Option D will result in an image that is rotated 180 degrees equation counterclockwise about the origin and then reflected across the y-axis, which will not map the image onto itself.
What is counterclockwise?Counterclockwise, also known as anticlockwise, is a direction of rotation that is opposite to the direction in which the hands of a clock move. It is the direction that is typically associated with the rotation of objects in the Northern Hemisphere.
counterclockwise rotation is the positive direction of rotation in a coordinate system, where the x-axis increases to the right and the y-axis increases upwards.
Option B, "Reflect over the y-axis, and then reflect again over the y-axis," will result in an image that maps onto itself.
When you reflect an image over the y-axis, the left and right sides of the image switch places. If you then reflect the already reflected image over the y-axis again, the left and right sides switch places once more, effectively returning the image to its original orientation.
Option A will result in an image that is rotated 180 degrees counterclockwise about the origin and then reflected across the x-axis, which will not map the image onto itself.
Option C will result in an image that is reflected over the y-axis and then reflected over the x-axis, which will produce an image that is flipped both horizontally and vertically and therefore not map the image onto itself.
Option D will result in an image that is rotated 180 degrees counterclockwise about the origin and then reflected across the y-axis, which will not map the image onto itself.
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Answer:
Option B i think
Step-by-step explanation:
hope this helps
A fish-tank has a length of 25 centimeters, a width of 10 centimeters, and a depth of 8 centimeters. Find the volume of the fish tank.
The volume of the fish tank is 2000 cubic centimeters, which is calculated by multiplying the length, width, and depth of the tank (25 x 10 x 8 = 2000).
The volume of a fish tank is an important piece of information to know when setting up a fish tank. To calculate the volume of a fish tank, you must multiply the length, width, and depth of the tank. In this example, the fish tank has a length of 25 centimeters, a width of 10 centimeters, and a depth of 8 centimeters. To calculate the volume of the fish tank, we would multiply these three measurements, 25 x 10 x 8 = 2000. This means that the fish tank has a volume of 2000 cubic centimeters. Knowing the volume of the fish tank is important for selecting the right type and size of filter, heater, and other equipment for the tank, as well as for selecting the right number and size of fish for the tank. Furthermore, it is necessary to know the volume of the tank when adding water and testing water parameters, such as pH and nitrate levels, as these readings are related to the size of the tank. Knowing the volume of a fish tank is essential for successful fish keeping.
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Please help ASAP I don’t understand this! I’m not good at math. Please explain. Thank you!
Answer:
e. y = sin(x) + π
Step-by-step explanation:
We can see that the graph of y = sin(x) has been shifted vertically. This means that the added π should be outside the trigonometric function.
Therefore, e. y = sin(x) + π is the correct answer.
See the attached image for how a, b, c, and d values change the graphs of sine and cosine.
In exercises 1-6, use the diagram to find the measure of the angle.
Please help me
The measure of the angle obtained from the specified measure of the arc CD and the diameter of the circle CF are;
m∠CAF = 60°m∠AFB = 30°m∠CEF = 60°m∠CFB = 60°m∠DCF = 30°m∠BCD = 30°What is an arc of a circle?An arc of a circle is a part or portion of the circumference of the circle.
1. The angle at C, obtained from the measure of the arc CD is; (360 - (120 + 120))/2 = 60 (Angle at the center of a triangle theorem)
Therefore; m∠CAF = 90° - 60°/2 = 60°
m∠CAF = 90° - 60°/2 = 60°
2. m∠AFB = m∠FCB = 30°
3. m∠CEF = m∠CAF = 60°
4. m∠CFB = m∠CAF = 60° (Corresponding angles theorem)
5. m∠DCF = m∠BCF = 30° (Sum of angles at a point and angles formed by the diameter of a circle)
6. m∠BCD = m∠BCF + m∠DCF
Therefore; m∠BCD = 30° + 30° = 60°
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Nico, Aditi, Erick, Raj, and Sandra are solving the equation. Two-fifths (5 + x) = 8 Each student begins to solve the problem as shown. Nico Aditi Erick Two-fifths (5 + x) = 8. (Five-halves) two-fifths (5 + x) = 8 (five-halves) Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8 Two-fifths (5 + x) = 8. Two-fifths (5 + x) minus 5 = 8 minus 5 Raj Sandra Two-fifths (5 + x) = 8. (one-half) two-fifths (5 + x) = 8 (one-half) Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8 Which students are correct in their approach to solving the problem? Select three options. Nico Aditi Erick Raj Sandra
The three students who are correct in their approach to solving the problem are Nico, Aditi, Sandra.
Describe Algebra?Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols to solve equations and solve problems. It involves using letters, symbols, and numbers to represent variables and unknowns in mathematical expressions, equations, and functions.
In algebra, variables represent quantities that can vary, such as the height of a building, the speed of a car, or the price of a product. Algebraic expressions and equations involve combining these variables, symbols, and numbers using operations such as addition, subtraction, multiplication, and division.
Algebra includes various topics such as linear algebra, quadratic equations, polynomials, matrices, and functions. It also includes the use of graphs and charts to represent mathematical relationships and solve problems.
The three students who are correct in their approach to solving the problem are:
Nico: Two-fifths (5 + x) = 8. (Five-halves)
Aditi: Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8
Sandra: Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8
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Determine the scale factor for each of the drawing scales 1/4" = 1'-0" 1/8" = 1'-0" 1" = 10' 1" = 20'
sydney needs to make exactly 8 dozen items for a bake sale
Answer: If Sydney needs to make exactly 8 dozen items for a bake sale, that means she needs to make a total of 8 x 12 = 96 items
Use the circle. a circle with a radius of 9 and arc with angle 135 degrees. what is the radian measure for the angle to the nearest hundredth? use 3.14 for pi.
The length of the bow of the circle is 9π/ 2 = 4.5 *3.14 = 14.13.
The bow time of a circle can be determined with the compass
and significant point of view exercising the bow time frame strategy.
⇒ angle = arc/ radius
⇒ 135 ° = bow/ 6
⇒ arc = 135 ° * 6
⇒ bow = 135 ° * π/ 180 ° * 6
⇒ bow = 9π/ 2
⇒ 9π/ 2 = 4.5 *3.14 ⇒14.13
In calculation, a bow is characterized as a piece of the limit of a circle or a bend. It can likewise be indicated as an open bend. The limit of a circle is the border or the distance around a circle, else called the circuit.
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the graph of a proportional relationship passes through (6,21). what is the equation for the relationship?
Answer:
The equation for the relationship is [tex]y=\frac{7}{2} \times x[/tex].
Step-by-step explanation:
Given that point [tex](x,y)=(6,21)[/tex] is part of a direct relationship. That is:
[tex]y \ \infty \ x[/tex]
[tex]y=k\times x[/tex] (1)
Where [tex]k[/tex] is the proportionality constant.
If we know that [tex]x=6[/tex] and [tex]y=21[/tex], then the proportionality constant is:
[tex]k=\dfrac{y}{x}[/tex]
[tex]k=\dfrac{21}{6}[/tex]
[tex]k=\dfrac{7}{2}[/tex]
Lastly, the equation for the relationship is [tex]y=\frac{7}{2} \times x[/tex].
What is the distance CD?
Step-by-step explanation:
c = 2,8 and d = 6,5
Use the distance formula ( kind of a modified Pythagorean theorem)
s^2 = (x1-x2)^2 + (y1-y2)^2 ( s = distance)
s^2 = ( 2-6)^2 + ( 8-5)^2
s^2 = 25
s = 5 units
find the measure of the missing angles. 105° 32° e f d
The measure of the missing angle is 43 degrees.
What is triangle?
A triangle is a geometric shape with three sides and three angles. It is a closed, two-dimensional figure with straight sides. The sum of the angles in a triangle always adds up to 180 degrees.
To find the measure of the missing angles, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, we can find the measure of the missing angle by subtracting the sum of the other two angles from 180 degrees.
Let's call the missing angle x. Then we have:
105° + 32° + x = 180°
Simplifying, we get:
x = 180° - 105° - 32°
x = 43°
Therefore, the measure of the missing angle is 43 degrees.
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we want to test if more than 6% of byu students are from texas. is the sampling distribution of p-hat approximately normal in this example? group of answer choices yes, because n > 30. no, because the sample distribution is not normal. no, because the sampling distribution of p-hat does not have a shape. yes, because np0 > 10 and n(1-p0) > 10.
Yes, because[tex]np0 > 10[/tex]and [tex]n(1-p0) > 10[/tex].
Thus, the sampling distribution of p-hat is approximately normal, given the conditions of [tex]np0 > 10 and n(1-p0) > 10.[/tex]
This is because the sampling distribution of p-hat follows the Central Limit Theorem, which states that when sample sizes are greater than 30,
the sampling distribution of the sample proportion will be approximately normal. The Central Limit Theorem is used in this example because the number of BYU students from Texas (n) is greater than 30, so the sample proportion (p-hat) is normally distributed.
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Complete the chart pleaseee
Compounded Principal Interest Rate per Compounding Period Number of Compounding Periods Final Amount
Annually $9,200 6% / year 1 $20,101.83
Semi-Annually $9,200 3% / 6 months 30 $20,480.73
Quarterly $9,200 1.5% / 3 months 60 $20,740.64
Monthly $9,200 0.5% / month 180 $21,027.54
Weekly $9,200 0.12% / week 780 $21,118.33
Daily $9,200 0.016% / day 5,475 $21,183.05
What is compound interest ?
Compound interest is a method of calculating interest where interest is added to the principal amount, and the interest is also calculated on the accumulated interest. This results in the growth of the principal amount over time. Compound interest is often used in investments, loans, and savings accounts. The formula for calculating compound interest is [tex]A = P (1 + r/n)^{nt}[/tex], where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
According to the question:
Compound Interest Formula: [tex]A = P(1 + r/n)^{nt}[/tex]
where A is the final amount, P is the principal invested, 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.
Compounded Principal Interest Rate per Compounding Period Number of Compounding Periods Final Amount
Annually $9,200 6% / year 1 $20,101.83
Semi-Annually $9,200 3% / 6 months 30 $20,480.73
Quarterly $9,200 1.5% / 3 months 60 $20,740.64
Monthly $9,200 0.5% / month 180 $21,027.54
Weekly $9,200 0.12% / week 780 $21,118.33
Daily $9,200 0.016% / day 5,475 $21,183.05
Note: The final amounts have been rounded to the nearest cent.
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In which number does the digit 3 have a value that is 10 times as great as the value of the digit 3 in 143,728?
A. 137,982
B. 142,398
C. 292,389
D. 392,097
The number in which the digit 3 has a value that is 10 times as great as the value of the digit 3 in 143,728 is 392,097.
Define unit digitThe unit digit of a number refers to the rightmost digit of that number when it is written in a positional numeral system. In the decimal system, which is the most common positional numeral system used today, the unit digit is the digit in the ones place.
Let's consider the options one by one:
A. 137,982: This number does not have any digit equal to 3.
B. 142,398: This number does not have a digit 3 with a value as 30,000.
C. 292,389: This number has a digit 3 in the hundred thousands place, which has a value of 3 x 100,000 = 300,000. This is more than 10 times the value of the digit 3 in 143,728, so this option does not satisfy the condition.
D. 392,097: This number has a digit 3 in the ten thousands place, which has a value of 3 x 10,000 = 30,000. This satisfies the condition, so the answer is (D) 392,097.
Therefore, the number in which the digit 3 has a value that is 10 times as great as the value of the digit 3 in 143,728 is 392,097.
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if a destination goal is created for a newsletter sign-up and a user completes the newsletter sign-up three times in three separate sessions, how many goal conversions will analytics count?3621
Analytics will count three goal conversions if a user completes the newsletter sign-up three times in three separate sessions.
When a goal is set up in analytics, it is assigned a unique ID. When a user completes the desired action that triggers the goal, the ID is recorded in the user's session data. Each time the user completes the action, a new session is created, and a new goal completion is recorded with a unique ID.
Therefore, if the user completes the newsletter sign-up three times in three separate sessions, analytics will count three goal conversions, each with a unique ID.
It's worth noting that while this behavior is typical for most analytics platforms, it's possible to configure goals in different ways, so the behavior may vary depending on the specific implementation. Therefore, it's important to consult the analytics documentation or work with a knowledgeable analyst to confirm the expected behavior.
Therefore, the correct answer is three goal conversions will be counted in analytics.
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I need somebodys help quickly please!
(look at the attachment it shows the math equation).
Answer:
First box is seven; second box is 16; third box is 14
Step-by-step explanation:
Since a square has all equal sides, we know that s+s+s+s or 4s=Perimeter.
SInce we are finding the area of a square, the equation would be s^2. 7 squared is 49, 16 squared is 256, and 14 squared is 196.
using euler's theorem explain why it is not possible for a polyhedron to have 6 vertices and 7 edges
Euler's theorem lets us draw the conclusion that a polyhedron cannot contain [tex]6[/tex] vertices or [tex]7[/tex] edges.
The number of faces of a polyhedron.Four or even more plane face (all polygons) that meet in pairs along an edge and at least three edges that meet at a vertex make up a solid figure. Full solution, step-by-step Polyhedron: A three-dimensional object with only polygonal faces. There must be a minimum of different faces on a polyhedron.
How do polygons and polyhedrons differ?A two-dimensional shape composed of line segments is known as a polygon. Square, triangle, hexagonal, etc. are a few examples. A polyhedron, on the other hand, is a three-dimensional object formed of polygons. For instance, a cube, a tetrahedron, etc.
[tex]V - E + F = 2[/tex]
In the case of a polyhedron with [tex]6[/tex] vertices and [tex]7[/tex] edges, we can plug in the values [tex]V=6[/tex] and [tex]E=7[/tex] to obtain:
[tex]6 - 7 + F = 2[/tex]
Simplifying this equation, we get:
[tex]F = 3[/tex]
Therefore, we can conclude that it is not possible for a polyhedron to have [tex]6[/tex] vertices and [tex]7[/tex] edges, based on Euler's theorem.
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Find the tangent of
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{\sqrt{21}}\\ a=\stackrel{adjacent}{YZ}\\ o=\stackrel{opposite}{3} \end{cases} \\\\\\ (\sqrt{21})^2= (YZ)^2 + (3)^2\implies 21=YZ^2+9 \\\\\\ 12=YZ^2 \implies \sqrt{12}=YZ \\\\[-0.35em] ~\dotfill[/tex]
[tex]\tan(Y )=\cfrac{\stackrel{opposite}{3}}{\underset{adjacent}{\sqrt{12}}}\implies \tan(Y )=\cfrac{3}{\sqrt{12}}\cdot \cfrac{\sqrt{12}}{\sqrt{12}}\implies \tan(Y )=\cfrac{3\sqrt{12}}{12} \\\\\\ \tan(Y )=\cfrac{3\sqrt{2^2\cdot 3}}{12}\implies \tan(Y )=\cfrac{6\sqrt{3}}{12}\implies \tan(Y )=\cfrac{\sqrt{3}}{2}[/tex]
A student had 50 minutes of homework on Monday and 30 minutes of homework on Tuesday. What is the percent decrease in homework time from Monday to Tuesday?
If a student had 50 minutes of homework on Monday and 30 minutes of homework on Tuesday, then there was a 40% decrease in homework time from Monday to Tuesday.
To calculate the percent decrease in homework time from Monday to Tuesday, we need to find the difference between the two values and then divide that difference by the original value (Monday’s homework time). The difference between 50 minutes and 30 minutes is 20 minutes. Dividing this difference by the original value (50 minutes) gives us:
(20 / 50) x 100% = 40%
Therefore, there was a 40% decrease in homework time from Monday to Tuesday.
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Please helppp
To keep some privacy about the students, a professor releases only summary
statistics about student scores on a difficult quiz.ctice problems
mean standard deviation minimum Q1
66.91
12.74
12
57
median
66
Q3 maximum
76
100
Based on this information, what can you know about outliers in the student scores?
A. There is an outlier at the upper end of the data.
B. There is an outlier at the lower end of the data.
C. There are outliers on both ends of the data.
D. There is not enough information to determine whether there are any outliers.
Answer:
B
Step-by-step explanation:
Evaluating functions
Linear and quadratic or cubic
Answer:
f(3) = -39g(-6) = -28Step-by-step explanation:
You want f(3) and g(-6) when f(x) = -4x² -3 and g(x) = 5x +2.
Function evaluationTo find the value of the function for a particular value of the variable, put that value in place of the variable and do the arithmetic.
f(3) = -4(3²) -3 = -4(9) -3 = -36 -3
f(3) = -39
g(-6) = 5(-6) +2 = -30 +2
g(-6) = -28
__
Additional comment
Your calculator can help with the arithmetic.
max has decided to cancel his reservation for a plot in an upcoming subdivision because of the delays the subdivider is experiencing. how long does the subdivider have to get the deposit back to max?
The subdivider has to get the deposit back to Max within 30 days.
What is a deposit?A deposit is an amount of money paid to a vendor or a seller to secure goods or services. A deposit is a partial payment made to a business in advance of a larger purchase or delivery.
What is a subdivision?A subdivision is a housing development built on a portion of land that has been divided into multiple lots. The subdivider divides a large piece of land into smaller plots and sells each lot to individuals who are looking to build their own homes, thus creating a subdivision.
Max can get his deposit back within 30 days. This is because the subdivider has to refund the deposit within 30 days if the buyer cancels the reservation of the plot due to any reason, including the delay that the subdivider has experienced.
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Students in ms seiko's made a line plot of the number of books they read over the summer what two numbers of books read occur the least frequently enter your answers in the boxes in increasing order
The two numbers of books read that occur the least frequently are 7 and 15.
To determine which two numbers occur the least frequently, we need to count the number of tally marks for each number on the line plot. Based on the line plot, we can see that the number of tally marks for each number is as follows:
7: 1 tally mark
8: 2 tally marks
9: 3 tally marks
10: 4 tally marks
11: 2 tally marks
12: 4 tally marks
13: 3 tally marks
14: 2 tally marks
15: 1 tally mark
The two numbers that occur the least frequently are 7 and 15, as they each have only one tally mark.
Therefore, the answers to the question are: 7 in the first box and 15 in the second box.
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Students in ms seiko's made a line plot of the number of books they read over the summer.
books read
7 8 9 10 11 12 13 14 15
what two numbers of books read occur the least frequently enter your answers in the boxes in increasing order?
What are the perimeter and area of triangle XYZ ?
Answer:
B) P = 42; A = 84
Step-by-step explanation:
Perimeter:
You have two right triangles, so you need to find the third side length.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]5^{2}[/tex] + [tex]12^{2}[/tex] = [tex]c^{2}[/tex]
25 + 144 = [tex]c^{2}[/tex]
169 = [tex]c^{2}[/tex]
[tex]\sqrt{169}[/tex] = [tex]\sqrt{c^{2} }[/tex]
13 = c
The top right missing outside length is 13
We do the same thing to find the missing bottom outside.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]12^{2}[/tex] + [tex]9^{2}[/tex] = [tex]c^{2}[/tex]
144 + 81 = [tex]c^{2}[/tex]
225 = [tex]c^{2}[/tex]
[tex]\sqrt{225}[/tex] = [tex]\sqrt{c^{2} }[/tex]
15 = c
The perimeter of triangle xyz is 5 + 9 + 13 + 15 = 42 units
Area:
a = 1/2 bh
a= 1/2 (5 + 9) (12)
a = 1/2 (14)(12)
a = 84 [tex]units^{2}[/tex]
Helping in the name of Jesus.
Does the long division process end or does it continue indefinitely?
Answer:
It depends, sometimes it continues with a pattern in the decimal places, sometimes it ends.
Step-by-step explanation:
Marika Perez's gross biweekly pay is 2,768 her earnings to date for the year total 80,272 what amount is deducted from her paycheck for social security taxes if the rate is 6. 2% what amount is deducted for medicare which is taxed at 1. 45%?
a) The amount deducted from Marika Perez's paycheck for social security taxes is $171.62
b) The amount deducted for Medicare taxes is $40.10.
To calculate the amount of social security taxes deducted from Marika Perez's biweekly pay, we need to multiply her gross pay by the social security tax rate of 6.2%. Similarly, to calculate the amount of Medicare taxes deducted, we need to multiply her gross pay by the Medicare tax rate of 1.45%.
The calculations are as follows
Social Security tax deduction = gross biweekly pay x social security tax rate
= $2,768 x 0.062
= $171.62
Medicare tax deduction = gross biweekly pay x Medicare tax rate
= $2,768 x 0.0145
= $40.10
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how do you do this question, I can't seem to get the answer
Answer:
74π cm²
Step-by-step explanation:
You want to know the painted area of a cone 10 cm in diameter and 12 cm high that has an unpainted hole in the base that has a 4 cm radius.
Lateral areaThe area of the curved surface of the cone is found using the given formula. To use that formula, we need to know the slant height of the cone. The slant height is the hypotenuse of a right triangle that is 12 cm high and has a base of 5 cm:
l² = r² +h²
l = √(5² +12²) = √(25 +144) = √169
l = 13 . . . . cm
Then the lateral area is ...
LA = πrl = π(5 cm)(13 cm) = 65π cm²
Base areaThe painted area of the base is the difference between the areas of circles 5 cm in radius and 4 cm in radius:
A = π(r₁² - r₂²) = π((5 cm)² -(4 cm)²) = π(25 -16) cm² = 9π cm²
Total painted areaThe painted area is the sum of the areas of the curved surface and the donut base:
A = 65π cm² +9π cm² = 74π cm²
__
Additional comment
The radius of the base is half the diameter. If you slice the cone through its vertex and perpendicular to its base, the cross section is an isosceles triangle with height 12 cm and base 10 cm. The altitude of that triangle divides it into two congruent right triangles that have base 5 cm and height 12 cm.
You may recognize this as the {5, 12, 13} right triangle, which tells you the slant height is 13 cm. If not, you can use the Pythagorean theorem to find the slant height, as above.
El complemento de x es 3x por que ?
write three orderer pairs in the form (x,y) that could be produced by the function y=12x+3x
The three orderer pairs in the form (x,y) that could be produced by the function y=12x+3x are (0,0), (1,15) and (-2,-30).
what is orderer pair?
The given function is:
y = 12x + 3x
Simplifying, we get:
y = 15x
To find ordered pairs in the form (x,y) that could be produced by this function, we can choose different values of x and substitute them into the equation to find the corresponding value of y. Here are three examples:
1. When x = 0:
y = 15x = 15(0) = 0
Therefore, the ordered pair is (0,0).
2. When x = 1:
y = 15x = 15(1) = 15
Therefore, the ordered pair is (1,15).
3. When x = -2:
y = 15x = 15(-2) = -30
Therefore, the ordered pair is (-2,-30).
In general, we can choose any value of x and find the corresponding value of y using the given function to obtain an ordered pair in the form (x,y).
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A poker hand consists of 5 cards from a standard deck of 52. How many hands will include all red cards or all black cards?
Answer:There are two cases to consider: a hand that consists of all red cards and a hand that consists of all black cards.
Case 1: All red cards
There are 26 red cards in a standard deck of 52 cards. To form a 5-card hand consisting of all red cards, we need to choose 5 cards from the 26 red cards. The number of ways to do this is:
C(26, 5) = (26!)/(5!21!) = 65,780
Case 2: All black cards
Similar to the first case, there are 26 black cards in a standard deck of 52 cards. To form a 5-card hand consisting of all black cards, we need to choose 5 cards from the 26 black cards. The number of ways to do this is:
C(26, 5) = (26!)/(5!21!) = 65,780
Therefore, the total number of hands that include all red cards or all black cards is the sum of the two cases:
65,780 + 65,780 = 131,560
So there are 131,560 hands that consist of either all red cards or all black cards.
Step-by-step explanation:
Find the nth term for the sequence 45, 40, 35, 30
The nth term of the sequence 45, 40, 35, 30 is given by the formula a(n) = 50 - 5n.
To find the nth term of the sequence 45, 40, 35, 30, we need to first identify the pattern that governs the sequence. Here, we can see that each term is obtained by subtracting 5 from the previous term.
So, we can express the nth term of the sequence as:
a(n) = a(1) + (n-1)d
where a(1) is the first term of the sequence, d is the common difference between consecutive terms, and n is the index of the term we want to find.
In this case, a(1) = 45 and d = -5, since we are subtracting 5 from each term to get the next one. Substituting these values into the formula, we get:
a(n) = 45 + (n-1)(-5)
Simplifying, we have:
a(n) = 45 - 5(n-1)
Expanding the brackets, we get:
a(n) = 45 - 5n + 5
Simplifying further, we get:
a(n) = 50 - 5n
Therefore, the nth term of the sequence 45, 40, 35, 30 is given by the formula a(n) = 50 - 5n.
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