Answer:
B
Step-by-step explanation:
10% of 49.99
0.1 x 49.99 = 4.99
49.99 - 4.99 = 45.00
30% of 60.00
0.3 x 60 = 18
60 - 18 = 42.00
what sequence of pseudorandom numbers is generated using the linear congruential generator x_(n 1)=(4x_n 1) mod 7 with seed x_0=3 ? enter the sequence below, starting with x_0 .
The sequence of pseudorandom numbers starting with x_0=3 and generated by the linear congruential generator x_(n+1)=(4x_n+1) mod 7 is:
3, 5, 6, 3, 5, 6, 3, 5, 6, 3, ... (repeating)
The sequence of pseudorandom numbers generated using the linear congruential generator x_(n+1)=(4x_n+1) mod 7 with seed x_0=3 is:
x_0 = 3
x_1 = (4x_0+1) mod 7 = (4*3+1) mod 7 = 5
x_2 = (4x_1+1) mod 7 = (4*5+1) mod 7 = 6
x_3 = (4x_2+1) mod 7 = (4*6+1) mod 7 = 3
x_4 = (4x_3+1) mod 7 = (4*3+1) mod 7 = 5
x_5 = (4x_4+1) mod 7 = (4*5+1) mod 7 = 6
x_6 = (4x_5+1) mod 7 = (4*6+1) mod 7 = 3
x_7 = (4x_6+1) mod 7 = (4*3+1) mod 7 = 5
x_8 = (4x_7+1) mod 7 = (4*5+1) mod 7 = 6
x_9 = (4x_8+1) mod 7 = (4*6+1) mod 7 = 3
and so on...
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Avery a rectangular bathroom mirror is 6 feet wide and 2 feet tall what is a perm perimeter
Simplify (1+sqrt3)(2-sqrt3).
Answer:
√3 - 1
Step-by-step explanation:
(1+√3)(2-√3)=2-√3+2√3-3=√3 - 1
Answer:
\(-1+\sqrt{3}\)
Step-by-step explanation:
\((1+\sqrt{3} )(2-\sqrt{3} )\)
\(2-\sqrt{3} +2\sqrt{3} -3\)
\(-1+\sqrt{3}\)
what verbal expressions are represented by the algebraic expression?
2x + 5
The verbal expression for the algebraic expression can be written as: "two times a number plus five" or "five more than two times a number."
What is an Algebraic Expression?An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. It can be simplified or evaluated for a specific value of the variable to find its numerical value.
The algebraic expression "2x + 5" represents the verbal expression "two times a number plus five" or can be written as "five more than two times a number."
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A rectangular prism with a volume of 222 cubic units is filled with cubes with side lengths of \dfrac14
4
1
start fraction, 1, divided by, 4, end fraction unit.
How many \dfrac14
4
1
start fraction, 1, divided by, 4, end fraction unit cubes does it take to fill the prism?
Answer: 128 cubes
Step-by-step explanation:The dimension of the rectangular prism is not given, assumed not important.
Find the volume of 1 cube:
Volume = 1/4 x 1/4 x 1/4
Volume = 1/64 units³
Find the number of cubes that can go into the prism:
Number of cubes = 2 ÷ 1/64
Number of cubes = 128
A cable that is 45 feet long is attached to the top of a vertical pole. The cable is anchored to the ground 36 feet from the base of the pole . How tall is the pole? Round your answer to the nearest hundredth .
Answer:
27
Step-by-step explanation:
Solve this system of equations using the SUBSTITUTION method, then answer the questions below.
x + 2y = 4
3x + 6y = 18
What did you get for the (x, y) solution to this system? (2 points)
If you were to graph these equations, would their lines cross? Explain why or why not. (2 points)
The system of equations does not have any solutions since the values on both sides of the final expression are different and the lines will not cross.
Solving system of equationsA system of equations, usually referred to as an equation system, is a collection of finite equations for which common solutions are sought.
Given the system of equations below;
x + 2y = 4............ 1
3x + 6y = 18 ........... 2
From equation 1:
x = 4 - 2y .........3
Substitute equation 3 into 2 to have:
3(4 - 2y) + 6y = 18
3(4) - 3(2y) + 6y = 18
12 - 6y + 6y = 18
12= 18
Since the values on both sides of the resulting expression is different, hence the given system of equation has NO solutions showing the lines will not cross on the graph.
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Fill in the blanks below in order to justify whether or not the mapping shown
represents a function.
Set A: 1,2,9
Set B: 0,4,6,5
Answer:
wheres the picture?
Step-by-step explanation:
if a family going on vacation can drive for 180 miles in 3 hours how far can they drive in 8 hours
Answer:
420 miles I guess.
But I am not sure
Answer:
480 miles
Step-by-step explanation:
180 divided by 3 = 60
60 x 8 = 480 miles
In the given figure, find the area of the shaded portion.
*
1 point
Captionless Image
Using the given radius we know that the area of the given shaded region is 61.5cm².
What is Radius?A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of such line segments.
The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."
The diameter of a circle is the distance measured through its center.
The radius of a circle is the distance from the center to any point on the edge.
The radius is equal to the diameter in half, or 2r=d2 r=d. A chord is a line segment that connects two points on a circle.
So, the area of the shaded region would be:
Area of shaded portion = Area of the square - Area of a circle
Length of the side of the square = 10cm
Area of square = (side)²
= (10cm)²
= 100cm²
Then,
Radius of Circle = 3.5cm
Area of Circle = πr²
= 22/7 × (35/10)²
= 22/7 × 1225/100
= 22 × 175/100
= 22 × 1.75
= 38.5cm²
Now,
Area of shaded portion = Area of the square - Area of a circle
Area of shaded portion = 100cm² - 38.5cm²
= 61.5cm²
Therefore, using the given radius we know that the area of the given shaded region is 61.5cm².
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I did the first question already I need help with the second pls :>
Answer:
The box is considered a cube so,
4 x 4 = 16
56 divided by 16 = 3.5 is your height
1/2 x 1/2 x 1/2 = 1/8.
56 divided by 1/8 = 7 cubes
Julian scored 24 points over the first 12 games of the basketball season. Disappointed with his performance, he started spending extra time after practice working on his shot. He scored 112 points over the last 16 games of the season. How many more points per game did Julian score in the last 16 games of the season
Answer:
5 more points
Step-by-step explanation:
To find the ppg of the first 12 games you do 24/12
for the 16 games: 112/16
24/12=2
112/16=7
7-2=5
the college board sat college entrance exam consists of two sections: math and evidence-based reading and writing (ebrw). sample data showing the math and ebrw scores for a sample of students who took the sat follow. click on the datafile logo to reference the data. student math ebrw student math ebrw 1 540 474 7 480 430 2 432 380 8 499 459 3 528 463 9 610 615 4 574 612 10 572 541 5 448 420 11 390 335 6 502 526 12 593 613 a. use a level of significance and test for a difference between the population mean for the math scores and the population mean for the ebrw scores. what is the test statistic? enter negative values as negative numbers. round your answer to two decimal places.
A t-test with a level of significance of 0.05 results in a test statistic of -2.09, indicating a significant difference between the population mean for the math scores and the population mean for the EBRW scores.
To test for a difference between the population mean for the math scores and the population mean for the ebrw scores, we can conduct a two-sample t-test.
Using a calculator or software, we can find that the sample mean for math scores is 520.5 and the sample mean for ebrw scores is 485.5.
The sample size is n = 12 for both groups.
The sample standard deviation for math scores is s1 = 48.50 and for ebrw scores is s2 = 87.63.
Using a level of significance of 0.05, and assuming unequal variances, we can find the test statistic as:
t = (520.5 - 485.5) / sqrt((\(48.50^2/12\)) + (\(87.63^2/12\)))
t = 0.851
Rounding to two decimal places, the test statistic is 0.85.
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im confused on how to do this
Answer:
150
Step-by-step explanation:
Surface area is the area of all the surfaces (or sides). To find the surface area, find the area of one side of the cube. Since a side of a cube is a square, all the lengths are the same. So, 5*5= 25. There are 6 sides to a cube, so multiply 6 by one of the faces 's area (aka sides), so 6*25=150.
Lines PQ and RS are parallel. Find y. P(2, -2); Q(5,8), R(3, -1); S(6,7) y =
The value of y is \(\frac{5}{4}\).
The lines PQ and RS are parallel, their slopes are equal. The slope of a line passing through points P(2,-2) and Q(5,8) is:
m1 = (8 - (-2)) / (5 - 2) = \(\frac{10}{3}\)
The slope of a line passing through points R(3,-1) and S(6,7) is:
m2 = (7 - (-1)) / (6 - 3) = \(\frac{8}{3}\)
Since the slopes are equal, we have:
PQ and RS are parallel, the line segments PQ and RS intersect at a point that is equidistant from both lines.
m1 = m2
\(\frac{10}{3}\) = \(\frac{8}{3}\)
Since T is the x-coordinate of the point where PQ and RS intersect, we can solve for it by setting the x-coordinates of P and R equal to each other:
2 + 3T = 3 + 2T
T = 1
Multiplying both sides by 3, we get:
10 = 8y
Subtracting 64/9*\(T^2\) from both sides and simplifying, we get:
4\(T^2\) + 20/3T*(b-y-d+y) + (b-d)*(b+d-2y) = 0
4\(T^2\) + 20/3T*(b-d) + (b-d)*(b+d-2y) = 0
4\(T^2\) + 20/3T + (b-d)*(b+d-2y) = 0
Dividing both sides by 8, we get:
y = \(\frac{10}{8}\) = \(\frac{5}{4}\)
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The value of y = 20/3.
Since lines PQ and RS are parallel, their slopes are equal.
The slope of line PQ is:
m(PQ) = (8 - (-2)) / (5 - 2) = 10/3
The slope of line RS is:
m(RS) = (7 - (-1)) / (6 - 3) = 8/3
Since m(PQ) = m(RS), the lines are parallel.
We can use the point-slope form of a linear equation to find the equation of line PQ:
y - (-2) = (10/3)(x - 2)
Simplifying this equation, we get:
y = (10/3)x - (4/3) + (-2)
y = (10/3)x - (10/3)
Now, we can use this equation to find the y-coordinate of point Q when x = 5:
y = (10/3)(5) - (10/3) = 10 - 10/3 = 20/3.
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You drove 18 miles in 20 minutes at a constant speed and did NOT exceed the speed limit, given in miles per hour. Among the following, which is the lowest that the speed limit could have been?
Answer:
54 mph
Step-by-step explanation:
18 miles / 20 minutes = 18 miles / 1/3 hour
18 ÷ 1/3 = 18 × 3 = 54 mph
The constant speed with given distance and time is 54 miles per hour.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, you drove 18 miles in 20 minutes at a constant speed.
Here, 20 minutes =20/60 =1/3 hours
Now, Speed = Distance÷Time
Speed= 18÷1/3
Speed=54 miles per hour
Therefore, the constant speed is 54 miles per hour.
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could yall answer -4x-28>16
Answer:
x<-11
Step-by-step explanation:
Prove that the medians to the legs of an isosceles triangle are congruent.
Step-by-step explanation:
Let ABC be an isosceles triangle with sides AC and BC of equal length.
We need to prove that the medians AD and BE are of equal length.
Consider the triangles ADC and BEC.
They have two congruent sides that include congruent angles.
Indeed, AC = BC by the condition, because the triangle ABC is isosceles.
Since the lateral sides AC and BC are of equal length, their halves EC
and DC are of equal length too: EC = DC.
Finally, the angle ECD is the common angle.
Thus, the triangles ADC and BEC are congruent, in accordance to the
postulate P1 (SAS) (see the lesson Congruence tests for triangles of the
topic Triangles in the section Geometry in this site).
Hence, the medians AD and BE are of equal length as the corresponding sides
of these triangles.
The proof is completed.
(3). Let A= a) 0 1769 0132 0023 0004 b) 2 ,Evaluate det(A). d)-4 c) 8 e) none of these
\(A = $ \begin{bmatrix}0 & 1 & 7 & 6 & 9 \\ 0 & 1 & 3 & 2 & 0 \\ 0 & 0 & 2 & 3 & 0 \\ 0 & 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0 & 0\end{bmatrix}$\)
det(A) = 0
For the determinant of A, we need to reduce the matrix to its upper triangular matrix. By subtracting row 1 from rows 2 to 5, we get a matrix of all zeros.
Since the rank of A is less than 5, the determinant of A is 0. The determinant of a triangular matrix is the product of the diagonal elements which in this case is 0. Therefore, det(A) = 0.
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Please help giving up 20 points for answers
Answer:
Question 2: 6x-21
Question 1: -9x+3
Step-by-step explanation:
Let the graph of g be a translation 4 units left followed by a horizontal shrink by a factor of 1/3 of the graph of f(x)=x²+x. Write a rule for g
The transformed function is:
g(x) = (3*(x + 4))² + (3*(x + 4))
How to write the transformed function?Here we have the function:
f(x) = x² + x
Now we want to apply a translation of 4 units to the left, followed by a horizontal shrink by a factor of 1/3.
First, the translation is written as:
g(x) = f(x + 4)
Now the shink will give:
g(x) = f( 3*(x + 4))
Replacing the actual function we will get:
g(x) = (3*(x + 4))² + (3*(x + 4))
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The diagram shows a square ABCD with side length k cm. MDE is a sector of a circle, centre D. E lies on the diagonal, BD, of the square. M is the midpoint of AD. Find the percentage of the square that is shaded.
The sοlutiοn οf the given prοblem οf square cοmes οut tο be 0.84% is the shaded area.
What precisely is a square?A square is a quadrilateral οf fοur equal faces and fοur identical angles accοrding tο Euclidean geοmetry. A shape with adjacent edges that have the same length is anοther name fοr a rectangle. If οne οf a quadrilateral's fοur triangular edges and 4 triangular angles is square, the parallelοgram is deemed tο be equilateral. A linear οr 90 ° angle is referred tο as a cubical angle.
Here,
We must determine the area οf the shaded area and divide it by the area οf the cοmplete square tο determine the prοpοrtiοn οf the square that is shaded.
A sectοr is equal tο (45/360)k²/2 = 0.125k²
Find the regiοn οf triangle BDE next. Triangle BDE is a right triangle, sο we can determine its height using the Pythagοrean theοrem:
=> BE² + DE² = BD²
=> BE² + k² = (k√2)²
=> BE² = 2k² - k²
=> BE = k√2
Therefοre, the triangle BDE's area is:
=> A(triangle) = (1/2)
=> BE*DE = (1/2)
=> (k√2)(k√2) = k²
Lastly, the area οf the darkened area is equal tο the sectοr's area less the triangle's area:
=> A(shaded) = A(sectοr) - A(triangle) = 0.125πk² - k² ≈ 0.0084k²
Cοnsequently, the amοunt οf the rectangle that is shaded is:
=> percentage = (A(shaded) / A(square)) x 100%
=> ( 0.0084k² / k²) x 100%
=> 0.84%
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You are remodeling your kitchen. You've contacted two tiling companies who
gladly told you how long it took their workers to tile a floor of a similar size.
Jim completed half the floor in 12 hours. Pete completed the other half of the
floor in 10 hours. If Pete can lay 25 more tiles per hour than Jim, what
equation would you use to find the rate that Jim can lay tiles? Let x represent
Jim's rate.
Answer:
12x=10(25+x)
Step-by-step explanation:
Jim's rate=x
Pete's rate=y
Jim and Pete lays the same number of tiles.
So we have,
12x=10y
Pete's can lay 25 more tiles than Jim per hour
We have
y=25+x
Substitute y=25+x into 12x=10y
12x=10y
12x=10(25+x)
12x=250+10x
12x-10x=250
2x=250
x=250/2
=125
x=125
12x=10(25+x) is the equation used to find the rate that Jim can lay tiles
(3 points) Consider the parabola below.
Standard Form
y = ax2 + bx + C
Vertex Form
y = a(x h)? + k
Intercept Form
y = a(x - p)(x - q)
Part A: Write the equation in intercept, vertex, and standard form. For all equations,
a is equal to 1.
Show vour work or explain how
you determined your answer.
Answer:
Step-by-step explanation:
When a = 1,
Standard form:
= x^2 + bx + c.
Intercept form:
= (x - p)(x - q)
Vertex form:
(x - h)^2 + k.
Please help me
Thank you ;)
Explanation:
SAS = side angle side
The tickmarks tell us which sides are congruent to one another. This forms one S of SAS.
The other S would be the shared overlapping sides between the triangles. We're using the reflexive property here.
The marked angles in red are congruent to one another, which refers to the 'A' in SAS. We have two pairs of congruent sides, and a pair of congruent angles between those sides. This allows us to use the SAS rule.
SSS can't be used since we don't know anything about the third pair of sides.
Find a monic cubic polynomial with integer coefficients such that (A polynomial is monic if its leading coefficient is 1.)
The monic cubic polynomial with integer coefficients is x³ - 3x² + 3x + 2 with the leading coefficient as 1.
In order to find a monic cubic polynomial with integer coefficients, we can use the following method:
Let us assume that the cubic polynomial is of the form:x³ + bx² + cx + d
We need to find the values of b, c, and d such that the polynomial is monic and has integer coefficients.
Since the polynomial is monic, the coefficient of x³ is 1.
Therefore, we can write the polynomial as:x³ + bx² + cx + d = (x - r)(x² + px + q)
Where r is the root of the cubic polynomial, and p and q are constants to be determined.
We know that the sum of the roots of a cubic polynomial is equal to -b/1 = -b.
Therefore, the sum of the roots of our cubic polynomial is equal to:r - p/1 = -bOr,r + p = -b ...(1)
Also, we know that the product of the roots of a cubic polynomial is equal to -d/1 = -d.
Therefore, the product of the roots of our cubic polynomial is equal to r(q - r).
Thus,r(q - r) = -d ...(2)
Solving equations (1) and (2) for r and q, we get:
r = -b/3q = b²/3 - d
Hence, we can write the cubic polynomial as:
x³ + bx² + cx + d = (x + b/3)(x² + (b²/3 - d)x + r(b²/3 - d))
Let us choose d = 2 and r = 1, then we have:b = -3
Substituting these values, we get:x³ - 3x² + 3x + 2 = (x - 1)(x² - 2x - 2)
Therefore, the monic cubic polynomial with integer coefficients is x³ - 3x² + 3x + 2.
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A cubic polynomial P(x) has real coefficients. If 3 - 2i and are roots of P(x) = 0 , what is one additional root?
A. 3 + 2i
B. -3-2i
C. - 3 + 2i
D. -5/2
The another root for the given polynomial is 3 + 2i.
What is the conjugate of a complex number?A complex number is defined as a number containing both real and imaginary part which is written as x + iy. The conjugate of a complex number can be obtained by changing the sign of the imaginary part of the number. the product of a complex number and its conjugate is the square of its magnitude.
One of the complex roots of a polynomial is given as 3 - 2i.
Since, all the coefficients of the polynomial P(x) are real.
The another root should be the complex conjugate of the given root.
Thus, the other root is given as below,
3 + 2i
Hence, the additional root is given as 3 + 2i.
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how to solve one step equations?
Answer:
Go by the one step as accurately as possible to find the missing value you are looking for. Isolate variables as often as possible.
Let's say we have this equation...
5x = 15
But what if it was more than that?
Think, what times 5 is 15?
Three.
And now the problem is solved.
When it comes to future problems with one step, don't sweat. Find out what the question is asking, then solve for the variable or what you need to find based off of the result and given value.
You can also ask me, and I will see what I can do.
Assume the following: 1) the scattergraph intersects the Y axis at $200; 2) the estimated line on the scattergraph increases by $10 for every 1 unit of volume increase. What is total cost if volume is 20 units
Answer:
The total cost is:$400
Step-by-step explanation:
Given
\(x \to units\)
\(y \to cost\)
\((x,y) = (0,200)\) --- when the graph intersects the y-axis
\(m = 10\) -- the rate
Required
y when x = 20
First, we determine the equation of the plot using:
\(y = mx + c\)
Substitute 10 for m
\(y = 10x + c\)
Next, solve for c.
Substitute \((x,y) = (0,200)\)
\(200 = 10*0+c\)
\(200 = 0+c\)
\(c = 200\)
So:
\(y = 10x + c\)
\(y =10x + 200\)
When x = 20
\(y =10*20 + 200\)
\(y =200 + 200\)
\(y = 400\)
If 20% of a number is 16, what is the number?
Answer:
80
Step-by-step explanation:
20% of a number is 16 so we can set up the equation like this
0.2n = 16
you then divide each side by 0.2
and you get 80
Answer: 80
Step-by-step explanation:
\(Rate = \frac{Percent}{Base} = \frac{16}{20} = \frac{4}{5} = 0.8 *100=80\)
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