Answer:
The radius C) of a circle centered at the origin measures the distance from the origin to any point on the circle
Final answer:
The radius of a circle centered at the origin is the distance from the origin to any point on the circle, represented by the equation x² + y² = r².
Explanation:
The radius of a circle centered at the origin measures the distance from the origin to any point on the circle. When we consider the set of all points (x, y) at a fixed distance r from the origin, the equation x² + y² = r² represents a circle of radius r.
This equation is derived using the Pythagorean theorem. The radius is not to be confused with the circumference, which is the distance around the circle, or the y-coordinate, which is simply the vertical position of a point. The radius squared (r²) refers to the square of the length of the radius.
Joe Bob wanted to find out how many hours of exercise the students at his school gets each week. He went to the school's gym and asked the following question:
"Do you work out every day like a healthy person, or are you a lazy couch potato who only works out once in a while?"
What is another way Joe Bob could word his question so that it does not contain any bias?
Although I am unsure what this question has to do with Mathematics, Joe Bob could simply say "How often do you work out in a week?"
Which polynomial is prime?
3x3 + 3x2 – 2x – 2
3x3 – 2x2 + 3x – 4
4x3 + 2x2 + 6x + 3
4x3 + 4x2 – 3x – 3
The prime polynomial out of the given options is 3x^3 + 3x^2 - 2x - 2.
Explanation:Out of the given polynomials, the polynomial that is prime is 3x3 + 3x2 - 2x - 2.
A polynomial is considered prime if it cannot be factored into a product of lower degree polynomials with integral coefficients.
In this case, the polynomial 3x3 + 3x2 - 2x - 2 is a cubic polynomial and cannot be factored further, so it is prime.
A company makes batteries with an average life span of 300
hours with a standard deviation of 75 hours. Assuming the
distribution is approximated by a normal curve fine the
probability that the battery will last:(give 4 decimal places for
each answer)
a. Less than 250 hours ___________
b. Between 225 and 375 hours __________
c. More than 400 hours ______________
Answer:
a) 0.2514
b) 0.6827
c) 0.0918
Step-by-step explanation:
Average life span of batteries = u = 300 hours
Standard deviation = s = 75 hours
Given that the distribution of life span of batteries is normally distributed, so we can use z-score to find the said probabilities.
Part a) Less than 250 hours
In order to find the probability that the life span of battery will be less than 250 hours we need to convert x = 250 into z-score and then use z-score to find the probability from the z-table.
The formula for z-score is:
[tex]z=\frac{x-u}{s}[/tex]
Using the values, we get:
[tex]z=\frac{250-300}{75}=-0.67[/tex]
From the z-table or z-calculator the probability of z-score being less than - 0.67 comes out to be 0.2514
P(z < -0.67) = 0.2514
Thus, the the probability that the life span of battery will be less than 250 hours is 0.2514
Part b) Between 225 and 375 hours
In order to find the probability that the life span of battery will be between 225 and 375 hours we need to convert them into into z-scores and then use z-score to find the probability from the z-table.
225 into z-score will be:
[tex]z=\frac{225-300}{75}=-1[/tex]
375 into z-score will be:
[tex]z=\frac{375-300}{75}=1[/tex]
Thus, from the z-table we now need to find that probability of z-score being in between -1 and 1. From the z-table this value comes out to be:
P(-1 < z < 1 ) = 0.6827
Thus, the probability that the life span of battery will be between 225 and 375 hours is 0.6827
Part c) More than 400 hours
In order to find the probability that the life span of battery will be more than 400 hours we need to convert x = 400 into z-score and then use z-score to find the probability from the z-table.
The formula for z-score is:
[tex]z=\frac{x-u}{s}[/tex]
Using the values, we get:
[tex]z=\frac{400-300}{75}=1.33[/tex]
From the z-table the probability of z score being more than 1.33 comes out to be:
P( z > 1.33) = 0.0918
Thus, the probability that the life span of battery will be more than 400 hours is 0.0918
Figure ABCD is a parallelogram.
What is the value of n?
Answer:
n = 17.
Step-by-step explanation:
The opposite angles of a parallelogram are congruent so we have:
4n - 2 = 2n + 32
4n - 2n = 32 + 2
2n = 34
n = 17.
What is the following sum? Assume x > 0 and y > 0 sqrt x^2y^2+2 sqrt x^3y^4+xy sqrt y
Answer:
[tex]xy(1+2y\sqrt{x}+\sqrt{y})[/tex]
Step-by-step explanation:
Given expression,
[tex]\sqrt{x^2y^2}+2\sqrt{x^3y^4}+xy\sqrt{y}[/tex]
[tex]=(x^2y^2)^\frac{1}{2} + 2(x^3y^4)^\frac{1}{2} + xy\sqrt{y}[/tex]
[tex]\because (\sqrt{x}=x^\frac{1}{2})[/tex]
[tex]=(x^2)^\frac{1}{2} (y^2)^\frac{1}{2} + 2(x^3)^\frac{1}{2} (y^4)^\frac{1}{2} + xy\sqrt{y}[/tex]
[tex](\because (ab)^n=a^n b^n)[/tex]
[tex]=x^{2\times \frac{1}{2}} y^{2\times \frac{1}{2}} + 2(x^{3\times \frac{1}{2}})(y^{4\times \frac{1}{2}})+xy\sqrt{y}[/tex]
[tex]\because (a^n)^m=a^{mn}[/tex]
[tex]=x^1 y^1 + 2x^{1\frac{1}{2}} y^2 + xy\sqrt{y}[/tex]
[tex]=xy+2x.(x)^\frac{1}{2} y^2 + xy\sqrt{y}[/tex]
[tex]=xy+2xy^2\sqrt{x}+xy\sqrt{y}[/tex]
[tex]=xy(1+2y\sqrt{x}+\sqrt{y})[/tex]
Answer:
B is the right option
Step-by-step explanation:
On edg :))
The altitude of the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 77 and 7. what is the length of the altitude?
Answer:
[tex]h=7\sqrt{11}\ units[/tex]
Step-by-step explanation:
The altitude to the hypotenuse of a right tringle is the geometric mean of the two segments that it divides the hypotenuse into.
1st segment = 77 units
2nd segment = 7 units
Altitude = h units
So,
[tex]h^2=77\cdot 7\\ \\h^2 =7\cdot 11\cdot 7\\ \\h=\sqrt{7\cdot 11\cdot 7}=7\sqrt{11}[/tex]
Which equation represents the slope-intercept form of the line below?
Answer:
Choice B: y = 1/2x + 8
Step-by-step explanation:
Given
slope = 1/2
y-intercept = (0,8)
Put in y = mx + b form
slope is indicated by m
y-intercept is indicated by b
y = 1/2x + 8
Answer
y = 1/2x + 8
Answer: B. [tex]y=\dfrac{1}{2}x+8[/tex]
Step-by-step explanation:
We know that the equation of a line in slope-intercept form is given by :-
[tex]y=mx+c[/tex], where m is the slope of the line and c is the y-intercept of the line.
For the given graph , we have
y-intercept = (0,8)
i.e. c=8
Slope =[tex]\dfrac{1}{2}[/tex]
i.e. m=8
Then, the equation of the given line in slope-intercept form will be :-
[tex]y=\dfrac{1}{2}x+8[/tex]
The temperature rose 9*F in three hours. If the starting temperature was -15*F what was the final temperature? Explain.
Answer:
-6*F
Step-by-step explanation:
-15+9=-6
How many deciliter are equivalent to 5 cups
Answer:
11.8294Step-by-step explanation:
Answer:
Step-by-step explanation:
How many deciliters are equivalent to 5 cups?
2.1097 deciliters
11.85 deciliters
118.5 deciliters
210.97 deciliters
ANSWER IS 11.85
Suppose f(x) = x^2. What is the graph of g(x) =f(4x)?
Answer:
your y-intercept is 0 and slope is 4 so any line with zero slope it will be horizontal
Answer: On mine it is D
Step-by-step explanation:
It is the small one facing up
Describe the steps you used to solve the equation and find the amount of Carrie’s allowance. Linear equation: 1 4 a + 1 3 a + 8 = 22
Sample Response: First, the like terms had to be combined using the lowest common denominator (LCD). Then the subtraction property of equality was used to isolate the variable term. Finally, both sides of the equation were multiplied by the reciprocal of the coefficient to solve for a.
Suppose you and some friends are going to the movies. The amount of money you spend for tickets varies directly with the number of people buying
tickets. If you spend $48 for six tickets, what is the constant of variation?
e r song to the movies. The amount of money you spend for tckets vantes directly w
6
Answer:
The constant variation, and the price of one ticket is 8.
Step-by-step explanation:
if a+b+c=-2 and x+y=-9 what is 9x + 4b + 9y +4c + 4a
Answer:
-89
Step-by-step explanation:
9x + 4b + 9y +4c + 4a (9x+9y)+(4a+4b+4c) =9(x+y)+4(a+b+c)
but : a+b+c = -2 and x+y = -9
9x + 4b + 9y +4c + 4a = 9(-9)+4(-2) = - 81 -8 =-89
What are the zeros of r(p) = -p2 + 14p?
[tex]-p^2 + 14p=0\\-p(p-14)=0\\p=0 \vee p=14[/tex]
Which value is equivalent to
[tex]\bf \left( \cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 5\cdot 2}{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 3} \right)^2 \times \left( \cfrac{5^0}{2^{-3}} \right)^3\times 2^{-9}\implies \left( \cfrac{5\cdot 2}{ 3} \right)^2 \times \left( \cfrac{1}{2^{-3}} \right)^3\times 2^{-9}[/tex]
[tex]\bf \left( \cfrac{10}{ 3} \right)^2 \times \left( 2^3 \right)^3\times 2^{-9}\implies \left( \cfrac{10}{ 3} \right)^2 \times 2^9\times 2^{-9}\implies \cfrac{10^2}{3^2}\times 2^{9-9} \\\\\\ \cfrac{100}{9}\times 2^0\implies \cfrac{100}{9}\times 1\implies \cfrac{100}{9}[/tex]
The sum of two numbers is 12, their product is 96. Compute these two numbers. Explain.
Answer:
The numbers are
[tex]6+2\sqrt{15}i[/tex] and [tex]6-2\sqrt{15}i[/tex]
Step-by-step explanation:
Let
x and y -----> the numbers
we know that
[tex]x+y=12[/tex] -----> [tex]y=12-x[/tex] ------> equation A
[tex]xy=96[/tex] ----> equation B
substitute equation A in equation B and solve for x
[tex]x(12-x)=96\\12x-x^{2}=96\\x^{2} -12x+96=0[/tex]
Solve the quadratic equation
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} -12x+96=0[/tex]
so
[tex]a=1\\b=-12\\c=96[/tex]
substitute
[tex]x=\frac{-(-12)(+/-)\sqrt{-12^{2}-4(1)(96)}} {2(1)}[/tex]
[tex]x=\frac{12(+/-)\sqrt{-240}} {2}[/tex]
Remember that
[tex]i^{2}=\sqrt{-1}[/tex]
[tex]x=\frac{12(+/-)\sqrt{240}i} {2}[/tex]
[tex]x=\frac{12(+/-)4\sqrt{15}i} {2}[/tex]
Simplify
[tex]x=6(+/-)2\sqrt{15}i[/tex]
[tex]x1=6+2\sqrt{15}i[/tex]
[tex]x2=6-2\sqrt{15}i[/tex]
we have two solutions
Find the value of y for the first solution
For [tex]x1=6+2\sqrt{15}i[/tex]
[tex]y=12-x[/tex]
substitute
[tex]y1=12-(6+2\sqrt{15}i)[/tex]
[tex]y1=6-2\sqrt{15}i[/tex]
Find the value of y for the second solution
For [tex]x2=6-2\sqrt{15}i[/tex]
[tex]y2=12-x[/tex]
substitute
[tex]y2=12-(6-2\sqrt{15}i)[/tex]
[tex]y2=6+2\sqrt{15}i[/tex]
therefore
The numbers are
[tex]6+2\sqrt{15}i[/tex] and [tex]6-2\sqrt{15}i[/tex]
Which is the graph of f(x) =4(1/2)^x
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]f(x)=4(\frac{1}{2})^{x}[/tex]
This is a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
a is the initial value
b is the base
r is the rate
b=1+r
In this problem we have
a=4 ----> initial value (y-intercept)
b=1/2
so
1+r=1/2
r=1/2-1=-1/2
r=-0.5=-50% ----> is negative because is a decrease rate
using a graphing tool
The graph in the attached figure
The paragraph below comes from the rental agreement Susan signed when she opened her account at Super Video.
"All rentals are due back by midnight of the due date as printed on the transaction receipt. Any rental not received by midnight on the day it is due is subject to a late charge of $1.50 for each day it is late. Any rental not returned by the fifth day after the due date will be transferred to a sale. The Customer will then be required to pay the purchase price of the item in addition to five (5) days of late fees. The Customer will not be required to return the product once the total balance is paid."
As of today, Susan's movie is currently five days late. She knows that if she doesn't get the movie back tonight, she will be charged $9.99, the purchase price of the movie, plus five days' worth of late fees. A round trip cab ride to the video store will cost about $10.
Which of the following statements is true?
a.
Taking a cab to return the movie is the cheapest action. Susan should call a cab.
b.
It would cost about the same to keep or return the movie. Susan should keep it.
c.
Keeping the movie and paying the purchase price and late fees is the cheapest option.
d.
If Susan returns the movie, she should not have to pay late fees. She should return it.
ANSWER IS D
Answer:
c. Keeping the movie and paying the purchase price and late fees is the cheaper option.
Step-by-step explanation:
1. If Susan takes a cab and pays late fees
Cost of cab = $10.00
Late fees = 5 × 1.50 = 7.50
TOTAL = $17.50
2. If Susan keeps the movie
Purchase price of movie = $9.99
Late fees = 5 × 1.50 = 7.50
TOTAL = $17.49
Keeping the movie and paying the purchase price and late fees is the cheapest option.
a. is wrong. Taking a cab is the more expensive option.
b. is wrong. Susan contracted to return the movie, so she should try to do so.
c. is correct. This is a statement of fact, not a judgement call.
d. is wrong. Susan contracted to pay the late fees if she did not return the video (but she should still return it).
A combination of a conditional statement and its converse written in the “if and only if” form. Both the conditional and the converse must be true before writing this statement .
Answer:
An angle is 90° if and only if it is a right angle.
Explanation:
The statement is: If an angle is 90°, then it is a right angle.
The converse of this statement would be:
If an angle is a right angle, it is 90°.
Clearly, both the conditional and converse of this statement is true.
I need help please.
Answer:
Step-by-step explanation:
p^8 q^6 / p ^4 q^3
In this expression the base of numerator and denominator is same:
We will change the division into multiplication and the denominator will become numerator will negative exponents:
p^8 q^6 * p ^-4 q^-3
Now simplify the terms with same base
The exponents of the same base will be added
=p^8+(-4) q^6+(-3)
=p^8-4 q^6-3
=p^4 q^3
The answer is p^4 q^3....
what is the area of the figure. please help show steps
Answer: [tex]143.99\ ft^2[/tex]
Step-by-step explanation:
We need to find the lenght AC and BC of the triangle by applying these identities:
[tex]cos\alpha=\frac{adjacent}{hypotenuse} \\\\sin\alpha=\frac{opposite}{hypotenuse}[/tex]
Then, AC is:
[tex]sin(45\°)=\frac{AC}{24}\\\\AC=24*sin(45\°)\\\\AC=16.97\ ft[/tex]
And BC is:
[tex]cos(45\°)=\frac{BC}{24}\\\\BC=24*cos(45\°)\\\\BC=16.97\ ft[/tex]
The area will be:
[tex]A=\frac{AC*BC}{2}[/tex]
Substituting values, we get:
[tex]A=\frac{(16.97\ ft)(16.97\ ft)}{2}=143.99\ ft^2[/tex]
A rectangle has vertices at (-1,6), (-1,-2), (3,6), and (3,-2). Sara says the area of the rectangle is 16 square units and her
work is shown below
Steps
Step 1
Step 2
Step 3
Sara's Work
Base: 113-4
Height: 161+F2-4
Area: 4x4-16 square units
Where, if at all, did Sara first make a mistake in finding the area of the rectangle?
Step 1
Step 2
Step 3
no mistake
Answer:
Step 2
Step-by-step explanation:
Let
[tex]A(-1,6), B(-1,-2), C(3,6), D(3,-2)[/tex]
Plot the vertices to better understand the problem
see the attached figure
The area of the rectangle is equal to
[tex]A=bh[/tex]
we have
[tex]b=BD\\ h=BA[/tex]
step 1
Find the base b (BD)
[tex] B(-1,-2),D(3,-2)[/tex]
[tex]b=\left|3\right|+\left|-1\right|=4\ units[/tex]
step 1 is correct
step 2
Find the height h (BA)
[tex]B(-1,-2),A(-1,6)[/tex]
[tex]h=\left|6\right|+\left|-2\right|=8\ units[/tex]
step 2 is not correct
step 3
Find the area
[tex]A=(4)(8)=32\ units^{2}[/tex]
Therefore
Sara first make a mistake in finding the area of the rectangle in Step 2
Answer:
step 2
Step-by-step explanation:
. Solve the triangle. A = 32°, a = 19, b = 12 B = 19.6°, C = 148.4°, c ≈22.5 B = 19.6°, C = 128.4°, c ≈28.1 Cannot be solved B = 19.6°, C = 128.4°, c ≈16.9
Answer:
Step-by-step explanation:
sin(32)/19 = sin(B)/12
cross multiply
12 sin(32) = 19 sin(B)
sin(B) = 12 sin(32) /19 = 0.334686
B = sin°-1(0.334686)
B = 0.321272 radian
B = (0.321272)*180/pi degrees = 19.55°
C = 180-32-19.55 = 128.45°
sin(32)/19 = sin(128.45)/ c
cross multiply
c sin(32) = 19 sin(128.45)
c = 19 sin(128.45) /sin(32) =28.08....
A cylinder has a radius of 6 inches and is 15 inches tall. What is the approximate volume of the cylinder? Express the answer in terms of pi.
Answer:
The volume of cylinder = 540π inches²
Step-by-step explanation:
Points to remember
Volume of cylinder = πr²h
Where r - Radius of cylinder and
h - Height of cylinder
To find the volume of cylinder
Here r = 6 inches and height h = 15 inches
Volume = πr²h
= π * 6² * 15
= π * 36 * 15
= 540 πinches²
The volume of cylinder = 540π inches²
What is the number three thousand eighty expressed in scientific notation?
Answer:
3.08 x [tex]10^{3}[/tex]
Step-by-step explanation:
3080 = 3.08 x 1000 = 3.08 x [tex]10^{3}[/tex]
Solve the equation by using the square root property.
2) (3z - 18)^2 +59 = 14
Answer:
Step-by-step explanation:
Z = i √5/3 +36
The given equation (3z - 18)^2 + 59 = 14 has no real solution because after isolating and simplifying the squared term, we would be taking the square root of a negative number, which is not possible in the real number system.
To solve the equation (3z - 18)^2 + 59 = 14 using the square root property, follow these steps:
(3z - 18)^2 = 14 - 59
(3z - 18)^2 = -45
It is important to note that squaring a real number always results in a non-negative number, so a square equal to a negative number indicates there are no real solutions to the equation.
Solve for x.
5(x + 1) = 4(x + 8)
Answer:
x =27
Step-by-step explanation:
5(x + 1) = 4(x + 8)
Distribute.
5x + 5 = 4x + 32
Move x term onto one side.
x + 5 = 32
Move integer onto one side.
x = 27
What is the scale factor of this dilation?
[Not drawn to scale]
The scale factor of the dilation is:
[tex]1\dfrac{1}{2}[/tex]
Step-by-step explanation:Scale factor--
It is a fixed amount by which the each of the dimension of the original figure is multiplied in order to obtain the dilated image of the figure.
Here we see that there is a enlargement dilation.
( since the side of the image increases after the dilation)
Let the scale factor be k.
From the figure we see that:
The side of length 6 units is transformed to get a side of length 9 units.
i.e.
[tex]6\times k=9[/tex]
i.e.
[tex]k=\dfrac{9}{6}\\\\i.e.\\\\k=\dfrac{3}{2}\\\\i.e.\\\\k=1\dfrac{1}{2}[/tex]
perform the indicated operation: (-1 1/2)(-3/2)
The operation (-1 1/2)(-3/2) gives 9/4 or 2 1/4 as a mixed number.
To perform the indicated operation: (-1 1/2)(-3/2), we need to multiply the two numbers.
First, convert the mixed number -1 1/2 to an improper fraction. It is -3/2 because 1 1/2 is equal to 3/2 and we keep the negative sign.Now, multiply the two fractions: -3/2 * -3/2.Since the signs are the same (both negative), the answer will be positive.Multiply the numerators: 3 * 3 = 9.Multiply the denominators: 2 * 2 = 4.So, the answer is 9/4, or 2 1/4 when converted to a mixed number.Find the student's error in solving the following
inequality.
31 <-5x + 6
25 <-5x
-5
x>7
Step-by-step explanation:
when dividing by a (-)
the inequality sign changes
Answer:
"The student should have switched the direction of the inequality sign to get –5> x for a final answer."
and the second one is:
The student should have added 4 to all parts (left, middle, and right) to get 6 < –3x < 9.
Step-by-step explanation:
i got that on edge