Answer:
{-3, √3, -√3, 13/3}
Step-by-step explanation:
Since the polynomial has rational coefficients, any irrational zeros must come in conjugate pairs. So, if √3 is a zero, then so is its conjugate, -√3.
We can write the polynomial with these zeros as:
p(x) = a(x + 3)(x - √3)(x + √3)(x - 13/3)
where a is some constant coefficient. Multiplying out the factors, we get:
p(x) = a(x + 3)(x^2 - 3)(x - 13/3)
To find the remaining zeros, we need to solve for x in the expression p(x) = 0. So we set up the equation:
a(x + 3)(x^2 - 3)(x - 13/3) = 0
This equation is true when any of the factors is equal to zero. We already know three of the zeros, so we need to solve for the fourth:
(x + 3)(x^2 - 3)(x - 13/3) = 0
Expanding the quadratic factor, we get:
(x + 3)(x - √3)(x + √3)(x - 13/3) = 0
Canceling out the (x - √3) and (x + √3) factors, we get:
(x + 3)(x - 13/3) = 0
Solving for x, we get:
x = -3 or x = 13/3
Therefore, the other zeros are -3 and 13/3.
The complete set of zeros is {-3, √3, -√3, 13/3}.
Hope it helps^^
Help please i would appreciated it
here is the picture is about Row Ops
The matrix operation add -4(row 1) to row 3 is[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]
Evaluating the matrix expressionFrom the question, we have the following parameters that can be used in our computation:
[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\4&-1&6&-8\end{array}\right][/tex]
From the question, we understand that
We are to add -4(row 1) to row 3
This means that
row 3 = row 3 - 4 * row 1
When these values are evaluated, we have
4: 4 - 4 * 1 = 0
-1: -1 - 4 * 2 = -9
6: 6 - 4 * 1 = 2
-8: -8 - 4 * -5 = 12
This means that we relace 4, -1, 6, and -8 in row 3 with 0, -9, 2 and 12
Using the above as a guide, we have the following:
[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]
Hence, the result of the matrix expression is [tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]
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Help with math problems
Answer:
Step-by-step explanation:
15.) [tex]\sqrt{12}[/tex]
[tex]\sqrt{4}[/tex] * [tex]\sqrt{3}[/tex]
Answer: 2[tex]\sqrt{3}[/tex]
17.) Distribute 3[tex]\sqrt{3}[/tex] into both sides of the parentheses
3[tex]\sqrt{3}[/tex] * 4 = 12[tex]\sqrt{3}[/tex]
3[tex]\sqrt{3}[/tex] * -3[tex]\sqrt{5}[/tex] = -9[tex]\sqrt{15}[/tex]
Answer: 12[tex]\sqrt{3}[/tex] - 9[tex]\sqrt{15}[/tex]
19.) Distribute 4[tex]\sqrt{15}[/tex] into both sides of the parentheses
4[tex]\sqrt{90}[/tex] + 4[tex]\sqrt{75}[/tex]
4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex] + 4*[tex]\sqrt{25}[/tex]*[tex]\sqrt{3}[/tex]
4*3*[tex]\sqrt{10}[/tex] + 4*5*[tex]\sqrt{3}[/tex]
12[tex]\sqrt{10}[/tex] + 20[tex]\sqrt{3}[/tex]
21.) Distribute [tex]\sqrt{15}[/tex] into both sides of the parentheses
2[tex]\sqrt{150}[/tex] - 4[tex]\sqrt{90}[/tex]
2*[tex]\sqrt{25}[/tex]*[tex]\sqrt{6}[/tex] - 4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex]
2*5*[tex]\sqrt{6}[/tex] - 4*3*[tex]\sqrt{10}[/tex]
10[tex]\sqrt{6}[/tex] - 12[tex]\sqrt{10}[/tex]
A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 2 tables is $25.
The cost of each chair and table is $2.5 and $8.75 respectively.
Given that the total cost to rent 3 chairs and 2 tables is $25 and total cost to rent 5 chairs and 6 tables is $65.
We need to find the cost of each chair and table,
Let the cost of each chair and table be x and y respectively,
3x+2y = 25.......(i)
5x+6y = 65.........(ii)
Multiply the equation (i) by 3 and subtract ii from i,
9x+6y = 75 - (5x+6y = 65)
4x = 10
x = 2.5
Put x = 2.5 in any equation to find the value of y,
3(2.5)+2y = 25
2y = 17.5
y = 8.75
Hence, the cost of each chair and table is $2.5 and $8.75 respectively.
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A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 7 centimeters by 3 and three-fifths centimeters by 2 and two-fifths centimeters.
What is the surface area of the prism?
Answer:
The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width and h is the height.
In this case, the length is 7 cm, the width is 3 and three-fifths cm (or 3.6 cm), and the height is 2 and two-fifths cm (or 2.4 cm). Plugging these values into the formula gives us a surface area of 2(7) (3.6) + 2(7) (2.4) + 2(3.6) (2.4), which simplifies to 50.4 + 33.6 + 17.28, or 101.28 square centimeters.
So, the surface area of this rectangular prism is 101.28 square centimeters.
Received message. The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is `2lw + 2lh + 2wh`, where `l` is the length, `w` is the width and `h` is the height. In this case, the length is 7 cm, the width is 3 and three-fifths cm (or 3.6 cm), and the height is 2 and two-fifths cm (or 2.4 cm). Plugging these values into the formula gives us a surface area of `2(7)(3.6) + 2(7)(2.4) + 2(3.6)(2.4)`, which simplifies to `50.4 + 33.6 + 17.28`, or **101.28 square centimeters**. So, the surface area of this rectangular prism is **101.28 square centimeters**.
Step-by-step explanation:
what is equilivent to 28/2
Answer:
14
Step-by-step explanation:
28/2 is equivalent to 14. This is because when you divide a number by 2, you are essentially cutting it in half. So, 28/2 is the same as cutting 28 into two equal parts, which is 14.
Answer:
28
2
looks like a fraction but it is actually the whole number 14.
There is an infinity number of equivalent fractions to 28
2
.
To find an equivalent fraction to 28
2
, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:
By dividing the original fraction by 2, we get:
28 ÷ 2
2 ÷ 2
= 14
1
By multiplying the original fraction by 2, we get:
28 × 2
2 × 2
= 56
4
Here is the full list of equivalent fractions to 28
2
.
14
1
, 28
2
, 42
3
, 56
4
, 70
5
, 84
6
, 98
7
, 112
8
, 126
9
, 140
10
, 154
11
, 168
12
, 182
13
, 196
14
, 210
15
, 224
16
, 238
17
, 252
18
, 266
19
, 280
20
...
Can yall help me with this
Answer:
x = 67
Step-by-step explanation:
The two triangles are identail.
Answer:
x = 67
because 67 and x the same
What is the surface area of a triangular prism
Answer:
surface area=bh+2ls+lb
Step-by-step explanation:
If you think it is too long to remember, just find the area of each of the shapes on it and add them together.
Hope this helps :)
determine whether the sample may be biased. a company randomly selects 500 customers from its computer database and then surveys those customers to find out how they like their service.
Answer:
Step-by-step explanation:
Based on the information given, it is not possible to determine whether the sample may be biased or not.
However, there is a possibility that the sample may be biased if the company's computer database does not accurately represent its entire customer base. For example, if the database contains only a specific type of customers, such as those who frequently make large purchases, then the sample may not be representative of the company's entire customer base. In this case, the survey results may not accurately reflect the opinions of all the company's customers.
It is also important to consider other factors such as how the survey was conducted and how the questions were framed, as these can also affect the validity of the survey results
Helppppppp pleaseee
The loudness of sound in decibels perceived by the human ear depends on the intensity levels according to
D=10log(I/lo)
Find the decibel level when I is 63, 096 times Io.
The decibel is -------------- dB when I is 63, 096 times Io.
Round your answer to the nearest whole number.
Answer:
We can use the given formula to calculate the decibel level D when the intensity level I is 63,096 times Io:
D = 10log(I/lo)
Where Io is the reference intensity level and is typically taken to be the threshold of hearing, which is 10^−12 watts/m^2.
So, substituting the values, we get:
D = 10log(63,096*Io/Io) = 10log(63,096)
Using a calculator, we find:
D ≈ 47.1 dB
Rounding this to the nearest whole number, we get:
The decibel level is 47 dB when I is 63,096 times Io.
I hope this helps mate.
Use words to describe the relationship between the number of miles and each corresponding number of gallons.
10 gallons 300 miles.
The unit rate that relates the two quantities of distance and volume of gas is:
U = 30 miles per gallon.
How to describe this relation?To do so, we can find the unit rate.
This would say how many gallons are consumed to drive a unit of distance, or which distance can you drive with one gallon.
Here we have the values:
10 gallons and 300 miles.
Then the unit rate is the quotient between these:
300miles/10 gallons = 30 miles per gallon
This says that with one gallon of gas you can travel 30 miles.
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4cos45°-2sin45°. Please let me know the answer with thorough steps.
We know that cos(45) = sin(45) = √2/2.
Substituting these values, we can simplify the expression as follows:
4cos(45) - 2sin(45)
= 4(√2/2) - 2(√2/2) (substituting cos(45) and sin(45) values)
= 2√2 - √2
= √2
Therefore, the answer is √2.
find the standard equation of a circle with the points (-18;-5), (-7;-16) and (4;-5)
Answer:
Step-by-step explanation:
To find the equation of a circle given three non-collinear points, we can use the following steps:
Find the equations of the perpendicular bisectors of the line segments connecting the pairs of points.
Find the intersection point of the two perpendicular bisectors. This point is the center of the circle.
Find the distance between the center and any one of the three points. This distance is the radius of the circle.
Let's apply these steps to the given points:
Find the midpoint and slope of the line segments connecting the pairs of points:
Midpoint of (-18, -5) and (-7, -16): ((-18+(-7))/2, (-5+(-16))/2) = (-12.5, -10.5)
Slope of (-18, -5) and (-7, -16): (-16 - (-5))/(-7 - (-18)) = -11/11 = -1
Midpoint of (-18, -5) and (4, -5): ((-18+4)/2, (-5+(-5))/2) = (-7, -5)
Slope of (-18, -5) and (4, -5): (-5 - (-5))/(4 - (-18)) = 0
Midpoint of (-7, -16) and (4, -5): ((-7+4)/2, (-16+(-5))/2) = (-1.5, -10.5)
Slope of (-7, -16) and (4, -5): (-5 - (-16))/(4 - (-7)) = 11/11 = 1
The equations of the perpendicular bisectors passing through the midpoints are:
x + 12.5 = -1(y + 10.5) or x + y + 23 = 0
y + 5 = 0
Find the intersection point of the two perpendicular bisectors:
Solving the system of equations:
x + y + 23 = 0
y + 5 = 0
yields: x = -18, y = -5
So, the center of the circle is (-18, -5).
Find the distance between the center and any one of the three points:
Using the distance formula:
Distance between (-18, -5) and (-18, -5): sqrt(((-18)-(-18))^2 + ((-5)-(-5))^2) = 0
Distance between (-18, -5) and (-7, -16): sqrt(((-18)-(-7))^2 + ((-5)-(-16))^2) = sqrt(221)
Distance between (-18, -5) and (4, -5): sqrt(((-18)-4)^2 + ((-5)-(-5))^2) = 22
The radius of the circle is sqrt(221).
Therefore, the equation of the circle in standard form is:
(x + 18)^2 + (y + 5)^2 = 221
The standard equation of a circle with the points (-18;-5), (-7;-16) and (4;-5) is:
(x + 13)² + (y + 1)² = 41
Standard equation of a circleFrom the question, we are to determine the standard equation of a circle with the given points
The given points are:
(-18;-5), (-7;-16) and (4;-5)
The standard equation of a circle is given by:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle
and r is the radius.
Using the given points (-18, -5), (-7, -16), and (4, -5), we can find the equation of the circle as follows:
Find the midpoint of the line segments connecting the pairs of points:
Midpoint of (-18, -5) and (-7, -16): ((-18 + -7)/2, (-5 + -16)/2) = (-12.5, -10.5)
Midpoint of (-7, -16) and (4, -5): ((-7 + 4)/2, (-16 + -5)/2) = (-1.5, -10.5)
Midpoint of (-18, -5) and (4, -5): ((-18 + 4)/2, (-5 + -5)/2) = (-7, -5)
Find the equations of the perpendicular bisectors of the line segments:
Perpendicular bisector of the line connecting (-18, -5) and (-7, -16):
Slope of the line: (−16 + 5)/(-7 + 18) = -11/5
Slope of the perpendicular bisector: 5/11
Midpoint: (-12.5, -10.5)
Equation: y + 10.5 = (5/11)(x + 12.5)
Perpendicular bisector of the line connecting (-7, -16) and (4, -5):
Slope of the line: (-5 + 16)/(4 + 7) = 11/7
Slope of the perpendicular bisector: -7/11
Midpoint: (-1.5, -10.5)
Equation: y + 10.5 = (-7/11)(x + 1.5)
Perpendicular bisector of the line connecting (-18, -5) and (4, -5):
Slope of the line: 0
Slope of the perpendicular bisector: undefined (perpendicular bisector is a vertical line)
Midpoint: (-7, -5)
Equation: x + 7 = 0
Find the point of intersection of any two perpendicular bisectors:
Intersection of perpendicular bisectors 1 and 2:
y + 10.5 = (5/11)(x + 12.5)
y + 10.5 = (-7/11)(x + 1.5)
Solving for x and y, we get:
x = -13
y = -1
Thus,
The center of the circle is (-13, -1).
Find the radius of the circle:
Using the center (-13, -1) and one of the given points, say (-18, -5):
r² = (-18 - (-13))² + (-5 - (-1))²
r² = 25 + 16
r² = 41
Hence, the equation of the circle is:
(x + 13)² + (y + 1)² = 41.
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Find F(7)…………………………………………
Based on the given function conditions of f(x) , the value of f(7) is equal to -6
To find f(7), we need to determine which function definition to use based on the value of x.
Since x = 7 is greater than 5, we know that we'll be using the third definition of the function: f(x) = -x + 1 for 2 < x ≤ 5.
Therefore, we can substitute x = 7 into the third definition of the function:
f(7) = -7 + 1 = -6
So, f(7) = -6.
In summary, to find f(7), we identified which function definition to use based on the value of x. Since x = 7 is greater than 5, we used the third definition of the function, f(x) = -x + 1 for 2 < x ≤ 5, and found that f(7) = -6.
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Show 2 different ways to find the value of x. What do you think is the most efficient method? Explain why.
We can use trigonometric relations or Pythagorean's theorem, we will see that x = 8ft.
How to find the value of x?We can see that x is the hypotenuse of the triangle, and we know the length of one leg and the angle between them, then we can use the cosine trigonometric relation:
cos(60°) = 4ft/x
solving for x:
x = 4ft/cos(60°) = 8ft
Other way to find x is first find the other side and then use the pyhtagorean theorem, to get the other side y we need:
tan(60°) = y/4ft
y = 4ft*tan(60°)
Then using Pythagorean's theorem we get:
x = √( (4ft)² + (4ft*tan(60°))²)
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Can anyone help with this part of my geometry notes ?
From the interior angle theorem:
m∠1 = ¹/₂(m∠AD + m∠BC)m∠2 = 180 - m∠1m∠AED = 77°m∠AEB = 103°m∠LK = 50°What is the interior angle theorem?The Interior Angle Theorem states that if two secants or chords intersect inside a circle, then the measure of the angle formed is equal to half the sum of the measures of the intercepted arcs.
Considering the given circles:
m∠AED = ¹/₂(45 + 109)
m∠AED = 77°
m∠AEB = 180 - 77
m∠AEB = 103°
m∠LK = (2 * 62) - 74)
m∠LK = 50°
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Find the missing side lengths. Leave your answers as radicals in simplest form. I need help quickly!
Answer:
[tex]m = \dfrac{4}{\sqrt{3}} \text{ or, in rational form: } m = \dfrac{4\sqrt{3}}{3}[/tex]
[tex]n = \dfrac{2}{\sqrt{3}} \text{ or, in rational form: } n = \dfrac{2\sqrt{3}}{3}[/tex]
Not sure which form your teacher wants the answers, would suggest putting in both
Step-by-step explanation:
The missing angle of the triangle = 180 - (60 + 90) = 30°
We will use the law of sines to find m and n
The law of sines states that the ratio of each side to the sine of the opposite angle is the same for all sides and angles
Therefore since m is the side opposite 90° and 2 is the side opposite 60°,
[tex]\dfrac{m}{\sin 90} = \dfrac{2}{\sin 60}}\\\\[/tex]
sin 90 = 1
sin 60 = √3/2
So
[tex]\dfrac{m}{1} = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2 \cdot 2}{\sqrt{3}} \\\\m = \dfrac{4}{\sqrt{3}}\\\\[/tex]
We can rationalize the denominator by multiplying numerator and denominator by √3 to get
[tex]m = \dfrac{4\sqrt{3}}{3}[/tex]
(I am not sure what your teacher wants, you can put both expressions, they are the same)
To find n
Using the law of sines we get
[tex]\dfrac{n}{\sin 30} = \dfrac{m}{\sin 90}\\\\\dfrac{n}{\sin 30} = m\\\\\dfrac{n}{\sin 30} = \dfrac{4}{\sqrt{3}}\\\\[/tex]
sin 30 = 1/2 giving
[tex]\dfrac{n}{1/2} = \dfrac{4}{\sqrt{3}}\\\\n = \dfrac{1/2 \cdot 4}{\sqrt{3}} \\\\n = \dfrac{2}{\sqrt{3}}[/tex]
In rationalized form
[tex]n = \dfrac{2\sqrt{3}}{3}}[/tex]
Help pls i dont understand this
The percentage increase in the number of water bottles the company manufactured from February to April is 19%.
How to find the percentage increase ?In March, the company manufactured 7% more water bottles than in February:
Number of water bottles in March = 4,100 + 7% of 4,100
Number of water bottles in March = 4,387
In April, the company manufactured 500 more water bottles than in March:
Number of water bottles in April = 4,387 + 500
Number of water bottles in April = 4,887
To find the percent increase from February to April, we can use the following formula:
percent increase = (new value - old value) / old value x 100%
percent increase = (4,887 - 4,100) / 4,100 * 100%
percent increase = 787 / 4,100 x 100%
percent increase = 19%
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Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
Answer:
x=9km
Step-by-step explanation:
Pythagorean Theorem: [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
The hypotenuse is [tex]c^{2}[/tex], so the equation will be
[tex]12^{2}[/tex] + [tex]b^{2}[/tex] = [tex]15^{2}[/tex]
Evaluating the equation gives us
144 + [tex]b^\\{2}[/tex] = 225
Subtract 144 from each side to have [tex]b^{2}[/tex] alone
[tex]b^{2}[/tex] = 81
square root on each side to get rid of the exponent
[tex]\sqrt{b^2[/tex] = [tex]\sqrt{81}\\[/tex]
[tex]\sqrt{b^2[/tex]'s square root is b and [tex]\sqrt{81[/tex]'s is 9,-9, giving us b=±9
As distance cannot be negative, x = 9km
State the dimensions of each matrix.
[3 -4 -9]
[2 -7 0]
Answer:
2 x 3 matrix
Step-by-step explanation:
Find an angle in each quadrant with a common reference angle with 285°, from 0°≤θ<360
The four angles, one in each quadrant, with a common reference angle of with 285° are: 15°, 165°, 195°, 345°
Understanding QuadrantA common reference angle is an angle that is shared by multiple angles in different quadrants when measured from the x-axis. The reference angle for an angle measured in degrees can be found by subtracting the nearest multiple of 90 degrees that is less than the angle.
For the angle 285°, the nearest multiple of 90 degrees that is less than it is 270°. Therefore, the reference angle for 285° is 285° - 270° = 15°.
Using this reference angle, we can find an angle in each quadrant with a common reference angle with 285° as follows:
First Quadrant: An angle in the first quadrant with a reference angle of 15° is 15° itself.Second Quadrant: An angle in the second quadrant with a reference angle of 15° can be found by subtracting the reference angle from 180°. Therefore, an angle in the second quadrant with a common reference angle with 285° is 180° - 15° = 165°.Third Quadrant: An angle in the third quadrant with a reference angle of 15° can be found by subtracting the reference angle from 180° and then adding 180°. Therefore, an angle in the third quadrant with a common reference angle with 285° is 180° + 15° = 195°.Fourth Quadrant: An angle in the fourth quadrant with a reference angle of 15° can be found by subtracting the reference angle from 360°. Therefore, an angle in the fourth quadrant with a common reference angle with 285° is 360° - 15° = 345°.Learn more about quadrant here:
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If the points A,B and C have the coordinates A (5,2), B (2,-3) and C (-8,3) show that the triangle ABC is a right angled triangle.
Answer:
Step-by-step explanation:
To show that the triangle ABC is a right-angled triangle, we need to prove that one of the angles of the triangle is a right angle, which means it measures 90 degrees.
We can use the Pythagorean theorem to check if the sides of the triangle satisfy the condition for a right-angled triangle. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's find the length of each side of the triangle:
AB = √[(5-2)² + (2-(-3))²] = √(3²+5²) = √34
BC = √[(2-(-8))² + (-3-3)²] = √(10²+6²) = √136
CA = √[(5-(-8))² + (2-3)²] = √(13²+1²) = √170
Now, let's check if the Pythagorean theorem is satisfied:
AC² = AB² + BC²
170 = 34 + 136
Since the Pythagorean theorem is satisfied, we can conclude that the triangle ABC is a right-angled triangle, with the right angle at vertex B.
We know that,
the distance between two points=√(x2-x1)²+(y2-y1)²
∴ The distance between points A and B, AB=√(2-5)²+(-3-2)²
=√(9+25)
= √(34)
∴ The length of side AB = √(34)
Again,
The distance between points B and C, BC= √[(-8-2)²+{3-(-3)}²]
= √(100+36)
= √136
∴ The length of side BC =√136
Also,
The distance between points A and D, AC= √(-8-5)²+(3-2)²
= √(169+1)
= √170
∴ The length of side AC=√170
Now, we get three sides of the triangle as AB = √(34), BC = √136, and AC=√170
Since AC is the longest side, we take it as hypotenuse, and the other sides as base and height in the Pythagoras theorem,
AC²=170
BC²=136
AB²=34
Clearly, 170=136+34
or, AC²=AB²+BC²
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e) Write a proof to show AABC ~ ACFD.
f) What is the longest cart that can pass through the second doorway?
Explain.
Some of the factory's products are long fragile rods that are carried through
the door by hand. The first door is 72 inches west of the start of the second
door. Assume the rod has zero width and BA = 13 in.
Answer:
Step-by-step explanation:
no
Find the probability that
event A or B takes place.
Probability that event A or B takes place is, P(A or B) = 16/21.
Here from the Venn diagram we can obtain that,
Probability of occurring event A = 2/21 + 4/21 = (2 + 4)/21 = 6/21
Probability of occurring event B = 10/21 + 4/21 = (10 + 4)/21 = 14/21
Probability of occurring event A and event B both = 4/21
So, P(A) = 6/21
P(B) = 14/21
P(A and B) = 4/21
We know that the union of events formula,
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 6/21 + 14/21 - 4/21
P(A or B) = (6 + 14 - 4)/21
P(A or B) = 16/21
Hence the value of P(A or B) = 16/21.
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How many yards are in 150 in.
The answer
4.16666667 yards
can someone help me please
here is the picture is about Row Ops
The result of engaging in the row multiplication operation in a matrix would be [ 1 /2 0 | 3 / 4 ]
[ -1 5 | 4 ].
How to multiply matrices ?First, you should multiply the first row by the value given of 1 / 4 to be:
( 1 / 4 ) x 2 = 1 / 2
( 1 / 4 ) x 0 = 0
( 1 / 4 ) x 3 = 3 / 4
Then you can replace the values found by the values in the matrix to be :
[ 1 / 2 0 | 3 / 4 ]
[ - 1 5 | 4 ]
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11. The angle of elevation to the top of a building is found to be 18 degrees from the ground at a distance of 510 feet from the base of the building. Using this information, find the height of the building to the nearest whole number.
Answer:
Set your calculator to degree mode.
Please sketch the figure to confirm my answer.
tan(18°) = h/510
h = 510tan(18°) = 165.7 feet
Answer:
Construction Model Stats
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Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?
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To find the mean, we add up all the values and divide by the number of values:
Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10
Mean = 36.7 / 10
Mean = 3.67
To find the median, we need to put the values in order:
2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4
The middle number is the median, which is 3.35 in this case.
To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.
To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:
2.5, 2.6, 2.8, 3.1, 3.2
The median of this lower half is 2.8, so Q1 = 2.8.
To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:
3.7, 3.8, 4.1, 9.4
The median of this upper half is 3.95, so Q3 = 3.95.
To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1
IQR = 3.95 - 2.8
IQR = 1.15
1.5 times the IQR is 1.5 * 1.15 = 1.725.
The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.
We can use trigonometry to solve this problem. Let h be the height of the building, and let d be the distance from the base of the building to the point where the angle of elevation is measured. Then we have:
tan(18 degrees) = h / d
Solving for h, we get:
h = d * tan(18 degrees)
Substituting d = 510 feet and using a calculator to evaluate the tangent of 18 degrees, we get:
h = 510 feet * tan(18 degrees)
h ≈ 157.3 feet
Rounding this to the nearest whole number, we get that the height of the building is approximately 157 feet.
Las ecuaciones de la demanda y la oferta de cierto producto están dadas por espacio 4 q al cuadrado más p al cuadrado igual 1405 y p igual q más 10 donde p está en dólares por unidad y q está en unidades. Para un precio de 27 dólares por unidad, determine el gasto real del consumidor.
The actual consumer spending at a price of $27 per unit is $268.26.
How to calculate the priceSubstitute the given price into the supply equation to get the corresponding quantity supplied:
p = q + 10
27 = q + 10
q = 17
Substitute q = 17 into the demand equation to get the corresponding price:
4q² + p² = 1405
4(17)² + p² = 1405
p² = 1405 - 1156
p² = 249
p = 15.78
The actual consumer spending can be calculated by multiplying the quantity demanded by the price:
Actual consumer spending = quantity demanded x price per unit
= 17 x 15.78
= $268.26
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The demand and supply equations for a certain product are given by space 4 q squared plus p squared equals 1405 and p equals q plus 10 where p is in dollars per unit and q is in units. For a price of $27 per unit, determine the actual consumer spending.
find cooordinates of point of interection
11x-6y=2
-8x+5y=3
Answer:
To find the coordinates of the point of intersection of the given equations, we need to solve the system of equations simultaneously. We can use the elimination method to do this:
11x - 6y = 2 (multiply both sides by 5)
-8x + 5y = 3 (multiply both sides by 11)
55x - 30y = 10
-88x + 55y = 33
Adding the two equations, we get:
-33x + 25y = 43
Solving for y, we get:
y = (33x + 43)/25
Substituting this expression for y into either of the original equations and simplifying, we get:
x = -1/7
Substituting this value of x into the equation for y, we get:
y = 1/35
Therefore, the coordinates of the point of intersection are (-1/7, 1/35).
Help me with this question please
Answer:
A line that is perpendicular to another is one that has a slope that is the multiplicative reciprocal of the original funtion's slope and it also has the opposite sign in front. Considering a slope with a value of [tex]\dfrac{1}{7}[/tex], the reciprocal multiplicative is 7, because is a number that equals 1 if multiplied by the original value. Then, we change the sign for it, making it -7.
Thus, correct answer is a. -7.
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Find a polynomial f(x) of degree 5 that has the following zeros.
0, 1 (multiplicity 2), -6, -3
Leave your answer in factored form.
This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.
How to solveA polynomial f(x) of degree 5 with the given zeros can be represented in factored form as:
f(x) = [tex]A(x - 0)(x - 1)^2(x + 6)(x + 3)[/tex]
Since the leading coefficient is not specified, we can leave A as a constant factor. Simplifying the expression, we have:
f(x) = [tex]A(x)(x - 1)^2(x + 6)(x + 3)[/tex]
This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.
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