The prime factors of 45 are 3 and 5.
Prime factors are the prime numbers that, when multiplied together, result in a given composite number.
To find the prime factors of 45, we can start by dividing it by the smallest prime number, which is 2.
45 ÷ 2 = 22 with a remainder of 1
Since the remainder is not 0, we move on to the next smallest prime number, which is 3.
45 ÷ 3 = 15
15 is divisible by 3, so we can divide it again
15 ÷ 3 = 5
Now, we have obtained the prime factorization of 45
45 = 3 × 3 × 5
Prime factors = 3 and 5
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I have solved the question in general, as the given question is incomplete.
The complete question is:
Find the prime factors of 45.
WILL GIVE BRAINLIEST
19) x = -12
20) r = -8
21) m = 10
22) r = 2
23) x = -16
24) x =6
25) x = -10
26) x = -20
27) r = -23
28) x = -52
A one-question survey is to be distributed to a random sample of 1500 adults in Ohio. The question asks if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let denote the proportion of adults in the sample who say they support the increase. Suppose that 40% of all adults in Ohio support the increase. What is the mean, , of the sampling distribution of ?
a.
40% ± 5%
b.
6%
c.
5%
d.
0.40
They support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let denote the proportion of adults in the sample who say they support the increase. Suppose that 40% of all adults in Ohio support the increase. the correct answer is (d) 0.40.
Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data
set. The mean, median and mode are the three commonly used measures of central tendency.
To calculate the mean, we need to add the total values given in a datasheet and divide the sum by the total number of
values.
The mean, μ, of the sampling distribution of p can be found using the formula
μ = p,
where p is the proportion of adults in the entire population who support the increase.
In this case, 40% of all adults in Ohio support the increase, so p = 0.40.
Therefore, the mean of the sampling distribution of p is:
μ = 0.40
So the correct answer is (d) 0.40.
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T/F the square root of a number will always have two outcomes one is positive and the other is negative.
we have only one outcome that is neither positive nor negative, then the statement is false.
What is square root?
A value known as the square root of a number is one that, when multiplied by itself, yields the original number. An alternative to square rooting a number is to use it. Therefore, the concepts of squares and square roots are connected. The original number is equal to the square root of any integer, which is equivalent to a number.
Let's assume that m is an integer that is positive, such that (m.m) = (m2) = m.
This seems to be true because:
-2*-2 = 2*2 = 4
So √4 = 2 and -2
But particularly the square root of zero is:
√0 = 0
So here we have only one outcome that is neither positive nor negative, then the statement is false.
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How can I solve for t?
Answer:
This is not possible with 2 equal symbols
Multiply −3x2(6x2 + 2x − 3).
Answer:
hope this will help you.
Which best states George Washington’s connection to the 1787 Constitutional Convention? He was an honorary delegate because he had led the Continental army. He delivered the new Constitution to Great Britain as an ambassador. He led the Constitutional Convention because he was respected throughout the nation. He led the Constitutional Convention because he was known for his wisd
Answer:
he led the constitutional convention because he was respected throughout the nation
Step-by-step explanation:
The best states George Washington’s connection to the 1787 Constitutional Convention is: He led the Constitutional Convention because he was respected throughout the nation.
What is Constitutional Convention ?The Philadelphia Convention is also known as the Constitutional Convention took place between May 14 and September 17, 1787, to resolve the problems of the United States government.
The delegate elected to George Washington to led the convention, the presence of Washington a national hero respected by all helped to legitimize the convention. This result of the Convention was the Constitution of the United States of America.
The best states George Washington’s connection to the 1787 Constitutional Convention is: He led the Constitutional Convention because he was respected throughout the nation.
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Write the slope-intercept form y = mx + b for the line passing through the points (0,11) and (5,4).
y = -7/5x +11
Y= -5/7x + 11
y = 5/7x +11
y = 5/7x +11
Answer:
A
Step-by-step explanation:
graphing calc
An rna sequence includes 21 bases. What is the maximum number of amino acids for which this sequence could code?.
RNA has adenine, uracil, guanine, and cytosine bases that get represented in a three-letter code called codons. As if RNA sequence includes 21 bases it means it can code for 7 amino acids.
What are amino acids?
Amino acids are the building blocks of protein that combine to form a polypeptide chain.
These are coded by codons that are formed by the combination of 3 bases of RNA.
As in the RNA sequence with 21 bases, 7 amino acids will get coded.
Thus, the maximum number of amino acids for which this sequence could code is 7
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Help!!!! Which represents the base of the cone
Answer:
the first option
Step-by-step explanation:
the 6 represents the diameter of the base
the 4 represents the height of the cone
if it needs a radius to solve the problem, divide the diameter by 2 (aka half of the diameter)
pls help out, what is the slope?
Answer:
Slope is 1 unit
I think so as the line is accurately tangential to the circumcircle by diagonal of a unit graph and hence diameter coincides with diagonal.
Solve the system of equations by elimination. Show all work neatly on your work page. Checking your answer is wise. :)
6x + 3y = -12
-6x - 2y = 4
Answer:
x=2
y=-8
Step-by-step explanation:
6x+3y=-12
-6x-2y=4
3y=-12-6x
y=(-12-6x)/3
y=-4-2x
substitute y
-6x-2(-4-2x)=4
-6x+8+4x=4
-2x=-4
x=2
6(2)+3y=-12
12+3y=-12
3y=-24
y=-8
check:
6(2)+3(-8)=-12
12-24=-12
-6(2)-2(-8)=4
-12=16=4
Six different names were put into a hat. A name is chosen 116 times and the name Grace is chosen 15 times. What is the experimental probability of the name Grace being chosen? What is the theoretical probability of the name Grace being chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
Answer:
Try this!!!
Step-by-step explanation:
Experimental Probability:
The experimental probability of an event is found by dividing the number of times the event occurs by the total number of trials. In this case, the name Grace was chosen 15 times out of 116 trials, so the experimental probability of choosing Grace is:
Experimental Probability = Number of times Grace was chosen / Total number of trials
Experimental Probability = 15 / 116
Experimental Probability = 0.1293 or approximately 12.93%
Theoretical Probability:
The theoretical probability of an event is found by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, there are six names in the hat, so the probability of choosing Grace is:
Theoretical Probability = Number of favorable outcomes / Total number of possible outcomes
Theoretical Probability = 1 / 6
Theoretical Probability = 0.1667 or approximately 16.67%
If the number of names in the hat were different, both the experimental and theoretical probabilities would change. For example, if there were only three names in the hat, the theoretical probability of choosing Grace would be 1/3 or approximately 33.33%. The experimental probability would also change based on the number of times Grace was chosen out of the total number of trials. As the number of names in the hat increases, the theoretical probability of choosing Grace decreases, and the experimental probability becomes more accurate as the number of trials increases.
To make a specific hair dye a hairstylist uses a ratio of one and 1/8 oz of red tone 3/4 oz of Gray tone and 5/8 oz of Brown tone if the stylist needs to make 20 oz of dye how much of each dye color is needed?
Answer: To make 20 oz of hair dye, the hairstylist needs to use 1 and 1/8 oz of red tone, 3/4 oz of gray tone and 5/8 oz of brown tone.
We can use proportionality to figure out how much of each dye color is needed.
Let's call the amount of red dye needed x, the amount of gray dye needed y and the amount of brown dye needed z.
According to the proportionality, we can write the following equation:
(1 + 1/8)x + (3/4)y + (5/8)z = 20
To find the amount of each dye color needed, we can solve this equation for x, y and z.
First, we can clear the fractions by multiplying all terms by 8:
(8 + 1)x + (6)y + (5)z = 160
Now we can solve for x:
9x + 6y + 5z = 160
x = (160 - 6y - 5z)/9
Similarly, we can solve for y and z:
y = (160 - 9x - 5z)/6
z = (160 - 9x - 6y)/5
Now we can substitute the desired amount of 20 oz into the equation and solve for x, y and z
Step-by-step explanation:
how to find the x component of this vector
12.1 meters 48.4 degrees
The magnitude of the x-component of this vector is 9.05m.
The angle of inclination of the vector is calculated as;
θ = 90 ⁰ - 48.4 ⁰
θ = 41.6 ⁰
The magnitude of the x-component of the vector is calculated as;
Vx = 12.1 m x cos ( 41.6 )
Vx = 9.05 m
A vector can be represented by an ordered set of numbers, called components, that indicate the magnitude and direction of the vector in a particular coordinate system. The components of a vector can be added or subtracted using vector addition and subtraction, and multiplied by a scalar (a real number) using scalar multiplication.
Vectors can be visualized as arrows in a two- or three-dimensional space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can also be represented as matrices, which can be used to perform various operations on vectors, such as dot product and cross product.
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Complete Question:-
What is the probability that the restaurant is located in a city with a population over 100,000, given that it is located in the southwestern United States
The probability that the restaurant is located in a city with a population over 100,000, given that it is located in the southwestern United States, is approximately 0.267 or 26.7%.
To find the probability that the restaurant is located in a city with a population over 100,000, given that it is located in the southwestern United States, we need to consider the percentage distribution provided in the table.
From the table, we can see that the probability of selecting a restaurant from the southwestern United States (SW) is 3%. Within the southwestern region, the probability of selecting a restaurant in a city with a population over 100,000 is given as 8%.
To calculate the conditional probability, we use the formula:
Probability (A|B) = Probability (A ∩ B) / Probability (B),
where A is the event of selecting a restaurant in a city with a population over 100,000 and B is the event of selecting a restaurant from the southwestern United States.
Applying the formula, we have:
Probability (A|B) = (Probability of selecting a restaurant in the southwestern United States with a population over 100,000) / (Probability of selecting a restaurant from the southwestern United States).
Probability (A|B) = 8% / 3%.
Simplifying, we find:
Probability (A|B) ≈ 0.267.
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Note the full question is 1) A fast-food restaurant chain with 700 outlets in the United States has recorded the geographic location of its restaurants in the accompanying table of percentages. One restaurant is to be chosen at random from the 700 to test market a new chicken sandwich. Region <10,000 Population of City 10,000 - 100,000 >100,000 NE 6% 15% 20% SE 6% 1% 4% SW 3% 12% 8% NW 0% 5% 20% What is the probability that the restaurant is located in a city with a population over 100,000, given that it is located in the southwestern United States?
The graph of the function f(x) = (x – 4)(x + 1) is shown below.
On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1.75, negative 6.2), and goes through (4, 0).
Which statement about the function is true?
The function is increasing for all real values of x where
x < 0.
The function is increasing for all real values of x where
x < –1 and where x > 4.
The function is decreasing for all real values of x where
–1 < x < 4.
The function is decreasing for all real values of x where
x < 1.5.
A scale model of a large, three-dimensional “real world” object uses a scale of 0.5 in. = 50 ft.
Fred was only able to measure the model using metric units. He measured the length of the model as 372.5 mm.
Fred knows that 1 inch = 2.54 cm and that 1 cm = 10 mm.
What is the approximate length of the actual “real world” object?
A.
244.3 ft
B.
122.2 ft
C.
2,932 ft
D.
1,467 ft
The approximate length of the actual object is 1465 ft, which is closest to option D.
What is a scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
First, let's convert the length of the model from millimeters to inches:
372.5 mm = 372.5/10 cm = 37.25/2.54 in ≈ 14.65 in
Next, we can use the scale of the model to find the length of the actual object in feet:
0.5 in. = 50 ft.
So, 1 in. = 100 ft.
Therefore, the length of the actual object in feet is:
14.65 in x (100 ft/in) = 1465 ft
Therefore, the closest length is 1467 feet.
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71. Lesson 3
Warm-Up
Determine the value of x that makes each equation true.
Equation
Value of x
2 + x=1
2.x=1
* -x=1
x. 11 = 1
4 3/4 - 6/4 = ? I need help .
The solution to the mixed fraction 4 3/4 - 6/4 is 3 1/4
What is a mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
To solve the question
Convert the mixed fractions into improper fractions
4 3/4 - 6/4
= 19/4 -6/4
we can simplify, since the denominators are the same
19-6/4
=13/4
converting to mixed fractions, we have
3 1/4
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"1. In which of the following categories of problems an 8-puzzle
problem can be placed? Discuss with appropriate reasoning.
Pathfinding problems
State finding problems
Decomposable problems
Pre"
The 8-puzzle problem can be categorized as a "Pathfinding problem."
The 8-puzzle is a classic problem in artificial intelligence and computer science. It involves a 3x3 grid with eight numbered tiles and one empty space. The objective is to rearrange the tiles from an initial configuration to a goal configuration by sliding them into the empty space.
The reason why the 8-puzzle problem is classified as a pathfinding problem is that it involves finding a sequence of moves or actions to reach a desired state or goal. In this case, the desired state is the goal configuration of the puzzle. The problem requires determining the optimal sequence of moves that lead to the goal state while considering the constraints and limitations of the puzzle.
Pathfinding problems involve finding the shortest or optimal path from a starting point to a goal or destination. In the 8-puzzle problem, the empty space serves as the movable "agent" that can slide adjacent tiles. The objective is to find the shortest sequence of moves or actions to transform the initial configuration into the goal configuration, effectively finding a path to the solution.
Therefore, due to its nature of finding an optimal sequence of moves to reach a goal state, the 8-puzzle problem can be categorized as a pathfinding problem.
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Somebody tell me the answer to this please
Answer:
its (0, 3) or (3, 0)
Step-by-step explanation:
its not A. or D.
Answer:
\((3,0)\)
Step-by-step explanation:
The x-intercept(s) of a function is the point(s) where the function intersects the x-axis, or the horizontal axis. If we look at the graph, we see that the function intersects the x-axis when \(x=3\) (we know this because \(3\) is directly in between \(2\) and \(4\)) and \(y=0\), so the answer is \((3,0)\). Hope this helps!
What is the forecast for May using a five-month moving average?(Round answer to the nearest whole number.) Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47
A. 43 B. 47 C. 52 D. 38 E. 39
The forecast for May using a five-month moving average is 39 (Option E).
Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.
According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47
We have to add the sales of these five months, which gives:
27 + 40 + 42 + 41 + 47 = 197
To find the moving average for May, we divide this sum by 5:
197 / 5 = 39.4
Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.
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a circle has radius of 5cm
(a) work out circumference of the circle
(b) work out area of the circle
Answer:
A) 31.4
B)78.5
Step-by-step explanation:
A)2(pi)(r)
2*3.14*5=31.4
B)(pi)(r^2)
3.14*5^2=78.5
1. You want to plant a flower garden in your yard so that you can make a beautiful bouquet to put on the alter at church for Easter Sunday services. There are two types of flowers that you are going to be planting. You will be planting some tulips and daffodils. At the store tulips come in packs of 4 and daffodils come in packs of 6.
a.What is the least amount of packs of daffodils and tulips you would need to buy to have the same amount of each?
b.How many should you have of each kind of flower?
2. Each pack of tulips costs $2.25 and each pack of daffodils cost $2.75. From the previous problem, you know how many packs of each you will need. The sales tax is 5.5%.
a.How much tax will you be paying for all the flowers, to the nearest cent?
b.How much total will you be paying for all flowers, to the nearest cent?
3. You remember that you have a discount coupon for $3.00 off your total purchase before tax.
a. How much did the flowers cost with the discount including tax (Round to the nearest penny)?
b.How much money did you save with the coupon including tax?
Answer:
1.a. The least common multiple of 4 and 6 is 12, so you would need to buy 3 packs of tulips and 2 packs of daffodils.
b. You will have 12 tulips and 12 daffodils.
2.a. The sales tax is 5.5%, so you will be paying $0.61 in tax for the tulips and $0.69 in tax for the daffodils. This means you will be paying a total of $1.30 in tax for all the flowers.
b. The total cost of the flowers is $2.25 x 3 + $2.75 x 2 = $11.50. With the tax, the total cost is $11.50 + $1.30 = $12.80.
3.a. With the $3.00 discount, the total cost of the flowers is $12.80 - $3.00 = $9.80. With the tax, the total cost is $9.80 + $0.54 = $10.34.
b. You saved $3.00 with the coupon before tax, and $0.54 with the coupon after tax. This means you saved a total of $3.54 with the coupon.
Which table represents a nonlinear function?
Answer:
I think D though I'm not sure
Step-by-step explanation:
Last night, Jasmine and her family went out for dinner. The questions below came up on their way to the restaurant or during the meal. Decide whether or not each question is a statistical question. Select all that apply.
●How far are we from the restaurant?
●How long will it be until we get there? ●Would you rather have burgers or pizza?
●How much should we leave for the tip? ●What was the most frequently ordered dish in the restaurant this evening?
●Did you like the pizza tonight?
●Which table's bill was the highest?
●How many people were sitting at each table this evening?
A statistical question is a question where the data collected can vary.
Ex. Statistical - "How old are the students in my class?" The data can vary based on which student you ask.
The following questions are statistical:
●Would you rather have burgers or pizza?
●How much should we leave for the tip?
●Did you like the pizza tonight?
●How many people were sitting at each table this evening?
These questions can vary based on who you ask or where you look
I hope this was helpful! =)
what assumptions are made to obtain the continuity equation in the form: a1v1=a2v2?
The assumptions are made to obtain the continuity equation in the form a₁v₁ = a₂v₂ are:
1. Incompressible Fluid
2. Steady Flow
3. Inviscid Flow
4. One-Dimensional Flow
5. Constant Density
To obtain the continuity equation in the form a₁v₁ = a₂v₂, the following assumptions are made:
1. Incompressible Fluid: The fluid flowing through the system is assumed to be incompressible, meaning its density remains constant throughout the flow.
2. Steady Flow: The flow of the fluid is assumed to be steady, meaning the flow parameters (such as velocity and cross-sectional area) do not change with time.
3. Inviscid Flow: The flow is assumed to be inviscid, neglecting any viscous effects such as friction between the fluid layers.
4. One-Dimensional Flow: The flow is assumed to be one-dimensional, meaning the fluid moves in a single direction along a streamline.
5. Constant Density: The fluid density is assumed to be constant, allowing the simplification of the equation.
Under these assumptions, the continuity equation, which is based on the principle of mass conservation, can be expressed as a₁v₁ = a₂v₂, where a₁ and a₂ are the cross-sectional areas of the fluid at two different points in the flow, and v₁ and v₂ are the corresponding velocities at those points. This equation represents the conservation of mass, stating that the mass flow rate remains constant in an incompressible flow.
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a virus is accidentally released from a cdc lab. the virus infects everyone in a 24 mile radius from the cdc lab where it was released. if the population density for the area is 18.8 residents per square mile, to the nearest hundred, how many people were infected?
If the population density for the area is 18.8 residents per square mile, to the nearest hundred, approximately 34,000 residents would be infected.
When a virus is accidentally released from a CDC lab, and it infects everyone within a 24-mile radius from the CDC lab, then if the population density for the area is 18.8 residents per square mile, to the nearest hundred, how many people were infected.
The number of people infected within the 24-mile radius from the CDC lab is calculated as follows:
The area of a circle with a radius of 24 miles is A = πr²,
which is A = π(24²) = 1,809.56 square miles, and the population density for the area is 18.8 residents per square mile.
Therefore, the number of people infected is calculated by multiplying the area by the population density:
Residents infected = area x population density
= 1,809.56 x 18.8 ≈ 34,037.
Approximating to the nearest hundred yields 34,000.
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Consider the periodic function obtained by replicating the following function over intervals of length 10:5(x)=x² ; 0
To obtain the periodic function by replicating this over intervals of length 10, we can write the extended function as f(x) = 5((x mod 10)^2) and as the function 5(x) = x² is even, its periodic extension f(x) is also even, meaning it is symmetric about the y-axis.
Since the period is 10, we can write the extended function as:
f(x) = 5(\((x mod 10)^2\)),
where "mod" denotes the modulo operator, which gives the remainder after division.
In other words, for any value of x, we first find its remainder when divided by 10 (i.e., the value of x "wrapped" around the interval [0,10]). Then we evaluate the original function 5(x) = x² at this wrapped value.
For example, if x = 8, then its wrapped value is 8 mod 10 = 8, so we have:
f(8) = 5((\(8)^2\)) = 5(64) = 320.
Similarly, if x = 13, then its wrapped value is 13 mod 10 = 3, so we have:
f(13) = 5(\((3)^2\)) = 5(9) = 45.
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what values of t place 85% of the area in the middle of the distribution? (use technology. round your answers to two decimal places.)
The values of t that place 85% of the area in the middle of the distribution are between -3.379 and 3.379.
To find the values of t that place 85% of the area in the middle of the distribution, we need to find the t-scores that correspond to the 7.5th and 92.5th percentiles of the t-distribution with 46 degrees of freedom.
We can use a t-table or a statistical software to find these values. Using a t-table, we can look up the critical t-values for the two tails of the distribution that include 7.5% and 92.5% of the area.
For a two-tailed test at the 5% significance level with 46 degrees of freedom, the critical t-value is approximately 2.013.
To find the t-scores for the 7.5th and 92.5th percentiles, we need to multiply the critical t-value by the corresponding t-multiplier for the degrees of freedom. For 46 degrees of freedom, the t-multiplier is approximately 1.678.
Thus, the t-score that corresponds to the 7.5th percentile is -2.013 x 1.678 = -3.379, and the t-score that corresponds to the 92.5th percentile is 2.013 x 1.678 = 3.379.
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The given question is incomplete, the complete question is:
Consider a t distribution with 46 degrees of freedom. What values of t place 85% of the area in the middle of the distribution?