The study design described is a cross-sectional study.
The study design in this scenario is a cross-sectional study. The study aims to examine the relationship between family status and school performance. The sample is selected by randomly choosing every 5th child from the list of children at the ABC elementary school. Data is collected from the school record for each child, and family status is operationalized by whether the child lives in a single-parent household, dual-parent household, or has a non-parent guardian in the household. The school performance is measured by administering a student math test and a student reading test to the child in April, with each test including 20 questions and each correct answer being worth five points.
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(co 3) a puck company wants to sponsor the players with the 10% quickest goals in hockey games. the times of first goals are normally distributed with a mean of 12.56 minutes and a standard deviation of 4.91 minutes. how fast would a player need to make a goal to be sponsored by the puck company? g
A player would need to make a goal in approximately 18.85 minutes or faster to be sponsored by the puck company.
To determine how fast a player needs to make a goal to be sponsored by the puck company, we'll need to find the
time cutoff for the top 10% quickest goals.
Step 1: Determine the z-score for the 90th percentile (since we want the top 10%).
We can use a standard normal distribution table (or a calculator) to find that the z-score for the 90th percentile is
approximately 1.28.
Step 2: Use the z-score formula to find the time cutoff.
The formula is: Z = (X - μ) / σ
Where Z is the z-score, X is the time cutoff we're looking for, μ is the mean (12.56 minutes), and σ is the standard
deviation (4.91 minutes).
Step 3: Solve for X.
Rearrange the formula to solve for X: X = Z × σ + μ
Plug in the values: X = 1.28 × 4.91 + 12.56
X ≈ 6.29 + 12.56
X ≈ 18.85
So, a player would need to make a goal in approximately 18.85 minutes or faster to be sponsored by the puck company.
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give the percentage of measurements in a data set that are above and below each of the following percentiles. a. th percentile b. th percentile c. th percentile d. th percentile
The percentage of measurements in a data set that are above and below each of the following percentiles are 68%, 95% and 99.7%.
We need to calculate the percentage of the measurements contained in each of the following intervals:
According to the empirical rule, approximately 68% of the measurements in a normally distributed data set will fall within one standard deviation of the mean. Therefore, approximately 68% of the measurements will fall within the interval (mean - s, mean + s).
Similarly, approximately 95% of the measurements in a normally distributed data set will fall within two standard deviations of the mean. Therefore, approximately 95% of the measurements will fall within the interval (mean - 2s, mean + 2s).
Likewise, approximately 99.7% of the measurements in a normally distributed data set will fall within three standard deviations of the mean. Therefore, approximately 99.7% of the measurements will fall within the interval (mean - 3s, mean + 3s).
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Multiply.
(3x-4y) (4x-7y)
Simplify your answer.
Answer:
To multiply (3x - 4y) and (4x - 7y), we need to use the distributive property, which states that: a(b + c) = ab + ac Using this property, we can expand the given expression as: (3x - 4y)(4x - 7y) = 3x(4x) + 3x(-7y) - 4y(4x) - 4y(-7y) Simplifying each term, we get: = 12x^2 - 21xy - 16xy + 28y^2 = 12x^2 - 37xy + 28y^2 Therefore, the simplified answer is 12x^2 - 37xy + 28y^2.
Question 5(Multiple Choice Worth 2 points)
(Box Plots MC)
The box plot shows the times for sprinters on a track team.
L
40 41
H
Sprinters' Run Times
45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
Time in Seconds
Which of the following lists the range and IQR for this data?
O The range is 10, and the IQR is 14.
O The range is 10, and the IQR is 13.
O The range is 14, and the IQR is 13.
O The range is 14, and the IQR is 10.how do I figure this out help pls
19 is the range and 14 is the IQR. So, "The range is 19, and the IQR is 14" is the appropriate response.
how can you describe range?The range in statistics is the distinction between the greatest and lowest values within a set of data. It is a gauge of variation that reveals the degree to which values within a dataset are dispersed.
You simply take the difference between the two values to determine the range. The range is given by: When the dataset, for instance, has the values 2, 3, 5, 8, et 10, the lowest value is 2, and the highest is 10.
Range = Highest value – Lowest value = 10 – 2 = 8 .The range in this instance is hence 8.
given
The range is the discrepancy between the data set's maximum and minimum values.
The box plot shows that the range is between 40 and 59, with 40 being the smallest value and 59 being the maximum.
Maximum value - Minimum value equals 59 - 40, which equals 19.
You may determine the values of Q1 and Q3 to be roughly 45 and 59, respectively, using the box plot.
IQR = Q3 - Q1 = 59 - 45 = 14
When the IQR is 14 and the range is 19, the answer is:
19 is the range and 14 is the IQR. So, "The range is 19, and the IQR is 14" is the appropriate response.
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Mr. Foster is a librarian at Eastside Library. In examining a random sample of the library's book collection, he found the following.
722 books had no damage,
75 books had minor damage, and
29 books had maior damage.
Based on this sample, how many of the 70,500 books in the collection should Mr. Foster expect to have no damage or minor damage? Round your answer to the nearest whole number. Do not round any intermediate calculations.
The number of books that had no damage or minor damage in the sample is:
722 + 75 = 797
To estimate the number of books in the entire collection that would have no damage or minor damage, we can assume that the proportion of books with no or minor damage in the sample is approximately equal to the proportion of books with no or minor damage in the entire collection.
The proportion of books with no or minor damage in the sample is:
797 / (722 + 75 + 29) = 0.9064
So we can estimate the number of books with no damage or minor damage in the entire collection as:
0.9064 x 70,500 = 63,912.6
Rounding to the nearest whole number, we get:
63,913
Ally needs 90 meters of tape for a project. Tape comes in different size rolls. If she bought 50 meters, 22.86 meters, and an 18.288-meter roll, how much tape will she have in all? ___________ meters
Ally will have 91.148 meters of tape in all if Ally needs 90 meters of tape for a project.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.
Ally needs a total of 90 meters of tape for her project. She bought three rolls of tape, one with 50 meters, another with 22.86 meters, and the last one with 18.288 meters. To find the total amount of tape she has, she needs to add the length of all three rolls together.
Adding the length of the first two rolls, we get:
50 meters + 22.86 meters = 72.86 meters
Then adding the length of the third roll to the sum above, we get:
72.86 meters + 18.288 meters = 91.148 meters
Therefore, Ally will have 91.148 meters of tape in all.
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Which statement is true for the absolute values of points P and Q on the number line? Responses A |−8| ≤ 6|−8| ≤ 6 B |6| > |−8||6| > |−8| C |−8| > |6||−8| > |6| D |−8| < |6||−8| < |6| Question 2 Which absolute value statement is TRUE? Responses A |−6| > |−8||−6| > |−8| B |−10| < |−5||−10| < |−5| C |−8| < |3||−8| < |3| D |−9| > |−8||−9| > |−8|
For the given statements the correct answer is B |6| > |−8| and C |−8| < |3|.
What is statement?
In mathematics, a statement is a declarative sentence that is either true or false, but not both. Statements are often expressed using variables, symbols, or mathematical notation, and they can describe mathematical objects, relationships, properties, or operations.
For the first question, the correct response is:
B |6| > |−8|
This is true because the absolute value of a number is always positive, and it represents the distance of that number from zero on the number line. So, the absolute value of 6 is greater than the absolute value of -8, because 6 is further away from zero than -8 on the number line.
For the second question, the correct response is:
C |−8| < |3|
This is true because the absolute value of -8 is greater than the absolute value of 3. Absolute values tell us the distance from zero on the number line, and the distance between -8 and 0 is greater than the distance between 3 and 0.
Therefore for the given statements the correct answer is B |6| > |−8| and C |−8| < |3|.
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Which of the following can be constructed by drawing an angle on tracing
paper and then folding the paper so that the rays forming the angle lie upon
each other?
A. Parallel lines
B. Perpendicular line segment
C. Angle bisector
D. Median of a line segment
C. Angle bisector can be constructed by drawing an angle on tracing paper and then folding the paper so that the rays forming the angle lie upon each other. When you fold the paper, the crease that is formed will be the angle bisector of the original angle.
100 POINTS
Divide.
(4x^4-4x^2-x-3)/(2x^2-3)
We can use polynomial long division to divide (4x^4 - 4x^2 - x - 3) by (2x^2 - 3):
2x^2 + 0x - 1
---------------------
2x^2 - 3 | 4x^4 + 0x^3 - 4x^2 - x - 3
4x^4 - 6x^2
-----------
2x^2 - x
2x^2 - 3
-------
x - 3
Therefore,
(4x^4 - 4x^2 - x - 3)/(2x^2 - 3) = 2x^2 + 0x - 1 with a remainder of (x - 3)/(2x^2 - 3).
So the final answer is
2x^2 - 1 + (x - 3)/(2x^2 - 3)
Assume all lines that appear parallel, are parallel. Solve for y.
The value of y is 10. we canget this answer by using fact ratios of the corresponding sides are equal. Using this fact, we can set up the proportion
what is corresponding sides?
In geometry, corresponding sides are sides in two or more figures that are in the same relative position or location. For example, if you have two triangles ABC and DEF, and AB is corresponding to DE, BC is corresponding to EF, and AC is corresponding to DF, then AB and DE are corresponding sides, BC and EF are corresponding sides, and AC and DF are corresponding sides.
In the given question,
To solve for y, we need to use the fact that line wt and line ye are parallel to each other. This means that the ratios of the corresponding sides are equal. Using this fact, we can set up the following proportion:
wt/ty = we/yc
Substituting the given values, we get:
(8 + x + 6)/16 = 10/y
Simplifying and solving for y, we get:
y = (160)/(14 + x)
Now we need to use the fact that the sum of the lengths of two sides of a triangle is always greater than the length of the third side. Using this fact for triangle ATY, we get:
AT + TY > AY
Substituting the given values, we get:
x + 6 + 16 > y
Simplifying and substituting y with its expression, we get:
x + 22 > (160)/(14 + x)
Multiplying both sides by (14 + x), we get:
x² + 22x + 14x + 352 > 160
Simplifying and rearranging, we get:
x² + 36x - 192 > 0
Now we can solve this quadratic inequality to get the range of possible values for x:
(x - 4)(x + 48) > 0
The solutions are x < -48 or x > 4. Since x represents a length, we can ignore the negative solution. Therefore, we have:
x > 4
Substituting this value into the expression we derived for y, we get:
y = (160)/(14 + x) = (160)/(14 + 4) = 10
Therefore, the value of y is 10.
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Mia buys 50 coats at $28 each.
She sells 38 of these coats at $49 each.
She sells the rest of the coats at $40 each.
Find the overall percentage profit Mia has made on these coats.
Answer: 1264.2857%
Step-by-step explanation:
Answer:
She earned 67.29% profit
Step-by-step explanation:
First let's find how much she spent on the coats.
50 x $28
$1400
So, her expense was $1400
Now, let's find how much she earned selling these coats.
We know she sold 38 of these coats at $49 each. Let's find how much she earned for these 38 coats.
38 x $49
$1862
She earned $1862 on these 38 coats.
Now, let's find how much she earned on the rest of the coats (50-38 which is 12). We know she sold the remaining for $40 each.
12 x $40
$480
She earned $480 on the rest of the coats.
The total she earned $2342
To find the profit:
Profit= $ Earned - Expenses
Profit= 2342-1400
Profit=$942
The question is asking for the percentage.
To find the percentage, we can use the percentage formula:
[tex]\frac{Profit}{Expense}[/tex] x 100
We know that the profit is $942 and the expense is $1400
(We want to find how much profit she made out of the expense)
[tex]\frac{942}{1400}[/tex] x [tex]\frac{100}{1}[/tex]
If you round your answer, you will get 67.29
Answer: She earned 67.29% profit
Find the volume of the pyramid
The volume of the given pyramid is 86 in³ respectively.
What is a pyramid?A three-dimensional shape is a pyramid.
A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base.
The bases are joined to the peak to create a pyramid.
The lateral face is a triangle face formed by the connection of each edge of the base to the apex.
A three-dimensional figure is a pyramid.
Its base is a flat polygon.
The remaining faces are all triangles and are referred to as lateral faces.
So, the formula for the volume of the pyramid is:
V = lwh/3
Now, insert values as follows:
V = lwh/3
V = 7.4*7*5/3
V = 86.33333
Rounding off: 86 in³
Therefore, the volume of the given pyramid is 86 in³ respectively.
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Determine the surface area of a right circular cone that has a slant height of 5.8 ft and a diameter of 6.4 ft? Round your answer to the nearest whole.
After answering the presented question, we can conclude that Rounding this to the nearest whole number, we get a surface area of 91 sq. ft.
What is diameter?In geometry, the diameter of a circle is any straight line segment that has an endpoint on the circle and travels through its centre. Another way to put it is the longest chord of a circle. Either idea can be used to define the diameter of a sphere. The diameter is the length of the line that runs tangent to the two points at either end of the circle. If you take length to be the distance between two points, diameter equals length. The diameter of a circle is the distance between its two furthest points.
First, we need to find the radius of the cone:
[tex]radius = diameter/2 = 6.4/2 = 3.2 ft[/tex]
Now we can use the Pythagorean theorem to find the height of the cone:
[tex]height^2 = slant height^2 - radius^2[/tex]
[tex]height^2 = 5.8^2 - 3.2^2[/tex]
[tex]height^2 = 20.84[/tex]
height ≈ 4.56 ft
Next, we can find the surface area of the cone by adding the area of the base to the lateral surface area. The base is a circle with radius 3.2 ft, so its area is:
base area =[tex]\pi (radius)^2[/tex]
base area =[tex]\pi (3.2)^2[/tex]
base area ≈ 32.17 sq. ft.
The lateral surface area is the curved surface area of the cone, which can be found using the slant height and the radius:
lateral surface area = [tex]\pi (radius)(slant height)[/tex]
lateral surface area = [tex]\pi (3.2)(5.8)[/tex]
lateral surface area ≈ 58.92 sq. ft.
Therefore, the total surface area is:
total surface area ≈ base area + lateral surface area
total surface area ≈ [tex]32.17 + 58.92[/tex]
total surface area ≈ 91.09 sq. ft
Rounding this to the nearest whole number, we get a surface area of 91 sq. ft.
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i need to find the product
Answer:
c ik this because I took the same question as you
The product of the given algebraic expression is [tex]\frac{4}{(x-1)}[/tex].
The given expression is [tex]\frac{8x+8}{x^2-2x+1} .\frac{x-1}{2x+2}[/tex].
Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
Here, [tex]\frac{4(2x+2)}{x^2-1x-1x+1} \times \frac{x-1}{2x+2}[/tex]
= [tex]\frac{4(2x+2)}{x(x-1)-1(x-1)} \times \frac{x-1}{2x+2}[/tex]
= [tex]\frac{4(2x+2)}{(x-1)(x-1)} \times \frac{x-1}{2x+2}[/tex]
Cancel the same factors, that is
= [tex]\frac{4}{(x-1)} \times \frac{1}{1}[/tex]
= [tex]\frac{4}{(x-1)}[/tex]
Therefore, the product of the given algebraic expression is [tex]\frac{4}{(x-1)}[/tex].
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Siza reads at a rate of 200 words per minute. Calculate how many minutes it will take her to read 300 words. Give your answer in minutes and seconds.
Answer:
1 minute and 30 seconds.
Step-by-step explanation:
200 words in 1 minute
200/2=100
1minute/2=30 seconds
100+200=300 words
1 minute+ 30 seconds= 1 minute and 30 seconds.
what is the value of 13.72x5.77?
-8(2x-4) i need help help
Answer:
Therefore, -8(2x-4) simplifies to -16x + 32.
Step-by-step explanation:
-8 * 2x - (-8 * 4)
Simplifying this expression further gives:
-16x + 32
Therefore, -8(2x-4) simplifies to -16x + 32.
Answer:
Step-by-step explanation:
A fair dice is thrown n times.
Find an expression for the probability of getting at least one six in the n throws.
The expression for the probability of getting at least one six in n throws of fair dice is 1 - (5/6)ⁿ.
The complement rule of Probability:The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.
In this problem, we use the complement rule to find the probability of getting at least one six in n throws of a fair dice by subtracting the probability of not getting any sixes in n throws from 1.
Here we have
A fair dice is thrown n times.
The probability of getting at least one six in n throws of a fair dice is equal to 1 minus the probability of not getting any sixes in n throws.
The probability of not getting a six on any one throw = 5/6
[ Since there are 5 possible outcomes that are not six and 6 possible outcomes in total ]
Therefore,
The probability of not getting any sixes in n throws is (5/6)ⁿ.
So, the probability of getting at least one six in n throws is:
P(at least one six) = 1 - P(no sixes) = 1 - (5/6)ⁿ
Therefore,
The expression for the probability of getting at least one six in n throws of fair dice is 1 - (5/6)ⁿ.
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i tried everything and it was wrong
Answer:
A = 28π meters or 87.92 meters
Step-by-step explanation:
A = 2πrh
Find radius
Diagonal = 14 so radius 14 : 2 = 7
A = 2πrh
A = 2π×7×2
A = 2π x 14
A = 28π meters or 87.92 meters
which of the following statements about the f distribution is false? group of answer choices the f distribution is always a left-tailed test. the f distribution is skewed to the right. the f statistic is greater than or equal to zero. as the degrees of freedom of for the numerator or denominator get larger, the curves approximates the normal distribution.
The statement that the f distribution is always a left-tailed test is false statement about the f distribution. So, the right choice for answer option (a).
The F distribution (Snedecor's F distribution) represents continuous probability distribution which occurs frequently as null distribution of test statistics. Let two independent
chi-square variables are x and y with n₁ and n₂ with degree of freedom respectively. So, F-distribution is defined as F = ( X/n₁)/ (Y/n₂)
Characteristics : The F random variable is non-negative variable and the distribution is skewed to the right.
The sampling distribution of F statistic does not involve any population parameters and depends only the degreFor large degrees of freedom n₁ & n₂. F tends to Normal distribution.The Available F tables gives the critical values of F for right-tailed test. P(F > Fx (n₁, n₂)) = αThe F for left tail test both right-tailed &left tailed. So, the false statement is option(a).
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Complete question:
which of the following statements about the f distribution is false? group of answer choices
a) the f distribution is always a left-tailed test.
b) the f distribution is skewed to the right.
c)the f statistic is greater than or equal to zero.
d) as the degrees of freedom of for the numerator or denominator get larger, the curves approximates the normal distribution.
select all the expressions equivalent to 80-20x
Answer:
where is the pic
Step-by-step explanation:
the height h (in feet) above the water of a cliff diver is modeled by h=-16t^2+10t+26 where t is time (in seconds). how long is the diver in the air?
Step-by-step explanation:
When the diver hits the water at Height = 0 , the diver is no longer in the air .
0 -16t^2 + 10t + 26 Use Quadratic Formula
a = -16 b = 10 c= 26
to find the positive value of t = 1.625 s
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7. Alonzo and Mandy are selling raffle tickets at school for a fundraiser. Alonzo sells 5 tickets less than three times what Mandy sells. Together they sell a total of 43 tickets. Let n equal the number of tickets Mandy sells. Use an equation to determine the number of tickets Alonzo sells. Show how you arrived at your answer.
That we know that Mandy sells 12 tickets, we can use the first equation to find out how many tickets Alonzo sells: a = 3n - 5 = 3(12) - 5 = 31
Alonzo sells 31 tickets.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
Let's use algebra to solve the problem:
Let's start by defining some variables:
Let n be the number of tickets Mandy sells.
Let a be the number of tickets Alonzo sells.
We know that:
Alonzo sells 5 tickets less than three times what Mandy sells. So we can write:
a = 3n - 5
Together they sell a total of 43 tickets. So we can write:
a + n = 43
We have two equations with two variables, so we can solve for a by substituting the first equation into the second equation:
(3n - 5) + n = 43
4n - 5 = 43
4n = 48
n = 12
Now that we know that Mandy sells 12 tickets, we can use the first equation to find out how many tickets Alonzo sells:
a = 3n - 5 = 3(12) - 5 = 31
Therefore, Alonzo sells 31 tickets.
So the answer is: Alonzo sells 31 tickets.
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help pls it's not too hard I'm just bad
Answer:
x=21
Step-by-step explanation:
Find the value of x, y and z
The values of x, y, and z in the given rhombus are: x = -31, y = 20, z = -87.
What do you mean by Equation ?An equation is a mathematical statement saying that two amounts or values are the same, for example 6 x4=12x
We know that the side of a rhombus are equal in length.therefore we can solve the given equation
4y + 8 = -3x - 5 = -z + 1 = 88
Solving each equation for the variables, we get:
4y + 8 = 88
4y = 80
y = 20
-3x - 5 = 88
-3x = 93
x = -31
-z + 1 = 88
-z = 87
z = -87
Heance , the values of x, y, and z in the given rhombus are:
x = -31, y = 20, z = -87.
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potassium 42 has a decay rate of 5.5% per hour. in how many hours will the original quantity be halved?
The half-life of Potassium-42 can be calculated using the following formula:
t1/2 = (ln 2) / λ
where t1/2 is the half-life, ln is the natural logarithm, and λ is the decay rate.
Substituting the values given, we get:
t1/2 = (ln 2) / 0.055
t1/2 ≈ 12.6 hours
Therefore, the original quantity of Potassium-42 will be halved in approximately 12.6 hours.
It will take approximately 13.51 hours for the original quantity of potassium 42 to be halved with a decay rate of 5.5% per hour.
How we can understand about how many hours will the original quantity be halved?To find the number of hours it takes for potassium 42 to be halved with a decay rate of 5.5% per hour, we can use the formula:
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The number of toy trucks in Mike's toy collection is 2/5 of the number of toy cars a,Express the number of toy cars as a fraction of the number of toy trucks. b,What is the ratio of the number of toy trucks to the total number of toy trucks and toy cars? c,What fraction of the total number of toy trucks and toy cars is the number of toy cars?
The number of toy cars to the number of trucks is 5/2,the number of toy trucks is 2/7 of the total number of toy cars and toy trucks and the number of toy cars is 5/7 of the total number of toy cars and toy trucks.
EquationsLet's represent the number of toy cars as 'c' and the number of toy trucks as 't'.
From the problem, we know that:
t = 2/5c
Express the number of toy cars as a fraction of the number of toy trucks:
c = 5/2t
c/t = (5/2t)/t = 5/2
Therefore, the number of toy cars is 5/2 times the number of toy trucks.
The total number of toy cars and toy trucks is:
c + t
Substituting t = 2/5c, we get:
c + (2/5)c = 7/5c
So the ratio of the number of toy trucks to the total number of toy cars and toy trucks is:
t/(c + t) = (2/5c) / (7/5c) = 2/7
Therefore, the number of toy trucks is 2/7 of the total number of toy cars and toy trucks.
The fraction of the total number of toy cars and toy trucks that is the number of toy cars is:
c / (c + t)
Substituting t = 2/5c, we get:
c / (c + 2/5c) = c / (7/5c) = 5/7
Therefore, the number of toy cars is 5/7 of the total number of toy cars and toy trucks.
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can somebody helppp please, do all the tasks from a and b.
Thank u!!!
in photo.
The solutions for the quadratic equations ax² + bx = 0 are:
a) x=0 or x=-2 for x²+2x=0;
x=0 or x=2 for x²-2x=0;
x=0 or x=2 for -x²+2x=0;
x=0 or x=-2 for -x²-2x=0.
b) x=0 or x=-5/3 for 3x²+5x=0;
x=0 or x=5/3 for 3x²-5x=0;
x=0 or x=5/3 for -3x²+5x=0;
x=0 or x=-5/3 for -3x²-5x=0.
How did we get these values?a) To solve the quadratic equations ax² + bx = 0, we need to factor out the common variable x, and then solve for x:
a) x²+2x=0
x(x+2)=0
x=0 or x=-2
b) x²-2x=0
x(x-2)=0
x=0 or x=2
c) -x² + 2x = 0
-x(x-2)=0
x=0 or x=2
d) -x²-2x=0
-x(x+2)=0
x=0 or x=-2
b) To solve the quadratic equations 3x²+5x=0, 3x²-5x=0, -3x²+5x=0, and -3x²-5x=0, we factor out the common variable x and then solve for x:
b) 3x²+5x=0
x(3x+5)=0
x=0 or x=-5/3
b) 3x²-5x=0
x(3x-5)=0
x=0 or x=5/3
c) -3x²+5x=0
x(-3x+5)=0
x=0 or x=5/3
d) -3x²-5x=0
x(-3x-5)=0
x=0 or x=-5/3
Therefore, the solutions for the quadratic equations ax² + bx = 0 are:
a) x=0 or x=-2 for x²+2x=0;
x=0 or x=2 for x²-2x=0;
x=0 or x=2 for -x²+2x=0;
x=0 or x=-2 for -x²-2x=0.
b) x=0 or x=-5/3 for 3x²+5x=0;
x=0 or x=5/3 for 3x²-5x=0;
x=0 or x=5/3 for -3x²+5x=0;
x=0 or x=-5/3 for -3x²-5x=0.
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The English translation of the question in the picture:
75. Solve the quadratic equations ax² + bx = 0
a) x²+2x=0,
x²-2x=0,
-x² + 2x = 0.
-x²-2x=0;
b) 3x²+5x=0,
3x²-5x=0.
-3x²+5x=0,
-3x²-5x=0;
The large dairy farm produced 936 eggs last year. How many dozen eggs did this
farm produce?
A
B
C
D
78
79
83
88
Answer: A=78
Step-by-step explanation: 936/12=78
936 eggs were produced last year by the sizable dairy farm. 78 dozen eggs are produced by this farm. The answer is option (A).
What is Algebra?The study of symbols for math and the procedures for using them to solve equations and comprehend the relationships between variables is the subject of the branch of mathematics known as algebra. When representing quantities and their relationships using letters and symbols, algebra uses graphs, functions, and expression manipulation in addition to equation and inequalities solving.
Numerous branches of science, technology, economics, and other disciplines make considerable use of algebraic concepts and methods. It is a fundamental area of mathematics that is frequently studied as a pre-requisite for more difficult maths and science courses.
Algebraic concepts that are important to know include:
Addition, subtraction, multiplication, and division are operations using numbers and variables.
Using variables to solve equations and inequalities
Algebraic expressions manipulation and simplification
Knowing how to graph both linear and nonlinear functions
Utilising matrices and vectors
studying trigonometric, rational, and polynomial functions
We must divide the total number of eggs by 12 to determine the number of dozen eggs produced.
936/12 = 78
We must divide the total number of eggs by 12 to determine the number of dozen eggs produced.
The answer is A) 78.
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assume that 11% of people are left-handed. if we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places:
The required probability of randomly selected people among 11% of left handed are,
Having some lefties (≥1) among the 5 people is 0.4416.
Having exactly 3 lefties in the group of 5 people is 0.01054.
Percentage of people left handed = 11%
Number of people selected at random = 5
Probability that there are some lefties (≥1) among the 5 people,
Probability of the complement event, which is that there are no lefties in the group.
Probability of selecting a right-handed person is
=1-0.11
=0.89.
Probability that all 5 people are right-handed is,
P(all right-handed)
= (0.89)^5
= 0.5584
Probability of there being some lefties (≥1) is the complement of this,
P(some lefties)
= 1 - P(all right-handed)
= 1 - 0.5584
= 0.4416
Probability of there being some lefties (≥1) among the 5 people is 0.4416.
Probability that there are exactly 3 lefties in the group of 5 people,
Use the binomial distribution formula,
P(X=3) = (⁵C₃) × (0.11)^3 × (1-0.11)^2
where X is the number of lefties in the group.
Using the binomial coefficient formula
ⁿCₐ= n! / (a! * (n-a)!)
P(X=3)
= (5!/(3!*(5-3)!)) × (0.11)^3×(0.89)^2
= 0.01054
Probability of there being exactly 3 lefties in the group of 5 people is 0.01054
Therefore, the probability of having some lefties ( ≥ 1) among the 5 people and exactly 3 lefties in the group is equal to 0.4416 and 0.01054 respectively.
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The above question is incomplete, the complete question is:
Assume that 11% of people are left-handed. if we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places:
a. There are some lefties ( ≥ 1) among the 5 people.
b. There are exactly 3 lefties in the group.