Answer:
at 95% confidence interval, the mean amount of sleep per night is ( 7.87, 8.05 ).
Option b) (7.87, 8.05) is the correct answer.
Step-by-step explanation:
Given the data in the question;
sample size n = 1140
sample mean x" = 7.96
standard deviation σ = 1.6
At 95% confidence interval,
significance level ∝ = 1 - 95% = 1 - 0.95 = 0.05
∝/2 = 0.05 / 2 = 0.025
Z-Critical [tex]Z_{\alpha /2[/tex] = [tex]Z_{0.025[/tex] = 1.96
Top get the Margin of error E;
E = [tex]Z_{\alpha /2[/tex] × ( σ /√n )
we substitute
E = 1.96 × ( 1.6 /√1140 )
E = 0.09
So, At 95% confidence interval of the population mean is;
⇒ x" ± E
⇒ x" - E or x" + E
we substitute
⇒ 7.96 - 0.09, 7.96 + 0.09
⇒ 7.87, 8.05
Therefore, at 95% confidence interval, the mean amount of sleep per night is ( 7.87, 8.05 ).
Option b) (7.87, 8.05) is the correct answer.
The work of a student trying to solve the equation 4(2x − 1) = 11 + 3x + 5 is shown below:
Step 1: 4(2x − 1) = 11 + 3x + 5
Step 2: 8x − 4 = 16 + 3x
Step 3: 8x + 3x = 16 − 4
Step 4: 11x = 24
Step 5: x = 2.18
In which step did the student first make an error and what is the correct step?
Step 2: 8x − 1 = 16 + 3x
Step 2: 8x − 8 = 6 + 3x
Step 3: 8x − 3x = 16 + 4
Step 3: 8x + 3x = 16 − 8
In which step did the student first make an error and what is the correct step?
Step 2: 8x − 1 = 16 + 3x
Step 2: 8x − 8 = 6 + 3x
Step 3: 8x − 3x = 16 + 4
Step 3: 8x + 3x = 16 − 8
Answer: 8x -3x = 16+4
Step-by-step explanation:
Find the area of the circle:
Answer:
12.56
Step-by-step explanation:
A = 3.14*2^2 = 12.56
Students were asked to choose their favorite sport. If 1/8 of the students chose soccer and 2/8 chose basketball, what fraction chose either soccer or basketball?
What is the solution to the equation 1.2m − 0.8 = −2.0m?
m = 0.25
m = 0.4
m = 1
m = 4
Answer:
m = 0.25
Step-by-step explanation:
1.2m − 0.8 = −2.0m
Both side +2.0m
1.2m+2.0m-0.8=-2.0m+2.0m
Both side +0.8
3.2m=0.8
Both side divided by 3.2m
[tex]\frac{3.2}{3.2}[/tex]m=[tex]\frac{0.8}{3.2}[/tex]
1×m=[tex]\frac{0.8}{3.2}[/tex]
m = 0.25
The answer is 0.25
Researchers studying two populations of wolves conducted a two-sample t-test for the difference in means to investigate whether the mean weight of the wolves in one population was different from the mean weight of the wolves in the other population. All conditions for inference were met, and the test produced a test statistic of t=2.771 and a p-value of 0.01.
Which of the following is a correct interpretation of the p-value?
a. Assuming that the mean weights of wolves in the populations are equal, the probability of obtaining a test statistic that is greater than 2.771 or less than −2.771−2.771 is 0.01.
b. Assuming that the mean weights of wolves in the populations are equal, the probability of obtaining a test statistic that is greater than 2.771 is 0.01.
c. Assuming that the mean weights of wolves in the populations are different, the probability of obtaining a test statistic that is greater than 2.771 or less than −2.771−2.771 is 0.01.
d. Assuming that the mean weights of wolves in the populations are different, the probability of obtaining a test statistic that is greater than 2.771 is 0.01.
e. Assuming that the mean weights of wolves in the populations are different, the probability of obtaining a test statistic that is less than 2.771 is 0.01.a
Answer:
c. Assuming that the mean weights of wolves in the populations are different, the probability of obtaining a test statistic that is greater than 2.771 or less than −2.771 is 0.01.
Step-by-step explanation:
Test if the sample means were different:
This means that we have a two-tailed test.
t=2.771 and a p-value of 0.01.
0.01 is the p-value of t = 2.771 multiplied by 2, as we have a two-tailed test(counting both more than 2.771 and less than -2.771). This represents the probabiility of obtaining a test statistic that is greater than 2.771 or less than −2.771 is 0.01, and the correct answer is given by option c.
Looking in her food pantry, Professor Martinez finds a package of 12 flavored water bottles. The package contains 5 strawberry flavored water bottles and 7 mango flavored water bottles, each without labeling. All the bottles look alike and have equal probability of being chosen. Three bottles are randomly selected without replacing them.
a. The probability that all (exactly three) bottles are strawberry flavored is: _______
b. The probability that at least one of the three bottles are strawberry flavored is: _________
c. The probability that exactly 2 bottles are strawberry flavored is: _________
Answer:
a) 12/24 * 11/24*10/24
b) 1 - 12/24 * 11/24*10/24
c) 12/24 * 11/24 *12/24
Step-by-step explanation:
Total number of bottles = 12 + 5+7 = 24
a. The probability that all (exactly three) bottles are strawberry flavored is: 212
12/24 * 11/24*10/24
b. The probability that at least one of the three bottles are strawberry flavored is:
1 - P (no strawberry bottle)
1 - (12/24*11/24*10/24)
c. The probability that exactly 2
12/24 * 11/24 *12/24
Use a table of values to find the solution to the equation f(x)=h(x) where
f (x) = 2/3-x and
h(x)= 3- 2x
Show your work
9514 1404 393
Answer:
x = 2 1/3
Step-by-step explanation:
We can examine the equations to see where the solution lies.
f(x) = (2/3) -x
This has an x-intercept where y=0, at x=2/3. It has a y-intercept where x=0, at y=2/3. Its slope is -1.
h(x) = 3 -2x
This has an x-intercept where y=0, at x=3/2. It has a y-intercept where x=0, at y=3. Its slope is -2.
__
In the first quadrant, the graph of h(x) is farther from the origin and steeper than the graph of f(x). The lines must cross in the 4th quadrant at some value of x that is greater than 3/2. The fraction in the definition of f(x) suggests that the solution will be a multiple of 1/3.
The attached table shows a couple of guesses at values of x that would make f(x) = h(x). We find that x = 7/3 is the solution we're looking for.
_____
Additional comment
Repetitive function evaluations are done conveniently and with fewer errors by a calculator or spreadsheet that can work with tables of values. Here, we have used a graphing calculator. These tools are readily available for free on almost any phone, tablet, or desktop computer platform.
Write the equation in slope intercept form. -2x-8y= 24
- please help
Answer:
y= -2/8x + 3
Step-by-step explanation:
Step-by-step explanation:
The slope-intercept form of the equation is :
y = mx+b
The given equation is :
-2x-8y= 24
Taking x term to RHS.
-8y = 24 +2x
Dividing both sides by -8
[tex]\dfrac{-8y}{-8} = \dfrac{24}{-8} +\dfrac{2x}{-8}\\\\y=-3-\dfrac{x}{4}\\\\or\\\\y=\dfrac{-1}{4}x+(-3)[/tex]
Hence, this is the required solution.
the perimeter p of a square is 4 times the length of a side x
Answer:
p = 4x
Step-by-step explanation:
The perimeter p of a square is 4 times the length of a side x
p = 4x
5/8 is the fraction that if added to 3/8 gives you the sum of 1 whole
Answer:
true
Step-by-step explanation:
your answer is correct
if a bag of rice weighs 55 kg find the weight of 123 bags of rice
Answer:
6765
Step-by-step explanation:
the answer is 6765
Answer: 6,765 kg
Step-by-step explanation:
55 x 123 = 6,765kg of Rice
Please help I’m stuck :((((((((((((((((((
Answer:
$3.72
hope this helps
have a good day :)
Step-by-step explanation:
Because 1 orange cost 0.93 so you multiply it by 4 to get 3.72
Answer:
$3.72
Step-by-step explanation:
ok so we need to divide 2.79÷3 so we can know how much each orange coast.
2.79÷3 = 0.93
now add 0.93 to 2.79
2.79+0.93 = 3.72
solve all of them for brianiest
Answer:
1.x= 3/-4-2 = x = 11/4
2.1.5x /1.5 = x
6/1.5=4
x=4
Laura uses 3 yards of fabric to make 2 skirts. She uses the same amount of
fabric to make each skirt. At this rate, what is the total amount of fabric, in
yards, she needs to make 6 skirts?
Answer:
9 yards
Step-by-step explanation:
3 yards make 2 skirts
2x3=6
3x3=9
9 yards make 6 skirts
Consider the sequence {3,6,9,12,15,…}. Find n if an = 735. Show all steps including the formulas used to calculate your answer.
Will mark brainliest!
Answer:
n = 245
Step-by-step explanation:
The given sequence is 3,6,9,12,15,…
nth term of the AP is 735
We know that, the nth term of an AP is given by :
[tex]a_n=a+(n-1)d[/tex]
d is common difference, d = 6-3 = 3
Put all the values to find n.
[tex]735=3+(n-1)3\\\\732=(n-1)3\\\\\dfrac{732}{3}=n-1\\\\n=244+1\\\\n=245[/tex]
So, there are 245 terms in the sequence.
I received a letter from your competitor that mentions a savings of 15% over your prices. Can you match this offer? My current rate is $129.00 per month."
discribe the sides of polygon c
The profit function of a manufacturer, in dollars, when x units of a certain commodity are produced and sold is given by
P(x)=200x−x2.
(a) The maximum profit is
dollars.
(b) The number of units produced and sold to get the maximum profit is
units.
Answer:
Derivative: P’(x) = 200 - 2x
If P’(x) = 0 , x = 100
Therefore P’ is positive and P increases until x = 100
So the maximum units to maximize profits is 100 units
And for 100 units the profit in dollar is:
20000 - 10000 = 10000
10000 dollars
in a fruit basket , there are 6 apples and 3 oranges . what fraction of the basket are apples ?
Answer:
6/9=2/3
hope this helps
have a good day :)
Step-by-step explanation:
Answer: 6/9
Step-by-step explanation:
btw can you please help me with my latest question in my profile? Would really appreciate it!
~Help please and ty~ ✨Brainilist✨
Answer:
[tex]\frac{10}{27}[/tex]
Step-by-step explanation:
[tex]-\frac{2}{9} (-\frac{5}{3})=[/tex]
-2 · 5/ -9 · 3 =
10/27 =
[tex]\frac{10}{27}[/tex]
Answer:
[tex]\frac{10}{27}[/tex]
Step-by-step explanation:
[tex]\frac{-2}{9} *\frac{-5}{3}[/tex]
multiply numerator with the other numerator
-2 × -5 = 10 (numerator)
multiply denominator with the other denominator
9 × 3 = 27 (denominator)
put it in its correct order
[tex]\frac{10}{27}[/tex]
I need answer to both of the questions please someone!! 20points
Answer:
Step-by-step explanation:
x+62=90 degree (being perpendicular)
x=90-62
x=28 degree
x+25=90 (being perpendicular)
x=90-25
x=65 degree
Answer:
1)X+62 =90
x+62-62=90-62
x =28
2) X+25+90+180 =360
x +295=360
x =360-295
x =65
Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and d are integers.
1. x2 - 6x + 8 = (ax + b)(cx + d)
2.3x3 - 6x2 - 24x = 3x(ax + b)(cx + d)
3. 2x2 - 2x - 24 = (ax + b)(cx + d)
Fill in the table with the missing values of a, b, c, and d.
9514 1404 393
Answer:
(a, b, c, d) = (1, -4, 1, -2)(a, b, c, d) = (1, -4, 1, 2)(a, b, c, d) = (1, -4, 2, 6)Step-by-step explanation:
Once you remove the common factor from the terms, you are looking for factors of the remaining constant term that have a sum equal to the coefficient of the linear term. These factors are the constants in the binomial factors.
__
1. 8 = (-4)(-2) ⇒ x^2 -6x +8 = (x -4)(x -2)
(a, b, c, d) = (1, -4, 1, -2)
__
2. -8 = (-4)(+2) ⇒ 3x^3 -6x^2 -24x = 3x(x -4)(x +2)
(a, b, c, d) = (1, -4, 1, 2)
__
3. -12 = (-4)(3) ⇒ 2x^2 -2x -24 = 2(x -4)(x +3) = (x -4)(2x +6)
(a, b, c, d) = (1, -4, 2, 6) or (2, -8, 1, 3)
PLEASEE HELPP ASAP!
Consider a right triangle which is
changing shape in the following
way. The horizontal leg is
increasing at the rate of 11 in/min
and the vertical leg is decreasing
at the rate of 5 in/min. At what rate <
is the hypotenuse changing in
in/min when the horizontal leg is 12
inches and the vertical leg is 9
inches?
Answer:
Step-by-step explanation:
GIVEN: dx / dt=5 in./min. and dy/ dt=−6 in./min.
FIND: dz/ dt when x=12 in. and y=9 in.
Use the Pythagorean Theorem to get the equation
x2+y2=z2
Now differentiate this equation with repect to time t getting
D{x2+y2}=D{z2} ⟶
2xdxdt+2ydydt=2zdzdt ⟶
(Multiply both sides of the equation by 1/2.)
x dx/ dt+y dy/ dt= z dz/ dt (DE)
Now let x=12 and y=9 and solve for z using the Pythagorean Theorem.
tex2html_wrap_inline125
122+92=z2 ⟶ z2=225 ⟶ z=15
Plug in all given rates and values to the equation (DE) getting
(12)(5)+(9)(−6)=(15)dz/ dt ⟶
6=15dzdt ⟶
dz/ dt=615=25 in/min.
Hope this answer helps you :)
Have a great day
Mark brainliest
Classify the triangle by its sides and angles. 48.3 cm 48.3 cm 48.3 cm not drawn to scale a. equilateral, right b. scalene, right C. isosceles, acute d. equilateral, acute
Answer:
D
Step-by-step explanation:
Equilateral acute because all sides are equal
If sin theta equals 12 divided by 13 and theta is in quadrant 2 cos20 equals? and cos theta equals?
Answers:
cos(2theta) = -119/169cos(theta) = -5/13=====================================================
The given info is:
sin(theta) = 12/13theta is in quadrant IIFrom that, we can use the pythagorean trig identity to find that cos(theta) = -5/13. Keep in mind that cosine is negative in quadrant II.
Now use the trig identity below to compute cos(2theta)
[tex]\cos(2\theta) = \cos^2(\theta)-\sin^2(\theta)\\\\\cos(2\theta) = \left(\frac{-5}{13}\right)^2-\left(\frac{12}{13}\right)^2\\\\\cos(2\theta) = \frac{25}{169}-\frac{144}{169}\\\\\cos(2\theta) = \frac{25-144}{169}\\\\\cos(2\theta) = -\frac{119}{169}\\\\[/tex]
Other options you could use are these identities
[tex]\cos(2\theta) = 2\cos^2(\theta)-1\\\\[/tex]
or
[tex]\cos(2\theta) = 1-2\sin^2(\theta)\\\\[/tex]
The question is in the picture (Alegbra 1)
Answer:
[tex] \frac{s}{s + 3} [/tex]
Answer:
S/S+3
Step-by-step explanation:
Hope this helps...
PLS ANWER ASAP!! person with correct answer will be marked brainliest
Answer:
62 degrees since there are supplementary angles
Step-by-step explanation:
∠PQO= 180 degrees - 118 degrees
∠PQO= 62 degrees is the answer.
∠PQO= 180°-∠RQO -------(Supplementary Angles)
∠PQO= 180° - 118°
∠PQO= 62° answer.
the perimeter of a square is 75 cm what is the length of one side of the square
Answer:
length of one side = 18.75cm
Step-by-step explanation:
Perimeter of a square = 4 x side
75 = 4 x side
[tex]side = \frac{75}{4} = 18.75cm[/tex]
Find the area of the figure
Answer:
75
Step-by-step explanation:
Answer:
Area of Figure = 75 sq. units
Step-by-step explanation:
Top Half-Portion: 30 sq. units
Dimensions: 6x5
6 x 5 = 30
Botton Half-Portion: 45 sq. units
Dimensions: 9x5
9 x 5= 45
45 + 30 = 75
What is the value of the following expression when
y = 4?
y³ + 6
Answer:
70
Step-by-step explanation:
y^3 +6
Let y=4
4^3 +6
64+6
70