Answers
Answer:
10 square unitsStep-by-step explanation:
It's a right triangle.
The formula of an area of a right triangle:
[tex]A=\dfrac{ab}{2}[/tex]
a, b - legs
Find x-intercept and y-intercept of a line 4x + 5y = 20.
x-intercept (y = 0):
4x + 5(0) = 20
4x + 0 = 20
4x = 20 divide both sides by 4
x = 5
y-intercept (x = 0):
4(0) + 5y = 20
0 + 5y = 20
5y = 20 divide both sides by 5
y = 4
Therefore the legs are a = 5, b = 4.
Substitute:
[tex]A=\dfrac{(5)(4)}{2}=\dfrac{20}{2}=10[/tex]
Look at the picture.
Related Questions
What are the coordinates of the image of vertex F after a
reflection across the line y = -x?
(-1, -3)
(3,-1)
(1,3)
(-3, 1)
G(-2, -3)
F(1.-3
E-1.-5)
H(2-5)
Answers
The answer is F(3,-1)
Hope this helps!
The coordinate of the vertex F across y = -x will be (3, -1). Then the correct option is B.
What is a reflection of the point?It is the image of the point which is located in the opposite direction of a given point.
The rule of the reflection is given will be
Firstly, the rule for reflecting a point about the line y = x is;
While reflecting on the line y = x, we get the reflected points by swapping the coordinates.
Now, the rule for reflecting a point about the line y = -x is;
While reflecting on the line y = -x, we get the reflected points by multiplying '-1' with the swapped coordinates.
The coordinates of the image are given below.
G(-2, -3), F(1, -3), E(-1, -5), and H(2, -5)
The reflection across the line y = -x.
Then the coordinate of the vertex F across y = -x will be (3, -1).
Then the correct option is B.
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the. expression to find the perimeter of a rectangle is 2 (lengtg+width) what is the perimeter in units of a rectangle of length 1/3 unit and width 1/2 unit
Answers
Answer:
5/3 units or 1 2/3 units
Step-by-step explanation:
P =2 (l+w)
We know the length = 1/3 and the width = 1/2
P = 2 (1/3+1/2)
Get a common denominator of 6
1/3 *2/2 = 2/6
1/2 *3/3 = 3/6
Therefore
P = 2(2/6+3/6)
= 2(5/6)
= 10/6
=5/3 units
Changing from an improper fraction
= 1 2/3 units
Which expression is equivalent to 6(3+0.05)?
A. 6(3)+0.05
B. (6+3)+(6+0.05)
C. 6(3)+6(0.05)
D. 6(3)×6(0.05)
Answers
[tex]\huge{\boxed{6(3)+6(0.05)}}[/tex]
The distributive property shows that you need to multiply the [tex]6[/tex] separately by each term in the parentheses. This means you multiply [tex]6*3[/tex] and [tex]6*0.05[/tex], then add them together to get [tex]6*3+6*0.05[/tex], or in the terms of your answer choices, [tex]\boxed{6(3)+6(0.05)}[/tex].
Option C is correct. The required equivalent expression will be 6(3)+6(0.05)
Given three values A, B and C expressed as A(B+C)
Using the law of distribution
A(B+C) = AB + AC
Applying this law on the expression 6(3+0.05)
6(3+0.05) = 6(3) + 6(0.05)
hence the required equivalent expression will be 6(3)+6(0.05)
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Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 3, -2 is the only other zero, leading coefficient is 2.
f(x)=?
Can some help?
Answers
Answer:
[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]
Step-by-step explanation:
we know that
2 is a zero of multiplicity 3 of the polynomial
so
we have that
x=2 is a solution of the polynomial
A factor of the polynomial is
[tex](x-2)^{3}[/tex] ----> is elevated to the cube because is a multiplicity 3
and the other solution is x=-2
since the polynomial is fifth degree, x=-2 must have a multiplicity 2
so
the other factor of the polynomial is
[tex](x+2)^{2}[/tex] ----> is squared because is a multiplicity 2
therefore
The polynomial is equal to multiply the factors by the leading coefficient
so
[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]
Find the zeros of y = x + 6x- 4 by completing the square.
Answers
Answer:
[tex]\large\boxed{x=-3\pm\sqrt{13}}[/tex]
Step-by-step explanation:
[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\x^2+6x-4=0\qquad\text{add 4 to both sides}\\\\x^2+2(x)(3)=4\qquad\text{add}\ 3^2=9\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=4+9\\\\(x+3)^2=13\Rightarrow x+3=\pm\sqrt{13}\qquad\text{subtract 3 from both sides}\\\\x=-3\pm\sqrt{13}[/tex]
Find the equationOf the line who slope is -3 and Y intercept is five
Answers
Remember that the slope intercept formula is:
y = mx + b
m is the slope
b is the y-intercept
It tells us that the slope (m) is -3 and the y-intercept (b) is 5. Plug this into the formula given above:
y = -3x + 5
Hope this helped!
~Just a girl in love with Shawn Mendes
Which of the following equations represents a line that is parallel to y = 3x +2
and passes through the point, (1,6)?
Answers
Answer:
y=3x+3 is slope-intercept form
y-6=3(x-1) is point-slope form
I don't know the form your equation(s) are in. There are other forms.
Step-by-step explanation:
The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.
So the slope of y=3x+2 is 3.
Parallel lines have the same slope. So the slope of the line we are looking for has a slope of 3.
Therefore, our equation his this form y=3x+b.
We need to now find b.
We know a point (x,y) on the line.
y=3x+b using (x,y)=(1,6).
6=3(1)+b
6=3+b
Subtract 3 on both sides:
3=b
So the equation is y=3x+3
Point-slope form is another form we can put our line into
y-y1=m(x-x1)
where m is the slope and (x1,y1) is a point on the line.
We have m=3 and a point (x1,y1) on the line is (1,6).
y-6=3(x-1)
[tex]\huge{\boxed{y=3x+3}}[/tex]
It could also be [tex]\boxed{y-6=3(x-1)}[/tex]
We can use point-slope to find this. Parallel lines have the same slope, and the given line has a slope of 3 ([tex]m[/tex] in [tex]y=mx+b[/tex]). This means that the parallel line will also have a slope of 3.
Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is a known point on the line.
Plug in the values. [tex]\boxed{y-6=3(x-1)}[/tex] (point-slope form)
Distribute. [tex]y-6=3x-3[/tex]
Add 6 to both sides. [tex]\boxed{y=3x+3}[/tex] (slope-intercept form)
According to the graph, what is the value of the constant in the equation
below?
Answers
Answer:
The value of the constant is 0.8Explanation:
The graph has the following properties:
Horizontal-axis (independent variable): widthVertical-axis (dependent variable): heightPoints on the curve:(0.5, 1.6), (0.8, 1), (1.6, 0.5), and (2, 0.4)
The equation represented by the graph is an inverse variation:
Height = constant / width.From that equation, you can solve for the contstant:
constant = height × widthNow, you can take any ordered pair to find the constant:
(0.5, 1.6) ⇒ constant = 0.5 × 1.6 = 0.8(0.8, 1) ⇒constant = 0.8 × 1 = 0.8(1.6, 0.5) ⇒ constant = 1.6 × 0.5 = 0.8(2, 0.04) ⇒ constant = 2 × 0.4 = 0.8Thus, you have obtained that the constant is 0.8.
The normal pulse rate of a 13-year-old is between 70 and 100 beats per minute. As part of a health program, the medical staff at Grant Middle School measured the resting pulse rate of 12 randomly selected students in grades 7 and 8. The box plot shows the data for each group. Which statement correctly compares the data sets?
Answers
Answer:From the box plot, it can be seen that for grade 7 students,
The least value is 72 and the highest value is 91. The lower and the upper quartiles are 78 and 88 respectively while the median is 84.
Thus, interquatile range of the resting pulse rate of grade 7 students is upper quatile - lower quartle = 88 - 78 = 10
Similarly, from the box plot, it can be seen that for grade 8 students,
The least value is 76 and the highest value is 97. The lower and the upper quartiles are 85 and 94 respectively while the median is 89.
Thus, interquatile range of the resting pulse rate of grade 8 students is upper quatile - lower quartle = 94 - 85 = 9
The difference of the medians of the resting pulse rate of grade 7 students and grade 8 students is 89 - 84 = 5
Therefore, the difference of the medians is about half of the interquartile range of either data set.
Step-by-step explanation: i hope it helps it took a long time to write!
Answer:
I hope this helps
Step-by-step explanation:
Which of the diagrams below represents the statement "If it is a square, then
it is a quadrilateral"?
Answers
A quadrilateral is a polygon with 4 number of sides and 4 vertices. The correct figure is figure B.
What is a quadrilateral?A quadrilateral is a polygon with 4 number of sides and 4 vertices. A few examples of a quadrilateral are square, rectangle, rhombus, parallelogram, etc.
For the above-given condition, "If it is a square, then it is a quadrilateral" figure B is correct because, as per the first diagram, not all the squares are quadrilateral, while as per the figure B every square is a quadrilateral.
Hence, the correct figure is figure B.
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I need help with 12.5•10•14 L•W•H
Answers
[tex]\huge{\boxed{\text{1750 units}^{3}}}[/tex]
Explanation:[tex]\begin{array}{cc}\text{First, multiply 12.5 by 10.}&125*14\\\text{Then, multiply 125 by 14.}&1750\end{array}[/tex]
the function f(x) = 3,005(1+0.03)^x represents the amount of money in a savings account where x represents time in years. what does 3,005 represent? a. the amount of money in the savings account after one year b. the amount of money added to the savings account each year c. the growth rate d. the initial amount of money placed in the savings account
Answers
Answer:
Option d. the initial amount of money placed in the savings account
Step-by-step explanation:
we have
[tex]f(x)=3,005(1+0.03)^{x}[/tex]
This is a exponential function of the form
[tex]f(x)=a(1+r)^{x}[/tex]
where
a is the initial value
r is the growth rate
(1+r) is the base
x is the number of years
f(x) is the amount of money in a savings account
In this problem we have
a=$3,005
r=0.03=3%
(1+r)=1.03
therefore
3,005 represent the initial value ( the amount of money for the value of x equal to zero)
Answer:
d. The initial amount of money placed in the savings account
Step-by-step explanation:
Given function that represents the amount of money after x years,
[tex]f(x)=3005(1+0.03)^x[/tex]
Which is an exponential growth function,
Since, in a growth function,
[tex]f(x)=ab^x[/tex]
a represents the initial value,
b is the growth rate per period,
x is the number of periods,
By comparing,
a = 3005,
Hence, 3005 must be represent the initial amount of money placed in the savings account,
Option 'd' is correct.
The perimeter of a rectangle is 215 feet. The short sides are each 24 feet long, but the lengths of the long sides are unknown. Which equation represents this situation?
24a=215
2(24)+2a=215
24+2a=215
2(24)a=215
Answers
Answer:
2 ( 24 ) + 2 a = 215
Step-by-step explanation:
Perimeter of the rectangle is 215 feet, the short sides are 24 feet long and we need to work out the long sides (we will call a long side 'a') so,
24 + 24 + a + a = 215
For this case we have to:
Let "a" be the variable that represents the length of the rectangle and let "b" be the variable that represents the width of the rectangle. Then the perimeter is given by:
[tex]P = 2a + 2b[/tex]
We have as data that:
[tex]P = 215 \ feet\\b = 24 \ feet[/tex]
Then, replacing:
[tex]215 = 2a + 2 (24)[/tex]
Answer:
Option B
The following set of coordinates most specifically represents which figure? (−5, 6), (−1, 8), (3, 6), (−1, 4) (6 points) Parallelogram Rectangle Rhombus Square
Answers
Answer:
Rhombus
Step-by-step explanation:
The given points are A(−5, 6), B(−1, 8), C(3, 6), D(−1, 4).
We use the distance formula to find the length of AB.
[tex]|AB|=\sqrt{(-1--5)^2+(8-6)^2}[/tex]
[tex]|AB|=\sqrt{16+4}[/tex]
[tex]|AB|=\sqrt{20}[/tex]
The length of AD is
[tex]|AD|=\sqrt{(-1--5)^2+(6-4)^2}[/tex]
[tex]|AD|=\sqrt{16+4}[/tex]
[tex]|AD|=\sqrt{20}[/tex]
The length of BC is:
[tex]|BC|=\sqrt{(-1-3)^2+(8-6)^2}[/tex]
[tex]|BC|=\sqrt{16+4}[/tex]
[tex]|BC|=\sqrt{20}[/tex]
The length of CD is
[tex]|CD|=\sqrt{(-1-3)^2+(6-4)^2}[/tex]
[tex]|CD|=\sqrt{16+4}[/tex]
[tex]|CD|=\sqrt{20}[/tex]
Since all sides are congruent the quadrilateral could be a rhombus or a square.
Slope of AB[tex]=\frac{8-6}{-1--5}=\frac{1}{2}[/tex]
Slope of BC [tex]=\frac{8-6}{-1-3}=-\frac{1}{2}[/tex]
Since the slopes of the adjacent sides are not negative reciprocals of each other, the quadrilateral cannot be a square. It is a rhombus
Answer:
answer is Rhombus
Step-by-step explanation:
7 × (–3) × (–2)2 = ?
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{7*(-3) * (-2)(2) = ?}[/tex]
[tex]\huge\text{7 * (-3) = -21}[/tex]
[tex]\huge\text{-21 * (-2)2 = ?}[/tex]
[tex]\huge\text{-21 * -2 = 42}[/tex]
[tex]\huge\text{42(2) = ?}[/tex]
[tex]\huge\text{42 * 2 = 42 + 42 = 84}[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: 84}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Find the product. Simplify using positive exponents.
4⁴ · 4³
2² · 2⁻⁴
Answers
Answer:
Step-by-step explanation:
=4⁴ · 4³
=4^{7}
=16 384
=2² · 2⁻⁴
=2^{-2}
=1/2^{2}
=1/4
A flare is shot straight up from a flare gun, from a height of 6 meters, and with a velocity of 60 m/s. How many seconds it takes for the flare to hit the ground? Use the formula below where v0 is the initial velocity and h0 is the initial height. Approximately how long will is take the object to hit the ground?
[tex]h(t) = -4.9t^2 + v_0t + h_0[/tex]
10.8 sec
11.4 sec
11.8 sec
12.3 sec
Answers
Answer:
Step-by-step explanation:
Answer: 12.3 seconds.
Step-by-step explanation: Hope It Helps :)
Charlene is wrapping the box below. How much wrapping paper will she need? 7in x 9in x 5in,?
Answers
Charlene will need 286 square inches of wrapping paper to cover all six sides of the box with dimensions of 7 inches by 9 inches by 5 inches. This is found by calculating the surface area of each side and then adding them together.
To determine how much wrapping paper Charlene will need to wrap a box with dimensions 7 inches by 9 inches by 5 inches, we calculate the surface area of the box. The box has 6 sides, with each side being a rectangle. The dimensions of the sides are 7x9 inches (two sides), 7x5 inches (two sides), and 9x5 inches (two sides).
To find the total surface area, we calculate the area of each of these rectangles and then sum them together:
Area for two 7x9 sides: 2 * (7in * 9in) = 2 * 63in2 = 126in²
Area for two 7x5 sides: 2 * (7in * 5in) = 2 * 35in2 = 70in²
Area for two 9x5 sides: 2 * (9in * 5in) = 2 * 45in2 = 90in²
Adding these together gives:
Total surface area = 126in² + 70in² + 90in² = 286in²
Charlene will need 286 square inches of wrapping paper to wrap the box.
6. Find the sum of the arithmetic series.
∑_(n=1)^5▒〖(9-4n)〗
7. Find the first five terms of the sequence described.
a_1=3,a_(n+1)=a_n+5
Answers
Evaluate the function rule for the given value. y = 4 • 2^x for x = –6
Answers
Answer:
y = 1/16
Step-by-step explanation:
y = 4 • 2^x
Let x = -6
y = 4 • 2^(-6)
The negative exponent puts it in the denominator
y = 4 • 1/ 2^6
y = 4 * 1/64
y = 4/64
y = 1/16
478,387 to the nearest ten thousand
Answers
ANSWER = 270,000
MARK BRAINLIST
Answer:
478,387.0000
Step-by-step explanation:
PLZ HELP WILL GIVE BRAINLIEST!!!
Type the correct answer in each BLANK. The line of best fit represents the number of miles Jean covered at different speeds during a trip. If the speed is represented by x and the distance covered is represented by y, the equation of the best line of fit is y =(BLANK) . She covered about (BLANK) miles at the speed of 50 miles per hour.
Answers
Answer:
y=2x
100 miles
Step-by-step explanation:
The slope is determined by change of y/ change of x
when using the points (0,0)-(50,100) is
100-0/50-0= 100/50=2
so the slope is 2.
Also there is no Y intercept on the equation bc it goes through the origin.
100 miles is the y point for 50 miles per hour
Answer:
The equation of the best line of fit is y = 2x
Step-by-step explanation:
The relationship between y and x is
y = mx + c
Where m = slope of the line
And c = intercept
At 50 miles per hour she has already covered a distance of 100 miles ---- from the graph
We can use this to calculate the slope of the line using the coordinates (0,0) (50,100)
Slope m is calculated as;
m = (y2 - y1)/(x2 - x1)
Where y2 = 100, x2 = 50
y1 = x1 = 0
Substitute these values
So m = (100 - 0)/(50 - 0)
m = 100/50
m = 2
Since there's no intercept, c = 0
The equation y = mx + c becomes
y = 2x + 0
y = 2x
Evaluate 12 sigma n=3 20(0.5)^n-1
9.99
19.95
29.98
39.96
Answers
Answer:
We have a geometric series in which:
a = 20
r = 1/2
Now, we know that: S2 = 20(1-r^2)/(1-r) and S12 = 20(1-r^12)/1-r
Therefore: sigma(3,12) = S12-S2 = 20[(1-r^12)/(1-r) - (1-r^2)/(1-r)] =5115/512 = 9.99023438
Therefore, the answer is: 9.99
Answer: Is D
Step-by-step explanation:
Nicholas has a fish tank that is 12 inches high, 14.5 inches long, and 6.5 inches wide. If he fills the tank halfway with water, how many cubic inches of water are in the tank?
Answers
Answer:
565.5 in^3
Step-by-step explanation:
To find the full volume of the tank
V = l*w*h
We know 12 inches high, 14.5 inches long, and 6.5 inches wide.
Substituting in
V = 12 * 14.5*6.5
V =1131 in ^3
He is filling it 1/2 full, that would be 1/2 of the volume
1/2 V = 1131/2 = 565.5 in^3
Answer:
answer is 565.5 in^3
Step-by-step explanation:
Which value of x makes the quotient of (5x^5+90x^2-135x)/(x+5) undefined?
Answers
Answer:
The value x=-5 makes the quotient undefined
Step-by-step explanation:
When we are looking for undefined values, we want values that make the denominator zero
x+5 =0
Subtract 5 from each side
x+5-5 =0-5
x=-5
The value x=-5 makes the quotient undefined
What are the zeros of the function f(x)=x^2+x-6 divides by x^2-x-6?
Answers
Answer:
It is B.
Step-by-step explanation:
x^2+x-6 / x^2-x-6 = 0
The numerator equates to zero:
x^2 + x - 6 = 0
(x + 3)(x - 2) = 0
the zeroes are {-3, 2).
The zeroes of the function f(x) = (x² + x - 6)/(x² - x - 6) are -3, 2.
Hence, option B. is the right choice.
What are functions?A function (say f(x)) is defined over x, when an expression in x, gives only one value f(x) for all the x in its domain.
What are zeroes of function?A zero of a function (say f(x)) is the value x, where f(x) = 0.
How do we solve the given question?We are asked to find the zeroes of the function
f(x) = (x² + x - 6)/(x² - x - 6).
To find the zeroes, we put the value of f(x) = 0, in the above equation to get:
(x² + x - 6)/(x² - x - 6) = 0
or, (x² + 3x - 2x - 6)/(x² + 2x - 3x - 6) = 0
or, {x(x + 3) -2(x + 3)}/{x(x + 2) -3(x + 2)} = 0
or, {(x - 2)(x + 3)}/{(x - 3)(x + 2)} = 0
Zeroes are where the numerator = 0, as the denominator can not be 0.
∴ (x + 3)(x - 2) = 0
∴ Zeroes of the function x + 3 = 0 ⇒ x = -3, and x - 2 =0 ⇒ x = 2, that is
-3, 2. Hence, option B. is the right choice.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10). Match each quadrilateral, described by its vertices, to the sequence of transformations that will show it is congruent to quadrilateral JKLM.
Answers
Answer:
1. W(5,1),X(1,7),Y(9,9) and Z(11,7).
2.A(-8,-4),B(-4,-10),C(-12,-12) and D(-14,-10).
3. E(5,6) ,F(1,12),G(9,14) and H(11,12).
4.O(10,1),P(6,7),Q(14,9) and R(16,7).
Step-by-step explanation:
We are given that a quadrilateral JKLM with vertices J(8,4),K(4,10),L(12,12) and M(14,10)
We have to match a quadrilateral with its correct transformation of given quadrilateral JKLM
1.a transformation 3 units down and 3 units left
By using transformation rule [tex](x,y)\rightarrow (x-3,y-3)[/tex]
The new vertices of quadrilateral is (5,1), (1,7),(9,9) and (11,7).
Hence, the quadrilateral WXYZ with vertices W(5,1),X(1,7),Y(9,9) and Z(11,7).
2.A sequence of reflection across x- axis and y-axis in order
Reflection across x- axis
The transformation rule [tex](x,y)\rightarrow (x,-y)[/tex]
By using this rule
The vertices of quadrilateral are (8,-4),(4,-10),(12,-12) and (14,-10).
After the reflection across y- axis
The transformations rule
[tex](x,y)\rightarrow (-x,y)[/tex]
By using this rule
We get the new vertices of quadrilateral are (-8,-4),(-4,-10),(-12,-12) and (-14,-10).
Hence, the quadrilateral ABCD with vertices A(-8,-4),B(-4,-10),C(-12,-12) and D(-14,-10).
3.a translation 3 unit left and 2 units up
The transformation rule [tex](x,y)\rightarrow (x-3,y+2)[/tex]
By using this rule
The new vertices are (5,6),(1,12),(9,14) and (11,12).
Hence, the quadrilateral EFGH with vertices E(5,6) ,F(1,12),G(9,14) and H(11,12).
4.a translation 2 units right and 3 units down
The transformation rule
[tex](x,y)\rightarrow (x+2,y-3)[/tex]
By using this rule
The new vertices are (10,1),(6,7),(14,9) and (16,7)
Hence, the quadrilateral OPQR with vertices O(10,1),P(6,7),Q(14,9) and R(16,7).
The formula for the circumference of a circle is C = 2tr,
where r is the radius and C is the circumference. The
equation solved for r is r= .
Answers
The correct formula to calculate the circumference of a circle is C = 2πr. To solve for r, the radius, we can rearrange the equation to r = C/(2π), which can be used to find the radius when the circumference is known.
Explanation:The formula for the circumference of a circle is given by C = 2πr, where 'C' represents the circumference and 'r' is the radius of the circle. The formula has been provided in an errorneous format, it should be 2πr not 2tr.
If we want to solve this equation for 'r', which represents the radius, we would need to isolate 'r' on one side of the equation. We can do this by dividing both sides of the equation by 2π. The resulting equation solved for r would be r = C/(2*π).
This equation can be utilized to find the radius if the circumference is known.
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Please help!!
A multiple-choice test consists of 28 questions with possible answers of a,b,c,d. Estimate the probability that with random guessing, the number of correct answers is at least 12.
Answers
Answer:
Approximately 0.0294.
Step-by-step explanation:
Assume that there's only one correct choice in each question.
The chance of getting a question correct by random guess is 1/4.The chance of getting a question wrong by random guess is 3/4.What's the probability that exactly 12 answers are correct?
12 out of the 28 answers need to be correct. [tex]\displaystyle \left(\frac{1}{4}\right)^{12}[/tex].The other 28 - 12 answers need to be incorrect. Multiply by [tex]\displaystyle \left(\frac{3}{4}\right)^{28 - 12}[/tex].There are more than one way of choosing 12 answers out of 28 without an order. Multiply by the combination "12-choose-28" [tex]\displaystyle \left(\begin{array}{c}12\\28\end{array}\right)[/tex].The probability of getting exactly 12 answers correct is:
[tex]\displaystyle \left(\frac{1}{4}\right)^{12} \times \left(\frac{3}{4}\right)^{28 - 12}\times \left(\begin{array}{c}28\\12\end{array}\right)\approx 0.0182[/tex].
With the same logic, the probability of getting [tex]x[/tex] ([tex]x\in \mathbb{Z}[/tex], [tex]12\le x\le 28[/tex]) correct out of the 28 random answers will be
[tex]\displaystyle \left(\frac{1}{4}\right)^{x} \times \left(\frac{3}{4}\right)^{28 - x}\times \left(\begin{array}{c}28\\x\end{array}\right)[/tex].
The probability of getting at least 12 correct out of 28 random answers is the sum of
the probability of getting exactly 12 correct out of 28, plusthe probability of getting exactly 13 correct out of 28, plusthe probability of getting exactly 14 correct out of 28, plusthe probability of getting exactly 15 correct out of 28, plusthe probability of getting exactly 16 correct out of 28, plus... all the way to the probability of getting exactly 28 correct out of 28.The Sigma notation might help:
[tex]\displaystyle \sum_{x = 12}^{28}{\left[\left(\frac{1}{4}\right)^{x} \times \left(\frac{3}{4}\right)^{28 - x}\times \left(\begin{array}{c}x\\28\end{array}\right)\right]}[/tex].
Evaluate this sum (preferably with a calculator)
[tex]\displaystyle \sum_{x = 12}^{28}{\left[\left(\frac{1}{4}\right)^{x} \times \left(\frac{3}{4}\right)^{28 - x}\times \left(\begin{array}{c}x\\28\end{array}\right)\right]} \approx 0.0294[/tex].
Consider the function f(x) = x2 + 2x - 15. What are the x-intercepts of the function?
Answers
Answer:
x = - 5, x = 3
Step-by-step explanation:
To find the x- intercepts equate f(x) to zero, that is
x² + 2x - 15 = 0 ← in standard form
Consider the factors of the constant term ( - 15) which sum to give the coefficient of the x- term ( + 2)
The factors are + 5 and - 3, since
5 × - 3 = - 15 and 5 - 3 = + 2, hence
(x + 5)(x - 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5 ⇒ (- 5, 0 ) ← x- intercept
x - 3 = 0 ⇒ x = 3 ⇒ (3, 0 ) ← x- intercept
Answer:
left most x intercept : ( -5, 0 )
right most x intercept : ( 3, 0 )
Step-by-step explanation:
Just got it right esketit