Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
A field estimates 40 by 80 yards. Larysa makes a scale drawing with a size of 1 in. to 5 yd., and Prakash makes his own scale drawing with a size of 1 in. to 8 yd.
The dimension of the Larysa drawing is given as,
⇒ 40 x 1/5
⇒ 8 in
⇒ 80 x 1/5
⇒ 16 in
The dimension of the Prakash drawing is given as,
⇒ 40 x 1/8
⇒ 5 in
⇒ 80 x 1/8
⇒ 10 in
The dimension of the Prakash's drawing is less than the dimension of the Larysa's drawing. The Larysa's drawing has the larger area.
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Amelia thinks of a number. Her number is a factor of both 18 and 12. Her number is odd. What is the largest number she could be thinking of?
Answer:
Step-by-step explanation:
First, Amelia thinks of a number that is a factor of both 18 and 12. This number is odd, so it can't be a whole number. Next, Amelia has to find the largest number that is a factor of both 18 and her chosen number. This number is 36.
Answer:
3
Step-by-step explanation:
You want the largest odd factor of both 18 and 12.
GCDThe greatest common divisor of both 18 and 12 is 6:
18 = 3·6
12 = 2·6
This is an even factor, which has two factors: 2 and 3. Only 3 is an odd factor of both 18 and 12.
The largest odd factor of both 18 and 12 is 3.
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Grayson owns a food truck that sells tacos and burritos. He only has enough supplies
to make 110 tacos or burritos. He sells each taco for $3.25 and each burrito for $7.
Grayson must sell a minimum of $560 worth of tacos and burritos each day. If x
represents the number of tacos sold and y represents the number of burritos sold,
write and solve a system of inequalities graphically and determine one possible
solution.
Using system of linear inequality, the number of tacos and burrito he sold was 56 and 54 respectively
System of Linear InequalityA system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
To solve this problem, we have to write two system of inequality and then graph the inequalities to show the solution.
Let;
x = tacosy = burritosx + y = 110 ...eq(i)
7x + 3.25y ≥ 560 ..eq(ii)
From eq(i)
x + y 110
x = 110 - y ..eq(iii)
Put eq(iii) into eq(ii)
7(110 - y) + 3.25y ≥ 560
770 - 7y + 3.25y ≥ 560
770 - 3.75y ≥ 560
-3.75y ≥ 560 - 770
-3.75y ≥ -210
y ≤ 56
Assuming y is less than or equal to 56, x will be
x + 56 = 110
x = 54
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The probability that a marksman will hit a target each time he shoots is 0. 89. If he fires 15 times, what is the probability that he hits the target at most 13 times?.
The probability that marksman will hits the target at most 13 times is 27.92%.
Explain the term binomial distribution?Let X be the quantity of times that target is hit and be a random variable. 15 rounds are fired, hence the number of trials ("n") is equal to 10 as a result. In a binomial distribution, "p" denotes the likelihood of success, and "q" is the likelihood of failure (where q = 1 - p). Since there is a 0.89 chance of striking the target, p = 0.89 and q = 0.11.The number of successes ("x") is the probability mass function for such binomial distribution.
P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ
We are interested in the likelihood that the target will be struck exactly five times, therefore the desired number of successes is five (i.e., x = 13).
P(X = 13) = ¹⁵C₁₃. (0.89)¹³ (0.11)²
P(X = 13) = 0.2792
P(X = 13) = 27.92%
Thus, the probability that marksman will hits the target at most 13 times is 27.92%.
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a lattice point is a point in the plane with integer coordinates. how many lattice points are on the line segment whose endpoints are $(3,17)$ and $(48,281)$? (include both endpoints of the segment in your count.) (a) 2 (b) 4 (c) 6 (d) 16 (e) 46
There are 4 lattice points on the line segment whose endpoints (3,17) &(48,281)
What is a Lattice point?
In a Cartesian coordinate system, a lattice point is a point whose x-coordinates and y-coordinates are both integers. A point in a regularly spaced array of points, known as a point lattice, that is at the intersection of two or more grid lines is referred to as a lattice point. Point lattices with unit cells that are square, rectangular, hexagonal, and other forms can be built in a plane. An unspecified point in a square array constitutes a point in a point lattice.
The difference in the y-coordinates is 281 - 17 = 264
the difference in the x-coordinates is 48 - 3 = 45.
The gcd of 264 and 45 is 3,
so the line segment joining (3,17) and (48,281) has a slope [tex]\[\frac{88}{15}\][/tex]
The points on the line have coordinates[tex]\[\left(3+t,17+\frac{88}{15}t\right).\][/tex]
If t is an integer, the y-coordinate of this point is an integer if and only if t is a multiple of 15.
The points where t is a multiple of 15 on the segment [tex]3\leq x\leq 48[/tex] are 3, 3+15, 3+30, and 3+45.
There are 4 lattice points on this line. Hence the answer is B
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Based on the stock price model, what is the best prediction of what the price will do next? a. hold value b. keep increasing c. start decreasing d. no way to predict
The best prediction the price will do next is keep increasing.
What is stock price?
The price at which one share of a company would be purchased is known as the share price or stock price. A share's price is not constant; rather, it changes over time in response to market factors. It is likely to rise if the business is thought to be doing well or fall if it isn't living up to expectations.
A company's price rising more quickly indicates that investors are supporting the rally and that the stock will rise further.
On the other hand, a declining price trend with high volume suggests a possible downward trajectory. A high trade volume could also indicate a change in trend.
Hence, the best prediction the price will do next is keep increasing.
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Paula bought a ski jacket on sale for $6 less than a quarter of the original price. She paid $45 for the jacket.
Write an equation that can be used to find the original price of the jacket, then solve you equation to find the
answer.
Answer:
let price of jacket be xx-6$=$45 as equationx-6$=$45x=45$+$6x=$51 therefore original price of jacket is $51design a rectangular milk carton box of width w, length l, and height h which holds 512 cm3 of milk. the sides of the box cost 1 cent/cm2 and the top and bottom cost 2 cent/cm2. find the dimensions of the box that minimize the total cost of materials used.
The dimensions of the box that minimize the total cost of materials used are:
L = W = 16 cm
H = 32 cm
What is the rectangular dimension?
Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth. A triangle's or an oval's interior likewise has two dimensions.
We have,
volume L* W * H = 512 cm³
sides of the box cost = 1 cent/cm²
top and bottom cost 2 cent/cm²
to find out
dimensions of the box that minimize the total cost of material use
we know here,
L* W * H = 512 cm³
where,
L is length and W is width and H is the height
so when we minimize the cost function
C( L, W, H ) = (1) 1 H ( L + W ) + (2) 1 L W
so put here H
substitute [tex]H = \frac{512}{LW}[/tex] we get,
C(L, W) = 512([tex]\frac{1}{l}, \frac{1}{W}[/tex]) + 2LW
so
minimum cost will be when the two partial derivatives is 0
dC/dL = 2W - 512/L² = 0
so
dC/dW = 2L - 512/W² = 0
L = 256/W²
so
by solving the above equation we get
L = W = (256)⁻³ = 16cm
and
H = 512/16 = 32
H = 32 cm
Hence, the dimensions of the box that minimize the total cost of materials used are:
L = W = 16 cm
H = 32 cm
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Out of 168 randomly selected adults in the United States who were surveyed, 89 exercise on a regular basis. Construct a 98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis. Round to three decimal places.
98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.
What does a statistical random sampling entail?
A selection of participants from a population are chosen at random by the researcher using simple random sampling, a sort of probability sampling. Every person in the population has the same chance of being chosen. Then, data are gathered from as much of this randomly selected subgroup as possible.P = x/n
= 89/168
= 0.53
α= 0.02
∴Zc = Zi - α/2
= 2.326
Now, C.I = P ± Zc * √[P(1-P)/n]
= 0.5 ± 2.326 * √[(0.53(1-0.53)) / 168
= (0.440, 0.619)
∴98% C.I. = 0.440 < P < 0.619
Hence, 98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.
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Pls help!! Trying to do asap! First answer will get brainleist
Answer:
84
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let, the dimension of cuboid are l=5x,b=4x and h=2x
Now, the surface area of cuboid =2(5x×4x+4x×2x+2x×5x)=76x2
Now,
76x2=1216
x2=16
x=4
Dimensions of cuboid are,
l=5x=5×4=20cm,b=4x=4×4=16cm
h=2x=2×4=8cm
Volume of cuboid=l×b×h=20×16×8=2560cm3
Hence, this is the answer.
The approximate distance from Earth to the moon is 240 thousand miles. The approximate distance from Earth to the sun is 93 million miles. In standard notation, the approximate distance from the sun to Earth is miles greater than the approximate distance from Earth to the moon. In scientific notation, the distance is m × 10n, where m is and n is
The approximate distance from the sun to Earth is miles greater than the approximate distance from Earth to the moon by 9.276 × 10^7.
What is the scientific notation?Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper. Furthermore, the numbers in the millions place after the decimal required to be represented in a simpler format.
In this case, the approximate distance from Earth to the moon is 240 thousand miles. This will be 2.4 × 10^5
The approximate distance from Earth to the sun is 93 million miles. This will be:
= 9.3 × 10^7
The difference will be:
= (9.3 × 10^7) - (2.4 × 10^5)
= 9.276 × 10^7
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in a science classroom, when labs are performed, students are seated at lab tables. if the teacher assigns 2 students to each lab table, 4 additional lab tables will be needed to seat all of the studetnds. if the teacher assigns 4 students to each lab table, 4 lab tables will not be used. how many students are in the science clas
Answer: 16 students
Step-by-step explanation:
2x + (2•4) = 4x
2x + 8 = 4x
-2x -2x
8 = 2x
(Divide by 2 on both sides)
vvv
2x/2= x
8/2 = 4
x = 4
(substitute 4 in for x)
2(4) + 8 = 4(4)
8+8 = 16
16 = 16
Software companies work hard to produce software without bugs. A particular company claims that 85% of the software it produces is bug free. A random sample of size 200 showed 156 softwareprograms were bug free.
a. Calculate the mean of the sampling distribution of the sample proportion.
The Central Limit Theorem establishes that the sampling distribution of the sample means with size n can be roughly equivalent to a normal distribution with mean and standard deviation for a normally distributed random variable X, with mean and standard deviation.
The Central Limit Theorem can also be used with skewed variables if n is at least 30.The mean of the sampling distribution of sample means is p for a proportion p in a sapling of size n, and the standard deviation is s=root of p(1-p)/n.This issue involves that:(A) Determine the sample proportion's sampling distribution's mean.The Central Limit Theorem states that 0.85
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if the cost of 1kg of apples is $12 what is the cost of 500g of apples
Answer:
the answer is $6
Step-by-step explanation:
This is because there are 1000g in 1kg, so 500g is half of that and half of 12 is 6.
How many times does the rotation R(120°, P) need to be applied to a figure to map the figure to itself?
The number of times the point R ( 120° , P ) needs to be rotated so that the figure is mapped to itself is 3 times
What is Rotation?
The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.
90° clockwise rotation: (x,y) becomes (y,-x)
90° counterclockwise rotation: (x,y) becomes (-y,x)
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
Given data ,
Let the number of rotation be = n
Let the point be R
Now , the coordinates of the point R is
R ( 120° , P )
Now , to map the figure onto itself it needs to rotate 360°
So ,the number of times 120° needs to rotate to reach 360° is calculated as
n x 120° = 360°
Divide by 120 on both sides , we get
n = 360 / 3
n = 3 times
Therefore , the value of n is 3
Hence , The number of times the point R ( 120° , P ) needs to be rotated so that the figure is mapped to itself is 3 times
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a measure of the long-run average value of a random variable used to represent the central location of a probability distribution is called a(n) .
The measure of the long -run average value of a random variable used to represent the central location of a probability distribution is called an expected value E(x).
As given in the question,
Reason with explanation :
The Mean represents the central location of the random variable.It represent the weighted average of the value taken by X.Weight represents the probability distribution.The expected average value of the many distributed value.The average value of a random variable to represents the central location is called expected value.Therefore, the measure of the long run average value of a random variable representing central location of the probability distribution is called the expected value.
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A survey of factories in five northeastern states found that 10% of the 300 workers surveyed were satisfied with the benefits offered by their employers. the margin of error for the population proportion, rounded to the nearest hundredth of a percent, is ±___%.
The margin of error for the population proportion is ± 3.39%
What is Error?Error is the difference between a genuine value and an estimate, or approximate, representation of that value in practical mathematics. The discrepancy between the mean of the complete population and the mean of a sample taken from that population is a frequent example in statistics.
Given that A survey of factories in five northeastern states found that 10% of the 300 workers surveyed were satisfied with the benefits offered by their employers
i.e. sample size n =300
Sample proportion p = 0.10
q=1-p=0.9
[tex]\sqrt{} \frac{pq}{n}[/tex] = [tex]\sqrt{\frac{0.1*0.9}{300} }[/tex]
Standard error ≈ 0.01732
Margin of error at 95% would be
1.96*std error
= 0.0339=3.39%
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-2x² + 3y² + 4x - 5y-11=0
x+3y-1=0
Given that the function graphed is f(x), what is f(3)?
Answer:
c. -24
Step-by-step explanation:
f(3) means the y value where x = 3, therefore f(3) = -24
1. Which method would be the simplest way to solve the system?
7x + 5y = 19
-7x - 2y = -16
Ographing
substitution
elimination
Odistributive
(1 point)
Answer: a
Step-by-step explanation:
when conducting a one-way independent anova with three levels on the independent variable, an f-ratio that is large enough to be statistically significant tells us:
One or more of the mean differences are statistically significant, but not the precise location of the group differences.
In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess. Age, for instance, might be an independent variable.
Dependent variables are so-called because, during an experiment, their values are examined on the assumption or presumption that they are governed by the values of other variables.
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what is the best way of writing a prolog rule that gives you all the possible coin combinations adding to a dollar?
The best way of writing a prolog rule that gives you all the possible coin combinations adding to a dollar is using membership rules and arithmetic condition.
The Prolog interpreter warns that it can only find one occurrence of one or more variables, which is strange, since typically variables are used to perform unification, pass values from one predicate to another, etc.
Arithmetic in Prolog
In arithmetic expression, + - * / symbols are special type of infix operator, and these operators are also known as arithmetic operators. In Prolog, operators are used as predicates but here operators are functions and these operators return a numerical value.
Arithmetic expressions can include variables, numbers, operators, and arithmetic functions. These will be written in parentheses with their arguments. These will return numerical values just like the arithmetic operators.
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a ball of radius 14 has a round hole of radius 8 drilled through its center. find the volume of the resulting solid
By using the volume of sphere, it can be calculated that
Volume of the sphere after the hole is drilled = [tex]352\sqrt{33} \pi[/tex]
What is volume of sphere?
Volume of sphere is the total space taken by the sphere.
If r is the radius of the sphere, then volume of the sphere is
[tex]v = \frac{4}{3} \pi r^3[/tex]
Radius of the ball = 14
Radius of the ball after the hole is drilled = 8
By Pythagoras Theorem,
Height of the ball after the hole is drilled =[tex]\sqrt{14^2 - 8^2}[/tex] = [tex]\sqrt{132}[/tex]
Volume of the ball after the hole is drilled = [tex]\frac{4}{3} \pi (\sqrt{132})^3[/tex]
= [tex]\frac{4\pi \times 132 \times 2\sqrt{33}}{3}\\352\sqrt{33} \pi[/tex]
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HELP ASAP
50 POINTS!! + WILL GIVE BRAINLEIST
Answer:
Step-by-step explanation:
2+2+4
Question 1-4
A punch bowl contained 4 liters of soda, 5 liters of orange juice, and 2 liters of raspberry juice.
Select the statements that are true.
The ratio of the entire punch bowl to the juices is 9: 11.
The ratio of the entire punch bowl to the orange juice is 11 to 5.
The ratio of orange juice to soda is 4 to 5.
4
The ratio of soda to the entire punch bowl is
11
The ratio of orange juice to raspberry juice is 5 : 2.
Answer:
Its the second one
Step-by-step explanation:
.
a magazine provided results from a poll of adults who were asked to identify their favorite pie. among the respondents, % chose chocolate pie, and the margin of error was given as percentage points. given specific sample data, which confidence interval is wider: the % confidence interval or the % confidence interval? why is it wider?
To be more certain that it captures the true value of the population proportion, a 95 % confidence interval must be larger than an 80 % confidence interval.
What is confidence interval?An area created using fixed-size samples of data from a population (sample space) that follows a certain probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% chance of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval.
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What is an equation of the line that passes through the point (8, 0) and is parallel to
the line x + y = 5?
Answer:
y = -x + 8
Step-by-step explanation:
x + y = 5
y = -x + 5
y = -x + b
0 = -(8) + b
b = 8
y = -x + 8
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Mia buys a t-shirt online for $15.. If shipping and
handling are an additional 30% of the price, how
much shipping and handling will Mia pay?
Mia will pay a total of $4.5 for the shipping and handling of the t-shirt
How to determine the shipping and handling price?From the question, we have the following parameters that can be used in our computation:
Cost of the shirt = $15
shipping and handling = 30%
The amount paid for the shipping and handling of the t-shirt can be calculated using the following equation
Amount paid = original price * + shipping and handling
Substitute the known values in the above equation, so, we have the following representation
Amount paid = 15 * 30%
Evaluate the products
Amount paid = 4.5
Hence, the amount paid is $4.5
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Factor polynomials
9x^2 - 3x - 2
Many thanks for someone to lend a helping hand!
Answer:
Step-by-step explanation:
(3x-2)(3x+1)
Answer:
(3x - 2)(3x + 1)
Step-by-step explanation:
9x^2 - 3x - 2 = 9x^ 2 - 6x + 3x - 2 =
=3x(3x - 2) + (3x - 2) = (3x - 2)(3x + 1)
The following problem refers to a geometric sequence:
If a1= 5 and r = 3 find an
an=___
If geometric sequence has a1= 5 and r = 3 then the A(n) will be; 5 × 3^(n-1)
What is a geometric sequence?There are three parameters which differentiate between which geometric sequence we're talking about. The first parameter is the initial value of the sequence. The second parameter is the quantity by which we multiply previous term to get the next term.
The General form of a geometric sequence:
[tex]A(n) = A_1 \times r^{(n-1)}[/tex]
If a1= 5 and r = 3 then
A(n) = 5 × 3^(n-1)
Therefore, If geometric sequence has a1= 5 and r = 3 then the A(n) will be; 5 × 3^(n-1)
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Marko has $22. He needs at least $42 to go to a concert. How much more money does Marko need?
Marko needs the amount of money which would be $20 to go to a concert.
What is the Subtraction operation?Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
We have been given that Marko has $22. He needs at least $42 to go to a concert.
We have to determine the required amount of money Marko
the required amount of money = cost of the concert - he has the amount
the required amount of money = $42 - $22
Apply the subtraction operation, and we get
the required amount of money = $20
Therefore, Marko needs the amount of money that would be $20.
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