P ( work/ senior ) = 0.14
The attached table
required
P ( work/ senior )
This is calculated using:
P ( work/ senior ) = n ( work/ senior )/ n ( senior ).
n ( work/ senior ) = 5
n ( senior ) = 25 + 5 + = 35
So:
P ( work/ senior ) = 5/35
P ( work/ senior ) = 0.14
Add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).
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trying to see what my answer would be
Answer:
B. [tex]2^{-14}*5^{10}[/tex].
Step-by-step explanation:
Use the power of a power property.
[tex](2^{-7}*5^{5} )^{2}[/tex]
Multiply all the exponents in the parenthesis by 2.
[tex](2^{-7}*5^{5} )^{2}=(2^{-14}*5^{10} )[/tex]
The answer is B. [tex]2^{-14}*5^{10}[/tex].
Hope this helps!
Please answer both questions.
Answer:
1) (x-6)^2=49
2) C
Step-by-step explanation:
Subtract 12 x and you get
-x^2-12x+13=0
You will be left with, after making a perfect square
(x-6)^2=49
To get rid of the squared/2nd power, add plus or minus to the opposite side and square root both sides. You will be left with
x-6=plus or minus 7
Your answer comes out to the to problem. Setting both to 0, you get -13, and 1. -6 plus 7 is 1, and -6 plus a -7 is -13.
What is the perimeter of the trapezoid
The perimeter of the trapezoid is 18 lines
How to determine the perimeterFormula for perimeter of a trapezoid is given as;
Perimeter = a + b+ c + d
a = 1
b = 4
c = 4
d = 9
Perimeter = 1 + 4 + 4 + 9
Perimeter = 18
Thus, the perimeter of the trapezoid is 18 lines
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1) (x-y)(y-2)(x+2) / 2x^2+4yz+6 =
2) 4(x+y)(x-y)(y-x) / t+d+m =
3) ( √25+√9 / 2 ) + √21675 =
4) (9x^2+3x+27)(3+6y)(4+6y) / 1+2a+38+4c+2000z =
5) (x^2+6x+5) / (x+2)(x+6) =
^^^Simplify
6) (xy/m) + (xm/y) - (m/x) = 63 x=
Isolate
Could anyone help me with these?
See below for the solution to each expression
How to solve the expressions?Expression 1
The expression is given as:
(x-y)(y-z)(x+z)/(2x^2+4yz+6)
Expand the numerator
(x^2 - y^2 -xz + yz)(x + z)/(2x^2+4yz+6)
Further, expand the numerator
(x^3 - xy^2 - x^2z + xyz + x^2z - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)
Evaluate the like terms
(x^3 - xy^2 + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)
Hence, the equivalent expression of (x-y)(y-z)(x+z)/(2x^2+4yz+6) is (x^3 - xy^2 + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)
Expression 2
The expression is given as:
4(x+y)(x-y)(y-x)
Apply the difference of two squares
4(x^2 - y^2)(y - x)
Expand the expressions in the brackets
4(x^2y - x^3 - y^3 + xy^2)
Open the bracket
4x^2y - 4x^3 - 4y^3 + 4xy^2
Hence, the equivalent expression of 4(x+y)(x-y)(y-x) is 4x^2y - 4x^3 - 4y^3 + 4xy^2
Expression 3
The expression is given as:
(√25+√9/2) + √21675
Take the square roots of 25, 9 and 21675
(5 +3/2) + 5√867
Evaluate the sum
13/2 + 5√867
Hence, the equivalent expression of (√25+√9/2) + √21675 is 13/2 + 5√867
Expression 4
The expression is given as:
(9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z
Factor out 3 and 2 from the numerator
3(3x^2 +x + 9) * 3(1 + 2y) * 2(2 + 3y)/1+2a+38+4c+2000z
This gives
18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z
The expression cannot be further simplified.
Hence, the equivalent expression of (9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z is 18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z
Expression 5
The expression is given as:
(x^2+6x+5)/(x+2)(x+6)
Factorize the numerator
(x + 1)(x + 5)/(x + 2)(x + 6)
Hence, the equivalent expression of (x^2+6x+5)/(x+2)(x+6) is (x + 1)(x + 5)/(x + 2)(x + 6)
Expression 6
6) (xy/m) + (xm/y) - (m/x) = 63
Factor out x
x(y/m + m/y) - m/x = 63
Evaluate the sum
x(y^2 + m^2)/y - m/x = 63
Multiply through by xy
x^2(y^2 + m^2) - my = 63xy
Add my to both sides
x^2(y^2 + m^2) = 63xy + my
The above implies that the variable x cannot be isolated from the equation
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The average rainfall in inches in miami from january to may is 1.61, 2.24, 2.99 3.15 5.35 and 9.68 while it is 2.24 2.8 3.03 2.05 2.09 and 6.69 during the same period in tampa. which city gets more rain and how much more.
Miami gets 6.12 more inches of rainfall more than Tampa.
What is average rainfall?The annual amount of precipitation that we anticipate is known as normal or typical rainfall (in a given area).
It is calculated and set by estimating the average (mean) of precipitation that has been observed in a region over a long period of time ( at least 30 years). The total amount of daily precipitation in a year is referred to as annual precipitation.
Calculation for the average rainfall-
The average rainfall (in inches) in Miami for 5 months are-
1.61, 2.24, 2.99, 3.15, 5.35, and 9.68,
Thus, the total rainfall in Miami in 5 months,
Total average rainfall = 1.61 +2.24 +2.99 +3.15 +5.35 + 9.68 = 25.02 inches
Similarly,
The average rainfall (in inches) in Tampa for 5 months are-
2.24, 2.8, 3.03, 2.05, 2.09, and 6.69.
Thus, the total rainfall in Tampa in 5 months,
Total average rainfall = 2.24 +2.8 +3.03 + 2.05 + 2.09 + 6.69 = 18.9 inches.
The difference between the total rainfall in Miami and Tampa is
25.02 - 18.9 = 6.12 inches
The total rainfall in Miami is 25.02 inches while the total rainfall in Tampa in the same time period is 18.9 inches.
Therefore, Miami gets 6.12 inches more rainfall during the same time period.
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write 1/c + 1/d - c-d/cd as a single fraction in its simplest form
imagine the cd/cd as 1 which is a whole number. then, add the denominators (d+c-cd)/cd
The diagram below shows a logo formed by removing a semicircle with diameter AB and a
rhombus DEFG from an isosceles trapezium ABCE where AE = BC.
Find the area of the logo.
The area of the logo is 136. 14 cm²
Determining the area
First, let's find the area of the semicircle
Area of semicircle = 1/2(πr²)
radius = 8/2 = 4cm
Substitute into the formula
Area of semicircle = [tex]\frac{1}{2} * 3. 142 * 4 * 4[/tex] = 25. 135 cm²
Now, let's find area of trapezium
Area of trapezium = [tex]\frac{a + b}{2} * h[/tex]
Area = [tex]\frac{12 + 10. 2}{2} * 10[/tex]
Area = [tex]11. 1 * 10[/tex]
Area = 111 cm²
Area of logo = Area of trapezium + area of semicircle
Area of logo = 111 + 25. 135
Area of logo = 136. 14 cm²
Thus, the area of the logo is 136. 14 cm²
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Pure beeswax has a density of 0.555 ounce per cubic inch. An online company sells pure beeswax at a price of $8.00 per ounce. What is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company
4.44 is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company given that pure beeswax has a density of 0.555 ounce per cubic inch and an online company sells pure beeswax at a price of $8.00 per ounce. This can be obtained by multiplying the values.
What is the selling price?Given that,
Density of pure beeswax = 0.555 ounce per cubic inch
Cost of beeswax per ounce = $8.00 per ounce
Selling price in dollars per cubic inch will be,
⇒0.555×$8.00 = $4.44
Hence 4.44 is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company given that pure beeswax has a density of 0.555 ounce per cubic inch and an online company sells pure beeswax at a price of $8.00 per ounce.
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Use the function f(x) = 5x² + 2x-3 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)
A)f(x)=3/5 and -1.
B)f(x)=(3/5, 0) and (-1, 0).
C)f(x)=(-0.2, -3.2)
D)f(x)= = -0.2.
What is factorization and example?Factorization in mathematics is dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the division of a number into its factors or divisors.For instance, the factorization of the integer 12 might appear as 3 times 4.Function: f(x) = 5x² + 2x-3.
a) Completely factor f(x)
f(x) = 5x² + 2x-3.
= 5x² + 5x-3x − 3
= 5x(x+1)-3(x+1)
=(5x-3)(x+1)
f(x)=3/5 and -1.
b)The x-intercepts of the graph of f(x):
f(x) = 5x² + 2x-3.
At f(x) = 0, the x-intercepts are present.
Therefore, x-intercepts are (3/5, 0) and (-1, 0).
c) The end behavior of the graph of f(x):
f(x) = 5x² + 2x-3.
The middle of the zeros is the vertex's x-coordinate.
=-0.2
Find the y-coordinate of the vertex, and substitute the found value of x into the given equation:
f(-0.2)= 5(-0.2)² + 2(-0.2) − 3
=-3.2
d)The steps you would use to graph f(x):
The axis of symmetry is the x value of the vertex.
Therefore, the graph is symmetrical at about x = -0.2.
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please help me i need to turn this in soon and i don't understand
Answer:
(a) C=88pi
A=1936pi
(b) Area
(c) Circumference
Step-by-step explanation:
Circumference formula = 2r(pi)
Area formula = pi(r^2)
Circumference = 2(44)(pi) = 88pi
Area = pi(44^2) = 1936pi
When something is paved it is the whole area not just the border so AREA
The chain will surround the place not fill it up so CIRCUMFERENCE
Which of the following is the graph of f(x) = x2 − 5x + 4? WILL MARK BRAINLIEST
A graph of a quadratic function with a minimum at 2, negative 9 and x intercepts at negative 1 and 5
B graph of a quadratic function with a minimum at 3, negative 4 and x intercepts at 1 and 5
C graph of a quadratic function with a minimum at 2.5, negative 2.4 and x intercepts at 1 and 4
D graph of a quadratic function with a minimum at negative 1.5, negative 6.2 and x intercepts at 1 and negative 4
C) graph of a quadratic function with a minimum at 2.5, negative 2.25 and x intercepts at 1 and 4
Step-by-step explanation:Standard Form of a Quadratic Function: ax² + bx + c = 0, where a ≠ 0
Given function: x² - 5x + 4
⇒ a = 1, b = -5, c = 4
The minimum of a function is the lowest point of its parabola. We can use the following formula to find the vertex or the minimum of the function: [tex]x=\dfrac{-b}{2a}[/tex] . This will give us the x-value of the vertex, and we will need to solve for the y-value.
The vertex or minimum.
Step 1: Find the x-value of the vertex.
[tex]\\\implies x=\dfrac{-(-5)}{2(1)}\\\\\implies x=\dfrac{5}{2}=2.5[/tex]
Step 2: Find the y-value of the vertex by substituting 2.5 as the value of x in the given function.
[tex]\\\implies x^2 - 5x + 4\\\\\implies 2.5^2-5(2.5)+4\\\\\implies 6.25-12.5+4\\\\\implies -2.25[/tex]
Vertex: (2.5, -2.25)
The x-intercepts (roots).
We can use the Quadratic Formula to find the roots of this function.
Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] when [tex]ax^2+bx+c=0[/tex]
Equation: x² - 5x + 4 = 0
⇒ a = 1, b = -5, c = 4
Step 1: Substitute the values of a, b, and c into the formula.
[tex]\\\implies x=\dfrac{\bold{-(-5)}\pm\sqrt{\bold{(-5)^2}\bold{-4(1)(4)}}}{\bold{2(1)}}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{25-16}}}{2}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{9}}}{2}\\\\\implies x=\dfrac{5\pm3}{2}[/tex]
Step 2: Separate into two possible cases.
[tex]x_1=\dfrac{5-3}{2}\implies \dfrac{2}{2}\implies \boxed{1}\\\\x_2=\dfrac{5+3}{2}\implies \dfrac{8}{2}\implies \boxed{4}[/tex]
The x-intercepts of the given function are 1 and 4.
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a brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches. the brick has a density of 2.7 grams per cubic centimeter. find the mass of the brick to the nearest gram a brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches. the brick has a density of 2.7 grams per cubic centimeter. find the mass of the brick to the nearest gram
The mass of brick is 2478 gram.
What is a rectangular prism?A rectangular prism has a total of 6 faces, 12 sides, and eight vertices. Like a cuboid, it has three dimensions- the base width, the height, and the length. The top and base of the rectangular prism are rectangular in shape. The pairs of opposite faces of a rectangular prism are identical or congruent.
A brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches.
The volume of rectangular prism = length×width×height
= 8×3.5×2
= 56
Thus volume of brick is 56 cubic inches.
Convert inches to centimeter
1 inch = 2.54 centimeter
Therefore,
56 cubic inches = 56 x 2.54 x 2.54 x 2.54 cubic centimeter
56 cubic inches = 917.676 cubic centimeter
Thus, we get,
volume of a rectangular prism = 917.676 cubic centimeter
The brick has a density of 2.7 grams per cubic centimeter
Density = 2.7 grams
The mass of brick is given by formula = density × volume
[tex]\Rightarrow[/tex] = 2.7 × 917.676
[tex]\Rightarrow[/tex] = 2477.72
[tex]\Rightarrow[/tex] ≅ 2478
Thus mass of brick is 2478 gram.
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Identify the segments that are parallel, if any, if ∠EDA≅∠HCB.
In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.
What is the line segment about?Note that by examining the the image if ∠EDA≅∠HCB, the two lines can never intersect even if they go a longer distance.
The reason why is that there are no parallel lines on it and as such, they cannot intercept.
Hence, In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.
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uppose you want to test the value of the mean in a population. You collect a random sample of 60 which yields a sample mean and sample standard deviation. You only know sampled information to perform the test. What type of procedure is appropriate for your data
To test the value of the mean in a population when only sample mean and sample deviation are known to perform the test then it is appropriate to use z-test procedure.
What is a Z-test?
A statistical method of testing a hypothesis is the z-test where either:
We are aware of the population variance, which is equal to 2.Despite the fact that we are unsure of the population variance, our sample size, n 30, is sizable. In this instance, we estimate the population variance using the sample variance.A t-test unlike of z-test must be used if the sample size is less than 30 and the population variance is unknown.Additional prerequisites for using the z-test include the following:
Data must follow a normal distribution.Independent data points are required.The variances for each sample must be equal.To know more about the z-test..........
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What is the area of triangle lmn? 3 square units 4 square units 6 square units 8 square units
The area of the triangle LMN is 4 units squared.
How to find area of a triangle?The area of a triangle can be described as follows:
The area of the triangle by using the base and height of the triangle.
area of a triangle = 1 / 2 bh
where
base of the triangleheight of the triangleTherefore,
base = NL = 4 units
height = PM = 2 units
Therefore,
area of the triangle = 1 / 2 × 4 × 2
area of the triangle = 8 / 2
area of the triangle = 4 units²
Therefore, the area of the triangle LMN is 4 unit squared.
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Answer: B. 4 Square Units
Step-by-step explanation:
Based on the graphs of the equations y = x + 7 and y = x2 – 3x + 7, the solutions are located at points:
The correct option is A. (4, 11) and (0, 7).
The solution of the equations y = x + 7 and y = x² – 3x + 7, the solutions are located at points: (4, 11) and (0, 7).
What is the system of linear equation?Estimate the y-intercept, slope, and express the equation in the form of the y-intercept (y = mx + b) to find the graphed equation. The slope is the difference between the y- and x-axis values.
A graph equation is an equation in graph theory where the unknown is a graph. Isomorphic ideas are one of the key issues in graph theory.
The equations are; y = x + 7 and y = x² - 3x + 7
At the solution, the u-values are equal, which gives;
y = y
x + 7 = x² - 3·x + 7
x² - 3·x + 7 - (x + 7) = 0
x² - 4·x = 0
x·(x - 4) = 0
x = 4, or x = 0
When x = 4, y = 4 + 7 = 11
When x = 0,
y = 0 + 7 = 7
Therefore, the solution for the equations y = x + 7 and y = x² - 3x + 7 are are located at points: (4, 11) and (0, 7).
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The complete question is-
Based on the graphs of the equations y = x + 7 and y = x² – 3x + 7, the solutions are located at points:
A. (4, 11) and (0, 7)
B. (4, 11) and (–7, 0)
C. (–7, 0) and (1.5, 4.75)
D. (1.5, 4.75) and (0, 7)
In the past, schools in Los Angeles County have closed an average of three days each year for weather emergencies. What is the probability that schools in Los Angeles County will close for four days next year
The probability that the schools in Los Angeles will be closed for four days next year is 0.1680.
What is Poisson's distribution formula?In order to comprehend separate events that happen at a steady pace over the course of a specified amount of time, Poisson's distributions are frequently utilized.
Formula for Poisson's distribution:
f(x) = ((λ^x)/x!).(e^(-λ))
x = Event to be calculated for
λ = Expected number of occurrences
P(X = x) = ((λ^x)/x!).(e^(-λ))
Here λ = 3 and x = 4
P(X = 4) = (81 / 4!).(e^(-3))
P(X = 4) = (81 * e^(-3))/24
P(X = 4) = (81 * 0.049)/24
P(X = 4) = 0.1680
Hence, the probability that schools in Los Angeles will be closed for four days next year is 0.1680.
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Which of the measurements of triangleBAC are correct
Answer:
yes
no
yes
Step-by-step explanation:
sin C = opp/hyp = 9/15 yes
tan B = opp/adj = 12/9 no
tan B = 12/9; B = tan^-1 12/9 = 53.13°
Find the area of each of these rectangles
verify commutative property of multiplication and addition 5 4
- -
2 5
then what will the answer of this with prof and detaling
The commutative property of multiplication addition is illustrated below.
How to illustrate the information?The commutative property implies that the changing of orders of the numbers doesn't have a effect on the value.
In this case, 5 × 4 = 20. Also, changing them to 4 × 5 is still 20.
Likewise 2 + 5 as 5 + 2 gives 7.
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An urn contains 11 balls, 3 white, 3 red, and 5 blue balls. Take out two balls at random, without replacement. You win $1 for each red ball you select and lose a $1 for each white ball you select. Let X be the random variable that notes the amount you win. Find the probability mass function (pmf) of X.
Let X be the number of times you win.
The total number of ways to select 2 balls (order does not matter) =>
The number of ways so that two balls are white:
= 3/55
The number of ways so that two balls are red:
= 3/55
The number of ways so that one ball is red, one is white:
= 9
The number of ways so that two balls are blue:
= 10
i.e. p = 10+9/55 = 19/55
The number of ways so that one ball is blue, one is white:
p = 15/55 = 3/11
The number of ways so that one ball is blue, one is red:
15/55 = 3/11
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PLEASE HELP BEST ANSWER GETS BRIANLIST
Answer:
-3
Step-by-step explanation:
So just like the picture provides, the slope can be defined as: [tex]\frac{\text{change in y}}{\text{change in x}}[/tex]. So this means we can take any two points and find the change in x and y to define the slope, since the slope is constant throughout the entire line, since it's a linear line, meaning it's straight.
So you can use the points (0, 15) and (2, 9). So let's look at the x-values, and you want to make sure, you maintain the order at which you look at the "change in x", for example I can define the change in x through the two points as 0 to 2, or 2 to 0, one case is 2, and the other is -2, but if I look at the change from 0 to 2, then I looked at the first point first then the second, this means when looking at the y-values I have to find the change from 15 to 9, and not 9 to 15, since I did 0 to 2 in the first case. I could look at the change from 9 to 15, but only if I looked at the changed from 2 to 0.
Anyways let's find the change from 0 to 2, it's 2. Now let's look at the change from 15 to 9, it's -6 (since the value went down). So this gives us equation: -6 / 2 = -3
The slope is -3
A survey of several 10 to 11 year olds recorded the following amounts spent on a trip to the mall: $18.31,$25.09,$26.96,$26.54,$21.84,$21.46 Construct the 98% confidence interval for the average amount spent by 10 to 11 year olds on a trip to the mall. Assume the population is approximately normal. Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
The 98% confidence interval for the average amount spent by 10 to 11-year-olds on a trip to the mall is 23.36 ± 2.933.
How to calculate the confidence interval and its critical value?The confidence interval for a given level of percentage is given by
C. I = μ ± Z(σ/√n)
Where,
μ - mean, σ - standard deviation, n - sample size, and z - critical value.
The critical value is calculated by
step 1: 100% - (the confidence level)
step 2: Converting the step 1 result into decimal value
step 3: dividing the step 2 result by 2
This is indicated by α/2. So, from the normal distribution table, the z-value at α/2 is said to be the required critical value and denoted by Z_(α/2) or Z.
Calculation:It is given that,
A survey of several 10 to 11-year-olds recorded the following amounts spent on a trip to the mall: $18.31,$25.09,$26.96,$26.54,$21.84,$21.46
Sample size n = 6
Step 1: Finding the mean for the given amounts of the survey:
Mean μ = (18.31 + 25.09 + 26.96 + 26.54 + 21.84 + 21.46)/6
= 23.36
Step 2: Finding the standard deviation:
Standard deviation σ = √summation(x - mean)²/n
On calculating, we get σ = 3.09
Step 3: Finding the critical value:
It is given that the confidence level is 98%
So, (100% - 98%) = 2%
Converting into decimal gives 0.02
So, α/2 = 0.02/2 = 0.01
Thus, at 0.01, the critical value Z = 2.326
Step 4: Constructing the confidence interval:
C.I = 23.36 ± (2.326) × (3.09/√6)
= 23.36 ± (2.326 × 1.261)
= 23.36 ± 2.933
So, the lower bound = 23.36 - 2.933 = 20.427
the upper bound = 23.36 + 2.933 =26.293
Therefore, the 98% confidence interval lies from 20.427 to 26.293.
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Which table represents a quadratic function?
Answer:
A (see attached)
Step-by-step explanation:
There are a couple of things you can look for to see if a table represents a quadratic function:
do the values increase, then decrease, or vice versado the differences have a constant difference.ObservationIn the first of the given tables, the f(x) values start out decreasing, and end up increasing. This is a good indication the table represents a quadratic function.
In the remaining tables, the f(x) values are always increasing.
table 2: differences are always +2 (linear function)table 3: differences are always +4.5 (linear function)table 4: table values have a common ratio of 2 (exponential function)AnalysisThe f(x) values in table 1 have differences of ...
-3, -1, 1, 3
These values have differences of ...
2, 2, 2
The constant "second differences" mean that the function can be represented by a 2nd-degree polynomial, a quadratic. In fact, the equation for this table is ...
f(x) = x² +2
In an algebra class, there are 10 less than twice as many boys as girls. If the total number of students is 38, how many boys and girls are there in class?
Answer: 16 girls and 22 boys
Step-by-step explanation:
This can be solved with simple algebra.
Let's say that the number of girls is x.
Since there are 10 less than twice as many boys as girls, the number of boys would be 2x-10. (2x for twice as many, and -10 for ten less.)
The total number of students is 38. Adding the girls, the equation is now 3x-10=38.
3x=48
x=16.
2x-10=the number of boys, as said earlier. SO, 32-10=22=the number of boys.
To check our work, add 16+22. This equals 38.
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The centreville city council conducts a survey to find out how many people would be willing to donate money to update the town's library. they randomly select 200 people for the survey, and 80 people say they would donate. if 9,800 people live in centreville, about how many people would likely donate?
a. 122
b. 280
c. 3,920
d. 5,880
(C) 3,920 people would likely donate.
What is the percentage?
A percentage (from Latin per centum "by a hundred") is a number or ratio stated as a fraction of 100 in mathematics. It is frequently symbolized with the percent sign, " percent ". A % is a dimensionless (pure) number; it does not have a unit of measurement.To find about how many people would likely donate:
First, find 80 is what percent of 200.
∴ [tex]\frac{80}{200} * 100 = 40%[/tex]
So, 80 is 40% of 200.
Centreville population is 9,800.
Now, take out 40% of 9,800.
[tex]\frac{x}{9,800} *100 = 40\\\frac{x}{98} =40\\98*40 = 3,920[/tex]
Therefore, (C) 3,920 people would likely donate.
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x is directly proportional to w²
When w = 4, x = 48
y is inversely proportional to x³
When x = 2, y = 14
Find a formula for y in terms of w.
Give your answer in its simplest form.
The formula for x in terms of w is x = 3w² and the formula for y in terms of x is y = (1/112)x³
Variationx = k × w²
w = 4, x = 48
48 = k × 4²
48 = k × 16
48 = 16k
k = 48/16
k = 3
So,
x = k × w²
x = 3 × w²
x = 3w²
y = k/x³
x = 2, y = 14
14 = k / 2³
14 × 2³ = k
14 × 8 = k
112 = k
So,
y = k/x³
y = 112/x³
y = (1/112)x³
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A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.
a. Find the probability of tossing a head and drawing a red marble. Explain your reasoning.
b. Find the probability of drawing two blue marbles if the first marble is not replaced. Explain your reasoning.
The probability of drawing two blue marbles if the first marble is not replaced is 1/5
How to determine the probabilities?The probability of tossing a head and drawing a red marble
The given parameters are:
White = 1
Blue =3
Red = 2
Total = 6
The probability of a head is
P(Head)= 1/2
The probability of drawing a red marble is
P(Red)= 2/6 = 1/3
The required probability is
P = P(Head) * P(Red)
This gives
P = 1/2 * 1/3
P =1/6
The probability of drawing two blue marbles if the first marble is not replaced.
Here, we have:
P(B1) = 3/6 = 1/2
P(B2) = 2/5
The required probability is
P = P(B1) * P(B2)
This gives
P = 1/2 * 2/5
P =1/5
Hence, the probability of drawing two blue marbles if the first marble is not replaced is 1/5
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12 yds
9 yds
3 yds
These triangles are similar. What value is x?
I
yds
Answer:
x=4
Step-by-step explanation:
the proportion between 9 and 3 is 1/3
so u just apply the fraction to the corresponding side
so 1/3 of 12 is 4
so x is 4