The required sample size for a margin of error of less than 0.04 is given as follows:
n = 601.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is defined as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
We have no estimate, hence the proportion is used as follows:
[tex]\pi = 0.5[/tex]
For a margin of error of 0.04, the sample size is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96 \times 0.5[/tex]
[tex]\sqrt{n} = \frac{1.96 \times 0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 0.5}{0.04}\right)^2[/tex]
n = 601.
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perla has 150 meters of fencing material and wants to form a rectangular pen with an area of 1300 square meters
a. let w= the width of the pen and L=length. Write a system of equations to determine w and L.
b.Solve the system and interpret your answer in the context of the problem.
Answer:
Step-by-step explanation:
At what points does the curve
y= -x²_3x +2 cut the x-axis?
The point y = -x² - 3x + 2 cuts the x-axis are x = -3.6 and 0.6
How to determine the point it cut the x-axisFrom the question, we have the following parameters that can be used in our computation:
y = -x² - 3x + 2
The point it cut the x-axis is when y = 0
Using the above as a guide, we have the following:
-x² - 3x + 2 = 0
So, we have
x² + 3x - 2 = 0
When solved using a graphing tool, we have
x = -3.6 and 0.6
Hence, the point it cuts the x-axis are x = -3.6 and 0.6
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A bag contains seven balls labeled 1 through 7. One ball will be randomly picked. What is the probability of picking an off number? Write your answer as a fraction in simplest form.
Answer:
The odd numbers between 1 and 7 are 1, 3, 5, and 7. There are four of them.
The total number of balls in the bag is 7.
Therefore, the probability of picking an odd number is:
number of odd numbers / total number of balls = 4/7
So the probability of picking an odd number is 4/7
Find the area of each face of the triangular prism and the total surface area.
Drag each tile to its matching measurement. Each number may be used once or not at all.
Answer:
Area of each triangular base
= (1/2)(6)(8) = 24 cm^2
Area of bottom rectangular base
= 8(20) = 160 cm^2
Area of back rectangular base
= 6(20) = 120 cm^2
Area of sloped rectangular base
= 10(20) = 200 cm^2
Total surface area
= 2(24) + 160 + 120 + 200 = 528 cm^2
The area of each face of the triangular prism and the total surface area will be; 528 cm²
The area of each triangular face ;
A = 1/2bh
The triangular faces have a base of b=8 cm and a height of h=6 cm thus area is ...
A = 1/2(8 cm)(6 cm) = 24 cm²
Since Each of the rectangular faces has a length of 20 cm. The width depends on which face is of interest.
the area is given...
A = LW
Bottom face:
A = (20 cm)(8 cm) = 160 cm²
Back face:
A = (20 cm)(6 cm) = 120 cm²
Sloped face:
A = (20 cm)(10 cm) = 200 cm²
Now we have total area is the sum of the areas of all of the faces and bases. There are two triangular bases,
(2×24 + 160 +120 +200) cm² = 528 cm²
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(Surface Area of Rectangular Prisms and Pyramids MC)
A net of a rectangular pyramid is shown.
What is the surface area of the pyramid?
The surface area of the pyramid in this problem is given as follows:
96.4 ft².
How to obtain the surface area?To obtain the surface area of a figure, we must add the areas of all the parts that compose the figure.
From the net given by the image presented at the end of the answer, the pyramid is composed as follows:
Rectangle of dimensions 4 ft and 8 ft.Two triangles of base 8 ft and height 5 ft.Two triangles of base 4 ft and height 6.1 ft.Hence the surface area of the figure is given as follows:
S = 4 x 8 + 2 x 1/2 x 8 x 5 + 2 x 1/2 x 4 x 6.1
S = 96.4 ft².
Missing InformationThe net is given by the image presented at the end of the answer.
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a scientist performed an experiment to study the effects of gravitational force on humans. In order for humans to experience twice Earth's gravity, they were placed in a centrifuge 58 feet long and spun at a rate of about 15 revolutions per minute
The scientists may also be looking for changes in cognitive and motor skills due to the increased gravitational force.
The centrifuge is a device which is used to simulate the effects of gravity on humans. In this experiment, the centrifuge was 58 feet long and spun at 15 revolutions per minute.
This would create a centrifugal force which would be twice Earth's gravity. This would allow the scientists to study the effects of a much higher gravitational force on humans than they would experience on Earth.
The effects that would be studied could include changes in heart rate, blood pressure, and other physiological parameters. In addition, the scientists may also be looking for changes in cognitive and motor skills due to the increased gravitational force.
Therefore, the scientists may also be looking for changes in cognitive and motor skills due to the increased gravitational force.
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Mariah bought a package of 8 cupcakes. She and her family ate 5 of the cupcakes. What fraction of the cupcakes did they eat and what fraction of the cupcakes were left?
They ate 5/8 of the cupcakes and 3/8 of the cupcakes are left.
Happy to help, have a great day! :)
A bottle holds 750 milliliters of iced tea.
I fluid ounce 30 milliliters
Approximately how many fluid ounces of iced tea does the bottle hold, rounded to the nearest whole number? Enter the answer in the
box.
fluid ounces
The bottle holds a total of 25 fluid ounce of iced tea.
Calculating the number of fluid ounces of iced tea the bottle holdfrom the question, we have the following parameters that can be used in our computation:
Volume of bottle = 750 milliliters of iced tea.
Also, we have
1 fluid ounce = 30 milliliters
This means that
1/30 fluid ounce = 1 milliliters
So, we have
Volume of bottle = 750 * 1/30 fluid ounce of iced tea.
Evaluate
Volume of bottle = 25 fluid ounce of iced tea.
Hence, the volume of bottle is 25 fluid ounce of iced tea.
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Write an expression equivalent to b^11/b^4 in the form b^m
The equivalent expression in the form of [tex]b^m[/tex] is [tex]b^7[/tex].
We have,
The expression:
[tex]b^{11}/b^4[/tex]
Now,
We will use the exponent's formula.
a³/a² = [tex]a^{3 - 1}[/tex] = 1
Where the base must be the same.
Now,
The expression:
[tex]b^{11}/b^4[/tex]
We will subtract 4 from 11 since b is the same base.
So,
= [tex]b^{11 - 4}[/tex]
= [tex]b^7[/tex]
Thus,
The equivalent expression in the form of [tex]b^m[/tex] is [tex]b^7[/tex].
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City Temperature (F°)
Fraser −5°
Grand Fork −1°
Barrow −16°
Harbin −10°
The table shows the average temperature in January for the cities. According to the table, which statement is correct?
Answer:
Step-by-step explanation:
The statement that is correct according to the table is: Barrow has the coldest average temperature in January.
Monthly payments on a house that cost 170,000 over 30 years and a interest rate of 4%
Determine the equation of the cirele with center (2, 3) containing the point (7, 15).
Answer:
IG: yiimbert
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
We are given that the center of the circle is (2, 3) and it contains the point (7, 15). To find the radius, we can use the distance formula between the center and the given point:
r = sqrt[(7 - 2)^2 + (15 - 3)^2]
r = sqrt[25 + 144]
r = sqrt(169)
r = 13
Substituting the given values into the equation of a circle, we get:
(x - 2)^2 + (y - 3)^2 = 13^2
Expanding the terms, we get:
x^2 - 4x + 4 + y^2 - 6y + 9 = 169
Simplifying and rearranging, we get:
x^2 - 4x + y^2 - 6y = 156
Therefore, the equation of the circle with center (2, 3) containing the point (7, 15) is:
x^2 - 4x + y^2 - 6y = 156
5. When
is the heart fully formed?
43
A frog starts jumping from the middle of a circular pond.
The pond is 12 metres across, from one side to the other.
The frog always jumps half the distance left to the edge of the pond.
How far is the frog from the edge after 3 jumps?
A 10.5m
B 75 cm
C 150 cm
D 5.25m
E 125C
150 cm far is the frog from the edge after 3 jumps. Therefore, option C is the correct answer.
1 jump the far from the edge
12/2 = 6 cm
2 jump the far from the edge
6/2 = 3 cm
3 jump the far from the edge
3/2 = 1.5 cm
We know that, 1 meter = 100 cm
Here, 1.5 cm = 150 cm
Therefore, option C is the correct answer.
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Suppose that 100 unique names are put into a hat and drawn at random without replacement. How many different ways can you draw all of the names from the hat? Remember that "without replacement" means that the names are not returned to the hat after they are chosen. Write your answer in factorial notation.
The solution is: 100! different ways can you draw all of the names from the hat.
Here, we have,
if we have n object, and as we know that arrangement given by = n!. (Permutation)
A permutation is a mathematical technique for determining the number of possible arrangements in a sentence where the order of arrangements is important. A common math problem involves choosing some items in a particular order from a set of items.
A permutation also called an "order number" or "sequence", is the rearrangement of the elements of an ordered list so that they correspond one-to-one with themselves. (Faculty; Ouspensky 1937, p. 18). Permutations are said to be ordered combinations. The number of permutations r of n objects acquired simultaneously is determined by the following formula: P(n,r)=n!(n-r)!
Hereafter taking each unique name, we will arrange it in raw, so we can say this problem is equivalently permutation problem, So we can say the way of drawing all names can be done in 100! Way.
So ANSWER IS 100!
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In your dresser, you have 10 pairs of socks, 6 are red, and 7 shorts, 4 of which are sport shorts. If you randomly
reach in and pull out a pair of socks and shorts, what is the probability the socks are red and you have sports
shorts?
The probability of pulling out a red pair of socks and sport shorts is 12/35.
We have,
10 pairs of socks, 6 are red, and 7 shorts, 4 of which are sport shorts.
So, The probability of pulling out a red pair of socks is given by:
= (number of red socks) / (total number of socks)
= 6 / 10
= 3 / 5
and, the probability of pulling out sport shorts is given by:
= (number of sport shorts) / (total number of shorts)
= 4 / 7
To find the probability of both events happening together
= P(red socks) x P(sport shorts)
= (3 / 5) x (4 / 7)
= 12 / 35
Therefore, the probability of pulling out a red pair of socks and sport shorts is 12/35.
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two books are proportional in size One book is two inches thick and fourteen inches long the second book is 1.5 inches thick how long is the second
Answer:
The length of the second book is 10.5 inches, while the first book's thickness is in a ratio of 2:1.5, which simplifies to 4:3. Similarly, the length of the first book is also in a ratio of 4:3 with the second book. Hence, we can calculate the second book's length as 14 divided by 4, multiplied by 3, which equals 10.5 inches.
Akeem invest $25,000 in an account that pays 4.75% interest compounded annually.
write an equation that will to determine how much money he will have in t years.
Answer:
Step-by-step explanation:
Zoe is doing a survey to find the time her classmates spend playing video games. She asks the following question:
Which student spends the most time playing video games?
Part A: Describe the data you would expect her to collect from this question.
Part B: Explain whether this is a statistical question. If this is not a statistical question, then modify the question to make it statistical.
i need help
Answer:
Part A: The data that Zoe would expect to collect from this question is the amount of time each student spends playing video games. She could collect this data by asking each student how many hours per week they spend playing video games.
Part B: This is not a statistical question because it is asking for a specific answer. A statistical question would be asking for a distribution of the data, such as the average amount of time students spend playing video games or the range of times students spend playing video games.
To make this question statistical, Zoe could ask the following question:
How much time do students in my class spend playing video games per week?
This question is statistical because it is asking for a distribution of the data. Zoe could then collect the data and use it to create a histogram or other graph to show the distribution of the data.
find the quotation of-4 1 over 6 and -3 1 over 3
The quotient of -4 1/6 and -3 1/3 is 5/4.
To find the quotient of -4 1/6 and -3 1/3, we need to divide the two mixed numbers. Here's how we can do it:
Step 1: Convert the mixed numbers to improper fractions.
-4 1/6 can be converted to an improper fraction as follows:
-4 1/6 = -25/6
Similarly, -3 1/3 can be converted to an improper fraction as:
-3 1/3 = -10/3
Step 2: Divide the two improper fractions.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
So, (-25/6) / (-10/3) becomes (-25/6) * (-3/10).
Step 3: Simplify the resulting fraction.
Multiply the numerators and denominators:
(-25 * -3) / (6 * 10) = 75/60
Step 4: Simplify the fraction, if possible.
The numerator and denominator have a common factor of 15:
75/60 = (5 * 15) / (4 * 15)
Simplifying, we get:
75/60 = 5/4
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An open water tank with length 20 cm and width 15 cm holds 4.8 litres of water. Calculate the height of the water level in the tank and the total surface area of the cuboid in contact with the water.
The total surface area of the cuboid in contact with the water is [tex]1300 cm^2.[/tex]
To solve this problemThe volume of a cuboid formula, V = lwh, can be used to first determine the height of the water level in the tank.
Where
V represents the water's volume in liters L is the tank's length in centimeters W is its width in centimetersH is the height of the water level in centimetersConverting the volume of the water to liters, we have:
[tex]4.8 L = 4800 cm^3[/tex]
Plugging in the values we have:
[tex]4800 cm^3 = 20 cm * 15 cm * h[/tex]
Simplifying this equation, we get:
h = 16 cm
Therefore, the height of the water level in the tank is approximately 16 cm.
The formula for the surface area of a cuboid can be used to determine the total surface area of the cuboid in contact with the water:
[tex]A = 2lw + 2lh + 2wh[/tex]
where A is the surface area of the cuboid in[tex]cm^2.[/tex]
Plugging in the values we have:
[tex]A = 2(20 cm * 15 cm) + 2(20 cm * 16 cm) + 2(15 cm * 16 cm)[/tex]
Simplifying this equation, we get:
[tex]A = 1300 cm^2[/tex]
So, the total surface area of the cuboid in contact with the water is[tex]1300 cm^2.[/tex]
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is there an association between grade level and receiving news from television?
Answer:
Yes
Step-by-step explanation:
In terms of grade level because he can conduct through the age of the students in variation the interest of each student is different so we might say that lower students like from grade 1 might not be interested in the news that was forecast in the television but with higher leverage considering its maturity and experience will define much more appropriate in receiving news school.
Which describes the value of a?
Answer:
(c) 0 < a < 1
Step-by-step explanation:
You want to know the value of 'a' in y = a·cot(x) that will cause a vertical compression without reflection.
Vertical scalingWhen a function value is multiplied by a factor greater than 1, its graph is expanded vertically. When that factor is less than 1, the graph is compressed, as in the attachment.
If the scale factor is negative, the graph will be reflected across the x-axis.
Here, you want compression without reflection. That requires a positive scale factor less than 1.
0 < a < 1
11 Use the formula below to find degree C when degree F is 41 degrees.* (1 Poin C° = (F° - 32) 8 O24 S 12
Answer: 5
have a good day
I need help with this ima give extra points
The volume of a sphere with 7 centimeter is 33.49 cubic centimeter.
Use the formula surface area=4πr²
3) Radius of sphere = 5 ft
Here, surface area=4×3.14×5²
= 314 square feet
4) Radius of sphere = 8 m
Here, surface area=4×3.14×8²
= 803.84 square feet
5) Radius of sphere = 12/2 =6 inches
Here, surface area=4×3.14×6²
= 452.16 square feet
Use the formula volume = 4/3 πr³
6) Radius of a sphere = 4 yd
Here, volume of a sphere = 4/3 ×3.14×4³
= 267.946 cubic yard
7) Radius of a sphere = 2 mm
Here, volume of a sphere = 4/3 ×3.14×2³
= 33.49 cubic mm
8) Radius of a sphere = 14/2 = 7 cm
Here, volume of a sphere = 4/3 ×3.14×7³
= 33.49 cubic cm
Use the formula volume = 2/3 πr³
9) Radius of hemisphere = 6 inches
Here, volume of a hemisphere = 2/3 ×3.14×6³
= 452.16 cubic inches
10) Radius of hemisphere = 1 ft
Here, volume of a hemisphere = 2/3 ×3.14×1³
= 2.067cubic feet
11) Radius of hemisphere = 4/2 =2 ft
Here, volume of a hemisphere = 2/3 ×3.14×2³
= 16.75 cubic feet
Therefore, the volume of a sphere with 7 centimeter is 33.49 cubic centimeter.
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For which data set would a stem display be preferred over a dot plot?
(A.) 45, 36, 48, 22, 56, 77, 51, 77, 32, 38
(B.) –4, –5, –7, –5, –5, –5, –2, –4, –4
(C.) 95, 96, 99, 98, 95, 95, 94, 94, 98
(D.) 19, 11, 14, 15, 14, 19, 11, 14, 15, 19
The data set that would be better displayed in a stem display is
(A.) 45, 36, 48, 22, 56, 77, 51, 77, 32, 38
How to find the better displayA stem-and-leaf display is generally preferred over a dot plot when the dataset contains a larger range of values or when the dataset has more values.
This is because a stem-and-leaf display can provide a clear and organized representation of the data, particularly when there is a need to observe patterns, identify outliers, or compare distributions.
Among the given options, dataset (A.) 45, 36, 48, 22, 56, 77, 51, 77, 32, 38 has a larger range of values and a greater number of values compared to the other options.
Therefore, a stem-and-leaf display would be preferred for dataset (A.) to effectively represent and analyze the data.
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The monthly rents (in dollars) paid by 9 people are given below.
(Note that these are already ordered from least to greatest.)
mean,median.
780,910,980,1000,1025,1045,1070,1095,1185
Suppose that one of the people moves. His rent changes from 1185 to 100
Answer:
increases by 30
Step-by-step explanation: its right
Solve for angles x and y in the triangle below. Round your angle to the nearest whole degree.
x =
y =
42 45 34 48 29 56
Hello !
1. ExplanationA rectangle triangle ABC :
A
I\
I \
I \
I \
B C
1.1 The ratioWe first look for the ratio of the angle.
1.1.1 If the ratio = opposite ; hypotenuse
⇒ It's the sinus.
In the triangle ABC it's :
sin(A) = opposite/hypotenuse
1.1.2 If the ratio = adjacent ; hypotenuse
⇒ It's the cosinus.
In the triangle ABC it's :
cos(A) = adjacent/hypotenuse
1.1.3 If the ratio = opposite ; adjacent
⇒ It's the tangente.
tan(A) = opposite/adjacent
2. Solve xx has the ratio opposite ; adjacent
⇒ It's the tangente.
tan(x) = opposite/adjacent = 4/6
arctan(4/6) ≈ 33,69 ≈ 34°
3. Solve yy has the ratio opposite ; adjacent
⇒ It's the tangente.
tan(y) = opposite/adjacent = 6/4
arctan(6/4) ≈ 56,30 ≈ 56°
The angle x = 34°
The angle y = 56°
Have a good day!
What is the area of this figure?
Answer:
70cm^2
Step-by-step explanation:
10×5=50cm^2 is the area of the rectangle
18-10=8 is the height of the triangle
8×2.5=20
20÷2=10 is area of half the triangle
10+10=20cm^2 is the area of the triangle
50cm^2+20cm^2=70cm^2
csc² 0 cot²0 sin² 0 = cos² 0
Answer:
Step-by-step explanation:
Given equation:
[tex]\csc^2 \theta - \cot^2\theta -\sin^2\theta =\cos^2\theta[/tex]
To verify the given trigonometric equation, we can use the following trigonometric identities:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Trigonometric Identities}\\\\$\csc^2 \theta = 1 + \cot^2 \theta$\\\\$\cos^2 \theta + \sin^2 \theta = 1$\\\end{minipage}}[/tex]
Therefore:
[tex]\begin{aligned}\csc^2 \theta - \cot^2\theta -\sin^2\theta &=(1+\cot^2\theta) -\cot^2\theta -\sin^2\theta \\&=1-\sin^2\theta\\&=(\cos^2\theta +\sin^2\theta) -\sin^2\theta \\&=\cos^2\theta \end{aligned}[/tex]