The answer to this question is 8
Which set of ordered pairs (x,y)(x,y) could represent a linear function?
A= {(-6, 6) (-3, 2) (0, -1) (3, -5)}
B= {(−9,5),(−1,3),(3,2),(7,1)}
C= {(−9,−3),(−3,0),(2,3),(8,6)}
D= {(−4,−5),(0,−2),(5,1),(9,4)}
The set of ordered pairs (x,y)(x,y) that could represent a linear function is A = {(-6, 6) (-3, 2) (0, -1) (3, -5)}.
What is a linear function?
The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
Here,
We have to find the set of ordered pairs (x,y)(x,y) that could represent a linear function.
Let's find out the slope of any two points in each option.
A = {(-6, 6) (-3, 2) (0, -1) (3, -5)}
Slope = (y₂ - y₁) /(x₂ - x₁)
= (2 - 6) /(-3 + 6) = -4/3
= (-5 +1) /(3 - 0) = -4/3
The slope of any two points is equal. So it represents a linear function.
Hence, the set of ordered pairs (x,y)(x,y) that could represent a linear function is A = {(-6, 6) (-3, 2) (0, -1) (3, -5)}.
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2.25 meters converted to centimeters
Answer: 225 centimeters
Step-by-step explanation:
every 1 meter is 100 centimeter
2.25 meters = 225 centimeters
Answer:
225 centimeters
Step-by-step explanation:
To convert meters to centimeters, you multiply the meters by 100 to get your centimeters.
Please help
A)Rewrite expression
B) determine constant percent rate of change
The answers are:
a. The new expression becomes 50.879(2.3)^(0.1x)
b. The constant percent change rate is 8.68%
c. A person in China ate 1611 kilocalories.
How to solveGiven:
f(x) = 50.879(2.3)^x
a. To rewrite the expression in years
One year is one-tenth of a decade, thus, the new expression becomes 50.879(2.3)^(0.1x)
b. The constant percent change rate:
Percent rate = new value - old value/old value x 100
Thus, if we put in the values,
55.298- 50.879/50.879 x 100
= 8.68%
c. To find the calories in kilo
g(0) = 1611(1.013)^6 = 1611
Therefore, a person in China ate 1611 kilocalories.
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90%; n = 10; σ is unknown; population appears to be normally distributed
With 90% confidence, we can estimate that the true population mean lies between 13.96 and 16.04.
If the population appears to be normally distributed, and σ (population standard deviation) is unknown, we can use a t-distribution to calculate the confidence interval.
To find the confidence interval, we need to use the following formula
CI = X' ± t_(α/2, n-1) × (s/√n)
Where X' is the sample mean, t_(α/2, n-1) is the critical t-value based on the desired confidence level (α) and the sample size (n-1), s is the sample standard deviation, and √n is the square root of the sample size.
Given that we have a confidence level of 90%, α = 0.10, and we need to find the critical t-value for a two-tailed test with 10-1=9 degrees of freedom. Using a t-distribution table, we find that the critical t-value is approximately 1.833.
Assuming that we have a sample mean of X' = 15 and a sample standard deviation of s = 2, we can now calculate the confidence interval
CI = 15 ± 1.833 × (2/√10)
CI = 15 ± 1.04
CI = (13.96, 16.04)
Therefore, with 90% confidence, we can estimate that the true population mean lies between 13.96 and 16.04.
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Need the answer to question 15
An equation in slope-intercept form for the perpendicular bisector of the segment with endpoints H (-3, 2) and K (7, -5) is y = -0.7x - 0.1.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-5 - 2)/(7 + 3)
Slope (m) = -7/10
Slope (m) = -0.7.
At data point (-3, 2) and a slope of -7/10, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = -7/10(x + 3)
y - 2 = -7x/10 - 21/10
y = -7x/10 - 21/10 + 2
y = -0.7x - 0.1
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Find the volume of the prism.
The volume is
cubic feet.
Answer: 8/125 or 0.064
Step-by-step explanation:
volume of a cube is w^3
(2/5)*(2/5)*(2/5)
8/125 or 0.064
What is the argument of z = StartFraction 1 Over 16 EndFraction minus StartFraction StartRoot 3 EndRoot Over 16 EndFraction i?
To find the argument of the complex number z = 1/16 - (sqrt(3)/16)i, we need to find the angle that the complex number forms with the positive real axis in the complex plane.
We can start by finding the magnitude of z, which is the distance between the origin and the point representing z in the complex plane:
|z| = sqrt( (1/16)^2 + (sqrt(3)/16)^2 )
= sqrt(1/256 + 3/256)
= sqrt(4/256)
= 1/4
Next, we can find the argument of z using the formula:
arg(z) = tan^(-1)(Im(z)/Re(z))
where Im(z) is the imaginary part of z, and Re(z) is the real part of z.
In this case, we have:
Re(z) = 1/16
Im(z) = -(sqrt(3)/16)
Therefore, we get:
arg(z) = tan^(-1)(Im(z)/Re(z))
= tan^(-1)(-(sqrt(3)/16)/(1/16))
= tan^(-1)(-sqrt(3))
= -60° (in degrees)
So, the argument of z is -60 degrees (or -π/3 radians).
Answer:
A
Step-by-step explanation:
The volume of a cylinder is given by the formula v - pi^h, where r is the radius of the cylinder and h is the height.
Which expression represents the volume of this cylinder?
The expression that represents the volume of the cylinder is:
V = π[tex]r^{2}[/tex]h
What is cylinder?
A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases. The cylinder can be thought of as a tube or a can. The lateral surface of the cylinder is formed by "unrolling" a rectangular shape along the circumference of the base.
There appears to be a typographical error in the given formula for the volume of a cylinder. The correct formula is:
V = π[tex]r^{2}[/tex]h
where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder.
Using this formula, the expression that represents the volume of the cylinder is:
V = π[tex]r^{2}[/tex]h
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Evaluate the expression when x = 7 (4x + 9) - 4(x - 1) + x use the answer choices in the diagram
Answer:
The answer is 20
Step-by-step explanation:
when x=7
(4x+9)-4(x-1)+x
(4(7)+9)-4(7-1)+7
28+9 -4(6)+7
37+7-24
44-24
=20
Kadeesha throws a ball up in the air. The graph below shows the height of the ball h in feet after t seconds. Height (in feet) 11 10 6 9 0.5 (0.75, 9) 1.5 (1.5, 0) 2.5
It takes 0.75 seconds to reach the highest position.
What is a graph?In a graph, the relationship between two sets of data or variables is represented visually, usually using lines or curves. In mathematics, a chart is a diagram or visual representation of facts or values that are ordered. The points on the graph are widely used to depict the relationship between two or more items.
Here, we have
Given: Kadeesha throws a ball up in the air. The graph below shows the height of the ball h in feet after t seconds.
The graph indicates that the peak is at (0.75, 9)
The x-axis displays the time in seconds, while the y-axis shows the height in feet.
Consequently, it takes 0.75 seconds to reach the highest position.
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When Jose had cable TV, he had 120 channels. He switched to satellite TV, and now he has 300 channels. What is the percent increase in the number of channels Jose has to watch? Round to the nearest percent.
The percent increase in the number of channels Jose has to watch is 150%.
What is percent?To find the percent increase in the number of channels Jose has to watch, we need to find the difference between the new number of channels and the old number of channels, divide that by the old number of channels, and then multiply by 100 to get the percentage increase.
The difference between the new and old number of channels is 300 - 120 = 180.
Dividing that by the old number of channels and multiplying by 100 gives us:
(180/120) x 100% = 150%
Therefore, the percent increase in the number of channels Jose has to watch is 150%. This means that Jose now has 150% more channels to watch than he did before he switched to satellite TV.
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What is the slope of the line?
-2
-1
1
2
Answer: positive 2
Step-by-step explanation:
HELP PLS EXPLAIN THISSSSS
Plugging in the values given into the expression, and simplifying, we would have our answer as: B. [tex]\frac{9}{25}[/tex]
How to Evaluate an Expression?To evaluate an expression, follow these steps:Identify the variables and constants in the expression.Substitute the given values for each variable in the expression.Simplify the expression until there are no more operations left.Given that, a = 5 and k = -2, substitute the values into the expression given and simplify:
[tex](\frac{3^2(5^{-2})}{3(5^{-1})} )^{-2}[/tex]
Simplify:
[tex](\frac{9 * \frac{1}{25} }{3* \frac{1}{5} } )^{-2}[/tex]
[tex](\frac{\frac{9}{25} }{\frac{3}{5} } )^{-2}\\\\(\frac{9}{25} * \frac{5}{3} } )^{-2}\\\\(\frac{3}{5} )^{-2}\\\\ = \frac{9}{25}[/tex]
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A store is giving out cards labeled 1 through 10 when customers enter the store. If the card is an even number, you get a 10% discount on your purchase that day. If the card is an odd number greater than 6, you get a 40% discount. Otherwise, you get a 25% discount. The table shows the results of 500 customers. What is the relative frequency for each discount? Use pencil and paper. If the manager of the store wants approximately half of the customers to receive the 25% discount, does this seem like an appropriate method? Explain.
Answer: We can use the data given in the table to calculate the relative frequency of each discount as follows:
- For a 10% discount: 160 customers received even-numbered cards, so the relative frequency is 160/500 = 0.32, or 32%.
- For a 25% discount: 222 customers received odd-numbered cards less than or equal to 6, so the relative frequency is 222/500 = 0.444, or 44.4%.
- For a 40% discount: 118 customers received odd-numbered cards greater than 6, so the relative frequency is 118/500 = 0.236, or 23.6%.
Regarding the question about whether this method will lead to approximately half of the customers receiving a 25% discount, we can see that the relative frequency for a 25% discount is actually higher than the desired 50%. Therefore, this method is not appropriate if the manager wants approximately half of the customers to receive a 25% discount.
To achieve this, the store can change the rule to offer a 25% discount for odd-numbered cards less than or equal to 5 and a 50% discount for odd-numbered cards greater than 5. This will result in the relative frequency for a 25% discount to be close to 50%.
Step-by-step explanation:
A rectangular plece of paper with length 28 cm and width 14 cm has two semicircles cut out of it, as shown below. Find the area of the paper that remains. Use the value 3.14 for 1, and do not round your answer. G ✓6 14 cm 0 00 H cm X 2023 McGraw Hill LLC As Rights Reserve
The area of the paper remains is 238.14 cm².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the paper that remains, we use the formula below.
Formula:
Area of the paper that remains(A) = Area of the rectangle(LW)-Area of the two semi circles [π(W/2)²]A = LW- [π(W/2)²]................ Equation 1Where:
L = Length of the rectangleW = Width of the rectangle = Diameter of the semi circleFrom the diagram in the question,
Given:
L = 28 cmW = 14 cmSubstitute these values into equation 1
A = (28×14)-[3.14(14/2)²A = 392-153.86A = 238.14 cm²Hence, the area is 238.14 cm².
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Last year, Big Bill's Department Store sold many pairs of shoes: 118,214 pairs of boots were sold; 37,092 more pairs of sandals than pairs of boots were sold; and 124,417 more pairs of sneakers than pairs of boots were sold.
How many pairs of shoes were sold last year?
Answer:279,723
Step-by-step explanation: 124,417+118,214+37,092=279,723
in a recent basketball game, shenille attempted only three-point shots and two-point shots. she was successful on 20% of her three-point shots and 30% of her two-point shots. shenille attempted 30 shots. how many points did she score?(2013 amc 12a
The probability of a score for a recent basketball game, shenille attempted only three-point shots and two-point shots is 18 points in the game. The answer is Option B.
Let x be the number of three-point shots and y be the number of two-point shots attempted by Shenille.
Then, we have:
x + y = 30 (total number of shots attempted)
Let's solve for one of the variables. For example, we can solve for x by subtracting y from both sides of the equation:
x = 30 - y
Now, we can express Shenille's points in terms of x and y:
Points = 3x + 2y
Substituting x = 30 - y, we get:
Points = 3(30 - y) + 2y
Points = 90 - y
Shenille's success rate for three-point shots is 20%, so the number of successful three-point shots she made is 0.2x. Similarly, the number of successful two-point shots she made is 0.3y.
Total points scored = (0.2x)(3) + (0.3y)(2)
Substituting x = 30 - y, we get:
Total points scored = (0.2(30 - y))(3) + (0.3y)(2
Total points scored = 18 + 0.4y
Now we need to maximize the total points scored by Shenille. Since she attempted 30 shots in total, we have:
y = 30 - x
Substituting this into the equation for total points, we get:
Total points scored = 18 + 0.4(30 - x)
Total points scored = 30 - 0.4x
This is a linear function, which is maximized at its endpoint. The maximum value of this function occurs at x = 0, which means Shenille attempted all two-point shots. In this case, y = 30, and the total points scored would be:
Total points scored = 0 + 0.3(30)(2)
Total points scored = 18
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The question is -
In a recent basketball game, Shenille attempted only three-point shots and two-point shots. She was successful on 20% of her three-point shots and 30% of her two-point shots. Shenille attempted 30 shots. How many points did she score?
(A) 12
(B) 18
(C) 24
(D) 30
(E) 36
From a horizontal distance of 80.0 m, the angle to the top of a flagpole is 18°. Calculate the height of the flagpole to the nearest tenth of a meter.
1. 24.7 meters
2. 76.1 meters
3. 26.0 meters
4. 25.3 meters
Answer:
The figure is omitted--please sketch it to confirm my answer.
Set your calculator to degree mode.
Let h be the height of the flagpole.
[tex] \tan(18) = \frac{h}{80} [/tex]
[tex]h = 80 \tan(18) = 25.994[/tex]
The height of the flagpole is approximately 26.0 meters. #3 is correct.
a slide caliper has 32 divisions per inch and a vernier of 8 divisions per major division. for this instrument the smallest resolution and uncertainty are:
The smallest resolution for this instrument is 1/256 inches.
This is also the instrument's uncertainty, as it represents the smallest measurable increment.
Let's first understand the terms mentioned:
Slide caliper:
A measuring instrument with a main scale and a vernier scale for taking precise measurements.
Divisions per inch:
The number of equal divisions on the main scale in one inch.
Vernier:
A short auxiliary scale that slides along the main scale, allowing for more precise readings.
Divisions per major division:
The number of equal divisions on the vernier scale that correspond to one division on the main scale.
Now, let's determine the smallest resolution and uncertainty for this instrument.
Calculate the main scale resolution
Main scale resolution = 1 inch / 32 divisions per inch = 1/32 inches
Calculate the vernier scale resolution
Vernier scale resolution = Main scale resolution / Vernier divisions per major division = (1/32 inches) / 8 = 1/256 inches.
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A circular garden is surrounded by a fence that is 47. 1 feet long. The surface soil Of the entire garden within the fencing needs to be turned prior to planting. Calculate the square feet of soil that must be turned. Use 3. 14 as a substitute for a. Show your work
The required square feet of soil that must be turned in the circular garden is 176.625 square feet.
A circular garden is surrounded by a fence that is 47.1 feet long.
That is, circumference of a circle = 2 π r = 2(3.14) r = 6.28r (in feet)
where, r represents the radius of the circular garden in feet.
Thus,
6.28r = 47.1
⇒ r=7.5 feet
Area of the circular garden is measured by the formula as,
= π r^2 square unit
= (3.14)( 7.5^2) square feet
= 176.625 square feet
Hence, the required square feet of soil that must be turned in the circular garden is 176.625 square feet.
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6. ____ tales and _____ tales
folk tales are storues with no known creator. they were originally passed down from one generation to another by word of mouth.
fairytales were often created to teach children behavior in an entertaining way.
what is the blank fictions/nonfictions?
The complete statement is folk tales and fairy tales
Both folk tales and fairy tales are types of fiction because they are imaginative stories that are not based on factual events or characters.
Explaining fictions and nonfictions?Folk tales
Folk tales are stories with no known creator. They were originally passed down from one generation to another by word of mouth. Folk tales are a type of traditional literature that is deeply rooted in the culture of a particular region or community.
They often feature supernatural elements, and their origins can be traced back many centuries.
Because they were passed down orally, different versions of the same tale may have developed in different regions, with variations in characters, plot, and theme.
Fairy tales
Fairy tales were often created to teach children behavior in an entertaining way. Fairy tales are a type of story that typically features magical creatures or events and often have a moral or lesson to teach. They were originally intended for both adults and children and were used as a way to teach moral values, societal norms, and important life lessons in an entertaining way.
The fairy tale genre has evolved over time, and modern fairy tales may have different themes and messages than traditional ones.
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As a nurse working in a hospital one of the jobs is to give appropriate doses of medicine
before surgery so the patient doesn't wake up during surgery. 4cc of this particular medicine is
meant for a 180lb man, what would be the correct dosage for a 145 lb. woman?
Answer:
the correct dosage of the medicine for a 145 lb. woman would be approximately 3.22 cc
Step-by-step explanation:
To calculate the correct dosage of the medicine for a 145 lb. woman, we can use the following formula:
dosage = (weight of patient / weight of reference patient) x reference dosage
where the weight of the reference patient is 180 lb. and the reference dosage is 4 cc.
Plugging in the given values, we get:
dosage = (145 / 180) x 4
= 3.22 cc (rounded to two decimal places)
Therefore, the correct dosage of the medicine for a 145 lb. woman would be approximately 3.22 cc. However, it's important to note that dosages of medications should only be determined by a qualified medical professional based on a number of factors, including the patient's weight, medical history, and current condition.
find the missing value of x,y and z
Answer:
x=60
y=30
z=64
Step-by-step explanation:
By using triangle sum theorem, 84+36+x=180
You then isolate the variable, resulting in x=60
x and y are complementary, therefore, x+y=90
Since x is already known, y must be isolated, resulting in 60+y=90 then y=30
By using triangle sum theorem, 86+y+z=180
Since y is already known, z must be isolated, resulting in 86+30+z=180 then z=64
If r=0.5 m, A = ???
(Use the r key.)
The calculated value of the angular velocity of the object is 2 rad/s.
Calculating the angular velocityThe angular velocity, denoted by the Greek letter omega (ω), represents the rate of change of the angle with respect to time.
For an object moving in a circular path, the angular velocity is related to the linear speed and the radius of the circle by the equation:
ω = v/r
where v is the linear speed and r is the radius.
In this case, the radius is 0.5m and the speed is 1ms−1. Thus, the angular velocity is:
ω = v/r = 1/0.5 = 2 radians per second (rad/s)
Therefore, the angular velocity of the object is 2 rad/s.
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Complete question
An object moves in a circular path of radius 0.5m with a speed of 1ms−1. What is its angular velocity (A)?
If r = 0.5 m, A = ???
What is the volume of 1 hemisphere created by cutting this sphere exactly in half?
Answer:
B. 1152π cm^3
Step-by-step explanation:
I'm 99.9% sure that this is correct!
I'm really really sorry if it's not! please tell me if I'm wrong!
James decided to share rocks collection. He gave 13 to Bill, 18 to lill, and 15 to mark. He had 32 left. How many rocks did he have to start with
James started with 78 rocks, as he gave away 46 rocks and had 32 rocks left.
The problem states that James gave away 13 rocks to Bill, 18 rocks to Lill, and 15 rocks to Mark. Therefore, the total number of rocks he gave away is the sum of these three amounts
13 + 18 + 15 = 46
This means that James had 46 fewer rocks after giving them away. The problem also states that he had 32 rocks left after giving some away. We can use this information to figure out how many rocks he started with by adding the number of rocks he had left to the number he gave away
46 + 32 = 78
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Please help me how to solve this step by step and the answer PLEASE AND ASAP
Answer:
7
Step-by-step explanation:
Area of a triangle is the height times the base divided by two. This triangle does not have a height that would work for this equation, so we will make a 'ghost' triangle of sorts to help us. I have drawn this in with dotted lines.
We know total height (2.8), and so we can make 'fake' right triangle (look at picture) and attatch it to the real traingle. This way, we have a height that works for our triangle equation. But by doing so, we need to find the new base of our new triangle. We can't use 5. This is done with Pythagorean theorem, where we find the base of our 'ghost' triangle, which is 1.01. The new base, then, is 5+1.01= 6.01.
With our base and height we can solve for total area.
2.8*(6.01)/2=8.507
BUT, this is only for when we add the ghost triangle. THIS ISN'T REAL. We need to get rid of the fake triangle area to find the real area.
The ghost triangle area is 1.507.
So, 8.507-1.507= 7
Circle A has radius AB and Circle X has radius XY. Points A and X are distinct points. Complete the statements below describing how to prove that the circles are similar.
Translate the center of circle A onto point __ __.
Then dilate the image of circle A about its center by a scale factor of __ __.
Translate the center of circle A onto point X.Then dilate the image of circle A about its center by a scale factor of XY/AB.
What is circle?A circle is a geometric shape consisting of points in a plane that are equidistant from a fixed point called the center, forming a closed curve.
According to the given information :
To prove that circles A and X are similar, we can follow the steps below:
1) Translate the center of circle A onto point X. This can be done by moving the center of circle A to point X while keeping the radius AB the same.
2) Dilate the image of circle A about its center by a scale factor of XY/AB. This means that we multiply the radius of the image of circle A by XY/AB. The result is a new circle that is similar to circle A and has the same center as circle X.
To summarize, the statements to complete are:
Translate the center of circle A onto point X.
Then dilate the image of circle A about its cent er by a scale factor of XY/AB.
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Translate the center of circle A onto point X.Then dilate the image of circle A about its center by a scale factor of XY/AB.
What is circle?
A circle is a geometric shape consisting of points in a plane that are equidistant from a fixed point called the center, forming a closed curve.
According to the given information :
To prove that circles A and X are similar, we can follow the steps below:
1) Translate the center of circle A onto point X. This can be done by moving the center of circle A to point X while keeping the radius AB the same.
2) Dilate the image of circle A about its center by a scale factor of XY/AB. This means that we multiply the radius of the image of circle A by XY/AB. The result is a new circle that is similar to circle A and has the same center as circle X.
To summarize, the statements to complete are:
Translate the center of circle A onto point X.
Then dilate the image of circle A about its center by a scale factor of XY/AB.
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call a positive integer kinda-prime if it has a prime number of positive integer divisors. if there are $168$ prime numbers less than $1000$, how many kinda-prime positive integers are there less than $1000$?
There are 173 kinda-prime positive integer less than 1000.
To find the number of kinda-prime positive integer less than 1000, we'll follow these steps:
1. Understand the definition of a kinda-prime number: A positive integer is kinda-prime if it has a prime number of positive integer divisors.
2. Determine the number of prime numbers less than 1000: There are 168 prime numbers less than 1000, as given.
3. Determine the possible prime number of divisors: Since 168 is not too large, we only need to consider 2 and 3 as possible prime numbers of divisors for a kinda-prime number.
4. Analyze the cases:
Case 1: Kinda-prime numbers with 2 divisors (prime numbers)
All prime numbers have exactly 2 divisors (1 and itself). Thus, all 168 prime numbers less than 1000 are kinda-prime.
Case 2: Kinda-prime numbers with 3 divisors
Let N be a kinda-prime number with 3 divisors. Then, N = p^2 for some prime number p. To find the suitable prime numbers p, we need[tex]p^2 < 1000[/tex]. The prime numbers that meet this condition are 2, 3, 5, 7, and 11 (since 13^2 = 169 > 1000). Therefore, there are 5 additional kinda-prime numbers ([tex]2^2, 3^2, 5^2, 7^2, and 11^2[/tex]).
5. Add the total number of kinda-prime numbers from both cases: 168 + 5 = 173.
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[tex]$(\pi(1000)-1)+11=\boxed{177}$[/tex] "kind a-prime" positive integers less than $1000$.
Let [tex]$n$[/tex] be a positive integer with[tex]$k$[/tex] positive integer divisors.
If [tex]$k$[/tex] is prime, then.
[tex]$n$[/tex] is a "kind a-prime" integer.
[tex]$k$[/tex] must be of the form.
[tex]$k=p$[/tex] or [tex]$k=p^2$[/tex] for some prime [tex]$p$[/tex].
If [tex]$k=p$[/tex], then [tex]$n$[/tex] must be of the form.
[tex]$p^{p-1}$[/tex] for some prime [tex]$p$[/tex]. Since [tex]$p < 1000$[/tex], there are.
[tex]$\pi(1000)$[/tex]possible values of [tex]$p$[/tex].
[tex]$p=2$[/tex] gives [tex]$2^1$[/tex], which is not prime, so we have to subtract.
[tex]$1$[/tex] from [tex]$\pi(1000)$[/tex] to get the number of possible.
[tex]$p$[/tex].
[tex]$\pi(1000)-1$[/tex] values of [tex]$p$[/tex] that give a "kind a-prime" integer of this form.
If [tex]$k=p^2$[/tex], then [tex]$n$[/tex] must be of the form.
[tex]$p^{p^2-1}$[/tex] for some prime[tex]$p$[/tex].
There are.
[tex]$\pi(31)=11$[/tex] primes less than [tex]$31$[/tex], and each of them gives a different "kind a-prime" integer of this form.
Since [tex]$31^5 > 1000$[/tex], no primes larger than [tex]$31$[/tex]can be used to form a "kind a-prime" integer of this form.
[tex]$11$[/tex] possible values of [tex]$p$[/tex] that give a "kind a-prime" integer of this form.
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There are 10 councillors and 12 planning department staff available to serve on a committee to look into re- establishing two way traffic on the streets of St. Catharines. If the committee will consist of 3 councillors and either 1 or 2 planning staff, how many different committees could the council choose?
The council could choose 14,040 different committees.
To form a committee, we need to choose 3 councillors out of 10 and either 1 or 2 planning staff out of 12.
Number of ways to choose 3 councillors out of 10 = 10C3 = (1098)/(321) = 120
Number of ways to choose 1 planning staff out of 12 = 12C1 = 12
Number of ways to choose 2 planning staff out of 12 = 12C2 = (1211)/(21) = 66
Therefore, the total number of different committees that the council could choose is the sum of the number of ways to choose 3 councillors and either 1 or 2 planning staff:
Total number of committees = (Number of ways to choose 3 councillors) x (Number of ways to choose 1 planning staff) + (Number of ways to choose 3 councillors) x (Number of ways to choose 2 planning staff)
Total number of committees = 120 x 12 + 120 x 66
Total number of committees = 14,040
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