Complete question:
One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hours is desired. Past studies suggest that a population standard deviation of 1.5 hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Answer:
111 students
Step-by-step explanation:
Given the following :
Margin of Error (E) = 0.28
Population standard deviation (sd) = 1.5
Recall:
Margin of Error(E) = Z * (sd/√n)
Taking a confidence interval of 95%
The Z value at a 95% confidence interval is 1.96
Plugging our values, we have :
Margin of Error(E) = Z * (sd/√n)
0.28 = 1.96 * (1.5/√n)
0.28 = 2.94 / √n
√n × 0.28 = 2.94
√n = 2.94 / 0.28
√n = 10.5
Square both sides to obtain n
n = 10.5^2
n = 110.25
solve 16y = 80
show work please i wanna understand!
Answer:
Step-by-step explanation:
16y = 80
You want to get y by itself so you divide 80 by 16
y = 80/16
y = 5
Hope I helped
The solution to the equation 16y = 80 is y = 5.
To solve the equation 16y = 80 for the variable y, you can follow these steps:
Step 1: Divide both sides of the equation by 16 to isolate the variable y:
(16y)/16 = 80/16
y = 5
Therefore, the solution to the equation is y = 5.
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given that -6,-6 is on the graph of f x find the corresponding point for the function f(3/4x)
Answer:
The corresponding point is (-8, -6).
Step-by-step explanation:
Given that
(-6,-6) lies on the graph of [tex]f(x)[/tex]
A function is represented in the form:
[tex]y = f(x)[/tex]
i.e. (-6,-6) means value of x = -6 is put and value y came out as -6.
[tex]f(-6) = -6[/tex]
Now, we have to find the corresponding point on [tex]f(\frac{3}{4}x)[/tex].
We know the value of [tex]f(-6)[/tex]
Let us find the value of x where [tex]\frac{3}{4}x[/tex] becomes equal to -6
[tex]\dfrac{3}{4}x=-6\\\Rightarrow 3x=-24\\ \Rightarrow x =-8[/tex]
So, let us put value of [tex]x = -8[/tex] in [tex]f(\frac{3}{4}x)[/tex]:
[tex]f(\frac{3}{4}\times (-8))\\\Rightarrow f(3\times (-2))\\\Rightarrow f(-6) = -6[/tex](as per given statement)
So, the corresponding point is (-8, -6).
A paintball court charges an initial entrance fee plus a
fixed price per ball.
P represents the total price (in dollars) as a function of
the number of balls used n.
P=0.80n + 5.50
What is the price for 10 balls, not including the
entrance fee?
$....
Answer:
$8
Step-by-step explanation:
Firstly, Let us identify the variables in the functions.
The function states that for every n ball, the price is $0.80. Plus the $5.50.
Now that we know what the function stands for, we can substitute 10 into n, and remove the entrance fee of $5.50.
P=0.80n
This gives us $8, which means the price for 10 balls not including the entrance fee is $8.
Suppose a shoe company estimates that its monthly cost is
C(x) = 300c2 + 200c and its monthly revenue is
R(x) = -0.5x3 + 900x2 – 500x + 400, where x is in thousands of pairs
of shoes sold. The profit is the difference between the revenue and the cost.
What is the profit function, P(x)?
O
A. P(x) = -0.5x3 + 600x2 – 700x + 400
B. P(2) = -0.5x3 + 1200x2 – 300x + 400
O C. P(x) = 0.523 + 60022 – 700.0 + 400
O D. P(x) = 0.523 – 600x2 + 700x – 400
PREVIOUS
I
Answer:
Hello,
Answer B
Step-by-step explanation:
[tex]C(x)=300*x^2+200*x\\\\R(x)=-0.5*x^3+900*x^2-500*x+400\\\\\\P(x)=R(x)-C(x)\\\\=-0.5*x^3+900*x^2-500*x+400-(300*x^2+200*x)\\\\=-0.5x^3+900x^2-300x^2-500x-200x+400\\\\=-0.5x^3+600x^2-700x+400\\[/tex]
Find the measure of a. A. 48 B. 90 C. 44 D. 84
Answer:
A. 48
Step-by-step explanation:
There is a diameter of the circle through point O. The bottom right angle is an inscribed and that intersects a diameter, so its measure is 90 deg.
a + 90 + 42 = 180
a + 132 = 180
a = 48
The measure of angle 'a' is 48°.
We need to find the measure of 'a'.
What is the circle theorem of diameter?Angles are formed by drawing lines from the ends of the diameter of a circle to its circumference from a right angle.
There is a diameter of the circle through point O. The bottom right angle is inscribed and that intersects a diameter, so its measure is 90°.
Now, a + 90°+ 42° = 180°
⇒a + 132°= 180°
⇒a = 48°
Therefore, the measure of angle 'a' is 48°.
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After a 20% reduction, you purchase a tv for $336. What was the price of the tv before the reduction?
Answer:
$420
.8 x = 336
x = 336/.8
X=$420
Step-by-step explanation:
a diagonal of rectangle forms a 30 degree angle with each of the longer sides of the rectangle. if the length of the shorter side is 3, what is the length of the diagonal
Answer:
Length of diagonal = 6
Step-by-step explanation:
Given that
Diagonal of a rectangle makes an angle of [tex]30^\circ[/tex] with the longer side.
Kindly refer to the attached diagram of the rectangle ABCD such that diagonal BD makes angles of [tex]30^\circ[/tex] with the longer side CD and BA.
[tex]\angle CDB =\angle DBA =30^\circ[/tex]
Side AD = BC = 3 units
To find:
Length of diagonal BD = ?
Solution:
We can use the trigonometric ratio to find the diagonal in the [tex]\triangle BCD[/tex] because [tex]\angle C =90^\circ[/tex]
Using the sine :
[tex]sin\theta = \dfrac{Perpendicular }{Hypotenuse }[/tex]
[tex]sin\angle CDB = \dfrac{BC}{BD}\\\Rightarrow sin30^\circ = \dfrac{3}{BD}\\\Rightarrow \dfrac{1}2 = \dfrac{3}{BD}\\\Rightarrow BD =2 \times 3 \\\Rightarrow BD = \bold{6 }[/tex]
So, the answer is:
Length of diagonal = 6
* Graph these numbers on a number line.
-5,3, -2,1
-5
-5,3,-2,1 on a number line
<-|----|----|----|----|----|----|----|----|->
-5 -2 0 1 3
Thomas had 19 problems correct of the 25 problems on a recent math quiz. What percent of the
problems on the quiz did he answer correctly?
A.
24%
B. 36%
C. 76%
D.95%
Hey There!!
Your best choice is 76%
Because, 19/25 = x/100
25x = 1900
x = 76
°He got 76% correct!!°
By °Itsbrazts°
Answer:
76%
Step-by-step explanation:
Thomas got 19/25 marks.
** Note: Percents are always out of 100.
We don't know how many marks he got out of 100.
=> 19/25 = x/100
There are two ways to solve it from now.
=> Multiply 19 and 100; 25 and x
=> 25x = 1900
Next, Divide 25 on each side.
=> 25x/25 = 1900/25
=> x = 76
He got 76% on the quiz.
Another way is:
=> 19/25 = x/100
=> We need to divide 25 from 100.
=> We get 4.
So, 25 x 4 = 100
=> 19 x 4 = x
=> x = 76
He got 76% on the quiz.
Both ways are correct.
PLS HELP ME!!!
A sample is generated from a population of 20 items. Each of the 20 items are given a label, and a 20-sided die is rolled 3 times to determine which 3 items are in the sample. This is an example of a __________.
A. systematic sample
B. random sample
C. convenience sample
D. self-selecting sample
Answer:
Option B, random sample
That should be the answer
the fastest land dwelling creature is the cheetah. fact or
opinion
Answer:
True.
Step-by-step explanation:
Cheetahs can reach speeds of 109.4–120.7 km/h (68.0–75.0 mph), and some have been recorded at over 80mph. The cheetah can accelerate from 0 to 96.6 km/h (60.0 mph) in under three seconds, though endurance is limited.
The second fastest land animal is the Pronghorn antelope at 98kph (60mph).
Answer:
It is a Fact because it can run 70mph or 112kph
Is 3+(-4) the same as -4+3 ? Explain
-18 = -3x + 6 can anybody help me solve this problem
Answer:
[tex]\huge\boxed{x = 8}[/tex]
Step-by-step explanation:
[tex]\sf -18 = -3x+6\\Subtracting \ 6 \ to \ both \ sides\\-18-6 = -3x\\-24 = -3x\\Dividing \ both \ sides \ by \ -3\\8 = x\\OR\\x = 8[/tex]
Answer:
x = 8
Step-by-step explanation:
Here, -3x = -24
x = 8
hope that helps you
Solve for xxx. 12x+7 4012x+7 40
Answer:
[tex]x = 2.75[/tex]
Step-by-step explanation:
I'm assuming you have an equation
[tex]12x + 7 = 40\\[/tex]
and you want to solve for x.
This is easy. First, subtract 7 from each side of the equation.
[tex]12x+7-7 = 40-7[/tex]
[tex]12x = 33[/tex]
Then divide both sides by 12, to get x alone on the left side.
[tex]\frac{12x}{12} = \frac{33}{12}[/tex]
[tex]x = \frac{33}{12} = 2.75[/tex]
Kelsey had $65 to spend on books. Each book cost $5.50, and there was a $7.50 fee for shipping. She let b equal the number of books she can purchase and wrote the inequality 5.50 b + 7.5 less-than 65 to represent the situation. Which statements describe the reasoning used to determine if Kelsey’s inequality is correct? Select two options. The inequality symbol is correct because she must spend less than $65. The inequality symbol is incorrect because she can spend up to and including $65. The expression 5.50b + 7.5 is correct because $5.50 per book is 5.50b and that is added to the shipping fee of $7.50 to determine the total purchase price. The expression 5.50b + 7.5 is incorrect because $5.50 per book and $7.50 should be combined to $9.50b to determine the total purchase price. The inequality symbol is correct because she cannot spend more than $65.
The statements that can be used to describe the reasoning used to determine if Kelsey’s inequality is correct include:
The inequality symbol is incorrect because she can spend up to and including $65. The expression 5.50b + 7.5 is correct because $5.50 per book is 5.50b and that is added to the shipping fee of $7.50 to determine the total purchase price.It should be noted that the inequality symbol is incorrect because she can spend up to and including $65.
Based on the information given, the correct expression that can be used to solve the question should be:
65 - (5.50b + 7.5)
In conclusion, the correct options are B and C.
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Answer:
B and C
Step-by-step explanation:
30 POINTS! PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!! Transformation
Options for center of dilation is located -->
At the center of the smaller circle, or at the center of the larger circle, or at at the top of the larger circle, or to the right of both circles, or to the left of both circles.
I WILL REPORT SCAMS.
The scale factor of the dilation is 0.78
The centre of dilation is located at (0,0)
The scale factor of a dilation is the ratio of the corresponding component of the final image to the original image.
According to the image given, the scale factor will be the ratio of the radius of the final image to the original image as shown below:
[tex]Scale \ factor = \frac{small \ radius}{large \ radius} \\Scale \ factor = \frac{7}{9}\\ Scale \ factor=0.78[/tex]
Hence the scale factor of the dilation is 0.78
The centre of dilation is located at the origin because the radius is the distance between the centre of the circle and its circumference. We can therefore conclude that the centre of dilation is located at (0,0)
The scale factor of the dilation is [tex]\frac{7}{9}[/tex].
The center of dilation is a point to the right of both circles.
From Analytical Geometry we know that every Circle is defined by its Radius, its form is directly proportional to its radius. Hence, the Scale Factor of the Dilation ([tex]f[/tex]) is the following ratio:
[tex]f = \frac{r_{2}}{r_{1}}[/tex] (1)
Where:
[tex]r_{1}[/tex] - Radius of the original circle.
[tex]r_{2}[/tex] - Radius of the dilated circle.
If we know that [tex]r_{1} = 9[/tex] and [tex]r_{2} = 7[/tex], then the scale factor of the dilation is:
[tex]f = \frac{7}{9}[/tex].
The scale factor of the dilation is [tex]\frac{7}{9}[/tex].
There is a geometrical approach to determine the location of the Center of Dilation. We draw two lines tangent (blue lines) to both circles and we extend to the right of the scene, the point in which both intersects each other is the location of the center of dilation. (representation is included in the image attached below)
In a nutshell, the center of dilation is a point to the right of both circles.
help me please and thank youu
Answer:
-3
Step-by-step explanation:
The probability that a civil servant own a car is 1/6,if two civil servants are selected at random.Find the probability that a.Each own a carb.Only one owns a car
Answer:
Step-by-step explanation: Given that a civil servant own a car is 1/6.
A) The Pr. that each own a car = Pr of each multiplied by the other.
Pr = 1/6 ×1/6
P = 1/36
B) Pr that only one owns a car
= 1/6 × (1-1/6) + 1/6 × (1-1/6)
= 1/6 × 5/6 + 5/6 × 1/6
= 5/36 + 5/36
= 10/36
= 5/18
Solve for X
1.) 5(4)^x=320 solve for x
2.) 7 (1/3)^x=7/27 solve for x
Answer:
[tex]5(4)^x=320\\\frac{5(4)^x}{5}=\frac{320}{5}\\ 4^x=64\\x*(log(4) )=log(64)\\x=\frac{log(64)}{log(4)}\\ x=3[/tex]
Step-by-step explanation:
Find the area of the shape shown below.
2
2
2
2
2
units
Answer:
8
Step-by-step explanation:
khan
Answer:
8
Step-by-step explanation:
is 11-2x the same as 2x-11
No they are not the same.
We can plug in x = 0 to get
11-2x = 11-2(0) = 11-0 = 11
2x-11 = 2(0)-11 = 0-11 = -11
We get the results 11 and -11 for the expressions 11-2x and 2x-11 respectively. Since we got different outputs, this is enough to show that the expressions are not the same. They would need to produce the same outputs for any given x value.
On a graph, y = 11-2x and y = 2x-11 are two different lines to show they are not the same expression.
note: if you plug in x = 11/2 = 5.5, then both outputs are the same; otherwise, you'll get different outputs.
Solve each inequality, and then drag the correct solution graph to the inequality.
The correct solution graph to the inequalities are
[tex]4(9x-18)>3(8x+12)[/tex] → C
[tex]-\frac{1}{3}(12x+6) \geq -2x +14[/tex] → A
[tex]1.6(x+8)\geq 38.4[/tex] → B
(NOTE: The graphs are labelled A, B and C from left to right)
For the first inequality,
[tex]4(9x-18)>3(8x+12)[/tex]
First, clear the brackets,
[tex]36x-72>24x+36[/tex]
Then, collect like terms
[tex]36x-24x>36+72\\12x >108[/tex]
Now divide both sides by 12
[tex]\frac{12x}{12} > \frac{108}{12}[/tex]
∴ [tex]x > 9[/tex]
For the second inequality
[tex]-\frac{1}{3}(12x+6) \geq -2x +14[/tex]
First, clear the fraction by multiplying both sides by 3
[tex]3 \times[-\frac{1}{3}(12x+6)] \geq3 \times( -2x +14)[/tex]
[tex]-1(12x+6) \geq -6x +42[/tex]
Now, open the bracket
[tex]-12x-6 \geq -6x +42[/tex]
Collect like terms
[tex]-6 -42\geq -6x +12x[/tex]
[tex]-48\geq 6x[/tex]
Divide both sides by 6
[tex]\frac{-48}{6} \geq \frac{6x}{6}[/tex]
[tex]-8\geq x[/tex]
∴ [tex]x\leq -8[/tex]
For the third inequality,
[tex]1.6(x+8)\geq 38.4[/tex]
First, clear the brackets
[tex]1.6x + 12.8\geq 38.4[/tex]
Collect likes terms
[tex]1.6x \geq 38.4-12.8[/tex]
[tex]1.6x \geq 25.6[/tex]
Divide both sides by 1.6
[tex]\frac{1.6x}{1.6}\geq \frac{25.6}{1.6}[/tex]
∴ [tex]x \geq 16[/tex]
Let the graphs be A, B and C from left to right
The first graph (A) shows [tex]x\leq -8[/tex] and this matches the 2nd inequality
The second graph (B) shows [tex]x \geq 16[/tex] and this matches the 3rd inequality
The third graph (C) shows [tex]x > 9[/tex] and this matches the 1st inequality
Hence, the correct solution graph to the inequalities are
[tex]4(9x-18)>3(8x+12)[/tex] → C
[tex]-\frac{1}{3}(12x+6) \geq -2x +14[/tex] → A
[tex]1.6(x+8)\geq 38.4[/tex] → B
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Answer:
4(9x − 18) > 3(8x + 12) = x > 9
(12x + 6) ≥ -2x + 14 = x ≤ -8
1.6(x + 8) ≥ 38.4 = x ≥ 16
Just follow the numbers with the dotted thing and see the numbers I underlined.
Step-by-step explanation:
Use the properties of inequality and real numbers to solve each inequality.
4(9x − 18) > 3(8x + 12)
36x − 72 > 24x + 36
12x − 72 > 36
12x > 108
x > 9
The graph has an open circle at 9, and moves toward the right on the number line.
(12x + 6) ≥ -2x + 14
12x + 6 ≤ 6x − 42
6x + 6 ≤ -42
6x ≤ -48
x ≤ -8
The graph has a closed circle at -8, and moves toward the left on the number line.
1.6(x + 8) ≥ 38.4
x + 8 ≥ 24
x ≥ 16
The graph has a closed circle at 16, and moves toward the right on the number line.
to make a set for a stage, you bought a piece of lumber 9 feet long. How many 2 1/4 foot pieces can you cut from this piece of lumber? please answer ASAP
Answer:
4 pieces
Step-by-step explanation:
Total length of lumber = 9 feet
How many 2 1/4 foot pieces can you cut from this piece of lumber
To find the number of 2 1/4 foot pieces of lumber in a 9 feet of lumber, we will divide the total length of lumber by the length of each piece of lumber
9 ÷ 2 1/4
= 9 ÷ 9/4
= 9 × 4/9
= 36/9
= 4 pieces of lumber
Therefore, 4 pieces of 2 1/4 foot of lumber can be gotten from 9 feet of lumber
Given the equation, 1 + 6k = 25, for some value of k, what is the value of k +7 for the same value
of k?
Step-by-step explanation:
1+6k=25
collect like terms
1-25=6k
-24=6k
divide both sides by 6
-4=k
;- k= -4
The dot plot represents a sampling of ACT scores:
dot plot titled ACT Scores with Score on the x axis and Number of Students on the y axis with 1 dot over 18, 3 dots over 19, 4 dots over 21, 4 dots over 22, 3 dots over 23, 2 dots over 24, 1 dot over 25
Which box plot represents the dot plot data?
box plot titled ACT Score with a minimum of 18, quartile 1 of 21, median of 22, quartile 3 of 23, and maximum of 25
box plot titled ACT Score with a minimum of 18, quartile 1 of 19, median of 21, quartile 3 of 22, and maximum of 25
box plot titled ACT Score with a minimum of 17, quartile 1 of 19, median of 21, quartile 3 of 22, and maximum of 25
box plot titled ACT Score with a minimum of 17, quartile 1 of 19, median of 21, quartile 3 of 25, and maximum of 26
The data from a dot plot can be analyzed to find the five number summary, from which a box plot can be constructed
The correct option for the details of the box plot that represents the dot plot data is;
Box plot titled ACT Score with a minimum of 18, quartile 1 of 21, median of 22, quartile 3 of 23, and maximum of 25
The process of deriving the five number summary of the box plot above is as follows;
Known:
The data from the dot plot can be expressed in increasing order for analysis of a box plot as follows;
18, 19, 19, 19, 21, 21, 21, 21, 22, 22, 22,22, 23, 23, 23, 24, 24, 25
The number of data points in the statistics, n = 18
Unknown:
The five number summary
Method:
Finding the five number summary as follows;
The minimum value = 18
The maximum value = 25
The first quartile, inclusive of the median Q₁ = The middle number of the lower half {18, 19, 19, 19, 21, 21, 21, 21, 22} = The (9 + 1)/2 th term∴ Quartile 1 = Q₁ = 5th term = 21
The second quartile, Q₂ = The median (the middle number) = (22 + 22)/2 = 22 = Quartile 2Quartile 2 = 22
The third quartile = The middle number of the upper half {22, 22,22, 23, 23, 23, 24, 24, 25} = Quartile 3 = 23Quartile 3 = 23
Combining the above 5 number summary, the correct option for the box plot representing the dot plot data, is therefore;
Box plot titled ACT Score with a minimum of 18, quartile 1 of 21, median of 22, quartile 3 of 23, and maximum of 25
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Point M is the midpoint of AB. The coordinates of point A are (-7, 1) and the coordinates of M are (-2,2).
What are the coordinates of point B?
Answer:
B = (3.3)
Step-by-step explanation:
Which expression is equivalent to x^6 – 5
Answer:
Amdjss
Step-by-step explanation:
please help. thank you so much
Answer:
XY = 17
Step-by-step explanation:
Intersect secant theorem, EX * EY = EZ*EW
34 * EY = 25.5 * 68
[tex]EY = \frac{25.5*68}{34}\\\\ = 25.5* 2\\\\ = 51.0 = 51[/tex]
EY = 51
EX + XY = 51
34 + XY = 51
XY = 51 - 34 = 17
13. PLEASE HELP ME
The area of a playground is 336 yd2. The width of the playground is 5 yd longer than its length. Find the length and width of the playground.
A. length = 16 yd, width = 21 yd
B. length = 21 yd, width = 26 yd
C. length = 21 yd, width = 16 yd
D. length = 26 yd, width = 21 yd
We know
[tex]\boxed{\sf Area=Length\times Width}[/tex]
Putting values[tex]\\ \sf\longmapsto 336=x(x+5)[/tex]
[tex]\\ \sf\longmapsto x^2+5x=336[/tex]
[tex]\\ \sf\longmapsto x^2+5x-336=0[/tex]
Using mid term split[tex]\\ \sf\longmapsto x^2-16x+21x-336=0[/tex]
[tex]\\ \sf\longmapsto x(x-16)+21(x-16)=0[/tex]
[tex]\\ \sf\longmapsto (x-16)(x+21)=0[/tex]
[tex]\\ \sf\longmapsto (x-16)=0\:or\:(x+21)=0[/tex]
[tex]\\ \sf\longmapsto x=16\:or\:x=-21[/tex]
Ignore negative value[tex]\\ \sf\longmapsto Length=x=16yd[/tex]
[tex]\\ \sf\longmapsto Width=x+5=16+5=21yd[/tex]
Option a is correctDavid’s family is driving from New York to Florida. They know the distance they will travel is about 1100 miles . If a map has a scale of 1 in = 80 mi about how far will the trip be on the map ?
You can do the proportion
1 inch/ 80 miles =x inch/ 1100 miles
1100=80x
11oo divided by 80 equals 13.75
The trip would be about 13.75 inches on the map
Feel free to brainliest :)
Answer:
13.75 inches
Step-by-step explanation:
To find an estimated distance on the map, we can simply create a proportion.
Let X represent the unknown distance in inches on the map.
1100 miles / 80 miles = X inches / 1 inch
Now let's solve for X.
X inches = (1100 miles / 80 miles) * 1 inch
X inches = 13.75 inches
So the approximate travel distance on the map will be 13.75 inches.