Cora wants to determine a 95 percent confidence interval for the true proportion p
of high school students in the area who attend their home basketball games. Out of n
randomly selected students she finds that that exactly half attend their home basketball games. About how large would n have to be to get a margin of error less than 0.04 for p

The point y = -x² - 3x + 2 cuts the x-axis are x = -3.6 and 0.6

From 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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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.

When 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

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]

The bottle holds a total of 25 fluid ounce of iced tea.

from 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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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

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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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.

They ate 5/8 of the cupcakes and 3/8 of the cupcakes are left.

Happy to help, have a great day! :)

The surface area of the pyramid in this problem is given as follows:

96.4 ft².

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:

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.

The net is given by the image presented at the end of the answer.

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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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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

Answer:

Step-by-step explanation:

The statement that is correct according to the table is: Barrow has the coldest average temperature in January.

Answer:

increases by 30

Step-by-step explanation: its right

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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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.

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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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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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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The data set that would be better displayed in a stem display is

(A.) 45, 36, 48, 22, 56, 77, 51, 77, 32, 38

A 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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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.

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

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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Answer:

Step-by-step explanation:

Hello !

A rectangle triangle ABC :

  A

  I\
  I  \
  I    \
  I      \  

  B       C

We 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

x has the ratio opposite ; adjacent

⇒ It's the tangente.

tan(x) = opposite/adjacent = 4/6

arctan(4/6) ≈ 33,69 ≈ 34°

y 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!

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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Answer: 5

have a good day

The total surface area of the cuboid in contact with the water is [tex]1300 cm^2.[/tex]

The volume of a cuboid formula, V = lwh, can be used to first determine the height of the water level in the tank.

Where

Converting 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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Answer:

Step-by-step explanation: