By the inclusion/exclusion principle,
[tex]P(A\cup B) = P(A) + P(B) - P(A\cap B)[/tex]
[tex]P(A\cup B) = \dfrac23 + \dfrac45 - \dfrac35[/tex]
[tex]P(A\cup B) = \dfrac{10}{15} + \dfrac{12}{15} - \dfrac9{15}[/tex]
[tex]P(A\cup B) = \boxed{\dfrac{11}{15}}[/tex]
a store pays $68 for a portable dvd player. the markup is 35% what is the sellng price?
Answer:
$91.80 selling price
Step-by-step explanation:
A store pays $68 for a portable DVD player. the markup is 35% what is the selling price?
35% = 0.35
The multiplier for markup of 35% = 1 + 0.35 = 1.35
68 * 1.35 = $91.80 selling price
write in simplest form
8 5/12 + 11 1/4
Answer:
19 2/3
Step-by-step explanation:
8+11=19, & 5/12+1/4=8/12
find the gradient and intercept of the following equation of line y= -2x - 5
You are given the line, y=-2x-5. This line is in slope-intercept form, y=mx+b, where m is the slope (or gradient) and b is the y-intercept.
The gradient of the given line is -2 and the y-intercept is -5.
If f(x) = 5x, what is f¹(x)?
f¹(x) = -5x
ƒ¹(x) = -1/5 x
f¹(x) = 1/5x
f¹(x) = 5x
Answer:
[tex]\displaystyle f^{-1}(x)=\frac{1}{5}x[/tex]
Step-by-step explanation:
[tex]f(x)=5x\\\displaystyle y=5x\\x=5y\\\frac{1}{5}x=y\\ f^{-1}(x)=\frac{1}{5}x[/tex]
The inverse of the given function f(x) will be x/5.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
To find the inverse function f⁻¹(x) for f(x) = 5x, we can use the following steps:
Replace f(x) with y: y = 5xSwap x and y: x = 5ySolve for y: y = x/5Therefore, the inverse function of f(x) = 5x is f⁻¹(x) = x/5.
Note that f⁻¹(x) is not equal to -5x, 1/5x, or 5x.
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What are the 2 types of scale?
2 types of scale are Nominal Scale, Ordinal Scale
What is Nominal Scale, Ordinal Scale?Nominal scale is a naming scale, where variables are simply “named” or labeled, with no specific order. Ordinal scale has all its variables in a specific order, beyond just naming them. Interval scale offers labels, order, as well as, a specific interval between each of its variable options.In this level of measurement, alphanumeric characters or names are used to categorize the data. For example, if gender is your variable, the responses will be male or female. Ordinal: Ordinal level variables have a meaningful order to them such as rankAn ordinal scale is a measurement scale that assigns values to objects based on their ranking with respect to one another. For example, a doctor might use a scale of 0-10 to indicate degree of improvement in some condition, from 0 (no improvement) to 10 (disappearance of the condition).To learn more about Nominal Scale, Ordinal Scale refers to:
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There are two types of scales: nominal scale and ordinal scale.
What are nominal scales and ordinal scales?Nominal scales are named scales where variables are simply "named" or labeled in no particular order. Ordinal scales go beyond mere naming to include all variables in a specific order. Interval scales provide the label, order, and specific spacing between each variable option.
This measurement level classifies data using alphanumeric characters or names. For example, if gender is the variable, the answer is male or female. Ordinal:
Ordinal level variables have the following meaningful order: B. rank
An ordinal scale is a measurement scale that assigns values to objects based on their ranking with respect to each other. For example, a doctor might use a 0 to 10 scale, ranging from 0 (no improvement) to 10 (condition disappeared) to indicate the degree of improvement in the condition.
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A store owner gathered data for several days about the methods customers used to pay for their purchases. The scatter plot shows the data she gathered and the line of best fit. The equation of the line of best fit is y = 0. 755x + 11. 339. Based on the line of best fit, approximately how many customers are predicted to use a card to pay on a day when 90 customers pay by cash? a. 68 b. 79 c. 92 d. 104.
According to the line of best fit, 79 consumers are predicted to use their card to pay during a day when 90 customers pay in cash. The correct answer is C.
The answer is 79. This is because the equation of the line of best fit is:
y = 0.755x + 11.339Which is a linear equation that represents the relationship between the number of customers who pay by cash (x) and the number of customers who pay by card (y).
To use this equation to predict the number of customers who pay by card on a day when 90 customers pay by cash, we can substitute x = 90 into the equation:
y = 0.755x + 11.339y = 0.755(90) + 11.339y = 67.95 + 11.339y = 80.284Y = 79.2879.28 ≈ 79, hence the correct answer is C.
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How do you dilate a triangle by 1 2 with a compass?
If the scale factor is 1/2, then every coordinate point of the original triangle is multiplied by the scale factor 1/2.
How do you dilate a triangle?Dilation is a technique for creating similar figures. Each point is stretched outwards from the center point D by multiplying distances by the scale factor. (Outwards if the scale factor is bigger than 1.) Move the points A, B, C to change the shape of the triangleAssume that, the origin (0, 0) be the center of dilation in the coordinate plane. If the scale factor is 1/2, then every coordinate point of the original triangle is multiplied by the scale factor 1/2. Dilation with scale factor 1/2, then multiply by 1/2.The basic formula to find the scale factor of a dilated figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.To learn more about dilate a triangle refers to:
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Write the expression using only positive exponents. Assume no denominator equals zero.
Answer:
[tex]\cfrac{x^{13}}{y^3}[/tex]-------------------------------------
Given expression:
[tex]\cfrac{(x^5y^2)^2}{x^{-3}y^7}[/tex]Rewrite it as follows, to get only positive exponents:
[tex]\cfrac{(x^5y^2)^2}{x^{-3}y^7}=\cfrac{x^{10}y^4}{x^{-3}y^7}=\cfrac{x^{10+3}}{y^{7-4}}=\cfrac{x^{13}}{y^3}[/tex]How do you memorize algebra rules?
Memorizing algebra rules can be challenging, but a few strategies may help: Practice, Mnemonics, Repeat, and Use flashcards.
Practice: The more you work with the rules, the more likely you will remember them.Mnemonics: Create a memorable phrase or acronym to help you remember a rule.Relate to real-world examples: Try to connect the algebra rule with a real-world scenario.Break it down: Break down complex rules into smaller, more manageable pieces.Repeat: Repeat the rules you are trying to memorize as often as possible.Teach someone else: Teaching the rule to someone else helps solidify the information in your own mind.Use flashcards: Write the algebra rule on one side of an index card and the explanation or example on the other side, then use them to quiz yourself.It's important to note that memorizing rules is not the best approach to understanding the concepts, the best approach is to understand the concepts, and the rules will come naturally.
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After allowing a discount of 20% on the marked price then
levying 10% VAT, a radio was sold. If buyer had paid Rs.320 for VAT how much had he got the discount?
Amount of discount allowed = 640 Rs.
What is VAT?VAT meaning value added tax that is attached to an item of product while bought by the buyer and also in each stage of production, distribution level. It is almost similar to a sales tax that is paid within the item price.
What is the value of discount?
given, discount allowed = 20% on the market price.
VAT = 10% on the market price.
Buyer paid as VAT = 320 Rs
Assume, market price of radio = X Rs
now amount of discount = 20/100× X = 0.2X
amount of VAT = 10/100×X = 0.1X
it is said that VAT paid by buyer = 320 Rs
now 320 = 0.1X
X = 320 / 0.1 = 3200 Rs
market price of radio = 3200 Rs
amount of discount = 20/100× 3200 = 640 Rs
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what is the weight of a square if a triangle weighs 4 grams?
Explain your reasoning
HHH
0
8. 2x
C. 4x
D. 2x
E. 4x
Answer: i believe is c or d i not 100% sure
A vertical number line is given.
A vertical number line starting at negative 2 with tick marks every one half unit up to positive 4. The value 1.25 is labeled.
When scuba diving, a student recorded the value plotted in the image. If 0 represents sea level, which of the following is true about the value?
The student is −1.25 ft above sea level, and the absolute value is 1.25 ft.
The student is −1.25 ft below sea level, and the absolute value is 1.25 ft.
The student is 1.25 ft above sea level, and the absolute value is 1.25 ft.
The student is 1.25 ft below sea level, and the absolute value is 1.25ft.
The true statement regarding the number line and the absolute value is given as follows:
The student is 1.25 ft above sea level, and the absolute value is 1.25 ft.
How to interpret the number line and the absolute value?The number line gives the heights relative to the sea level, and thus their signal are interpreted as follows:
Positive numbers: heights that are above sea level.Negative numbers: heights that are below sea level.The absolute value of a number represents the distance that the number is from the origin. In the context of this problem, it will give the distance of the measure from the sea level of 0 ft.
The height is given as follows:
1.25 ft.
Which is a positive measure, hence the correct option is given by the third option.
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In circle O shown below, diameter DB is perpendicular to chord AC at E.
If DB = 34, AC = 30, and DE > BE, what is the length of
BE?
The length of each segment is: DF=3, FR= 2 2/3, DE=3, GH=4 1/2, EH= 4 5/6.
What is the length of EH ?Length of each segment
16. Length of segment DF
DF=-1-(-4)
DF=3
19. Length of segment FR
FR=-1 1/3-(-4)
FR= 2 2/3
17. Length of segment DE
DE=2 -(-1)
DE=3
20. Length of segment GH
GH= 3 1/2 -(-1)
GH=4 1/2
18. Length of segment FG
FG=3 1/2 -2
FG=1 1/2
21. Length of segment EH
EH=3 1/2-(-1 1/3)
EH= 4 5/6
Therefore the length of each segment is: DF=3, FR= 2 2/3, DE=3, GH=4 1/2, EH= 4 5/6.
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find the total surface area of this cuboid measurements are 5cm 4cm 6cm the answer measurements must be cm squared
This cuboid's total surface area measured 5cm, 4cm, and 6cm is 120 cm³.
What is total surface area?The surface area of a solid item is a measurement of the entire area occupied by the object's surface. The total surface area includes the base(s) and the curving portion. It is the whole area covered by the object's surface. The total area of a form with a curved surface and base is the sum of the two areas. The total surface area is obtained by summing all the areas on the surface: the areas of the object's base, top, and lateral surfaces (sides).
Here,
total surface area of cuboid,
=l*b*h
=5*4*6
=120 cm³
The total surface area of this cuboid measured 5cm, 4cm and 6cm is 120 cm³.
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-9 + (-27x) please help
Answer:−
-9−27x
Step-by-step explanation:
A girl answered 38 questions on a reading app named lightsail.
The system indicated that she was 60% complete
How many questions are there in total?
Answer:
its either 63 or 64, im not really sure
HELP ME On the planet vreel, there are 8 alabers to ever 5 totts. if farmer joogh has 30 totts on his gepsil farm, how many alabers are on the farm? your answer may be exact or accurate to the nearest tenth
Answer:
48
Step-by-step explanation:
[tex]\frac{8}{5}[/tex] = [tex]\frac{x}{30}[/tex]
In the ratio there are 5 totts. The farmer has 30 totts.
5 x 6 = 30, so 8 x 6 = 48
Answer:
Step-by-step explanation: i pretty sure it 240 because there is 8 on every 5 so 8x5 and there is 8 on every 30 8x30=240
Help Please need correct answer.
A company produces equal numbers of footballs in three different colors. The manager wants to check each kind of football produced for errors. Which of the following is an example of stratified random sampling?
A) Check first 10 footballs of each color.
B) Group the footballs by their color and then randomly check 10 from each group.
C) Group the footballs by their color and then check the first 3 footballs from each
group.
D) Check the 4th football, and then every 5th football of each color
Answer: C
Step-by-step explanation:
Answer:
for anyone with the quiz its B!!
i just guessed at random and it was right.
HELP PLSS!! Find cos (A) given the triangle!!
You will be writing a short essay on how you can apply the processes you have learned in this unit to solve one of those questions
Calculating Unit Price for Business Owner
A restuarant owner is trying to choose a vendor for their supplies needed for their to-go operation. Since COVID their to-go orders have sky rocketed. Below he has listed how many of each item he has used in the past 6 month. Choose between the two vendors pricing sheets to decide who would be the best option. Give a detailed breakdown of unit prices and amount needed by the particular business to choose between the vendor.
6-month inventory break down:
large to-go boxes: 2,575
small to-go boxes: 1,890
to-go cups w/ lid: 3,010
Vendor 1 pricing:
large to-go boxes: $45.49/case (200 boxes per case)
small to-go boxes: $45.51/case (400 per case)
to-go cups w/ lid: $59.49/case (600/case)
Vendor 2 pricing:
large to-go boxes: $25.49/case (150 boxes per case)
small to-go boxes: $40.51/case (500 per case)
to-go cups w/ lid: $37.50/case (500/case)
Answer:
large to-go boxes: $45.49/case (200 boxes per case)
small to-go boxes: $45.51/case (400 per case)
Step-by-step explanation:
large to-go boxes: $25.49/case (150 boxes per case)
small to-go boxes: $40.51/case (500 per case)
to-go cups w/ lid: $37.50/case (500/case)
Need the answer to the problem below.
((1 * 4) ^ 2) ^ 6 =
Answer:
Here is your answer
((1 * 4) ^ 2) ^ 6 =
(4 ^ 2) ^ 6 =
16 ^ 6 = 16777216
Step-by-step explanation:
Answer: 16777216
Step-by-step explanation:
neena is listening to a song. It has a consistent beat. She counts 11 beats in 5 sec. what is the C.O.P for the realtionships of beats to minute.
Answer:
Step-by-step explanation:
The proportional relation is y= 2.2x
What is proportion?
In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Neena counts 11 beats in 5 seconds
So, x=11 and y=5
Using the proportionality
y = k x
k= y/x
k= 11/5
k= 2.2
Hence, the proportional relation is y= 2.2x
Answer:
2.2
Step-by-step explanation:
1. COP= constant of proportionality
What does that mean? This is how much of something you need for the variables to be proportional no matter their value. For example, if you pay 1.99 for 1 gallon of gas but then 30 dollars for 2 gallons at the same gas station, it doesn't make sense. You need to pay $3 for 2 gallons, and so on.
2. How do we find COP?
K is going to represent the constant of proportionality (COP), what we are solving for. Your equation should be k=b/a.
3. B is what comes first in the ratio, and is second. They said "beats to minutes" so beats= b and minutes= a
3. Solve: 11/5= 2.2
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The function a(g)=10-log base 3(g+1) represents the home attendance of a football team in hundreds depending on the number of home games, g.
How many people will attend the second home game?
How many people will attend the eighth home game?
At which game were there 500 attendees? Does this answer seem reasonable based on context of the problem?
The number of people that will attend each game is given as follows:
Second game: 9,000.Either game: 8,000.The number of attendees will be of 500 on the 857th game, which does not make sense in the context of this problem, as a football team plays at most nine home games during a season. (taking the NFL in context).
What is the logarithmic function?The logarithmic function for this problem is defined as follows:
[tex]a(g) = 10 - \log_3{(g + 1)}[/tex]
Hence the number of people that will attend the second home game, when g = 2, is given as follows:
[tex]a(2) = 10 - \log_3{(2 + 1)}[/tex]
a(2) = 10 - 1
a(2) = 9.
Hence 9,000 people, as a(g) is measured in thousands.
The number of people that will attend the eight home game is given as follows:
[tex]a(8) = 10 - \log_3{(8 + 1)}[/tex]
a(8) = 10 - 2
a(8) = 8. (8,000, considering the unit of a(g)).
The game in which 500 people will attend is obtained as follows:
[tex]0.5 = 10 - \log_3{(g + 1)}[/tex]
[tex]\log_3{(g + 1)} = 9.5[/tex]
Applying the cube to both sides, we have that:
g + 1 = 9.5³
g = 857.
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Find and graph the image of quadrilateral PQRS after a dilation centered at the origin with a scale factor of 1/4. What are the coordinates of Q'?
The coordinates of point Q after dilation will be (2,-1). The correct option is B.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that the coordinate is Q(8,-4). The point is dilated by a factor of 1/4.
The dilation of the point will be calculated as,
Q(8,-4) = Q'(8/4, -4 / 4)
Q(8,-4) = Q'(2, -1)
Hence the dilated point is Q'(2,-1).
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I need help with this problem. I've never been good at math.
Find the sum of the first 47 terms of the following series, to the nearest integer. 13, 18,23,...
The sum of the first 47 terms of the following series is 6016
What type of series is this?The series of numbers is an arithmetic progression. In an arithmetic progression, the subsequent terms are gotten by the addition of a common difference to the terms.
The series is 13, 18,23,...
The first term is = 13.
The common difference is = 18-13 = 5
The nth term is 47
the formula for sum of nth term is given by
Sn = n/2{2a + (n-1)d}
S₄₇ = 47/2{2*13 + (47-1)5}
Simplifying the expression we have
S₄₇ = 23.5 [26 + (46*5)]
S₄₇ = 23.5 [26 +230]
S₄₇ = 23.5 * 256
This shows that the S₄₇ = 6016
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The radius of a circle is increasing at a constant rate of 0. 5 meter per second. What is the rate of increase in the circumference of the circle at the instant when the radius of the circle is 3 meters?.
The rate of increase in the circumference of the circle at the instant when the radius of the circle is 3 meters is 3 phi m/s
From the question, we have the following information :
1. Constant rate of increasing radius with respect of time (t)
= [tex]\frac{dR}{dt}[/tex] = 0.5 m / s
2. Radius of circle is 3 meters ( 3m )
To find constant rate of increasing circumference, we have to know formula of circumference.
We know that circumference = 2 π R
Constant rate of increasing circumference with respect of time (t) can be formulated from contant rate of increasing radius multiply with formula to find circumference
[tex]\frac{dC}{dt}[/tex] = 2πR [tex]\frac{dR}{dt}[/tex]
[tex]\frac{dC}{dt}[/tex] = 2πR ( 0.5 )
= πR
From above equation, we know that the rate of increasing circumference is πR
When R = 3 m, we just simply subtitute πR with R=3
The constant rate will be :
Rate of increasing circumference = πR m/s
= π (3) m/s
= 3π m/s
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Drag the expressions into the boxes to correctly complete the table.
The polynomial equations are
A = x^(1/4) - ∛x + 4√x - 8x + 16
B = 3x² - 5x⁴ + 2x - 12
C = x³ - 7x² + 9x - 5x⁴ - 20
D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1
The non polynomial equations are
E = 4/x⁴ + 3/x³ - 2/x² - 1
F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the polynomial equations be represented as A , B , C , D , E , F
Substituting the values in the equation , we get
And , any algebraic equation with a negative exponent or fractional exponent is not a polynomial equation. So , expressions with negative exponents are not polynomials.
A = x^(1/4) - ∛x + 4√x - 8x + 16
It is a polynomial
B = 3x² - 5x⁴ + 2x - 12
It is a polynomial
C = x³ - 7x² + 9x - 5x⁴ - 20
It is a polynomial
D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1
It is a polynomial
E = 4/x⁴ + 3/x³ - 2/x² - 1
It is not a polynomial
F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1
It is not a polynomial
Hence , the polynomials are solved
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the first term in this number pattern is 5. 5,10,15,20,25,30...
The first pattern has a difference of 5 while the second is 10 and become by multiplying 2 in pattern 1 so options (A), (B), and (E) will be correct.
What is the pattern?A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint. The hint which is present in a given pattern hides in the pattern only.
Given the two patterns.
In the first pattern, each term become by adding 5 so option (A) is correct.
In the second pattern, each term become by adding 10 so option (B) is correct.
The term in the second pattern becomes by multiplying 2 in pattern 1
For example 5× 2 = 10 and 10 × 2 = 20 so option (E) will be correct.
Hence, "The first pattern has a difference of 5 while the second is 10 and become by multiplying 2 in pattern 1".
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yann just started a new job. for every 5 hours he works yama earns $90. the graph represents yamas earnings for diffrent numbers of hours
Answer:
12
Step-by-step explanation:
2x3 4+5