Answer:
[tex]P(Dogs) = 0.2025[/tex]
Step-by-step explanation:
Given
[tex]Proportion, p = 45\%[/tex]
Required
Probability of two people having dog
First, we have to convert the given parameter to decimal
[tex]p = \frac{45}{100}[/tex]
[tex]p = 0.45[/tex]
Let P(Dogs) represent the required probability;
This is calculated as thus;
P(Dogs) = Probability of first person having a dog * Probability of second person having a dog
[tex]P(Dogs) = p * p[/tex]
[tex]P(Dogs) = 0.45 * 0.45[/tex]
[tex]P(Dogs) = 0.45^2[/tex]
[tex]P(Dogs) = 0.2025[/tex]
Hence, the probability of 2 people having a dog is [tex]P(Dogs) = 0.2025[/tex]
20
#1. Which statement is the converse to: If a polygon is a triangle, then it
has 3 sides. *
O A polygon is a triangle, if and only if, it has 3 sides.
If a polygon has 3 sides, then the polygon is a triangle.
If the polygon does not have 3 sides, then it is not a triangle
If a polygon is not a triangle, then it does not have 3 sides
Answer:
If a polygon has 3 sides, then the polygon is a triangle.
Step-by-step explanation:
Bold = hypothesis
Italic = conclusion
Statement:
If p, then q.
Converse: If q, then p.
To find the converse, switch the hypothesis and conclusion.
Statement:
If a polygon is a triangle, then it has 3 sides.
Now we switch the hypothesis and the conclusion to write the converse of the statement.
If it has 3 sides, then a polygon is a triangle.
We fix a little the wording:
If a polygon has 3 sides, then it is a triangle.
Answer: If a polygon has 3 sides, then the polygon is a triangle.
The converse statement will be;
⇒ If a polygon has 3 sides, then the polygon is a triangle.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The statement is,
''If a polygon is a triangle, then it has 3 sides. ''
Now,
Since, The statement is,
''If a polygon is a triangle, then it has 3 sides. ''
We know that;
The converse of statement for p → q will be q → p.
Thus, The converse statement is find as;
⇒ If a polygon has 3 sides, then the polygon is a triangle.
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Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.
Answer:
[tex] \sqrt{4 {}^{2} + ( - 4) {}^{2} } [/tex]
[tex] \sqrt{32} [/tex]
and the angle
[tex] \tan( \alpha ) = - 4 \div 4 = - 1[/tex]
and since the sin component is -ve, we have our angle on 4th quadrant, which equals 315 degrees
Options:
Determine two pairs of polar coordinates for the point (-4, 4) with 0° ≤ θ < 360°. (5 points)
Group of answer choices
(4 , 135°), (-4 , 315°)
(4 , 45°), (-4 , 225°)
(4 , 315°), (-4 , 135°)
(4 , 225°), (-4 , 45°)
Step-by-step explanation:
The guy asking forgot to provide the options you can comment the awnswe in the comments just do it before brainly turns off comments to try and prevent people from learning
What expression describes 2a in the expression 2a2+2a-11
Answer:
Step-by-step explanation:
2a is the middle term of a quadratic expression. 2 is the coefficient of a to the first power.
Not much more you can say about this.
Please, if the original question includes answer choices, share those choices. Thank you.
A population of bacteria P is changing at a rate of dP/dt = 3000/1+0.25t where t is the time in days. The initial population (when t=0) is 1000. Write an equation that gives the population at any time t. Then find the population when t = 3 days.
Answer:
- At any time t, the population is:
P = 375t² + 3000t + 1000
- At time t = 3 days, the population is:
P = 13,375
Step-by-step explanation:
Given the rate of change of the population of bacteria as:
dP/dt = 3000/(1 + 0.25t)
we need to rewrite the given differential equation, and solve.
Rewriting, we have:
dP/3000 = (1 + 0.25t)dt
Integrating both sides, we have
P/3000 = t + (0.25/2)t² + C
P/3000 = t + 0.125t² + C
When t = 0, P = 1000
So,
1000/3000 = C
C = 1/3
Therefore, at any time t, the population is:
P/3000 = 0.125t² + t + 1/3
P = 375t² + 3000t + 1000
At time t = 3 days, the population is :
P = 375(3²) + 3000(3) + 1000
= 3375 + 9000 + 1000
P = 13,375
5 STARS IF CORRECT! Can you find the value of an expression when values for x and y are given? Explain.
If the expression has only two variables [tex] x[/tex] and $y$, or if there's just one variable out of these two, then the answer is yes.
If the expression has more variables (other than X and y), then the answer is no.
Find the vector and parametric equations for the line through the point P(0, 0, 5) and orthogonal to the plane −1x+3y−3z=1. Vector Form: r
Answer:
Note that orthogonal to the plane means perpendicular to the plane.
Step-by-step explanation:
-1x+3y-3z=1 can also be written as -1x+3y-3z=0
The direction vector of the plane -1x+3y-3z-1=0 is (-1,3,-3).
Let us find a point on this line for which the vector from this point to (0,0,5) is perpendicular to the given line. The point is x-0,y-0 and z-0 respectively
Therefore, the vector equation is given as:
-1(x-0) + 3(y-0) + -3(z-5) = 0
-x + 3y + (-3z+15) = 0
-x + 3y -3z + 15 = 0
Multiply through by - to get a positive x coordinate to give
x - 3y + 3z - 15 = 0
How dose this input and output table work?
Aswer:I am sure of the answer it is 6 and 42
Step-by-step explanation:
5+30=3512+30=4230+30=6036+30=6640+30=60I tried something similar to the notation of (x+2)^7, etc, did not get close at all, how would this be solved?
[tex] 24 = 3 \cdot 2^3 [/tex]
[tex]96=3\cdot 2^5 [/tex]
[tex] 384=3\cdot2^7[/tex]
hence it is a geometric progression, with a multiplied constant [tex]3[/tex]
Sum of G.P. of [tex]n[/tex] terms [tex] S_n = a\dfrac{r^n-1}{r-1}\quad \text{where } r \text{ is the common ratio and } a \text{ is the first term} [/tex]
and [tex] r=-2^2=-4[/tex]
Note that the constant should be separated, so
[tex] a= -8 [\tex]
after plugging the values, you'll get the answer
[tex] -26216 \times 3 [/tex]
which option C
Answer:
C
Step-by-step explanation:
-24+96-384+...
a=-24
r=96/(-24)=-4
[tex]s_{7}=a\frac{1-r^7}{1-r} \\=-24\frac{1-(-4)^7}{1-(-4)}\\=-24\frac{1+4^7}{1+4} \\=-24\frac{1+16384}{5} \\=-24\frac{16385}{5} \\=-24 \times 3277\\=-78648[/tex]
Find the derivative of the function f(x) = (x3 - 2x + 1)(x – 3) using the product rule.
then by distributing and make sure they are the same answer
Answer:
Step-by-step explanation:
Hello, first, let's use the product rule.
Derivative of uv is u'v + u v', so it gives:
[tex]f(x)=(x^3-2x+1)(x-3)=u(x) \cdot v(x)\\\\f'(x)=u'(x)v(x)+u(x)v'(x)\\\\ \text{ **** } u(x)=x^3-2x+1 \ \ \ so \ \ \ u'(x)=3x^2-2\\\\\text{ **** } v(x)=x-3 \ \ \ so \ \ \ v'(x)=1\\\\f'(x)=(3x^2-2)(x-3)+(x^3-2x+1)(1)\\\\f'(x)=3x^3-9x^2-2x+6 + x^3-2x+1\\\\\boxed{f'(x)=4x^3-9x^2-4x+7}[/tex]
Now, we distribute the expression of f(x) and find the derivative afterwards.
[tex]f(x)=(x^3-2x+1)(x-3)\\\\=x^4-2x^2+x-3x^3+6x-4\\\\=x^4-3x^3-2x^2+7x-4 \ \ \ so\\ \\\boxed{f'(x)=4x^3-9x^2-4x+7}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
(3.5x10^8)x(4.0x10^-12)=
Answer:
Below
Step-by-step explanation:
● (3.5× 10^8) × (4×10^(-12))
● (3.5×4) × (10^8 × 10^(-12) )
● 14 × 10^ (-12+8)
● 14 × 10^(-4)
● 14/10^4
Find the doubling time of an investment earning 8% interest if interest is compounded continuously. The doubling time of an investment earning 8% interest if interest is compounded continuously is ____ years.
Answer:
Step-by-step explanation:
Using FV = PV(1 + r)^n where FV = future value, PV = present value, r = interest rate per period, and n = # of periods
1/PV (FV) = (PV(1 + r^n)1/PV divide by PV
ln(FV/PV) = ln(1 + r^n) convert to natural log function
ln(FV/PV) = n[ln(1 + r)] by simplifying
n = ln(FV/PV) / ln(1 + r) solve for n
n = ln(2/1) / ln(1 + .08) solve for n, letting FV + 2, PV = 1 and rate = 8% or .08 compound annually
n = 9
n = ln(2/1) / ln(1 + .08/12) solve for n, letting FV + 2, PV = 1 and rate = .08/12 compound monthly
n = 104 months or 8.69 years
n = ln(2/1) / ln(1 + .08/365) solve for n, letting FV + 2, PV = 1 & rate = .08/365 compound daily
n = 3163 days or 8.67 years
Alternatively
A = P e ^(rt)
Given that r = 8%
= 8/100
= 0.08
2 = e^(0.08t)
ln(2)/0.08 = t
0.6931/0.08 = t
t= 8.664yrs
t = 8.67yrs
Which ever approach you choose to use,you will still arrive at the same answer.
Scores on a University exam are normally distributed with a mean of 68 and a standard deviation of 9. Using the 68-95-99.7 rule, what percentage of students score above 77?
Answer:
0.1585, or 15.85%
Step-by-step explanation:
On a standard bell curve, the area from 77 to 100 falls within the 95.45 to 99.73 range.
99.73 - 68.27 = 31.46
31.46 / 2 =15.73
99.7 - 68 = 31.7
31.7 / 2 = 15.85
For lunch, Kile can eat a sandwich with either ham or a bologna and with or without cheese. Kile also has the choice of drinking water or juice with his sandwich. The total number of lunches Kile can choose is
Answer:
8
Step-by-step explanation:
Ham with or without cheese-2 choices
Bologna with or without cheese-2 choices
Bologna with cheese with water or juice-2 choices
Bologna without cheese with juice or water-2 choices
Ham with cheese with juice or water -2 choices
Ham without cheese with juice or water -2 choices
2+2+2+2=8
Kile has 8 choices for lunch
Given two points M & N on the coordinate plane, find the slope of MN , and state the slope of the line perpendicular to MN . (there's two questions)
1) M(9,6), N(1,4)
2) M(-2,2), N(4,-4)
Answer:
Problem 1) [tex] m = \dfrac{1}{4} [/tex] [tex] slope_{perpendicular} = -4 [/tex]
Problem 2) [tex] m = \dfrac{1}{3} [/tex] [tex] slope_{perpendicular} = -3 [/tex]
Step-by-step explanation:
[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] slope_{perpendicular} = \dfrac{-1}{m} [/tex]
Problem 1) M(9,6), N(1,4)
[tex] slope = m = \dfrac{6 - 4}{9 - 1} = \dfrac{2}{8} = \dfrac{1}{4} [/tex]
[tex] slope_{perpendicular} = \dfrac{-1}{\frac{1}{4}} = -4 [/tex]
Problem 2) M(-2,2), N(4,-4)
[tex] slope = m = \dfrac{4 - 2}{4 - (-2)} = \dfrac{2}{6} = \dfrac{1}{3} [/tex]
[tex] slope_{perpendicular} = \dfrac{-1}{\frac{1}{3}} = -3 [/tex]
Write 11 numbers in a row so that the sum of any 3 consecutive numbers is negative, while the sum of all the numbers is positive.
Answer:
Step-by-step explanation:
Hello, if I take the following
2, 2, -5, 2, 2, -5, 2, 2, -5, 2, 2
The sum is 8*2-5*3=16-15=1 > 0
and
2 + 2 -5 < 0
2 - 5 + 2 < 0
-5 + 2 + 2 < 0
2 + 2 -5 < 0
2 - 5 + 2 < 0
-5 + 2 + 2 < 0
2 + 2 -5 < 0
2 - 5 + 2 < 0
-5 + 2 + 2 < 0
2 + 2 -5 < 0
2 - 5 + 2 < 0
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Which parent functions have an intercept at (0,0)Choose all that are correct.
Linear
Quadratic
Radical
Absolute Value
Rational
Exponential
Logarithmic (Log)
Cubic
Cube Root
Answer:
Linear, Quadratic, Radical, Absolute Value, Cubic, Cube Root
Step-by-step explanation:
To find:
Which functions have an intercept at (0, 0).
That means, when we put a value [tex]x=0[/tex] in the [tex]y =f(x)[/tex], value of [tex]y=0[/tex].
Let us discuss each parent function one by one:
1. Linear:
[tex]y = x[/tex]
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
2. Quadratic:
[tex]y = x^2[/tex]
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
3. Radical:
[tex]y = \sqrt x[/tex]
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
4. Absolute Value:
[tex]y = |x|[/tex]
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
5. Rational:
[tex]y = \dfrac{1}{x}[/tex]
When we put [tex]x = 0\Rightarrow y \rightarrow \infty[/tex]
Therefore, it does not have intercept at (0, 0).
6. Exponential:
[tex]y = b^x[/tex]
b is any base
When we put [tex]x = 0\Rightarrow y =1[/tex]
Therefore, it does not have intercept at (0, 0).
7. Logarithmic:
[tex]y = logx[/tex]
When we put [tex]x = 0 \Rightarrow y\rightarrow[/tex] Not defined
Therefore, it does not have intercept at (0, 0).
8. Cubic:
[tex]y = x^3[/tex]
When we put [tex]x = 0\Rightarrow y =0[/tex]
Therefore, it has intercept at (0, 0).
9. Cube Root:
[tex]y = \sqrt[3]x[/tex]
When we put [tex]x = 0\Rightarrow y =0[/tex]
Therefore, it has intercept at (0, 0).
Help I’m really bad at this
Answer:
72
Step-by-step explanation:
The formula for surface area is SA = 2lw + 2wh + 2lh
W = width
L= length
H = height
A = 2(wl + hl + hw)
2·(6·3+2·3+2·6)
Simplify that down to get the answer 72
6x+6+9x+9=? Please help
Answer:
15x + 15
Step-by-step explanation:
Combine like terms. Like terms are terms with the same amount of variables. Set the equation so that the terms are grouped:
6x + 9x + 6 + 9
Combine like terms:
(6x + 9x) = 15x
(6 + 9) = 15
15x + 15 is your answer.
~
Answer:
15x+15
Step-by-step explanation:
6x+9x=15x
9+6=15
6x+6+9x+9=15x+15
A line passes through A(3,7) and B(-4,9). Find the value of a if C(a, 1) is on the line.
Answer: a=24
Step-by-step explanation:
Lets find the line's formula (equation of the line).
As known the general formula of any straight line (linear function) is
y=kx+b
Lets find the coefficient k= (Yb-Ya)/(Xb-Xa)=(9-7)/(-4-3)=-2/7
(Xb;Yb)- are the coordinates of point B
(Xa;Ya) are the coordinates of point A
Now lets find the coefficient b. For this purpose we gonna use the coordinates of any point A or B.
We will use A
7=-2/7*3+b
7=-6/7+b
b=7 6/7
So the line' s equation is y= -2/7*x+7 6/7
Now we gonna find the value of a usingcoordinates of point C.
Yc=1, Xc=a
1=-2/7*a+7 6/7
2/7*a= 7 6/7-1
2/7*a=6 6/7
(2/7)*a=48/7
a=48/7: (2/7)
a=24
Answer:
a=24
Step-by-step explanation:
One way to calculate the target heart rate of a physically fit adult during exercise is given by the formula h=0.8( 220−x ), where h is the number of heartbeats per minute and x is the age of the person in years. Which formula is equivalent and gives the age of the person in terms of the number of heartbeats per minute?
Answer:
The answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
Step-by-step explanation:
Given:
[tex]h=0.8( 220-x )[/tex]
Where [tex]h[/tex] is the heartbeats per minute and
[tex]x[/tex] is the age of person
To find:
Age of person in terms of heartbeats per minute = ?
To choose form the options:
[tex]A.\ x=176-h\\B.\ x=176-0.8h\\C.\ x=-1.25h+220\\D.\ x=h-0.8220[/tex]
Solution:
First of all, let us have a look at the given equation:
[tex]h=0.8( 220-x )[/tex]
It is value of [tex]h[/tex] in terms of [tex]x[/tex].
We have to find the value of [tex]x[/tex] in terms of [tex]h[/tex].
Let us divide the equation by 0.8 on both sides:
[tex]\dfrac{h}{0.8}=\dfrac{0.8( 220-x )}{0.8}\\\Rightarrow \dfrac{1}{0.8}h=220-x\\\Rightarrow 1.25h=220-x[/tex]
Now, subtracting 220 from both sides:
[tex]\Rightarrow 1.25h-220=220-x-220\\\Rightarrow 1.25h-220=-x[/tex]
Now, multiplying with -1 on both sides:
[tex]-1.25h+220=x\\OR\\\bold{x = -1.25h+220}[/tex]
So, the answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
When the scale factor is one what is the ratio of the side length of the side opposite angle a and the length of the hypotenuse
Answer:
me ajuda por favor matemática
To find ∫ (x − y) dx + (x + y) dy directly, we must parameterize C. Since C is a circle with radius 2 centered at the origin, then a parameterization is the following. (Use t as the independent variable.)
x = 2 cos(t)
y = 2 sin(t)
0 ≤ t ≤ 2π
With this parameterization, find the followings
dy=_____
dx=_____
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]x=x(t)=2cos(t)\\\\dx=\dfrac{dx}{dt}dt=x'(t)dt=-2sin(t)dt[/tex]
and
[tex]y=y(t)=2sin(t)\\\\dy=\dfrac{dy}{dt}dt=y'(t)dt=2cos(t)dt[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The values of dx and dy are give as -2sin(t)dt and 2cos(t)dt respectively. The answer to the given problem can be stated as,
dy = 2cos(t)dt
And, dx = -2sin(t)dt.
What is the integration of a function?The integration can be defined as the inverse operation of differentiation. If a function is the integration of some function f(x) , then differentiation of that function is f(x).
The given integral over C is ∫ (x − y) dx + (x + y) dy.
And, the parameters for C are as follows,
x = 2cos(t)
y = 2sin(t)
0 ≤ t ≤ 2π
Now, on the basis of these parameters dx and dy can be found as follows,
x = 2cos(t)
Differentiate both sides with respect to t as follows,
dx/dt = 2d(cos(t))/dt
=> dx/dt = -2sin(t)
=> dx = -2sin(t)dt
And, y = 2sin(t)
Differentiate both sides with respect to t as follows,
dy/dt = 2d(sin(t))/dt
=> dy/dt = 2cos(t)
=> dy = 2cos(t)dt
Hence, the value of dx and dy as per the given parameters is -2sin(t)dt and 2cos(t)dt respectively.
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Find
two consecutive numbers
odd numbers such that the
sum of the
greater number
and 5 times the smaller
number is 92. Please give detailed step by step answer
Answer:
The two odd numbers are 15 and 17
Step-by-step explanation:
Given
Let the odd numbers be represented with x and y
Let x be the greater number
[tex]x + 5y = 92[/tex]
Required
Find x and y
Since x and y are consecutive odd numbers and x is greater, then
[tex]x = y + 2[/tex]
Substitute y + 2 for x in [tex]x + 5y = 92[/tex]
[tex]y + 2 + 5y = 92[/tex]
Collect Like Terms
[tex]y + 5y = 92 - 2[/tex]
[tex]6y = 90[/tex]
Divide both sides by 6
[tex]\frac{6y}{6} = \frac{90}{6}[/tex]
[tex]y = \frac{90}{6}[/tex]
[tex]y = 15[/tex]
Substitute 15 for y in [tex]x = y + 2[/tex]
[tex]x = 15 + 2[/tex]
[tex]x = 17[/tex]
Hence; the two odd numbers are 15 and 17
Answer:
Maths
Step-by-step explanation:
Answer:
The two odd numbers are 15 and 17
Step-by-step explanation:
Given
Let the odd numbers be represented with x and y
Let x be the greater number
Required
Find x and y
Since x and y are consecutive odd numbers and x is greater, then
Substitute y + 2 for x in
Collect Like Terms
Divide both sides by 6
Substitute 15 for y in
Hence; the two odd numbers are 15 and 17
Shane biked 1 mile less than three times the number of miles Lissette biked. Shane biked a total of 7 miles. Write an equation to determine how many miles Lissette biked.
Answer:
2.67 miles (or 8/3 miles which is also 3 2/3 miles)
Step-by-step explanation:
S (shane) = 7
L (lissette) = ??
S = 3(L) - 1
7 = 3L - 1
8 = 3L
L = 2.67 miles
Solve for x: 7 > x/4
Answer: x < 28
Step-by-step explanation:
which expression have a value of 2/3
A: 8+(24 divided by 12) X 4
B:8+24 divided by (12X4)
C: 8+24 divided 12X4
D: (8+24) divided (12X4)
Select the correct answer. If , which statement is true? if g(x) = f(1/3x)
A. The graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g.
B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.
C. The graph of function f is compressed horizontally by a scale factor of to create the graph of function g.
D. The graph of function f is compressed vertically by a scale factor of to create the graph of function g.
Answer:
B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.
Step-by-step explanation:
The rules for linear transformations are that
g(x) = a·f(b·(x-c)) +d
stretches the graph vertically by a factor of "a" (before the shift)
compresses the graph horizontally by a factor of "b" (before the shift)
shifts it to the right by amount "c"
shifts it up by amount "d".
Your equation has b=1/3, so the graph is compressed by a factor of 1/3, which is equivalent to a stretch by a factor of 3.
The appropriate choice of description is ...
b) the graph of g(x) is horizontally stretched by a factor of 3
Answer:
B
Step-by-step explanation:
Correct on Plato
A height is labeled on the triangle below.
Which line segment shows the base that corresponds to the given height of the triangle
Option A,B,C
Answer:
A
Step-by-step explanation:
The height is always perpinducular to the base. The height here is perpendicular to line segment A.
Answer:
A
Step-by-step explanation:
How many cubic inches of a milkshake can you fit up to the brim of this cup without letting it overflow? The
cup is 10 inches tall, and the rim of the cup is 4 inches across. (Hint: the radius is half of the diameter.)
Assuming the cup is a right circular cylinder, it's volume is [tex]V=\pi r^2 h[/tex]
$h=10$, $r=\frac 42$
So the volume is $\pi\cdot(2)^2\cdot10=125.66$
hence you can fill up to 125.66 cubic Inches of milkshake
.
I NEED HELP ASAP
FUND THE VALUE OF X
Answer:
2 sqrt(41) = x
Step-by-step explanation:
This is a right triangle so we can use the Pythagorean theorem
a^2 + b^2 = c^2
8^2 + 10 ^2 = x^2
64+ 100 = x^2
164 = x^2
Take the square root of each side
sqrt(164) = sqrt(x^2)
sqrt(4) sqrt(41) = x
2 sqrt(41) = x
