Answer:
0.05543Step-by-step explanation:
The formula for calculating the margin of error is expressed as;
[tex]M.E = z * \sqrt{\frac{p*(1-p)}{n} }[/tex] where;
z is the z-score at 95% confidence = 1.96 (This is gotten from z-table)
p is the percentage probability of those that watched network news
p = 40% = 0.4
n is the sample size = 300
Substituting this values into the formula will give;
[tex]M.E = 1.96*\sqrt{\frac{0.4(1-0.4)}{300} }\\ \\M.E = 1.96*\sqrt{\frac{0.4(0.6)}{300} }\\\\\\M.E = 1.96*\sqrt{\frac{0.24}{300} }\\\\\\M.E = 1.96*\sqrt{0.0008}\\\\\\M.E = 1.96*0.02828\\\\M.E \approx 0.05543[/tex]
Hence, the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V. viewers who watch network news programs is approximately 0.05543
Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 18 of the 52 boxes on the shelf have the secret decoder ring. The other 34 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
Answer:
3/26
Step-by-step explanation:
Probability of the first box to have the secret decoder ring is 18 out of 52:
18/52= 9/26Probability of the second box to have the ring is 17 out of 51, because one box with the ring already selected and not counted:
17/51= 1/3Probability that both of them have the secret decoder ring:
9/26*1/3= 3/26So the answer is 3/26
Jamie's dog eats 3/4 pound of dog food each day. How many pounds of dog
food does Jamie's dog eat in 4 days?
Answer:
The dog will eat 3 lbs
Step-by-step explanation:
Take the amount eaten per day and multiply by the number of days
3/4 * 4 = 3
The dog will eat 3 lbs
Answer:
3 pounds
Step-by-step explanation:
Multiply the amount of dog food per day with the number of days.
[tex]\frac{3}{4} \times 4[/tex]
[tex]\frac{12}{4} =3[/tex]
In 4 days, Jamie's dog will eat 3 pounds of dog food.
Use an appropriate series to find Taylor series of the given function centered at the indicated value of a. Write your answer in summation notation.
sinx, a= 2π
Answer:
The Taylor series is [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
Step-by-step explanation:
From the question we are told that
The function is [tex]f(x) = sin (x)[/tex]
This is centered at
[tex]a = 2 \pi[/tex]
Now the next step is to represent the function sin (x) in it Maclaurin series form which is
[tex]sin (x) = \frac{x^3}{3! } + \frac{x^5}{5!} - \frac{x^7}{7 !} +***[/tex]
=> [tex]sin (x) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
Now since the function is centered at [tex]a = 2 \pi[/tex]
We have that
[tex]sin (x - 2 \pi ) = (x-2 \pi ) - \frac{(x - 2 \pi)^3 }{3 \ !} + \frac{(x - 2 \pi)^5 }{5 \ !} - \frac{(x - 2 \pi)^7 }{7 \ !} + ***[/tex]
This above equation is generated because the function is not centered at the origin but at [tex]a = 2 \pi[/tex]
[tex]sin (x-2 \pi ) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x - 2 \pi)^{2n+1}][/tex]
Now due to the fact that [tex]sin (x- 2 \pi) = sin (x)[/tex]
This because [tex]2 \pi[/tex] is a constant
Then it implies that the Taylor series of the function centered at [tex]a = 2 \pi[/tex] is
[tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
(SAT Prep) In the given figure, a║b. What is the value of x? A. 70° B. 45° C. 80° D. 65° I NEED THIS FAST PLZZZZZZ!!!!!!!!!!!!
Answer:
70
Step-by-step explanation:
You have to find the vertical of x. To the right of the vertical, we see that there is an angle of 25 (since the 25 up top corresponds to that blank angle). Once you add 25 + 85 + x = 180 (since this is a straight line), we see that x is 70, and its vertical is also 70.
A small company that manufactures snowboards uses the relation below to model its profit. In the model,
represents the number of snowboards in thousands, and P represents the profit in ten thousands of dollars.
What is the maximum profit the company can earn? How many snowboards must it produce to earn this
maximum profit?
a. Factor P =
4x2 + 32x + 336 to find the roots.
b. Find the axis of symmetry then use it to find the vertex.
c. Therefore, we need to see snowboards to make a maximum profit of
Answer:
a) x₁ = 14
x₂ = - 6
b) x = 4
c) P(max ) = 4000000 $
Step-by-step explanation:
To find the axis of symmetry we solve the equation
a) -4x² + 32x + 336 = 0
4x² - 32x - 336 = 0 or x² - 8x - 84 = 0
x₁,₂ = [ -b ± √b² -4ac ]/2a
x₁,₂ = [ 8 ±√(64) + 336 ]/2
x₁,₂ = [ 8 ± √400 ]/2
x₁,₂ =( 8 ± 20 )/2
x₁ = 14
x₂ = -6
a) Axis of symmetry must go through the middle point between the roots
x = 4 is the axis of symmetry
c) P = -4x² + 32x + 336
Taking derivatives on both sides of the equation we get
P´(x) = - 8x + 32 ⇒ P´(x) = 0 - 8x + 32
x = 32/8
x = 4 Company has to sell 4 ( 4000 snowboard)
to get a profit :
P = - 4*(4)² + 32*(4) + 336
P(max) = -64 + 128 + 336
P(max) = 400 or 400* 10000 = 4000000
The function f is defined as follows.
f(x) =4x²+6
If the graph of f is translated vertically upward by 4 units, It becomes the graph of a function g.
Find the expression for g(x).
Answer:
g ( x ) = 4x^2 + 10
Step-by-step explanation:
Solution:-
The translation of a function f ( x ) in the cartesian coordinate domain can be done by following the given guidelines:
Translation guidelines
Horizontal shifts
Right : f ( x ) -> f ( x - a )Left : f ( x ) - > f ( x + a )
Vertical shifts
Up : f ( x ) -> f ( x ) + bDown : f ( x ) - > f ( x ) - bGeneral shift ( Horizontal and Vertical shift )
f ( x ) - > f ( x ± a ) ± b
We are given a function f ( x ) which is to be translated vertically upward 4 units. We will use the guidelines for Vertical shifts, where in this case the magnitude of b = 4.
f ( x ) = 4x^2 + 6
f ( x ) - > f ( x ) + b
g ( x ) = f ( x ) + 4
g ( x ) = 4x^2 + 6 + 4
g ( x ) = 4x^2 + 10 ... Answer
help!! I have problem to solve this question
Answer:
Step-by-step explanation:
[tex]\frac{x-1}{2} =t\\\frac{y-2}{3} =t\\\frac{z-3}{4} =t\\so~eq.~of~line~L_{1}~is\\\frac{x-1}{2} =\frac{y-2}{3} =\frac{z-3}{4} \\its~d.r's~are~2,3,4\\again~\frac{x-2}{1} =s\\\frac{y-4}{2} =s\\\frac{z+1}{-4} =s\\so~eq. ~of~line~L_{2}~is\\\frac{x-2}{1} =\frac{y-4}{2} =\frac{z+1}{-4} \\its~d.r's ~are~1,2,-4\\let ~the ~d.r's~of~line~perpendicular~to~both~L_{1}~and~L_{2}~be~a,b,c,~then~\\2a+3b+4c=0\\1a+2b-4c=0\\solving\\\frac{a}{3*-4-4*2} =\frac{b}{4*1-2*-4} =\frac{c}{2*2-3*1} \\[/tex]
[tex]\frac{a}{-20} =\frac{b}{-4} =\frac{c}{1} \\d.r's~of ~reqd~line~is~-20,-4,1~or~20,4,-1[/tex]
now you find the point of intersection.
then calculate the angle.
the result of two forces acting on a body has a magnitude of 80 pounds. The angles between the resultant and the forces are 20 degrees and 52 degrees. find the magnitude of the large force
Answer:
Larger force= 66.28 pounds
Step-by-step explanation:
The angle of the resultant force 80 pounds = 180-(52+20)
The angle of the resultant force 80 pounds = 180-72
The angle of the resultant force 80 pounds = 108°
The larger force is the force with 52°
Let the larger force be x
Magnitude of the larger force
x/sin52 = 80/sin108
X= sin52 *(80/sin 108)
X= 0.7880*(80/0.9511)
X = 0.7780*(84.1131)
X = 66.28 pounds
2. Write as a complex number.
Answer:
Your answer is correct ✔️
Step-by-step explanation:
Hope this is correct and helpful
HAVE A GOOD DAY!
Answer:
2√3 + 3i is the answer
Step-by-step explanation:
On an uphill hike Ted climbs at 3mph. Going back down, he runs at 5mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike?
Answer:
10 miles
Step-by-step explanation:
3 mi/1 hr x (h hours + 2/3 hr) = 5 mi/1 hr x h hours
3h + 2 = 5h
2 = 2h
h = 1 hour
3mi/hr x 1 2/3 hr = 5 miles
5 mi/hr x 1 hr = 5 miles
He hiked 10 miles. (
Which ordered pair is a solution to the system of linear equations? 2x + 3y= 6 –3x + 5y = 10
Answer:
(0,2)
Step-by-step explanation:
solve by addition/elimination
2x + 3y= 6
–3x + 5y = 10
multiply first equation by 3 and second one by 2 to eliminate x)
6x+9y=18
-6x+10y=20 (add the two equations)
6x+9y-6x+10y=38
19y=38
y=38/19=2
2x+3y=6
2x=6-6
x=0
Answer:
a
Step-by-step explanation:
what is the answer. plz heelp 5h+2(11-h)= -5
Answer:
h = -9
Step-by-step explanation:
5h+2(11-h)= -5
Distribute
5h +22 -2h = -5
Combine like terms
3h +22 = -5
Subtract 22 from each side
3h +22-22 = -5-22
3h = -27
Divide by 3
3h/3 = -27/3
h = -9
Which graph best models the inequality y<_ -2/5x+2
Answer:
Step-by-step explanation:
Simplify each term.
y ≤ −2x/5 + 2
Find the slope and the y-intercept for the boundary line.
Slope: -2/5
Y-intercept: 2
Graph a solid line, then shade the area below the boundary line since
y is less than -2x/5 + 2
y ≤ −2x/5 + 2
Hope this can help
i give you brailenst
Answer:
The answer is #3 which is 24%.
Step-by-step explanation:
6 × 100
25
25 into 100 is 4, then 6×4 = 24%
I really hope this helps :)
Find the points of intersection of the following function graphs: y=20x−70 and y=70x+30
Answer:
(-2,-110)
Step-by-step explanation:
First solve for x
20x−70=70x+30
x= -2
Now substitute x for -2
y=20x−70
y=20(-2)-70
y = -110
A college graduate is curious about the proportion of graduates who have loan debt 20 years after graduating. Let the proportion of graduates who have loan debt 20 years after graduating be p. If the college graduate wishes to know if the proportion of graduates who have loan debt 20 years after graduating is less than 18%, what are the null and alternative hypotheses?
Answer: Null Hypothesis [tex]H_{0}[/tex]: p = 0.18
Alternative Hypothesis [tex]H_{a}[/tex]: p < 0.18
Step-by-step explanation: When doing an experiment, first define the hypotheses you want to test. These hypotheses are Null Hypothesis and Alternative Hypothesis
Null Hypothesis is a general assumption and discloses that there is no relationship between the conditions under consideration. It is the hypothesis the researcher is trying to disprove. It is denoted by the symbol [tex]H_{0}[/tex].
For the college graduate curiosity, the hypothesis the graduate is trying to disprove is that the proportion of students who have loan debt after 20 years of graduation is 18%. Then, Null Hypothesis is [tex]H_{0}[/tex]: p = 0.18
Alternative Hypothesis is the a statement describing a relationship between the collected data. It is what researches try to prove and the results are observations of real causes. It is denoted by the symbol [tex]H_{a}[/tex].
For the graduate study, the alternative is that the proportion is less tahn 18% or 0.18. Then, Alternative Hypothesis: [tex]H_{a}[/tex]: p < 0.18
The Orchard Cafe has found that about 15% of the diners who make reservations don't show up. If 77 reservations have been made, how many diners can be expected to show up? Find the standard deviation of this distribution
Answer:
65 dinners are expected to show up
The standard deviation of the distribution is 3.13
Step-by-step explanation:
Given
Proportion = 15%
Population = 77
Required
Expected Number that'll show up
Standard Deviation
If 15% won't show up; then
100% - 15% = 85% will show up
Expected Number, E(x) of Dinner is calculated as thus;
[tex]E(x) = np[/tex]
Where [tex]p = 85\%[/tex] (calculated above)
and [tex]n = 77[/tex]
Convert p to decimal
[tex]p = 0.85[/tex]
So;
[tex]E(x) = 0.85 * 77[/tex]
[tex]E(x) = 65.45[/tex]
[tex]E(x) = 65[/tex]
65 dinners are expected to show up
Calculating Standard Deviation, SD
Standard Deviation is calculated as;
[tex]SD = \sqrt{np(1-p)}[/tex]
Substitute 0.85 for p and 77 for n
[tex]SD = \sqrt{77 * 0.85 * (1-0.85)}[/tex]
[tex]SD = \sqrt{77 * 0.85 * 0.15}[/tex]
[tex]SD = \sqrt{9.8175}[/tex]
[tex]SD = 3.13328900678[/tex]
[tex]SD = 3.13[/tex] (Approximated)
The standard deviation of the distribution is 3.13
What is the total amount of 2/5+5/3+9/3 and the lowest common denominator?
The lowest common denominator is lcm(5, 3), which is 15.
The sum of 2/5 + 5/3 + 9/3 is 6/15 + 25/15 + 45/15, which is 76/15 or [tex]5\frac{1}{15}[/tex].
Question 15: (5 points)
Find one possibie missing coordinate so that the point becomes a solution to the given inequality.
(x, 7) is a solution to 2 x - 3<y.
=
In a few sentences, please explain how you arrived at your answer
Answer:
[tex](4,7)[/tex]
Step-by-step explanation:
Given
[tex]2x - 3 < y[/tex]
[tex](x,7)[/tex]
Required
Find one possible value of x
From the given parameters;
[tex](x,7)[/tex] is a possible solution of [tex]2x - 3 < y[/tex] where y= 7
Substitute 7 for y
[tex]2x - 3 < 7[/tex]
Add 3 to both sides
[tex]2x - 3 + 3 < 7 + 3[/tex]
[tex]2x < 10[/tex]
Divide both sides by 2
[tex]2x/2 < 10/2[/tex]
[tex]x < 5[/tex]
The result of the inequality implies that x is less than 5; So, the possible values of x is all real numbers less than 5;
Having said that;
[tex](4,7)[/tex] is one possible coordinate of [tex]2x - 3 < y[/tex]
Help ASAP!!!
Identify the correct trigonometry formula to use to solve for x.
Answer:
The answer is option 2.
Step-by-step explanation:
You have to apply Cosine Rule, cosθ = adjacent/hypotenuse. Then, you have to substitute the values into the formula :
[tex]cos(θ) = \frac{adj.}{hypo.} [/tex]
[tex]let \: θ = 55[/tex]
[tex]let \: adj. = 11[/tex]
[tex]let \: hypo. = x[/tex]
[tex]cos(55) = \frac{11}{x} [/tex]
The correct trigonometry formula to use to solve for x is [tex]\frac{11}{x}[/tex] . Thus option 1 is correct.
According to the question, we have
base = 11
hypotenuse = x
here for [tex]cos Ф[/tex]Ф, it is not required to find the value of perpendicular,
we know that in a right-angle triangle using trigonometric ratio, we get
[tex]cos Ф[/tex] Ф = [tex]\frac{base }{hypotenuse}[/tex]
[tex]cos Ф[/tex] Ф = [tex]\frac{11}{x}[/tex]
here Ф = [tex]55 ^0[/tex]
[tex]cos 55^o = \frac{11}{x}[/tex]
Thus, the value of the trigonometry formula to use to solve for x is [tex]\frac{11}{x}[/tex].
Thus option 1 is correct.
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What is the lateral surface area of the cone? A cone with diameter 18 centimeters, height of 12 centimeters, and slant height of 15 centimeters. L A = pi r l 108 pi centimeters squared 135 pi centimeters squared 180 pi centimeters squared 270 pi centimeters squared
Answer:
3051.08 cm squared
Step-by-step explanation:
The equation to find lateral surface area of a cone:
SA = pi r sqrt(h^2 * r^2)
Plug your values in.
SA = 3.14 * 9 * sqrt(144*81)
SA = 3.14 * 9 * 108
SA = 3051.08
The lateral surface area is 3051.08 cm squared.
Answer:
424.12cm^2
Step-by-step explanation:
make sure you have the radius, half of the diameter!
remember to use this formula! Lateral surface area = πrs = πr√(r2 + h2)
hope this helped!
r=radius
h=hight
s=slant
what is the answer 2×3+4×100-50+10
Answer:
366
Step-by-step explanation:
2×3+4×100-50+10
PEMDAS says multiply and divide from left to right
6 + 400 - 50 +10
Then add and subtract
406-50+10
356+10
366
Answer:
[tex]\boxed{366}[/tex]
Step-by-step explanation:
[tex]2 \times 3+4 \times 100-50+10[/tex]
Multiplication is first.
[tex]6+400-50+10[/tex]
Add or subtract the numbers.
[tex]350+10+6[/tex]
[tex]366[/tex]
Which algebraic expression represents the phrase "six less than a number"?
SERE
6x - X
X-6
6- X
X - 6x
Answer:
The answer is option B.
Step-by-step explanation:
six less than a number is written as
x - 6
Hope this helps you
In △ABC, m∠A=27 °, c=14 , and m∠B=25 °. Find a to the nearest tenth.
Answer:
a = 8.1
Step-by-step explanation:
Firstly, since we have a triangle, automatically, we have 3 interior angles
Mathematically the sum of these angles = 180
A + B + C = 180
27 + 25 + C = 180
52 + C = 180
C = 180-52
C = 128
We use the sine rule to find a
The sine rule posits that the ratio of a side to the sine of the angle facing that side is equal for all the sides of a triangle
Thus, mathematically according to the sine rule;
c/Sin C = a/Sin A
14/sin 128 = a/sin 27
a = 14sin27/sin 128 = 8.0657
which to the nearest tenth is 8.1
helpppppppppppppppppppppp pleaseeeeeeeeeeeeeeeeeeeeeee
Answer:
0.29
Step-by-step explanation:
There are 29 squares shaded in. In all, there are 100 squares in the 10 × 10 square, so there are 29 shaded squares out of 100 squares in all. That is basically:
[tex]\frac{29}{100}[/tex]
[tex]\frac{29}{100}[/tex] can be converted to 0.29.
Answer:
0.29
Step-by-step explanation:
Since the grid is a 10x10, it means there are 100 total 'blocks' in the grid. So, since there are 29 shaded in out of the 100 'blocks total, the decimal would be .29, since the decimal means 29 hundredths, and it also means that there is 29 hundredths of the total grid shaded in.
what is 1.8÷0.004? using long division
Answer:
Hi! Answer will be below.
Step-by-step explanation:
The answer is 450.
If you divide 1.8 and 0.004 the answer you should get is 450.
Below I attached a picture of how to do long division...the picture is an example.
Hope this helps!:)
⭐️Have a wonderful day!⭐️
HELP WILL GIVE BRAINLIEST FOR ANSWER QUICKLY PLEASE HELP
Answer:
We have sinθ = 12/13
The method here is to figure out the value of θ
Using a calculator sin^(-1)(12/13) =67.38°
67.38° is in quadrant 1 so we must substract 67.38° from 180° wich is π
180-67.38= 112.61° ⇒ θ= 112.61°Now time to calculate cos2θ and cosθ using a calculator
cosθ = -5/13 cos2θ = -0.7The values we got make sense since θ is in quadrant 2 and 2θ in quadrant 3
7987.1569 to the nearest thousandth
Answer:
7987.1569 to the nearest thousandths is 7987.157
Step-by-step explanation:
In order to sustain itself in its cold habitat, a Siberian tiger requires 25 pounds of meat per day.
How much meat would seven Siberian tigers need for the month of April?
Select one:
a. 750 pounds
b. 175 pounds
c. 5425 pounds
d. 5250 pounds
Answer:
d. 5250 pounds
Step-by-step explanation:
25 lbs per day
There are 30 days in april
25 lbs/ day * 30 days
1 tiger would eat 750 lbs
There are 7 tigers
7 * 750 =5250 lbs
Answer:
D. 5250 pounds
Step-by-step explanation:
What you need to do is multiply 25 pounds by 30 because there are 30 days in the month of April.
25 x 30 = 750
Then multiply that amount by seven because there are 7 tigers.
750 x 7 = 5250
A sample of radioactive material disintegrates from 6 to 4 grams in 100 days. After how many days will just 3 grams remain?
Answer:
150 days
Step-by-step explanation:
6-4=2
100/2=50
50*3=150
The number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
The rate of disintegration varies directly proportional to the quantity of the material.
As such, we can say:
[tex]\mathbf{=\dfrac{dN}{dt}\ \alpha \ N}[/tex]
[tex]\mathbf{\implies \dfrac{dN}{N}\ = k dt}[/tex]
Taking the integral form;
[tex]\mathbf{\implies \int \dfrac{dN}{N}\ =\int k dt}[/tex]
[tex]\mathbf{\implies In N =kt+ C---- (1)}[/tex]
When t = 0, N = 6 grams
In(6) = C
∴
When t = 100, N = 4 grams
In (4) = 100k + In6
100 k = 1n (4) - In(6)
[tex]\mathbf{100 k = In (\dfrac{4}{6})}[/tex]
[tex]\mathbf{k = \dfrac{1}{100} In(\dfrac{4}{6})}[/tex]
∴
From equation (1):
[tex]\mathbf{In N = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
when,
n = 3 grams; we have:[tex]\mathbf{In (3) = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
[tex]\mathbf{\implies \dfrac{t}{100} In(\dfrac{4}{6}) = In \dfrac{ 3}{ 6}}[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{In (\dfrac{ 3}{ 6})}{ In(\dfrac{4}{6}) }\Big) }[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{0.69314}{ 0.40048}\Big) }[/tex]
t = 173.077 days
Therefore, the number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
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