There is a 21.5% chance that a point in a square with nine congruent circles drawn there won't be within one if it is chosen at random.
It is given to us that :
Nine congruent circles are inscribed in a square
The square has a side length of 126
We have to find out the probability that the point is not in a circle, if a point in the square is chosen at random.
It is known that the square has a side length of 126.
=> Area of the square = [tex](Length)^{2}[/tex]
=> Area of the square = [tex]126^{2}[/tex]
=> Area of the square = 15876 ------ (1)
It is also known to us that nine congruent circles are inscribed in the square that has a side length of 126.
=> Diameter of each circle = 126/3
=> Diameter of each circle = 42
=> Radius of each circle = 21 ------ (2)
We know that the area of a circle is given as -
Area of circle = [tex]\pi r^{2}[/tex] ------ (3)
where,
r = radius of the circle
Substituting the value of r from equation (2) in equation (1), we have
Area of circle = [tex]\pi r^{2}[/tex]
=> Area of circle = [tex]\pi (21)^{2}[/tex]
=> Area of circle = 1385.44
=> Area of 9 circles = 12468.96 ----- (4)
Now, we can say that -
Area not in a circle = Area of square - Area of 9 circles
=> Area not in a circle = 15876 - 12468.96 [From equation (1) and (4)]
=> Area not in a circle = 3407.04 ------ (5)
We know that the probability of a outcome is given as -
Probability = Number of favorable outcomes/Total number of outcomes
So, the probability that the point is not in a circle can be calculated as -
Probability = Area not in a circle/Area of square
=> Probability = 3407.04/15876
=> Probability = 0.215
=> Probability = 21.5%
Thus, if there are nine congruent circles inscribed in a square and a point in the square is chosen at random, the probability that the point is not in a circle is 21.5%.
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The gardening club at school is growing vegetables. The club has 300 square feet of planting beds. Cucumber plants require 6 square feet of growing space, and tomato plants require 4 square feet of growing space. The students want to plant some of each type of plant and have at least 60 plants.
Select all of the equations or inequalities that could describe this situation. Let c represent the number of cucumber plants and t represent the number of tomato plants.
Answer:
There are several equations or inequalities that could describe this situation. Here are a few examples:
- The total number of plants cannot exceed 60: c + t ≤ 60
- The total number of plants must be at least 60: c + t ≥ 60
- The total amount of growing space must not exceed 300 square feet: 6c + 4t ≤ 300
- The total amount of growing space must be at least 300 square feet: 6c + 4t ≥ 300
Step-by-step explanation:
Any equation or inequality that accurately represents the given constraints on the number and types of plants, and the amount of growing space available, could be used to describe this situation.
If CD=9 and DE= 15. AB = 20, what is the length of AD?
Answer:
12
Step-by-step explanation:
How much work have you done if you lift a 5 newton box 1.5 meters off the ground?
Answer:
7.5 joules
Step-by-step explanation:
The amount of work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force applied to the box is 5 newtons and the distance over which the force is applied is 1.5 meters.
The amount of work done on the box is therefore 5 newtons * 1.5 meters = 7.5 joules. This is the amount of energy that has been transferred to or from the box as a result of the force applied to it.
Rob and Ahab are in Las Vegas for vacation. They get a taxi to drive
them around town. The taxi charges a flat fee of $5.00 plus $1.25 per
mile of traveling. They want to spend less than $45.00 for their taxi
fare.
Write an inequality to represent this situation. Use x for the variable.
The inequality to represent this situation is 5 + 1.25x < 45.
How to use inequality to represent a situation?Rob and Ahab are in Las Vegas for vacation. They get a taxi to drive
them around town. The taxi charges a flat fee of $5.00 plus $1.25 per
mile of traveling. They want to spend less than $45.00 for their taxi
fare. The inequality to represent the situation is as follows:
let
x = number of miles
Therefore, the inequality is as follows:
5 + 1.25x < 45
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Amadou bought a pair of sunglasses online for $60. He used a coupon code to get a 40% discount. The website also applied a 15% processing fee to the price after the discount. How much was the discount, in dollars and cents?
A total discount of $18.6 and 1860 cents is availed by Amadou in buying pair of sunglasses after the final step of processing charge.
Given the intital price as $60 i.e cost price
given he had a coupon code to get discount of 40%
so after apply discount the price of pair of sunglasses is [tex]\frac{100-40}{100} *60[/tex]
=> 0.6 *60
=>36
so the current price of pair of sunglasses is $36
now we need to apply 15% processing fee after the discount so the current price of pair of sunglasses will increase from previous value and is given by:
[tex]36 + \frac{15}{100} *36[/tex]
=>36 + 5.4
=> 41.4
so the final price of pair of sunglasses is $ 41.4
Total discount = initial price - final price
=> 60- 41.4
=> $18.6
$1 = 100 cents
so total discount = 18.6 *100 = 1860 cents
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If the simple interest on $1,000 for 6 years is $300, then what is the interest rate?
The rate is ___ %
PLEASE HELP!!!
Answer: 30%
Step-by-step explanation:
First, take 300 divided by 1000, then times 100% = 30% for 6 years
If you want to find the rate for each year
The take 30% divided by 6
You get 5% each year
I'LL GIVE BRAINLIEST!!
A train travels from City A to City B. The table below shows the distance and the amount of time it takes on the train.
Answer:
The train does not go the same distance each minute.Approximately 6 minutes.--------------------------------------------
The distance traveled in each minute is a speed.
Find the speed per min for each distance:
9/3 = 3 km/min,12/4 = 3 km/min,18/9 = 2 km/min.Since the speed is not same over the total distance, the first choice is correct.
Find the average speed over the given distance:
(9 + 12 + 18)/(3 + 3 + 2) = 39/8 = 4.875 km/minFind the predicted time to travel 30 km:
30 / 4.875 ≈ 6.15 min
Mr. Johnson instructed his students to use the Pythagorean Theorem to draw a line that is precisely 13−−√ units long from the star to another grid point. The dots are one unit apart. Using right triangles to determine the distance, how many different lines could Mr. Johnson’s students create without going off the paper?
The distance between the two given points is 13 units.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
The Pythagorean theorem is given by the following formula:
h² = a² + b²
Where h is the hypotenuse and a and b are the legs of the right triangle.
In the given image, when you construct a right triangle with the line of the two points as a hypotenuse, you have for a and b:
a = 5
b = 12
Replace the previous values of a and b in the formula for h:
h² = (5)² + (12)²
h² = 25 + 144
h² = 169
h = √169
h = 13
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The cuboid-shaped cake below has a total height of 7 cm. The top layer, the cream, and the jam have a combined height of 2 cm. Work out the volume of the bottom layer of the cake. Give your answer in cm³.
Answer:
360 cm³
Step-by-step explanation:
height of bottom layer = 7 - 2 = 5cm
Volume = 9 · 8 · 5 = 360 cm³
Ryan invested \$4,800$4,800 in an account in the year 1990, and the value has been growing exponentially at a constant rate. The value of the account reached \$6,300$6,300 in the year 1998. Determine the value of the account, to the nearest dollar, in the year 2007.
The value of the account to the nearest dollar in 2007 is $6,929.76
How to determine the value of an account?We should know that value is the amount left in an account at a particular time
The given parameters are
In 1990 the value is = $4,800.
In 1998, the value is =$6,300
From 1990 to 1998 there are 8 years
Increase in the investment
Using simple interest,
SI= (P*T*R)÷100
Applying the figures in the formula
1500=(4800*8*R)÷100
⇒ 15000=30400R
Making R the subject we have
R= 4.93%
⇒ 4.93% of 4800 *9 = $2129.76
Add initial cost of investment and the interest for 9 years
=$(4800+2129.76)
=$6929.73
In conclusion, the value of the account would on the $6929.76
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Prove that the difference between quare of conecutive even number i alway a multiple of 4
let n tand for any integer in your working
It is proved that the difference between squares of consecutive even numbers is always a multiple of 4.
Let's consider two consecutive even numbers.
If n = a positive integer
Then the 1st even number would be = 2n
Let the next consecutive even number = 2(n+1)
The consecutive even numbers would be:
2n, 2(n+1)
The square of each consecutive even number is given by -
(2n)² = 2n ×2n = 4n²
[2(n+1)]² = (2n+2)² =(2n+2)(2n+2)
Expanding, we get,
= 4n² +4n +4n+4
[2(n+1)]² = 4n²+8n+4
To determine if the difference between squares of consecutive even numbers is always a multiple of 4, we would substitute values for ' n ' to find the differences between the squares of each consecutive even number.
Let n = 1, 2, 3
For n= 1,
4n² = 4(1)² = 4×1 = 4
4n²+8n+4 = 4(1)² + 8(1) + 4
= 4+8+4 = 16
Thus, the difference between the squares of consecutive even numbers = 16-4 = 12
For n= 2,
4n² = 4(2)² = 4×4 = 16
4n²+8n+4 = 4(2)² + 8(2) + 4
= 16+16+4 = 36
Thus, the difference between the squares of consecutive even numbers = 36-16 = 20
For n= 3
4n² = 4(3)² = 4×9 = 36
4n²+8n+4 = 4(3)² + 8(3) + 4
= 36+24+4 = 64
Thus, the difference between the squares of consecutive even numbers = 64-36 = 28
Clearly, we can see that 12, 20, and 28 are multiples of 4.
Therefore, the difference between squares of consecutive even numbers is always a multiple of 4.
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the researcher will conduct a chi-square test of independence. which pair of variables can the researcher use?
The researcher can use two categorical variables or two values from a contingency table to perform chi - squared test.
A standard hypothesis test used to analyze contingency tables with large sample sizes is the chi-squared approach. This test is designed to examine if two categorical factors influence the test statistic independently. Pearson's chi-squared test and its variants are true when the test statistic equals chi-squared under the null hypothesis.
Pearson's chi-squared test is used to determine whether there is a statistically significant difference between expected and observed frequencies for one or more contingency table categories. For contingency tables with fewer samples, a Fisher's exact test is employed instead.
In the traditional application of this exam, observations are classified into mutually exclusive kinds. If the null hypothesis is correct and there are no variations in the population between classes, the test statistic generated by the data has a two-frequency distribution.
The test's purpose is to estimate how likely observed observed frequencies are if the null hypothesis is true.
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Complete the two-column proof.
Given: <1 and <6 are supplementary
Prove: a//b
The lines a and b are parallel. The proof is given.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Given:
Statement 1:
∠1 and ∠6 are supplementary.
Justification:
If two angles sum up to 180 degrees, they are referred to as supplementary angles.
That means,
∠1 + ∠6 = 180°
∠1 = 180°- ∠6
∠1 =∠5, given that the angles are made by intersecting lines.
Statement 2:
∠1 ≅∠4
Justification:
Vertical angles are also congruent angles, meaning they are equal or have the same measurement.
Two crossing lines actually create two sets of opposite angles that, when the measures of their angles, are added all together.
Since, ∠1 ≅∠4
That means, ∠4 and ∠6 are supplementary.
Statement 3:
∠4 and ∠6 are supplementary.
Justification:
If two angles sum up to 180 degrees, they are referred to as supplementary angles.
Statement 4:
a and b are parallel lines.
Justification:
This means that lines a and b make the same angle with the intersecting line, meaning they don't intersect each other at any point.
a and b are parallel lines.
Therefore, the all statements are true.
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or
A school needs 6,062 slices of pizza for a pizza party. If each pizza has 14 slices, how many pizzas should the school buy?
Answer:
433 pizzas
Step-by-step explanation:
6062 / 14 = 433
A man is considering two companies from which to rent a truck. Triangle Truck Rental charges $20 per day and 35 cents a mile. Circle Rent-A-Truck charges $35 a day and 30 cents a mile. How far would need to drive in one day for the both companies to have the same total cost?
Answer: 300 miles
Step-by-step explanation:
Let x be the number of miles
We have the equation below
20 + 0.35x = 35 + 0.30x
Subtract 20 from both sides
0.35x = 15 + 0.30x
Then subtract 0.30x from both sides
0.05x = 15
Then divide by 0.05 from both sides
x = 300 miles
What i the denity of an object that ha ma of 73,430 kilogram and a volume of 7m exponent 3
The Density of object is 10,490 kg/m³
What is Density, Mass and Volume ?
Measurement of the amount of matter (or stuff) in an object is MassMeasurement of the amount of space an object takes object up is VolumeDensity is defined as mass per unit volume.Given,
Mass = 73,430 Kg
Volume = 7 m³
We know,
Density = Mass / volume
Now, plug in the values
Density = 73430/7
= 10, 490 kg/m³
Hence, the Density of object is 10,490 kg/m³
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how can graphics and/or statistics be used to misrepresent data? where have you seen this done?
(1) We incorrectly interpret the beta number, compare the two, and draw the inference that because the beta for years is greater than the beta for income, the beta for years of experience is stronger.
(2) The ANOVA will reveal who consistently does better in terms of the typical amount of time needed to finish a job.
1) Assume you predicted the variable "Number of Promotion Earned" by regressing it against just two other variables, "Income in $s" and "Years of Experience."
When compared to the beta for years of experience, the income beta is quite modest. You incorrectly interpret the beta number, compare the two, and draw the inference that because the beta for years is greater than the beta for income, the beta for years of experience is stronger.
But until we standardize the variables, this is incorrect. Then they can be put side by side.
2) As HR, I was questioned about whether employees who earn more money perform better. Do those with higher salaries complete the same task more quickly? I've been given data with two columns: "HIGH" salary people's income, and "LOW" salary people's income.
I conduct an ANOVA method test on two groups of individuals and track their typical completion time. The ANOVA will reveal who consistently does better in terms of the typical amount of time needed to finish a job.
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The complete question is:
First, how can graphics and/or statistics be used to misrepresent data? Where have you seen this done? Second, image that you are a human resources (HR) analyst reporting to a recently hired supervisor. Your supervisor has asked you to provide an example of data processed by HR. Describe one type of data that an HR department may process, and discuss a corresponding statistical method that may be used to summarize the data.
Persevere with Problems Suppose an online store has an item that costs $50. The item is on sale for 10% off the original price.
In one well-developed paragraph with a topic sentence and supporting details, compare and contrast the experience of reading "The Highwayman" with listening to it. Explain, using examples from the text, how hearing the poem read aloud changes or increases your understanding of a poem.
If f(x) is a third degree polynomial function and g(x) = f(2x), which of the following must be true?
A f(x) and g(x) have the same x-intercepts.
B f(x) and g(x)have the same y-intercepts.
Option A is the correct answer
what is a polynomial?
A polynomial function is made up of terms called monomials; If the expression has exactly two monomials it’s called a binomial. A third-degree polynomial is of the form f(x) = ax³ + bx²+ cx + d where is not equal to zero. It is also called a cubic polynomial as it has a degree of 3.
Given here the polynomial as g(x) = f(2x)
=8ax³ + 4bx²+2cx + d
Both the polynomial have the same constant d and therefore the same y-intercept.
Hence, the correct option is B
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What i the lope of the line that pae through the point (1, -9)(1,−9) and (4, -7)(4,−7)?
The slope of the line is 2/3.
What is a line?
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
Given coordinates of the points are A(1,-9) and (4,-7).
The formula of slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
Here x₁ = 1, y₁ = -9, x₂ = 4, and y₂ = -7
m = (-7 - (-9))/(4 - 1)
m = 2/3
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what is the average rate of change of the number of chevy car sales from 1990 to 1992? model year color sales chevy 1990 red 5 chevy 1990 white 87 chevy 1990 blue 62 chevy 1991 red 54 chevy 1991 white 95 chevy 1991 blue 49 chevy 1992 red 31 chevy 1992 white 54 chevy 1992 blue 71 ford 1990 red 64 ford 1990 white 62 ford 1990 blue 63 ford 1991 red 52 ford 1991 white 9 ford 1991 blue 55 ford 1992 red 27 ford 1992 white 62 ford 1992 blue 39
The average rate of change of the number of chevy car sales from 1990 to 1992 is 1
What is the average change rate?
The average rate of change is the rate at which one value in a function changes in relation to another. Usually, the average rate of change is used to calculate the slope of a graphed function.
The average rate of change of a function is determined by the slope of the line connecting the two endpoints of a specific interval (known as the secant line).
According to the given question:
The average rate of change of the number of chevy car sales from 1990 to 1992 is (total chevy car sold in 1992- total chevy car sold in 1990)/ Total difference in no. of years
That gives (156-154)/2
So, the average rate of change of the number of chevy car sales from 1990 to 1992 is 1
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Gives brainliest for best answer and easy to understand!
Answer: the right answer is D
Step-by-step explanation:
If you multiply 4 by 2 you get 8. If this goes on the answers are aways the same and it’s going to be proportional
Which of the following is a linear function? a.f(x)=2x-3 b.f(x)=x²+3 c.f(x)=2x³ d.x=3-2x?
Answer: A
Step-by-step explanation:
:D
the answer is A. because x² is quardatic function and x³ is cubic function
Can someone help me with Question 2b of this assignment? I'd deeply appreciate it! :)
Value of x is -6
According to question
(x/2)-6 = 2+(2x+1)
⇒x-12/2 = 3+2x
⇒x-12=2(3+2x)
⇒x-12=6+4x
⇒-3x=18
⇒x=18/-3
∴x=-6
The value of x is -6.
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Answer:
x = - 6
Step-by-step explanation:
(b)
[tex]\frac{1}{2}[/tex] x - 6 = 2 + (2x + 1) ← remove parenthesis
[tex]\frac{1}{2}[/tex] x - 6 = 2 + 2x + 1
[tex]\frac{1}{2}[/tex] x - 6 = 2x + 3 ( add 6 to both sides )
[tex]\frac{1}{2}[/tex] x = 2x + 9 ( multiply through by 2 to clear the fraction )
x = 4x + 18 ( subtract 4x from both sides )
- 3x = 18 ( divide both sides by - 3 )
x = - 6
Fluffy Stuffy Stuffed Animals wants to sell their stuffed animals in a local toy store. In which store should they sell their products if they hope to make the most money?
the number of miles mario can drive varies directly with the amount of gas that he has. he can drive 18 miles on ½ a gallon of gas. how many miles can mario drive with 9 gallons of gas?
324 miles can Mario drive with 9 gallons of gas.
ProportionalThe term "proportional" refers to any connection where the ratio and amount fluctuate directly with one another.
As per the details share in the above question we get,
The data are as follow,
Mario has a driving range of 18 miles ½ gallon of gas.
Here we have to find how many miles can mario drive with 9 gallons of gas.
Thus we know that,
He can travel 18 miles on just half a gallon of fuel.
Let x be the amount of miles that 9 gallons of gas will cover.
Thus, if we use the notion of proportion, we obtain
⇒ 18 / (1/2) = x / 9
⇒ 18 × 2 = x / 9
⇒ 36 × 9 = x
⇒ x = 324 miles
Mario can travel 324 miles on 9 gallons of gas.
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A eed company planted a floral moaic of a national flag. The perimeter of the flag i 2,320 Determine the flag' width and length if the length i 260 ft greater than the width
By solving the system of equation, length of flag = 1290ft and width = 1030 ft.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. An equation typically consists of two expressions separated by an equals sign (=), and it states that the expressions are equal in value.
What is substitution method of equation solving?The substitution method is a technique for solving a system of equations, which is a set of two or more equations that contain multiple variables. The goal of the substitution method is to find the values of the variables that make all of the equations in the system true simultaneously.
To solve a system of equations using the substitution method, you follow these steps:
Identify one of the equations that contains only one variable.
Solve that equation for that variable.
Substitute the expression you found for the variable into the other equation(s) in the system.
Solve the resulting equation(s) for the remaining variable(s).
Substitute the values you found for the variables back into one of the original equations to check your solutions.
To find the width and length of the flag, we can set up the following system of equations:
width + length = 2,320
length = width + 260
We can solve this system of equations by substitution. First, we can solve for width in the second equation by subtracting 260 from both sides:
length - 260 = width
Then, we can substitute this expression for width into the first equation:
(length - 260) + length = 2,320
2 * length - 260 = 2,320
2 * length = 2,580
length = 1,290
Now that we know the value of length, we can substitute it back into the second equation to find the value of width:
length = width + 260
1,290 = width + 260
width = 1,030
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Jack ee 7 bue. Each bu ha 10 people on it. Which number entence can be ued to find how many people are on all the bue?
The number sentence to find how many people are on all the buses is 7 x10 = ?. (Option C)
A number sentence refers to an equation or inequality which expresses using numbers and mathematical symbols. Examples of number sentences include 32 + 57 = ? or 5 x 6 = ?. In the given situation, Jack sees 7 buses and each bus has 10 people on it. In order to determine the total number of buses on all the buses, multiplication operation is used. Multiplication, one of the four basic mathematical operations of arithmetic, refers to an operation that represents the basic idea of repeated addition of the same number. Hence, it is used to combine groups of equal sizes. As in the given case, the group of equal size i.e., the number of people on each bus is seen in 7 buses, the total number of people would be the product of two and would be represented by 7 x10 = ?.
Note: The question is incomplete. The complete question probably is: Jack sees 7 buses. Each bus has 10 people on it. Which number sentence can be used to find how many people are on all the buses? A. 7 + 10 = ? B. 10 – 7 = ? C. 7 x10 = ? D. 10 ÷ 7 = ?
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HELP ME PLEASE
Drag the tiles to the correct locations on the table. Not all tiles will be used.
Match each quadratic function with the attributes of its parabolic graph.
The quadratic functions given are matched with the parameters as follows
f(x) = -0.3(x - 2)² + 5 f(x) = 0.2(x + 2)² - 5
vertex (-2, 5)
axis of symmetry, x = -2 axis of symmetry, x = 2
focus f (-2, 4 1/6) focus f (2, -3 3/4)
How to find the axis of symmetry of parabolic functionBoth the vertex form and the standard form of the quadratic equation are used in the axis of symmetry formula. Any geometric shape is divided into two equal halves by the symmetry.
Parabolic equation in vertex form is written as
f(x) = a (x - h)² + k
the vertex is v (h, k)
f(x) = -0.3(x - 2)² + 5, v (-2, 5)
f(x) = 0.2(x + 2)² - 5, v ( 2, -5)
The axis of symmetry formula is given as, x = h
f(x) = -0.3(x - 2)² + 5, x = -2
f(x) = 0.2(x + 2)² - 5, x = 2
the focus, f (h, k + 1/4a)
f(x) = -0.3(x - 2)² + 5, f (-2, 5 + 1/(4 * -0.3)) = f(-2, 5 - 5/6) = f (-2, 4 1/6)
f(x) = 0.2(x + 2)² - 5, f (2, -5 + 1/(4 * 0.2)) = f(2, -5 + 1/0.8) = f (2, -3 3/4)
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the test for the equality of two population variances is based on group of answer choices the difference between the 2 population variances. the difference between the sample variances divided by the difference between the sample means. the ratio of the 2 sample variances. the difference between the 2 sample variances.
This ratio is used to compare the variances of the two samples and determine if they are statistically equal.
The test for the equality of two population variances is a statistical test used to determine whether or not the variances of two populations are equal. This test is based on the ratio of the two sample variances, which is calculated by dividing the difference between the two sample variances by the difference between the two sample means. This ratio is then compared to the value of a critical statistic to determine whether or not the two population variances are statistically equal. If the ratio is greater than or equal to the critical statistic, then the two population variances are considered equal. If the ratio is less than the critical statistic, then the two population variances are considered unequal. This test is useful for determining if the two populations have similar amounts of variation or if one population has more variation than the other.
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