Algerbra One Question

Final answer:

Using the formula for the distance fallen under gravity, the height of the building is found to be approximately 70.856 meters, given a drop time of 3.8 seconds.

Explanation:

The question asks, "What is the height of a building in meters if it takes a rock 3.8 seconds to drop from its roof?" To solve this, we'll use the physics formula for the distance (height) fallen by an object under gravity, which is given by d = ½ gt², where d is the distance in meters, g is the acceleration due to gravity (approximately 9.8 m/s²), and t is the time in seconds.

Substituting the given values into the equation, we have:

d = ½ × 9.8 m/s² × (3.8 s)²

= ½ × 9.8 × 14.44

= 70.856 meters

Therefore, the height of the building is approximately 70.856 meters.

Answer:

46 jumps per minute.

Step-by-step explanation:

We have been given that Delilah does 184 jumping jacks in 4 minutes.

Since Delilah is jumping jacks at a constant rate, so the number of jumps per minute would be 184 divided by 4.

[tex]\text{Number of jumps per minute}=\frac{\text{184 jumps}}{\text{4 minutes}}[/tex]

[tex]\text{Number of jumps per minute}=\frac{\text{46 jumps}}{\text{minute}}[/tex]

Therefore, Delilah is jumping at a rate of 46 jumps per minute.

To simplify the expression 7^6 x 7 x 7^-4 using positive exponents, we can apply the rule of multiplying powers with the same base.

To simplify the expression 7^6 x 7 x 7^-4 using positive exponents, we can apply the rule of multiplying powers with the same base. First, let's simplify 7^6 x 7. This can be rewritten as 7^(6+1) or 7^7. Next, let's simplify 7^7 x 7^-4. Applying the rule of multiplying powers with the same base, we get 7^(7-4) or 7^3. Therefore, the simplified expression is 7^3.

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Answer:  The required value of x is 64.

Step-by-step explanation:  We are given to find the value of x from the figure.

From the figure, we see a right-angled triangle in which an acute angle has measurement x°.

And, for the angle with measurement x°, the base has a length of 3.0 units and hypotenuse has a length of 6.8 units.

Therefore, the cosine of that angle will be

[tex]\cos x^\circ=\dfrac{base}{hypotenuse}\\\\\\\Rightarrow \cos x^\circ=\dfrac{3.0}{6.8}\\\\\\\Rightarrow \cos x^\circ=0.4411\\\\\Rightarrow x^\circ=\cos^{-1}(0.4411)\\\\\Rightarrow x^\circ=63.83^\circ\\\\\Rightarrow x=63.83.[/tex]

So, to the nearest whole number, we get

x = 64.

Thus, the required value of x is 64.

The measure of center that best represents the daily average of customers at the coffee shop is the mean, which is calculated by summing up all the numbers and dividing by the total count.

To find the measure of center that best represents the daily average of customers at the coffee shop, we can calculate the mean, median, and mode of the given data set. The mean is the sum of all the numbers divided by the total count, the median is the middle value when the numbers are arranged in increasing order, and the mode is the number that appears most frequently.

Mean: Add up all the numbers and divide by the total count: (135+124+140+122+409+132+119+128+136+125)/10 = 157.

Based on these calculations, we can conclude that the measure of center that best represents the daily average of customers at the coffee shop is the mean since it takes into account all the values in the data set.

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The volume of the wooden peg game in the shape of a triangular prism is calculated by finding the area of the triangular base and multiplying by the prism's height. The area of the triangle is 54 square inches, and the volume of the game is 108 cubic inches.

To find the volume of the wooden peg game, we will use the formula for the volume of a prism, which is the area of the base times the height of the prism. The base of the prism is a triangle, so first, we need to find the area of the triangular base. The area of a triangle is calculated by multiplying the base by the height and then dividing by 2.

First, we calculate the area of the triangle base:

Next, we multiply the area of the base by the height of the prism to find the volume:

Therefore, the volume of the wooden peg game is 108 cubic inches.

Answer:

As per the given statement: A forest ranger wants to determine the radius of the trunk of a tree. She measures the circumference to be 8.6 feet.

Shape of the trunk of a tree is circle.

Use the circumference formula:

[tex]C = 2\pi r[/tex]

where C is the circumference of a circle and r is the radius of a circle.

Solve for r;

Given: C = 8.6 feet and use [tex]\pi = 3.14[/tex]

Substitute the given value we get;

[tex]8.6 = 2 \times 3.14 \times r[/tex]

Simplify:

[tex]8.6 = 6.28r[/tex]

Divide both sides by 6.28 we get;

r = 1.6942675 feet

Therefore, the trunk's radius to the nearest tenth foot is, 1.4 ft

Answer:1.4

Step-by-step explanation:

that is it its not that hard

Answer:

The equation of the ellipse is :

[tex]\frac{x^2}{1316^2}+\frac{y^2}{1669^2}=1[/tex]

Step-by-step explanation:

Formula for the equation of an ellipse is given by :

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

where a and b are the horizontal and vertical intercepts of the ellipse on the coordinate axis.

Here, a = 959 + 357

             = 1316

And, b = 959 + 710

           = 1669

So, the equation of the ellipse is :

[tex]\frac{x^2}{1316^2}+\frac{y^2}{1669^2}=1[/tex]

Answer:

Step-by-step explanation:

Alright, lets get started.

The surface area of green solid is :

[tex]2 (3*3 + 3*3 + 3*3) = 2*27=54[/tex]

The surface area of orange solid is :

[tex]2(5*5 + 5*5 + 5*5) =2*75= 150[/tex]

So the ratios of their surface area will be :

[tex]\frac{54}{150}[/tex]

[tex]\frac{18}{50}[/tex]

[tex]\frac{9}{25}[/tex]

Hence the answer is 9:25   :  Answer Hope it will help :)

Answer:

The margin of error for the Camp Verde survey will be between one and three times as great as the margin of error for the Gilbert survey.

Step-by-step explanation:

The statement which is true, the margin of error for the Camp Verde survey will be between and the size of the margin of error for the Gilbert survey.

The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.

[tex]MOE_\gamma=z_{\gamma}\dfrac{\sigma ^2}{n}[/tex]

Here, γ is the confidence interval, σ is standard deviation and n is the sample.

The mayor of Gilbert, AZ, randomly selects 300 of its residents for a survey while the mayor of Camp Verde, AZ, randomly selects 100 of its residents and asks them the same question. Thus,

[tex]n_1=300\\n_2=100[/tex]

Both surveys show that 15% of the residents of each town want Arizona to start using daylight savings like most of the rest of the country.

The confidence level for both surveys is 95% (z*-value 1.96). Thus, comparing the MOE of both the data as,

[tex]\dfrac{MOE_2}{MOE_1}=\dfrac{z_{\gamma}\sqrt{\dfrac{\sigma ^2}{n_2}}}{z_{\gamma}\sqrt{\dfrac{\sigma ^2}{n_1}}}\\\\\dfrac{MOE_2}{MOE_1}=\dfrac{\sqrt{\dfrac{1}{100}}}{\sqrt{\dfrac{1}{300}}}\\\dfrac{MOE_2}{MOE_1}=1.73[/tex]

Thus, the statement which is true, the margin of error for the Camp Verde survey will be between and the size of the margin of error for the Gilbert survey.



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To repeat the pattern, the angle of x needs to be 360 degrees divided by the number of times the pattern is repeated.

To repeat the pattern of the border around the top of the walls in your room, the angle of x needs to be 360 degrees divided by the number of times the pattern is repeated. For example, if the pattern is repeated 4 times around the room, the angle x would be 360 degrees divided by 4, which is 90 degrees.

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There are 5 sides (a pentagon). The perimeter is the length of one side times the number of sides.

The polygon has 5 sides. The specific type of polygon with 5 sides is called a pentagon.

The perimeter of a polygon is the total length of all its sides. In a regular polygon, all sides are equal in length. So, if each side of the polygon is 2.5 cm and the perimeter is 12.5 cm, we can find the number of sides by dividing the perimeter by the side length:

Number of sides = Perimeter / Side length

Number of sides = 12.5 cm / 2.5 cm

Number of sides = 5

The area of the circle for the given circumference is 36π square units.

Every point in the plane of a circle, which is a closed, two-dimensional object, is evenly separated from the center. All lines that cross the circle join together to produce the line of reflection symmetry. Every angle also possesses rotational symmetry about the center.

Given circumference of circle = 12π

the circumference is given by 2πr

where r is the radius,

2πr = 12π

2r = 12

r = 6 units

and the area of a circle is πr²

A = πr² = π(6²)

A = 36π square units

Hence the area of circle is 36π square units.

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The area of the circle with circumference [tex]\( 12\pi \)[/tex] is [tex]\( \boxed{36\pi} \)[/tex] square units.

To find the area of a circle when given its circumference, we start by using the formula relating circumference ([tex]\( C \)[/tex]) and radius ([tex]\( r \)[/tex]):

[tex]\[ C = 2\pi r \][/tex]

Given that the circumference [tex]\( C \)[/tex] is [tex]\( 12\pi \)[/tex], we set up the equation:

[tex]\[ 12\pi = 2\pi r \][/tex]

Next, solve for [tex]\( r \)[/tex] by dividing both sides by [tex]\( 2\pi \)[/tex]:

[tex]\[ r = \frac{12\pi}{2\pi} \][/tex]

[tex]\[ r = 6 \][/tex]

Now that we have found the radius [tex]\( r = 6 \)[/tex], we can find the area ([tex]\( A \)[/tex]) of the circle using the formula for the area of a circle:

[tex]\[ A = \pi r^2 \][/tex]

Substitute [tex]\( r = 6 \)[/tex]:

[tex]\[ A = \pi \cdot (6)^2 \][/tex]

[tex]\[ A = \pi \cdot 36 \][/tex]

[tex]\[ A = 36\pi \][/tex]

Therefore, the area of the circle with a circumference of [tex]\( 12\pi \)[/tex] is [tex]\( \boxed{36\pi} \)[/tex].

Answer:

B. Variable

Step-by-step explanation:

A Variable expense is a type of expense that may vary from month to month. This type of expense includes things like electricity, groceries, clothing, and gas. When it comes to the groceries, it is considered to be a variable expense only if the household need the items that are purchased.

Answer:

B) variable

A variable expense is a cost that may happen each month, but one who's total amount may change from month to month.