Answer:
(a) In a school trip the ratio of adults to students is 1:10 , and all of the students are in year 10 or year 11. The ratio of year 10 to year 11 is 1:4, so the fraction of all the people on the trip who are year 11 students is 1/5.
(b) In a cinema the ratio of adults to children is 2:3, and the children are either boys or girls. The ratio of boys to girls is 5:2 , so the fraction of all the people in the cinema who are girls is 2/5.
a vehicle factory manufactures cars. the unit cost (the cost in dollars to make each car) depends on the number of cars made. if cars are made, then the unit cost is given by the function . how many cars must be made to minimize the unit cost? c(x)
The number of cars that must be made to minimize the unit cost is 300 cars which is determined by differentiation.
Differentiation is a mathematical process that determines the instantaneous rate of change of a function based on one of its variables. The most common example is velocity, which is the rate of change of displacement with respect to time. Anti-differentiation is the inverse of finding a derivative.
Differentiation is used to calculate the rate of change of quantities in real time.
Since, we have been given the cost function to be function [tex](cx)= 1.1^{2} - 660x+107,357[/tex] then we have to find the first differentiation in order to get the value and this will be:-
[tex](cx)= 1.1^{2} -660x+107,357\\2.2x=660\\x=\frac{660}{2.2} \\x=300[/tex]
Therefore, the number of cars that must be made to minimize the unit cost is 300 cars.
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Martha made 3 birthday cards and she wants to make more. If she makes 5 cards an hour, how many cards will she have after 6 hours?. pls help
Answer:33
Step-by-step explanation: 5 cards times 6 hours is 30 and before you had 3 so 30+3=33.
Let sets A and B be defined as follows.
A is the set of integers greater than or equal to -9 and less than or equal to - 3
B=1-29, -26, -23, 30}
(a) Find the cardinalities of A and B.
n(A) =
n (B) =
The cardinalities:
n(A) = 3
n (B) = 1.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
Let sets A and B be defined as follows.
A is the set of integers greater than or equal to -9 and less than or equal to - 3
A = {n ≥ -9 or n ≤ -3}
B = {1-29, -26, -23, 30}
B = {-28, -26, -23, 30}
The cardinalities:
n(A) = 3
n (B) = 1.
Therefore, n(A) = 3 and n (B) = 1.
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a full circle has 360° or 2π radians. given this, how many degrees are in 1 radian?
Answer:
1 radian ≈ 57.2958
BIG IDEAS MATH
Chapter 3: 3.4-3.6 Quiz > Quiz 3
6
Write an equation of the line passing through the point (5, 2) that is perpendicular to the line -x + 3y = 12.
The equation of the line is y=x+
helppppp
Equation of the line passing through the point (5, 2) that is perpendicular to the line -x + 3y = 12 is y=-3x+17.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We have to find equation of the line passing through the point (5, 2) that is perpendicular to the line -x + 3y = 12.
3y=12+x
y=1/3x+4
slope of given line is 1/3
So the slope of perpendicular line will be -3
Now let us find the y intercept
y=-3x+b
2=-3(5)+b
2=-15+b
b=17
So, equation of the line passing through the point (5, 2) that is perpendicular to the line -x + 3y = 12 is y=-3x+17.
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Mr. Hesch has 4 stations set up in his classroom. Each
station is labeled with a color: blue, purple, green, or yellow.
As each student enters the classroom, they spin the
spinner to decide at which station they will start. What is
the probability a student spins purple?
O
O
P
G
3100
8
25%
B
Y
Y B
G
P
The probability a student spins purple will be 25%.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of samples
Given that Mr. Hesch has 4 stations set up in his classroom. Each station is labeled with a color: blue, purple, green, or yellow. As each student enters the classroom, they spin the spinner to decide at which station they will start.
The probability will be calculated as:-
Probability = Probability = Number of favorable outcomes / Number of samples
Probability = 1 / 4
Probability = 0.25 or 25%
Hence, the probability will be 25%.
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How do you round off 73 659,650 and 793,548 to one decimal
Answer:
Below
Step-by-step explanation:
They have no decimal parts to round, so they are basically
73 659 650 .0
793 548 . 0
Triangle RST and triangle XYZ are shown.
Based on the diagrams, which information is true for triangle RST and triangle XYZ?
a. The measure of R is congruent to Y, and the measure of S is congruent to Z. If two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles are also congruent. Therefore, RST and XYZ are not similar because the sides appear to be different lengths.
b. The measure of R is congruent to Y, and the measure of S is congruent to Z. If two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles are also congruent. Therefore, RST and XYZ are similar.
c. RST and XYZ are similar because they have two pairs of congruent angles and the lengths of the sides are different.
d. RST and XYZ are not similar because although two pairs of angles are congruent, the third pair does not have to be congruent.
The information that is true for triangle RST and triangle XYZ is that:
The measure of R is congruent to Y, and the measure of S is congruent to Z. If two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles are also congruent. Therefore, RST and XYZ are not similar because the sides appear to be different lengths. (option A)
What are similar triangles?Similar triangles are triangles that have the same shape and angle but their sizes may vary.
angle R is congruent to angle Y and
angle T is congruent to and Y.
This means that angle S is congruent to angle Z
therefore the angle in the two triangles are thesame, thus ,they are similar.
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a student asked classmates how tall they are, in which month they were born, and whether they are in a relationship. how many of these variables are quantitative and how many of these variables are categorical? one is quantitative. two are categorical. three are quantitative. none is categorical. two are quantitative. one is categorical. none is quantitative. three are categorical.
The correct answer is option (B). The answer is one is quantitative and two are categorical.
Given that,
A student quizzed his or her peers about their height, birth month, and relationship status. what proportion of these variables are categorical and what proportion are quantitative.
To find : How many variables are quantitative and categorical ?
A variable where the data indicate the amounts is referred to be a quantitative variable (e.g. height, age). Any variable where the data represent groupings is referred to as categoric variable.
Any trait that cant be quantified is referred to as categorical variable (also known as a qualitative variable). Nominal or ordinal categorical variables are also acceptable.
Therefore, option is the appropriate response (B). One is a quantitative response, and two is a categorical one.
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-3[tex]\sqrt{-49}[/tex]
HELP ME PLEASE
Write the equation of the table in
slope-intercept for function form.
X= -10,-20,-30
Y= 10,20,30
Step-by-step explanation:
please refer to the attached for details
Rhonda and Amir are both shopping for sunglasses.
Use the drop-down menus to complete the statements about Rhonda's and
Amir's purchases.
With regard to the prompt on Percent Error, when Rhonda and Amir are both shopping for sunglasses, note that:
Rhonda's purchase was $5 off the actual cost of $20. That is a percent error of 25%.Amir's purchase was $10 off the actual cost of $100. That is a percent error of 10%.Because Amir's sunglasses cost $80 than Rhonda's sunglasses, each dollar of error in measurement results in a 35% error.What is the percent Error?A data value's approximation error is the difference between an exact value and some approximation to it.
This inaccuracy can be stated as either an absolute or relative error. A computing machine's accuracy or measurement mistake can generate an approximation error.
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-5y+9y please help me with this
Answer: answer is 4y
Step-by-step explanation:
Answer: 4y
Step-by-step explanation:
-5y + 9y - Collect like terms by calculating the sum or difference of their coefficients.
(-5 + 9)y - Calculate the sum
Which will leave you with the answer: 4y
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The polynomial x^2 + 3x - 1 is a factor of x^4 + 3x^3 - 2x^2 - 3x + 1. Please select the best answer from the choices provided T F
Yes, it is true that [tex]x^{2}[/tex] + 3x - 1 is a factorization of [tex]x^{4}[/tex] + 3[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 3x + 1.
How to factorize?Let us factorize the equation,
[tex]x^{4}[/tex] + 3[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 3x + 1
=> [tex]x^{4}[/tex] - 2[tex]x^{2}[/tex] + 1 - 3x + 3[tex]x^{3}[/tex]
Let's construct a complete square using the terms provided:
=>[tex](x^{2}) ^{2}[/tex]- 2 × [tex]x^{2}[/tex] × 1 + [tex]1^{2}[/tex] + 3[tex]x^{3}[/tex] - 3
=> [tex](x^{2} - 1)^{2}[/tex] + 3[tex]x^{3}[/tex] - 3x
After completing the above calculation, take the common 3x from 3x^3 - 3x.
=>[tex](x^{2} - 1)^{2}[/tex] + 3x([tex]x^{2}[/tex] - 1)
=>([tex]x^{2}[/tex] - 1) ( ([tex]x^{2}[/tex] - 1)+ 3x )
=>([tex]x^{2}[/tex] - 1) ([tex]x^{2}[/tex] + 3x - 1)
Hence, ([tex]x^{2}[/tex] - 1) and ([tex]x^{2}[/tex] + 3x - 1) are two factors of the
equation [tex]x^{4}[/tex] + 3[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 3x + 1.
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help (50) points
Sam had seven eighths of a pizza. He ate two-fourths of it for dinner. How much of the pizza did Sam eat for dinner?
nine-twelfths
fourteen thirty-seconds
sixteen twenty-eighths
twenty-eight sixteenths or one and twelve-sixteenths
Answer:
nine-twelfths
Step-by-step explanation:
a study compares online instruction with a standard lecture for teaching statistics. the proper way to design such a study is:
The proper way to design a study comparing online instruction with a standard lecture for teaching statistics would be to use a randomized controlled trial.
Participants should be randomly assigned to either the online instruction group or the standard lecture group. Both groups should cover the same content and have equivalent opportunities for interaction and assessment. The effectiveness of the two methods should then be compared by measuring the performance of participants on a common set of assessments. It is also important to control for potential confounders such as prior knowledge, motivation, and learning style. By following these steps, the study can accurately determine the effectiveness of online instruction compared to the standard lecture method.
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What is one weakness of the maximum likelihood principle?a) only quantitative decisions are made by using the maximum likelihood principleb) it ignored other available information, such as other possible events and their consequencesc) the maximum likelihood principle focuses on objective possibilities and ignore subjective possibilitiesd) it overcompensates for socio-economic outcomes
b) The greatest likelihood concept has a fault in that it ignores other accessible information, such as alternative probable occurrences and their effects.
What is maximum likelihood principle?The maximum likelihood principle is a strategy for determining the best values for the parameters that form a model. In doing so, you improve the possibility that your model will approach the "true" model. Maximum Likelihood Estimation (MLE) is a probabilistic strategy to determining model parameter values. Parameters may be thought of as blueprints for the model because they are the foundation upon which the algorithm operates. MLE is a popular approach in machine learning, time series analysis, panel data analysis, and discrete data analysis.
Here,
The greatest probability principle is concerned with determining the parameters that best suit the observed data, but it ignores any other elements or information that may be significant. This may result in oversimplification and maybe inaccurate conclusions.
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The town of Todsham currently has a population of 300,000.
Each year, the population of Todsham will reduce by 5%.
How many fewer people will live in Todsham in 6 years compared with now?
Give your answer to 3 s.f.
PLEASEEEE HELLPPP BEGG!!!
In 6 years, there will be 90,000 fewer people living in Todsham compared with now.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that town of Todsham currently has a population of 300,000.
Each year, the population of Todsham will reduce by 5%.
We need to find the number of people will live in Todsham in 6 years compared with now
The population reduction in one year will be 5% of 300,000, which is:
300,000 ×0.05 = 15,000
Now in 6 years, the population reduction
15,000×6 = 90,000 people.
Therefore, in 6 years, there will be 90,000 fewer people living in Todsham compared with now.
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The tree diagram represents the sample space for the repeated experiment of a coin being tossed 4 times.
Determine P(at least 2 heads).
0.8125
0.6875
0.4375
0.0625
The probability of obtaining at least 2 heads is 0.6875.
option B.
What is the probability of getting at least 2 heads?
The probability of obtaining at least 2 heads in 4 coin tosses can be calculated by adding the probabilities of getting exactly 2 heads, exactly 3 heads, and exactly 4 heads. This can be done using the binomial distribution formula:
P(X >= 2) = P(X = 2) + P(X = 3) + P(X = 4)
Where;
X is the number of heads in 4 coin tossesEach coin toss has a probability of 0.5 of landing heads.
P(X = 2) = 4C2 x (0.5)^2 x (0.5)^2 = 6 x 0.25 x 0.25 = 0.375
P(X = 3) = 4C3 x (0.5)^3 x (0.5)^1 = 4 x 0.125 x 0.5 = 0.25
P(X = 4) = 4C4 x (0.5)^4 = 1 x 0.0625 = 0.0625
The total probability is calculated as follows;
P(X >= 2) = 0.375 + 0.25 + 0.0625 = 0.6875
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Answer:
The probability of obtaining at least 2 heads is 0.6875.
option B.
Step-by-step explanation:
7. Find the equation of the line that goes through the point (-2, -2) and has a slope of -4. y = -4x - 2 y = -4x - 10 y = -2x - 2 y = -2x - 4
The required equation of the line that goes through the point (-2, -2) and has a slope of -4 is y = -4x - 10. Option B is correct.
What is the intercept in the equation?In the equation intercept is the value of the linear function where either of the variables is zero.
The equation of a line with slope m and passing through the point (x₁, y₁) can be found using the point-slope formula:
y - y₁ = m (x - x₁)
Plugging in m = -4, x₁ = -2, and y₁ = -2, we get:
y - (-2) = -4 (x - (-2))
Simplifying, we get:
y + 2 = -4 (x + 2)
Expanding the right-hand side:
y + 2 = -4x - 8
Isolating y on one side:
y = -4x - 10
Thus, the equation of the line is y = -4x - 10.
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Put the numbers in order from smallest to largest. 54,900, 535,728, 535,740, 536,312.
Answer:
Put the numbers in order from smallest to largest. 54,900, 535,728, 535,740, 536,312.
54,900, 535,728, 535,740, 536,312
Step-by-step explanation:
You're welcome.
Answer:
All numbers in order:54,312,535,535,536,728,740,900
Step-by-step explanation:
Find the numbers that have the least amount of value. Then put the numbers with the greater value towards the end.
Solve for x for each triangle. Find the length of each side. perimeter=42 ft
Answer:
10 ft
Step-by-step explanation:
As the triangle is equilateral, perimeter = (x + 4) * 3 = 42 ft
x + 4 = 42/3 = 14
x = 14 - 4 = 10 ft
define a positive integer n to be a factorial tail if there is some positive integer m such that the base-ten representation of m ! ends with exactly n zeros. how many positive integers less than 1992 are not factorial tails?
The number of positive integers which are less than 1992 and not factorial tails are 396.
Positive integer are defined as the all the integers greater then zero.There are positive integers, zero, and negative integers.
Let for some positive integer with exactly n zeros be m
Number at the end of zeros of m! be f(m)
f(m) = ( m /5 ) + ( m /25 ) + ( m /125 ) + ( m /625 ) + ....
Here 'm' is multiple of 5
So ,f(m) = f( m + 1) = f( m + 2) = f( m + 3 ) = f( m + 4 )
And f(m) ≤ ( m /5 ) + ( m /25 ) + ( m /125 ) + ( m /625 ) +...
= m / 4.03
= m / 4
Value of m greater than 7964 such that f(m) = 1991
f( 7975 ) = 1991
Number of distinct positive integer 7975 / 5 = 1595 less than 1992
Number of positive integers less than 1992 and they are not factorial tails are equal to
= 1991 - 1595
= 396.
Therefore, there are 396 positive integers which are less than 1992 and are not factorial tails.
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write a congruence statement for the quadrilateral you created in figure AFEKJB and the image of the quadrilateral in figure MBJKGH
One of the congruence statement can be written as AFEB = MBJH.
What are Quadrilaterals?Quadrilaterals are four sided polygons which also have four vertices and four angles.
Sum of all the interior angles of a quadrilateral is 360 degrees.
Given is a figure.
First we have to draw a line segment to make two quadrilaterals out of this figure.
We can join line EB and JH to form the quadrilaterals AFEB and MBJH.
These two quadrilaterals are congruent to each other as
FA = BM
FE = BJ
EB = JH
AB = MH
Hence the congruence statement can be written as AFEB = MBJH.
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The complete question is :
Figure MBJKGH is the image of figure AFEKJB after being rotated 90 degrees counterclockwise about point K.
Imagine drawing a segment in figure AFEKJB to create a quadrilateral and also the image of the segment when rotated 90 degrees counterclockwise about point K.
Write a congruence statements for the quadrilateral you created in figure AFEKJB and the image of the quadrilateral in figure MBJKGH.
Sandra Beal opened a new credit card in January. She paid a membership fee of $15 and a balance transfer fee of 5% when she moved $823.46 from her old card to her new card. During the year, she paid these finance charges: February $3.56; May, $5.82; July, $4.92; and September $2.18. What was the total annual cost of the card to Sandra?
The total annual cost of the card to Sandra is $72.65
How to find the total annual cost of the card to Sandra?To find the total annual cost of the card to Sandra, we have to add all the money Sandra paid for the new credit card for the year. This can be calculated as follow:
Membership fee = $15
Balance transfer fee of 5% of $823.46 = 5/100 * $823.46 = $41.17
February $3.56; May, $5.82; July, $4.92; and September $2.18
Total annual cost = $15 + $41.17 + $3.56 + $5.82 + $4.92 + $2.18 = $72.65
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ude is a full-time student working in the library at sioux city college in sioux city, iowa. what is the minimum hourly wage that jude may receive?
The minimum hourly wage that Jude may receive per hour in Sioux City is $7.25. It depends on the applicable federal and state minimum wage laws in effect in Sioux City, Iowa.
As of my knowledge cut-off in 2021, the federal minimum wage is $7.25 per hour. However, some states, including Iowa, have set a higher minimum wage. As of 2021, the minimum wage in Iowa is $7.25 per hour.
It's worth noting that the minimum wage may have changed since my training data cut-off, so I would advise checking the current laws in your area to determine the exact minimum wage that Jude may receive. Therefore the average wage per hour in Sioux City is $7.25.
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The correct question for the answer is
Jude is a full-time student working in the library at Sioux city college in Sioux city, Iowa. what is the minimum hourly wage that Jude may receive?
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What is the ratio of 2/3 to 4?
The ratio of two thirds to four is given as follows:
1 : 6.
How to obtain the ratio between two amounts?The ratio between two amounts a and b is obtained applying a proportion.
A proportion is applied because the ratio is given by the division of the amount a by the amount b.
The parameters for this problem are given as follows:
Amount a: 2/3.Amount b: 4.Hence the ratio of two thirds and four is calculated as follows:
(2/3)/4 = 2/3 x 1/4 = 2/12 = 1/6.
In ratio notation, it is given as follows:
1 : 6.
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what is the effect of increasing sample size on the cost of collecting data and the quality of the data collected?
The relationship between sample size and data quality is likewise straightforward; the quality of the data will increase as the sample size increases and vice versa.
It is typically impossible, or at least impractical, to collect data from all of the subjects you are interested in when conducting research on your clients, patients, or products. Instead, we take a sample (or subset) of the relevant population and try to learn as much as we can about the population from that sample.
Numerous factors can impact how well our sample represents the population, and hence, how valid and dependable our results will be. In this blog post, we discuss some of the important ideas that should be taken into account while conducting a survey, such as power, effect sizes, and confidence intervals and margins of error.
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Solve for m (type out your work and the answer)
M/8 =11
Answer: 44
Step-by-step explanation:
44/4 = 11
Answer:
88
Step-by-step explanation:
M/8 = 11
Cross multiply
M = 8×11
M = 88
the sum of two numbers is 23 less than twice the first number. their difference is 19 less than twice the second number. find each number
The first number is 12.5, and the second number is -3.25.
Let x be the first number, and y be the second number.
2x + 23 = 2y
y - 19 = 2x
Subtracting the second equation from the first:
24 = y
Substituting 24 for y in the first equation:
2x + 23 = 48
2x = 25
x = 12.5
Substituting 12.5 for x in the second equation:
12.5 - 19 = 2y
2y = -6.5
y = -3.25
The first number is 12.5, and the second number is -3.25.
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