Answer:
As 0.17 is below the upper limit of the confidence interval, so we can conclude that the population proportion is less than 0.17.
Step-by-step explanation:
We are given that a survey of 270 young professionals found that one dash eighth of them use their cell phones primarily for e-mail.
Firstly, the Pivotal quantity for 95% confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of people who use their cell phones primarily for e-mail = [tex]\frac{1}{8}[/tex] = 0.125
n = sample of young professionals = 270
p = population proportion
Here for constructing 95% confidence interval we have used One-sample z test for proportions.
So, 95% confidence interval for the population proportion, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
95% confidence interval for p = [[tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]
= [ [tex]0.125-1.96 \times {\sqrt{\frac{0.125(1-0.125)}{270} } }[/tex] , [tex]0.125+1.96 \times {\sqrt{\frac{0.125(1-0.125)}{270} } }[/tex] ]
= [0.08 , 0.16]
Therefore, 95% confidence interval for the population proportion who use cell phones primarily for e-mail is [0.08 , 0.16].
Since, the above confidence interval have values which is less than 0.17; so we conclude that the population proportion is less than 0.17.
x2 -20x + y^2 - 10y+25=0
identify center of the circle and radius
Answer:
Center of the circle = (10, 5)
Radius = 10
Step-by-step explanation:
Look at the picture
For each right triangle fine the length of the side that is not given. Round your answer to the nearest tenth.(one Decimal place)
Answer:
√157
Step-by-step explanation:
Use Pythagorean theorm.
[tex]11^2 + 6^2 = ?^2[/tex]
121 + 36 = ?^2
157 = ?^2
√157 = ?
Can't simplify.
Answer:
12.5 m
Step-by-step explanation:
You are given the lengths of the legs of a right triangle.
We can use the Pythagorean theorem to find the length of the hypotenuse.
a^2 + b^2 = c^2
(6 m)^2 + (11 m)^2 = c^2
36 m^2 + 121 m^2 = c^2
c^2 = 157 m^2
c = sqrt(157 m^2)
c = sqrt(157) m
Answer: 12.5 m
Which inequality is equivalent to y-8 less than or equal to -2
what is 584+106
plz help some math i’m so tired
Answer:
690
Step-by-step explanation:
587+106=690
The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring, versus 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?
Answer:
The combination that gives the most profit is 12 VIP rings and 12 SST rings (900 $/day).
Step-by-step explanation:
This is a linear programming problem.
The objective function is profit R, which has to be maximized.
[tex]R=40V+35S[/tex]
being V: number of VIP rings produced, and S: number of SST rings produced.
The restrictions are
- Amount of rings (less or equal than 24 a day):
[tex]V+S\leq24[/tex]
- Amount of man-hours (up to 60 man-hours per day):
[tex]3V+2S\leq60[/tex]
- The number of rings of each type is a positive integer:
[tex]V, \;S\geq 0[/tex]
This restrictions can be graphed and then limit the feasible region. The graph is attached.
We get 3 points, in which 2 of the restrictions are saturated. In one of these three points lies the combination of V and S that maximizes profit.
The points and the values for the profit function in that point are:
Point 1: V=0 and S=24.
[tex]R=40V+35S=40\cdot 0+35\cdot 24=0+840\\\\R=840[/tex]
Point 2: V=12 and S=12
[tex]R=40V+35S=40\cdot 12+35\cdot 12=480+420\\\\R=900[/tex]
Point 3: V=20 and S=0
[tex]R=40V+35S=40\cdot 20+35\cdot 0=800+0\\\\R=800[/tex]
The combination that gives the most profit is 12 VIP rings and 12 SST rings (900 $/day).
Which is a correct expansion of (2x+3)(2x^{2} -5)?
Answer:
4x^{3} + 6x^{2} -10x -15
Step-by-step explanation:
(2x+3)(2x^{2} -5)
2x × 2x^{2} + 2x× (-5) + 3× 2x^{2} + 3 ×(-5)
=4x^{3} -10x + 6x^{2} -15
= 4x^{3} + 6x^{2} -10x -15
4¹²=4ᵃ‐3, what is the value of a?
Answer:
a = 15
Step-by-step explanation:
Perhaps your question is:
[tex] 4^{12}= 4^{a-3}[/tex]
If it is so then let us solve:
[tex] 4^{12}= 4^{a-3}[/tex]
Since, bases are equal hence exponents will also be equal. Therefore,
12 = a - 3
12 + 3 = a
a = 15
Which equation is the inverse of (x-4)2- ß-by-122
O y=6x2-3x+42
6x-
34
O y=4+ /6x-
34
O y=-4+ /6x-
0 -(x-4)2 -> --6y+12
Answer:
see below
Step-by-step explanation:
Interchange x and y, then solve for y.
[tex](x-4)^2-\dfrac{2}{3}=6y-12\qquad\text{given}\\\\(y-4)^2=6x-\dfrac{36-2}{3}\qquad\text{swap x,y; add 2/3}\\\\y-4=\pm\sqrt{6x-\dfrac{34}{3}}\\\\\boxed{y=4\pm\sqrt{6x-\dfrac{34}{3}}}[/tex]
Consider the polynomial function p(x) = 4x^8- 6x^7+ 3x^3- 10.
What is the end behavior of the graph of p?
Answer:
As x gets smaller, pointing to negative infinity, the value of p increases, pointing to positive infinity.
As x increases, pointing to positive infinity, the value of p increases, pointing to positive infinity.
Step-by-step explanation:
To find the end behaviour of a function f(x), we calculate these following limits:
[tex]\lim_{x \to +\infty} f(x)[/tex]
And
[tex]\lim_{x \to -\infty} f(x)[/tex]
At negative infinity:
[tex]\lim_{x \to -\infty} (4x^{8} - 6x^{7} + 3x^{3} - 10)[/tex]
When the variable points to infinity, we only consider the term with the highest exponent. So
[tex]\lim_{x \to -\infty} (4x^{8} - 6x^{7} + 3x^{3} - 10) = \lim_{x \to -\infty} 4x^{8} = 4*(-\infty)^{8} = \infty[/tex]
Plus infinity, because the exponent is even.
So as x gets smaller, pointing to negative infinity, the value of p increases, pointing to positive infinity.
At positive infinity:
[tex]\lim_{x \to \infty} (4x^{8} - 6x^{7} + 3x^{3} - 10) = \lim_{x \to \infty} 4x^{8} = 4*(\infty)^{8} = \infty[/tex]
As x increases, pointing to positive infinity, the value of p increases, pointing to positive infinity.
Answer:
A - As x -> infinity, p(x) -> infinity, and as x -> -infinity, p(x) -> infinity.
Step-by-step explanation:
A 4 1/2 ounce hamburger patty has 25 1/2 grams of protein. Determine the grams of protein per ounce each type of food.
Select from the drop down menus to correctly complete each statement
Answer:
Option c. 5.7 grams
Option b. 5.3 grams
Step-by-step explanation:
(a) A [tex]4\frac{1}{2}[/tex] ounce hamburger patty has [tex]25\frac{1}{2}[/tex] grams of protein.
first we convert mixed fraction to improper fraction.
Amount of protein a [tex]\frac{9}{2}[/tex] ounce hamburger patty has = [tex]\frac{51}{2}[/tex] grams
∴ Amount of protein a 1 ounce hamburger patty has = [tex]\frac{\frac{51}{2} }{\frac{9}{2} }[/tex]
= [tex]\frac{51}{2} \times \frac{2}{9}[/tex]
= [tex]\frac{51}{9}[/tex]
= [tex]\frac{17}{3}[/tex] = [tex]5\frac{2}{3}[/tex] = 5.7 grams
(b) A 6 ounces of fish has 32 grams of protein.
∴ The amount of protein a 1 ounce of fish has = [tex]\frac{32}{6}[/tex]
= 5.3 grams
A hamburger patty has approximately 5.7 grams of protein per ounce.
A fish has approximately 5.3 grams of protein per ounce.
What is the angle bec and the angle Abe?
Answer quick please!
70°
Answer:
160°
Step-by-step explanation:
[tex](3x - 5) \degree + (4x + 10) \degree = 180 \degree \\ (straight \: line \: \angle s) \\ (7x + 5) \degree = 180 \degree \\7x + 5 = 180 \\ 7x = 180 - 5 \\ 7x = 175 \\ x = \frac{175}{7} \\ \huge \orange{ \boxed{x = 25}} \\ \\ m\angle BEC = (3x - 5) \degree \\ m\angle BEC = (3 \times 25 - 5) \degree \\ m\angle BEC = (75 - 5) \degree \\ \huge \red{ \boxed{m\angle BEC = 70 \degree}} \\ \\ by \: remote \: interior \: angle \: theorem : \\ m\angle ABE = m\angle BEC + m\angle BCE \\ m\angle ABE = 70 \degree + 90 \degree \\ \huge \purple{ \boxed{m\angle ABE = 160 \degree }}[/tex]
Is the origin located at the intersection of the x - and y -axis
yes it is because thats exactly where its located
please helpppp i don’t know what do to :/ if you answer thank you so much
Answer:
(4,6)-(-2,-1)
Step-by-step explanation:
A ladder, leaning against a wall, makes an angle of 20° with the ground. The foot of the ladder is 3 m from the wall. How long is the ladder?
Answer:
0.136m
Step-by-step explanation:
This is because if you draw a diagram, and label all the sides of the triangle (opp, hyp, adj), the adjacent angle is 3m. You can now use the sine rule to find the hypotenuse (length of ladder) by doing: cos 20= 3/h. You divide cos(20) by 3 and you get the answer of 0.13602m.
Given the system y= 2x + 2 and y= 2*, which statement below is true?
There are no solutions
The system has exactly one solution.
(3, 8) is a solution of the system.
(8,3) is a solution of the system.
Answer:
(3, 8) is a solution of the system
Step-by-step explanation:
We assume your second equation is intended to be ...
y = 2^x
This system of equations can be solved graphically or by trial and error. There are no algebraic methods for solving it.
A graph shows that (3, 8) is one of the two solutions.
John wants to evaluate the expression (5 + 3)^2.
As a first step, he writes 5^2+ 3^2. Will he get the correct value for the
expression? If not, what should he do to evaluate the expression?
Please help write the correct answer.
Answer:
5+3 x 2=64
Step-by-step explanation:
(5+3) x 2 5^2+3^2=34 not 64
8 x 2 = 64
Answer:
64
Step-by-step explanation:
Hope this helped
Aright triangle with an area of X2-4 square units has a leg that measures
2x + 4 units.
Determine the length of the other leg of the triangle.
Answer:
x - 2
Step-by-step explanation:
First, we know that the area of a triangle can be found using the formula: a = 1/2(bh).
We also know that the area of this triangle can be represented by (x^2-4).
Lastly, we know that one of the legs (let's call it the base) can be represented by (2x+4).
Let's plug in those values to the original formula: x^2 - 4 = 1/2(2x + 4)h
Now, let's solve for h!
We can multiply both sides by 2, then divide each side by (2x + 4) to isolate/solve for h.
If you need help on dividing polynomials, feel free to reach out!! I'd be happy to explain.
h = (x - 2)
Megan has practiced the piano for 7.5 hours over the course of this week. She practices on Tuesdays, Thursdays, and Saturdays. How many minutes is Megan's average practice.
Answer:
150
Step-by-step explanation:
you have three days and 7.5 so decide 7.5 by 3 it equals 2.5 which in minutes is 150
In a class full of men and women,
3
5
of the class are women. What is the ratio of men to women in its simplest form?
Answer:
2:3
Step-by-step explanation:
3/5 women, that makes men 2/5, and total 5/5
men to women
2:3
Find the mode of the data. please Helppppp!!!
Answer:
pizza
Step-by-step explanation:
Mode is the one that appears most often
Pizza appears 4 times
Cheeseburger, spaghetti appears only 3 times
apples, hot dogs 2 times
Answer: the mode is pizza
Step-by-step explanation:
Pizza: 4
Spaghetti: 3
Cheeseburger: 3
Apples: 2
Hotdog: 2
Pizza is the most so, it is the mode.
The length of a rectangle is 7 cm more than 4 times the width. If the perimeter of the rectangle is 44 cm, what are its dimensions?
Answer:
3 by 19
Step-by-step explanation:
What’s the correct answer for this?
Answer:
(x + 5)² + (y - 7)² = 13
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (- 5, 7) and r = [tex]\sqrt{13}[/tex] , thus
(x - (- 5))² + (y - 7)² = ([tex]\sqrt{13}[/tex] )² , that is
(x + 5)² + (y - 7)² = 13 ← equation of circle
What is the area of ABCDE?____sq cm
got very confused on this part
Answer:
A= 30 sq. cm
Step-by-step explanation:
We want to find the area of both triangles seprately than add them together. For the area of a traingle, we use the equation 1/2 base times height. For triangle ABE we do this:
[tex]A = \frac{1}{2} (12)(4)[/tex]
[tex]A = (6) (4)[/tex]
[tex]A = 24[/tex]
For triangle BDC, we do this:
[tex]A = \frac{1}{2} (6) (2)[/tex]
[tex]A = (3) (2)[/tex]
[tex]A=6[/tex]
Now we have to add both areas ot get A=30 sq cm
Solve for x in this equation 1/5x = 7/35. Simplify.
Answer:
x=1
Step-by-step explanation:
1/5x = 7/35.
Multiply each side by 5
1/5 x * 5 = 7/35 *5
x = 7/7
x=1
Of the 50 people who started a math class meeting at 10:00 each morning, only 37 finished the class. What fraction of people finished the class?
Answer:
37/50
Step-by-step explanation:
So 37 out of 50 who finished the class, so 37/50 .
And you can't simplify it.
in a football tournament at group stage there are five football teams in a group, Brazil, England, Scotland, Argentina and France. Each team plays every other team in their group. There are ten matches altogether. Two teams are picked at random to play the first match. Work out the probability that the first game will be played by a European team and a South American team.
Answer:
6/25
Step-by-step explanation:
Because england, scotland and france are european team and they make up 3/5 of all the teams, you multiply 3/5 by 2/5 because the south american teams are brazil and argentina which make up 2/5 of the total teams. So the probability that a european team will play a south american team is 3/5*2/5 which is 6/25
What is the first step to verify that the following identity is true?
Cot^2 x sec x = cos x/ sin^2 x
Step-by-step explanation:
this right ans according to your question
Find the median, and mode(s) of the data. 15, 4, 3, 12, 20, 12, 13
Answer:
median: 12 mode: 12
Step-by-step explanation:
to find the median arrange the number in ascending order and then find the one that's in the middle. to find the mode just figure out which number shows up the most
Answer:
they both are 12
100%
Step-by-step explanation:
what is the quotient 7^-6/7^2
Answer:
7 to the power of negative 8
Answer:
7^-8 = 1/5764801
Step-by-step explanation:
The appropriate rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
So, ...
7^-6/7^2 = 7^(-6-2) = 7^-8 = 1/5764801
A spinner has 5 equal-sized sections with different colors. You spin the spinner 50 times. The results are shown in the table. Find the theoretical and experimental probabilities of spinning blue.
Red Green Blue Yellow Orange
8 11 15 9 7
The theoretical probability is
.
The experimental probability is
.
Question 2
What do you think will happen to the experimental probability when you spin the spinner 400 times?
The experimental probability will stay the same.
The experimental probability will get farther from the theoretical probability.
The experimental probability will get closer to the theoretical probability.
Answer:
a) If the spinner is fair, then each color must have the same probability, this means that the probability for each color is the number of times that the color (in this case blue) is in the spinner divided the total amount of colors in the spinner, then the theoretical probability for each color is:
Pt = 1/5 = 0.20
The experimental probability can be found by dividing the number of times that the spinner landed on a given color (in this case for blue we have 15 times) divided the total number of spins ( 50)
Pe = 15/50 = 0.30
B) As we increment the number of spins, we should see that the experimental probability gets closer to the theoretical probability.