The probability that there exists people who share the same birthday is 0.995.
Considering that all the 365 days are equally likely to be the birthday of a person and all the events that a person has birthday on 'y' are independent of others.
Under the said assumptions, let's say that there are n number of people in the room. If we number the people from 1 to n, then the total number of possibilities of birthdays are (365)^n.
Therefore, the possible combinations that all birthdays are different:
365 * 364 * 363 * .... * (365- n+1)
Thus, the probability that all birthdays are different is:
[tex]\frac{365* 364 * 363* .... (365- n+1)}{365^n}[/tex]
To get the probability of at least two people sharing the same birthday is,
[tex]1- \frac{365* 364 * 363* .... (365- n+1)}{365^n}[/tex]
= 1 - 0.0058
= 0.9942
=0.995
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Work out the value of x. Show your working clearly.
D Study the Example showing how to write the equation of a line in slope-intercept form from a graph. Then solve problems 1-5. Example An oceanographer is studying the growth of giant kelp. She selects one giant kelp plant and records its height each day. Then she draws this graph. What is the equation of the line in slope-intercept form? Define your variables. (0, 10) and (2, 60) are two points on the line. 60 - 10 2-0 = 50, or 25 m= Height (cm) 120 100 80 y 60 40 20 0 The slope is 25. The line intersects the y-axis at (0, 10). The y-intercept is 10. The equation y = 25x + 10 shows the height, y, of the giant kelp plant after x days. 0 1 3 4 2 Time (days) What do the slope and y-intercept in the Example represent in this situation?
The slope of the line in the example is 25 and the y-intercept is 10. These values can be used to write the equation of the line in slope-intercept form, y = 25x + 10.
The slope, m, represents the rate of change of the height of the giant kelp plant. In this case, the slope is 25, meaning that for every day that passes, the height of the giant kelp plant increases by 25 centimeters.
The y-intercept, b, represents the height of the giant kelp plant at time = 0. In this case, the y-intercept is 10, meaning that the giant kelp plant is 10 centimeters tall at time = 0.
So in this situation the slope represents how much the height of the kelp plant changes with respect to time and the y-intercept represents the initial height of the kelp plant at time = 0.
claim sizes are 100, 1200, 1800, 2000, 3000 and 5000. the true probabilities are 0.5, 0.2, 0.1, 0.1, 0.05, 0.05, respectively. determine the coefficient of variations, skewness and kurtosis of the observations.
The coefficient of skewness is 0 and coefficient of Kurtosis is 0.125.
A coefficient is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial. It is usually a number, but sometimes may be replaced by a letter in an expression. For example, in the expression: ax2 + bx + c, x is the variable and 'a' and 'b' are the coefficients.
coefficient refers to a number or quantity placed with a variable. It is usually an integer that is multiplied by the variable and written next to it. The variables which do not have a number with them are assumed to be having 1 as their coefficient.
Let [tex]$x$[/tex] denote the claim sizes
[tex]& x= \begin{cases}100 & ; p=0.05 \\200 & ; p=0.2 \\300 & ; p=0.5 \\400 & ; p=0.2 \\500 & ; p=0.05\end{cases}[/tex]
[tex]& \mu_1^{\prime}=\varepsilon(x)=\sum x^0 p(x=x)=300 \\\\& \mu_2{ }^{\prime}=\sum x^2 p(x)=98000 \\\\& \mu_3^{\prime}=\sum x^3 p(x)=342 \times 10^5 \\[/tex]
[tex]& \mu_4^{\prime}=\sum x^4 p(x)=1.262 \times 10^{10} \\\\& \mu_2=\mu_2^{\prime}-\left(\mu_1^{\prime}\right)^2=8000 \\\\& \mu_3=\mu_3^{\prime}-3 \mu_2^{\prime} \\\\\mu_1^{\prime}+2\left(\mu_1^{\prime}\right)^3=0 \\\\& \mu_4=\mu_4^{\prime}-4 \mu_3^{\prime} \mu_1^{\prime}+6[/tex]
[tex]\mu_2^{\prime} \mu_1^{\prime 2}-3 \mu_1^{\prime 4} \\& \mu_4=2 \times 10^8 \\\\& \beta_1=\frac{\mu_3{ }^2}{\mu_2^3}=0 \quad \Rightarrow y_1=0 \\\\& \beta_2=\frac{\mu_4}{\mu_2{ }^2}=\frac{2 \times 10^8}{64 \times 10^6}=3.125\\ \\& y_2=\beta_2-3=0.125 \\[/tex]
Therefore, coefficient of skewness is 0 and coefficient of Kurtosis is 0.125.
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A number is picked at random from the set of consecutive integers from 29! – 2992 to 29! + 2992 inclusive. What is the probability that it is divisible by 1995?
When a number is randomly selected from the set of consecutive integers, it has a 3/4 chance of being divisible by 1995.
what is probability ?A branch of mathematics called probability theory determines the likelihood that an event will occur or that a statement is true. A chance is a number between zero and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or chance that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed in percentages ranging from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain occurrence relative to all possible outcomes.
given
99-20+1 = 80 potential outcomes.
Now, a number that may be divided by 12 must include the digits 2*2*3.
The realisation that c(c21)(21) = c(c1)c(c+1) is the same as c3c3 is perhaps the trickiest.
The latter statement indicates that you indeed have a group of three consecutive integers that are divisible by 12. Every three consecutive integers must be divisible by three, according to a rule.
The main question is how many of the numbers you choose are divisible by 22=4 22=4.
In this scenario, c can either be 21, 23, 25, 95, 97, 99, so 99212 9921/2 + 1 = 40 OR 20, 24, 26, 92, 96, so 96204 9620/4 + 1 = 20.
Thus, 40+2080 = 60/80 and 40+20/80 = 40/80
60/80 = 3/4
When a number is randomly selected from the set of consecutive integers, it has a 3/4 chance of being divisible by 1995.
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Given the triangle below, what is the value of x?
An interior designer recently spent £1359.55 buying 25 kettles and 20 toasters for a smaller group of new houses. For her current assignment she needs 80 kettles and 56 toasters. If the price of each kettle and each kettle is the same in all three cases, how much should she allow for this cost on her current assignment?
She should allow $4107.2 for her current assignment.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that an interior designer recently spent £1359.55 buying 25 kettles and 20 toasters for a smaller group of new houses. For her current assignment she needs 80 kettles and 56 toasters.
The price of kettle and toaster is same. So, we can write -
25x + 20x = 1359.55
45x = 1359.55
x = 30.2
Therefore, the total cost of 80 kettles and 56 toasters will be -
(80 x 30.2 + 56 x 30. 2)
$4107.2
Therefore, she should allow $4107.2 for her current assignment.
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the grade 6 cla 40 pupil .if thre are 18 girl in a cla what i the ratio of girl to the boy?
The ratio of girls to boys in the 6th grade class of 40 pupils is 18:22.
This can be calculated by first finding the total number of boys in the class. 40-18=22. We then use the formula for ratio, which is the ratio of two or more numbers. In this case, it is the ratio of girls to boys. 18:22. This ratio can also be expressed as 18/22 or 0.818181818181818181818181818181818181818181818182 (to three decimal places). A ratio is a comparison of two numbers and can be used to compare different parts of a whole. It can also be used to compare different groups or classes of people. In this case, it is used to compare the number of girls to boys in a 6th grade class.
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the random variable x is the number of occurrences of an event over an interval of 10 minutes. it can be assumed the probability of an occurrence is the same in any two time periods of an equal length. it is known that the mean number of occurrences in 10 minutes is 4.2. the probability there are 8 occurrences in 10 minutes is
The likelihood of 8 occurrences in a period of 10 minutes is around 0.091 or 9.1%.
According to the Question
A Poisson distribution issue exists here. The Poisson distribution is a discrete probability distribution that quantifies the likelihood of a certain number of events occurring at a certain average rate, regardless of the interval between occurrences, in a given amount of time or space.
The following formula determines the likelihood that x will occur in a Poisson distribution with parameter λ :
P(x; λ) is equal to x / (λx * e(-λ))!
where
λ = the average number of occurrences within the specified time period.
λ in this situation is 4.2. (the mean number of occurrences in 10 minutes).
In order to determine the likelihood of 8 occurring in 10 minutes:
P(8; 4.2) = (4.2^8 * e^(-4.2)) / 8!
⇒ P(8; 4.2) = 0.091 or 9.1%.
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you roll a fair six-sided die with the hopes of rolling a 5 or a 6. these two events are because they have no sample points in common. a. complements b. mutually exclusive events c. posterior events d. independent events
you roll a fair six-sided die with the hopes of rolling a 5 or a 6. these two events are because they have no sample points in common mutually exclusive events
Hence, option (b) is the correct choice.
Two occurrences are mutually exclusive or disjoint in logic and probability theory if they cannot occur at the same time. The set of outcomes of a single coin toss, which can result in either heads or tails but not both, is a good example.
Events that are mutually exclusive do not occur at the same time. For example, when a coin is tossed, the outcome will be either head or tail, but we cannot obtain both. Such occurrences are also known as disjunct events since they do not occur at the same time.
Events that are mutually incompatible cannot occur at the same moment. Right and left hand turns, even and odd numbers on a dice, winning and losing a game, or running and walking are all examples.
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Multiply the complex numbers below and simply your answer. Show work.
(3i-2)(51-6)
Step-by-step explanation:
(3i-51)*(2-6)
(-48) (-4)
192
Randall purchased a flat screen TV for $1090. The tax rate was 8.5%. What was the total cost of his purchase?
Answer:
$1182.65
Step-by-step explanation:
(8.5/100)×$1090
(85/1000)×1090
$1853/20
=$92.65
thus, $1090+$92.65
=$1182.65
Which phrase represents this expression?
7 × 4 + 3
Responses
3 more than the product of 7 and 4
the product of 7 and the sum of 4 and 3
the product of 7 and the difference of 4 and 3
3 less than the product of 7 and 4
Answer:
The Answer is 49
Step-by-step explanation:
4+3 =7 and 7 x 7 = 49
hope this helps
find cot theta, cos theta, sec theta,
we would here like to find out the values of given trigonometric ratios . A right angled triangle is given to us with perpendicular= 3 and hypotenuse= 8
Firstly by Pythagoras theorem, we have ,
[tex]\longrightarrow h^2 = p^2 + b^2\\ [/tex]
[tex]\longrightarrow 8^2 = 3^2 + b^2 \\[/tex]
[tex]\longrightarrow 64 = 9 + b^2\\ [/tex]
[tex]\longrightarrow b^2 = 64 -9 = 55\\ [/tex]
[tex]\longrightarrow b =\sqrt{55}\approx 7.41 [/tex]
now as we know that,
[tex]\longrightarrow \cos\theta = \dfrac{base}{hypotenuse}=\dfrac{7.41}{8}\\ [/tex]
[tex]\longrightarrow \underline{\underline{ \cos\theta = 0.92 \approx 1}} [/tex]
And ,
[tex]\longrightarrow \cot\theta =\dfrac{base}{perpendicular}=\dfrac{7.41}{3}\\[/tex]
[tex]\longrightarrow \underline{\underline{\cot\theta = 2.47 \approx 2 }} [/tex]
Finally,
[tex]\longrightarrow \sec\theta =\dfrac{hypotenuse}{base}=\dfrac{8}{7.41}\\[/tex]
[tex]\longrightarrow \underline{\underline{\sec\theta = 1.07 \approx 1 }} [/tex]
and we are done!
What is the solution to the system?.
8x - 8y =-8
X=-3y=13
5. On Monday, Mandy made 25 cupcakes for her bakery On Thursday, she made twice the amount of cupcakes from Monday minus eight cupcakes. Write an expression to show how many total cupcakes Mandy made on Monday and Thursday.
Answer:y=25 x 2 -8
Step-by-step explanation:
25 x 2-8
IIn the figure, m∠POR = 170° and m∠ROQ = 52°. If m∠POQ = x, which equation could be used to solve for x? A. X + 170° = 52° B. X + 52° + 170° = 180° C. X + 52° = 170° D. X = 170° + 52°n the figure, m∠POR = 170° and m∠ROQ = 52°. If m∠POQ = x, which equation could be used to solve for x? A. X + 170° = 52° B. X + 52° + 170° = 180° C. X + 52° = 170° D. X = 170° + 52°
Option C is correct - X + 52 = 170.
Angle
A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
Straight line
A line is a geometry object characterized under zero width object that extends on both sides. A straight line is just a line with no curves. So, a line that extends to both sides to infinity and has no curves is called a straight line.
According to the question,
∠POR = 170°
∠ROQ = 52°
∠POQ = x,
it is clear by the question,
on the basis of figure attached with this solution,
two angles together make the third angle,
so,
first angle is 52 degree
second angle is x degree,
∠ROQ + ∠POQ =∠POR
x + 52 = 170
so the answer is x + 52 = 170.
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The table shows the number of tickets sold for a concert one different prices are charged write an equation of a line of fit for the data round all values to the nearest 10th
As per the following table, the equation of a line of fit for the data round all values to the nearest 10th is y = -6.199 x 85+ 548.7
In math the term called equation is known as a mathematical statement that is made up of two expressions connected by an equal sign.
Here we have the following table with the value of ticket price and the number of tickets sold.
Here the First steps is calculated by using the linear regression feature that defines the line of best fit is
=> y = -6.199x + 548.7
When we take the value of x = 85, then we get,
=> y = -6.199 x 85+ 548.7
When we simplify this one then we get
=> y = 21.785 ≈ 22
Hence here this seems a reasonable model to predict the number of tickets sold because we can see that as the ticket price increase, and the number of tickets sold decreases.
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Pam has some dimes and quarters. Pam has fewer than 9 coins.
The coins have a total value of $1. 45.
Pam has
quarters and
dimes.
Number of quarters and dime with Pam with the total value of $1.45 is equal to 4 and 4.5 respectively.
Let 'x' represents the number of quarters coins.
And 'y' represents the number of dimes coins.
Value of quarter and dime in dollars is :
1 quarter = $0.25
1 dime = $ 0.10
Total value of all the coins = $1.45
⇒ $0.25x + $0.10y = $1.45
⇒2.5x + y = 14.5
⇒y = 14.5 - 2.5x __(1)
Number of coins < 9 coins
x + y < 9
⇒ x < 9 - y __(2)
Substitute the value of 'y' from (1) we get,
x < 9 - 14.5 + 2.5x
⇒2.5x - x > 14.5 - 9
⇒1.5x > 5.5
⇒ x > 5.5./1.5
⇒ x > 3.7
⇒ x = 4 ( next possible integer)
⇒ y = 14.5 -2.5(4)
⇒y = 4.5
⇒ y = 4.5
Therefore, the number of quarters and dime with Pam is equal to 4 and 4.5 respectively.
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can someone help me with this, please
Equations -7 x+7 y = 11 and -4 x + y = 11 have answers of [tex]x=-\frac{11-7 y}{7}$$[/tex] and [tex]x=-\frac{11-y}{4}$$[/tex], respectively.
What do you meant by solving an equation ?solve for [tex]$x,-7 x+7 y=11 \quad: \quad x=-\frac{11-7 y}{7}$[/tex]
-7 x+7 y = 11
-7 x = 11 - 7 y Shift 7 y to the right side and subtract 7 from both sides.
[tex]\frac{-7 x}{-7}=\frac{11}{-7}-\frac{7 y}{-7}$$[/tex]
Simplify
[tex]x=-\frac{11-7 y}{7}$$[/tex]
solve for [tex]x,-4 x+y=11: x=-\frac{11-y}{4}$[/tex]
Adjust Y to the right by -4 x=11-y.
Divide -4 from both sides.
[tex]\frac{-4 x}{-4}=\frac{11}{-4}-\frac{y}{-4}$$[/tex]
Simplify
[tex]x=-\frac{11-y}{4}$$[/tex]
Finding an equation's solutions—which are the values (numbers, functions, sets, etc.) that satisfy the equation's condition—is known as solving an equation in mathematics. An equation often consists of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.
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The citizens of Herrington County have an existing dog
park for dogs to play, but have decided to build another
one so that one park will be for small dogs and the other
will be for large dogs. The plan is to build a rectangular
fenced in area adjacent to the existing dog park, as
shown in the sketch. The county has enough money in
the budget to buy 1000 feet of fencing.
What should the dimensions of the dog park be to maximize the area?What is the maximum area of the park?
To maximise the area it should be build as a square having side=250 feet each and having area=62500 feet.
what are squares?
A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.
The most important properties of a square are listed below:
All four interior angles are equal to 90°.All four sides of the square are congruent or equal to each other.The opposite sides of the square are parallel to each other.The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other.The square has 4 vertices and 4 sides.The diagonal of the square divides into two similar isosceles triangles.The length of diagonals is greater than the sides of the square.Area of square=(side)²
Perimeter of square=4*side
Now,
Given
total fencing available=1000feet
perimeter=1000
4*s=1000
s=250 feet
Therefore,
Area=250^2
=62500 feet^2
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Question 5 of 10
Whitney's steel house is located in the country. If her building property
insurance is $603. 50 per year, how much is her house worth?
Annual Premium per $100 of coverage
Brick
Steel
Mixed
Wood
Area
Building Contents Building Contents Building Contents Building Contents
rating
City 0. 39 0. 43 0. 5 0. 54 0. 55 0. 65 0. 66 0. 76
Suburb 0. 45 0. 52 0. 56 0. 63
0. 74 0. 83 0. 85
Rural 0. 6
0. 69 0. 71
0. 89
0. 91 1
1. 02
0. 72
0. 8
O A. $17,350
The correct answer is B. $60,350.00. To calculate the value of Whitney's steel house, you need to multiply the annual premium per $100 of coverage ($0.43) by the annual property insurance premium ($603.50) and then divide that by 100. This works out to $60,350.00.
To determine the annual premium per $100 of coverage, you need to look at the table provided in the question. Since Whitney's steel house is located in the country, the annual premium per $100 of coverage is $0.43. Multiplying this by the annual property insurance premium of $603.50 gives you the total value of the house, which is $60,350.00. To summarize, the value of Whitney's steel house can be calculated by multiplying the annual premium per $100 of coverage by the annual property insurance premium and then dividing that by 100. In this case, the value of the house is $60,350.00.
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Question 5 of 10 Whitney's steel house is located in the country. If her building property insurance is $603. 50 per year, how much is her house worth? Annual Premium per $100 of coverage Brick Steel Mixed Wood Area Building Contents rating City 0. 39 0. 43 0. 5 0. 54 0. 55 0. 65 0. 66 0. 76 Suburb 0. 45 0. 52 0. 56 0. 63 0. 74 0. 83 0. 85 Rural 0. 6 0. 69 0. 71 0. 89 0. 91 1 1. 02 0. 72 0. 8 O A. $17,350.00 B. $60,350.00 C. $171,050.00 D. $603.50
Determine the domain of the function h(x)=9x/x(x2-49).
The domain of the function h(x)=9x/x(x²-49) is (-∞, -7) ∪ (-7, 0) ∪ (0, 7) ∪ (7, ∞).
In math the term called the domain of a function is the set of its possible inputs which is the set of input values where for which the function is defined.
Here we have know the function is h(x)=9x/x(x²-49)
And we need to find the domain of the function.
Here we know that this function is defined for values where the denominator is not equal to zero.
Which is written as,
=> x(x²-49) ≠ 0
When we elaborate the equation based on the difference between the two squares property, it can be written as,
=> x(x + 7)(x - 7) ≠ 0
Based on this we have identified that the value of x must not be
=> x ≠ -7, 7, 0
Then the domain of the function is written as,
=> (-∞, -7) ∪ (-7, 0) ∪ (0, 7) ∪ (7, ∞).
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How many teaspoons are there in 6 milliliters?
The number of teaspoons that are there in 6 milliliters is 1.21731 US teaspoons.
How can the conversion be done?The concept that will be used here is conversion of units. Unit conversion is the process of changing measurements of the same quantity between different units by multiplying or dividing them. The act of converting something from one form to another in mathematics, such as from inches to millimeters or from liters to gallons, is known as conversion.
1 tsp = 4.93 mL
Then Xtsp = 6ml
The cross multiply, Xtsp= (1 tsp *6ml)/4.93 mL
Then 6 milliliters= 1.21731 US teaspoons
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What is the equation for the graph below.
The equation of the straight line will be -
y = x - 4.
What is the general formula of a straight line?The general formula of a straight line will be -
y = mx + c
Given is a graph of straight line as shown in the image.
We can write the equation as -
y = mx + c
Now, we can write the slope as -
m = (0 + 4)(4 - 0) = 4/4 = 1
{m} = 1
{y} - intercept = - 4
{c} = - 4
We can write the equation as -
y = x - 4
Therefore, the equation of the straight line will be -
y = x - 4.
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A chemist has a 25% and a 50% acid solution. How much of each solution should be
used to form 200 ml of a 35% acid solution?
P.S: no decimal is used in this solving. For example 0.25, 0.50, and 0.35 is converted to 25%, 50% and 35%.
The required amount each type of solution to make mixture are 120 ml of 25% acid and 80 ml of 50% acid.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Explain Acid solution.A liquid mixture known as an acidic solution is created when water and hydrogen ions react. The Brnsted-Lowry theory states that whereas bases "receive" hydrogen protons, acids "give" hydrogen protons. Different solutions have different levels of acidity.
According to question:Let there be (200 - x) ml of 50% acid and x ml of 25% acid.
200*0.35 = 0.25x+0.5(200-x)
0.25x +100 -0.5x = 70
30 = 0.25x
x=120
200 - x = 200 - 120 = 80, resulting in 120 ml of 25% acid and 80 ml of 50% acid.
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For the mixture, 120 ml of 25% acid and 80 ml of 50% acid are needed for each type of solution.
What is a percentage?A percentage is a term used in mathematics to describe a value or ratio that may be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should first divide it by 100 before multiplying it by the remainder. Therefore, the percentage refers to a component per 100. The word percent simply means "per 100." Its symbol is the letter "%."Describe Acid solution.Water and hydrogen ions react to form an aqueous mixture known as an acidic solution. According to the Brnsted-Lowry theory, while bases "get" hydrogen protons, acids "give" them. Acidity levels vary among various solutions.Let's say there are (200 - x) ml of 50% acid and x ml of 25% acid.200*0.35 = 0.25x+0.5(200-x) (200-x)0.25x +100 -0.5x = 7030 = 0.25xx=120200 minus x equals 200 minus 120 equals 80, yielding 120 ml of 25% acid and 80 ml of 50% acid.To learn more about percentage refer:
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PLEASE HELPP,TEST QUESTION LIMITED TIME!!
Question- Given circle C with center (3, 4) and radius of 10, and circle D with center (0,1) and radius of 2, what sequence of transformations should be used to prove circle C is similar to circle D by mapping C onto D? Show all work and explain your reasoning.
Answer: it’s A
Step-by-step explanation:
Solve this system of equations by graphing. First graph the equations, and then type the solution.
3x-y=-6
y=x+4
The solution is (_,_)
The solution to the system of equations in this problem is given as follows:
(5,9).
How to obtain the solution to the system of equations?The system of equations for this problem is defined as follows:
3x - y = 6.y = x + 4.We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
From the image given at the end of the answer, the solution to the system of equations is given as follows:
(5,9).
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What is the median of this data set? {13, 13, 13, 15, 15, 16, 16, 17, 177
I NEED HELP ASAP PLEASE
Answer:15
Step-by-step explanation:
its the middle number
Answer: i think it's 15!!
hope this helps lol
The length of a rectangle is 6 inches more than its width. The area of the rectangle is 16 inches. Which quadratic equation could you use to find the dimensions of the rectangle?
The quadratic equation we use to find the dimensions of the rectangle is w^2 + 6w - 16 = 0
What is Quadratic equation?
The second-degree equation is a quadratic equation. This indicates that it has at least one (1) squared phrase. Ax^2 + bx + c = 0 is one of the most used formulas for solving quadratic equations. Here, a, b, and c are constants or numerical coefficients.
What is Rectangle?
A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equal sides.
Let W be the width of rectangle.
then, length of the rectangle is W + 6 .
and the Area, A = 16 inches^2
And the area of recatngle is A = L x W
Hence, A = (W+6)W
So, 16 = W^2 + 6W
Hence the quadratic equation whichuse to find the dimensions of the rectangle is ;
W^2 + 6W - 16 = 0
By the quadratic formula we have
[tex]w = \frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]w = \frac{-6 \pm \sqrt{6^{2}-4*1*(-16) } }{2*1}[/tex]
[tex]w = \frac{-6 \pm \sqrt{36 + 64} }{2}[/tex]
[tex]w = \frac{-6 \pm 10 }{2}[/tex]'
Hence, we take width as a positive because width never be negative .
so,the value of width is ;
w = 2
and length o rectangle is ;
l = w + 6 = 2 + 6 = 8
l = 8
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Solve for a.
a+ (−4) = −13
Answer: a= -9
Step-by-step explanation:
a+ (−4) = −13
a - 4 = -13 (the 4 becomes -4 as when it comes to + or - it is always -)
a = -13 +4 (when you switch the side -4 becomes +4)
a= -9