Part of the population of 7,000 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 7 of them are infected. How many elk are likely to be infected?
Answer:
620
Explanation:
When the sample is given, the number of elk are likely to be infected is to be considered as the 620.
Calculation of the number of elk:
Since the population is 7,750.
The random sample is 50.
So here be like
= 620
hence, When the sample is given, the number of elk are likely to be infected is to be considered as the 620.
Soledad buys 5 ounces of frozen yogurt for $2.25. What is the unit price of the frozen yogurt in dollars per ounce?
Answer:
0.45
Step-by-step explanation:
You divided 2.25 by 5
Mandy has $40 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much will she have in 2 years?
To the nearest cent, the amount she would have in 2 years is $44.10
What is future value of the deposit in savings account?
The future value of the savings account deposit is accumulated balance in the account after 2 years which includes the initial deposit plus interest earned over 2 years
FV=PV*(1+r)^N
FV=accumulated balance after 2 years=unknown
PV=initial deposit=$40
r=interest rate per year=5%
N=number of years that the deposit would last=2
FV=$40*(1+5%)^2
FV=$44.10
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a 9 by 12 rectangular piece of paper is folded so that two opposite corners coincide. what is the length of the crease
The length of the crease is 15 cm.When a 9 by 12 rectangular piece of paper is folded so that two opposite corners coincide, the length of the crease is 15 cm. When we fold a rectangular paper so that the opposite corners meet, we get a crease that runs through the diagonal of the rectangle.
In this case, the 9 by 12 rectangle's diagonal can be determined using the Pythagorean Theorem which states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. In this case, the two sides are the length and width of the rectangle.
The length of the diagonal of the rectangle can be determined as follows:\(`(9^2 + 12^2)^(1/2)`\) = 15 cm. Therefore, the length of the crease is 15 cm.
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Use Green's Theorem to evaluate F dr. C (Check the orientation of the curve before applying the theorem.) F(x, y) = y - cos y, x sin y , C is the circle (x ? 8)2 + (y + 9)2 = 16 oriented clockwise.
Green's Theorem:
We will use the theorem
to solve the problem which relates the line integral with the surface integral here we will consider the region is bounded by the closed loop. For the formula to hold, the line integral above must have a counterclockwise orientation.
The integration over y is performed first. The limits of y are from 0 to 4 and the limits of x are from 0 to 2π. Therefore, the answer is 0. Hence, the required value of F dr. C is 0.
The circle C is (x - 8)2 + (y + 9)2 = 16 when the function F(x, y) = y - cos y, x sin y is given. Green's theorem must be used to evaluate F dr. Before applying the theorem, the curve's orientation must be verified. "The line integral around a closed curve is equal to the surface integral over the enclosed region," states Green's Theorem. "Where F(x, y) = (P, Q) and C is a shut bend situated counterclockwise.
Then, we can assess the line necessary of F over C utilizing Green's Hypothesis by utilizing the twofold essential of the twist of F over the locale R encased by C, that is,int ∂Q/∂x - ∂P/∂y dA = ∮FdRwhere R is the area encased by the shut bend C and D is the inside of C.Let's most memorable track down twist of F, ∂Q/∂x - ∂P/∂y = sin y + sin y = 2 sin y∮FdR = ∫∫R 2 sin y dAUsing Green's hypothesis, we have∮FdR = ∫∫R ( ∂Q/∂x - ∂P/∂y ) dA= ∫∫R 2 sin y dAwhere R is the locale encased by the circle (x - 8)² + (y + 9)² = 16.Then, we want to track down the limits of the district. The radius of the circle is 4, and its center is at (8, -9) in this case.
Therefore, it is evident that the region R can be represented in polar coordinates as 0 r 4 and 0 r 2; consequently, FdR = R 2 sin y dA= 0 2 4 2 r sin dr d= 0 Using the integration formula, ab g(x) h(x) f(x,y) dy dx= ab [ g(x) h(x) f(x The boundaries of y range from 0 to 4, while those of x range from 0 to 2. In this manner, the response is 0. Consequently, the necessary value of F dr. C is 0.
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What is the x intercept of
5x - 10y + 40 = 0
Answer:
The x intercept is -8
Step-by-step explanation:
To find the x intercept, set y = 0 and solve for x
5x - 10y + 40 = 0
5x - 10(0) +40 =0
5x +40 = 0
Subtract 40 from each side
5x = -40
Divide by 5
5x/5 = -40/5
x = -8
The x intercept is -8
The three-dimensional figure below is a cylinder with a hole in the shape of a rectangular prism going through the center of it. The radius is 10 yards. Find the volume of the solid in cubic yards, rounded to the nearest ten.
Answer: 1,510
Step-by-step explanation: using the formula
(pie•r2•height) - (width•length•height)
I plugged in the numbers to get
(Pie•10(2)•5) - (4•3•5)
This gives you
1,570 - 60
= 1,510
can i get some help pls
Answer:
216
Step-by-step explanation:
Since a=-6,b=-4 and c= 3,we have to multiply them including the extra three
Find the value of x that would make the equation modeled below true
From the solution of algebraic equations, the value of x that will make the equation modeled in attached figure true is equals to the \( \frac{5}{4}.\)
Algebraic equations are equations that contain only algebraic operations, such as addition, subtraction, multiplication, and division. Word problems, are example of algebraic equations. Now, we have the equation model as present in attached figure. To solve this problem, we have to drive an equation based on figure, wherein the value of the left side of the figure is equivalent to the value on the right side of the figure.
Consider the left side of the figure, we have 4 triangles with each having a value of x. So, multiply the number of triangles by their values, that's result 4 × x = 4xAlso, on the left side, we have 4 circles with each having a value of -1. So, multiply the number of circles by their values. This results, 4× -1 = -4. In the last, add these two representations and the left side expression looks 4x - 4.Similarly consider the right side of the figure. It contains four triangles (each value -x) and 6 circles (each value 1). The right side expression is represented as 4x + 6. Now, equate the representations on both sides for determining the value of x. So, \(4x -4 = 6 - 4x\)
=> \(4x + 4x = 6 + 4 \)
=> \(8x = 10 \)
=> x = \( \frac{5}{4} \)
Therefore, to make the equation true, the value of x is \( \frac{5}{4}.\)
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Complete question:
The attached figure complete the question.
A two-day moving truck rental from Best Rentals costs $60 and $0.35 per mile driven. A two-day moving truck rental from Easy Movers costs $80 and $0.25 per mile driven. Let m represent the number of miles driven. Which equation can be used to find the number of miles for which the rentals would cost the same amount? 60 + 0.35 m = 80 + 0.25 m 60 m + 0.35 = 80 + 0.25 m 60 + 0.35 m = 80 m + 0.25 m 60 m + 0.35 = 80 m + 0.25
Answer:
A is the correct answer.
Step-by-step explanation:
3 Maria has a bag containing 18 fruit drop sweets. 10 are apple flavoured and 8 are blackberry
flavoured. She chooses a sweet at random and eats it. Then she chooses another sweet at
random. Calculate the probability that:
a)) both sweets were apple flavour
b)) both sweets were blackberry flavored
c)) the first was apple and the second was blackberry
Answer:
Step-by-step explanation:
It could be apple because there is more apple that blackberry fruit drops
Step-by-step explanation:
apple flavoured and 8 are blackberry
flavoured. She chooses a sweet at random and eats it. Then she chooses another sweet at
random. Calculate the probability
a storage tank holds 50,000 gallons of water. what is this volume in cubic meters? 1 gallon =3.785 lt
If a storage tank holds 50,000 gallons of water then its volume is 189.25 cubic meters.
The volume of the storage tank in cubic meters can be calculated by first converting the volume from gallons to liters and then converting from liters to cubic meters.
Step 1: Convert the volume from gallons to liters:
50,000 gallons * 3.785 liters/gallon = 189,250 liters
Step 2: Convert the volume from liters to cubic meters:
189,250 liters * (1 cubic meter/1000 liters) = 189.25 cubic meters
Therefore, the volume of the storage tank is 189.25 cubic meters.
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Please answerrrrrrrrrr pleaseeeeeeee
Answer:
\(\Huge\boxed{x=53}\)
Step-by-step explanation:
Hello There!
Once again we need to use trigonometry to solve for X
Here are the Trigonometric Ratios:
Sin = Opposite divided by hypotenuse
Cos = adjacent divided by hypotenuse
Tan = Opposite divided by adjacent
We are given the adjacent side of x (45) and the hypotenuse (75) so we need to use cos
Remember cos = adjacent divided by hypotenuse
Now we create an equation
\(cos(x)=\frac{45}{75}\\\frac{45}{75} =.6\)
now we have
\(cos(x)=.6\)
like always we want to get rid of cos
to do so we take the inverse of cos (arccos^-1) and apply that to each side
\(arccos^-^1(cos(x))=x\\arccos^-^1(.6)=53.13010235\)
finally we round to the nearest degree
we're left with x = 53
Sam earns $33.00 for babysitting 4 hours. At this rate, how much will he earn if he babysits for 12 hours?
Sam will earn $99 for 12 hours of babysitting.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, Sam earns $33 for babysitting for 4 hours.
4 hours = $33
4 ×3 hours = $33×3
12 hours = $99
Hence, Sam will earn $99 for 12 hours of babysitting.
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let pheta be an acute angle. if cos2pheta+cos^2pheta=1, then cospheta=
2/3
1
√6/3
√2/3
The required value of value of cospheta = √2/3, here correct option is d) √2/3.
The given equation is a Trignomatric Equation,
cos2pheta+cos^2pheta = 1
These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
cos2pheta + cos^2pheta = 1
Now we know that,
\(cos2x\) = \(cos^2x -1\)
so, substituting cos2pheta = 2cos^2pheta - 1
2cos^2pheta-1 + cos^2peta = 1
3cos^2peta = 2
cos^2pheta = 2/3
cospheta = √2/3
Thus, the required value for the cospheta = √2/3.
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2 people can plough through a field in 6 hours How long will it take for 1 person to plough through a field How long will it take for 3 people to plough through a field
Answer:
3 people 4 hours and and one person 12 hours
Step-by-step explanation:
your welcome
2 fractions with different denominators that add up to 6 1/3
The two fractions with denominators of 2 and 6 that add up to 19/3 are 3/6 and 29/3, respectively.
First, let's break down what that mixed number means in terms of fractions. 6 1/3 is the same as 19/3.
Now, we need to find two fractions with different denominators that add up to 19/3. One way to do this is to use a common denominator. To find a common denominator, we need to find the least common multiple (LCM) of the two denominators.
Let's say we want to find two fractions that add up to 19/3, with denominators of 2 and 6. The LCM of 2 and 6 is 6. So, we can rewrite the fractions with a denominator of 6:
1/2 = 3/6
x/6
Now we need to find the value of x that makes the sum of the fractions equal to 19/3:
3/6 + x/6 = 19/3
To solve for x, we can multiply both sides by 6:
3 + x = 38/3
Then, we can subtract 3 from both sides:
x = 29/3
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The table shows Peter's net worth statement. Assets are shown as positive numbers, and liabilities are shown as negative numbers. The value of Peter's house is not given. Peter's net worth is $101,800. Based on the information in the table, what is the current value of Peter's house?
Answer:
Value of House = $98000
Step-by-step explanation:
The sum of all of the assets and liabilities + value of the house = $101,800
Value of House + $900 - $3400 + $16900 - $16300 + $4500 + $1200 = $101,800
=> Value of House + $3800 = $101,800
=> Value of House = $101,800 - $3800
=> Value of House = $98000
The current value of Peter's house will be $98000.
A table is given which shows Peter's net worth and assets are shown as positive numbers, and liabilities are shown as negative numbers.
We have to find out the current value of Peter's house if , Peter's net worth is $101,800.
What will be the resulting value ; 35 - 10 - 5 + 10 = ?
The resulting value will be 30.
As per the question ;
The sum of all of the assets and liabilities plus value of the house is equal to $101,800.
Assume value of house = x
⇒ x + $900 - $3400 + $16900 - $16300 + $4500 + $1200 = $101,800
⇒ x + $3800 = $101,800
⇒ x = $101,800 - $3800
⇒ x = $98000
Thus , the current value of Peter's house will be $98000.
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Consider a circular function that tracks the height, h, of a point traversing a unit circle centered at (0,0), h=f(d) where d is the distance traveled around the circle from the starting point (1, 0). What is the exact value of f(pi)?
The exact value of f(pi) is 0 since when the point on the unit circle has traveled pi distance from its starting point (1,0), it will be at the same height as the starting point.
Let us consider a point on a unit circle centered at (0,0), starting at the point (1,0) and moving around the circle for a distance d. As the point moves around the circle, its height, h, above the x-axis will vary. To find the exact value of f(pi), we need to determine the height of the point when it has traveled a distance of pi around the circle.
When the point has traveled half the distance around the circle, i.e., pi/2, it will be at the point (-1,0), and its height will be 0 since it is on the x-axis. As the point continues to move around the circle, its height will increase until it reaches its maximum height at the point (0,1), where its height is 1.
As the point continues to move around the circle, its height will decrease until it reaches point (1,0), where its height is again 0. Therefore, f(pi) is equal to the height of the point when it has traveled a distance of pi around the circle, which is equal to the height of the point when it is at the point (1,0). Thus, f(pi) = 0.
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40 points answer ASAP PLEASE!
For what values of x does f(x) = 0?
A.−4, 0, 2
B.−2, 0, 4
C.−5, 0, 17
D.−17, 0, 5
I think it is 2, 0, 4 but it would be very helpful if you put in an image of the graph.
Have a great day :D
CAN SOMEONE PLS PLSSS ANSWER ME IT IS ONLY ODD NUMBERS BUT I AM IN SOOO MUCH TROUBLE SO I NEEDIT FAST BUT I WILL GIVE 20 POINTS TO ANYONE THAT ANSWERS AND I WILL MAKE THEM BRAINLIEST I PROMISE
Step-by-step explanation:
3) 7 - 5t = 17
-7 -7
-5t = 10
Divide -5 and 10 by -5
t = -2
5) idk whats the equation for 5
9)
a. You would need to buy 20 songs plus the 10 dollar fee which would equal the other apps fee, 30 dollars.
b. I would buy the first one because 25 dollars for the music and the fee. But if I got the second app I would be paying 5 dollar extra .
Tell whether the following function is linear. If so; graph the function: 2x + 3y = 5.
Consider functions h and k h(x)=3/x+1 what is the value of (h*k)(2) here is the answer to it
Answer: -3
Step-by-step explanation:
The value of (h o k) (2) is -3.
Given,
Consider functions h(x) and k(x).
h(x)=3/x+1.
We need to find what is the value of (h o k)(2).
What is a composite function?Two functions together are called composite functions.
Example:
f(x) and g(x) are functions.
The composite function is given by:
( f o g ) ( x) = f ( g (x) )
We have,
From the figure:
k(-2) = -2
k ( -1) = -5
k (0) = -6
k (1) = -5
k (2) = -2 _____(1)
We have,
h(x)=3/x+1 ______(2)
(h o k) (2):
= h ( k(2) )
From (1)
= h ( -2)
From (2)
= 3 / ( -2 +1 )
= 3 / -1
= -3/1
= -3
Thus the value of (h o k) (2) is -3.
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Please help me out fast. And make sure to Write and solve an inequality. Or it isn't right.
Answer:75x+160
8 is the answer exactly 8
Step-by-step explanation:
Answer:
Set variable d for number of days: 75d + 160 < 760; 75d < 600; d < 8. The van has to be rented for less than 8 days for the family to spend less than $760.
Out of a total of N students at a school, the number of students who have seen a new television program increases at a rate proportional to the product of the number of students who have seen the program and the number of students who have not seen the program. If S denotes the number of students who have seen the program at time t, which of the following differential equations could be used to model this situation, where is a positive constant? A) ks - kt ( N1) -AS (N-S) D - KS (- N)
Based on the given information, we can create a differential equation to represent the situation. Let S denote the number of students who have seen the program at time t and let N be the total number of students.
The number of students who have not seen the program is (N - S). The rate of change of students who have seen the program is proportional to the product of these two quantities, and we represent this proportionality with a positive constant k.
The differential equation to model this situation would be:
dS/dt = kS(N - S)
This equation represents the rate of change of the number of students who have seen the program (dS/dt) as proportional to the product of the number of students who have seen the program (S) and the number of students who have not seen the program (N - S), with k being the positive constant of proportionality.
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Rebekah performed an experiment with a standard number cube. She rolled the cube and recorded the results in the frequency table. The frequency table is given below. Find the experimental probability of the cube landing on three.
Answer:
Step-by-step explanation:
The experimental probability of the cube landing on three is 1/10.
Which describes the process that could be used as the first step in solving this equation? 6x = 4 + 5(x + 8) A) Combine like terms by adding 4 + 5. B) Use distributive property to multiply 5(x + 8). C) Use division property of equality to divide both sides of the equation by 6. D) Use subtraction property of equality to subtract 6x from both sides of the equation.
Answer: B) Use distributive property to multiply 5(x + 8).
Step-by-step explanation:
trust me its right
The first step in solving this equation 6x = 4 + 5(x + 8) is,
⇒ Use distributive property to multiply 5(x + 8).
Option B is true.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 6x = 4 + 5(x + 8)
Now, We can solve the expression as;
⇒ 6x = 4 + 5(x + 8)
⇒ 6x = 4 + 5x + 40
⇒ 6x - 5x = 44
⇒ x = 44
Thus, The first step in solving this equation is,
⇒ Use distributive property to multiply 5(x + 8).
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15+26+56+19+17+19+9+19
Answer:
180
Step-by-step explanation:
Answer:
180
Step-by-step explanation:
A total of 11 trucks was used to carry 126 tonnes of iron. Some of the trucks carry
16 tonnes each, and the rest carry 6 tonnes each. Form an equation and solve it to
find the number of 16 tonne trucks.
Step-by-step explanation:
x = number of trucks with 16 tonnes capacity
y = number of trucks with 6 tonnes capacity
x + y = 11
16x + 6y = 126
the first equation gives us
x = -y + 11
and we use that in equation 2 :
16(-y + 11) + 6y = 126
-16y + 176 + 6y = 126
-10y = -50
10y = 50
y = 5
x = -y + 11 = -5 + 11 = 6
the number of 16 tonne trucks was 6.
Determine whether each pair of expressions is equivalent. Explain your reasoning.
The answer is:
\(\large\textbf{They aren't equivalent.}}\)
In-depth explanation:
To determine the answer to this problem, we will use one of the exponent properties:
\(\sf{x^{-m}=\dfrac{1}{x^m}}\)
And
\(\sf{\dfrac{1}{x^{-m}}=x^m}\)
Now we apply this to the problem.
What is 4⁻³ equal to? Well according to the property, it's equal to:
\(\sf{4^{-3}=\dfrac{1}{4^3}}\)
And this question asks us if 4⁻³ is the same as 1/4⁻3.
Well according to the calculations performed above, they're not equivalent.