There are total 4*5*3 = 60 ways of wearing one each.
What is Fundamental Counting Principle?
A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle.
Solution:
Let,
for three events A, B, and C, number of outcomes be a,b, and c respectively.
So, the total number of outcomes is given by the product of outcomes of all the events i.e. by using Fundamental Counting Principle.
In the question mentioned,
a = 4
b = 5
c = 3
So, total outcomes = 4*5*3 = 60 ways
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tan 20 degrees + tan 40 degrees/1-tan 20 degrees tan 40 degrees
The value of (tan20° + tan40°)/(1 - tan20°tan40°) is √3.
What is the formula for tan(A + B)?tan(A + B) = (tanA + tanB)/(1 - tanA.tanB).
Given, tan 20 degrees + tan 40 degrees/1-tan 20 degrees tan 40 degrees
which is,
= (tan20° + tan40°)/(1 - tan20°tan40°).
= tan(20 + 40)°.
= tan60°.
= √3.
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Linda makes 8 dollars for each hour of work. Write an equation to represent her total pay p after working in hours.
Raina's penny bank is 1/10 full. After she adds 480 pennies, it is 1/2 full. How many pennies can Raina's bank hold?
Answer:
1,200 pennies
Step-by-step explanation:
What is the total surface area of the triangular prism in square centimeters?
A. 240 cm^2
B. 368 cm^2
C. 320 cm^2
D. 344 cm^2
Answer: option a
Step-by-step explanation:
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −52, ordered pair: (−1,3)
Answer:
[tex] \huge{ \boxed{y = - 52x - 49}}[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is given by
[tex]y = mx + c[/tex]
where
m is the slope
c is the y intercept
From the question
m = -52
In order to find c we substitute the points (−1,3) into the equation and find c
We have
[tex]3 = ( - 52)( - 1) + c \\ 3 = 52 + c \\ c = 3- 52 \\ c = -49[/tex]
We have m and c now so we substitute it into the main equation
We have the final answer as
[tex] \bold{y = - 52x - 49}[/tex]
Hope this helps you
What is the sum of this geometric series?
$1,300 at 5% for 6 years
Answer:
$1742.12
Step-by-step explanation:
I'm assuming it would be compounded annually so,
A = 1300(1 + 0.05)^6
A = 1742.12
Find a polynomial function of degree 7 with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
The polynomial function with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1 will be x³+9x²+16x.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that the polynomial is given with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
Each zero, such as a, corresponds to a linear factor, such as (x a). The repeating of such components is corresponding to multiplicity. The following polynomial thus meets the requirements in our example:
= (x-(-3))³(x-0)¹
=(x³-3x²(-3)+3x(-3)²-(-3)²)(x)
=x³+9x²+27x-9x
=x³+9x²+16x
Thus, the polynomial function with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1 will be x³+9x²+16x.
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Use the marginal tax rate chart to answer the question.
Marginal Tax Rate Chart
Tax Bracket Marginal Tax Rate
$0–$10,275 10%
$10,276–$41,175 12%
$41,176–$89,075 22%
$89,076–$170,050 24%
$170,051–$215,950 32%
$215,951–$539,900 35%
> $539,901 37%
Determine the amount of taxes owed on a taxable income of $38,520.
The effective tax rate for a taxable income of $75,400 is 24%.
What is the Marginal tax rate?The amount of additional tax paid for each new dollar of income received is known as the marginal tax rate. Total taxes paid divided by total income earned is the average tax rate.
WE have Given that;
Marginal Tax Rate Chart Tax Bracket
$0 –$10,275 10%
$10,276 –$41,175 12%
$41,176 –$89,075 22%
$89,076 –$170,050 24%
$170,051 –$215,950 32%
$215,951 –$539,900 35%
> $539,901 37%
Hence, the effective tax rate for income of $95, 600 lies in the range of a marginal tax rate of; 24%.
thus, the effective tax rate;
= 72,026/ 95600
= 24 %
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Answer:
4,416.90
Step-by-step explanation:
12% tax bracket: $38,520 - 10,725 = 27795(0.12) = 3335.4
1027.50+3335.4 = 4416.90
Graph the solution to the equation y=1/4+2 and y=–2x–7
Answer:
Step-by-step explanation:
y= 1/4x+2
y=-2x-7
Graphs below
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 8. If there were 8918 total votes, how many yes votes were there?
In 5-7 Sentences, please explain each of these vocabulary terms. You may give an example or write the definition: 1.Outlier 2.Cluster 3.Positive linear association 4.Negative linear association 5.No association 6.Non-linear association
Extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.
What is an outlier?An outlier, to put it simply, is a data point in a data graph or dataset you're dealing with that is abnormally high or abnormally low in comparison to the nearest data point and the rest of the nearby coexisting values.
The vocabulary term is explained as,
1.Outlier - Extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.
2. Cluster - An identifiable cluster of values in a numerical variable's distribution that is close to one another and appears notably more frequently than values on either side of them.
3. Positive linear association - When the variable on the x-axis grows as the variable on the y-axis increases, a positive linear connection exists. An upward-sloping linear regression line demonstrates this.\
4. Negative linear association - A negative linear correlation exists when one variable rises while the other falls. An upwardly sloping straight regression line illustrates this.
5.No association - There is a "negative correlation" when one variable rises while the other one falls. The points in the scatterplot have no connection if there is no correlation between the variables.
6. Non-linear association - When two variables have a nonlinear relationship, the slope of the curve illustrating the relationship alters when the value of one of the variables varies. Any curve whose slope alters when one of the variables' values changes is said to be nonlinear.
Thus, extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.
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The Johnson's purchased a car. If the total price, including a 6% sales tax, was $19,674, find the price of the car before tax
Answer:
Step-by-step explanation:
The price of the car before tax was $18,560.3
Let the price of the car be x. Then,
x + 6% of x = $19,674
106x/100 = $19,674
x = $ 19,673*100/106
with BODMAS, we get
x= $18560.3
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Which expression is equivalent to (3x4y5)-²?
Answer:Equivalent expressions Calculator Get detailed solutions to your math problems with our Equivalent expressions step-by-step calculator. Practice your math skills and learn step by step.
Answer:
Answer:Equivalent expressions Calculator Get detailed solutions so your math problems with ur Equivalent expressions
Step-by-step explanation:
Make the subject of
9x = u
For sake of simplicity, let us assume that you have won exactly three punches for the game AND that no
prizes are removed after each punch. You are then shown the punching board, which contains 50 slots
with the following dollar amounts: (5) $100, (10) $250, (10) $500, (10) $1000, (8) $2500, (4) $5000, (2)
$10000, (1) $25000. You get to punch one slot at a time and either keep the amount you found or
continue with your other punches.
Working backwards, if you have already used and thrown away your first two punches, there is no
strategy for the third punch. You take whatever you get. Now examine the second punch.
QUESTION 1: What is the expected value of your third punch? Again, for sake of simplicity, assume that
your first two punches were put back into the mix. (Essentially no prizes are removed so there are still
50 holes to punch) Show all calculations necessary for you answer.
Also the question in the picture
The expected value of your third punch is 5660.
What is probability?
A linear scale from 0 (impossibility) to 1 (certainty) or as a percentage between 0 and 100% expresses the likelihood that a specific event (or series of events) will occur.
Given that,
This is the third and last punch and also there is no removal of prizes after each punch. Hence, the expected value would be equal to the mean of all the possibilities available.
E(third punch) = Σ x p(x)
= 100× (5/50) + 250 × (10/50) + 500 × (10/50) + 1000 × (10/50) + 2500 ×(8/50) + 5000 × (4/50) + 100000 × (2/50) + 25000 × (1/50)
= 5660
Let us find the median of the given possibilities,
5 100's, 10 250's, 10 500's, 10 1000's, 8 2500's, 4 5000's, 2 100000's, 1 25000
There is a total of 50 possibilities and hence the median will be the average of the 25th and 26th terms.
25th term = 500
26th term = 1000
Median = (500 + 1000) / 2 = 750
The next available possibility greater than 750 is 1000.
Probability of getting more than 1000 in third punch = P (x > 1000) = (No. of terms greater than 1000) / Total no. of possible outcomes = 15 / 50 = 0.3
Probability of getting less than 1000 in third punch = P (x > 1000) = (No. of terms lesser than 1000) / Total no. of possible outcomes
= 25 / 50 = 0.5
Hence, in the second chance of punch, 1000 or anything greater than 1000 is preferred because the probability of getting more than 1000 in the next chance is less than the probability of getting less than 1000.
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Which ordered pair in the form (x, y) is a solution of this equation?
x + 7y= 10
Answer: (3, 1)
Step-by-step explanation:
Plug in each coordinate and see if the equation holds true:
[tex](13, 2)\\13+2(7)=13+14=27\neq 10[/tex]
[tex](2, 1)\\2+7(1)=2+7=9\neq 10[/tex]
[tex](4, 1)\\4+7(1)=4+7=11\neq 10[/tex]
[tex]3+7(1)=3+7=10[/tex]
Factor f(c)=4x^3+19x^2-58x+35 into linear factors given that -7 is a zero of f(k)
The polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factors is f(c)=(x-1)(x+7)(4x-5)
To express the polynomial as a product of linear factors we have to find the zeros of the polynomial.
Here,
We have Given that f(c)=4x^3+19x^2-58x+35 and -7 is a zero of f(k) and we need to find the polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factor
Now,
-7 is a zero of f(k)
i.e. (x+7) is a linear factor of f(k)
now,
we will find out the linear factor of f(c)
so,
f(c)=4x^3+19x^2-58x+35
f(c)=4x^3-4x^2+23x^2-23x-35x+35
f(c)=(x-1)(4x^2+23x-35)
f(c)=(x-1)(4x^2+28x-5x-35)
f(c)=(x-1)(4x(x+7)-5(x+7))
f(c)=(x-1)(x+7)(4x-5)
Hence,
The polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factor is f(c)=(x-1)(x+7)(4x-5)
Thus,
the linear factor of given polynomial is (x-1)(x+7)(4x-5)
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IXL Please Help Fast!
Determine the length of the line segment shown.
line segment from negative 10 comma 9 to 5 comma negative 1
4 units
18 units
19 units
21 units
The length of the line segment is 18 units. option B is the correct answer.
We know that
The distance(D) between two points (x₁ , y₁) and (x₂, y₂) is
D = √( y₂ - y₁)² + (x₂ - x₁)²
From the question, we have
Two endpoints of the line segment are (-10, 9) and (5, -1).
D = √( y₂ - y₁)² + (x₂ - x₁)²
D = √(-1 - 9)² + (5 - (-10))²
D = √100 + 225
D = √325
D = 18 units (approx.)
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
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Answer: 18 units
Step-by-step explanation: I got it right on the quiz
Solve the system. 2x + y = 3 −2y = 14 − 6x Write each equation in slope-intercept form. y = -2 x + 3 y = 3 x + -7 How do the slopes and y–intercepts of the two equations compare?
The slopes and the y-intercepts of two equations are different.
How to calculate the slope-intercept form of the equation?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the y-intercept.How to determine the slopes and y–intercepts of the two equations?From the information provided, we have the following equations:
2x + y = 3 ....equation 1.
−2y = 14 − 6x ....equation 2.
In slope-intercept form, the first equation can be written by subtracting 2x from both sides as follows:
2x + y - 2x = 3 - 2x
y = 3 - 2x
y = -2x + 3
Therefore, m = -2 and c = 3.
For the second equation, we would divide both sides by -2 as follows:
−2y/-2 = 14/-2 − 6x/-2
y = -7 + 3x
y = 3x - 7
Therefore, m = 3 and c = -7.
In this context, we can reasonably and logically deduce that the slopes and the y-intercepts are quite different.
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Answer:
y = -2x + 3
y = 3x + -7
The slopes and the y-intercepts are different.
The system represents lines that Intersect at one point
Exactly one solution
Step-by-step explanation:
Edge2022
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shoe store a is having a sale in which every pair of shoes is 40% off. shoe store is having a sale in which $40 is deducted from the regular price. gwen buys 3 identical pairs of shoes at store a. because of the sale, she saves 73.50. what is the regular price of each pair
The percentage discount of 40% from the regular price of shoes and the $73.5 Gwen saves indicates that the regular price of each pair of shoe she buys is $61.25
What is a percentage in mathematics?A percentage is the expression of a proportion based on a scale of 100. A percentage can be described as a fraction that has 100 as the denominator.
The percentage discount = 40%
The amount Gwen saves = $73.50
The number of shoes she buys = 3
The discount on each shoe = $73.5 ÷ 3 = $24.5
Let x represent the regular price of each shoe, from the information in the question, we have;
40% of x = $24.5
40% × x = $24.5
The regular selling price is therefore the ratio of $24.5 and 40% as follows;
The regular selling price = $24.5 ÷ 40% = $61.25
Each pair of shoe regularly costs $61.25
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-a+√-4+b
a²- b
if a = -2 and b = 8
The value of expression a²-b is 12 and value of equation -a+√-4+b id 10+2i where a is -2 and b is 8.
What is expression?In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure.
Here,
if a = -2 and b = 8
a²-b=(-2)²-8
=-4
-a+√-4+b=-(-2)+2i+8
=10+2i
The equation a²-b has a value of 12 and the expression -a+-4+b has a value of 10+2i, where a is -2 and b is 8.
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Mai has 5 loves of bread and jeff has 3 loves.Mia and Jeff decide to share their bread witha hungry stranger.they all sit down and they have an equal amount of bread. the stranger gives them 8 coins to split for there generosity. describe the most equitable way mia and jeff should split the coins based on how much bred they gave
The most equitable way to share the coin between Mai and Jeff is ratio 5:3. Mai will have 5 coins and Jeff 3 coins
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b.
Mai dropped 5 loaves and Jeff 3 loaves. This means that the ratio of brad dropped by Mia and Jeff is 5:3.
The stranger dropped 8coins. the most equitable way to share the coin is to share it in ratio 5:8
Using this ratio, the total ratio is 8
therefore Mia will have 5/8×8=5coins
Jeff will have 3/8×8= 3coins
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3. The half-life of a certain radioactive substance is 14 days and there are 6.58 g
present initially. When will there be 1 gram remaining?
Using the initial amount of the radioactive substance, in 1 gram 913.28 hours remaining.
In the given question;
The half- life of the radioactive substance is
[tex]t_{1/2}[/tex]=14days
For changing this into hours we have to multiply 24 in 14 because in 1 day have 24 hours.
[tex]t_{1/2}[/tex]=14*24
[tex]t_{1/2}[/tex]=336 hours
Initial amount of the radioactive substance is:
N(0)=6.58g
Now here we use the radioactive substance formula
[tex]N(t)=N(0)(\frac{1}{2})^{t/t_{1/2}}[/tex]
Where; N(t)= the radioactive substance after t hours
N(0)= Initial amount of the radio active substances
[tex]t_{1/2}[/tex] = Half lie
t=time (in hours)
Now put the value in formula
N(t)=6.58[tex](\frac{1}{2})^{t/336}[/tex]
N(t)=6.58[tex](0.5)^{t/336}[/tex]
By the question we know
N(t)=1
1=6.58[tex](0.5)^{t/336}[/tex]
Divide by 6.58 on both side, we get
1/6.58=[tex](0.5)^{t/336}[/tex]
[tex](0.5)^{t/336}[/tex]=1/6.58
Now taking the log on both side:
log [[tex](0.5)^{t/336}[/tex]]=log [1/6.58]
t/336 log[0.5]=log[1/6.58]
The formula of log used here, is as follows: Log(m^b)=blog(m)
Multiply by 336 on both side,we get
t*log[0.5]=336 log[1/6.58]
t=(336 log[1/6.58])/ log[0.5]
t=913.28hours
Hence, In 1 gram 913.28 hours remaining.
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Please help an 8th grader in needdddd!!!
We can find the linear equation by using the given graph, the equation is:
y = 4.8*x + 24
How to write the equation for the line?On the graph we can see the best fit line, remember that a linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
On the graph we can see that the y-intercept is at y = 24, then:
y = m*x + 24
Now, notice that when x = 5, the value of y is 48, replacing these values we get:
48 = m*5 + 24
48 -24 = m*5
24/5 = m
4.8*m
The linear equation is:
y = 4.8*x + 24
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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 110, and the sample standard deviation, s, is found to be 10. (a) Construct an 80% confidence interval about μ if the sample size, n, is 13. (b) Construct an 80% confidence interval about μ if the sample size, n, is 26. (c) Construct a 98% confidence interval about μ if the sample size, n, is 13. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
The confidence intervals for this problem, using the t-distribution, are given as follows:
a) 80% confidence level, n = 13: (106.24, 113.76).
b) 80% confidence level, n = 26: (107.42, 112.58).
c) 98% confidence level, n = 13: (102.56, 117.44).
d) These intervals could not be computed if the population had not been normally distributed, as the sample size is less than 30.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical values, using a t-distribution calculator, for the two-tailed 95% intervals, are given as follows:
80% confidence, n = 13, 12 df: t = 1.3562.80% confidence, n = 26, 25 df: t = 1.3163.98% confidence, n = 13, 12 df: t = 2.681.The mean and the standard deviation are given as follows:
[tex]\overline{x} = 110, s = 10[/tex]
For item a, with n = 13, the bounds of the interval are given as follows:
110 - 1.3562 x 10/sqrt(13) = 106.24.110 + 1.3562 x 10/sqrt(13) = 113.76.For item b, with n = 26, the bounds of the interval are given as follows:
110 - 1.3163 x 10/sqrt(26) = 107.42.110 + 1.3163 x 10/sqrt(26) = 112.58.For item c, with n = 13, the bounds of the interval are given as follows:
110 - 2.681 x 10/sqrt(13) = 102.56.110 + 2.681 x 10/sqrt(13) = 117.44.The Central Limit Theorem states that the intervals can be obtained for non-normal populations only if the sample size is equal or greater than 30.
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Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y=a( x− ℎ)^2+k and how they can be identified from the equation.
Please help
When a quadratic equation is given in the form y = a( x− ℎ )^2 + k the easily seen features are
coordinates of the vertex = v(h, k) the axis of the parabola - y axisthe opening of the curve in the axis - open upwardWhat is equation of a parabola?Equation of a parabola is the equation used to trace the path of a parabola. this equation is a quadratic equation
The quadratic equation in the factored form is written as
y = a ( x − ℎ )^2 + k
This equation shows the coordinates of the vertex which is v(h, k)
The axis of symmetry refers to the axis where the parabolic curve can be bisected. this is in the y axis
"a" helps to determine if the curve opens upwards or downwards. when a is:
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The population of a city has increased by 28% since it was last measured. If the current population is 80,000, what was the previous population?
The previous population of the city is 62500
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 3x + 4y = 14, 5x − 4y = 4.
if the previous population is represented by x and the increment by y, then
y= x×28/100
y = 28x/100 equation 1
the new population = previous population+ increment
therefore x+y= 80,000
represent 28x/100 for y in equation 2
x+28x/100= 80000
making the LHS a single fraction
(100x+28x)/100= 80000
128x= 80000×100
divide both sides by 128
x= 8000000/128
x= 62500
therefore the previous population is 62500
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A bottle holds 96 fluids ounce of lemonade. How much is this in pints?
Answer:
12 pints
Step-by-step explanation:
[tex]\frac{1}{8}[/tex] = [tex]\frac{8}{96}[/tex]
8 ounces is equal to 1 pint. 8 x 12 = 96, so 1 x 12 is 12