Answer:
Maximum number of 3x3x2 bricks = 23.
Step-by-step explanation:
The volume of the box = 13 x 8 x 4 = 416 cubic unit
The volume of the brick with the dimensions = 18 cubic unit
Now as per the question, we want to fill an empty box with 416 cubic unit with the help of bricks which are 18 cubic unit each.
The maximum number of bricks required to fill the box = Volume of the box ÷ Volume of one brick.
→ The number of bricks required to fill the box = 416 ÷ 18 = 23.11
But, number of bricks can never be in fraction so it means a maximum of 23 bricks can accommodate in the given box. We will not choose 24 or more than 24 bricks because these much bricks will go out of the dimensions.
Note: Volume of a cuboid = length x breadth x height (l x b x h).
To solve the problem, you divide each dimension of the box by the corresponding dimension of the brick, rounding down to the nearest whole number to get the number of bricks that can fit in each direction. You then multiply these together to get the total. In this case, a maximum of 16 bricks can fit.
Explanation:The problem at hand requires spatial reasoning and division. The challenge is to determine how many 'bricks' (which we'll engage as 3x3x2 units) can fit into a larger 'box' (which is 13x8x4 units). This can be determined by individually dividing the dimensions of the box by the dimensions of the brick.
For instance, considering the length, we divide 13 by 3 to get approximately 4.33. Considering that we can't fractionate a brick, we can place only 4 bricks along the length. Using the same approach, we divide 8 by 3 for the width to get approximately 2.67, and we can place 2 bricks here. It's the same for the height; 4 divided by 2 is 2. Therefore, we can place 2 bricks along the height.
To get the total number of bricks that can fit in the box, multiply the numbers together: 4 (length) x 2 (width) x 2 (height), giving a result of 16 bricks. Hence, a maximum of 16 bricks of size 3x3x2 can fit into a box of size 13x8x4 without going out of the box or overlapping.
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A street lamp casts a shadow 31.5 feet long, while an 8 foot-tall street sign casts a shadow of 14 feet long. What is the length and height of the lamp?
Answer:
The answer to your question is the height of the lamp is 18.2 ft
Step-by-step explanation:
Data
Street lamp shadow = 31.5 ft
Street sign height = 8 ft
Street sign shadow = 14 ft
Street lamp height = x
Process
1.- To find the height of the lamp use proportions. In this kind of problem, we do not look for the length, but the shadow.
Street lamp height/street lamp shadow = street sign height/street sign
shadow
Substitution
x / 31.5 = 8 / 14
Solve for x
x = (31.5)(8) / 14
Simplification
x = 254.4 / 14
Result
x = 18.2 ft
To find the length and height of the lamp, set up proportions using the shadow lengths and given values, then solve for the lamp height and length based on the information provided.
Explanation:The length of the lamp:
Set up a proportion using the shadow lengths:
find the equation of the line that is perpendicular to y=3x and passes through the point (4,-2)
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
y = 3x
Comparing with the slope intercept form, slope = 3
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.
Therefore, the slope of the line passing through (4,-2) is - 1/3
To determine the intercept, we would substitute m = - 1/3, x = 4 and
y = -2 into y = mx + c. It becomes
- 2 = - 1/3 × 4 + c = 4/3 + c
c = - 2 + 4/3 = - 2/3
The equation becomes
y = - x/3 - 2/3
to find the probability of flipping heads at least once if you flip a coin two times. The possible outcomes (we don't care about the order) are (each equally likely) TT, TH, HT, HH. Three out of four have an H in them, so the probability is 34. Is this correct? Is there a better and efficient way (especially when dealing with a higher number of flips? Please use only very basic terminology and concepts from probability because I've never taken a class.
Answer:
The probability of flipping Heads at least once is [tex]\frac{3}{4}[/tex].
Step-by-step explanation:
The probability of an event, say E, is the ratio of the favorable outcomes to the total number of outcomes, i.e.
[tex]P (E) = \frac{Favorable\ outcomes}{Total\ outcomes}[/tex]
The sample space of flipping two coins is:
S = {HH, HT, TH and TH}
Total number of outcomes = 4
Compute the probability of flipping Heads at least once as follows:
Let X = heads.
P (X ≥ 1) = P (X = 1) + P (X = 2)
[tex]=\frac{2}{4}+\frac{1}{4} \\=\frac{3}{4}[/tex]
Thus, the probability of flipping Heads at least once is [tex]\frac{3}{4}[/tex].
The experiment of flipping a coin is a binomial experiment.
Since there are only two outcomes of the experiment, either a Heads or a Tails.
So if X is defined as the number of heads in n flips of a coin then the random variable X follows a binomial distribution with probability p = 0.5 of success.
I was doing my math homework and I was clueless when it came to this question, my best friend and I both came up with 30 and Get More Math Said it was incorrect. Can you help?
Start of Questions
Write sinπ/5cosπ/8+cosπ/5sinπ/8 as a trigonometric function of one number. Keep π in your answer. Be sure to PREVIEW your answer before submitting!
Answer:
sin(13π/40)
Step-by-step explanation:
The given expression matches the pattern ...
sin(a)cos(b) +cos(a)sin(b) = sin(a+b)
Then ...
sin(pi/5)cos(pi/8) + cos(pi/5)sin(pi/8) = sin(π/5 +π/8)
= sin(13π/40)
_____
π/5 +π/8 = π(1/5 +1/8) = π(8/40 +5/40) = π(13/40)
The trigonometric expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 can be simplified to sin(13π/40) by using the sine addition formula.
Explanation:The expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 resembles the formula for the sine of a sum, sin(a+b) = sin(a)cos(b) + cos(a)sin(b). By applying this trigonometric identity, we can rewrite the expression as the sine of a single angle. Therefore, sinπ/5 cosπ/8 + cosπ/5 sinπ/8 is equivalent to sin(π/5 + π/8). To simplify it further, we must find a common denominator for the two angles, π/5 and π/8, which is 40. Thus, we get sin((8π + 5π)/40), which simplifies to sin(13π/40).
The average radius of Jupiter is 4.34 x 10^4 miles. The average sun radius of the sun is 4.32 x 10^5. How many times greater is the average radius of the sun?
Answer:
The average radius of sun is approximately 9.95 times the average radius of Jupiter.
Step-by-step explanation:
We are given the following in the question:
Average radius of Jupiter =
[tex]4.34\times 10^{4}\text{ miles}[/tex]
Average radius of the sun =
[tex]4.32\times 10^{5}[/tex]
Relation between average radius of sun and average radius of Jupiter =
[tex]\displaystyle\frac{\text{Average radius of Sun}}{\text{Average radius of Jupiter}}\\\\= \frac{4.32\times 10^{5}}{4.34\times 10^{4}}\\\\\displaystyle\frac{\text{Average radius of Sun}}{\text{Average radius of Jupiter}} = 9.953917\\\\\text{Average radius of Sun} \approx 9.95\times \text{(Average radius of Jupiter)}[/tex]
Thus, the average radius of sun is approximately 9.95 times the average radius of Jupiter.
To determine how many times greater the Sun's radius is compared to Jupiter, divide the Sun's radius (695,700 km) by Jupiter's radius (71,400 km), resulting in the Sun being approximately 9.75 times greater than Jupiter in size.
Explanation:The question asks how many times greater the average radius of the Sun is compared to that of Jupiter. To find this, we will divide the Sun's radius by Jupiter's radius. The radius of Jupiter is given as 71,400 km, while the radius of the Sun is much larger at 695,700 km.
Calculating the ratio, we get:
Radius of the Sun / Radius of Jupiter = 695,700 km / 71,400 km.This simplifies to approximately 9.745.Therefore, the average radius of the Sun is roughly 9.75 times greater than that of Jupiter.
1. New Jersey Lottery Let A denote the event of placing a $1 straight bet on the New Jersey Pick 3 lottery and winning. There are 1000 different ways that you can select the three digits (with repetition allowed) in this lottery, and only one of those three-digit numbers will be the winner. What is the value of P1A2? What is the value of P1A2?
Answer:
P1A2= 0.001
P1A'2=0.999
Step-by-step explanation:
Probability = number of ways A occurs/ number of different simple events
P1(A2) =1/1000=0.001
P1A2 = 1-(1/1000)= 999/1000 = 0.999
Probabilities are used to determine the outcome of an event.
The probability of winning is 0.001
Given
[tex]n = 1000[/tex] --- ways
Only one of the 1000 digits is a winning digit.
So, the probability of winning, P(A) is:
[tex]P(A) = \frac{1}{n}[/tex]
So, we have:
[tex]P(A) = \frac{1}{1000}[/tex]
Express as a decimal
[tex]P(A) = 0.001[/tex]
Hence, the probability of winning is 0.001
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Segment GH has endpoints at G(-2,9) and H(10,3). Point J lies on GH between G and H such that GJ:GH=1:3. Find the coordinates of J. Watch out, there is something slightly different here.
Answer:
( 1, 7.5 )
Step-by-step explanation:
First I found the midpoint of the G and H coordinates. Then I found the midpoint of that new coordinate and G.
The coordinate of point J is given by the section formula with ratio 1: 3 is (1, 7.5).
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of line, etc.
Segment GH has endpoints at G(-2,9) and H(10,3). Point J lies on GH between G and H such that GJ: GH is 1: 3.
Let the coordinate of the J be (x, y).
We know that the section formula is given as
[tex]\rm (x, y) = ( \dfrac{m_1x_2 + m_2x_1}{m_1 + m_2}, \dfrac{m_1y_2 + m_2y_1}{m_1 + m_2})\\\\(x, y) = ( \dfrac{1*10+3(-2)}{1+3}, \dfrac{1*3+ 3*9}{1+3})\\\\(x, y) = ( \dfrac{4}{4}, \dfrac{30}{4})\\\\(x, y) = (1, 7.5)[/tex]
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Nathan is building a model of his father sailboat with a scale factor of 1/32 The actual sale is in the shape of a right triangle with a base of 8 m and a hypotenuse of 13 m what will be the approximate perimeter of the sale on the model boat
Answer:
Perimeter of the model is approximately 1 m.
Step-by-step explanation:
Given:
Scale factor = [tex]\frac{1}{32}[/tex]
Actual base length of the sailboat (b) = 8 m
Actual hypotenuse length of the sailboat (h) = 13 m
Using Pythagoras theorem, we can find the third side of the right angled sailboat. Let the third side be 'l' m. So,
[tex]h^2=b^2+l^2\\\\13^2=8^2+l^2\\\\l^2=169-64\\\\l=\sqrt{105}=10.25\ m[/tex]
Now, actual perimeter of the sailboat = Sum of all the 3 sides
Actual perimeter = 13 m + 8 m + 10.25 m = 31.25 m
Now, we know that,
Scale factor = Model dimensions ÷ Actual dimensions
So, in terms of perimeter,
Scale factor = Model perimeter ÷ Actual perimeter
[tex]\frac{1}{32}=\frac{Model\ perimeter}{31.25}\\\\Model\ perimeter=\frac{31.25}{32}=0.97\approx1\ m[/tex]
So, perimeter of the model is approximately 1 m.
If Alex and Brandon work together, they will finish cleaning the school in 15 hours. Working alone, Brandon can finish the same job in 20 hours. How long will it take Alex to do the job by himself?
Answer:
Alex can do the job in 60 days alone.
Step-by-step explanation:
Alex and Brandon working together, they can finish the job of cleaning the school in 15 hours. Brandon alone in 20 hours can finish the job.
So, Brandon can complete [tex]\frac{1}{20}[/tex] part of the job in one hour.
Let, Alex alone can finish the same job in x hours.
So, Alex can complete [tex]\frac{1}{x}[/tex] part of the job in one hour.
So, working together they do [tex](\frac{1}{20} + \frac{1}{x}) = \frac{x + 20}{20x}[/tex] part of the whole job in one hour.
Hence, from the conditions given we can write
[tex]\frac{x + 20}{20x} = \frac{1}{15}[/tex]
⇒ 15x + 300 = 20x
⇒ 5x = 300
⇒ x = 60 days.
Therefore, Alex can do the job in 60 days alone. (Answer)
Aim for a weight loss of between 5% and 10% of your current weight within a six-month period true or false
Answer:
true
Step-by-step explanation:
it is possible through thorough work out and exercises
and secondly a numbers of diets has to be avoided such starchy foods and junks
You are asked to put aluminum siding on the two ends of a house. Siding cost $18.50 per square yard and you charge $12.40 per square yard fir installation. How much should you charge to put siding on the ends of the house
Answer:
$1510.32 (Select option closest to this)
Step-by-step explanation:
Given:
- Siding material cost = $18.50 per square yard
- installation cost = $12.40 per square yard
- width of one side = 22 ft
- height of one side = 10 ft
Find:
- How much should you charge to put siding on the ends of the house
Solution:
- Assuming the the cost of material is also borne by you. Summing the rate of material and installation for both sides for you per square yard:
Total rate for both side = 2*($18.50 per square yard + $12.40 per square yard
Total rate for both side = $ 61.8 per square yard
- Area covered by a side is:
Area covered = 10 * 22 = 220 ft^2 * (yard^2 / 9 ft^2) = 24.44 yard^2
- Total amount you will be charging is:
Total amount = Total rate for both side * Area covered
Total amount = $ 61.8 per square yard * 24.44 yard^2 = $1510.32
Ruben has his dad are building a tree house the treehouse . The tree house has an area of 384 square feet the width of the tree house is 3/8 its length.What is the length of the treehouse
Answer:
12.25 ft
Step-by-step explanation:
(3/8)x + (5/8)x = √384
0.375x + 0.625x = 19.6
x = 19.6
Since L = 5/8 * 19.6 = 12.25 ft
The length of the treehouse, we use the area (384 square feet) and the given ratio (width is 3/8 the length). After setting up the equation, we solve for the length to find that the length of the treehouse is 32 feet.
The length of the treehouse, we can set up an equation using the given area and the relationship between the width and length. Let L represent the length and W represent the width. According to the problem, W = {3}/{8}L.
The area of the treehouse is given as 384 square feet. The formula for the area of a rectangle is Area = Length imes Width, so we have:
L times W = 384 square feet
L times {3}/{8}L = 384
{3}/{8}L² = 384
L² = rac{384 times 8}{3}
L² = 128 times 8
L² = 1024
L =[tex]\sqrt{1024}[/tex]
L = 32 feet
Therefore, the length of the treehouse is 32 feet.
The high school debate team is developing a logo to represent their club. A scale drawing of the logo design is presented below, where each unit of the grid represents 3 inches in length. The team is printing out an enlargement of the new logo, where the enlargement has a height of 105 inches. The area of the enlargement will be inches2, which is times the size of the original scale drawing.
Answer:
c
Step-by-step explanation:
Answer:
The enlargement will be 2,250 which is 25 the times
Step-by-step explanation:
In the provided scale drawing, each unit represents 3 inches in length. Use this scale to add the real world measurements to the scale drawing as shown.
It can be seen from the figure that the total height of the scale drawing is 9 in + 3 in + 9 in = 21 in. It is given that the enlargement has a height of 105 inches. Find the scale factor between the scale drawing and the enlargement by dividing as shown.
The scale factor of 5 means that each dimension of the enlargement will be 5 times larger than the matching dimension of the scale drawing. So, the dimensions of the enlarged figure are shown below.
The logo is made up of three polygons: two triangles and one square. To find the total area of the logo, the area of each region must be found and added together.
To calculate the area of a triangle, use the formula below where b is the length of the base of the triangle and h is the height of the triangle.
To calculate the area of a square, use the formula below, where s is the length of the side of the square.
Now, calculate the areas of of the two logos.
Finally, determine how many times larger the area of the enlargement is than the scale drawing by dividing, as shown below.
Therefore, the area of the enlargement will be 2,250 inches2, which is 25 times the size of the original scale drawing.
A group of 5 friends go to a baseball game. Each person buys a ticket for the game and 2 hotdogs. Let t represent the cost of ticket and h represent the cost of a hotdog.
The expression that represents the total cost of the baseball game will be 5t + 2h.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
An expression or formula is a finite collection of signs and is well thus according to context-dependent norms.
A gathering of 5 companions goes to a ball game. Every individual purchases a ticket for the game and 2 hotdogs. Allow t to address the expense of a ticket and h to address the expense of hotdogs.
Then the expression of the total cost is given as,
⇒ 5t + 2h
The expression that represents the total cost of the baseball game will be 5t + 2h.
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Describe and sketch the surface in R^3 represented by the equation x + y = 2
Answer:
The Surface in R^3
Step-by-step explanation:
Represented by the equation x+y=2
when y=0
then 0=2-x
x=2
similarly
when x=0
then 0=2-y
y=2
the sketch and description is in attached file
Answer: The equation is a plane.
Graph is attached.
The equation [tex]x + y = 2[/tex] is an equation of a plane in [tex]R^3[/tex].
z can take any value and x and y must satisfy the equation [tex]x + y = 2[/tex].
3 such points are: [tex]A = (0, 2, 0), B = (2, 0, 0), C = (1, 1, 3)[/tex].
Then we plot the points and draw a plane through them.
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Please help me, i am horrible at geometry.
Answer:
m<BCD is equivalent to 148*
Step-by-step explanation:
We know this due to the inscribed angle always being congruent to the angle that it inscribes. Hope this helps
Answer:
106°
Step-by-step explanation:
m arc BCD=148
∠A=1/2*148=74°
∠BCD=180-74=106°
At Joe's Pizza a 16 inch diameter pizza and a 12-inch-diameter pizza cost the same per square inch of top surface area. If the cost of a large pizza is 9.60, what is the cost, in dollars, of the small pizza?
Answer:
5.4
Step-by-step explanation:
Surface area of the large 16 in diameter pizza is
[tex]A = \pi(d/2)^2 = \pi8^2 = 64\pi[/tex]
Cost per unit surface area is
[tex]c = \frac{9.6}{64\pi} = \frac{0.15}{\pi}[/tex]
Surface area of the small 12-in diameter pizza is
[tex]a = \pi(12/2)^2 = \pi6^2 = 36\pi[/tex]
So the total cost for that much surface area of pizza is
[tex]ac = 36\pi*\frac{0.15}{\pi} = 5.4[/tex]
How do you do this question?
Step-by-step explanation:
The integral is the area under the curve. When the curve is above the x-axis, the area is positive. When the curve is below the x-axis, the area is negative. The integral equals 0, so we want to find the value of b such that the area of the quarter circle is canceled out by the area of the triangle.
Area of the quarter circle is:
A = π/4 r²
A = 9/4 π
Area of the triangle is:
A = ½ bh
9/4 π = ½ (b − 3) (b − 3)
9/2 π = (b − 3)²
b − 3 = 3√(π/2)
b = 3 + 3√(π/2)
b = 6.760
The CEO of a large electric utility company claims that 80 percent of his 1,000,000 customers are very satisfied with the service they receive. To test this claim, the local newspaper surveyed 100 customers, using simple random sampling. After performing the appropriate statistical test, they find the p-value to be 0.894. What conclusion can we make?
Answer:
Conclusion: The proportion of customers satisfied with the service they receive from the large electric utility company is different from 80%, the claim made by the CEO.
Step-by-step explanation:
To test the claim made by the CEO of a large electric utility company the newspaper must conduct a hypothesis test for one proportion.
Assumption:
The significance level (α) of the test can be assumed to be 5%.
Hypothesis:
[tex]H_{0}:[/tex] The proportion of customers satisfied with the service they receive is 0.80, i.e. [tex]p=0.80[/tex]
[tex]H_{a}:[/tex] The proportion of customers satisfied with the service they receive is different from 0.80, i.e. [tex]p\neq 0.80[/tex]
Decision Rule:
If the p-value of the test is less than the significance level (α) then the null hypothesis may be rejected. But if the p-value is more than the significance level (α) then we cannot reject the null hypothesis.
Test Statistics:
As the sample size is large, i.e.n = 100 > 30, then according to the central limit theorem sampling distribution of sample proportion will follow the normal distribution.
The test statistic used is:
[tex]z=\frac{\hat p-p}{\frac{\sqrt{p(1-p)}} {n} }[/tex]
Given:
The p-value of the hypothesis test is computed to be 0.894.
That is:
[tex]p-value=0.894>\alpha =0.05[/tex]
This implies that we fail to reject the null hypothesis at 5% level of significance.
Conclusion:
The null hypothesis was failed to be rejected at 5% level of significance.
Thus, concluding that the proportion of customers satisfied with the service they receive from the large electric utility company is different from 80%, the claim made by the CEO.
The graph shows the distance y, in centimeters, a pendulum moves to the right (positive displacement) and to the left (negative displacement), for a given number of seconds x.
How many seconds are required for the pendulum to swing from its position furthest to the right to its position furthest to the left?
Time required for the pendulum to swing from its position furthest to the right to its position furthest to the left: 1.25 seconds
Step-by-step explanation:
A pendulum is a system consisting of a rod/string connected to a mass which is left free to oscillate back and forth around its equilibrium position, straight vertical.
The period of a pendulum is the time the pendulum takes to complete one full oscillation, that means it is the time the pendulum takes to go from its furthest position on the left to the same position again. It is calculated as
[tex]T=2\pi \sqrt{\frac{L}{g}}[/tex]
where L is the length of the pendulum and g the acceleration of gravity.
The figure in this problem represents the position of the pendulum. We observe that the time it takes for the pendulum to do one complete oscillation is 2.5 seconds.
The time it takes for the pendulum to swing from its position furthest to the right to its position furthest to the left is half the period: therefore, it is
[tex]\frac{T}{2}=\frac{2.5}{2}=1.25 s[/tex]
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A has the coordinates (-4,3) and B has the coordinates (4,4). If Do1/2 (x,y) is a dialation of ABC, what is true about the image A’B’C? Check all that apply
Answer:
The answer is A B C
I just took the test
Step-by-step explanation:
Answer:
ABC
Step-by-step explanation:
AB is parallel to A'B'.
DO,1/2(x, y) = (one-half x, one-half y)
The distance from A' to the origin is half the
Please assist me with this problem
Answer:
The answer to your question is 90 dB
Step-by-step explanation:
Data
I = 10⁻³
I⁰ = 10⁻¹²
Formula
Loudness = 10log ([tex]\frac{I}{Io}[/tex])
Process
1.- To solve this problem, just substitute the values in the equation and do the operations.
2.- Substitution
Loudness = 10 log [tex](\frac{10^{-3}}{10^{-12}} )[/tex]
3.- Simplify
Loudness = 10log (1 x 10⁹)
Loudness = 10(9)
Loudness = 90
Students who attend Washington Middle School are either in seventh or eighth grade. At the end of the first semester 25% of the students at Washington Middle School were on the honor roll. Seventh graders represented 60% 60 % of the students on the honor roll. If 124 124 students on the honor roll were in eighth grade, how many students attend Washington Middle School? There are students who attend Washington Middle School.
Answer:
There are 1240 students who attended Washington Middle School.
Step-by-step explanation:
Given:
Students who attend Washington Middle School are either in seventh or eighth grade.
At the end of the first semester 25% of the students at Washington Middle School were on the honor roll.
Seventh graders represented 60% of the students on the honor roll.
If 124 students on the honor roll were in eighth grade.
Now, to find the students attend Washington Middle School.
Let the total number of students be [tex]x.[/tex]
So, the students at Washington Middle School were on the honor roll:
25% of [tex]x[/tex]
[tex]=\frac{25}{100} \times x[/tex]
[tex]=\frac{25x}{100}[/tex]
[tex]=\frac{x}{4}[/tex]
As, given seventh graders represented 60% of the students.
So, the students on the honor roll represented as seventh graders:
[tex]60\%\ of\ \frac{x}{4}[/tex]
[tex]=\frac{60}{100} \times \frac{x}{4}[/tex]
[tex]=0.6\times \frac{x}{4}[/tex]
[tex]=\frac{0.6x}{4}[/tex]
As, 124 students on the honor roll were in eighth graders.
Thus,
According to question:
[tex]\frac{x}{4} -\frac{0.6x}{4} =124[/tex]
[tex]\frac{x-0.6x}{4} =124[/tex]
[tex]\frac{0.4x}{4} =124[/tex]
Multiplying both sides by 4 we get:
[tex]0.4x=496[/tex]
Dividing both sides by 0.4 we get:
[tex]x=1240.[/tex]
Therefore, there are 1240 students who attended Washington Middle School.
A 72.5-foot rope from the top of a circus tent pole is anchored to the ground 44.4 feet from the bottom of the pole. What angle does the rope make with the pole? (Assume the pole is perpendicular to the ground.
Which of the following variables are qualitative and which are quantitative? If the variable is quantitative, then specify whether the variable is discrete or continuous.a. Points scored in a football game.b. Racial composition of a high school classroom.c. Heights of 15-year-olds.
Quantitative in general involves number while qualitative does not involves number. For example, you can count the point scored in a football game which is considered as quantitative. While you cannot count racial composition because it involves different quality or type.
Quantitative is further divided into two type; discrete and continuous. Discrete variable involves integers while in between two values of a continuous variable, there are an infinite number which is valid and this is not the case for discrete variables.
Qualitative is variable something that you cannot count.
Answer:
A. Points scored in a football game - Quantitative; discrete
B. Racial composition of a high school classroom - Qualitative
C. Heights of 15-year-olds - Quantitative; continuous
Points scored in a football game is a discrete quantitative variable, racial composition of a high school classroom is a qualitative variable, and heights of 15-year-olds is a continuous quantitative variable.
Explanation:The variables given in this question can be classified as either qualitative or quantitative.
Points scored in a football game: This is a quantitative variable as it involves numerical measurements. Moreover, since points scored in a game can only take on whole number values (for example, you cannot score 2.5 points in a football game), it is specifically a discrete variable.Racial composition of a high school classroom: This is a qualitative variable as it involves non-numerical categories or types, namely, different races.Heights of 15-year-olds: This variable is quantitative, as it involves measurement of a physical characteristic (height). Furthermore, since height can take on any value within a certain range (for example, a 15-year-old could be 1.52 meters tall or 1.523 meters tall), this is a continuous variable.Learn more about Qualitative vs Quantitative Variables here:https://brainly.com/question/31565073
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Olivia wants to cut 3 3/4 inches from a piece of string.She has already cut off 2 9/16 inches from the piece of string.How much more string should she cut off.
Olivia should cut off an additional 19/16 inches of string.
We have,
Total length to be cut off: 3 3/4 inches
Length already cut off: 2 9/16 inches
First, let's convert the mixed numbers to improper fractions:
3 3/4 = (4 x 3 + 3)/4 = 15/4
2 9/16 = (16 x 2 + 9)/16 = 41/16
Now, subtract the length already cut off from the total length to be cut off:
3 3/4 - 2 9/16
= 15/4 - 41/16
= (60 - 41)/16
= 19/16
Therefore,
Olivia should cut off an additional 19/16 inches of string.
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Olivia needs to cut off another 1 3/16 inches of string. We found this by converting the mixed numbers to improper fractions, finding a common denominator, then subtracting and converting the result back to a mixed number.
Explanation:In this mathematics problem, Olivia wants to cut 3 3/4 inches from a piece of string but she has already cut off 2 9/16 inches. To find out how much more she should cut, we subtract the amount she has already cut from the total amount she wants to cut.
Here's the process: 3 3/4 - 2 9/16
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A ball is thrown 178 m upward and then falls back to earth. Neglecting air resistance, how long will it be in the air? The acceleration of gravity is 9.8 m/s 2 .
After calculating the initial velocity with which the ball was thrown upwards, the time taken for the ball to reach its peak and fall back to earth was calculated to be approximately 38 seconds.
Explanation:In order to find out how long the ball will be in the air, we are essentially dealing with an example of free fall in Physics. When the ball reaches its maximum height, its velocity will be zero and it will have spent a certain amount of time t to reach there. But the total time it will be in the air is twice this amount, as it will take the same amount of time to go up and come back down.
Using the second equation of motion, v = u + gt (where v = final velocity, u = initial velocity, g = acceleration due to gravity and t = time), when the ball reaches maximum height, its final velocity (v) is zero. If we rearrange this equation, we get t = (v - u) / -g.
As the problem doesn't state the initial velocity with which the ball is thrown upward, we need to find it first. We can do this by applying the equation of motion: v² = u² + 2gs, where s = displacement. If we set v = 0 at maximum height, the equation becomes u = √(2gs). Given s = 178 m and g = 9.8 m/s², we find u ≈ 186.26 m/s. Substituting these values into our time equation, we get t ≈ 19 seconds for the time to reach maximum height. As mentioned, the ball will take the same time to fall back, hence the total time in air will be around 38 seconds.
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What is the repulsive force between two pith balls that are 13.0 cm apart and have equal charges of −24.0 nC?
Answer:
The repulsive force is [tex]3.067\times10^{-4}N[/tex].
Step-by-step explanation:
Consider the provided information.
The coulomb's law to calculate the repulsive force: [tex]F=\frac{kQ_1Q_2}{r^2}[/tex]
Where the value of k is 9.00×10⁹ Nm²/C²
Substitute the respective values in the above formula.
[tex]F=\frac{9\times10^9\frac{N\cdot m^2}{c^2} \times(-24\times10^{-9}C)^2}{[(13 cm)(\frac{1m}{100cm} )]^2}[/tex]
[tex]F=\frac{9\times10^9\frac{N\cdot m^2}{c^2} \times(-24\times10^{-9}C)^2}{(0.13 m)^2}[/tex]
[tex]F\approx0.0003067N[/tex]
[tex]F=3.067\times10^{-4}N[/tex]
Hence, the repulsive force is [tex]3.067\times10^{-4}N[/tex].
An isosceles triangle has exactly two sides that are equal in length (congruent). If the base (the third side) measures 46 inches and the perimeter is 119 inches, find the length of the two congruent sides, called legs.
Answer:
36.5 Inches
Step-by-step explanation:
The perimeter of the triangle is the sum of all three(3) sides.
let the length of one congruent side be 'a', Therefore;
a + a + 46 = 119
2a = 119 - 46
a = 73/2
a = 36.5 inches.