Using proportions, the explanation for this is that a basketball game has four quarters, hence half-time is at the end of the second quarter.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the basic arithmetic operations, especially multiplication and division with the unit rates in the problem.
The entirety of a basketball game is composed by:
4 quarters.
Hence the mid-point of the game is calculated as follows:
0.5 x 4 quarters = 2 quarters.
This means that the end of the second quarter is the mid-point of the game, which is why the halftime is positioned at the end of the second quarter.
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chegg a 12 ft ladder is leaning against a wall. if the top of the ladder slides down the wall at a rate of 4 ft/s, how fast (in ft/s) is the bottom moving along the ground when the bottom of the ladder is 6 ft from the wall?
The bottom is moving at a rate of [tex]4\sqrt{3}[/tex] ft/s along the ground when the botton of the ladder is at a distance of 6 ft from the wall.
Here we have been mentioned that a 12 feet ladder is leaning against the wall which is represened by AC in the below given triangle.
We have AB = y = distance of top of the ladder from the wall
BC = x = distance of bottom of the ladder from the wall
AC = z = height of the ladder = 12 ft (given)
The top of the ladder AB is sliding down at a rate of 4 [tex]ft/s[/tex]
∴ [tex]\frac{dy}{dt}[/tex] = - 4 ft/s (negative sign indicates that the top is sliding downwards)
Let the rate at which the bottom of the ladder is sliding be [tex]\frac{dx}{dt}[/tex]
Now in the right angled triangle [tex]ABC[/tex] by using Pythagoras theorem we have,
[tex]AB^{2} + BC^{2} =[/tex][tex]AC^{2}[/tex]
[tex]y^{2} +x^{2} = z^{2}[/tex] (equation 1)
When x = 6ft and z = 12 ft,
[tex]y^{2} +6^{2} = 12^{2}[/tex]
⇒ [tex]y^{2} = 144 - 36[/tex]
⇒ [tex]y^{2} = 108[/tex]
⇒ y = √108
⇒ y = 6 √3 ft
Differentiating equation 1 with respect to [tex]time[/tex] we get,
[tex]\frac{d}{dt} (y^{2} +x^{2} ) = \frac{d}{dt} (z^{2})[/tex]
⇒ 2y[tex]\frac{dy}{dt}[/tex] + 2x[tex]\frac{dx}{dt}[/tex] = 2z[tex]\frac{dz}{dt}[/tex]
Putting the values of dz/dt = 0 (as the height is constant) , dy/dt = - 4 ft/s , y = 6 √3 ft, x = 6ft and z = 12ft we have,
∴ 2(6√3) (-4) + 2(6)[tex]\frac{dx}{dt}[/tex] = 2(12)(0)
⇒ -48√3 + 12[tex]\frac{dx}{dt}[/tex] = 0
⇒ 12[tex]\frac{dx}{dt}[/tex] = 48√3
⇒ [tex]\frac{dx}{dt} = \frac{48\sqrt{3} }{12}[/tex]
⇒ [tex]\frac{dx}{dt} = 4\sqrt{3}[/tex] ft/s
Hence the rate at which the bottom of the ladder is sliding is [tex]\frac{dx}{dt} = 4\sqrt{3}[/tex] ft\s
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From a temperature of -29.03° F, a solution heats up 26.5° F.
What is the resulting temperature of the solution?
Think about the situation. What operation does the situation require?
Drag a word to the box to correctly complete the statement.
Answer:
Remember, a positive and a negative while being added is always a negative outcome, so when you add -29.03 + 26.5, you get -2.53
The distance of a golf ball from the hole can be represented by the right side of a parabola with vertex (-1,8). The ball reaches the hole 1 second after it is hit. What is the equation of the parabola, in vertex form, that represents the ball's distance, y, from the hole, x seconds after the ball is hit?
The equation of the parabola, in vertex form, that represents the ball's distance, y, from the hole, x seconds after the ball is hit is
y = (-2m/s²)t² + (-2m/s)t + 6m.
Given:
Let's assume that the hole is at y = 0m, with x seconds as the time.
The vertex of the parabola can be written as (-1s, 8m) where the time variable, x, is supposed to be in seconds, while the distance variable, y, is supposed to be in meters.
The ball reaches the hole at x = 1s, so we have point (1s, 0m)
The vertex of the parabola y = ax² + bx + c is known to be at
x = -b/2a,
So, -1 = -b/2a
We have the following equations,
8m = a(-1s)² + b(-1s) + c
0m = a*(1s)² + b(1s) + c
-1s = -b/2a
b = 2a × 1s
Substituting the value of b in the equations and simplifying them,
8m = a×1s² - 1s×2a×1s + c
⇒ 8m = a( 1s² - 2s²) + c = -a×1s² + c.
0m = a×1s² + 1s×2a×1s + c
⇒ 0m = a(1s² + 2s²) + c = a×3s² + c
Deriving the value of c from the second equation we put it in the first equation,
c = - a×3s²
The first equation is as,
8m = -a×1s² - a×3s² = -a×4s²
a = 8m/-4s² = -2m/s²
From the value of a we can calculate the values of b and c.
c = -a×3s² = -(-2m/s²)×3s²= 6m.
b = 1s×2a = 1s×(-2m/s²) = -2m/s.
Then the equation is:
y = (-2m/s²)t² + (-2m/s)t + 6m
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We would like to estimate the proportion of uf students who owns a scooter to within 1% of the truth, with 95% confidence. We believe around 20% of students do. How many students should be sampled?.
It is determined that 188 students should be sampled to use the confidence interval for a proportion.
What is mean by the term confidence interval?A confidence interval is indeed the mean of the estimate plus and minus its variation.We get the very next confidence interval of percentages in a sample of n people surveyed with a success probability of π and a confidence level of.π ± z√π(1-π)/n
In which case,
z is indeed the z-score with the p-value of 1+α/2
The error margin is as follows:
M = z√π(1-π)/n
In this case:
z does have a p-value of at 95% confidence, so z = 1.96.Thus p = 0.2, a 20% estimate.Taking into account, this same sample size is n. M = 0.02.Then:
M = z√π(1-π)/n
0.02 = 1.96√0.02(1-0.02)/n
√n = 13.72
n = 188.23
To summarize:
A total of 188 students must be sampled to estimate the proportion of of students who owns a scooter.
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if 333.33...points is 1 dollar, how much is 100points
Answer:
0.30 dollar
Step-by-step explanation:
333.33 points == 1 dollar
: 333.33
1 points == 0.003 dollar
* 100
100 points == 0.30 dollar
50% of $99.97
Two answers
Answer:
Step-by-step explanation:
you would cut 99 in half and make your way down until nothing left which gives you 48.985 or
49.99$ rounded
A bag of fertilizer that weighs 18 3/4 pounds can cover 5000 square feet. how many pounds of fertilizer will be needed to cover 27,000 square feet? how many bags of fertilizer are needed?
We know how many pounds are needed to cover 5000 ft^2, and we need to find how many are needed to cover 27000ft^2. To find this value, divide 27000 by 5000 and multiply the result by the weight.
27000/5000 x 18.75
5.4 x 18.75
101.25
So, we need 101 1/4 pounds of fertilizer. How many bags is that?
101.25/18.75
5.4
We'll say that since the 0.4 of a bag will still need to be used, that you need 6 bags to cover 27000ft^2.
Kaitlin has a bookcase with books. There are 50 shelves in the bookcase. Each shelf has the same number of 5 books. How many books does each shelf have?
In parallelogram ABCD, AB = 3 cm and the diagonals AC and BD are 5.8 cm and 4.2 cm respectively. If the diagonals AC and BD intersect at O, then the perimeter of ∆AOB is
In parallelogram ABCD, AB = 3 cm and the diagonals AC and BD are 5.8 cm and 4.2 cm respectively. If the diagonals AC and BD intersect at O, then the perimeter of ∆AOB is 8 cm
How to find the perimeterperimeter of a triangle = length 1 + length 2 + length 3
assuming
length 1 = AB = 3 cm
length 2 = 5.8 / 2
length 3 = 4.2 / 2
Reason for length 2 and length 3 is when the diagonal of a parallelogram intersect they bisect each other. bisect means divide each other into two equal parts
substituting the values
perimeter of the triangle = 3 + 5.8 / 2 + 4.2 / 2
= 3 + 2.9 + 2.1
= 8 cm
The perimeter of the triangle formed is 8 cm
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Multiply or divide.write the productor quotient in simplest form. 1 4/9 (-2 4/7
Answer:
-3 [tex]\frac{5}{7}[/tex]
Step-by-step explanation:
Is this the problem?
1 4/9 (-2 4/7)
[tex]\frac{13}{9}[/tex][tex](\frac{-18}{7})[/tex] = [tex]\frac{-26}{7}[/tex]
-3 [tex]\frac{5}{7}[/tex]
Under her cell phone plan, Mei Mei pays a flat cost of $46 per month and $5 per
gigabyte. She wants to keep her bill under $70 per month. Write and solve an
inequality which can be used to determine g, the number of gigabytes Mei Mei can
use while staying within her budget.
The flat cost of the plan = is $46 per month
Cost per gigabyte = $5 per gigabyte
Number of gigabytes = g
The maximum amount Mei Mei wants to spend on the bill = is $70 per month,
So, for each month,
$46 + $5(g) < $70
⇒ $5(g) < $70 - $46
⇒ $5(g) < $24
⇒ g < $24/$5
⇒ g < 4.8
The number of gigabytes to be used per month should be less than or equal to 4.8.
What is Inequality?Inequalities are algebraic expressions that show how one term is less than, less than or equal to, greater than, or greater than or equal to another rather than how both sides of an equation are equal to each other.The collection of all real numbers that satisfy the inequality is its solution. As a result, x can have any value that resolves the inequality.The values indicated by the symbols < (greater than) and > (less than) are not included in the answer.An inequality with terms of the type of ab, where a and b are real positive numbers or variable expressions, is referred to as a "power inequality." They frequently show up in exercises from mathematics Olympiads.To learn more about Inequality, refer to:
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Inequality: 5g+46<70
Answer: g<4.8
Paula completely covered a square wall using 52.5 ft2 of wallpaper without any overlap. Which measurement is closest to the side
length of this wall in feet?
O 9 ft
O 7ft
O 22 ft
O 44 ft
3. Ross wrote a check for $124 and received a notice 4.
from the bank stating he was $51 overdrawn. His
account now shows a negative balance. How much
money did he have in his account before writing the
check?
SC
1
3
Answer:
$73
Step-by-step explanation:
[tex]2-\frac{x+1}{x-2} -\frac{x-4}{x+2}[/tex] can be written as a single fraction in the form [tex]\frac{ax+b}{x^{2} -4}[/tex] where a and b are integers.
work out the value of a, and the value of b
Answer:
a = 3 , b = - 18
Step-by-step explanation:
2 - [tex]\frac{x+1}{x-2}[/tex] - [tex]\frac{x-4}{x+2}[/tex]
express as a fraction with common denominator (x - 2)(x + 2)
= [tex]\frac{2(x-2)(x+2)-(x+1)(x+2)-(x-4)(x-2)}{(x-2)(x+2)}[/tex]
= [tex]\frac{2(x^2-4)-(x^2+3x+2)-(x^2-6x+8)}{x^2-4}[/tex]
= [tex]\frac{2x^2-8-x^2-3x-2-x^2+6x-8}{x^2-4}[/tex]
= [tex]\frac{3x-18}{x^2-4}[/tex]
compare to [tex]\frac{ax+b}{x^2-4}[/tex]
with a = 3 and b = - 18
I need to write an solve an inequality that describes the width of the lot in terms of w
Given:
The length of the rectangle is 50 yards. The perimeter is less than 180 yards.
Required:
Write the solution inequality in terms of width w.
Explanation:
Let the width of the rectangle is w.
The perimeter of the rectangle is given by the formula:
[tex]P=2(length+width)[/tex][tex]\begin{gathered} 2(50+w)<180 \\ 50+w<90 \\ w<90-50 \\ w<40 \end{gathered}[/tex]Final Answer:
The first option is the correct answer.
If I rotated Block C by 90 degrees clockwise where would it be?
After the 90° rotation, Block C will resemble this in some ways (see the image below).
What is rotation?The concept of rotation in mathematics has its roots in geometry. Any rotation is a movement of a specific area while maintaining at least one point. It may be used to describe, for instance, how a rigid body moves around a fixed point. As an example of rotation in the real world, we know that the earth revolves around its own axis. A group of people walking in a circle while holding hands and rotating either clockwise or counterclockwise.So, rotate block C by 90°:
Block C will look somewhat like this (Refer to the image attached below) after the rotation of 90°.
Therefore, after the 90° rotation, Block C will resemble this in some ways (see the image below).
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what is the answer to 7.25x348
Answer:2,523
Step-by-step explanation:
find two consecutive integers such that 3 times the larger exceeds twice the smallest by 34
Answer:
31 & 32
Step-by-step explanation:
3 x 32 = 96
2 x 31 = 62
62 + 34 = 96
Please please help me with this I’ll give brainly
Hello!
The ratio between pig and other animals
==> looks like [tex]\text{number of pigs}: \text{ number of other animals}[/tex]
Since there are 8 pigs and 11 other kind of animals
⇒ the ratio is ⇒ 8: 11
Hope that helps!
i do NOT understand at all desperate need of help !!
Lets first look at the cost per round with the 25 round pass
Take the total cost and divide by the number of rounds
$84 / 25 rounds
$ 3.36 per round
OR
They can pay 3.25 per round with the single pay
$3.25 is less than 3.36 so it is cheaper ( less per round) to pay the single round price
Option 2 $3.25 is cheaper
ANSWER QUICK FOR BRAINIEST!
Solve the equation for x. −0.28x − 15.3 = 1.92 x = 61.5 x = −61.5 x = 47.8 x = −47.8
The value of x is −61.5 . option B
What is an algebraic expression?An algebraic expression is simply seen as one with terms, factors, variables, coefficients, constants.
These expressions may also consist of arithmetic operations, some of which includes;
AdditionDivisionSubtractionMultiplicationBracketParentheses, among others.Based on the information given, we have;
−0.28x − 15.3 = 1.92
To determine the value of the variable 'x' we need to take the following steps;
collect like terms from the equation
-0. 28x = 1. 92 + 15. 3
Add like terms
-0. 28x = 17.22
Divide both side by the coefficient of x
x = 17. 22/-0.28
x = - 61. 5
Hence, the value is - 61. 5
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y= 24 will this be a vertical or horizontal line?
It will be a horizontal line
Miranda and Lily both bought a used car on the same day. Miranda's used car has 5,132 miles on it already, and she drives 525 miles per month. Lily's car has 4,789 miles on it already, and she drives 723 mile per month.
The months will they have same number of miles. is 1.732 months.
How to illustrate the information!Miranda's used car has 5,132 miles on it already, and she drives 525 miles per month. This will be expressed as y = 5132 + 525x
Lily's car has 4,789 miles on it already, and she drives 723 mile per month. This will be:
y = 4789 + 723x
x = number of months
y = miles
The number of months will be gotten by equating the equations. This will be:
5132 + 525x = 4789 + 723x
Collect like terms
198x = 343
Divide
x = 343 / 198
x = 1.732 months.
The number of months is 1.732.
The complete question is written below.
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Miranda and Lily both bought a used car on the same day. Miranda's used car has 5,132 miles on it already, and she drives 525 miles per month. Lily's car has 4,789 miles on it already, and she drives 723 mile per month. How many months will they have same number of miles.
The following is a list of 4 measurements.10, 11, 15, 6Send data to calculatorSuppose that these 4 measurements are respectively labeled X1, X2, ..., *4. Compute the following.4Σi=1
Given the measurements:
x1 = 10
x2 = 11
x3 = 15
x4 = 6
We're asked to find:
[tex]\sum ^4_{i=1}(x_i)^2=x^2_{1^{}}+x^2_2+x^2_3+x^2_4[/tex]Which is
100+121+225+36
=482
Alayna is hanging a picture frame in the center of a wall that is 8 feet wide. If the picture frame is 21 1 over 4
inches wide, how far will each side of the picture frame be from the edge of the wall (in inches)? First, estimate the amount and then find the exact measurement. In two or more complete sentences, explain how you solved the problem. You may include a diagram in your explanation if you wish.
8 feet is known to equal 96 inches.
48 inches are divided in half,
and because the image is hung in the middle of the wall,
the subject of the image is that,
11 inches on each side, as well.
This is,
37 inches of wall on each side of 48-11.
How do you figure out a rectangle's area?A rectangle is a closed figure with four equal and opposite sides. Consequently, the length, which is also known as the height, and the width of a rectangle can be used to define it (sometimes called breadth).
The formula for a rectangle's surface area is as follows:
A=lxw
A=l×w
where:
A is the surface area of the rectangle;
L specifies the length of the rectangle.
Usually, it refers to the longest side of the rectangle.
W is the rectangle's width which is rectangle's shortest side.
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a community assesses a random sample of its residents by telephone questionnaire. obesity is strongly associated with diagnosed diabetes. this study design is best described as which one of the following: a. experimental b. cohort c. cross-sectional d. case-control
The study design is best described as a case-control study.
A community uses a telephone survey to rate a representative sample of its citizens.
Diabetes is significantly correlated with obesity.
Non-experimental or observational study designs include cohort designs. In a cohort study, the participants don't already have the desired result. They are chosen based on the person's exposure status.
A case-control study is a sort of observational research in which two existent groups with outcomes that differ from one another are found and compared on the basis of a purported causal factor.
An example of an observational study design is the cross-sectional study design. In a cross-sectional study, the researcher simultaneously assesses the participants' exposures and outcomes.
Therefore, the study is a case-control study.
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A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 7(1.06)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 13.29 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 4 to d = 11, and what does it represent? (4 points)
From the given function, it is found that:
a. A reasonable domain for the function is of 0 ≤ d ≤ 11.
b. The y-intercept of the graph represents that the initial radius of the algae is of 7 mm.
c. The average rate of change between the 4th and the 11th day of the function means that the radius of the algae grew by an average of 0.64 mm a day.
What does the function represent?The function is modeled according to the following rule:
f(d) = 7(1.06)^d
In which:
d is the number of days.f is the radius of the algae.When the biologist concluded her study, the radius of the algae was approximately 13.29 mm, hence the upper bound of the domain is found as follows:
[tex]13.29 = 7(1.06)^d[/tex]
[tex](1.06)^d = \frac{13.29}{7}[/tex]
[tex]\log{(1.06)^d} = \log{\left(\frac{13.29}{7}\right)}[/tex]
[tex]d\log{1.06} = \log{\left(\frac{13.29}{7}\right)}[/tex]
[tex]d = \frac{\log{\left(\frac{13.29}{7}\right)}}{\log{1.06}}[/tex]
d = 11.
The smallest possible number of days is of 11, hence a reasonable domain for the function is:
0 ≤ d ≤ 11.
The y-intercept of the graph represents that the initial radius of the algae, as it is calculated when d = 0, hence it's value is given by:
[tex]f(0) = 7(1.06)^0 = 7[/tex]
The average rate of change of a function is given by the change in the output divided by change in the input, hence:
[tex]f(11) = 7(1.06)^{11} = 13.29[/tex][tex]f(4) = 7(1.06)^{4} = 8.84[/tex]r = (13.29 - 8.84)/(11 - 4) = 0.64 mm a day.
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Shiloh is starting a new workout regimen. Her trainer recommends that she increase the number squats she does by 35% every week. If in the second week Shiloh is doing 108 squats, how many squats did she do during her first week?
Middle School Math
The number of squats she did in the first week is 81 squats.
What is a Percentage Increase?This refers to the amount of value that a thing is incremented by, in a percentage, which is over 100.
Calculations and ParametersGiven that she had a percentage increase by 35%
And started doing 108 squats
To find the number of squats she did during the first week would be:
100-35= 75%
75/100 * 108= 81 squats.
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9. Find the area of the shaded region.
22 cm
10 cm
7cm
Using the area of triangles and rectangles, we know that the area of the shaded region is 255cm².
What is the formula for the area of a rectangle and triangle?Area of rectangle = length x widthArea of triangle = 1/2 x base x heightIn the given shaded region there is one rectangle and one triangle.
First, find the area of the shaded rectangle.
Here, length = 22 cm and width = 10 cm.So, Area of rectangle = length x width = 22 x 10Area of rectangle = 220 square cm.Now find the area of the shaded triangle.
Here, base = 10 cm and height = 7 cm.So, the Area of the triangle is:
Area = 1/2 × 10 × 7= 35cm²Therefore, the total area of the shaded region is:
Area of shaded region = Area of rectangle + Area of triangle= 220 + 35Area of shaded region = 255 square cm.Therefore, using the area of triangles and rectangles, we know that the area of the shaded region is 255cm².
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Which expressions are equivalent to 211? Select all that apply.
What do the answer?
Answer:
A,B,C
Step-by-step explanation: