Total number of monthly payments, not including the final balloon payment is $1,195.77
How to solve the problem?The monthly payment is the sum that must be paid each month for the duration of the loan to cover the principal balance. When a loan is taken out, not only the principal—the amount that was initially loaned out—but also the interest—which accrues—must be repaid.
Step1
M = 350,000(0.071/12)(1+0.071/12)² /(1+0.071/12)¹² =3,618.02
M = P(r/12) (1+r/12)¹²×n/(1+r/12)¹²×n -1
Step2:
3,618.02 × 12 × 12 = 520,994.88
The total paid is the product of the monthly payment and the number of payments.
520,994.88 - 350,000 = 170,994.88
= 170,994.88÷143
= 1,195.77
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the slope field for the given differential equation is provided. sketch both branches of particular solution curve that passes through the point
The solution curve for the differential equation dy/dx = (y - y²) / x is plotted in the slope field.
What is a slope field?
The solutions to a scalar function's first-order differential equation are shown graphically by slope fields, also known as direction fields. Functions depicted as solid curves are solutions to a slope field. In order to determine the estimated tangent slope at a point on a curve, where the curve is some solution to the differential equation, one can use a slope field, which displays the slope of a differential equation at specific vertical and horizontal intervals on the x-y plane.
The slope field is a cartesian grid where you draw lines in various directions to represent the slopes of the tangents to the solution. Therefore by drawing a curve through consecutive slope lines, we can find a solution to the differential equation.
The differential equation is dy/dx = (y - y²) / x.
The solution curve is drawn using the solution points (1,2) for the differential equation.
Therefore, the solution curve is obtained.
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Topic Probability
If you roll unbiased dice 600 times. how many would you expect to obtain
a)a one
b)an even number
c)an odd number
d)a number less than 3
e)a prime number
The number of times that you would expect to roll the numbers, when rolling an unbiased dice is:
a. 100 times
b. 300 times
c. 300 times
d. 200 times
e. 200 times
How to find the number of times ?There is only a single 1 in a six sided unbiased dice so the number of rolls is:
= 1 / 6 x 600
= 100 times
There are 3 even numbers ( 2, 4, and 6) so the number of rolls :
= 3 / 6 x 600
= 300 times
There are 3 odd numbers ( 1, 3, 5 ) so number of rolls is:
= 3 / 6 x 600
= 300 times
There are 2 numbers less than 3 which are 1 and 2 :
= 2 / 6 x 600
= 200 times
There are 2 prime numbers ( 2 and 3 ):
= 2 / 6 x 600
= 200 times
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Can you work out at what height the ladders cross?
Are you surprised that we don't need to know the distance between the
two walls?
Suppose now the first ladder is 10m above the
base of the second wall, with the second ladder
remaining as before.
Can you work out at what height the ladders
cross now?
5m
Suppose the first ladder meets the wall at a
height of a metres, as in the diagram.
At what height do the ladders cross now?
Suppose the second ladder meets the wall at a
height of b metres, as in the diagram.
At what height do the ladders cross now?
5m
nrich.maths.org/510
© University of Cambridge
10m
a
Three degrees of freedom remain after applying five equations to eight variables. The other five variables may theoretically be solved for by specifying any three of them.
What is the height of ladder ?Five equations link these eight variables together. There are two equations given by the Pythagorean Theorem.
[tex]a^ 2=x^ 2+w^2 \ b^2=y^2+w^{\} 2[/tex]\
Two more are provided by the side ratios of similar triangles.
[tex]x/w=c/v[/tex]
[tex]y/w=c/u[/tex]
The two triangles are connected by the fifth equation, which is a straightforward linear relationship.
[tex]w=u+v[/tex]
Three degrees of freedom remain after applying five equations to eight variables. The other five variables may theoretically be solved for by specifying any three of them. But it might or might not be simple. What comes next will involve two distinct circumstances.
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A triangle is partitioned into three triangles and a quadrilateral by drawing two lines from vertices to their opposite sides. The areas of the three triangles are 10, 20, and 16, as shown. What is the area of the shaded quadrilateral? （ ）
A. 24
B. 28
C. 32
D. 36
E. 44
the area of the shaded quadrilateral is equal to the sum of area of triangle AOC and BOC is equal to 110 unit square.
Suppose area of triangle CEO = x and area of COD =y
OE : OB = 16:20 (Ratios of the areas of AEO and AOB)
Hence, Area of CEO : Area COB = 16:20
Area of CEO : (Area of COD +Area of DOB) = 16;20
x : (y+10) = 16:20
10x=5(y+10) ........(1)
AO : OD = 20:10 (Ratios of the areas of AOB and DOB)
Hence, Area of AOC : Area DOC = 20:10
(Area of AOE + Area of COE) : Area of DOB= 20:10
(16+x) : y = 20:10
16+x=2y.......(2)
From (1) and (2)
x=68 and y=42
so the area of quadrilateral is 110.
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If p is a prime number greater than 3, which of the following is not a factor of 6p
When p is a prime number greater than 3, the. option that is not a factor of 6p is A. p^2 (B
What is the factor about?The process of factorization simply has to do with the division of arithmetic algebraic expressions into the sum of their factors. in this case, multiplying the variables will yield the original expression. It means the writing of a number into smaller or simpler numbers that give the original number.
6*p / 6*p = 1
6*p / 3*p = 2
6*p / 2*p = 3
6*p / 3 = 2*p
6*p / p^2 = 6 / p which is not divisible by any prime number greater than 3.
The correct option is A.
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Complete question
If p is a prime number greater than 3, which of the following is NOT a factor of 6p ?
(A) p^2 (B) 6p (C) 3p (D) 2p (E) 3
Round 38.297 to the nearest hundredth
Find each angle measure to the nearest degree
sin x = 0.7547
The each angle measure of the trigonometric ratios are obtained.
Define the term trigonometric ratios?A mathematical discipline called trigonometry examines connections between triangles' sides and angles. Due to the fact that every straight-sided form can be decomposed into a group of triangles, trigonometry may be found across all of geometry.The given values is:
sin x = 0.7547,
Using trigonometric properties,
cos x = √(1 - sin²x)
= √(1 - 0.7547²)
cos x = 0.6560
Cosec x = 1 / sin x
= 1 / 0.7547
Cosec x = 1.3250
Now,
1 + cot²x = cosec²x
cot x = √(cosec²x - 1)
= √(1.3250² - 1)
cot x = 0.8692
tan x = 1 / cot x
= 1 / 0.8692
tan x = 1.1544
Thus, the each angle measure of the trigonometric ratios are obtained.
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In this problem, we will look at properties of solids with base on the xy-plane given by the circle x2+y2=a2 and its interior, where a>0
is to be given in parts (i) and (ii) below.
(i). Let a=4, and assume that cross-sections of thesolid perpendicular to the x -axis are circular disks with diameters lying in the xy-plane. Find the area A(x) of the cross-section at location x.
(ii). Let a=9, and assume that cross-sections of the solid perpendicular to the x-axis are equilateral triangles with bases in the xy-plane. Find the area A(x) of the cross-section at location x.
(iii). Find the volume of the solid described in (i) above.
The area A(x) of the cross-section at location x for a=4 is given by A(x)=π(4-x)2, where x is the distance from the origin. This can be derived from the equation A(x)=π(a2-x2).
The area A(x) of the cross-section at location x for a=9 is given by A(x)= 3√3(9-x)2/4, where x is the distance from the origin. This can be derived from the equation A(x)=3√3(a2-x2)/4.
(iii). The volume of the solid described in (i) can be calculated using the equation V=∫A(x)dx, where A(x) is the area of the cross-section at location x, and the integral is taken from 0 to 4. Substituting A(x)=π(4-x)2, we have V=π∫(4-x)2dx, which gives V=π(16 - 8x + x3/3) evaluated from 0 to 4, or V=64π/3.
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List the values of x at which f has a local minimum. Select the correct
choice below and fill in any answer boxes within your choice.p
The values of x at which the function has a local minimum are x = -4, 12.
What is the local minimum?The point in the domain of the functions with the lowest value is known as the local minimum. You may calculate the local minimum by determining the function's derivative. The first derivative and second derivative tests are the two key techniques for locating a function's local minimum.
There are several applications for the local minimum notion in business, economics, and engineering.
The least value of the function f(x) in the specified domain is essentially what the local minimum is.
From the graph, we observe
The value of the function f(x) is minimum at x = - 4 and x = 12
Therefore, x = -4, 12
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Need Help ASAP
I still don't understand this
Read carefully and do as it says
By using divisibility rule, the possible factors of number are-
495 : 3, 5 and 9924 : 3 and 4210 : 2, 5 and 10Explain the term divisibility rule?A simple technique to determine if a given number may be divided by such a fixed divisor before carrying out the division operation is to run a divisibility test. When a number is fully divided by yet another number, the remainder should equal zero and the quotient ought to be a whole number. A factor is really a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, or else the numbers we are adding are factors of both the product since the product is divisible by them.For the stated number:
495 : 3, 5 and 9 as 495 is completely divisible by 3, 5 and 9.924 : 3 and 4, as 924 is completely divisible by them.210 : 2, 5 and 10 as 210 is completely divisible by 2 and 5.To know more about the divisibility rule, here
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What is the result of isolating y^2 in the equation below? 4x^2 + 25y^2= 100
Answer:
In factored form: [tex]y=\sqrt{-\frac{1}{25}(2x-10)(2x+10)}[/tex]
In standard form: [tex]y=\sqrt{-\frac{4}{25}x^2+4}[/tex]
Step-by-step explanation:
Generally for these type of equations we want to get the term with "y" by it self (ignoring coefficients and any operations such as square root, etc...) so we want to get rid of the [tex]4x^2[/tex] from the left side which we can do by subtracting this from both sides to maintain equality and get rid of it on the left side.
[tex]25y^2=-4x^2+100[/tex]
One thing I want to note here is we can actually factor the right side which we generally want to do, we can rewrite it as: [tex]-(4x^2-100)[/tex] and from here we have a difference of squares: [tex]a^2-b^2=(a-b)(a+b)[/tex] so we can rewrite this as: [tex]-(2x-10)(2x+10)[/tex]
[tex]25y^2=-(2x-10)(2x+10)[/tex]
From here we divide both sides by 25:
[tex]y^2=-\frac{1}{25}(2x-10)(2x+10)[/tex]
Now from here to get rid of that square we do the inverse which is taking the square root:
[tex]y=\sqrt{-\frac{1}{25}(2x-10)(2x+10)}[/tex]
The reason factoring is useful in this case is we can now easily determine the domain of the function since inside the square root we have a quadratic which is opening down meaning it's only not negative between the zeroes (including the zeroes since they're... zero not negative) and this would be the domain of the graph. But if we wanted it to not be in factored form we would just put back what we had so we would have:
[tex]y=\sqrt{-\frac{1}{25}(4x^2-100)}[/tex]
then distribute the -1/25 to get:
[tex]y=\sqrt{-\frac{4}{25}x^2+4}[/tex]
2
10 points
(2p+3)(3p-2)
O5p²-23p-10
O 6p²+5p-6
O 6p²-6
O 5p²-10
Answer:
B. 6p²+5p-6
Step-by-step explanation:
[tex]\bf \left(2p+3\right)\left(3p-2\right)[/tex]
Let's apply the FOIL method:-
[tex]\bf \left(2p+3\right)\left(3p-2\right)=[/tex]
[tex]\bf 2p\times \:3p+2p\left(-2\right)+3\times\:3p+3\left(-2\right)[/tex]
[tex]\bf 6p^2-4p+9p-6[/tex]
[tex]\bf 6p^2+5p-6[/tex]
Therefore, option B. 6p²+5p-6, is your answer!
__________________
Hope this helps!
Have a great day!
In contrast to Supervised learning, Unsupervised learning has more models and more evaluation meth used in order to ensure the outcome of the model is accurate. This statement is overall a false statement.
An unsupervised learning model might give a less accurate outcome if compared to supervised learning.
1. Algorithms of unsupervised learning are taught using the data that are unlabeled.
2. The model of unsupervised learning doesn't take any feedback.
3. In unsupervised learning, we see that only input data is supplied to the model, no output data.
Assess reasonableness a monument will be at the circumcenter of a triangular plot of land at the state capital. on the coordinate grid, the vertices of the triangular plot of land are a(1, 5) , b(7, 5) , and c(8, 0) .
Overall, the statement that Unsupervised learning has more models and more evaluation methods used in order to ensure the outcome of the model is accurate is false. Unsupervised learning algorithms are taught using data that may be labeled, but in most cases the labels are not used to infer the model. The model of unsupervised learning does not take any feedback, as it is not supervised, and only input data is supplied to the model, no output data. The evaluation of unsupervised learning models relies on different metrics such as clustering accuracy, silhouette coefficient, etc. Unsupervised learning algorithms are used for tasks such as clustering, anomaly detection and density estimation.
assess reasonableness a monument will be at the circumcenter of a triangular plot of land at the state capital. on the coordinate grid, the vertices of the triangular plot of land are a(1, 5) , b(7, 5) , and c(8, 0) .
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while grading her students' most recent quiz on equation solving, mrs. jones calculated that approximately forty percent of her students answered question number 14 with multiple choice option b, while the other sixty percent answered a or c. question #14 from Mrs. Jones's students' most recent quiz:
14) Solve the single variable equation for n.
a.n=3
b.no solution
c.infinitely many solutions
Use complete sentences to compare the similarities and differences of each of the multiple choice answer options A-C. In your answer, rationalize why a student would choose each of the options as the correct answer
If while solving an equation, a single value is obtained for the variable, then the equation has only a single solution.
The option (a) is n=3.
If while solving an equation, a single value is obtained for the variable, then the equation has only a single solution. If n=3 is obtained after solving the equation, then the student should chose option (a) as the answer.
The option (b) is "no solution".
While solving an equation, if we obtain an equation which is mathematically false, then the equation will have no solution. So, no solution is chosen when no value is obtained for n and the final equation is mathematically false.
The option (c) is "infinitely many solutions".
While solving an equation, if we obtain an equation which is mathematically correct such as 0=0, 7=7 etc., then the equation will have infinietly many solutions. So, infinitely many solutions is chosen when no value is obtained for n and the final equation is mathematically correct.
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1,3,6,10,15,21,28 as a function
It seems that the sequence you provided is the sequence of triangular numbers. The function that generates this sequence could be defined as:
f(n) = n*(n+1)/2
Where n is the position of the number in the sequence.
So, for example:
f(1) = 1*(1+1)/2 = 1
f(2) = 2*(2+1)/2 = 3
f(3) = 3*(3+1)/2 = 6
and so on.
Please help me...I neep help
By using the formula for the mean:
(x₁ + x₂ + ...)/N
We will see that the mean is 7 minutes.
What is the mean of the times?If we have a set of N elements:
{x₁, x₂, x₃...}
The mean of these values is given by:
(x₁ + x₂ + ...)/N
Here we have a set of 3 points, such that the points are {5, 6, 10} the mean of these points is:
M = (5 + 6 + 10)/3
M = 21/3
m = 7
The mean of the tmes is 7 minutes.
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FILL IN THE BLANK when a study uses the__________method of data collection, participants complete a questionnaire about their thoughts, feelings, and behavior at the end of each day.
The correct answer is Diary.
We acquire a different understanding of participants' experiences than we might from other techniques when participants immediately record their observations or perceptions. Participants may feel more comfortable expressing themselves in a diary than in an interview since sometimes personal reflections are more open. The participant's commitment to following through is, of course, a requirement of diary systems. It can be difficult to anticipate someone's availability to write within the time range set by the researcher. To get over these challenges, contemporary diary researchers employ a range of strategies, including as utilizing apps and technology or combining textual and artistic techniques
Hence, The correct answer is Diary Method.
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Vigorous exercise helps people live several years longer (on average). Whether mild activites like slow walking extend life is not clear. Suppose that the added life expectancy from regular slow walking is just 2 months. A statistical test is more likely to find a significant increase in mean life expectancy if:
(a) it is based on a very large random sample and a 5% significance level is used.
(b) it is based on a very larg random sample and a 1% significance level is used.
(c) it is based on a very small random sample and a 5% significance level is used.
(d) it is based on a very small random sample and a 1% significance level is used.
(e) the size of the sample doesnt have any effect on the significance of the test.
A statistical test is more likely to find a significant increase in mean life expectancy if it is based on a very large random sample and a 1% significance level is used.
As per the given data
Vigorous exercise helps people live several years longer.
The mild activities like slow walking extend life is not clear.
The added life expectancy from regular slow walking is just 2 months.
Here we have to determine that when a statistical test is more likely to find a significant increase in mean life expectancy.
The increase in life expectancy regarding regular slow walking should be considerably greater than 2 months, which means that the a larger sample is needed to give a more precise result
The chances of finding significant results increases when we increase sample size or use a higher significance level.
So, among the given options, significant results will be achieved
If it is based on a very large random sample and a 1% significance level is used.
Therefore option (b) is correct.
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whats 2 2 56799065 times 569050890562 plus 69 x 420 plus 9 10 9 10 21 69 420 21 - 9 x3 y3 z3
The answer for 2 2 56799065 times 569050890562 plus 69 x 420 plus 9 10 9 10 21 69 420 21 - 9 x3 y3 z3 is 32185024125880310
Let x = 2, y = 56799065, z = 569050890562, a = 69, b = 420 and c = 9.
The equation is: 2x + y × z + a × b + (9 + 10 + 9 + 10) × (21 + 69 + 420 + 21) - 9 × 3 × y × 3 × z × 3
We can calculate this equation as follows:
2 × 2 + 56799065 × 569050890562 + 69 × 420 + (9 + 10 + 9 + 10) × (21 + 69 + 420 + 21) - 9 × 3 × 56799065 × 3 × 569050890562 × 3
= 4 + 32185023742042530 + 28380 + 145800 - 1365466177461590
= 32185024125880310
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Briley answered 85% of the 60 quiz questions correctly. How many questions did she answer correctly?
Answer:
51 questions she answered correctly.
Step-by-step explanation: 85/100 x 60
= 510/10
= 51
Answer:
51 questions
Step-by-step explanation:
To do this we need to realize that 85% is equal to 85/100. This can be simplified in fraction form to .85.
Looking at the question, we see that it says "Briley answered 85% of the 60 quiz..." A key word here is of. Of always means multiply. So we can see if we were going to form an equation, we would be multiplying.
Briley answered correctly = (85%) times (60 questions)
Mathematically, ?=(.85)x(60)=51
So we know she answered 51 correctly, and that 51 is 85% of 60.
I hope this helps you!
X = y+9, y = 4x+10 solve for X and y
The value of x and y for the given equations are - (19/3) and -46/3 respectively.
What are equations?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For instance, 2x - 5 = 13.
Given the two equations are as follows:
x = y + 9 and y = 4x + 10
Substitute the value of y in the first equation:
x = y + 9
x = 4x + 10 + 9
Isolate the value of x:
x - 4x = 19
-3x = 19
x = - (19/3)
Substitute the value of x in the first equation:
x = y + 9
- 19/3 = y + 9
Isolate the variable y:
y = -19/3 - 9
y = - 46/3
Hence, the value of x and y for the given equations are - (19/3) and -46/3 respectively.
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the 16-cm diameter disk in (figure 1) can rotate on an axle through its center. what is the net torque about the axle?
The net torque about the axle is zero, as no external forces are acting on the disk. Since there are no external forces acting on the disk, the sum of all the torques must be zero. Therefore, the net torque about the axle is zero.
The net torque about the axle is calculated by summing up all the torques about the axle due to external forces. Since there are no external forces acting on the disk, the sum of all the torques must be zero. Therefore, the net torque about the axle is zero.
The net torque about the axle of the 16-cm diameter disk in is zero, since there are no external forces acting on the disk. To calculate the net torque about the axle, we need to take the sum of all the torques about the axle due to external forces. Since there are no external forces, this sum must be zero. This means that the net torque about the axle is zero. This is because there is no force causing the disk to rotate and therefore, the net torque about the axle must also be zero. This result is consistent with the law of conservation of angular momentum, which states that when no external forces are acting on an object, the total angular momentum of the system must remain constant. Thus, the net torque about the axle of the 16-cm diameter disk in is zero.
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(-1,-4) that is perpendicular to the line Y=-2/3x+1
the equation of line perpendicular to y=-2/3x+1 will be y = 3/2x -5/2.
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The line given y=-2/3x+1
here the slope is -2/3
So the slope of the required line will be m2 = - 1/m1
m2 = 3/2
The required line equation will be [tex]\frac{y+4}{x+1}[/tex] = 3/2
2(y+4) = 3(x+1)
2y+8= 3x+3
y = 3/2x -5/2
Hence the equation of line perpendicular to y=-2/3x+1 will be y = 3/2x -5/2.
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One cubic foot of a chemical weighs 60 pounds. How many pounds of the chemical can a container with the dimensions shown hold?
The number of pounds of the chemical container can hold with given dimension is, 3600 pounds
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.
Given that,
1 ft³ = 60 pounds
A container which has dimensions,
length = 6 ft
height = 4 ft
width = 5/2 ft
Volume of container = length × height × width
= 6 × 4 × 5/2
= 60 ft³
1 ft³ = 60 pounds
60 ft³ = 60 × 60 pounds
= 3600 pounds
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Someone help me please
∠A and ∠B are vertical angles. If angle A=(8x-23) and angle B=(6x-5) then find the measure of ∠A.
The measure of ∠A is 49.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Vertical angles are equal.
∠A = 8x - 23
∠B = 6x - 5
Now,
8x - 23 = 6x - 5
8x - 6x = -5 + 23
2x = 18
x = 9
Now,
∠A.
= 8x - 23
= 8 x 9 - 23
= 72 - 23
= 49
Thus,
∠A is 49.
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Which facts could be applied to simplify this expression? Check all that apply. 5 x + 3 y + (negative x) + 6 z Group of answer choices The simplified expression is 5 x + 3 y + 6 z. To add like terms, add the coefficients, not the variables. First add 5x + x. Only combine terms which contain the same variable. The simplified expression is 4 x + 3 y + 6 z.
Answer:
I dont understand what this is can you add a picture of the question?
Step-by-step explanation:
Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning
The pair of figures are similar because:• Both figures are parallelograms
• All sides are congruents and • Scale factor 1: 2.5
A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The pair of figures are similar because:
• Both figures are parallelograms
• All sides are congruents
• Angles W and Y are congruent with angles P and R
• Angles X and Z are congruent with angles S and Q
• Scale factor 1: 2.5
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What is the greatest common factor of {42,10}
Answer:
5
Step-by-step explanation:
ap stats the random variable x has mean 12 and standard deviation 3 the random variable w is defined as w
The mean of the random variable w is 15, and the standard deviation is 3.46.
The formula for the mean of a random variable is μ = E(x), and the formula for the standard deviation of a random variable is σ = sqrt(Var(x)). In this case, the mean of the random variable x is 12, and the standard deviation is 3. We can calculate the mean and standard deviation of the random variable w as follows:
E(w) = E(x) + 3 = 12 + 3 = 15
Var(w) = Var(x) + 9 = 9 + 9 = 18
SD(w) = sqrt(Var(w)) = sqrt(18) = 3.46
Therefore, the mean of the random variable w is 15, and the standard deviation is 3.46.
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