Answer:
natural, whole, integer, rational
Step-by-step explanation:
Natural Number:
All the numbers in the set {1, 2, 3, …} are natural numbers, 1256 lies in this set.
Whole Number:
All the numbers in the set {0, 1, 2, 3, …} are whole numbers, 1256 lies in this set.
Integer:
All the numbers in the set {… ,-1, 0, 1, 2 …} are integers, 1256 lies in this set.
Rational Number:
1256 can be represented as [tex]\dfrac{1256}{1}[/tex] or [tex]\dfrac{2512}{2}[/tex] etc., which is in the rational form (division of two non zero integers). therefore 1256 is also a rational number.
Hopefully this answer helped you!!
Mr. and Mrs. Hawell want to file their income tax return together. Which filing status should they use?
On solving the provided question we can say that Mr. and Mrs. Hawell, unitary assuming they are lawfully married and living together, have two alternatives for submitting their federal income tax return.
what is income tax return
An income tax return is a document or form filed by an individual or a business with the tax authorities, such as the Internal Revenue Service (IRS) in the United States or the HM Revenue and Customs (HMRC) in the United Kingdom.
to report their income, expenses, and other relevant financial information for the purpose of calculating and paying their income taxes.
The income tax return typically includes information such as the taxpayer's income from various sources, deductions, and credits that they may be eligible for, and the amount of taxes owed or overpaid.
Filing an income tax return is generally required by law, and failure to do so can result in penalties or legal consequences.
Mr. and Mrs. Hawell, assuming they are lawfully married and living together, have two alternatives for submitting their federal income tax return:
In general, most married couples file jointly since it results in reduced taxes and greater tax advantages. Yet, there may be times when filing separately is preferable, such as when one spouse has large medical costs or there are issues about the veracity of the other spouse's tax record.
Therefore, To identify the optimal filing status for a certain scenario, it is always preferable to speak with a tax specialist.
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Joshua goes to a café.
Revive Café Price List
Soup & roll £3.50
Sandwich £3.90
Jacket potato £4.50
Cake £2.95
Hot drink £2.50
Cold drink £1.75
Josh wants to buy a cake and a hot drink. He has £5 to spend can he buy what he wants?
Joshua wants to buy a cake and a hot drink. He has £5 to spend
Can he buy what he wants?
2. Here are four equations of absolute value functions and three coordinate
pairs. Each coordinate pair represents the vertex of the graph of an
absolute value function.
Match the equation of each function with the coordinates of the vertex of its
graph. The vertex coordinates of the graph of one equation are not shown.
A p(x) = |x-9|
B q(x) = |x|+9
C r(x) = |x+9|
O t(x) = |x|-9
1 (-9, 0)
2 (9,0)
3 (0, -9)
The equation for given coordinates are A) p(x) = |x - 9| C), r(x) = |x + 9| O) ,t(x) = |x| - 9
What are coordinates ?
Coordinates are sets of numbers used to locate points on a grid or map. In mathematics, the most common type of coordinates are Cartesian coordinates, which consist of an ordered pair of numbers (x, y). The x-coordinate represents the horizontal position of the point on the x-axis, and the y-coordinate represents the vertical position of the point on the y-axis.
For example, in a two-dimensional coordinate system, the point (2, 3) has an x-coordinate of 2 and a y-coordinate of 3. This means that the point is located 2 units to the right and 3 units up from the origin, which is the point (0, 0) where the x-axis and the y-axis intersect.
According to the question :
We can determine which equation corresponds to each set of vertex coordinates by observing the general form of the equation of an absolute value function and how the vertex coordinates affect it. The general form of an absolute value function is:
f(x) = |x - h| + k
where (h, k) represents the vertex coordinates of the graph.
The vertex coordinates are (-9, 0). The value of h is -9, which means the equation involves a shift to the right by 9 units. The absolute value of x is the distance from x to 0, so when x is less than -9, the absolute value of x - (-9) will be positive, and when x is greater than -9, the absolute value of x - (-9) will be negative. Therefore, the equation with vertex coordinates (-9, 0) is:
C) r(x) = |x + 9|
The vertex coordinates are (9, 0). The value of h is 9, which means the equation involves a shift to the left by 9 units. The absolute value of x is the distance from x to 0, so when x is less than 9, the absolute value of x - 9 will be negative, and when x is greater than 9, the absolute value of x - 9 will be positive. Therefore, the equation with vertex coordinates (9, 0) is:
A) p(x) = |x - 9|
The vertex coordinates are (0, -9). The value of k is -9, which means the equation involves a vertical shift downwards by 9 units. The absolute value of x is the distance from x to 0, so the equation with vertex coordinates (0, -9) is:
O) t(x) = |x| - 9
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Can anyone help me with this question please?
Answer : -0.65
:)
aidez moi svp, je comprend rien
Answer:
its to sloppy i cant make out what it says
Step-by-step explanation:
Lorenzo looked at a chart of the record high temperatures in North America by country/region. The coldest record high temperature is from Greenland at 86.2°F, and the hottest is from the United States at 134°F. The median record high temperature is 101.25°F, and the interquartile range is 17.25°F. All the record temperatures sounded very hot to Lorenzo, whose hometown high temperature that day was 12°F.
An IQR of 17.25°F suggests that there is some variation in the record high temperatures across North America, but it is not extremely large.
What is temperature?
Temperature is a measure of the average amount of thermal energy or heat in a substance or system. It is a physical quantity that describes how hot or cold something is relative to some standard or reference point. Temperature is typically measured in degrees Celsius (°C) or degrees Fahrenheit (°F) in everyday life, or in kelvins (K) in scientific contexts.
The interquartile range (IQR) is a measure of how much the record high temperatures vary in North America. It is calculated as the difference between the 75th percentile and the 25th percentile of the data set. In this case, the IQR is given as 17.25°F, which means that the range of record high temperatures between the 25th and 75th percentile is 17.25°F.
The IQR is a measure of variability that is less sensitive to extreme values than the range. It provides a measure of how much the data is spread out from the middle 50% of the values. A larger IQR indicates that the record high temperatures vary more widely in North America, while a smaller IQR indicates that the temperatures are more consistent or clustered around a central value.
In this case, an IQR of 17.25°F suggests that there is some variation in the record high temperatures across North America, but it is not extremely large.
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2. Apply the brute-force method to find the minimum cost Hamilton Circuit for the given graph. Start
with vertex A.
Circuit
AC,AD, AB
BA, BD, BC
I
B
8
D
Weight
26
20
20
C
The minimum cost Hamilton circuit starting with vertex A is A -> B -> D -> A, with a total cost of 48.
what is circuit?
In graph theory, a circuit is a closed path in a graph that starts and ends at the same vertex. In other words, a circuit is a sequence of vertices and edges that starts and ends at the same vertex, and every vertex in the sequence (except the first and last vertex) is visited exactly once.
In the given question,
To find the minimum cost Hamilton Circuit using the brute-force method, we need to try all possible Hamilton circuits and choose the one with the minimum cost. Since there are only 3 vertices in this graph, there are only 3! = 6 possible Hamilton circuits. We can enumerate all of them and calculate their costs to find the minimum.
Here are the 6 possible Hamilton circuits, starting with vertex A:
A -> B -> C -> A
Total cost = 26 + 20 + 20 = 66
A -> C -> B -> A
Total cost = 20 + 8 + 26 = 54
A -> B -> D -> A
Total cost = 20 + 8 + 20 = 48
A -> D -> B -> A
Total cost = 20 + 26 + 8 = 54
A -> C -> D -> A
Total cost = 8 + 20 + 26 = 54
A -> D -> C -> A
Total cost = 26 + 20 + 8 = 54
Therefore, the minimum cost Hamilton circuit starting with vertex A is A -> B -> D -> A, with a total cost of 48.
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Find the maximum volume of a rectangular box with three faces in the coordinate planes and a vertex in the first octant on the plane x+y+z=1.
The maximum volume of a rectangular box with three faces in the coordinate planes and a vertex in the first octant on the plane x+y+z=1, is equals to the 1/27.
Volume of something is defined as the amount of space it takes up inside. When we measure inside of something then we measure volume. We have, a rectangular box with three faces in the coordinate planes and a vertex in the first octant on the plane x + y + z = 1 --(1)
First from the above equation, z = 1 -x- y.
The volume of the box is, V = xyz --(2)
Plug the value of z from equation (2),
=> V = xy(1 − x − y)
=> V = xy - x²y - xy²
Now, we determine the partial derivatives to determine the critical points, Vₓ = y − 2xy − y² , Vᵧ = x - x² - 2xy
For maxima and minima we equate the partial derivatives equal to zero, Vₓ = 0 and Vᵧ = 0
=> y − 2xy − y² = 0
=> y² + y( 2x - 1) = 0
=> 2x + y = 1 --(3)
Also, x - x² - 2xy = 0
=> x( 1 - x - 2y ) = 0
=> x + 2y = 1 --(4)
Solving equations (3) and (4), x = 1/3 and y = 1/3.
So, from equation (1), z = 1 - 1/3 - 1/3 = 1/3. Therefore, volume of box is V
= (1/3)(1/3)(1/3)
= 1/27
Hence, required volume is 1/27 cubic units.
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HELP ASAP Aaron is the manager for the Mathland Middle School math team. They are trying to put the events in order of likeliness of the event occurring.
Which event is UNLIKELY?
P(honor roll) = 100%
P(left-handed) = 33%
P(failing math) = 0%
P(taking Spanish) = 60%
P(honor roll)
P(failing math)
P(taking Spanish)
P(left-handed)
Therefore , the solution of the given problem of probability comes out to be , the occurrence that is UNLIKELY is P (failing math).
What precisely is probability?Each of the procedure's criteria-based methods have as their main objective determining the likelihood that a statement is accurate or that an event will take place. Any number from zero to one, where 0 typically represents percentage and 1 typically reflects degree of certainty, can be used to symbolize chance. A probability illustration shows the likelihood that a particular occurrence will occur.
Here,
From most likely to least likely, the following occurrences are most likely to occur:
=> P(Honor score) = 100% Spanish class = 60%
=> P(left-handedness) = 33% P(math failure) = 0%
Because there is no chance of it happening, the occurrence that is UNLIKELY is P (failing math).
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Solve each quadratic equation using the method of your choice. List each root in its own box or write prime in both if you cannot factor it. Express
any non-integers as fractions.
A. 2x2-17x+8=0
B. x² - 4x-12=0
A. To solve the quadratic equation 2x² - 17x + 8 = 0, we can use the factoring method. We need to find two numbers whose product is 16 (the product of the coefficients of x² and the constant term) and whose sum is -17 (the coefficient of x). These two numbers are -1 and -16, so we can rewrite the equation as:
2x² - 17x + 8 = (2x - 1)(x - 8) = 0
Setting each factor equal to zero, we get:
2x - 1 = 0 or x - 8 = 0
Solving for x, we get:
2x = 1 or x = 8
x = 1/2 or x = 8
Therefore, the roots of the quadratic equation are x = 1/2 and x = 8.
B. To solve the quadratic equation x² - 4x - 12 = 0, we can use the factoring method. We need to find two numbers whose product is -12 (the product of the coefficients of x² and the constant term) and whose sum is -4 (the coefficient of x). These two numbers are -6 and 2, so we can rewrite the equation as:
x² - 4x - 12 = (x - 6)(x + 2) = 0
Setting each factor equal to zero, we get:
x - 6 = 0 or x + 2 = 0
Solving for x, we get:
x = 6 or x = -2
Therefore, the roots of the quadratic equation are x = 6 and x = -2.
Choose which of these polynomials is a difference of squares?
x^2 -12x -36
x^2+ 12x + 36
x^2 - 36
x^2 + 36
Then factor the polynomial that is a difference of squares.
Your answer should include a polynomial from the above options and its factored form
The pοlynοmial that is a difference οf squares is: x² - 36 factοred as: (x + 6)(x - 6)
What is Pοlynοmial?A pοlynοmial is a mathematical expressiοn that cοnsists οf οne οr mοre terms, where each term is a prοduct οf a cοefficient and οne οr mοre variables raised tο nοn-negative integer pοwers. Pοlynοmials can be used tο mοdel variοus real-wοrld phenοmena and are fundamental tο many areas οf mathematics and science.
The pοlynοmial that is a difference οf squares is: x² - 36
This pοlynοmial can be factοred as: (x + 6)(x - 6)
Tο see why this wοrks, we can write x² - 36 as (x)² - (6)², which is a difference οf squares. Then, we can use the fοrmula fοr the difference οf squares, which states that a² - b² = (a + b)(a - b), tο factοr x² - 36 as (x + 6)(x - 6).
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We want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately . We would like to be 90% confident that the estimate is within 5 of the true population mean. How large of a sample size is required?
A sample size of at least 44 is required to estimate the population mean with 90% confidence and a margin of error of 5, assuming the population standard deviation is approximately .
How to determine how large of a sample size is requiredTo find the sample size required to estimate a population mean with a certain level of confidence and margin of error, we can use the formula:
n = (z * σ / E)^2
where:
n = sample size
z = z-score corresponding to the desired level of confidence (in this case, 90% confidence corresponds to a z-score of 1.645)
σ = population standard deviation
E = margin of error
Plugging in the given values, we get:
n = (1.645 * / 5)^2
Simplifying this expression, we get:
n = 43.56
Rounding up to the nearest whole number, we get:
n = 44
Therefore, a sample size of at least 44 is required to estimate the population mean with 90% confidence and a margin of error of 5, assuming the population standard deviation is approximately .
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100 POINTS!!!!!!
HELP ASAP
Answer: 36 cm^2
Step-by-step explanation:
The right part of this shape is a triangle so we just need to find the area of a triangle and the area of the rectangle and add them to get the total area.
Area of a triangle:
We know the height is 4. The base will be 10 - 8 = 2 since the 10 includes the 8cm which need to be subtracted.
A = b*h/2
= 4*2/2
= 4 cm^2
Area of rectangle:
The height is 4 and the base is 8.
A = b*h
= 4*8
= 32 cm^2
Now we add them to get the total area
A = 4 + 32
A = 36 cm^2
A vehicle covers a distance of 43.2km in 2.4 litre petroleum. How much distance will it cover one litre petroleum?
Answer:
18 km
Step-by-step explanation:
43.2/2.4 = 18
Helping in the name of Jesus.
Which is the smallest? A. -1 B. -1/2 C. -1/4 D. O
Answer:
C. -1/4
The negative value are smaller then 0
Answer: C. -1/4
Step-by-step explanation: 0 and -1 is greater than -1/4. -1/2 is also greater than -1/4 as -1/4 goes to the left of a number line and going to the left of a number line makes the number smaller
if it's wrong, im sorry
hope this helps!!
Which of the following comparisons are true? Select all that apply. A. 3 . 2 > 0 . 32 3 . 2 > 0 . 32 B. 4 . 7 < 4 . 70 4 . 7 < 4 . 70 C. 2 . 6 > 2 . 59 2 . 6 > 2 . 59 D. 2 . 09 = 2 . 9
Answer:
A. 3 . 2 > 0 . 32
C. 2 . 6 > 2 . 59
Step-by-step explanation:
YES - A. 3 . 2 > 0 . 32
3.2 is greater than .32
NO - B. 4 . 7 < 4 . 70
these are the same so they are =
YES - C. 2 . 6 > 2 . 59
2.6 is greater than 2.59
NO - D. 2 . 09 = 2 . 9
these two are not equal, 2.09 < 2.9
please help I'm tired of people who want to answer to just to steel points
Answer:
a = 7.95c = 7.4Step-by-step explanation:
Given system of equation to us is ,
3a + 2c = 38.65
1a + 2c = 22.75
Here the given system of equation are linear equations in two variables. We can use various methods to solve them like substitution method, elimination method, etc . Here i will make use of elimination method. For that ;
Subtract both the equations , that would result to ;
3a + 2c - ( 1a + 2c ) = 38.65 - 22.75
3a + 2c - 1a - 2c = 15.9
2a = 15.9
a = 15.9/2
a = 7.95
To find out the value of c , plug in a = 7.95 in any of the two equations, as ;
a + 2c = 22.75
2c = 22.75 - 7.95
2c = 14.8
c = 14.8/2
c = 7.4
Hence the value of a is 7.95 and that of c is 7.4 .
Consider the following expression.
2v+4u+7+3u
Select all of the true statements below.
7 is a constant.
2v is a factor.
4u and 3u are like terms.
2v is a term.
2v is a coefficient.
None of these are true.
Please asap need help!!
Answer:
[tex]7 \: is \: a \: constant. \\ 4u \: and \: 3u \: are \: like \: terms[/tex]
A car was purchased for $33950.00 and is expected to be worth $12950.00 in 7 years. Determine the rate at which the van depreciates in value.
Answer:
$220,150 depreciates each year and increases in value with inflation of 7.2% per year? the useful life of the oven is considered 7 years. 10. The manager of a hotel bought...
Step-by-step explanation:
If it's wrong report the answer.........XD
1/2(8x+4)=6(x+2) I need help please
Answer:
x=-5
Step-by-step explanation:
(8x+4)/2=6x+12
4x+2=6x+12
-2x=10
x=-5
Answer:
x = -5
Step-by-step explanation:
Given equation:
[tex]\dfrac{1}{2}(8x+4)=6(x+2)[/tex]
Multiply both sides of the equation by 2 to eliminate the fraction on the left side:
[tex]\implies 2\cdot\dfrac{1}{2}(8x+4)=2\cdot6(x+2)[/tex]
[tex]\implies (8x+4)=12(x+2)[/tex]
[tex]\implies 8x+4=12(x+2)[/tex]
Distribute the right side of the equation:
[tex]\implies 8x+4=12\cdot x+12 \cdot 2[/tex]
[tex]\implies 8x+4=12x+24[/tex]
Switch sides:
[tex]\implies 12x+24=8x+4[/tex]
Subtract 8x from both sides of the equation:
[tex]\implies 12x+24-8x=8x+4-8x[/tex]
[tex]\implies 4x+24=4[/tex]
Subtract 24 from both sides of the equation:
[tex]\implies 4x+24-24=4-24[/tex]
[tex]\implies 4x=-20[/tex]
Divide both sides of the equation by 4:
[tex]\implies \dfrac{4x}{4}=\dfrac{-20}{4}[/tex]
[tex]\implies x=-5[/tex]
Therefore, the value of x is -5.
Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
Click to view page 1 of the table. LOADING... Click to view page 2 of the table. LOADING...
115
A graph with a bell-shaped curve, divided into 2 regions by a vertical line. The vertical line extends from the bell curve to the x-axis, and is located on the right half, under the curve. The region on the left of this line is shaded. The x-axis below the vertical line is labeled 115.
Question content area bottom
Part 1
The area of the shaded region is enter your response here. (Round to four decimal places as needed.)
The area of the given shaded region is 0.1587 which can be calculated using the cumulative area of the normal distribution.
What is z-score?The z-score is the number of standard deviations a data point is away from the mean. It can be calculated by subtracting the mean from the data point, and then dividing by the standard deviation.
To calculate the area of the shaded region, the z-score for the value of 115 must first be determined.
In this case, the z-score= (115 - 100)/15, or 1.
The area of the shaded region is then calculated using the cumulative area of the normal distribution.
As the area of the shaded region is the probability of a data point being greater than 115, the cumulative area of the normal distribution should be subtracted from 1 to get the area of the shaded region.
The cumulative area of the normal distribution for a z-score of 1= 0.8413,
as z-score= x - μ/σ
so the area of the shaded region
=1 - 0.8413
= 0.1587.
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5) A $40 shirt now selling for $28 is discounted by what percent?
A. 20%
B. 30%
C. 40%
D. 60%
Discriminate of 6x^2+21x=5x^2+7x
Answer:-14
Step-by-step explanation:
Answer:
Step-by-step explanation:
The roots of this discriminant x=0 or x=-14
Precalculus.
Please show all your work and answer all the questions
Using trigonometric ratio and trigonometric identities, the angle of elevation is 19.5 degrees and [tex]\cos(\arcsin(-\sqrt{2}/2)) = \frac{\sqrt{2}}{2}[/tex]
What is the angle of elevation?To determine the angle of elevation, we will need to apply trigonometric ratio here;
Length of cable = hypothenuse = 300ft
Distance of parasailer to surface = opposite = 100 ft
Since we have the value of opposite side and hypothenuse, we can use the sine ratio;
sinθ = opposite / hypothenuse
sinθ = 100/300
sinθ = 1/3
θ = sin⁻¹(1/3)
θ = 19.5°
2. Let;
[tex]\theta = \arcsin(-\sqrt{2}/2)$. Then, $\sin\theta = -\sqrt{2}/2[/tex]
Since θ is in the fourth quadrant, cos θ is positive. To find cos θ, we can use the trigonometric identity
[tex]\sin^2\theta + \cos^2\theta = 1[/tex]
\begin{align*}
[tex]\cos^2\theta &= 1 - \sin^2\theta \\&= 1 - \left(-\frac{\sqrt{2}}{2}\right)^2 \\&= 1 - \frac{1}{2} \\&= \frac{1}{2}[/tex]
Taking the positive square root, we get:
[tex]\cos\theta = \sqrt{\frac{1}{2}} = \frac{\sqrt{2}}{2}[/tex]
Therefore,
[tex]\cos(\arcsin(-\sqrt{2}/2)) = \frac{\sqrt{2}}{2}[/tex]
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MAX POINTS
5. Samantha measures 1.5 amps on her electric blanket. If the voltage on the circuit is 120 volts, what is the resistance in ohms, to the nearest tenth of an ohm? Use the formula R =
The resistance of the electric blanket is approximately 80 ohms.
What is Ohm's law?Ohm's law, a fundamental tenet of physics, explains how voltage, current, and resistance interact in an electrical circuit. It claims that the voltage across two locations and the resistance between them determine the relationship between the current flowing through a conductor between those two sites.
Ohm's law is mathematically represented as:
V = IR
where the three variables are voltage (V), current (I), and resistance (R). Given the values of the other two variables, this equation may be rewritten to account for any one of the three variables.
The resistance is given as:
R = V / I
Substituting the values of voltage and current we have:
R = 120 / 1.5
R = 80 ohms
Hence, the resistance of the electric blanket is approximately 80 ohms.
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David, a psychologist, believes that owning a pet can make a difference in stress levels. Thus, he wants to investigate whether individuals who own a pet dog differ significantly from non-dog-owners in terms of their stress levels. Two groups of American individuals were studied and the score of each individual was recorded on the David Stress Scale (scores were out of 50). Higher scores represent higher levels of stress. Using the following data in the table below, compute the appropriate analysis. Set alpha = .01.
There is a significant difference in stress levels between dog owners and non-dog owners.
Define statisticsStatistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves techniques for designing experiments, surveys, and observational studies to gather data, as well as methods for summarizing, visualizing, and drawing conclusions from the data.
Step 1: State the null and alternative hypotheses:
Null hypothesis: There is no significant difference in stress levels between dog owners and non-dog owners.
Alternative hypothesis: There is a significant difference in stress levels between dog owners and non-dog owners.
Step 2: Determine the level of significance (alpha) and the degrees of freedom :
Alpha = 0.01 (given in the problem)
Degrees of freedom = n₁ + n₂ - 2, where n1 and n2 are the sample sizes of the two groups.
n₁ = 20 (from the table)
n₂ = 15 (from the table)
Degrees of freedom = 20 + 15 - 2 = 33
Step 3: Calculate the sample means and standard deviations:
For dog owners:
Sample mean (x₁) = 28.25
Sample standard deviation (s₁) = 9.24
For non-dog owners:
Sample mean (x₂) = 36.20
Sample standard deviation (s₂) = 7.96
Step 4: Calculate the t-statistic:
t = (x₁ - x₂) / √[(s₁²/n₁) + (s₂²/n₂)]
t = (28.25 - 36.20) / √[(9.24²/20) + (7.96²/15)]
t = -2.75
Step 5: Determine the critical t-value:
Using a t-table with 33 degrees of freedom and a one-tailed alpha of 0.01, the critical t-value is -2.449.
Step 6: Make a decision:
Since the calculated t-value (-2.75) is less than the critical t-value (-2.449), we reject the null hypothesis.
Therefore, we can conclude that there is a significant difference in stress levels between dog owners and non-dog owners.
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Least common factor multiple of 15 and 6 ? Pls need ASAP
Answer: 30
Step-by-step explanation: 15x2=30 6x5=30 so: the least common multiple is:30
know the meaning of least multiple
(Score for Question 1:
of 2 points)
1.) Quincy is a shoe designer and salesperson. Last week he sold $4,125 in shoes. He earns a 4%
commission. How much did he make in commission? Be sure to show the formula you use to solve.
Answer:
Quincy earned $165 in commission for the week.
How much did Quincy make in commission?Given that, Quincy sold $4,125 in shoes, and he earns a 4% commission on his sales.
To find out how much he made in commission, we can use the following formula:
commission = sales × commission rate
Where "sales" is the total amount of shoes sold, and "commission rate" is the percentage commission earned on the sales.
In this case, Quincy's sales were $4,125, and his commission rate was 4% (4% = 4/100 = 0.04 as a decimal).
Plugging these values into the formula, we get:
commission = sales × commission rate
commission = $4,125 × 0.04
commission = $165
Therefore, Quincy made $165.
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105 visitors purchased no costume. 41 visitors purchased exactly one costume. 8 visitors purchased more than one costume. Based on these results, express the probability that the next person will purchase one or more costumes as a decimal to the nearest hundredth.
Answer:
Probability is 0.32
Step-by-step explanation:
The info we have is 105 people bought nothing. 41 + 8, that is 49 people bought something. That makes a total of 154 people. The total goes on the bottom of a fraction (to find the probability)
So far, we have
?/154
Probability of "buy something is:
49/154
(because the data shows that 49 out of 154 people bought something)
Let's use a calculator and divide 49÷154
We get 0.3181818...
(if you are not allowed to use a calculator, reduce 49/154 to 7/22 and use long division to get 0.3181818...)
The question asks for the nearest hundredth, that's two decimal places.
Probability is 0.32
find sin^2a-cos^2a, where cosa+Sina=1/2, 0<a<2π
Answer:
We know that:
sin^2a + cos^2a = 1 (1)
Also, we have:
cos a + sin a = 1/2
Squaring both sides of the above equation, we get:
cos^2a + 2cos a sin a + sin^2a = 1/4
Using equation (1), we can simplify this to:
1 + 2cos a sin a = 1/4
Subtracting 1 from both sides, we get:
2cos a sin a = -3/4
Squaring both sides, we get:
4cos^2a sin^2a = 9/16
Using the identity:
sin^2a = 1 - cos^2a
We can rewrite the above equation as:
4cos^2a (1 - cos^2a) = 9/16
Expanding and rearranging, we get:
4cos^4a - 4cos^2a + 9/16 = 0
Multiplying both sides by 16, we get:
64cos^4a - 64cos^2a + 9 = 0
Letting x = cos^2a, we can rewrite this as a quadratic equation:
64x^2 - 64x + 9 = 0
Solving for x using the quadratic formula, we get:
x = (64 ± √16384)/128
x = 1/2 or x = 9/64
Since 0 < a < 2π, we know that cos a is positive, so we can take the positive square root:
cos a = √(1/2) = 1/√2
Substituting this into the equation sin a + cos a = 1/2, we get:
sin a = 1/2 - cos a = 1/2 - 1/√2 = (√2 - 1)/2
Therefore:
sin^2a - cos^2a = ((√2 - 1)/2)^2 - (1/√2)^2
= (3 - 2√2)/4
Therefore, sin^2a - cos^2a = (3 - 2√2)/4.