The boy can wear 720 different outfits to school if he must wear one of each item, we need to find the number of combinations of one pair of pants, one shirt, one tie, and one jacket. The number of different combinations of pants he can wear is 8.
The number of different combinations of shirts he can wear is 5.
The number of different combinations of ties he can wear is 3.
The number of different combinations of jackets he can wear is 6.
To find the total number of different outfits, we multiply the number of combinations of each item:
8 * 5 * 3 * 6 = 8 * 90 = 720
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Claire says that the AA Criterion should be called the AAA Criterion. Explain why Claire might say this. Do you agree? Explain.
No, AA Criterion should not be called the AAA Criterion, because we need only two angles to be equal to prove the similarity.
What is AA criterion?According to the AA triangle similarity criterion, two triangles are considered similar if their three angles are identical to one another. Equi-angular triangles are comparable in a nutshell.
Since just two pairs of angles must be equal in order for the third pair to be automatically equal thanks to the angle sum property of triangles, the proper term for this criterion would then be the AAA(Angle-Angle-Angle) criterion. However, we refer to it as the AA criterion instead.
Hence, no, because we need only two angles to be equal to prove the similarity.
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predict the number of people in a household with 2.5 pounds of waste pounds of waste 0.27,1.41,2.19,2.83,2.19,1.81,0.85,3.05
The number of people in a household with 2.5 pounds of waste are = 11
and we calculate this on the basis of question below
Predict the number of people in a household with 2.5 pounds of waste pounds of waste 0.27,1.41,2.19,2.83,2.19,1.81,0.85,3.05. In Home 2 3 3 6 4 2 1 5
pound 0.27 ,1.41, 2.19 ,2.83 ,2.19 ,1.81 ,0.85, 3.05
people 2 3 3 6 4 2 1 5
so now the question is complete
in pound section we have to take care which value are greater than 2.5
so 2.83 and 3.05 is greater than 2.5 so here number of people who's home have greater than 2.5 pound of waste are 6+6=11
and rest people who's home has less than 2.5 pound waste are 2+3+3+4+2+1=15
so final ans is 11.
so this question was in complete and this ans is valid for this Question only.
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Jack opens a savings account with $470. The account earns 4.4% annual interest compounded quarterly. Part A Enter a function to represent the balance A in the account after t years.
The function that represents the balance after t years is ,
FV = $470( 1.011)^4t
What is the function that represents the balance after t years?The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value
P = Present value
R = interest rate
m = number of compounding
N = number of years
here, we have,
given that,
P = Present value= $470.
R = interest rate = 4.4%/4 =
m = number of compounding =4
N = number of years = t
FV = $470( 1.011)^4t
Hence, The solution is, a function to represent the balance A in the account after t years is, FV = $470( 1.011)^4t
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Identify the graph of the system of linear inequalities.
$y\le x-3$y≤x−3
y is greater than or equal to x plus 1$y\ge x+1$y≥x+1
Responses
A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph is shaded above y equals x plus 1.
Image with alt text: A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph is shaded above y equals x plus 1.
A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph is shaded between the boundary lines.
Image with alt text: A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph is shaded between the boundary lines.
A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph is shaded below y equals x minus 3.
Image with alt text: A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph is shaded below y equals x minus 3.
A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph has no shading.
Image with alt text: A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph has no shading.
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The solution for the inequalities, y≥x+1 is (0, 1) and (-1, 0).
and, solution for the inequalities, y≤x−3 is (0, -3) and (3, 0).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
y≤x−3.........(1)
y≥x+1.............(2)
If we solve the inequality using the graphical method we can see that the inequalities gives the parallel line.
Also, the solution for the inequalities, y≥x+1 is (0, 1) and (-1, 0).
and, the solution for the inequalities, y≤x−3 is (0, -3) and (3, 0).
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Find the length of the third side. If necessary, write in simplest radical form.
Answer:
8
Step-by-step explanation:
If my calculations are correct the third side is 8
f(x)=x2 g(x)=– 3x+1 Write your answer as a polynomial or a rational function in simplest form.
The simplest form of the polynomial is (x²)-3x+1.
A polynomial is a mathematical expression consisting of constants, variables, and exponents. It can be written in the form of a polynomial equation, which is a mathematical equation with one or more variables.
In this example, we have two functions, f(x) and g(x). The polynomial of these two functions can be written in simplest form by combining the functions together.
The polynomial of f(x) and g(x) is written in simplest form as (x²)-3x+1.
This means that for any value of x, the polynomial will evaluate to the value given by the equation.
If x=2, then the polynomial will evaluate to (2(2)²)-3(2)+1=3.
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For summer Nicole charges a flat fee of $5, plus $20 per hour.
1. Write an equation for babysitting.
2. What is the slope
3.what does the slope represent
4.what is the y-intercept
5.what does the y-intercept represent
Answer:
The equation for babysitting can be written as y = 20x + 5, where y is the total cost and x is the number of hours.
The slope of the equation is 20, which represents the rate of change in the total cost (y) with respect to the number of hours (x).
The slope represents the rate at which the total cost changes for each unit change in the number of hours. In this case, for each hour of babysitting, the total cost increases by $20.
The y-intercept of the equation is 5, which represents the cost when x = 0, i.e. when there is no babysitting time.
The y-intercept represents the starting value of the total cost, in this case, the amount charged for babysitting even when there is no babysitting time.
Step-by-step explanation:
What is the range of this relation?
(8,9)
(9,8)
(2,10)
(8,8)
(4,8)
(2,7)
Answer:
(9,7,10,8,7)
Step-by-step explanation:
range is the value of y.
When converting .000056 into scientific notation, the decimal point will move ___ spaces.
When converting 0.000056 into scientific notation, the decimal point will move 5 spaces to the right.
The resulting number in scientific notation would be 5.6 x 10^-5.
During a class election 28 people voted for candidate A. If there were 64 votes total, what is the ratio of votes for candidate B compared to candidate A?
need help asap find x in the picture
Answer: 60
A triangle can only be 180 degrees so if one side is 60 so is the other two sides
If you roll 2 dice, what is the exact binomial probability that the total number rolled will add up to 3 or less
The exact binomial probability that the total number rolled will add up to 3 or less is 1/12.
What is the exact binomial probability?
The exact binomial probability that the total number rolled will add up to 3 or less is calculated as follows;
The total number that can be rolled with 2 dice is 2 to 12, with 7 being the most likely outcome (the sum of two dice has a maximum of 7).
The probability that the total number is 3 or less is the sum of the probabilities of rolling a 2 and a 1;
The probability P = (1/36) + (2/36)
P = 3/36
P = 1/12
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Is there a relationship between the raises administrators at State University receive and their performance on the job? A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the straight-line regression model
y ^= β0 +β1x.
Using the method of least squares, the faculty group obtained the following prediction equation:
y ^= 14,000 - 2,000x
Interpret the estimated y-intercept of the line.
A) For an administrator who receives a rating of zero, we estimate his or her raise to be $14,000.
B) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000.
C) The base administrator raise at State University is $14,000.
D) There is no practical interpretation, since rating of 0 is nonsensical and outside the range of the sample data
Using the method of least squares, the faculty group obtained, the estimated y-intercept of the line is For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000.
The relationship between the variables is calculated and represented as an equation in regression analysis. The dependent variable, independent variables, and line equation constants are all included in this equation. Variables may be related in ways that are linear, quadratic, polynomial, etc.
In this instance, the performance is the independent variable and the increase is the dependent variable. Simple linear regression is the name of the equation, which is shown as a straight-line equation.
Regression analysis makes use of the relationship between independent and dependent variables' relationship equation to forecast the values of the dependent variable y given the values of the independent variable x.
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Can you help me figure out the equation
The sine function for a specified range of angles is shown graphically in the sine graph. A trigonometric graph's horizontal axis is the angle, which is typically denoted by the symbol, and the y-axis is the sine function of that angle.
How is a sine graph drawn?To graph the sine function, we place the sine of each angle on the vertical y-axis and indicate the angles along the horizontal x axis.
The Sin Formula: What Is It?The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: hypotenuse/perpendicular = sin. sin(n+2) = sin for each n.
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when lena arrived at her friend's birthday party there were 9 3/8 pizzas after lana and the other party guests had eaten pizza there was 2 5/8 pizzas left how much pizzas has eaten was eaten during the party
During the party, 6 3/4 pizzas were consumed.
To calculate the amount of pizza consumed during the party, subtract the remaining pizza from the original amount.
The original quantity of pizza was 9 3/8 pizzas, and the remaining quantity was 2 5/8 pizzas, resulting in:
6 3/4 pizzas = 9 3/8 - 2 5/8 pizzas
During the party, 6 3/4 pizzas were consumed.
This is the same as subtracting 2 and 5/8 from 9 and 3/8 and then reducing the result to the smallest fraction form.
The process of determining the difference between two fractions is known as fraction subtraction. To subtract two fractions, do the following:
Check that the fractions have a common denominator: If the denominators are not the same, you must find one. The least common multiple of two fractions' denominators is the smallest common denominator.
Subtract the numerators: Once the fractions have a common denominator, the numerators can be subtracted.
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Find the final value of an investment of £2500 that earns 0. 5% per month for the first six months but then depreciates at a rate of 0. 25% per month for the next 9 months
The final value of the investment is £2517.04.
Calculate the total amount earned over 6 months at 0.5% per month
At 0.5% per month, the investment of £2500 will earn £12.50 per month for six months.
Therefore, the total amount earned over 6 months is £12.50 x 6 = £75.
Determine the value of the investment after 6 months
The value of the investment after 6 months will be the initial investment plus the total amount earned over 6 months.
Therefore, the value of the investment after 6 months will be £2500 + £75 = £2575.
Determine the total amount lost over 9 months at 0.25% per month
At 0.25% per month, the investment of £2575 will lose £6.44 per month for nine months.
Therefore, the total amount lost over 9 months is £6.44 x 9 = £57.96.
Calculate the final value of the investment
The final value of the investment will be the value of the investment after 6 months minus the total amount lost over 9 months.
Therefore, the final value of the investment is £2575 - £57.96 = £2517.04.
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The final value of the investment would be £2491.97. To find the final value of the investment, we need to calculate the interest earned in the first 6 months.
When the rate was 0.5% per month, and then subtract the depreciation that occurred in the next 9 months when the rate was 0.25% per month.
First, calculate the interest earned in the first 6 months:
£2500 * (0.5/100) * 6 = £75Next, add this interest to the initial investment to get the value after 6 months:
£2500 + £75 = £2575Finally, calculate the depreciation in the next 9 months:
£2575 * (0.25/100) * 9 = £59.34Subtract the depreciation from the value after 6 months to get the final value:
£2575 - £59.34 = £2515.66 ≈ £2491.97.Learn more about Depreciation:
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4. The expression for sum of numbers a and b subtracted from their product is:
(a) a+b-ab
(b) ab-a+b
(c) ab - (a + b)
(d) ab+a-b
14 units to the right of-2 of a number line
Answer: 11 (Or I'm wrong)
Step-by-step explanation: -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
can someone help me here please! thankyou (complete solution)
Answer:
1. See below.
[tex]\textsf{2.} \quad \log_x256=\dfrac{1}{2}[/tex]
[tex]\textsf{3.} \quad x^6=1000000[/tex]
[tex]\textsf{4.} \quad \log_2\left(\dfrac{1}{64}\right)=x[/tex]
Step-by-step explanation:
Question 1
Please note that this question is incorrect.
I assume the question is missing an "x" term, since log₉27 ≠ -3.
Let's assume 27 should be "x":
[tex]\implies \log_9x=-3[/tex]
[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff b=a^c[/tex]
[tex]\implies x=9^{-3}[/tex]
If, however, the 9 is supposed to be "x":
[tex]\implies \log_x27=-3[/tex]
[tex]\implies x^{-3}=27[/tex]
Question 2Given exponential equation:
[tex]\sqrt{x}=256[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt{a}=a^{\frac{1}{2}}:[/tex]
[tex]\implies x^{\frac{1}{2}}=256[/tex]
[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies \log_x256=\dfrac{1}{2}[/tex]
Question 3Given logarithmic equation:
[tex]\log_x1000000=6[/tex]
[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies x^6=1000000[/tex]
Question 4Given exponential equation:
[tex]2^x=\dfrac{1}{64}[/tex]
[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies \log_2\left(\dfrac{1}{64}\right)=x[/tex]
what’s the value of x
Check the picture below.
[tex]\cfrac{24+x}{24}~~ = ~~\cfrac{36+12}{36}\implies \cfrac{24+x}{24}=\cfrac{48}{36}\implies \cfrac{24+x}{24}=\cfrac{4}{3} \\\\\\ 72+3x=96\implies 3x=24\implies x=\cfrac{24}{3}\implies x=8[/tex]
A pop quiz contains five questions: two
multiple choice questions with four options
each and three true-false questions. If Brad
randomly guesses, what is the probability
that he gets all five answers correct?
The probability that Brad gets all five answers correct is 1/128.
What is the probability that he gets all five answers correct?From the question, we have the following parameters that can be used in our computation:
true of false = 3
Multichoice = 2
For each multiple choice question, Brad has a 1/4 chance of getting the correct answer by guessing.For each true-false question, Brad has a 1/2 chance of getting the correct answer by guessing.So, the probability that Brad gets all five answers correct is (1/4)^2 * (1/2)^3 = 1/128.
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A ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. Twenty minutes later the angle of depression was 6°.
If a ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. The fire travelled 31,968 meters.
How to find the metre the fire travelled?Distance = d = v * t
Let v represent speed of the fire .
Where :
t = time elapsed in seconds = 20 * 60 = 1200 seconds
Using the tangent function:
d / v = tan(6°) - tan(4°)
Simplify this expression using the identity:
tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
Applying this to the above equation, we get:
d / v = (tan(6°) - tan(4°)) / (1 + tan(6°)tan(4°))
Using a calculator to evaluate the tangent values
d / v = 26.64 / v
d = 26.64 * v
Substituting the value of t, we get:
d = 26.64 * v
= 26.64 * 1200
= 31,968 meters (rounded to the nearest meter)
Therefore the fire travelled 31,968 meters.
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The complete question is:
A ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. Twenty minutes later the angle of depression was 6°. The fire travelled m (to nearest metre)
please help me I NEED HELP HELP
Bold = reason (in reasons 3 and 4 the formatting is odd and goes into the next line)
Statement Reason
1. line segment ʜᴏ is parallel to line segment EL, 1. Given
line segment HN intersects line segment OE at W,
the measure of HW is equal to the measure of NW*
2. angle HWO is congruent to angle NWE 2. Vertical angle theorem
3. angle OHW is congruent to angle WNE 3. alternate interior angles theorem
*4. line segment HW is congruent to line segment NW 4. definition of congruent
5. triangle HOW is congruent to triangle NEW 5. ASA postulate
*step 4 might not be needed; I don't know whether the "given" is saying that the measure of line segment HW is equal to the measure of line segment NW, or if it's saying that the two line segments are congruent
You might have to change the reasons for the statements, but this is the gist of how to prove it.
A rectangular room is 6 meters longer than it is wide, and its perimeter is 36
meters. Find the dimension of the room.
TH
L
Step-by-step explanation:
length = width + 6
the perimeter of a rectangle is
2×length + 2×width
by using the first equating as identity in the second we get
36 = 2×(width + 6) + 2×width =
= 2×width + 12 + 2×width = 4×width + 12
24 = 4×width
width = 6 m
length = width + 6 = 6 + 6 = 12 m
he dimensions of the rectangular room are 6 meters by 12 meters of the rectangular room is 6 meters longer than it is wide, and its perimeter is 36 meters by solving equations and geometric measurements.
Given that the room is 6 meters longer than it is wide, we can represent the width as W. Therefore, the length of the room would be W + 6.
The perimeter of a rectangle is calculated by adding all four sides, which in this case is given as 36 meters. We can express this as an equation:
Perimeter = 2 * (Length + Width)
Substituting the values, we get:
36 = 2 * (W + (W + 6))
Simplifying the equation further, we have:
36 = 2 * (2W + 6)
Dividing both sides of the equation by 2, we get:
18 = 2W + 6
Subtracting 6 from both sides, we obtain:
12 = 2W
Dividing both sides by 2, we find:
W = 6
Now that we have the width, we can calculate the length:
Length = Width + 6 = 6 + 6 = 12
Therefore, the dimensions of the rectangular room are 6 meters by 12 meters of the rectangular room is 6 meters longer than it is wide, and its perimeter is 36 meters by solving equations and geometric measurements.
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Mr McClean wants to hire a taxi. He ring three different taxi companies and asks them for their prices. A1 Taxis: A 5 mile journey costs £15 Crazy Cabs: A4 mile journey costs £13 Value Cars: A 10mile journey costs £28 Order the taxi companies from best to least value for money
Answer:
Value Cars
Step-by-step explanation:
A1 Taxis: A 5-mile journey costs £15
15 divided by 5 = £3 per mile
Crazy Cabs: A 4-mile journey costs £13
13 divided by 4 = £3.25 per mile
Value Cars: A 10-mile journey costs £28
28 divided by 10 = £2.80 per mile
The volume of 10,000 drops of a liquid is 10 fluid ounces. What is the volume of 100 drops?
Answer:
Step-by-step explanation:
if 10,000/10, find 100drops by moving decimal place
100.00/0.10
so volume is 0.1 flOz
Use the table to find the average rate of change over the interval [1,9]
Type your answer in the blank, with no spaces.
Answer:
1.6
Step-by-step explanation:
[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\\\=\frac{f(9)-f(1)}{9-1}\\ \\=\frac{15.8-3}{8}\\ \\=\frac{12.8}{8}\\ \\=1.6[/tex]
In the number 455,025, which place value is 1000 times the value of the 2?
A. Hundreds
B. Thousands
C. Ten thousands
D. Hundred thousands
Answer:
Ten thousands
Step-by-step explanation:
20 x 1000 = 20,000 therefore, ten thousands
ASAP
A boat starts at point A. It travels a distance of 7 km on a bearing of 135° to point B. From B it travels 12 km on a bearing of 250° to point C. Using a scale of 1 cm: 1 km, draw a diagram to show these bearings and journeys.
The diagram that represent the distance and the journeys is added as an attachment
How to make the diagramFrom the question, we have the following parameters that can be used in our computation:
Initial point = ADistance of 7 km on a bearing of 135° to point B.From B it, travels 12 km on a bearing of 250° to point CUsing the above as a guide, we have the following:
Next, we create the diagram (see attachment)
The attached figure represents the required diagram
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referring to exercise 9, what is the probability that a person diagnosed as having cancer actually has the disease?
The probability that a patient who has been diagnosed with cancer truly has the illness 0.406
It is known from prior experience that there is a 0.05 chance of choosing a cancer-positive adult over 40 in a certain area of the nation. What is the likelihood that an adult over the age of 40 will be given a cancer diagnosis if the probability of a doctor correctly diagnosing a person with cancer as having the disease is 0.78 and the probability of a doctor incorrectly diagnosing a person without cancer as having the disease is 0.06.
We wish to compute P(C | D) this time. Bayes rule is used in this process.
[tex]& P(C \mid D)=\frac{P(C n D)}{P(D)} \\\\& =\frac{P(C) P(D \mid C)}{P(C) P(D \mid C)+P\left(C^{\circ}\right) P\left(D \mid C^*\right)} \\\\& =\frac{0.05 * 0.78}{(0.05 * 0.78)+(0.95 * 0.06)} \\\\& =\frac{0.039}{0.039+0.057} \\\\& =\frac{0.039}{0.096} \\\\& =0.406[/tex]
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