Problem
8 ( 11 - 2b ) = -4 ( 4b - 22 )
Solution
We can distribute the terms in the equation and we got:
88 -16b = -16b +88
If we add 16b in boh sides we got:
88 =88
Then for this case we can conclude that this equation has infinite solutions
Solve the following system using the elimination method. Enter your answer as an ordered pair in the form (x,y) If there is one unique solution. Enter all if there are infinitely many solutions and enter none if there are no solutions 6x - 5y = 41 2x + 6y = 6
Okay, here we have this:
Considering the provided system, we are going to solve it using the elimination method, so we obtain the following:
[tex]\begin{gathered} \begin{bmatrix}6x-5y=41 \\ 2x+6y=6\end{bmatrix} \\ \begin{bmatrix}6x-5y=41 \\ (-3)2x+6y=6(-3)\end{bmatrix} \\ \begin{bmatrix}6x-5y=41 \\ -6x-18y=-18\end{bmatrix} \end{gathered}[/tex]Now we will add the equations to eliminate the y term:
[tex]\begin{gathered} \begin{bmatrix}-23y=23\end{bmatrix} \\ \begin{bmatrix}y=\frac{23}{-23}\end{bmatrix} \\ \begin{bmatrix}y=-1\end{bmatrix} \end{gathered}[/tex]Finally, let's replace in the first equation to find the value of x:
[tex]\begin{gathered} \begin{bmatrix}6x-5(-1)=41\end{bmatrix} \\ \begin{bmatrix}6x+5=41\end{bmatrix} \\ \begin{bmatrix}6x=36\end{bmatrix} \\ \begin{bmatrix}x=\frac{36}{6}\end{bmatrix} \\ \begin{bmatrix}x=6\end{bmatrix} \end{gathered}[/tex]Finally we obtain that the unique solution for the system is the ordered pair: (6, -1).
I need help on 4 please it says find the value of x round each answer to the nearest tenth
The pythagorean theorem is :
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse
a and b are the legs of the triangle.
From the problem, a = x, b = 19.1 and c = 30.5
Using the formula :
[tex]\begin{gathered} 30.5^2=x^2+19.1^2 \\ 930.25=x^2+364.81 \\ x^2=930.25-364.81 \\ x^2=565.44 \\ x=\sqrt[]{565.44} \\ x=23.779 \end{gathered}[/tex]The answer rounded to the nearest tenth is x = 23.8
A 40 kilogram bag of seeds are spread out throughout the entire yard, how much in kilograms of seeds will not be watered? Percentage of my previous question is 96.1%In the last question 96.1% of grass was covered in water Their were 123 squares that got water except 5 of them so I divided 123 by 128 to find the percentage of grass covered by waterIf their were 5 squares that didn’t get water out of 128 then can’t we work from that? To find the 40 kilograms that wouldn’t get water from those 5 squares
5 squares of 128 didn't get water.
If 40kg are spread out throughout the entire yard, how much in kilograms of seeds will not be watered?
Use a rule of three to solve the question:
[tex]\begin{gathered} x=\frac{40\cdot5}{128} \\ \\ x=\frac{200}{128} \\ \\ x=1.56 \end{gathered}[/tex]Then, 1.56 kilograms of seeds will not be watered
One canned juice drink is 20% orange juice, another is 10% orange juice. How many liters of each should be mixed together in order to get 10L that is 11% orangeNice?
Let:
x = Liters of 20% orange juice
y = Liters of 10% orange juice
z = Liters of 11% orange juice
so:
[tex]0.2x+0.1y=10\cdot0.11[/tex]so:
[tex]\begin{gathered} 0.2x+0.1y=1.1 \\ y=10-x \\ so\colon \\ 0.2x+0.1(10-x)=1.1 \\ 0.2x+1-0.1x=1.1 \\ 0.1x=0.1 \\ x=\frac{0.1}{0.1} \\ x=1 \\ so\colon \\ y=10-1=9 \end{gathered}[/tex]Answer:
1 liters of 20% orange juice
9 liters of 10% orange juice
15 1/3 ÷ 3 5/6 A. 45 6/9 B. 5 1/4 c . 4 d. 4 1/3
To compute 15 1/3 ÷ 3 5/6, first transform the mixed numbers into fractions, as follows:
[tex]15\frac{1}{3}=\frac{15\cdot3+1}{3}=\frac{46}{3}[/tex][tex]3\frac{5}{6}=\frac{3\cdot6+5}{6}=\frac{23}{6}[/tex]Then, 15 1/3 ÷ 3 5/6 = 46/3 ÷ 23/6. Dividing by a fraction is equivalent to multiply by its inverse, then 46/3 ÷ 23/6 = 46/3 x 6/23:
[tex]\frac{46}{3}\cdot\frac{6}{23}=\frac{46}{23}\cdot\frac{6}{3}=2\cdot2=4[/tex]Find the first six terms of the sequence.a = 2n² - 2
We are given the nth term of a sequence:
[tex]a_n=2n^2\text{ - 2}[/tex]We are required to find the first six terms.
For each term, we substitute for n and evaluate.
First term (n =1)
[tex]\begin{gathered} a_1\text{ = 2 }\times(1)^2\text{ - 2} \\ =\text{ 2 -2 } \\ =\text{ 0} \end{gathered}[/tex]Second term (n = 2)
[tex]\begin{gathered} a_2\text{ =2 }\times(2)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 4 -2} \\ =\text{ 8 - 2} \\ =\text{ 6} \end{gathered}[/tex]Third term (n = 3)
[tex]\begin{gathered} a_3\text{ = 2 }\times(3)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 9 - 2} \\ =\text{ 18 - 2} \\ =\text{ 16} \end{gathered}[/tex]Fourth term (n =4)
[tex]\begin{gathered} a_4\text{ = 2}\times(4)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 16 - 2} \\ =\text{ 32 - 2} \\ =\text{ 30} \end{gathered}[/tex]Fifth term ( n = 5)
[tex]\begin{gathered} a_5\text{ = 2 }\times(5)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 25 - 2} \\ =\text{ 50 - 2} \\ =\text{ 48} \end{gathered}[/tex]Sixth term ( n = 6)
[tex]\begin{gathered} a_6\text{ = 2 }\times(6)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 36 - 2} \\ =\text{ 72 - 2} \\ =\text{ 70} \end{gathered}[/tex]Hence, the first six terms of the sequence are : 0, 6, 16, 30, 48 and 70
The population of Boom town is 775,000 and is increasing at a rate of 6.75% each year. How many years will it take to reach a population of 1,395,000?
To study population growth, we use the following formula
[tex]P=P_0\cdot e^{rt}[/tex]Where,
[tex]\begin{gathered} P=1,395,000 \\ P_0=775,000 \\ r=0.0675 \end{gathered}[/tex]Let's replace the values above, and solve for t.
[tex]\begin{gathered} 1,395,000=775,000\cdot e^{0.0675t} \\ e^{0.0675t}=\frac{1,395,000}{775,000} \\ e^{0.0675t}=1.8 \\ \ln (e^{0.0675t})=\ln (1.8) \\ 0.0675t=\ln (1.8) \\ t=\frac{\ln (1.8)}{0.0675} \\ t\approx8.7 \end{gathered}[/tex]Hence, it would take 8.7 years to reach a population of 1,395,000.If a triangle ABC is at: A = ( 2, 9 ) B = ( 5, 1 ) C = ( - 6, - 8 ) and if it is translated right 2 and down 7, find the new point B'.
Solution
Step 1
Triangle ABC is at: A = ( 2, 9 ) B = ( 5, 1 ) C = ( - 6, - 8 )
Step 2
If it is translated right 2 and down 7
B = (5, 1)
B' = ( 5+2, 1-7)
B' = ( 7, -6)
Final answer
B' = ( 7, -6)
Divide 30.4cm into 8 equal parts.
Find the length of each part.
Answer:
304/10÷8/1
304/10×1/8
38/10
3.8
or
304÷8
=38
Working with special triangles. Find y. I have attached the picture.
In this case, we'll have to carry out several steps to find the solution.
Step :
Data:
diagram:
right triangle
Step 02:
special right triangles:
we must analyze the triangle to find the solution.
special right triangle example:
right triangle:
side y:
[tex]\begin{gathered} 88\text{ = }\sqrt{2}y\text{ } \\ \\ \frac{88}{\sqrt{2}}\text{ = y} \end{gathered}[/tex]That is the full solution.
What is the meaning of the x-intercept? A) Olivia's maximum distance from the pool was about 10.5 meters. B) It takes Olivia about 3.2 seconds to enter the pool. C) Olivia's dive was from a 10-meter platform. D) Olivia's speed was not constant.
Explanation:
X- intercept is the value of x when y is equal to zero.
On the graph, we have distance(meters) over time (secs).
The time is in the x axis. The value of x when y is equal to zero is a bit above 3.
This means when Olivia's distance is at point 0 meters, the seconds it takes to enter to pool is a bit over 3 secs (around 3,
From the options, the correct answer is It takes Olivia about 3.2 seconds to enter the pool (option B)
Bradley rolls two fair 6-sided dice with faces numbered 1 through 6. What is the probability that the sum of her two rolls has an odd number of factors?
Answer:
The probability that the sum of her two rolls has an odd number of factors will be;
[tex]P=\frac{7}{36}[/tex]Explanation:
We want to find the probability that the sum of her two rolls has an odd number of factors.
For the two rolls the total number of possible outcomes is;
[tex]6\times6=36[/tex]Let us list out the possible outcomes of the two rolls;
[tex]\begin{gathered} (\text{outcome)= sum= number of factors of the sum} \\ \mleft(1,1\mright)=2=2\text{ factors} \\ (1,2)=3=2\text{ factors} \\ (1,3)=4=3\text{ factors} \\ (1,4)=5=2\text{ factors} \\ (1,5)=6=4\text{ factors} \\ (1,6)=7=2\text{ factors} \\ \end{gathered}[/tex][tex]\begin{gathered} (2,1)=3=2\text{ factors} \\ (2,2)=4=3\text{ factors} \\ (2,3)=5=2\text{ factors} \\ (2,4)=6=4\text{ factors} \\ (2,5)=7=2\text{ factors} \\ (2,6)=8=4\text{ factors} \end{gathered}[/tex][tex]\begin{gathered} (3,1)=4=3\text{ factors} \\ (3,2)=5=2\text{ factors} \\ (3,3)=6=4\text{ factors} \\ (3,4)=7=2\text{ factors} \\ (3,5)=8=4\text{ factors} \\ (3,6)=9=3\text{ factors} \end{gathered}[/tex][tex]\begin{gathered} (4,1)=5=2\text{ factors} \\ (4,2)=6=4\text{ factors} \\ (4,3)=7=2\text{ factors} \\ (4,4)=8=4\text{ factors} \\ (4,5)=9=3\text{ factors} \\ (4,6)=10=4\text{ factors} \\ \end{gathered}[/tex][tex]\begin{gathered} (5,1)=6=4\text{ factors} \\ (5,2)=7=2\text{ factors} \\ (5,3)=8=4\text{ factors} \\ (5,4)=9=3\text{ factors} \\ (5,5)=10=4\text{ factors} \\ (5,6)=11=2\text{ factors} \end{gathered}[/tex][tex]\begin{gathered} (6,1)=7=2\text{ factors} \\ (6,2)=8=4\text{ factors} \\ (6,3)=9=3\text{ factors} \\ (6,4)=10=4\text{ factors} \\ (6,5)=11=2\text{ factors} \\ (6,6)=12=6\text{ factors} \end{gathered}[/tex]From the listed possible outcomes, the number of oucomes with odd number of factors of the sum is;
[tex]n_A=7[/tex]Total number of possibles outcomes is;
[tex]n_T=36[/tex]The probability that the sum of her two rolls has an odd number of factors will be;
[tex]\begin{gathered} P=\frac{n_A}{n_T}=\frac{7}{36} \\ P=\frac{7}{36} \end{gathered}[/tex]A sample was done , collecting the data below. Calculate the standard deviation,to one decimal place
By definition, the standard deviation is
[tex]\sigma = \sqrt{\frac{\sum_{i=1}^{n}\left(x_i-\bar{x}\right)^2}{n}}[/tex]It seems hard so let's do it step by step, first, let's find the mean of the data
[tex]\begin{gathered} \bar{x}=\frac{24+29+2+21+9}{5} \\ \\ \bar{x}=17 \end{gathered}[/tex]Now we have the mean value, let's do each value of the set minus the mean value
[tex]\begin{gathered} x_1-\bar{x}=24-17=7 \\ \\ x_2-\bar{x}=29-17=12 \\ \\ x_3-\bar{x}=2-17=-15 \\ \\ x_4-\bar{x}=29-17=4 \\ \\ x_4-\bar{x}=9-17=-8 \end{gathered}[/tex]Now we have the difference between each element and the mean value, let's do the square of all values
[tex]\begin{gathered} (x_1-\bar{x})^2=7^2=49 \\ \\ (x_2-\bar{x})^2=12^2=144 \\ \\ (x_3-\bar{x})^2=(-15)^2=225 \\ \\ (x_4-\bar{x})^2=4^2=16 \\ \\ (x_5-\bar{x})^2=(-8)^2=64 \end{gathered}[/tex]Now we have the square of the difference we sum them
[tex]\begin{gathered} \sum_{i=1}^5\left(x_i-\bar{x}\right)^2=\left(x_1-\bar{x}\right)^2+\left(x_2-\bar{x}\right)^2+\left(x_3-\bar{x}\right)^2+\left(x_4-\bar{x}\right)^2+\left(x_5-\bar{x}\right)^2 \\ \\ \sum_{i=1}^5\left(x_i-\bar{x}\right)^2=49+144+225+16+64 \\ \\ \sum_{i=1}^5\left(x_i-\bar{x}\right)^2=498 \end{gathered}[/tex]Now we have the sum we must divide by the number of elements, in that case, 5 elements
[tex]\frac{\sum_{i=1}^5\left(x_i-\bar{x}\right)^2}{5}=99.6[/tex]Now we take the square root of that value to have the standard deviation!
[tex]\sigma=\sqrt{99.6}=9.979[/tex]We write it using only one decimal the result would be
[tex]\sigma=9.9[/tex]With no rounding.
Final answer:
[tex]\sigma=9.9[/tex]Maria's earnings vary directly with the number of hours she works. Suppose that she worked 6 hours yesterday and earned
$96. If she earned $144 today, how many hours did she work today?
Answer:
9 hours
Step-by-step explanation:
96÷6 =16
So she earns 16 for 1 hour so 144÷16=9 so she worked 9 hours
A rectangle or televisions length is 3 inches more than twice its width the perimeter of the television is 144 inches what is the width of the television
The width of the television is 23 in.
What is rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles. The opposite sides of a rectangle are equal and parallel.
Given that, A television's length is 3 inches more than twice its width the perimeter of the television is 144 inches
Perimeter of a rectangle = 2(length+width)
According to question,
l = 3+2w
Therefore,
Perimeter = 2(w + 3+2w) = 144
3w + 3 = 72
3w = 69
w = 23
Hence, The width of the television is 23 in.
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3x squared negative 4x squared plus 7x 4x squared negative 4x
ANSWER
[tex]12x^5-28x^4+44x^3-28x^2[/tex]EXPLANATION
First we have to find the partial products by multiplying each term of the first polynomial by each term of the second polynomial:
Now the second term of the second polynomial:
And now we just have to add these partial products:
What is the best estimation of the equation [-å? Drag the numbers into the boxes. Numbers may beused once, twice, or not at all.1142011/21/8
Answer:
[tex]1-\frac{1}{2}=\frac{1}{2}[/tex]Explanation:
Given the below expression;
[tex]\frac{7}{8}-\frac{6}{11}[/tex]We can see that 7/8 is closer to 1 and that 6/11 is closer to 1/2, so we'll now have;
[tex]1-\frac{1}{2}=\frac{2-1}{2}=\frac{1}{2}[/tex]So the best estimation of the equation is 1 - 1/2 = 1/2
So basically I have to reflect triangle STU across line ST and I need to find a valid reason of why the image of U will coincide with J. I need guidance please
Solution
- The reflection of an object across a line implies that the distance between the object and the reflection line is the same as the distance between the image and the reflection line.
- This implies that if the distance between the point U and the reflection line ST is x, then, the distance between the reflection line and the image of U must be a distance of x as well.
- This is illustrated below:
- From the above, we can see that distance x is a perpendicular distance from point U to reflection line ST.
- However, we must not just assume that distance x lands at point J.
- We can however show that this is the case because of the SSS congruency. That is,
[tex]\begin{gathered} SU\cong SJ\text{ \lparen Given in the question\rparen} \\ UT\cong TJ\text{ \lparen Given in the question\rparen} \\ ST\text{ is a common side for both triangles SUT and SJT} \end{gathered}[/tex]- Since both triangles are congruent, we can proceed to conclude that from line ST to point J is also a distance of x.
- Therefore, the image of U will coincide with J given that ST is the reflection line
Which of the following division problems CANNOT be completed?
155 ÷ (-3)
10 ÷ 0
0 ÷ 5
⅔ ÷ ¼
Answer:
I think the first one
but if it's a multiple choice answer then the second and third
Step-by-step explanation:
I was gonna say 0 and 5 because since in algebra you can't divide anything with 0 and you can divide the last one
The are of a square is 49m2. What is its side length?
We know that the area of a square is 49 square meters.
The area of a square is defined by
[tex]A=l^2[/tex]Where l is the length of each side.
Replacing the given are, we have
[tex]\begin{gathered} 49=l^2 \\ l=\sqrt[]{49} \\ l=7 \end{gathered}[/tex]Therefore, the side length is 7 meters long.Write the ratio as a fraction in lowest terms.35 minutes to 5 hours
7 : 60
Explanation:Note that:
1 hour = 60 minutes
5 hours = 5 x 60 minutes
5 hours = 300 minutes
35 minutes : 5 hours = 35 minutes : 300 minutes
35 minutes : 5 hours = 35 : 300
Divide both the numerator and denominator by 5
35 minutes : 5 hours = (35 ÷ 5) : (300 ÷ 5)
35 minutes : 5 hours = 7 : 60
Convert 1 in^3 into cm^3 using the measurement conversion 1 inch= 2.54 cm. Round yo two decimals.
A cubic inch is the same an inch to the third power.
[tex]in^3=in\times in\times in[/tex]If we use our measurement conversion
[tex]1in=2.54\operatorname{cm}[/tex]In our previous equation, we have
[tex]in\times in\times in=2.54\operatorname{cm}\times2.54\operatorname{cm}\times2.54\operatorname{cm}[/tex]Solving this product, we have
[tex]2.54\operatorname{cm}\times2.54\operatorname{cm}\times2.54\operatorname{cm}=16.387064cm^3[/tex]Then, this is our answer.
[tex]1in^3=16.387064cm^3[/tex]Joanna is wrapping a present in the box shown.find the amount of wrapping paper in square inches that Joanna needs
First we need to convert 1 ft to inches
1ft= 12 in
We will use the formula of surface area
[tex]SA=2lw+2lh+2wh[/tex]where l is the length, w is the width and h is the height
In our case
l=12 in
w=8in
h=6 in
we substitute
[tex]SA=2(12)(8)+2(12)(6)+2(8)(6)[/tex]we simplify
[tex]SA=432\text{ in}^2[/tex]She needs 432 square inches
2. Given the degree and zero of a polynomial function, identify the missing zero and then find the standard form of the polynomial
Degree: 2; zero: -7 + 2i
The missing zero is:
+
i
The expanded polynomial is:
The expanded quadratic equation with real coefficients is y = x² + 14 · x + 45.
How to determine the least polynomial that contains a given root
In this problem we need to determine the expanded quadratic equation with real coefficients such that one of its roots is - 7 + i 2. According with the quadratic formula, quadratic equations can have two conjugated complex roots, that is:
r₁ = α + β, r₂ = α - β
Then, the complete set of roots of the quadratic equation are r₁ = - 7 + i 2 and r₂ = - 7 - i 2. Then, the factor form of the polynomial is:
y = (x + 7 - i 2) · (x + 7 + i 2)
y = x · (x + 7 + i 2) + (7 - i 2) · (x + 7 + i 2)
y = x² + 7 · x + i 2 · x + (7 - i 2) · x + 7 · (7 - i 2) + i 2 · (7 - i 2)
y = x² + 7 · x + i 2 · x + 7 · x - i 2 · x + 49 - i 14 + i 14 - i² 4
y = x² + 14 · x + 45
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How to find the inverse of the matrix Question number 19
Okay, here we have this:
We need to find the inverse of the matrix, let's do it:
[tex]\begin{bmatrix}{2} & {4} & {1} \\ {-1} & {1} & {-1} \\ {1} & {4} & {0}\end{bmatrix}[/tex]For that we are going to make the augmented form with the identity matrix and convert the original matrix into the identity:
[tex]\begin{gathered} \begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ -1 & 1 & -1 & | & 0 & 1 & 0 \\ 1 & 4 & 0 & | & 0 & 0 & 1\end{pmatrix} \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 1 & 4 & 0 & | & 0 & 0 & 1\end{pmatrix}\text{ }R_2\leftarrow R_2+\frac{1}{2}R_1 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 2 & -\frac{1}{2} & | & -\frac{1}{2} & 0 & 1\end{pmatrix}\text{ }R_3\leftarrow R_3-\frac{1}{2}R_1 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 0 & -\frac{1}{6} & | & -\frac{5}{6} & -\frac{2}{3} & 1\end{pmatrix}R_3\leftarrow R_3-2/3R_2 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_3\leftarrow-6R_3 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & 0 & | & 3 & 3 & -3 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_2\leftarrow R_2+\frac{1}{2}R_3 \\ =\begin{pmatrix}2 & 4 & 0 & | & -4 & -4 & 6 \\ 0 & 3 & 0 & | & 3 & 3 & -3 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow R_1-R_3 \\ =\begin{pmatrix}2 & 4 & 0 & | & -4 & -4 & 6 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_2\leftarrow\frac{1}{3}R_2 \\ =\begin{pmatrix}2 & 0 & 0 & | & -8 & -8 & 10 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow R_1-4R_2 \\ =\begin{pmatrix}1 & 0 & 0 & | & -4 & -4 & 5 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow\frac{1}{2}R_1 \end{gathered}[/tex]Finally the inverse is on the right side of the augmented matrix:
[tex]=\begin{pmatrix}-4 & -4 & 5 \\ 1 & 1 & -1 \\ 5 & 4 & -6\end{pmatrix}[/tex]A student takes a 10 question multiple choice quiz- each question having 4 choices. Suppose a student randomly picks an answer for each question. Find the following.
Assume that an A is a 90% (getting at least 9 questions out of 10 right).
The probability that exactly 9 questions are right is 10 (choose one question to get wrong) * (1/4)^9 (1/4 chance of getting each question right) * (3/4) (chance of getting the wrong question wrong) = 10∗3∗(1/4)10 .
The probability that all 10 questions are right is (1/4)10 (1/4 chance of getting each question right).
The total probability of getting an A is (10∗3+1)(1/4)10=31410, or about 0.002956%.
I hope I helped! If I misinterpreted your question, please let me know and I'll try my best to help.
Simplify. In the form of a paragraph, explain in complete sentences the steps necessary to simplify the expression andinclude the final answer in your explanation. Complete your work in the space provided or upload a file that can displaymath symbols if your work requires it.
1. When dividing with exponents, the exponent of a variable in the denominator is subtracted from the exponent in the numerator for the same variable. Then, first step to simplify is subtract the exponents of x and y in the fraction in parentheses:
[tex]\begin{gathered} =(x^{3-1}y^{1-2})^{-2} \\ =(x^2y^{-1})^{-2} \end{gathered}[/tex]2. To remove the parentheses you multiply each exponent in the parentheses by the exponent out of the parentheses:
[tex]\begin{gathered} =x^{2\cdot(-2)}y^{(-1)\cdot(-2)} \\ \\ =x^{-4}y^2 \end{gathered}[/tex]3. When you have a negative exponent (as the x powered to -4) you divide 1 in to the term with negative exponent (after you divide the exponent turns into a positive exponent):
[tex]=\frac{1}{x^4}\cdot y^2[/tex]4. Then, the given expression simplified is:
[tex](\frac{x^3y}{xy^2})^{-2}=\frac{y^2}{x^4}[/tex]A bottlenose dolphin is 10 feet belo sea level. Then it begins to dive at a rate of 9 feet per second. What is the equation of the line that represents its elevation,y, after x seconds
The list price for a case of medicine is $275.49 Your pharmacy will receive a 18% trade discount. What is the amount of the discount? b) What is the net cost of the case of medicine?
The amount of the discount is $49.59, and the net cost after the discount is applied is $225.90.
What is the amount of the discount?If we have a original price P and we apply a discount of X, where X is a percentage, the amount of the discount is given by the formula:
D = P*(X/100%)
In this case, the original price is $275.49 and the discount is of 18%, then the amount of the discount is:
D = $275.49*(18%/100%) = $275.49*0.18 = $49.59
b) To get the net cost we need to take the difference between the original price and the amount of the discount, we will get:
net cost = $275.49 - $49.59 = $225.90
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What is the value of this matrix at az?Matrix A
ANSWER:
27
STEP-BY-STEP EXPLANATION:
A matrix is represented by an uppercase letter (A,B, …) and its elements with the same lowercase letter (a,b, …), with a double subscript where the first indicates the row and the second the column a the one that belongs.
Just like that:
Therefore, if we look at the matrix of the statement, we can determine that a2,1 is equal to 27
