The amount of cards in each row is a factor of 60 in each scenario, ensuring that Vildia will utilize all 60 cards and that there will be an equal number of cards in each row.
What is combination?In mathematics, a combination is a way of selecting a subset of items from a larger set, where the order of the selected items does not matter. A combination is different from a permutation, which is a way of selecting a subset of items from a larger set, where the order of the selected items does matter.
Here,
If Vildia wants to set up a card game using 60 cards and wants to make an array with the same number of cards in each row, she could arrange the cards in the following ways:
1 x 60: In this case, Vildia would arrange all 60 cards in a single row.
2 x 30: In this case, Vildia would arrange the cards in two rows, each containing 30 cards.
3 x 20: In this case, Vildia would arrange the cards in three rows, each containing 20 cards.
4 x 15: In this case, Vildia would arrange the cards in four rows, each containing 15 cards.
5 x 12: In this case, Vildia would arrange the cards in five rows, each containing 12 cards.
6 x 10: In this case, Vildia would arrange the cards in six rows, each containing 10 cards.
10 x 6: In this case, Vildia would arrange the cards in ten rows, each containing 6 cards.
12 x 5: In this case, Vildia would arrange the cards in twelve rows, each containing 5 cards.
15 x 4: In this case, Vildia would arrange the cards in fifteen rows, each containing 4 cards.
20 x 3: In this case, Vildia would arrange the cards in twenty rows, each containing 3 cards.
30 x 2: In this case, Vildia would arrange the cards in thirty rows, each containing 2 cards.
60 x 1: In this case, Vildia would arrange all 60 cards in a single column.
Note that in each case, the number of cards in each row is a factor of 60, which ensures that Vildia will use all 60 cards and that there will be an equal number of cards in each row.
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A small class has 9 students, 4 of whine are girls and 5 of whom are boys. Teacher is going to choose two of the students at random. What is the probability that the teacher will choose two girls? Write your answer as a fraction in simplest form.
The probability that the teacher will choose two girls would be = 1/6
What is probability?Probability is defined as the expression that shows the possibility of an outcome of an event which may or may not happen.
The total number of students in the class = 9
The total number of girls = 4
The total number of boys = 5
The formula for finding probability = No of favourable outcome/Total number of outcomes.
The probability that teacher choose first girl = 4/9
One girl is selected we must reduce the number of girls available for selection to 4 - 1 = 3.
We must also reduce the number of children available for selection 9 - 1 = 8.
The probability that teacher choose second girl = 3/8
Thus, the probability = 4/9 × 3/8 = 1/6
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Elise is considering two different pricing plans for the school carnival. She is thinking that they could charge a $7 entrance fee and then $8 for each ride ticket. The other option is to charge a $15 entrance fee, but only $6 for one per-ride ticket. Write and graph an equation to represent each pricing plan option. At what point do the lines intersect?
Answer:
7 + (8 × t) = p, 15 + (6 × t) = p
Step-by-step explanation:
The equation you can use for charging a $7 entrance fee and then $8 for each ride ticket can look like this:
(let t = ride ticket & p = price)
7 + (8 × t) = pThe equation you can use for charging a $15 entrance fee and then $6 for each ride ticket can look like this:
15 + (6 × t) = pTherefore, the equations you can use are listed above.
The sum of four times a number and seven is 27. Find the number.
Provide your answer below:
Answer:
Look at the screenshot.
graph translation of (x,y) (x, y-2)
Answer:
can you explain a bit better what the problem is?
I wonder about polynomial and the use of polynomials in the real world?
Answer:
Step-by-step explanation:
Polynomials are a type of mathematical expression that involve variables raised to powers and added or subtracted together. They have many applications in the real world, ranging from science and engineering to finance and economics. Here are a few examples:
Physics: Polynomials are used to describe the motion of objects in space. For example, the position of a moving object over time can be represented by a polynomial function.
Engineering: Polynomials are used to design and analyze complex systems, such as electrical circuits and control systems.
Computer graphics: Polynomials are used to create curves and shapes in 3D modeling and computer graphics.
Finance: Polynomials are used in financial modeling to represent trends and make predictions. For example, a polynomial function could be used to model the growth of a company's revenue over time.
Data analysis: Polynomials are used to fit curves to data in order to make predictions or gain insights. For example, a polynomial function could be used to model the relationship between a company's advertising budget and its sales.
Overall, polynomials are a powerful tool in mathematics and have many practical applications in various fields.
Point
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(−4,−3)C, prime, left parenthesis, minus, 4, comma, minus, 3, right parenthesis is the image of
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C(−2,−3)C, left parenthesis, minus, 2, comma, minus, 3, right parenthesis under a translation.
Answer:
Step-by-step explanation:
What are you trying to do?
It's hard ot understand the problem.
Answer:
The image of point (–2, –3)C under the translation would be point (–4, –3)C.
the video shows many statistics in which douglas county is higher than most communities in the united states. what is the one area in which the statistics presented suggest that douglas county is actually lower than many other communities? home ownership number of companies that employ residents diversity education which is the most likely used method to compute the average commute time to work in douglas county? researchers collected a random sample of people in douglas county and asked them for their commute time. they added up all of these commutes times and then divided this number by the number of people in the sample. researchers collected a random sample of people in douglas county and asked them for their commute time. they added up all of these commute times and then divided this number by the total population of douglas county. researchers collected a random sample of people in douglas county who are employed and asked them for their commute time. they added up all of these commute times and then divided this number by the number of people in the sample. researchers collected a random sample of people in douglas county who are employed and asked them for their commute time. they added up all of these commute times and then divided this number by the total number of employed residents in douglas county. the video lists the major employers in douglas county, but does not list any statistics with these names. which of the following statistics would help you understand why they describe these companies as major employers in douglas county? the number of employees of each of these companies. the percentages of employed douglas county residents who work for each of these companies. the percentage of employees of each of these companies who live in douglas county. the number of employees who are douglas county residents in each of these companies.
The video does not provide information to answer the question about which area suggests that Douglas County is lower than many other communities.
What is Statistics ?Statistics in mathematics is the study of data gathering, organization, interpretation, analysis, and presentation. Planning the acquired data for experimental designs and statistical surveys is the major goal of employing statistics. A mathematical science that deals with numerical data is statistics. In short, statistics is an important process that aids in decision-making based on facts.
The video does not provide information to answer the question about which area suggests that Douglas County is lower than many other communities.
The most likely used method to compute the average commute time to work in Douglas County is: researchers collected a random sample of people in Douglas County who are employed and asked them for their commute time. They added up all of these commute times and then divided this number by the number of people in the sample.
To understand why the video describes certain companies as major employers in Douglas County, the most relevant statistic would be the number of employees of each of these companies.
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If f is one-to-one and f(7)=3, then f^1(3)= ___, and (f(7))^-1= ___
Answer:
[tex]f^{-1}(3) = \boxed{7}[/tex]
[tex]f(f(7))^{-1} = \boxed{7}[/tex]
Step-by-step explanation:
These follow from two of the properties of inverse functions:
If [tex]f[/tex] is a one-to-one function then
[tex]if\; f(x) = y \;then\; f^{-1}(x) = y}[/tex][tex]f^{-1}(f(x) = x\\\\f^{-1}(f(x) \;is\;the\;same\;as; ((f(x))^{-1}[/tex]A fair coin is trowsed twice what probability of optioning
1. Excalty one head
2. No tail
3. A least two tails
4. A head and two tails
The probability of obtaining a specific outcome on a coin toss is 1/2. Using this information, we can calculate the probabilities for the following outcomes:
1. Excalty one head = 1/2
2. No tail = 1/4
3. A least two tails = 1/2
4. A head and two tails = 3/8
Probability can be defined as the ratio of favorable outcomes to the total number of events.
To obtain exactly one head, we can either get a head on the first toss and tails on the second, or tails on the first toss and heads on the second. The probability of each of these outcomes is (1/2) × (1/2) = 1/4. Therefore, the probability of obtaining exactly one head is the sum of these two probabilities, which is 1/4 + 1/4 = 1/2.
To obtain no tails, we must get heads on both tosses. The probability of this is (1/2) × (1/2) = 1/4.
To obtain at least two tails, we must get tails on both tosses or tails on the first toss and heads on the second. The probability of getting tails on both tosses is (1/2) × (1/2) = 1/4, and the probability of getting tails on the first toss and heads on the second is also 1/4. Therefore, the probability of obtaining at least two tails is the sum of these two probabilities, which is 1/4 + 1/4 = 1/2.
To obtain one head and two tails, we must get heads on one of the tosses and tails on the other two tosses. There are three ways to do this: heads on the first toss and tails on the second and third, heads on the second toss and tails on the first and third, or heads on the third toss and tails on the first and second.
The probability of each of these outcomes is (1/2) × (1/2) × (1/2) = 1/8.
Therefore, the probability of obtaining one head and two tails is the sum of these three probabilities, which is 1/8 + 1/8 + 1/8 = 3/8.
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The figure shows the graph of the function.
f(x)=
The domain are the possible input while the range are the possible output of a function.
(a) The domain = [-√2, √2], the range = [0, 2]
(b) The domain = [-1, 1], the range = [0, 1]
(c) The domain = [-1, 1], the range = [0, -1]
(d) The domain = [0, 2], the range = [0, 1]
(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]
Reasons:
The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1
Therefore, we have;
(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2
The x-intercept of the above function are, x = √2, and x = -√2
Which gives;
The domain = [-√2, √2]
The range = [0, 2]
(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3
At the x–intercepts, we have;
-3·x² + 3 = 0
x = ±1
The domain = [-1, 1]
The maximum value of y is given at x = 0, therefore;
= -3 × 0² + 3 = 3
The range = [0, 1]
(c) y = -f(x) = -(-x² + 1) = x² - 1
At the x–intercepts, x² - 1 = 0
x = ± 1
The domain = [-1, 1]
The minimum value of y is given at x = 0, which is y = -1
The range = [0, -1]
(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x
At the x–intercepts, we have; -x² + 2·x = 0, which gives;
(-x + 2)·x = 0
Which gives, x = 0, or x = 2
The domain = [0, 2]
The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1
y = f(1) = -1² + 2×1 = 1
Therefore;
The range = [0, 1]
(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2
At the x–intercepts, we have; -x² - 4·x - 2 = 0, which gives;
x = -(2 + √2) or x = x = √2 - 2
The domain = [-(2 + √2), (√2 - 2)]
The maximum value of y is given when x = -4/(2)) = -2
Which gives;
-(-2)² - 4·(-2) - 2 = 2
The range = [0, 2]
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how do you solve a 3 collumn table
The way to solve a 3 column table depends on the information in the table but there are general steps to follow shown below.
How to work with a three column table ?First, identify the headings for each column. Then, determine the type of data being presented in each column because the data may be numerical (such as measurements or quantities), categorical (such as types or classifications), or a combination of both.
Analyze the data in each column and use mathematical operations or formulas to calculate or analyze the data, if necessary. Finally, draw conclusions or make inferences based on the data in the table.
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Assume that when you take a bath, you fill a tub to the halfway point. The tub measures 6 feet by 2 feet by 2.5 feet.
When you take a shower, you use a shower head with a flow rate of 1.71 gallons per minute, and you typically spend
10 minutes in the shower. There are 7.5 gallons in one cubic foot. Complete parts (a) through (c) below.
The comparison of the volume of water used for bathing and showering are as follows;
A. The amount of water used bathing is 12.7 cubic feet more than the amount of water used for showering
B. The time it takes to use the amount of water for bathing while showering is about 65.8 minutes
How can the volume be found from the flowrate?The volume of a fluid is the product of the constant flowrate and the time of flow of the fluid.
The level to which the tub is filled when taking a bath = The halfway point
The dimensions of the tub = 6 feet by 2 feet by 2.5 feet
The flowrate of the shower head = 1.71 gallons per minute
The time usually spent in the shower = 10 minutes
The number of gallons per cubic foot = 7.5 gallons
The amount of water used in bathing = 6 × 2 × 2.5 × (1/2) = 15
The volume of water used for bathing is 15 cubic feet of water
A. The amount of water used for showering = 1.71 gallons/minute × 10 minutes = 17.1 gallons
17.1 gallons = (17.1 gallons/7.5 gallons/ft³) = 2.28 ft³
The volume of water used for showering = 2.28 cubic feet
The difference in the volume of water used for bathing and the volume used for showering = 15 - 2.3 = 12.7
Therefore; you are using 12.7 more cubic feet of water than you do taking a shower; you use 12.7 more cubic feet of water than taking a bath.
B. The duration of a shower, t, that is equivalent to a bath can be found as follows;
1.71 gal/min = (1.71 gal/7.5 gal/ft³) = 0.228 gal/min
t = 15 gal/0.228 gal/min ≈ 65.8 min
The time it takes to use as mush water showering as the amount of water used bathing is about 65.8 minutes
Part of the question, obtained from a similar question posted online includes;
A. The method that use more water, showering or bathing
B. The duration of showering such that the amount of water used for bathing is used
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Triangle ABC is similar to triangle DEF. A 4 cm 5 cm B 3 cm C E D 6 15 cm 9 cm Which proportion can be used to find the length of DE in centimeters?
The length of DE is 12 centimeters.
How to find the length of DE in centimeters?Since triangles ABC and DEF are similar, we know that their corresponding sides are in proportion. That is:
AB/DE = BC/EF = AC/DF
We can use any of these proportions to find the length of DE, since they are all equal.
To use the proportion that involves DE, we can rearrange it as follows:
AB/DE = BC/EF
DE = AB * EF / BC
Now we can substitute the given lengths:
DE = 4 cm * 9 cm / 3 cm = 12 cm
Therefore, the length of DE is 12 centimeters.
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Nikki is going to use SSS to prove that PQR SQR.
Which of these is a necessary step in Nikki's proof?
A.
Prove that PQR SQR by vertical angles.
B.
Prove that PQ QR by CPCTC.
C.
Prove that QR QR by the reflexive property.
D.
Prove that QPR QSR by the transitive property.
Prove that QR QR by the reflexive property.
The triangles are congruent by reflexive property of SSS
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be ΔPQR
Let the second triangle be ΔQRS
And , the side QR is the common side
Now , measure of side PQ = measure of side QS
And , measure of side PR = measure of side RS
So , the three sides are equal (SSS: side, side, side) and they are congruent triangles
And , QR ≈ QR by the reflexive property.
Hence , the triangles are congruent by SSS
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The complete question is attached below :
Nikki is going to use SSS to prove that PQR SQR.
Which of these is a necessary step in Nikki's proof?
A.
Prove that PQR SQR by vertical angles.
B.
Prove that PQ QR by CPCTC.
C.
Prove that QR QR by the reflexive property.
D.
Prove that QPR QSR by the transitive property.
suppose the correlation coefficient r between x and y is 0.97. do we need to look at the scatterplot of x and y ? yes, to see if there is a non-linear relationship between x and y. yes, to see if there are any outliers. both (a) and (b). no, the scatterplot will not give any additional information as r is high.
Yes, to see if there is a non-linear relationship between X and Y.
What is correlation coefficient?The intensity and direction of a relationship between two variables is indicated by a correlation coefficient, which is a number between -1 and 1. In other words, it illustrates the degree to which measurements of two or more variables are comparable throughout a dataset.
Given:
The correlation coefficient r between x and y is 0.97.
As, On a scatterplot, the correlation coefficient, or r, quantifies the magnitude and axis of a linear relationship between two variables.
and, The relationship between two variables is generally considered strong when their r value is larger than 0.7.
So, here the correlation of 0.97 indicates a strong positive linear relationship between variable x and y.
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Austin runs 7 miles in 51 minutes.How many minutes does he take per mile?
Answer:
7 min 48 sec / mile
Step-by-step explanation:
51 min ÷ 7 miles = 7.2857142857142
Rounds to 7
Help asap please
Asap
The correct matching of the fractions
0.1 - 1/10
0.01 - 1/100
100% - 1
What is a fraction?A fraction is a way of representing a part of a whole or a quantity that is less than one. Fractions consist of two numbers separated by a horizontal or diagonal line, with the number above the line being called the numerator and the number below the line being called the denominator.
The numerator represents how many parts of the whole are being considered, while the denominator represents the total number of equal parts that the whole is divided into.
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It’s urgent please someone help
Answer:
I ammm really sorry for the question
i don't know sorry
Can somebody help..? The question is down below
The required measures of the angles are the following: ∠J = 135°, ∠F = 45°, ∠B = 135°, and ∠C = 22°.
What are supplementary angles?The supplementary angles are illustrated as when pairing of angles addendum to 180° then they are called supplementary angles.
The measure of the angles are given as follows:
∠I = 22°
∠A = 23°
∠J = 180° - ∠I - ∠A (sum of interior angles in a triangle)
∠J = 180° - 22° - 23° = 135°
∠F = 180° - ∠J (supplementary angles)
∠F = 180° - 135° = 45°
∠B = 360° - 90° - 90° - 45° (sum of interior angles in the quadrilateral)
∠B = 135°
∠C = 180° - ∠A - ∠B (sum of interior angles in a triangle)
∠C = 180° - 23° - 135° = 22°
Thus, the required measures of the angles are the following: ∠J = 135°, ∠F = 45°, ∠B = 135°, and ∠C = 22°.
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From a deck of regular playing cards, one card is chosen at
random. Find the probability the card is a diamond or a face card.
The probability that now the card is indeed a diamond or a face card is [tex]\frac{11}{26}[/tex].
What are probability and examples?The probability that any random event will occur is referred to as probability. This expression is used to calculate the likelihood that a given event will occur. When we fling a coin into the air, as an illustration. Probability: P(A) = f / N calculates the probability that an event will take place. Ratios and probability are related, but the former determines the latter. When calculating the likelihood of an event, it is necessary to know the probability of that event.
When we find the probability, we obtain:
A typical deck of cards contains 52 cards. There are 12 face cards, known as the Kings, Queens, and Jacks, because there are four suits. There are a total of 13 diamonds, of which 3 are previously counted face cards. Hence, there are 10 diamonds that are faceless.
So, total Diamond & face card =22
Probability =[tex]\frac{22}{52}[/tex]=[tex]\frac{11}{26}[/tex].
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let's define the simple events of selecting math majors as m1 and m2 and the events of selecting statistics majors as s1, s2, and s3. because two students are selected, the possible outcomes are all possible pairs of students. list the possible outcomes. (enter your answers as a comma-separated list.) m1m2, m1s1, m1s2, m1s3, m2s1, m2s2, m2s3,
The probability of rolling a 3 on a single six-sided die is 1/6, or 16.7%.
What is probability?Probability is a mathematical study of outcomes in uncertain situations it is used to describe the like would an event occurring and it can be expressed as a number between 0 to 1 probability is used to quantify the uncertainty associated with any given event it helps us understand how likely it is that something will happen and it can be used to make a prediction about futures even probability theory is it of modern statistic and is widely used in fields such as financial economics and science.
Therefore, the probability of rolling at least one 3 when rolling two six-sided dice is 2 × 1/6, or 33.3%. This is because the probability of rolling a 3 on one die is independent of the probability of rolling a 3 on the other die. This means that the probability of rolling at least one 3 is equal to the sum of the probabilities of rolling a 3 on each of the two dice (1/6 + 1/6 = 2/6). As a result, the probability of rolling at least one 3 when rolling two six-sided dice is 33.3%.
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Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form
Point-slope form: y - (-2) = -4(x - 2)
Slope-intercept form: y = -4x - 6
Own integers:
Point-slope form: y - 2 = -2(x - 4)
Slope-intercept form: y = -2x - 6
What does point slope form mean?Point slope form is a type of linear equation that describes the relationship between two points on a line. It is written in the form: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. Point slope form is used to find the equation of a line when given its slope and one point on the line. It can also be used to find the slope of the line when given two points on the line.
For example, if the point (2, 3) is given and the slope is 4, the point-slope form of the equation would be y - 3 = 4(x - 2).
The point-slope form of an equation of a line is an equation of the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this equation, (x1, y1) = (2, -2) and m = -4, so the point-slope form of the equation is y - (-2) = -4(x - 2).
The slope-intercept form of an equation of a line is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept of the line. In this equation, m = -4 and b = -6, so the slope-intercept form of the equation is y = -4x - 6.
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Find the perimeter of the triangle whose vertices are (−1,−14)
, (7,1)
, and (−1,7)
. Write the exact answer. Do not round.
To find the perimeter of the triangle, we need to calculate the length of each of its sides and then add them up.
Let's start by finding the length of the side between (-1, -14) and (7, 1). We can use the distance formula for this:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
distance = sqrt((7 - (-1))^2 + (1 - (-14))^2)
= sqrt(8^2 + 15^2)
= sqrt(289)
= 17
So the length of the first side is 17.
Now let's find the length of the side between (-1, -14) and (-1, 7):
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
distance = sqrt((-1 - (-1))^2 + (7 - (-14))^2)
= sqrt(0^2 + 21^2)
= 21
So the length of the second side is 21.
Finally, let's find the length of the side between (7, 1) and (-1, 7):
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
distance = sqrt((-1 - 7)^2 + (7 - 1)^2)
= sqrt((-8)^2 + 6^2)
= sqrt(100)
= 10
So the length of the third side is 10.
Now we can add up the lengths of all three sides to get the perimeter:
perimeter = 17 + 21 + 10
= 48
Therefore, the perimeter of the triangle is 48.
The scrap value of a machine at the end of its useful life is given by S(n)=C(1-r), where C is the original cost, n is the useful life
of the machine in years, and r is the constant annual percentage of value lost. Find the scrap value of the following machine.
Original cost, $41,000; life, 10 years; annual rate of value lost, 13%
Answer:
$ 2,484.23
Step-by-step explanation:
The formula for scrap value is
S(n) = C( 1- r)ⁿ
where
S(n) = scrap value after n years
C = original cost
r = rate of value lost in decimal
n = number of years
First convert r to a decimal by dividing by 100
r = 13/100 = 0.13
S(10) = 10,000(1 - 0.13)¹⁰
= 10,000 x (0.87)¹⁰
= 10000 x 0.248423
= $ 2,484.23
Given f(x) = 3x - 4 and g(x) = x ^ 2 - 3 find (g f) (x) .
A) 9x ^ 2 - 24x + 19
B) 9x ^ 2 + 13
C) 3x^2 - 13
D) 9x ^ 2 - 24x + 13
Answer:
D
Step-by-step explanation:
f(x) = 3x - 4
Substituting f(x) into g(x) gives:
g(f(x)) = (3x - 4)^2 - 3
Expanding the squared term, we get:
g(f(x)) = 9x^2 - 24x + 16 - 3
Simplifying, we get:
g(f(x)) = 9x^2 - 24x + 13
Ashley has a deck that measures 12 feet by 10 feet. She wants to increase each dimension by equal lengths so that its area is tripled. By how much should she increase each dimension?
If Ashley has a deck that measures 12 feet by 10 feet. Ashely should increase each dimension by 8feet.
How to find the dimension?The original area of the deck is:
12 feet x 10 feet = 120 square feet
To triple this area, Ashley needs to increase the area by a factor of 3. That means the new area should be:
3 x 120 square feet = 360 square feet
Let's say Ashley increases the length and width of the deck by x feet. The new dimensions of the deck will be:
(12 + x) feet by (10 + x) feet
The new area of the deck will be:
(12 + x) feet x (10 + x) feet = 120 + 22x + x^2 square feet
We want this area to be 360 square feet, so we can set up the equation:
120 + 22x + x^2 = 360
Simplifying this equation, we get:
x^2 + 22x - 240 = 0
We can solve this quadratic equation by factoring:
(x + 30)(x - 8) = 0
The solutions are x = -30 and x = 8, but we can discard the negative solution since we are looking for a positive increase in dimension.
Therefore, Ashley should increase each dimension by 8 feet in order to triple the area of her deck.
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When will the graph meet the line y=5 ? Explain how you know.
By solving the logarithmic equation for x when y = 5, we determined that the graph would meet the line y = 5 when x = 10^5
Solving logarithmic equationFrom the question, we are to determine when the graph will meet the line y = 5
From the given information,
The given function is
y = log10 (x)
To determine when the graph would meet the line y = 5, we will determine the value of x when y = 5 in the function
y = log10 (x)
5 = log10 (x)
Applying the exponent law of logarithm, we get
10^5 = (x)
Therefore, x = 10^5
Hence, the graph would meet the line y = 5 when x = 10^5
The point (100, 2) is on the graph because, x = 100, y = 2 is true for the function
That is,
y = log10 (x)
2= log10 (100)
Applying the exponent law
10^2 = 100
100 = 100
This shows why the point (100, 2) is on the graph
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The following information pertains to Mason Company for Year 2.
Beginning inventory 90 units at $40
Units purchased 310 units at $45
Ending inventory consisted of 30 units. Mason sold 370 units at $90 each. All purchases and sales were made with cash. Operating expenses amounted to $4,100.
What is the Net Income using FIFO, LIFO, and Weighted Average?
The net income using FIFO, LIFO, and Weighted Average methods are $16200, $12700, $14100.3
What is the Net IncomeTo calculate the net income using different inventory valuation methods, we need to calculate the cost of goods sold (COGS) first, which is:
COGS = Beginning Inventory + Purchases - Ending Inventory
For each inventory valuation method, we will calculate the COGS and then subtract it from the total sales to find the net income.
1.
FIFO (First-in, First-out) method:
Under the FIFO method, we assume that the units sold are from the earliest inventory purchased. Therefore, the ending inventory consists of the most recently purchased units.
a. COGS:
Beginning inventory: 90 units at $40 = $3,600
Purchases: 310 units at $45 = $13,950
Total cost of goods available for sale = $3,600 + $13,950 = $17,550
Cost of goods sold = Total cost of goods available for sale - Ending inventory
= $17,550 - 30 units at $45 = $16,200
b. Net Income:
Sales = 370 units at $90 = $33,300
COGS = $16,200
Operating expenses = $4,100
Net income = Sales - COGS - Operating expenses
= $33,300 - $16,200 - $4,100
= $13,000
2.
LIFO (Last-in, First-out) method:
Under the LIFO method, we assume that the units sold are from the most recently purchased inventory. Therefore, the ending inventory consists of the earliest purchased units.
a. COGS:
Beginning inventory: 90 units at $40 = $3,600
Purchases: 310 units at $45 = $13,950
Total cost of goods available for sale = $3,600 + $13,950 = $17,550
Cost of goods sold = (Ending inventory at $40) + (Remaining units sold at $45)
= (30 units at $40) + (340 units at $45)
= $1,200 + $15,300
= $16,500
b. Net Income:
Sales = 370 units at $90 = $33,300
COGS = $16,500
Operating expenses = $4,100
Net income = Sales - COGS - Operating expenses
= $33,300 - $16,500 - $4,100
= $12,700
3.
Weighted Average method:
Under the weighted average method, we calculate the average cost per unit and use it to value both the cost of goods sold and ending inventory.
a. Average Cost per unit:
Total cost of goods available for sale = Beginning inventory + Purchases
= $3,600 + $13,950
= $17,550
Total units available for sale = Beginning inventory + Purchases + Ending inventory
= 90 + 310 + 30
= 430
Average cost per unit = Total cost of goods available for sale / Total units available for sale
= $17,550 / 430
= $40.81
b. COGS:
Cost of goods sold = Units sold x Average cost per unit
= 370 units x $40.81
= $15,099.7
c. Net Income:
Sales = 370 units at $90 = $33,300
COGS = $15,111.70
Operating expenses = $4,100
Net income = Sales - COGS - Operating expenses
= $33,300 - $15,099.7 - $4,100
= $14,100.3
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[tex]12x^{2}-17x-5=0[/tex]
Answer:
Step-by-step explanation:
In a company, 90% of the workers are men. If 410 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
The total number of workers if, In a company, 90% of the workers are women, If 440 people work for the company who aren't women is 4400.
What is percentage?
As it is clear from the term per-cent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.
Given:
In a company, 90% of the workers are women,
If 440 people work for the company who aren't women,
Calculate the percentage of people who aren't women as shown below,
The percentage of people who aren't women = 100% - the percentage of women
The percentage of people who aren't women = 100% - 90%
The percentage of people who aren't women = 10%
Assume that there are a total of x workers then according to the statement,
10% of x = 440
10 / 100 × x = 440
x = 440 × 100 / 10
x = 4400
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