Don can create 112 different outfits by choosing a pair of shoes, a pair of pants and a shirt from his available options.
Given, Don has eight pairs of shoes. Each pair of shoes can be viewed as a possible shoe choice for him. Don also has two sets of trousers. Each pair of trousers can be thought of as a possible choice of clothing on the lower body.
Don also has seven shirts. Each shirt can be thought of as a possible option for the dress of its upper body. We must take into account all possible permutations of these alternatives to determine the overall number of alternative associations. The number of options for each category is multiplied, and the result is:
8 (shoe options) * 2 (pants options) * 7 (shirt options) = 112
Therefore, Don can create 112 different outfits by choosing a pair of shoes, a pair of pants and a shirt from his available options. This assumes that each combination of shoes, pants, and shirt is considered a unique outfit.
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Which of the following transformations will not produce a congruent image?
A.
rotation
B.
translation
C.
dilation
D.
reflection
Answer:
Translation, rotation and reflection
Step-by-step explanation:
please brainliest <3
a- What are the different logs used to obtain porosity? Explain the principles of measurement, quantity measured and its relation to porosity. Illustrate with equations and/or sketches.
Different logs measure different physical properties of the formation that are related to porosity, and the relationship between the log measurement and porosity can be expressed through equations.
The different logs used to obtain porosity and their principles of measurement, quantities measured, and relation to porosity.
There are three main types of logs used to obtain porosity: neutron logs, density logs, and sonic logs.
Neutron logs: These logs measure the hydrogen content in a formation, which is directly related to porosity. The tool emits neutrons that interact with hydrogen atoms, and the resulting gamma rays are measured. The count rate decreases with increasing porosity. The neutron log can be expressed as:
Porosity = (neutron log reading - matrix reading) / (fluid reading - matrix reading)
Density logs: Density logs measure the bulk density of a formation, which can be related to porosity. The tool emits gamma rays that interact with the formation, and the scattered gamma rays are measured. The bulk density decreases with increasing porosity. The density log can be expressed as:
Porosity = (matrix density - bulk density) / (matrix density - fluid density)
Sonic logs: Sonic logs measure the travel time of sound waves through a formation, which can be related to porosity. The tool sends an acoustic wave and measures the time it takes to travel a specific distance. The travel time increases with increasing porosity. The sonic log can be expressed using Wyllie's time-average equation:
Porosity = (sonic log reading - matrix reading) / (fluid reading - matrix reading)
In summary, neutron logs measure hydrogen content, density logs measure bulk density, and sonic logs measure travel time of sound waves. These measurements can be used to calculate porosity using the respective equations provided.
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Which of the following show the expanded and simplified version of the expression
g(x) = 6(x + 2)2 + (x - 3)(x - 5)
a) 5x² + 16x +39
Ob) 7x² + 32x +39
Oc) 7x² + 16x +39
d) 7x² + 32x +9
Answer:
c) 7x² + 16x +39
Step-by-step explanation:
g(x) = 6(x + 2)² + (x - 3)(x - 5)
g(x) = 6(x² + 2*2x + 2²) + (x² - 3x - 5x + 15) =
= 6x² + 24x + 24 + x² - 8x + 15 = 7x² + 16x + 39
the germination rate is the rate at which plants begin to grow after the seed is planted. a seed company claims that the germination rate for their seeds is 90 percent. concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. what are the
The correct hypothesis for a one-sample z-test for a population proportion p for germination is p <0.9
A hypothesis is an informed estimate about the solution to a scientific issue that is supported by sound reasoning. It is the expected result of the trial, though it is not evidence in an experiment. Depending on the information collected, it might be supported or might not be allowed at all.
The material provided indicates that the following is the appropriate theories for a one-sample z-test for a population proportion where H0 is p = 0.9 and H1 <0.9. Thus, at the null hypothesis, it is tested if the germination rate is actually of 90%, that is H = 0.9 and at the alternative hypothesis, it is tested if the germination rate is of less than 90%, that is H1 <0.9.
Complete Question:
The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample z-test for a population proportion p ?.
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together, a piece of pie plus ice cream costs $2.20 in total. the pie costs $2 more than the ice cream. how much does the ice cream cost?
The ice cream costs $0.10 and the pie costs $2.10.
Let's call the cost of the ice cream "x".
According to the problem,
The pie costs $2 more than the ice cream, so the pie costs x + $2.
And, together, the pie and ice cream cost $2.20, so:
x + (x + $2) = $2.20
Expanding and solving for x:
2x + $2 = $2.20
2x = $0.20
x = $0.10
A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept.
The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.
Ax+By=C is the typical form for linear equations in two variables.
2x+3y=5, for example, is a simple linear equation.
It is rather simple to get both intercepts when an equation is stated in this way (x and y).
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Solve for x.
3x + 2
2x + 6
x = [?]
Answer:
4
Step-by-step explanation:
Im assuming you mean the first and second equation equal each other:
3x+2=2x+6
x=4
complete the table to show the factored form and expanded form of each expression.
The table above should be completed as follows;
Factored form Expanded form
c(c - 5) c² - 5c
4(2a - b) 8a - 4b
3(2w - 7x) 6w - 21x
-(3y - 2x) -3y + 2x
2x(6 - 7x) 12x - 14x²
n(3 - 10) 3n - 30
y(5 - 7) 5y - 7y
What is a factored form?In Mathematics and Geometry, a factored form can be defined as a type of quadratic expression that is typically written as the product of two (2) linear factors and a constant.
In this scenario and exercise, we would complete the table above by showing the factored form and expanded form of each of the given expressions as follows;
c(c - 5) ⇒ c² - 5c
8a - 4b ⇒ 4(2a - b)
3(2w - 7x) ⇒ 6w - 21x
-(3y - 2x) ⇒ -3y + 2x
12x - 14x² ⇒ 2x(6 - 7x)
n(3 - 10) ⇒ 3n - 30
5y - 7y ⇒ y(5 - 7)
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Barry is 7 years older than Meisha. Which equation shows Barry’s age (b) in terms of Meisha’s age (m)?
Answer:
b-m= 7
Step-by-step explanation:
Let Barry's age is b and Meisha's age is m.
Barry is 7 years older than Meisha. Older means Barry's age is more than Meisha's age.
We can the equation as follows :
b = 7+m
or
Subtract m from both sides,
b-m= 7
Hence, the required equation is "b-m= 7".
The solution to
1.4=I/3.5
\(1.4 = 1 \frac{3}{5} \)
Solution:\(1.4 = 1 \frac{3}{5}\)
Convert the expression
\( \frac{7}{5} = \frac{1}{7} \\ \frac{}{2} \)
Simplify the expression
\( \frac{7}{5} = \frac{2}{7} \)
Cross-Multiply
\(49 = 10\)
Check the equality
Answer:\(false\)
Hey there!
1.4 = l/3.5
L/3.5 = 1.4
MULTIPLY 3.5 to BOTH SIDES
l/3.5 * 3.5 = 1.4 * 3.5
WORK IT OUT!
NEW EQUATION: l = 1.4 * 3.5
SIMPLIFY IT!
l = 4.9
Therefore, your answer should be: l = 4.9
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Bob is standing 25 feet from a lamppost that is to his left and 30 feet from a lamppost that is to his right. The distance between the two lampposts is 20 feet. What is the measure of the angle formed from the line from each lamppost to Bob? Approximate to the nearest degree. 1. 202 = 252 302 − 2(25)(30)cos(A) 2. 400 = 625 900 − (1500)cos(A) 3. 400 = 1525 − (1500)cos(A) 4. −1125 = −(1500)cos(A) degrees.
Answer:
The answer is 41
Step-by-step explanation:
400 = 900 + 625 - 1500 cos x
400 - 1525 = -1500 cos x
-1125 = -1500 cos
cos x = -1125/-1500
x = cos⁻¹ 0.75
x = 41.409622109
x ≈ 41°
Answer:
41
Step-by-step explanation:
A car can travel 40 miles per gallon of petrol . How many kilometres can it travel on 5 gallons of petrol?
Answer:
6(172) = 1032
Step-by-step explanation:
Since 42 gallons is 6 times the 7 gallons
he will go 6 times as far
Work out the value of 5 to the power of a if it equal 1/125
Answer:
a = -3
Step-by-step explanation:
Step 1: Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:
5^a = 1/125
Step 2: Take the log of both sides
log(5^a) = log(1/125)
Step 3: According to the power rule of logs, we can bring a down and multiply it by log(5):
a * log(5) = log (1/125)
Step 4: Divide both sides by log(5) to solve for a:
(a * log(5) = log(1/125)) / log(5)
a = -3
Optional 5: We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:
5^-3 = 1/125
1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator
1/125 = 1/125
Let U = {(x, y, z) € R^3 | x + 2y – 3z =0}. a) (2pt) Show directly (by verifying the conditions for a subspace) that U is a subspace of R^3. You may not invoke results learned in class or from the notes. b) (2pts) Find a basis for U. You must explain your method. c) (1pt) Using your answer from part b) determine Dim(U).
a) U is subspace of R^3.
b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.
c) 2.
a) To show that U is a subspace of R^3, we need to verify the following three conditions:
i) The zero vector (0, 0, 0) is in U.
ii) U is closed under addition.
iii) U is closed under scalar multiplication.
i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.
ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:
x1 + 2y1 - 3z1 = 0 (by definition of U)
x2 + 2y2 - 3z2 = 0 (by definition of U)
Adding these two equations, we get:
(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0
which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.
iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:
x + 2y - 3z = 0 (by definition of U)
Multiplying both sides of this equation by c, we get:
cx + 2cy - 3cz = 0
which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.
Since U satisfies all three conditions, it is a subspace of R^3.
b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:
x = 3z - 2y
y = (x - 3z)/2
Substituting z = t into these equations, we get:
x = 3t - 2y
y = (x - 3t)/2
Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:
(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)
Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.
c) Since the basis for U has two elements, the dimension of U is 2.
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it takes john ten minutes to swim two laps how long in minutes will it take john to swim fie laps
Answer:
it will take john 25 minutes to swim five laps
Step-by-step explanation:
Since it takes john 10mins to swim 2 laps, we can tell that it would have taken him about 5 minutes to swim 1 lap, that's 5mins per lap, and 5 times 5 =25
Hope that helps!
PLEASE HELP QUICKLY!!!!!!!
Penelope and Georgia are each saving money to take a vacation. Penelope started with $710 and saved $25 each week. Georgia opened her account with $570 and saved $45 each week. In how many weeks will they have the same amount of money? Group of answer choices 7 weeks 8 weeks 13 weeks 14 weeks
Answer:
8 weeks
Step-by-step explanation:
Write each decimal as a fraction or mixed number in simpliest form.
-0.18...
The decimal number -0.18 expressed in its simplest form is -9/50
Converting decimal to fractionFractions are written as a ratio of two integers. For instance a/b is a fraction.
According to the question, we are to write the decimal -0.18 as a fraction or mixed number.
Convert to fraction
-0.18 = -18/100
Write in its simplest form
-18/100 = -9*2/50*2
The value of 2 will cancel out at both numerator and denominator to have;
-18/100 = -9/50
Hence the decimal number -0.18 expressed in its simplest form is -9/50
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A spinner with 10 equally sized slices is shown below. (2 slices are red, 4 are blue, and 4 are yellow.) The dial is spun and stops on a slice at random. What is the probability that the dial stops on a slice that is not red?Write your answer as a fraction or a whole number.
We will have the following:
Since there are 8 slices that are not red, the probability will be given by:
\(p=\frac{8}{10}\Rightarrow p=\frac{4}{5}\Rightarrow p=0.8\)So, the probability will be of 4/5, that is 80%.
Katherine bought 12 bananas for $2. What was the cost of the bananas in bananas
per dollar?
a boy travelled a distance of 10 km in 2 minutes calculate the speed of that boy
Step-by-step explanation:
(i hope this helps)
speed=distance/time taken
x and y stand in a line at random with 10 other people. what is the probability that there are 3 people between x and y?
The probability that there are 3 people between x and y is 1/659470.
The total number of ways in which x and y can stand in a line with 10 other people is (12C2) = 66.
To find the number of ways in which there are exactly 3 people between x and y, we can treat x and y as a single entity and arrange them along with the 10 other people in 8 available spots in the line. This can be done in (8C1) = 8 ways.
Within this arrangement, there are 3 spots where x and y can be placed with 3 people between them,
Once x and y have been placed in one of these 3 spots, the remaining people can be arranged in the remaining spots in
10!/(10-8)! = 1814400 ways.
So the number of ways in which there are exactly 3 people between x and y is,
8 * 3 * 1814400 = 43545600.
Therefore, the probability that there are 3 people between x and y is,
43545600/66 = 659469.69 (rounded to 2 decimal places)
So, the probability is approximately 1 in 659470 or 1/659470.
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The acceleration y, in meters per second squared, of an object after x seconds is given by y = 7 sin (pi/4 x). During the first 10 seconds, over which intervals is the acceleration increasing?
(2, 6)
(4, 8)
(0, 2) and (6, 10)
(0, 4) and (8, 10)
Answer: (0, 2) and (6, 10)
Step-by-step explanation:
The acceleration is:
y = 7*sin( x*pi/4).
Over which interval is the acceleration increasing?
First, let's study the sin function:
Sin(θ) increases between -pi/2 and pi/2
Sin(θ) decreases between pi/2 and (3/2)*pi.
And so on.
Here we have:
θ = x*(pi/2)
When x = 0, θ = 0.
And sin(θ) is increasing in θ = 0.
Then we must choose one of the options that start with x = 0.
now it will stop increasing when:
θ = pi/2 = x*(pi/4)
x = 2.
So the acceleration is increasing in the segment (0,2)
And it will start increase again when:
θ = (3/2)*pi = x*(pi/4)
(3/2)*pi*(4/pi) = 6 = x.
So at x= 6 the acceleration starts increasing again, and the acceleration is only deffined until x = 10, then
the correct option is: (0, 2) and (6, 10)
Answer:
C. (0, 2) and (6, 10)
Step-by-step explanation:
Took the final test and can confirm that this is the correct answer.
Timothy is at an elevation of –17.65 meters below sea level. He descends by 3
meters to observe a coral. What is his new elevation relative to sea level?
How many 1 U.S Liquid quarts to Fluid ounces?
Answer:
32
Step-by-step explanation:
A quart is equal to 32 fluid ounces.
Please answer quickly
Answer:
\(y+2=\frac{5}{2} (x-6)\)
Step-by-step explanation:
point-slope form: y-y1=m(x-x1)
x1=6
y1=-2
m=5/2
\(y+2=\frac{5}{2} (x-6)\)
Can someone help please! Can someone help please!Can someone help please!
Answer:
A
Step-by-step explanation:
Answer:
Step-by-step explanation:
nooooooo
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 18 inches long, and the height of the equilateral triangle is 15.6 inches. The pyramid's slant height is 19 inches. What is its surface area?
The surface area of the pyramid is 592. 2 square inches
How to determine the surface areaThe formula for calculating the surface area of a triangular pyramid is expressed as;
SA = A + 3a
Given that the parameters are;
A is the area of the pyramid's basea is the area of one of the pyramid's facesSA is the surface area of the pyramidArea of the base = 1/2 × 18 × 19 = 171 square inches
Area of the pyramid's face = 1/2 × 18 × 15. 6 = 140. 4 square inches
Substitute the values, we get;
Surface area = 171 + 3(140.4)
expand the bracket
Surface area = 592. 2 square inches
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evaluate 8^-2 pls only real answers
Step-by-step explanation:
By Law of Indices,
8^(-2) = 8^0 / 8^2
= 1 / 64.
1) Ed invests $1,000 into a money market account that earns 8% annual interest compounded quarterly. How much money will
he have earned after 8 years?
The money market account earns 8/4 = 2% interest per quarter.
In one year, there are 4 quarters.
so, the formula to calculate the balance after 8 years is:
A = P (1 + r/n)^(nt)
where A is the final balance, P is the principal (initial investment), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the money is invested for.
Substituting in the given values,
A = 1000 (1 + .02)^(4*8)
A = 1000 (1.02)^32
A = 1000 (1.8587)
A = 1858.7
So after 8 years, Ed will have earned $1858.7.
The measure of ∠3 is (4x + 1)° and the measure of ∠6 is (6x – 29)°. Find the value of x and the measures of ∠3 and ∠6.
The measure of <3= 61 degree and <6 = 61 degree.
what is vertical angles?According to this theorem, when two straight lines cross, they create two sets of linear pairs with matching angles. The adjacent angles created by the junction of these two lines are likewise said to be supplementary, or equivalent to 180 degrees.
Postulate for Vertical Angles Two angles are congruent if they are vertical angles (have equal measures). Exact one line passes through a location that is not on a line and is parallel to that line.
Given:
∠3 = (4x + 1)°
∠6 = (6x – 29)°
If <3 and <6 are vertical angles.
<3 = <6
4x+ 1 = 6x- 29
-2x= -30
x= 15
So, the measure of <3 = 4(15) + 1= 61 degree.
and <6 = 6(15) - 29 = 61 degree
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What is the solution to the system of equations?
y= 1/3x-10
2x + y = 4
34756Step-by-step explanation: