = 2*8 = 256
Note that your "log (down)^2 and the function y = 2^x are inverse functions that effectively cancel one another.
Test the claim that the proportion of people who own cats is significantly different than 80% at the 0.2 significance level. The null and alternative hypothesis would be:______.
A. H0 : μ = 0.8 H 1 : μ ≠ 0.8
B. H0 : p ≤ 0.8 H 1 : p > 0.8
C. H0 : p = 0.8 H 1 : p ≠ 0.8
D. H0 : μ ≤ 0.8 H 1 : μ > 0.8
E. H0 : p ≥ 0.8 H 1 : p < 0.8
F. H0 : μ ≥ 0.8 H 1 : μ < 0.8
The test is:_____.
a. left-tailed
b. right-tailed
c. two-tailed
Based on a sample of 200 people, 79% owned cats.
The test statistic is:______.
The p-value is:_____.
Based on this we:_____.
A. Fail to reject the null hypothesis.
B. Reject the null hypothesis.
Answer:
C. H0 : p = 0.8 H 1 : p ≠ 0.8
The test is:_____.
c. two-tailed
The test statistic is:______p ± z (base alpha by 2) [tex]\sqrt{\frac{pq}{n} }[/tex]
The p-value is:_____. 0.09887
Based on this we:_____.
B. Reject the null hypothesis.
Step-by-step explanation:
We formulate null and alternative hypotheses as proportion of people who own cats is significantly different than 80%.
H0 : p = 0.8 H 1 : p ≠ 0.8
The alternative hypothesis H1 is that the 80% of the proportion is different and null hypothesis is , it is same.
For a two tailed test for significance level = 0.2 we have critical value ± 1.28.
We have alpha equal to 0.2 for a two tailed test . We divided alpha with 2 to get the answer for a two tailed test. When divided by two it gives 0.1 and the corresponding value is ± 1.28
The test statistic is
p ± z (base alpha by 2) [tex]\sqrt{\frac{pq}{n} }[/tex]
Where p = 0.8 , q = 1-p= 1-0.8= 0.2
n= 200
Putting the values
0.8 ± 1.28 [tex]\sqrt{\frac{0.8*0.2}{200} }[/tex]
0.8 ± 0.03620
0.8362, 0.7638
As the calculated value of z lies within the critical region we reject the null hypothesis.
