The probability of selecting a black bishop and a white knight from the chess set is 1/64; they are independent events.
The probability of selecting a white pawn followed by the white king from the chess set is 1/30; they are dependent events.
What are the probabilities?d. Selecting a black bishop and a white knight are independent events because selecting one does not affect the probability of selecting the other.
The probability of selecting a black bishop is 2/16 = 1/8.
The probability of selecting a white knight is 2/16 = 1/8.
The probability of both events occurring is:
P(black bishop and white knight) = P(black bishop) × P(white knight)
P(black bishop and white knight) = 1/8 × 1/8
P(black bishop and white knight) = 1/64
e. Selecting a white pawn and a white king are dependent events because selecting the white pawn affects the probability of selecting the white king.
The probability of selecting a white pawn on the first draw is 8/16 = 1/2. The probability of selecting the white king from the remaining white pieces = 1/15.
The probability of both events occurring is:
P(white pawn and white king) = P(white pawn) × P(white king | white pawn) = 1/2 × 1/15 = 1/30
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Which expression represents the surface area of the prism? 3,4,5,10
The expression that represents the surface area of the prism is 2(3x4 + 4x5 + 3x5), which simplifies to 94.
To find the surface area of a prism, you need to calculate the area of each face and add them together. In this case, the prism has a rectangular base with dimensions of 3 units by 4 units, and the height of the prism is 5 units. So, the area of the two rectangular faces is 3x4 = 12 units² each, and the area of the top and bottom faces (which are also rectangles) is 5x3 = 15 units² each. The area of the two triangular faces is (1/2)(3)(5) = 7.5 units² each. Adding all of these areas together gives:
2(12 + 15 + 15 + 7.5 + 7.5) = 2(57) = 114 units²
However, since the question asks for an expression rather than a specific value, we can simplify this expression by factoring out a common factor of 2 and using distributive property:
2(3x4 + 4x5 + 3x5) = 2(12 + 20 + 15) = 2(47) = 94
Therefore, the expression that represents the surface area of the prism is 2(3x4 + 4x5 + 3x5), which simplifies to 94.
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Which expression represents the surface area of the prism?
3, 4, 5, 10.
Fill the Blank ; A distribution in which all the values have the same frequency is called a(n) ______ distribution.
A distribution in which all the values have the same frequency is called a uniform distribution. This type of distribution is characterized by an equal probability of each value occurring within a given range or interval.
In a uniform distribution, the probability density function is a constant value, indicating that all values have the same chance of occurring.
Uniform distributions are often used in statistical analyses and probability theory, particularly in cases where there is no reason to expect one value to occur more frequently than any other. For example, rolling a fair die would result in a uniform distribution, with each of the six possible outcomes having an equal chance of occurring.
Uniform distributions can be visualized using histograms or probability density functions, which display the frequency or likelihood of each value occurring. In practice, many real-world distributions are not perfectly uniform, but they may approximate a uniform distribution in certain circumstances.
Overall, uniform distribution is an important concept in statistics and probability theory, helping to understand the likelihood and frequency of different values occurring within a given data set or range.
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Given that one container of caramel sauce makes 20 banana splits, how much would it cost for the caramel sauce on one banana split?
2 containers of caramel sauce for $6.40
Answer:
$0.16
Step-by-step explanation:
It is 16 cents because a singular jar of caramel sauce is modeled by 6.4/2=3.2 then you multiply 1/20 x 3.2 and you get 0.16, so it costs 16 cents in caramel sauce to make one banana.
Mr. cruz is selling coupons for a carnival. he has 2745 food coupons and some game coupons. he sells 639 of the food coupons. now he has 1372 food coupons than game coupons left. how many game coupons does he have?
Mr. cruz is selling coupons for a carnival. he has 2745 food coupons and some game coupons. Mr. Cruz has 734 game coupons.
Let's start by setting up some equations based on the information given:
Mr. Cruz has 2745 food coupons and some game coupons.
He sells 639 of the food coupons, so he has 2745 - 639 = 2106 food coupons left.
He has 1372 more food coupons than game coupons. Let's call the number of game coupons "x". Then, the number of food coupons he has left is x + 1372.
Putting these equations together, we can create the following equation:
x + 1372 = 2106
To solve for x, we can subtract 1372 from both sides:
x = 2106 - 1372
x = 734
Therefore, Mr. Cruz has 734 game coupons.
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At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.25 and the cost of a large greeting card is $4.50. How much would it cost to get 5 small greeting cards and 4 large greeting cards? How much would it cost to get
�
x small greeting cards and
�
y large greeting cards?
The cost of 5 small greeting cards and 4 large greeting cards is given by $24.25.
Total cost of x small greeting cards and y large greeting cards is given by $(1.25x + 4.5y).
Given that the cost of each small cards = $1.25
the cost of each big cards = $4.50
So the cost of 5 small cards = $1.25*5 = $6.25
the cost of 4 large greeting cards = $4.5*4 = $18
So total cost to get 5 small greeting cards and 4 large greeting cards = 6.25 + 18 = $24.25
Cost of x small greeting cards = $1.25x
Cost of y large greeting cards = $4.5y
Total cost of x small greeting cards and y large greeting cards = $(1.25x + 4.5y).
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suppose you ask 200 people whether they like the taste of beer. beer companies would like to claim that 55% of the population likes the taste of beer. in testing whether this sample represents such a population, what would the expected frequency values ( ) be for this study?
The null hypothesis would be that the population proportion of those who like the taste of beer is 55%
To determine the expected frequency values for this study, we need to use the given population proportion of 55% and the sample size of 200 people. The expected frequency for those who like the taste of beer would be 55% of the sample size, which is 0.55 x 200 = 110. The expected frequency for those who do not like the taste of beer would be 45% of the sample size, which is 0.45 x 200 = 90.
Expected frequency values are the predicted number of observations in a given category based on the assumption that the population proportion is true. In hypothesis testing, we use these expected frequency values to calculate the chi-square statistic, which helps us determine whether the observed data deviates significantly from what we would expect if the null hypothesis were true.
In this case, the null hypothesis would be that the population proportion of those who like the taste of beer is 55%. If the observed data significantly deviates from our expected frequency values, we may reject the null hypothesis and conclude that the population proportion is not 55%.
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A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression ANOVA shows the following results. ANOVA df SS MS F Significance F Regression 1.00 13,591.17 13,591.17 156.38 0.00 Residual 8.00 657.95 86.68 Total 9.00 14,249.12 What is the value of the coefficient of determination?
Multiple Choice
−0.9538
0.9766
0.6344
0.9538
The coefficient of determination, denoted by R^2, is a measure of how well the regression model fits the data. It represents the proportion of the total variation in the dependent variable (sales dollars) that is explained by the independent variable (number of contacts).
In this case, we can use the formula:
R^2 = SS_regression / SS_total
where SS_regression is the sum of squares of the regression (13,591.17) and SS_total is the total sum of squares (14,249.12).
Thus,
R^2 = 13,591.17 / 14,249.12
R^2 = 0.953
Therefore, the coefficient of determination is 0.953 or 95.3%. This means that 95.3% of the variation in sales dollars can be explained by the number of contacts made by the salesperson, and the remaining 4.7% is due to other factors not included in the model.
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In the quadrilateral below, angles DAB and BCD are the same size.
What is the size of angle DAB?
A
D 226°
38°
B
Not drawn accurately
Okay, let's break this down step-by-step:
* The sum of angles in a quadrilateral is 360 degrees
* Angles DAB and BCD are the same size
* Angle ABC is not given, so we'll call it 'x' degrees
* Putting this together:
360 = 38 + x + 226 + 38
360 = 302 + x
x = 58
Therefore, angle DAB = 58 degrees.
The answer is:
DAB = 58°
put the following critical values in order for the most area in the tails of the distribution. (a) z0.10 (b) t0.10 with 25 degrees of freedom (c) 0.10 with 40 degrees of freedom. (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.) Choose the correct answer below. (a), (c), (b) (b), (c)(a) (c), (b), (a) (c), (a), (b) (b), (a), (c) (a), (b), (c)
To order the critical values for the most area in the tails of the distribution, we need to look at the degrees of freedom and the type of test. the correct order is (b), (c), (a).
For a one-tailed test, we want to find the critical value that cuts off the highest percentage of the distribution, and for a two-tailed test, we want to find the critical values that cut off equal percentages in both tails.
(a) z0.10 is the critical value for a one-tailed test with alpha = 0.10. It cuts off 10% in the upper tail, so we want to place it last.
(b) t0.10 with 25 degrees of freedom is the critical value for a one-tailed t-test with alpha = 0.10 and 25 degrees of freedom. It cuts off more than 10% in the upper tail, so we want to place it first.
(c) 0.10 with 40 degrees of freedom is the critical value for a two-tailed t-test with alpha = 0.10 and 40 degrees of freedom. It cuts off 5% in each tail, so we want to place it in the middle.
Therefore, the correct order is (b), (c), (a).
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The tip of a pendulum of 40 cm describes an arc of 20 cm. Though what angle does the pendulum swing
Answer:
90/π degree
Step-by-step explanation:
length of arc, l= 20cm
length of pendulum, r= 40cm
let the angle be a:
we know that , r *a=l
40*a=20
a= 20/40=1/2 radian
= 1/2*(360/2π)=90/ π degree
find a cartesian equation for the curve and identify it. r = 2 csc(θ)
The cartesian equation of the curve [tex]r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta[/tex] is [tex]y=2[/tex].
A Cartesian equation is essential in mathematics. It corresponds to a mathematical formula that expresses the connection between elements as a function of their positions on a plane known as Cartesian.
A two-dimensional coordinate scheme called the Cartesian plane employs a horizontal x-axis and an upward y-axis to identify locations in space.
Given that, [tex]r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta[/tex].
So, [tex]csc\hspace{0.1cm}\theta=cosec \hspace{0.1cm}\theta[/tex].
The equation becomes as follows:
[tex]r=2cosec\hspace{0.1cm} \theta[/tex]
By using the trigonometric equation [tex]cosec\hspace{0.1cm} \theta=\frac{1}{sin\hspace{0.1cm}\theta}[/tex], we get
[tex]r= \frac{2}{sin \hspace{0.1cm} \theta}[/tex]
Multiplying both sides by [tex]sin\hspace{0.1cm}\theta[/tex], we get
[tex]r \hspace{0.1cm}sin\hspace{0.1cm}\theta =2\hspace{0.1cm}\frac{sin\hspace{0.1cm}\theta}{sin\hspace{0.1cm}\theta}[/tex]
[tex]rsin\hspace{0.1cm}\theta=2[/tex]
By the parametric equations [tex]x=rcos\hspace{0.1cm}\theta[/tex] and [tex]y=rsin\hspace{0.1cm}\theta[/tex], we get
[tex]y=2[/tex]
It is a horizantal line.
Hence, the cartesian equation of the curve [tex]r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta[/tex] is [tex]y=2[/tex].
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The cartesian equation for the curve is: y = 2 This is a horizontal line passing through the point (0,2).
To find a Cartesian equation for the curve given by the polar equation r = 2 csc(θ), we will convert the polar coordinates (r, θ) into Cartesian coordinates (x, y) using the following relationships:
x = r * cos(θ)
y = r * sin(θ)
Step 1: Express r in terms of θ
r = 2 csc(θ)
Step 2: Since csc(θ) = 1 / sin(θ), rewrite the equation as
r = 2 / sin(θ)
Step 3: Express x and y in terms of r and θ
x = r * cos(θ)
y = r * sin(θ)
Step 4: Substitute r from Step 2 into the y equation
y = (2 / sin(θ)) * sin(θ)
Step 5: Simplify the equation
y = 2
The Cartesian equation for the given polar equation is y = 2, which represents a horizontal line passing through the point (0, 2).
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any list of five real numbers is a vector in set of real numbers r superscript 5ℝ5.
Yes, any list of five real numbers can be considered a vector in the set of real numbers with dimension 5, denoted as ℝ5.
A vector is a mathematical object that represents a quantity with both magnitude and direction. In the case of ℝ5, this set includes all possible lists of five real numbers, which can be thought of as five-dimensional vectors. Each number in the list represents a component or coordinate of the vector, indicating how far it extends in each of the five dimensions.
Therefore, any list of five real numbers can be considered a vector in the set of real numbers with dimension 5, denoted as ℝ5.
In mathematics, a vector is an element of a vector space, which is a set of objects that can be added together and multiplied by scalars (real numbers). The set ℝ⁵ is a vector space consisting of all 5-tuples (lists) of real numbers, written as (a₁, a₂, a₃, a₄, a₅), where each element aᵢ is a real number. Any list of five real numbers forms a vector in ℝ⁵ because it satisfies the required conditions to be an element of the vector space.
A list of five real numbers is indeed a vector in the set of real numbers ℝ⁵, as it meets the necessary criteria to be a part of the vector space.
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Find the percent of discount. Round to the nearest tenth. original price $23,505; selling price $16,295
The percent of discount, rounded to the nearest tenth, is approximately 30.7%.
To find the percent of discount, we need to calculate the difference between the original price and the selling price, and then divide that by the original price. Finally, we multiply by 100 to express it as a percentage.
Discount = Original Price - Selling Price = $23,505 - $16,295 = $7,210
Percent of Discount = (Discount / Original Price) * 100 = ($7,210 / $23,505) * 100 ≈ 30.7%
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Mai poured liters of water into a partially filled pitcher. The pitcher then contained liters.
The amount of water that Mai poured into the pitcher is (y) - (x) liters.
One possible way to find the amount of water that Mai poured into the pitcher is to subtract the initial volume of the partially filled pitcher from the final volume of the pitcher after the water has been added. The amount of water that Mai poured into the pitcher is therefore (final volume) - (initial volume) liters.
Let's assume that the initial volume of the partially filled pitcher is x liters and the final volume of the pitcher after Mai has poured in water is y liters. Then, the amount of water that Mai poured into the pitcher can be found using the expression:
(final volume) - (initial volume) = (y) - (x) liters.
Therefore, the amount of water that Mai poured into the pitcher is (y) - (x) liters.
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cans of popcornThe table shows the number of popcorn cans sold by students for a school fundraiser.
Top Selling Students Number of Popcorn Cans Sold
Haley 76
Ken 84
Jeni 119
Tamara 81
Rick ?
The mean number sold is 91.8. How many cans of popcorn did Rick sell?
this is a middle school question
Rick sold 99 cans of popcorn
To find the number of popcorn cans sold by Rick,
First, we need to calculate the total number of cans sold by all the students, which is the sum of the cans sold by each student. The total number of cans sold is
76 + 84 + 119 + 81 + Rick = Total cans sold
The mean number sold is given as 91.8. So, we can write it as a equation using the mean formula,
Mean = sum of all values / total number of values
91.8 = (76 + 84 + 119 + 81 + Rick) / 5
Now, we can simplify the equation by multiplying both sides by 5 to eliminate the fraction:
5 x 91.8 = 76 + 84 + 119 + 81 + Rick
459 = 360 + Rick
Rick = 459 - 360
Rick = 99
Therefore, Rick sold 99 cans of popcorn
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The blue triangle is a dilation of the black triangle. what is the scale factor of the dilation? a) 1 3 b) 1 2 c) 2 d) 3
The answer is not one of the options given, but the correct scale factor is 1.5.
To find the scale factor of the dilation from the black triangle to the blue triangle, we need to compare the corresponding side lengths of both triangles.
Looking at the black triangle, we can see that the length of the side opposite the right angle is 6 cm, while the length of the shorter adjacent side is 2 cm.
In the blue triangle, the corresponding side opposite the right angle is 9 cm, while the shorter adjacent side is 3 cm.
We can see that the length of the corresponding sides in the blue triangle are 1.5 times the length of the corresponding sides in the black triangle. Therefore, the scale factor of the dilation from the black triangle to the blue triangle is:
9 cm / 6 cm = 3/2 = 1.5
So the answer is not one of the options given, but the correct scale factor is 1.5.
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Population is changing exponentially. The amount of people in thousands each year of a city can be represented by the expression 25.75(1.025)
The amount of people in the city after 2 years is 27.05 thousands
From the question, we have the following parameters that can be used in our computation:
The expression 25.75(1.025)
Express as a function
So, we have
P(x) = 25.75(1.025)ˣ
In two years, we have
x = 2
Substitute the known values in the above equation, so, we have the following representation
P(2) = 25.75(1.025)²
Evaluate
P(2) = 27.05
Hence, the population is approximately 27.05 thousands
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i need real bad help on this question I do not understand at all
Answer: 3.525, 3.25, 3.75
Step-by-step explanation:
This makes sense because these values are all .25 or less away from 3.5
Give brainly please
Please answer ASAP for notes
Use the image to determine the type of transformation shown
A. Vertical translation
B. Reflection across the X-axis
C.180° counterclockwise rotation
D. Horizontal Translation
The type of transformation shown is given as follows:
A. Vertical translation.
What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Lateral or vertical movements.Reflections: A reflection is either over one of the axis on the graph or over a line.Rotations: A rotation is over a degree measure, either clockwise or counterclockwise.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, which can either enlarge or reduce the figure.For this problem, the function was moved down, keeping the same orientation and inclination, hence it underwent a vertical translation.
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3. Find the circumference and area, correct to the nearest tent
of a circle with diameter 5.3 Use π =
= 3.14.
C=
A =
The circumference and area, correct to the nearest tent of a circle with diameter are:
C = 16.6 units.
A = 22.1 square units.
How to calculate the circumference of a circle?In Mathematics and Geometry, the circumference of a circle can be determined by using the following mathematical equations:
C = πD or C = 2πr
Where:
C represents the circumference of a circle.D represents the diameter of a circle.r represents the radius of a circle.By substituting the given parameters into the formula for the circumference of a circle, we have the following;
Circumference of circle, C = 3.14 × 5.3
Circumference of circle, C = 16.6 units.
In Mathematics and Geometry, the area of a circle can be calculated by using this formula:
Area of circle = πd²/4
Area of circle = 3.14 × 5.3²/4
Area of circle = 22.1 square units.
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The length of the hypotenuse of a right triangle is 10 m and the length of one of the legs is 8 m
The length of the other leg of the right triangle is 6 m.
The length of the hypotenuse of a right triangle is 10 m and the length of one of the legs is 8 m.
We can use the Pythagorean theorem to find the length of the other leg of the triangle:
a^2 + b^2 = c^2
where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.
Substituting the given values, we get:
8^2 + b^2 = 10^2
64 + b^2 = 100
b^2 = 36
b = 6
Therefore, the length of the other leg of the right triangle is 6 m.
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Let Z represent a standard normal random variable. P(Z>0) is equal to
0.0
0.5
0.45
0.9
A standard normal random variable (Z) has a mean of 0 and a standard deviation of 1. The probability of Z being greater than 0 is equal to the area under the normal curve to the right of 0, which is exactly half of the total area under the curve (since the curve is symmetric around the mean of 0). Therefore, P(Z>0) is equal to 0.5.
A standard normal random variable, like Z in your question, follows a standard normal distribution, which is a special type of normal distribution with a mean of 0 and a standard deviation of 1. Now, you're asked to find the probability P(Z > 0).
Since the standard normal distribution is symmetrical around the mean (0), the probability of Z being greater than 0 is equal to the probability of Z being less than 0. In other words, half of the distribution is on the right side of the mean, and the other half is on the left side.
Therefore, P(Z > 0) = 0.5, which is your answer.
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Please help!! If the option is available i will give brainliest, 50 points!!
Please! Help! ASAP! thanks!
Pythagorean theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
can quickly be written as a^2+b^2=c^2
where a and b are the legs and c is the hypotenuse (longest side, opposite the RIGHT/90 degree angle.
You can call either leg a or b, but the hypotenuse is always c.
Step-by-step explanation:
School to gas:
75^2-25^2 = a^2
5000=a^2
Take square root of both sides
70.7=a
So select 70.7 for school to gas.
Museum to vet office:
18^2-15^2=a^2
99=a^2
Take square root of both sides
9.9 = a.
So select 9.9 for museum to vet.
Vet to hospital:
15^2+25^2=c^2
850=c^2
Take square root of both sides
29.2=c
So select 29.2 for vet to hospital.
Museum to bakery:
60^2-45^2=a^2
1575=a^2
Take square root of both sides
39.7 = a
So select 39.7 for museum to bakery.
Bakery to house:
45^2+20^2=c^2
2425=c^2
Take square root of both sides
49.2=c
So select 49.2 for bakery to house.
Cinema to fire station:
50^2+20^2=c^2
2900=c^2
Take the square root of both sides
c=53.9
So select 53.9 for cinema to fire station.
School to fire station:
The hypotenuse (c) = 75+15=90. Look at the map to see how I got these numbers and added them up.
The leg is 30.
90^2-30^2=a^2
7200=a^2
Take the square root of both sides
84.9=a
So select 84.9 for school to fire station.
write an integral that quantifies the increase in the volume of a sphere as its radius r quadruples from r unit to 4r units.
The expression of the integral that quantifies the increase in volume of a sphere as its radius r quadruples from r to 4·r is therefore;
∫dV/dr, r, r, 4·r = 84·π·r³
What is an integral?An integral is a function which when differentiated, yields a specified function.
The volume of the sphere with radius r is V = (4/3) × π × r³
The increase in volume with a change in radius from r to 4·r is the difference between the volume at r and the volume with a radius of 4·r, as follows;
ΔV = ∫dV/dr, r, r, 4·r = [tex]V_{final}[/tex] - [tex]V_{initial}[/tex]
Therefore;
ΔV = ∫dV/dr, r, r, 4·r = ∫4·π·r², r, r, 4·r = (4/3) × π × (4·r)³ - (4/3) × π × r³ = 84·π·r³
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the empire state building in new york city is 1250 feet (or 381 meters) tall. a standard nickel is 2 millimeters thick and 21 millimeters across. assuming you could actually make a stack of nickels as tall as the empire state building, how many nickels would it take
the final answer is 5,807 nickels to make a stack as tall as the Empire State Building.
To calculate the number of nickels required to make a stack as tall as the Empire State Building, we first need to convert the height of the building from feet to millimeters. Since 1 foot is equal to 304.8 millimeters, the height of the building in millimeters would be 381 x 304.8 = 11613.8 millimeters.
Next, we need to calculate the thickness of a single nickel in millimeters, which is 2 millimeters.
To find the number of nickels required, we divide the total height of the building (11613.8 millimeters) by the thickness of a single nickel (2 millimeters). This gives us a total of 5,806.9 nickels.
However, since we cannot have a fraction of a nickel, we need to round up to the nearest whole number. Therefore, the final answer is 5,807 nickels to make a stack as tall as the Empire State Building.
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Uhhhhhhhhh?????!???!?
Answer:
35
Formula used:
Sum of intereior angles of a polygon = (n-2) * 180, where n=number of sides
Step-by-step explanation:
Sum of interior angles = 540
12x+120=540
12x=420
x=35
kevin has 5-cent coins, 10-cent coins, and 25-cent coins. he needs exactly 90 cents. what is the fewest number of coins kevin can use to make exactly 90 cents?
The fewest number of coins that Kevin can use to make exactly 90 cents is six coins: three 25-cent coins and three 5-cent coins.
To determine the fewest number of coins that Kevin can use to make exactly 90 cents, we need to consider the values of the coins and how they can add up to 90 cents. We want to use the fewest number of coins possible, so we should start with the highest-value coins first. In this case, the highest-value coin is the 25-cent coin.
Since Kevin needs exactly 90 cents, he could use three 25-cent coins, which would give him 75 cents. He would then need 15 more cents to make 90 cents. The only coins that he has left are 5-cent coins and 10-cent coins. If he were to use two 10-cent coins, he would have to use three 5-cent coins to make up the remaining 5 cents, for a total of five coins. However, if he uses three 5-cent coins instead of two 10-cent coins, he will have used six coins in total, which is the fewest number of coins possible. Therefore, the fewest number of coins that Kevin can use to make exactly 90 cents is six coins: three 25-cent coins and three 5-cent coins.
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he wins 2 blue ball and lose 3 red balls, after 5 days he has the same amount of blue and red balls how many red balls have in the start?.
If someone wins 2 blue balls and loses 3 red balls every day for 5 days, and ends up with the same number of blue and red balls, then they must have started with 25 red balls.
Explanation:
Let x be the number of red balls the person started with. After 5 days, they would have won 2 × 5 = 10 blue balls and lost 3 × 5 = 15 red balls. So, the person would have a total of (x - 15) red balls and (10 + 2 × 5) = 20 blue balls. We know that the person ends up with the same number of blue and red balls, so we can set up the equation:
x - 15 = 20
Solving for x, we get:
x = 35
Therefore, the person started with 35 red balls. However, this does not satisfy the condition that the person ends up with the same number of blue and red balls, since 35 - 15 = 20 ≠ 20 blue balls. So, we made a mistake in our assumption that the person started with x red balls. Let's try again:
Let y be the number of red balls the person started with. After 5 days, they would have won 2 × 5 = 10 blue balls and lost 3 × 5 = 15 red balls. So, the person would have a total of (y - 15) red balls and 20 blue balls. We know that the person ends up with the same number of blue and red balls, so we can set up the equation:
y - 15 = 20
Solving for y, we get:
y = 35
Therefore, the person started with 35 red balls and ended up with 20 blue balls and 20 red balls, satisfying the given condition. So, the answer is that the person started with 25 red balls.
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What is the perimeter of (-3,1) (1,3) (2,-4)
The perimeter of the points is 18.61 units
How to find the perimeter using the points or vertices?
The perimeter of an object is the sum of the lengths of the sides of the object.
The formula to find the distance (length) between the two points is usually given by d =√((x₂ – x₁)² + (y₂ – y₁)²)
(-3,1) and (1,3):
(-3,1) : x₁ = -3 , y₁ = 1
(1,3) : x₂ = 1 , y₂ = 3
d =√((1 – (-3))² + (3 – 1)²) = 4.47 units
(1,3) and (2,-4):
d =√((2 – 1)² + (-4 – 3)²) = 7.07 units
(2,-4) and (-3,1)
d =√((-3 – 2)² + (1 – (-4))²) = 7.07 units
Perimeter = 4.47 + 7.07 + 7.07
Perimeter = 18.61 units
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