Answer:
12
Step-by-step explanation:
If 113 divided by a number leaves a remainder of 5, then we need to find the prime factorization of 108.
If 135 divided by a number leaves a remainder of 3, then we need to find the prime factorization of 132.
If 160 divided by a number leaves a remainder of 4, then we need to find the prime factorization of 156.
108 = 2² × 3³
132 = 2² × 3 × 11
156 = 2² × 3 × 13
The GCF of 108, 132, and 156 is common factors with lower exponent.
GCF = 2² × 3 = 12
Answer: 12
dr. raynor, a school psychologist, tracks the number of students that are reported by teachers as having concerning behaviors in the classroom. at the end of the year, she calculated that 12.4% of the students in her school have been identified as having behaviors that impact their performance in the classroom. she understands that there is a margin of error to this estimate and reports that the number of children who have behavior problems at school may be as low as 10.2% and as high as 14.6%. what is the term used to describe the 12.4% calculation made by dr. raynor?
Dr. Raynor is 95% confident that the true population proportion of students with concerning behaviors that impact their performance in the classroom is between 10.2% and 14.6%.
The 12.4% calculation made by Dr. Raynor is referred to as a confidence interval. A confidence interval is a range of numbers that is likely to contain a population parameter. In this case, the population parameter is the percentage of students in the school with concerning behaviors that impact their performance in the classroom. To calculate the confidence interval, Dr. Raynor first determined the sample proportion, which is 12.4%. Then, she used the following formula to calculate the confidence interval:
Confidence Interval = (Sample Proportion ± Margin of Error)
In this case, the margin of error was 2.2%, which is calculated by multiplying the sample proportion by 1.96 (1.96 being the critical value for a 95% confidence interval). Thus, the confidence interval of 10.2% to 14.6% was determined. This confidence interval means that Dr. Raynor is 95% confident that the true population proportion of students with concerning behaviors that impact their performance in the classroom is between 10.2% and 14.6%.
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What is the perimeter of a square if the area is 49cm^2
Answer:
Step-by-step explanation:
take length as x,
perimeter= 28cm
Answer:
28cm
Step-by-step explanation:
7+7+7+7
5. What is the value of x to the nearest tenth?
A 4.8
B 7.7
8.8
D14.1
8.2
282
126⁰
The required value of the x to the nearest tenth is given as x = 8.8. Option C is correct.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal 180°
Here,
Since the question seems to be incomplete, the complete question has been attached at the last of the solution,
Now, A triangle is shown in the image attached,
To evaluate the measure of x, we apply the sine rule,
8.2/(sin(180-126-28)) = x/sin28
8.2/sin26 = x/sin28
x = 8.2sin28/sin26
x = 8.8
Thus, the required value of the x to the nearest tenth is given as x = 8.8. Option C is correct.
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the t-value changes depending on the number of data points collected.
Yes, that is correct. The t-value is used to calculate the significance of the difference between two sample means.
It is used in a t-test, which is a type of hypothesis test that is commonly used in statistical analysis. The t-value changes depending on the number of data points (sample size) collected, as well as the level of confidence desired and the standard deviation of the population. A larger sample size typically results in a smaller t-value, which means that the difference between the two sample means is more significant. On the other hand, a smaller sample size leads to a larger t-value, which means that the difference between the two sample means is less significant. Yes, that is correct. The t-value is used to calculate the significance of the difference between two sample means.
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which of the following shows 87 and 1/2% as a fraction? 7/8, 5/8, -8/75, none of these
Answer: none of these
Step-by-step explanation:
87 and 1/2% should be written as 87.5%
an opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. a commentator believes that more than half of all adults favor such a ban. the null and alternative hypotheses you would use to test this claim are
The currect option is (b) H0: p = 0.5; Ha: p > 0.5
p represents the population proportion.
A null hypothesis is a statement from the population parameter which is either rejected or accepted (fail to reject) upon testing. It is expressed using the equality sign.
An alternate hypothesis is also a statement from the population parameter which negates the null hypothesis and is accepted if the null hypothesis is rejected. It is expressed using any of the inequality signs.
An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. a commentator believes that more than half of all adults favor such a ban. the null and alternative hypotheses you would use to test this claim are
a) H0:p^=0.5;Ha:p^>0.5
(b) H0:p=0.5;Ha:p>0.5
(c) H0:p=0.5;Ha:p<0.5
(d) H0:p=0.5;Ha:p≠0.5
(e) H0:p>0.5;Ha:p=0.5
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The manager of an office supply store can sell 10 boxes of pencils at a price of $2. 19 per box. If the price is $1. 70, she can sell 24 boxes. The total cost of buying x boxes of pencils is C(x)=0. 55x+20 dollars.
Assuming the demand function is linear, find an equation for D(x). Do not round your answer
The profit generated from selling x boxes of pencils is a linear function of x, with a slope of $0.80 and a y-intercept of -$12.60
In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range) with the property that each input is related to exactly one output.
Let us first define the demand function as D(x), where x is the number of boxes of pencils sold. We know that the manager can sell 10 boxes of pencils at a price of $2.19 per box, which means that the revenue generated from this sale is:
10 * $2.19 = $21.90
Similarly, when the price is $1.70, she can sell 24 boxes of pencils, which gives a revenue of:
24 * $1.70 = $40.80
Now, we can use these two data points to find the equation of the demand function. Since we assume that the demand is linear, we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept. In our case, y represents the revenue generated by selling x boxes of pencils.
To find the slope, we use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the two data points we have.
m = ($40.80 - $21.90) / (24 - 10)
m = $18.90 / 14
m = $1.35
To find the y-intercept, we can use either of the two data points and solve for b:
$21.90 = $1.35 * 10 + b
b = $7.40
Therefore, the demand function for the pencils is:
D(x) = $1.35x + $7.40
This means that for each additional box of pencils sold, the revenue generated increases by $1.35. The y-intercept of $7.40 represents the revenue generated when no pencils are sold, which includes fixed costs such as rent, utilities, and wages.
We also have the cost function C(x) = 0.55x + $20, which represents the total cost of buying x boxes of pencils. The profit function P(x) is defined as the difference between the revenue and the cost:
P(x) = D(x) - C(x)
Substituting the expressions for D(x) and C(x), we get:
P(x) = ($1.35x + $7.40) - (0.55x + $20)
Simplifying this expression, we get:
P(x) = $0.80x - $12.60
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Determine each segment length in right triangle ABC . Right triangle ABC with right angle at vertex B. Point D lies on side AC. Dashed segment BD is drawn. Angle BAD measures 30 degrees and angle BCD measures 60 degrees. Angle BDC is a right angle. Side AC is labeled 8 and segment CD is labeled 2. 2 2 4 3 6 4 2 2 3 4 B C arrowRight A D arrowRight A B arrowRight B D
The right triangle ABC with right angle at vertex B has the length of the segment is; 4√2 unit.
What is Pythagorean theorem?The Pythagorean theorem state that in any right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the two shorter sides. In this case, side AC is the hypotenuse and side AB and BC are the two shorter sides.
We can find the lengths of all three sides using the Pythagorean theorem and the information given. Side AB is equal to the square root of the sum of the squares of sides AC and BC. Since we are given that angle ABC is a right angle, we can find that side BC is equal to the length of side AB.
The side lengths are 8/2 = 4
Now, Another side length that is x
So , the equation formed is;
xcos45 = 4
x/√2 = 4
x = 4√2
Hence the length of the segment is; 4√2 unit.
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What is the cube of 4?
Answer:
64
Step-by-step explanation:
The height of a cone is 10 centimeters. The radius is 4 centimeters. What is the volume of this cone? Around your answer to the nearest hundredth. Do not include units in your answer.
in Triangle MNK, MN=NK, m Please answer quick!
The value of MN is 3.05
What is Geometry?Along with arithmetic, geometry is one of the earliest subfields of mathematics. It is concerned with spatial characteristics like the separation between objects, their shape and size, and their relative positions.
Since MN=NK,
draw an isosceles triangle (two sides are equal).
Mark the angle N as 110 degrees.
Now, draw a line from N to the opposite side at a right angle. This line will divide MK=5 in half since MN = NK.
It will also divide angle N into half. So, we will end up with a right triangle with one side 5/2 = 2.5 and the opposite angle 55 degrees.
sin(55) = opposite / hypotenuse = 2.5 / MN = 0.82
MN = 2.5 / 0.82 = 3.05
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a group of roommates equally shared the 6000$ in rent for an apartment. when four of the roomates moved out, those roomates remaining still shared the 6000$ rent equally, but each roomate's share of the rent increased by 250$. how many roomates were there orginally
The original number of roommates was 6, determined by comparing the original and new shares of rent per roommate and solving for the minimum number of roommates that satisfies the inequality.
Let's assume that there were 'x' original roommates in the apartment.
When the rent was shared equally among 'x' roommates, each roommate's share was:
[tex]6000/x[/tex]
After four roommates moved out, the remaining roommates continued to share the same rent of $6000 but each person's share increased by $250. So the new share per roommate is:
[tex](6000/x) + 250[/tex]
Since the number of roommates decreased by 4, the new number of roommates is:
[tex]x - 4[/tex]
We know that the new share per roommate is greater than the original share per roommate, so we can set up the following inequality:
[tex](6000/x) + 250 > 6000/x[/tex]
Simplifying the inequality, we get:
[tex]250 > 6000/x - 6000/x[/tex]
[tex]250 > 6000/x^2[/tex]
[tex]x^2 > 24[/tex]
[tex]x > 4.9[/tex]
Since the number of roommates must be a whole number, the minimum value for x is 6.
Therefore, there were originally 6 roommates in the apartment.
The solution involves setting up an inequality to compare the original share of the rent per roommate with the new share of the rent per roommate, and then solving for the minimum number of original roommates that satisfies the inequality.
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A GP surgery is recording the waiting time of its patients and produces the
cumulative frequency graph shown below.
100
Cumulative frequency
80
60
40
20
0
5
10
15
Waiting time (mins)
20
25
a) How many patients waited for more
than 20 minutes?
b) Find the median waiting time.
17
patients
minutes
The number of patients that waited for more than 20 minutes is 74
The median waiting time is 17
How to determine the number of patientsFrom the question, we have the following parameters that can be used in our computation:
The graph
Where
x = Waiting time
y = Cumulative frequency
This means that
y = Number of patients that waited x or more time
From the graph, we have
(x, y = (20, 74)
So, the number of patients is 74
The median waiting timeFrom the question, we have the following parameters that can be used in our computation:
Maximum CF = 100
Divide by 2 to calculate the median
Median = 100/2
Evaluate
Median = 50
From the graph, we have
(x, y = (50, 17)
So, the median is 17
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Mae Ling earns a weekly salary of $320 plus a 6. 0% commission on sales at a gift shop. How much would she make in a work week if she sold $4,500 worth of merchandise?
Mae Ling make $590 in a work week if she sold $4,500 worth of merchandise.
The given is:
We need to find how much she would earns in a work week
Mae Ling earns a weekly salary of $320
She earns a 6.0% commission on sales
She sold by $4,500 in that week
Add $320 to the product of 6.0% and $4,500
She made = 320 + (6.0% × 4,500)
6.0% = 6.0 ÷ 100 = 0.06
She made = 320 + (0.06 × 4,500)
She made = 320 + 270
She made = 590
She would make $590 in a work if she sold $4,500 worth of merchandise.
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The total cost of an order of personalized invitations from a company includes the cost of each invitation, plus a one-time design fee. The cost of each invitation is the same regardless of how many invitations are ordered.
The invitation company provides the following examples to customers in order to estimate the total cost of an order:
50 invitations $298.50
500 invitations $2049
The total cost of an order is $900 if 50 invitations cost is $298.50
To calculate the cost of an order of personalized invitations, you would need to know the cost of each invitation and the one-time design fee.
Let calculate the cost of each invitation and the one-time design fee as follows:
50 Invitations: $298.50 / 50 = $5.97 per invitation
500 Invitations: $2049 / 500 = $4.098 per invitation
Design Fee: ($2049 - ($5.97 × 50)) / 500
= $3.90 one-time design fee
If you wanted to order 150 personalized invitations, the cost would be:
150 Invitations x $5.97 per invitation = $896.50
Plus one-time design fee of $3.90 = $890.40
Total cost = $896.50 + $3.90 = $900.
Hence, the total cost of an order is $900 if 50 invitations cost $298.50
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FIFTEEN 15 POINTS! pls help with functions :)
Answer:
A
Step-by-step explanation:
If you look at the graph it starts at 30 and the next time it lines up on the lines is 3 up and 2 over. Therefore it is 3/2x+30
terry invests a sum of money at a rate of 3.7% p.a. compound annually. After 4 years he withdraws $2000, and moves the moves the remaining money into an account earning 4.5% p.a. compounded annually. After 3 more years, there is $5635.66 in the account. How much did terry initially invest?
Answer:
To solve it, you need to use compound interest. Let me show you how.
Let P be the initial amount that Terry invested. Then after 4 years, the amount in the account is:
P × (1 + 0.037)^4
After withdrawing $2000, the remaining amount is:
P × (1 + 0.037)^4 - 2000
This amount is then moved to another account earning 4.5% p.a. compounded annually. After 3 more years, the amount in the account is:
(P × (1 + 0.037)^4 - 2000) × (1 + 0.045)^3
We are given that this amount is equal to $5635.66. So we can write an equation:
(P × (1 + 0.037)^4 - 2000) × (1 + 0.045)^3 = 5635.66
Simplifying the equation, we get:
P × 1.1597 - 2000 = 5635.66 / 1.1406
Adding 2000 to both sides, we get:
P × 1.1597 = 5635.66 / 1.1406 + 2000
Dividing both sides by 1.1597, we get:
P = (5635.66 / 1.1406 + 2000) / 1.1597
Using a calculator, we get:
P ≈ 5000.01
Therefore, Terry initially invested about $5000.01.
Step-by-step explanation:
Find the slope and the y-intercept of the graph of the linear equation.
4x+y=5
HELP ASAP PLEASEEEEEEEEE LIKE RNRN
The y-intercept is 5, and the slope is -4. As a result, the line's equation is y = -4x + 5, where -4 is the slope and 5 is the y-intercept.
What exactly is a linear equation?A linear equation is an algebraic equation of the form y = mx + b, where the slope is m and the y-intercept is b, and only a constant and a first-order (linear) term are included.
The slope and y-intercept of the linear equation 4x + y = 5,
we need to solve for y and put the equation in slope-intercept form, y = mx + b,
where the slope is m and the y-intercept is b
4x + y = 5
Subtract 4x from both sides:
y = -4x + 5
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b) A factor of 24 is chosen at random.
What is the probability, as a decimal, that it is a 2-digit number?
Answer
2.5
Step-by-step explanation:
have a nice day.
is petid good to uniquely identify each data record of the pet relation? why does personid in the pet relation need to be a part of the primary key of the pet relation
Using petid as a primary key in the pet relation is generally a good way to uniquely identify each data record in the relation. However, in some cases, it may be necessary to include personid as part of the primary key of the pet relation.
This is because each pet should have a unique identifier, and petid is specifically designed to serve this purpose. This would be the case if a person can have more than one pet in the database, and if the same petid value is used for more than one pet (which would violate the uniqueness requirement of a primary key).
By including personid as part of the primary key of the pet relation, we ensure that each pet in the database has a unique identifier (i.e., a unique combination of petid and personid). This allows us to avoid any confusion that might arise if two or more pets in the database had the same petid value. It also allows us to link each pet to its owner via the personid attribute, which can be useful for querying and reporting on the data.
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the bakery made $600 Donuts they made 384 more Donuts than Bagels the bakery made 216 Bagels
The bakery made 384 donuts and 216 bagels
What is bakery?
A bakery is a business that produces and sells baked goods, such as bread, cakes, pastries, and cookies.
Let's use the variable "x" to represent the number of bagels made.
From the problem, we know that:
The number of donuts made is 384 more than the number of bagels made, so the number of donuts is x + 384.
The bakery made 216 bagels.
We also know that the bakery made a total of 600 donuts. So, we can set up an equation to represent the total number of pastries made:
x + 384 + 216 = 600
Simplifying and solving for x:
x + 600 = 600
x = 600 - 600 + 384
x = 384
So, the bakery made 384 + 216 = 600 pastries in total.
Therefore, the bakery made 384 donuts and 216 bagels.
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FIND THE PERIMETER AND AREA OF THE TRIANGLE BELOW
Answer:
perimeter = 8a³b + 4ab
area = 4a^4b²
Step-by-step explanation:
perimeter = 2a³b + 6a³b + 4ab
perimeter = 8a³b + 4ab
area = bh/2
area = 4ab × 2a³b / 2
area = 4a^4b²
Neeeeeed hellppppppppll
To draw a centroid for ΔABC, follow the steps below.
Draw the triangle ABC with the line segment CD bisecting it. Line segment CD is called a median and it connects the midpoint of side AB to the opposite vertex, C.Using a protractor, measure the distance between B and C, place the protractor on C and make an arc on both sides of the triangle. Place the protractor on B and repeat the same step. place your ruler such that the ruler is actactly in between the twin arcs on both sides of the triangle, mark the point where the ruler crosses the line segment BC.Call this point long BC point x.repeat this for LIne segment AC.Call the point on line AC y.Draw another line segment from point B to the midpoint of side BC, that is point x and repeat same for point y.The intersection point of line segments CD and XY is the centroid of the ΔABC. Label this point as G.
See the sample attached. Note that this is not constructed to scale.
What is a Centroid?The centroid is the point where the three medians of a triangle intersect.
A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. In this case, line segment CD is one of the medians of triangle ABC because it connects the midpoint of AB (which is also the midpoint of CD) to vertex C. The other two medians connect the midpoints of the other two sides to their opposite vertices.
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Need this for a math lesson
The upper quartile score on the final exam is 83.
What is Upper quartile?Upper quartile, represented as Q₃, also known as third quartile is the value in a data set such that 75% of the points in the data set are below this value, after arranging in an ascending order.
Given data set is the scores for the final exam in an 8th grade math class.
58, 72, 74, 92, 84, 40, 74, 81, 76, 83.
First arrange the data in an ascending order.
40, 58, 72, 74, 74, 76, 81, 83, 84, 92.
Median is the middle element.
Median = (74 + 76) / 2 = 75
Upper quartile is the median of the second half.
Consider the second half.
76, 81, 83, 84, 92.
Median = 83
Third quartile = 83
Hence 83 is the upper quartile score on the final exam.
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(5 pts) interpolation is used to determine values beyond a given set of data points. a) true b) false
The statement "interpolation is used to determine values beyond a given set of data points" is true
The given statement is " interpolation is used to determine values beyond a given set of data points"
The interpolation is a method in statistics that used to determine or estimate the unknown values in the given set of values. So it is usually used to estimate the price and the potential yield of security
In the interpolation, we use the values from the given set of the data point and estimate the unknown values or values beyond the given set of data points
Therefore, the given statement is true
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y=-1/2x-1
y=1/4x-4
graphing method
3, -24, 192, ... Find the 19th term:
Answer:
Step-by-step explanation:
a
n
=ar
n−1
a
3
=ar
2
=24...(1)
a
6
=ar
5
=192...(2)
dividing (2) by (1) we get
ar
2
ar
5
=
24
192
r
3
=8⇒r=2
From (1)
ar
2
=24
a=
2
2
24
=6
∴a
10
=(6)(2)
10−1
=3072
how many pattern block triangles would create 2 hexagons
To make two hexagons out of pattern blocks, you would need a total of 12 triangles. Six triangles are needed for each hexagon.
To make two hexagons out of pattern blocks, you would need a total of 12 triangles. Each hexagon requires six triangles to make it, so two hexagons would need double that amount. Since the pattern blocks come in the shapes of triangles, you can easily construct the hexagons by placing the triangles together. Each triangle has two sides that fit together and two sides that overlap, so the six triangles will create a complete hexagon when they are all put together. Once you have two hexagons constructed, they will fit together to make a larger shape, depending on how you place them. With this method, you can easily make two hexagons out of pattern blocks.
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1. An awning that covers a sliding glass door that is 88 inches tall forms an angle of 50' with the wall.
The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation
of the Sun is more than 65'. See the figure. Find the length of L of the awning. Round to the nearest
Inch.
according to the american diabetes association (links to an external site.), 34.2 million americans, or 10.5% of the population, had diabetes in the year 2018. what is the probability that a randomly chosen person has diabetes?
The probability that a randomly chosen person has diabetes is 34.2 million / (0.105 * total population).
The probability that a randomly chosen person has diabetes is equal to the number of people who have diabetes divided by the total population:
probability = number of people with diabetes / total population
Substituting the given values:
probability = 34.2 million / (10.5% of the total population)
To calculate this, we need to convert the percentage to a decimal by dividing by 100:
probability = 34.2 million / (0.105 * total population)
Assuming the total population remains constant between 2018 and now, and that the percentage of people with diabetes has also remained constant, we can use this probability to estimate the current number of people with diabetes in the United States.
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