The percent of error is 20.9302%. The solution has been obtained by using percent error.
What is percent error?
The difference between the estimated value and the actual value in respect to the actual value is known as the percent error.
We are given that the estimate number of balls in each bag was 86 but it turned out to be 104.
So, the percent error is
⇒Percent error = [Estimated Value - Actual value] / Actual value
⇒Percent error = [104 - 86] / 86
⇒Percent error = 18 / 86
⇒Percent error = 20.9302%
Hence, the percent of error is 20.9302%.
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A solid cylinder is cut vertically through its center. Its radius and height are 6 cm and 15 cm, respectively. What is the area of the resulting shape?
The area of the resulting shape is 90 sq meters
How to determine the area of the resulting shape?The cylinder represents the given parameter
Such that we have the following dimensions
Radius = 6 cm
Height = 15 cm
When the solid cylinder is cut vertically through its center, we have a rectangle with the following dimensions
Length = 6 cm
Width = 15 cm
The area is then calculated as
Area = Length * Width
So, we have
Area = 6 * 15
Evaluate
Area = 90
Hence, the area is 90 square meters
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PLEASE HELP IM TIMED!
The value of the function (f·g)(-9) is 186.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions f(x)=2x²-4x-15 and g(x)=x+12.
Here, (f·g)(x)=f(x)+g(x)
= 2x²-4x-15+x+12
= 2x²-3x-3
(f·g)(-9)=2(-9)²-3(-9)-3
= 2×81+27-3
= 162+27-3
= 162+24
= 186
Therefore, the value of (f·g)(-9) is 186.
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A Box Contains 16 Silver Counters, 8 Brown Counters And 20 Pink Counters. What Is The Ratio Of Silver To Brown To Pink Counters In Its Simplest Form?
Answer:
4-2-5
Step-by-step explanation:
16, 8, and 20 can all be divided by 4
Leaving you with 4 2 and 5.
The ratio is 4 to 2 to 5
6. Complete the frequency table and ogive for the number of heads flipped. (a) (Excel object) Determine the frequency of each of the indicated intervals. Make sure that these frequencies are entered i
To complete the frequency table and ogive for the number of heads flipped, we need to determine the frequency of each of the indicated intervals. We can do this by counting the number of times each interval appears in the data set and entering the frequencies into the table.
Here is how to do it step-by-step:
1. Start with the first interval, which is 0-4 heads. Count the number of times this interval appears in the data set. For example, if there are 3 occurrences of 0-4 heads, enter 3 in the frequency column for this interval.
2. Repeat this process for each of the remaining intervals, counting the number of occurrences and entering the frequencies into the table.
3. Once you have entered all the frequencies, you can create the ogive by plotting the cumulative frequencies on a graph. Start with the first interval and plot the cumulative frequency at the upper limit of the interval. For example, if the first interval is 0-4 heads and the frequency is 3, plot the point (4,3) on the graph.
4. Continue this process for each of the remaining intervals, adding the frequency of each interval to the cumulative frequency and plotting the point at the upper limit of the interval.
5. Once you have plotted all the points, connect them with a line to create the ogive.
Here is the completed frequency table and ogive for the number of heads flipped:
| Interval | Frequency |
|----------|-----------|
| 0-4 | 3 |
| 5-9 | 5 |
| 10-14 | 4 |
| 15-19 | 2 |
| 20-24 | 1 |
Ogive:
(4,3) (9,8) (14,12) (19,14) (24,15)
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Given a right triangle with leg lengths 19 inches and 17 inches, find the length of the
hypotenuse. Round to the nearest tenths.
Step-by-step explanation:
always remember Pythagoras for life :
c² = a² + b³
c is the Hypotenuse (the longest side of the right-angled triangle, it is opposite of the 90° angle). a and b are the legs.
c² = 19² + 17² = 361 + 289 = 650
c = sqrt(650) = 25.49509757... in ≈ 25.5 in
the Hypotenuse is about 25.5 in long.
The amount of money that is left in a medical savings account is expressed by the equation y = negative 24 x + 379, where x represents the number of weeks and y represents the amount of money, in dollars, that is left in the account. After how many weeks will the account have $67 left in it
In the word problem, The account have left $67 in 13 weeks.
What is word problem?Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here the given expression represents the medical savings account.
=> y=-24x+379
Here y represent of money and x represent number of weeks.
Here Amount of money y = $67 then,
=> 67=- 24x+ 379
=> -24x = 67-379
=> -24x= -312
=> x = -312/-24
=> x = 13
Hence The account have left $67 in 13 weeks.
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Jermaine was in charge of buying milk for a class picnic for 32 students.
Answer: ??
Step-by-step explanation:
In a right triangle, the length of the long leg is 2 inches more than the length of the short leg. The hypotenuse is 8 inches less than three times the length of the short leg. What is the length of each side of the triangle?
The length of the short leg is 2 inches, the length of the long leg is 8 inches, and the length of the hypotenuse is 10 inches.
In a right triangle, if the length of the long leg is 2 inches more than the length of the short leg and the hypotenuse is 8 inches less than three times the length of the short leg, then the length of the short leg is x and the length of the long leg is [tex]x+2[/tex] and the hypotenuse is [tex]3x-8[/tex].
We can use the Pythagorean theorem to solve for the lengths of each side. The Pythagorean theorem states that [tex]a^{2} = b^{2} + c^{2}[/tex], where a and b are the lengths of the legs and c is the length of the hypotenuse.
So, [tex]x^{2} + (x+2)^{2} = (3x-8)^{2}[/tex]
We can solve for x, which gives us x = 6. Therefore, the length of the short leg is 2 inches, the length of the long leg is 8 inches, and the length of the hypotenuse is 10 inches.
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Simplify 7-5/6•7-7/6
To simplify 7-5/6•7-7/6, we need to follow the order of operations (PEMDAS) and perform the multiplication and division before addition and subtraction.
7-5/6•7-7/6
= 7 - (5/6) * 7 - (7/6) (Multiplication first)
= 7 - (35/6) - (7/6) (Simplify the multiplication)
= (42/6) - (35/6) - (7/6) (Convert 7 to a fraction with a common denominator)
= (42 - 35 - 7) / 6 (Subtract the numerators)
= 0 / 6
= 0
Therefore, 7-5/6•7-7/6 simplifies to 0.
Answer: 0
Step-by-step explanation:
7 - 5 / 6 • 7 - 7 / 6
7 - 35 / 6 - 7 / 6
7 - 42 / 6
7 - 7
0
Mrs. Brown has 11 more boys than girls in her class and has a total of 28 students. Which of the following systems of equations could be used to solve this problem?
A. B + 11 = G and B + G = 28
B. B = G – 11 and B + G = 28
C. G = B + 11 and B + G = 28
D. B = G + 11 and B + G = 28
B
B=G-11 and B+G=28 could be used to solve the problem
The length of a rectangular speaker is three times its width and the height is four more than the width. Write an expression for the volume V of the rectangular prism in terms of its width, w.
Formula: V = (length)(height)(width)
L=
W=
H=
PLEASE SHOW WORK
Answer:
Step-by-step explanation:
W = w
L = 3w
H = w+4
Now V = LHW
= (3w)(w+4)(w)
= (3w²+12w)(w)
= 3w³+12w²
Which of the statements best describe the origin on the coordinate system? I. The x- and y-axes intersect at the origin. II. The origin is the distance from right to left. III. The point, (0 , 0), is the ordered pair at the origin. IV. The origin is the distance from top to bottom. A. I and III B. IV only C. I only D. II and IV
I WILL GIVE 50 POINTS
Find m for the investment of $1000.00 for 2 years at 1.8% compounded semi-annually. A) 1
B) 0.9% C) 2 D) 4
(B) 0.9%. We can use the formula for compound interest to find the value of the investment after 2 years:
A = P(1 + r/n)^(nt)
where A is the amount of money after the time period, P is the principal (initial investment), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
Plugging in the given values, we get:
A = 1000(1 + 0.018/2)^(2*2)
= 1000(1 + 0.009)^4
= 1000(1.009)^4
≈ 1083.02
So the investment is worth approximately $1083.02 after 2 years.
To find the interest rate per year, we can use the formula:
r = n[(A/P)^(1/nt) - 1]
Plugging in the values we know, we get:
r = 2[(1083.02/1000)^(1/(2*2)) - 1]
= 2[(1.08302)^(1/4) - 1]
≈ 0.9%
Therefore, the answer is (B) 0.9%.
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PLS HELP I ONLY HAVE ONE DAY TO FINISH THIS (IMAGE ATTACH)
Answer:
84
Step-by-step explanation:
6.3+16.1=22.4
22.4/2=11.2
11.2x7.5=84
Answer:
78.12 cm^2
Step-by-step explanation:
i will call the 6.3 cm line A, 7.5 line B and 16.1 cm C
first we divide this into two shapes, a rectangle and a triangle
THE RECTANGLE:
the formula to find the area of a rectangle: L x W
A x B
6.3 x 7.5 = 47.25 cm^2
THE TRIANGLE:
this is a right angle triangle
formula to find the area of a right angle triangle: (1/2) x BASE x H
B is parallel to H and share the same length
to find BASE we need to subtract 6.3cm from 16.1cm (check attachment)
16.1 - 6.3 = 9.8
(1/2) x 9.8 x 6.3 = 30.87 cm^2
FINAL VALUE:
now we simply add our two values of area together
30.87 + 47.25 = 78.12 cm^2
Peter and Dan shared some beads. After Peter gave away 1/4 of his beads and Dan gave away 1/5 of his beads, both had the same number of beads left. If Peter had 7 beads more than Dan at first, how many beads did each of them have at the end?
Peter ended up with 31 beads, and Dan ended up with 28 beads.
What is the fraction?
A fraction is a mathematical expression that represents a part of a whole. It is written in the form of a ratio between two numbers, with the top number called the numerator and the bottom number called the denominator.
Let's represent the number of beads that Peter and Dan had at the start by P and D, respectively. Then we can set up an equation based on the information given in the problem:
After giving away 1/4 of his beads, Peter had 3/4 of his original number of beads, which is (3/4)P.
After giving away 1/5 of his beads, Dan had 4/5 of his original number of beads, which is (4/5)D.
According to the problem, both had the same number of beads left after giving away some of their beads:
(3/4)P = (4/5)D
We also know that Peter had 7 more beads than Dan at the start:
P = D + 7
We can use substitution to solve for D:
(3/4)(D+7) = (4/5)D
9D/20 + 21/20 = 4D/5
D = 35
So Dan had 35 beads at the start. Using the equation P = D + 7, we can find that Peter had:
P = D + 7 = 35 + 7 = 42
After giving away 1/4 of his beads, Peter had (3/4)P = (3/4)*42 = 31.5 beads, which we can round down to 31 beads since we're dealing with whole numbers of beads. After giving away 1/5 of his beads, Dan had (4/5)D = (4/5)*35 = 28 beads.
Therefore, Peter ended up with 31 beads, and Dan ended up with 28 beads.
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Mail went to buy some veg he bought x kgs of tomato and y kgs of potato the total cost of veg comes out to be rs 200 now if the cost of 1 kg of tomato is rs50 and 1 kg of potato rs20 then ans the follow (1) liner equation to represent the total cost (2) if mail bought x kg of tomato and 2.5 kg of potato find the value of x (3) find the point at which the graph of 5x+2y=20 cuts x axis
Answer:
Linear equation to represent the total cost:
Let x be the number of kgs of tomatoes Mail bought, and y be the number of kgs of potatoes Mail bought. The cost of x kgs of tomato at Rs. 50 per kg is 50x, and the cost of y kgs of potato at Rs. 20 per kg is 20y. Therefore, the total cost of the vegetables is:
Total cost = 50x + 20y
Substituting the value of total cost as Rs. 200, we get:
50x + 20y = 200
This is the required linear equation to represent the total cost.
Finding the value of x:
Let's assume that Mail bought x kgs of tomato and 2.5 kgs of potato. Using the equation derived above:
50x + 20(2.5) = 200
Simplifying the equation:
50x + 50 = 200
50x = 150
x = 3
Therefore, Mail bought 3 kgs of tomato.
Finding the point at which the graph of 5x+2y=20 cuts x-axis:
To find the point at which the graph of 5x+2y=20 cuts the x-axis, we need to set y = 0 in the equation and solve for x:
5x + 2(0) = 20
5x = 20
x = 4
Therefore, the point where the graph of 5x+2y=20 cuts the x-axis is (4,0).
Given the information, please find the simple multiplier in the economy:
AD: y = 710 -30p + 5g
AS: y = 10 + 5p - 2s
g is government purchases, and s is the world price of some commodity.
Please explain how to do this, I don’t need the answer unless I have the steps
Answer:
To calculate the simple multiplier in this economy, you need to subtract the autonomous spending (AS) from the aggregate demand (AD). This will give you the amount that changes in consumer spending influences all other economic variables. In this case, subtract 10 + 5p - 2s from 710 - 30p + 5g. The result is 700 - 35p + 3g, which shows how a change in consumer spending affects government purchases and the world price of some commodity.I really need some help please
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
multiply x by y multiply x by y multiply x by y 3 plus 5 minus 5 to the power of 2 then divide 3 plus 87 then you give your mom and dad a high five then go make out with a girl for an hour and then your answer is 72 to the power of x multiplyed by y.
Find the value of the variable.
Answer:
28
Step-by-step explanation:
So for this problem, you need to use the midsegment formula. The midsegment formula is [tex]SG = \frac{1}{2} (b_{1} + b_{2})[/tex]. In this case, [tex]b_{1}[/tex] is 21 and [tex]b_{2}[/tex] 35.
Adding these together get 56. The next part of the formula is dividing by two, so [tex]\frac{56}{2} = 28[/tex] so you answer is x=28
Which pair. of integers would be used to rewrite the middle term when factoring 6t^(2)+5t-4 by grouping?
The pair of integers to be used to rewrite the middle term when factoring 6t^(2)+5t-4 by grouping is (5t - 4) and (6t^2 + 5t). By factoring by grouping, we can factor the middle term out of the polynomial and then factor the remaining terms separately.
First, the middle term is factored out of the equation. This is done by multiplying the first and last terms together, which in this case is (6t^2)(-4). This results in the equation 6t^2 + 5t - 4 being rewritten as 6t^2 + (5t - 4)(-4).
Next, the remaining terms are factored separately. The first term, 6t^2, is a perfect square and can be factored as (3t)(2t). The second term, (5t - 4)(-4), can be factored by taking out a common factor from each term. In this case, the common factor is (-4). This results in the equation being rewritten as (3t)(2t) + (-4)(5t - 4).
The final step is to group the terms together and factor out the greatest common factor. In this equation, the greatest common factor is (3t)(-4). Thus, the equation 6t^2 + 5t - 4 can be rewritten as (3t)(-4)(2t + 5).
In conclusion, the pair of integers used to rewrite the middle term when factoring 6t^2 + 5t - 4 by grouping is (5t - 4) and (6t^2 + 5t).
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What is the future value of $2000 earning 18% interest,
compounded monthly, for 4 years? (Round your answer to two decimal
places.)
The future value of $2000 earning 18% interest, compounded monthly, for 4 years is $6,116.23.
To calculate the future value, we use the formula:
[tex]FV = P(1 + r/n)^{nt}[/tex]
Where:
FV is the future value
P is the principal amount ($2000)
r is the annual interest rate (18%)
n is the number of times the interest is compounded per year (12 for monthly compounding)
t is the number of years (4)
Plugging in these values, we get:
[tex]FV = 2000(1 + 0.18/12)^{12*4}[/tex]
FV = 6116.23
Therefore, the future value of $2000 earning 18% interest compounded monthly for 4 years is approximately $6,116.23. This means that if you invest $2000 today and earn 18% interest compounded monthly for 4 years, your investment will grow to $6,116.23 at the end of the 4-year period. It's important to note that the actual value may vary depending on the exact compounding method used by the bank or financial institution.
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5.6 Use pivotal condensation to evaluate the determinant of \[ \mathbf{A}=\left[\begin{array}{lll} 0 & 2 & 2 \\ 1 & 0 & 3 \\ 2 & 1 & 1 \end{array}\right] \] We initialize \( D=1 \) and use elementary
Using Pivotal Condensation, the determinant of matrix A is 5.
Step 1: We start by initializing D as 1.
Step 2: We use the first row for pivotal condensation.
Row 0: 0 * D + 2 * 1 + 2 * 0 = 0
Row 1: 1 * D + 0 * 1 + 3 * 0 = 1
Row 2: 2 * D + 1 * 1 + 1 * 0 = 2
Step 3: We make the first row entries 0 by multiplying the entire row by (-2).
Row 0: -0 * D - 2 * 1 - 2 * 0 = 0
Row 1: 1 * D + 0 * 1 + 3 * 0 = 1
Row 2: 2 * D + 1 * 1 + 1 * 0 = 2
Step 4: We add row 0 to row 1 and row 0 to row 2.
Row 0: 0 * D + 2 * 1 + 2 * 0 = 0
Row 1: 1 * D + 0 * 1 + 3 * 0 = 1
Row 2: 0 * D + 3 * 1 + 3 * 0 = 3
Step 5: We make the entries of the second row 0 by multiplying the entire row by (-1/3).
Row 0: 0 * D + 2 * 1 + 2 * 0 = 0
Row 1: -1/3 * D - 0 * 1 - 3 * 0 = -1/3
Row 2: 0 * D + 3 * 1 + 3 * 0 = 3
Step 6: We add row 1 to row 0 and row 1 to row 2.
Row 0: 1/3 * D + 2 * 1 + 2 * 0 = 1/3
Row 1: -1/3 * D - 0 * 1 - 3 * 0 = -1/3
Row 2: 3/3 * D + 3 * 1 + 3 * 0 = 5
Step 7: We multiply the entries of the first row by (-3) to make the entries of the first row 0.
Row 0: 0 * D + 6 * 1 + 6 * 0 = 0
Row 1: -1/3 * D - 0 * 1 - 3 * 0 = -1/3
Row 2: 3/3 * D + 3 * 1 + 3 * 0 = 5
Step 8: We multiply the last row by D.
Row 0: 0 * D + 6 * 1 + 6 * 0 = 0
Row 1: -1/3 * D - 0 * 1 - 3 * 0 = -1/3
Row 2: 5 * D + 3 * 1 + 3 * 0 = 5D
Step 9: We subtract row 1 from row 0 and row 1 from row 2.
Row 0: 4/3 * D + 6 * 1 + 6 * 0 = 4/3D
Row 1: -1/3 * D - 0 * 1 - 3 * 0 = -1/3
Row 2: 4/3 * D + 3 * 1 + 3 * 0 = 4/3D
Step 10: We calculate the determinant by multiplying the last row entries.
Determinant of matrix A is 5.
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Consider the polynomial:
p(x) = x4+12x-5
A) Use the Rational Root Theorem to list the four possible rational zeros of p.
B) The complex number r= 1-2i is a zero of p. Give exact values for all four zeros.
A) The Rational Root Theorem states that the only rational zeros of p(x) = x4+12x-5 must be a factor of -5 divided by a factor of 1. Therefore, the four possible rational zeros are -5, -1, 1, and 5.
B) The other three zeros is 1 - 2i, 1 + 2i, 1 - √(7), 1 + √(7)
A) The Rational Root Theorem states that if a polynomial with integer coefficients has a rational root r = p/q (where p and q have no common factors), then p must divide the constant term of the polynomial and q must divide the leading coefficient.
The constant term of p(x) = x^4 + 12x - 5 is -5, which has the factors ±1 and ±5. The leading coefficient is 1, which has the factors ±1. Therefore, the possible rational roots are:
±1/1, ±5/1, ±1/5, ±5/5 (which simplifies to ±1)
B) If r = 1 - 2i is a zero of p(x), then its complex conjugate r* = 1 + 2i is also a zero of p(x), since p(x) has real coefficients. Therefore, we can factor p(x) as:
p(x) = (x - r)(x - r*)(x²+ bx + c)
where b and c are the coefficients of the quadratic factor. We can expand this and compare coefficients to get:
x⁴ + 12x - 5 = (x - 1 + 2i)(x - 1 - 2i)(x² + bx + c)
Expanding the first two factors gives:
(x - 1 + 2i)(x - 1 - 2i) = x² - 2x + 5
Therefore, we have:
x⁴ + 12x - 5 = (x² - 2x + 5)(x² + bx + c)
Expanding the right side and comparing coefficients, we get:
b = -2 and c = -6
So the quadratic factor is:
x² - 2x - 6
We can find its roots using the quadratic formula:
x = [2 ± √(4 + 4(6))] / 2
x = 1 ± √(7)
Therefore, the four zeros of p(x) are:
1 - 2i, 1 + 2i, 1 - √(7), 1 + √(7)
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Convert 6 1/3 to an improper fraction.
Answer:
19/3
Step-by-step explanation:
Manuel rewrote the expression 6x-x+5 as 6+5 are 6x-x+5 and 6+5 equivalent expression? Explain.
The expression 6x - x + 5 as 6 + 5 are not equivalent expression because one of the expression contain a variable while the other doesn't.
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided above, we have the following mathematical expression:
Expression = 6x - x + 5
Expression = 5x + 5
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I need quick help with this, please.
Answer:
c
Step-by-step explanation:
it makes sense
R is inversely proportional to A. R=12 when A=1.5 work out the value of R when A=9
Step-by-step explanation:
R=A\1... Given tha R is inversely proportional to AR=9/1... We are given the value of A which is 9R=9 final answerCan you help me with these questions please
The solution is, the initial amount that you invested is $1200.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
here, we have,
Let the initial amount that you invested be $ x.
We are told that the new balance after investing $500 is $1760.
Thus, the balance you had before the deposit $500 us;
$1760 - $500 = $1260
So, when the amount invested was $x, the balance was $1260.
Since this money earned 5% interest on the amount you initially
Thus;
$1260 = initial deposit + (5% of inital deposit)
Thus;
x + (5% * x) = 1260
x + (0.05x) = 1260
1.05x = 1260
x = 1260/1.05
x = $1200
Hence, The solution is, the initial amount that you invested is $1200.
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Consider the following matrix \( A \) : \[ A=\left[\begin{array}{ccc} 3 & 6 & -6 \\ -1 & -2 & 5 \\ -1 & -2 & 2 \\ -1 & -1 & 0 \end{array}\right] \] For each of the following vectors, determine whether
To determine whether a given vector is a solution to the equation \(A\vec{x}=\vec{0}\), we need to multiply the matrix A with the vector \(\vec{x}\) and check if the resulting vector is equal to the zero vector \(\vec{0}\).
Let's consider the first vector \(\vec{x_1}=\left[\begin{array}{c} 2 \\ 1 \\ 1 \end{array}\right]\). Multiplying the matrix A with this vector, we get:
\[ A\vec{x_1}=\left[\begin{array}{ccc} 3 & 6 & -6 \\ -1 & -2 & 5 \\ -1 & -2 & 2 \\ -1 & -1 & 0 \end{array}\right] \left[\begin{array}{c} 2 \\ 1 \\ 1 \end{array}\right]=\left[\begin{array}{c} 12 \\ -4 \\ -3 \\ -3 \end{array}\right] \]
Since the resulting vector is not equal to the zero vector \(\vec{0}\), the vector \(\vec{x_1}\) is not a solution to the equation \(A\vec{x}=\vec{0}\).
Similarly, we can check for the other vectors:
For the vector \(\vec{x_2}=\left[\begin{array}{c} -1 \\ 2 \\ -1 \end{array}\right]\):
\[ A\vec{x_2}=\left[\begin{array}{ccc} 3 & 6 & -6 \\ -1 & -2 & 5 \\ -1 & -2 & 2 \\ -1 & -1 & 0 \end{array}\right] \left[\begin{array}{c} -1 \\ 2 \\ -1 \end{array}\right]=\left[\begin{array}{c} 6 \\ 1 \\ 1 \\ 1 \end{array}\right] \]
Again, the resulting vector is not equal to the zero vector \(\vec{0}\), so the vector \(\vec{x_2}\) is not a solution to the equation \(A\vec{x}=\vec{0}\).
For the vector \(\vec{x_3}=\left[\begin{array}{c} 1 \\ -1 \\ 1 \end{array}\right]\):
\[ A\vec{x_3}=\left[\begin{array}{ccc} 3 & 6 & -6 \\ -1 & -2 & 5 \\ -1 & -2 & 2 \\ -1 & -1 & 0 \end{array}\right] \left[\begin{array}{c} 1 \\ -1 \\ 1 \end{array}\right]=\left[\begin{array}{c} 0 \\ 0 \\ 0 \\ 0 \end{array}\right] \]
In this case, the resulting vector is equal to the zero vector \(\vec{0}\), so the vector \(\vec{x_3}\) is a solution to the equation \(A\vec{x}=\vec{0}\).
Therefore, only the vector \(\vec{x_3}=\left[\begin{array}{c} 1 \\ -1 \\ 1 \end{array}\right]\) is a solution to the equation \(A\vec{x}=\vec{0}\).
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Blake has a 52% free throw success rate so his coach wants him to practice. What is the probability of him making more than 7 out of 25 shots in practice?
Therefore, the probability of Blake making more than 7 out of 25 shots in practice is 0.9984.
To determine the probability of Blake making more than 7 out of 25 shots in practice, we can use the binomial probability formula: P(X = x) = (n choose x) * p^x * (1-p)^(n-x), where n is the number of trials, x is the number of successes, and p is the probability of success.
In this case, n = 25, p = 0.52, and we want to find the probability of x > 7. We can calculate this by finding the probability of x ≤ 7 and subtracting it from 1.
P(X > 7) = 1 - P(X ≤ 7)
= 1 - [(25 choose 0) * (0.52)^0 * (0.48)^25 + (25 choose 1) * (0.52)^1 * (0.48)^24 + ... + (25 choose 7) * (0.52)^7 * (0.48)^18]
= 1 - 0.0016
= 0.9984
Therefore, the probability of Blake making more than 7 out of 25 shots in practice is 0.9984.
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