Answer:
a. (0.313,0.447)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Researchers investigating a new drug selected a random sample of 200 people who are taking the drug. Of those selected, 76 indicated they were experiencing side effects from the drug.
This means that [tex]n = 200, \pi = \frac{76}{200} = 0.38[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.38 - 1.96\sqrt{\frac{0.38*0.62}{200}} = 0.313[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.38 + 1.96\sqrt{\frac{0.38*0.62}{200}} = 0.447[/tex]
The correct answer is given by option A.
x^2=-28 square root method
Answer:
2i[tex]\sqrt{7}[/tex],-2i[tex]\sqrt{7}[/tex]
Hurry up please timed test
Answer:
the second option
hope this helps!
f
Solve the equation + 22 = 17.
3
Answer: subtract 22 on both sides
Step-by-step explanation:
Now you would have -5 to solve take 3 and multiply on both sides to get f=-15
Hope this helps
Answer: -5
Step-by-step explanation:
Jamal borrowed $316 for nine months. He paid it off by paying $38.27 monthly.
What will he pay in finance charges?
The finance charge payed by Jamal is $28.43.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Amount borrowed by Jamal for nine months = $316
His monthly payment = $38.27
Total amount payed by Jamal for nine months = [tex]9(38.27)[/tex]
⇒ [tex]\$344.43[/tex]
Thus his finance charge = [tex]344.43-316[/tex]
⇒ [tex]\$28.43[/tex]
Hence we can conclude that the finance charge payed by Jamal is $28.43.
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Which of the following could be the equation of the function below?
y=0.5cos(2(x-pi/2))+2 y=0.5cos(4(x+pi/2))-2 y=0.5cos(4(x+pi))+2 y=0.5cos(2(x-pi))-2
Answer:
D y=0.5cos(2(x-pi))-2
Step-by-step explanation:
The Equation of the function is y=0.5 cos (4(x+π/2))-2
The correct option is B.
As, y=a cos (b(x+c))+d
Here, y max=-1.5 and y min=-2.5
So, d=(max + min)/2
d=(-1.5+(-2.5))/2
d=(-1.5-2.5)/2
d=(-4.0)/2
d=-2.0
and, the horizontal axis is
y=-2
Then, y= a cos(b(x+c))+(-2)
y=a cos (b(x+c))-2
The amplitude (a) is
a = max-d = d- min
a=-1.5-(-2)=-2-(-2.5)
a=-1.5+2=-2+2.5
a=0.5.
We have the period is π/2
P=2π/b
π/2=2π/b
πb=4π
b=4
Now, y=0.5 cos (4(x+c))-2
Thus, the required function is y=0.5 cos (4(x+π/2))-2.
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Which statements are true about the graph of y s 3x + 1 and y 2 -x + 2? Check all that apply.
O The slope of one boundary line is 2.
O Both boundary lines are solid.
A solution to the system is (1, 3).
O Both inequalities are shaded below the boundary lines
O The boundary lines intersect.
===========================================================
Explanation:
Let's go through each of the answer choices to see which are true and which are false.
----------------
Choice A
The general slope intercept form is y = mx+b
m = slope and b = y intercept.
For y = 3x+1, the boundary line of the first inequality, the slope is 3.
For y = -x+2, the slope is -1.
None of the slopes are 2.
Choice A is false.
We'll use the concept of slope again in choice E.
----------------
Choice B
The "or equal to" part of the inequality sign is what directly determines the boundary line being solid. This is because we include points on the boundary.
Choice B is true.
----------------
Choice C
Plug x = 1 and y = 3 into the first inequality
[tex]y \le 3x+1\\\\3 \le 3(1)+1\\\\3 \le 3+1\\\\3 \le 4\\\\[/tex]
The last inequality is true, so the first inequality is true when (x,y) = (1,3). This makes (1,3) a solution to [tex]y \le 3x+1\\\\[/tex]
Repeat those steps for the other inequality given to us
[tex]y \ge -x+2\\\\3 \ge -1+2\\\\3 \ge 1\\\\[/tex]
which is also true, so that makes (1,3) also a solution to [tex]y \ge -x+2\\\\[/tex]
The point (1,3) is a solution to both inequalities at the same time, making it a solution to the system overall.
Choice C is true
----------------
Choice D
When y is fully isolated, the "less than" inequality indicates the shading is below the boundary. This is due to us considering points of y coordinates smaller than the boundary line. So we'll shade below the boundary for [tex]y \le 3x+1\\\\[/tex]
We don't do the same for [tex]y \ge -x+2\\\\[/tex]. Instead, we'll shade above the solid boundary line.
Choice D is false.
----------------
Choice E
If two lines have equal slopes, but different y intercepts, then we have parallel lines. Parallel lines never intersect.
If on the other hand, the slopes are different values, then the two lines will intersect somewhere on the xy grid. There will only be exactly one point of intersection.
The given system has boundary lines of slopes 3 and -1, for the first and second inequality respectively. Refer back to choice A. These differing slopes tell us that the boundary lines intersect somewhere.
Choice E is true
Let's go through all the options one at a time and look for the correct ones
Option 1: The slope of one boundary line is 2
We have 2 equations of lines, where the coefficients of are 3 and -1 respectively
because the coefficient of x denotes the slope of a line, we know that the lines have the slope 3 and -1, not 2
Hence, this option is Incorrect
Option 2: Both boundary lines are solid
In order for the boundary lines to be solid, the inequality must have an 'equal to', like ≤ (less than or equal to) or ≥ (greater than or equal to)
we can see that that's the case in our case and hence, this option is Correct
Option 3: A solution to the system is (1, 3)
To confirm this, we'll plug these coordinates into the given inequalities and see if it stands correct
y ≤ 3x + 1
3 ≤ 3(1) + 1
3 ≤ 4 which is correct because 3 is less than 4
Second equation:
y ≥ 2 - x
3 ≥ 2 - 1
3 ≥ 1
Which is also true because 3 is greater than 1
Now, we can say that (1 , 3) is a solution to the system because it satisfies both the equations and is Correct
Option 4: Both inequalities are shaded below the boundary lines
For an inequality to be shaded below the boundary line, it must have the ≤ inequality (in case of solid line) and < inequality (in case of dotted line)
because the second inequality listed includes the ≥ inequality, which was not mentioned above, it won't be shaded below
another way to think about it is that any 'greater than' inequality will shade everything above the line and the 'lesser than' inequality will shade below the line
which means that this option is Incorrect
Option 5: The boundary lines intersect
In order for the boundary lines to intersect, they must have have different slopes.
as we mentioned in the explanation of the first option, that the slopes of the lines is 3 and -1, which are different slopes
Therefore, this option is Correct
if the radius of an argon atom is 0.0000000000098m, write in scientific notation
Answer:
90
Step-by-step explanation:
A line that passes through points (x, 4) and (6, -1) has a slope of 5/6. What value of x will yield the given slope?
A: x = -12
B: x = 0
C: x = -6
D: x = 12
In parallelogram LMNO, the measure of N= 98° and the measure of 0= 82°. Find the measure of M.
Answer:
82
Step-by-step explanation:
180 - 98=82
The sum of two angels is 180
If the triangles below are similar, find the value of x. 42 х 11 22
9514 1404 393
Answer:
28
Step-by-step explanation:
Corresponding sides are proportional.
x/42 = 22/(22+11)
x = 42(2/3)
x = 28
The spinner has 8 congruent sections. What is the probability of
spinning a number divisible by 3 two times in a row?
Answer:
1/16 or 0.0625
Step-by-step explanation:
There are two numbers on the chart that are divisible by 3.
So the odds of spinning and getting one of those on the first try would be 2/8 or 1/4.
The odds are then multiplied by the chance of spinning it again on the second try, which would still be 1/4.
To get: 1/16
What is the probability that the card is not a heart, GIVEN that the card is a face card??
Best answer gets brainliest!!
Answer:
.75
Step-by-step explanation:
Conditonal probability formula:
A|B= (A∩B)/B
let NH= Not heart
Let F= Face
NH|F= NH∩F/F
not hearth and face is 9
face is 12
9/12=.75
Please no troll include work
Answer Choices:
A. 0.26
B. 0.56
C. 0.52
D. 0.31
If you answer back with a link your comment will be reported.
Find the value of x in the isosceles triangle below.
need this ASAP! Please include an explanation if possible
Answer:
x = 64
Step-by-step explanation:
Remark
The markings on the triangle tell us that the sides are equal. There is no marking on the third side, so it is not equal to the other two. The important fact is the angles opposite equal sides are also equal. That means that the angle on the lower right is equal to x.
Equation
So you have two angles = to x.
x + x + 52 = 180 All triangles have interior angles of 180
2x + 52 = 180 Combine the like terms on the left.
- 52 -52 Subtract 52 from both sides
2x = 128 Divide by 2
2x/2 = 128/2
x = 64
3 9 26
a. Use eoch digit once, make the smallest 4-digit number:
b. Use each digit once, moke the largest 4-digit number :
c. You can use one diga twice, make the smallest 4-digit number:
c. You con use one digit twice make the largest 4-digit number
.
I’m confused can somebody answer this?
14 is the asnwer because sqaure root of 200 is 14.14213562 and if you round that it is 14
There are 44 rabbits. What is 44 rounded to the nearest 10?
Answer:
4
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
44 is closer to 40 than 50 because 44-40 = 4, 50-44=6 and 4<6
Solve for 44.
4 4 = [?]
510
51
44/42
Angle 4 is an exterior angle which is equal to the sum of the two opposite inside angles.
The two opposite inside angles are given as 51 and 51
Angle 3 = 51 + 51 = 102 degrees.
Answer:
[tex] \displaystyle \angle4 = {108}^{ \circ} [/tex]
Step-by-step explanation:
the sum of the interior angles of a triangle is 180°
thus our equation is
[tex] \displaystyle {51}^{ \circ} + {51}^{ \circ} + \angle2 = {180}^{ \circ} [/tex]
simplify addition:
[tex] \displaystyle {102}^{ \circ} + \angle2 = {180}^{ \circ} [/tex]
cancel 102° from both sides:
[tex] \displaystyle \angle2 = {72}^{ \circ} \cdots \text{I}[/tex]
By straight line theorem we acquire:
[tex] \displaystyle \angle4 + \angle2 = {180}^{ \circ} [/tex]
substitute:
[tex] \displaystyle \angle4 + {72}^{ \circ} = {180}^{ \circ} [/tex]
cancel 72° from both sides:
[tex] \displaystyle \angle4 = {108}^{ \circ} [/tex]
hence, the measure of [tex]\angle 4[/tex] is 108°
What is the value of n in the equation shown below?
2² x 21 = (24)3
Answer:
4
Step-by-step explanation:
i hope this helped :]
X-y=6, x+y=8, zx+zy=20
Answer:
Step-by-step explanation:
x = 6 + y
6 + y + y = 8
y = 1
x - 1 =6
x = 7
zx + zy = z(x + y) = 20
z = 2.5
Answer:
X = 7
Y = 1
Z = 2/5
Step-by-step explanation:
7-1 = 6
7+1 = 8
2/5 × 7 + 2/5 = 20
If Rashid faces north and then turns clockwise half a turn, in which direction does he face
Answer:naneeeeee
Step-by-step explanation:
Help with Math Question 1
Answer:
Step-by-step explanation:
X is also 67° Like the interior angle
3b.) Nora is buying a used car valued at $22,730. It is expected to
depreciate an average of 9.5% each year. Predict the value of Nora's car in
6 years.
Help ??
Answer:
$12487.86
Step-by-step explanation:
Given data
Cost of car= $22,730
Rate of decrease= 9.5%
Time= 6 years
We can predict the value by using the exponential decay function'
A= P(1-r)^t
substitute
A= 22730(1-0.095)^6
A= 22730(0.905)^6
A= 22730*0.5494
A=$12487.86
Hence the value will be $12487.86
you have it $15 for the movie the cost of a movie ticket is $3 write an inequality to show how much money you can spend on treats.
Answer:
$3+x is less than or equal to $15
Step-by-step explanation:
I can't write the sign but it's < with a line under it
Step-by-step explanation:
y≥15-3
I am not sure
Lin drew this set of axes and plotted the points A=(1,2), B=(-3, -5), C=(5,7), D=(-4, -3), and E=(-4, 6) on them. Identify her mistakes! Which points were plotted incorrectly?
Answer:
B=(-3, -5)
Step-by-step explanation:
In square units!!! Real answers only please no links!!!!
don’t mind the pencil writing
Answer:
Length = 22 cm
Width = 4 cm
Step-by-step explanation:
Area = 88 cm²
Length = x + 7
Width = x - 11
Area of rectangle = length*width
Therefore:
(x + 7)(x - 11) = 88
x(x - 11) +7(x - 11) = 88
x² - 11x + 7x - 77 = 88
Add like terms
x² - 4x - 77 = 88
x² - 4x - 77 - 88 = 88 - 88
x² - 4x - 165 = 0
Factorize
x² - 15x + 11x - 165 = 0
x(x - 15) +11(x - 15) = 0
(x + 11)(x - 15) = 0
x = -11 or x = 15
Let's use the positive number.
Therefore:
Length = x + 7
Plug in the value of x
Length = 15 + 7 = 22 cm
Width = x - 11 = 15 - 11 = 4 cm
solve each of the following systems, if possible. indicate whether the system has a unique solution, infinitely many solutions, or no solution.
a. 2x + 10y = 9
3x + 15y = 13
b. 2x + 8y = 5
3x + 12y = 7.5
c. y = 3-x
d. 5x -8y = -1
-5/2 x + 4y = 1/2
Answer:
(a) No solution
(b) Infinitely many solution
(c) No solution
(d) Infinitely many solution
Step-by-step explanation:
Solving (a):
[tex]2x + 10y = 9[/tex] --- (1)
[tex]3x + 15y = 13[/tex] --- (2)
Multiply (1) by 1.5
1.5 * [[tex]2x + 10y = 9[/tex]]
[tex]3x + 15y = 13.5[/tex] --- (3)
Subtract 2 and 3
[tex]3x - 3x + 15y - 15y = 13.5 - 13[/tex]
[tex]0 = 0.5[/tex]
The above is false; Hence, the system has no solution
Solving (b):
[tex]2x + 8y = 5[/tex] --- (1)
[tex]3x + 12y = 7.5[/tex] -- (2)
Multiply 1 by 1.5
1.5 * [[tex]2x + 8y = 5[/tex]]
[tex]3x + 12y = 7.5[/tex]
Subtract 2 and 3
[tex]3x - 3x + 12y - 12y = 7.5 - 7.5[/tex]
[tex]0 = 0[/tex]
The above implies that the system has infinitely many solutions
Solving (c):
[tex]y = 3 - x[/tex]
A second equation is required to solve for (c)
Solving (d):
[tex]5x - 8y = -1[/tex] --- (1)
[tex]-\frac{5}{2}x+ 4y = \frac{1}{2}[/tex] --- (2)
Multiply (2) by 2
[tex]-5x + 8y = 1[/tex] --- (3)
Add 1 and 3
[tex]5x - 5x -8y + 8y = -1 + 1[/tex]
[tex]0 = 0[/tex]
The above implies that the system has infinitely many solutions
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using Minitab, resulting in the accompanying output.
Variable N Mean St Dev SEMean Z P -Value
lifetime 50 738.44 38.20 5.40 -2.14 0.016
What conclusion would be appropriate for a significance level of .05? A significance level of .01? What significance level and conclusion would you recommend?