a) The estimate for the total number of deer in the park is given as follows: 630 deers.
b) The assumption that he made was that the proportion was followed.
How to estimate the total number of deer in the park?The total number of deer in the park is estimated applying the proportions in the context of this problem.
The next week, the gamekeeper caught 70 deer. 10 of the deer had a tag around one of their hooves, hence the fraction of marked deers is given as follows:
10/70 = 1/7.
He had marked 90 deers, hence the estimate for the total number of deers, considering a constant proportion, is given as follows:
1/7 x n = 90
n = 90 x 7
n = 630 deers.
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prove that (n+5)^2(n+3)^2 is a multiply of 4
The proof that (n+5)^2(n+3)^2 is a multiple of 4 is below
How to prove the expressionWe can prove that (n+5)^2(n+3)^2 is a multiple of 4 by showing that both (n+5)^2 and (n+3)^2 are multiples of 4.
From the question, we can see that the exponents of both factors is 2
When these exponents are added, we have
Sum = 2 + 2
Evaluate the sum
Sum = 4
4 is a multiple of 4
Hence, (n+5)^2(n+3)^2 is a multiple of 4
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the dencity of apple juice is
Answer:
density of apple juice
1.034-1.051g.cm‐³
the patterson family went to eat lunch at a new restaurant. They spent $52.30 on their meal. The restaurant will add 7 1/4% tax to the cost of the meal. Mr patterson was very happy with the food and service so he gave a 20% tip to the waitress. How much does the lunch cost, including tax and tip?
the lunch cost, including tax and tip 67.31$.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, the Patterson family went to eat lunch at a new restaurant. They spent $52.30 on their meal. The restaurant will add a 7 1/4% tax to the cost of the meal.
total cost after the tax = 52.30*(1 + 7 1/4)%
total cost after the tax = 52.30* 7.25/100 + 52.30
total cost after the tax = 3.79 + 52.30
total cost after the tax = 56.09
Since,
Mr Patterson was very happy with the food and service so he gave a 20% tip to the waitress.
Thus,
Total cost after the tip = 56.09(1 +20/100)
Total cost after the tip = 56.09 * 1.2
Total cost after the tip = 67.308
Therefore, the lunch cost, including tax and tip 67.31$.
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Help please i need answer asap
The correct matching of the given numbers is as follows:
√30 - Real, Irrational root-26 - Real, Rational, Integer√64 - Real, Rational Root, Whole Number1/4 - Real, Rational0.36336333633336.... - Real, Irrational decimal0.42424242..... - Real, Rational decimal✓ 7, or 7i - Imaginary NumberWhat are real and imaginary numbers?Natural numbers, whole numbers, integers, rational numbers, and irrational numbers can all be classified as real numbers.
An imaginary number is created by multiplying a real number by i where i = (-1). To calculate the square root of negative values, we employ imaginary numbers. For instance, (√-7) Equals (-1) √7
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HELP ASAP, WILL GIVE FIRST ANSWER BRAINLIEST,
The table shows the results of tossing a number cube 50 times.
Outcome Frequency
1 9
2 11
3 8
4 6
5 9
6 7
Determine the experimental probability of landing on a number greater than or equal to 4.
P(≥ 4) = 0.68
P(≥ 4) = 0.44
P(≥ 4) = 0.32
P(≥ 4) = 0.06
Answer:
P(≥ 4) = 0.44
Step-by-step explanation:
The experimental probability of landing on a number greater than or equal to 4 can be calculated by adding the frequency of outcomes 4, 5, and 6 and dividing by the total number of trials.
The frequency of outcomes 4, 5, and 6 is 6 + 9 + 7 = 22.
The experimental probability of landing on a number greater than or equal to 4 is 22/50 = 0.44.
So, the answer is B. P(≥ 4) = 0.44.
Answer:
P(≥ 4) = 0.44
Step-by-step explanation:
I took the test and it was right!
what is the domain of this exponential expression?
Answer:
all real number
Step-by-step explanation:
domain are the value of x axis. as you can see the the graph goes for ever. there is no limitation. basically the domain of exponential graph are all really number.
5. what if you increase the height from which the pennies are dropped? your instructor may choose to stack two tables for you to test this.
The height of the drop can be increased by stacking tables, and we can then observe the effect on the pennies' trajectory.
To increase the height from which the pennies are dropped, we can stack two tables. To do this, first, place one of the tables on a level surface. Then, move the other table so that it is parallel to the first table, and place it on top. Make sure that the two tables are securely stacked and do not wobble. Then, use a ruler to measure the height of the two tables combined. This will give us the new height from which the pennies will be dropped. After that, drop the pennies from the new height and observe their trajectory. We can then compare the trajectory of the pennies when dropped from the increased height with the trajectory when dropped from the original height. This will allow us to determine the effect of the increased height on the pennies' trajectory.
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Explain how the coordinates of a point and its reflection across the x-axis are the same and how they are different
Answer: The coordinates of a point in the plane are represented by a pair of values, (x, y), where x is the horizontal position and y is the vertical position.
When a point is reflected across the x-axis, the x-coordinate remains the same, but the sign of the y-coordinate changes. This is because the x-axis acts as a mirror, flipping the point over to the opposite side of the axis.
So, the coordinates of the reflected point would be (x, -y).
In summary, the x-coordinates of a point and its reflection across the x-axis are the same, while the y-coordinates are different (one is positive, and the other is negative).
Step-by-step explanation:
Find the perimeter of ABCD.
The perimeter of ABCD is, √18 + 5 + √29 + √10
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The diagram of ABCD is shown.
Now, The coordinate of the ABCD are,
⇒ A = (- 3, 2)
⇒ B = (0, 5)
⇒ C = (3, 1)
⇒ D = (-2, - 1)
Hence, Distance between A and B is,
⇒ f = √(- 3 - 0)² + (2 - 5)²
⇒ f = √9 + 9
⇒ f = √18
Distance between B and C is,
⇒ g = √(3 - 0)² + (1 - 5)²
⇒ g = √9 + 16
⇒ g = √25
⇒ g = 5
Distance between C and D is,
⇒ h = √(- 2 - 3)² + (- 1 - 1)²
⇒ h = √25 + 4
⇒ h = √29
Distance between D and A is,
⇒ i = √(- 3 + 2)² + (2 + 1)²
⇒ i = √1 + 9
⇒ i = √10
Hence, The perimeter of ABCD is,
⇒ f + g + h + i
⇒ √18 + 5 + √29 + √10
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The Tour de France is not a 3500 km race, it is a 3500 km cycling race. The diameter of the bike wheels used in the race must be between 55 cm and 75 cm. To find the minimum number of rotations
The minimum number of rotations required for a 3500 km race is 52,800 rotations.
This is calculated by dividing the total distance of the race, 3500 km, by the circumference of the wheel, which is 2πr, where r is the radius of the wheel. The radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm). So, the minimum number of rotations is given by 3500/(23.14r), where r is the minimum radius of the wheel. Substituting in r = 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.
To arrive at this result, we must first calculate the circumference of the wheel, which is given by 2πr, where r is the radius of the wheel. Since the diameter of the wheel must be between 55 cm and 75 cm, the radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm).
We then divide the total distance of the race, 3500 km, by the circumference of the wheel, which is given by 2πr. Substituting in the minimum radius of the wheel, 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.
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Solve this problem pls
Answer:
[tex]\frac{43}{15}[/tex]x + 30
Step-by-step explanation:
3[tex]\frac{2}{3}[/tex]x - [tex]\frac{4}{5}[/tex] (x - 3[tex]\frac{3}{4}[/tex])
[tex]\frac{11}{3}[/tex]x - [tex]\frac{4}{5}[/tex] (x - [tex]\frac{15}{4}[/tex])
[tex]\frac{11}{3}[/tex]x - [tex]\frac{4}{5}[/tex] x + [tex]\frac{60}{20}[/tex]
[tex]\frac{11}{3}[/tex]x - [tex]\frac{4}{5}[/tex] x + 30
[tex]\frac{55}{15}[/tex]x - [tex]\frac{12}{15}[/tex] x + 30
[tex]\frac{43}{15}[/tex]x + 30
The population of a certain animal species decreases at a rate of 12.5% per year. In 2021, at the beginning of the study, you counted 97 of the animal species you are studying in their natural habitat. Write a function that models the change in the animal population.
P should stand for the population in a certain year. P = 97*(0.875) is the function to model the population change (year-2021).
P should stand for the population in a certain year. To simulate how the animal population changes over time, we can utilise a function. The 12.5% annual reduction rate will be considered by the function. This can be stated mathematically as P = 97*(0.875), which is how it will appear in the equation (year-2021). In this equation, the number 97 stands in for the population in 2021, and the number 0.875 denotes the 12.5% annual decline rate. The exponent (year 2021) represents the number of years that have passed since 2021, allowing the equation to take the population decline over a number of years into consideration. As a result, the equation can be used to determine the animal species' population at the start of a particular year.
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If the variance of a distribution is 13.53, what is its standard deviation? If the standard deviation of a distribution is 3.45, what is its variance?
If the variance of a distribution is 13.53, the value of its standard deviation is, 3.68.
And, If the standard deviation of a distribution is 3.45, the value of variance is, 11.90
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.
Given that;
The variance of a distribution is 13.53,
And, The standard deviation of a distribution is 3.45.
We know that;
⇒ Standard deviation = √ Variance
Now, If the variance of a distribution is 13.53,
The value of its standard deviation is,
⇒ Standard deviation = √ Variance
⇒ Standard deviation = √13.53
⇒ Standard deviation = 3.68
And, If the standard deviation of a distribution is 3.45.
The value of variance is,
⇒ Standard deviation = √ Variance
⇒ 3.45 = √ Variance
⇒ Variance = 3.45²
⇒ Variance = 11.90
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WILL GIVE brainliest HELP ASAP
Answer:2/5x+2/5y
Step-by-step explanation: Since you are multiplying both terms by 2/5, just distribute and you get that value for both the coeffiencents.
If M(-4,3) and N(1,0) are two fixed points and P(x, y) is a moving point which moves such that PM^2 -PN^2=20, find the locus of the point P.
The locus of point P is a circle with center at the midpoint of points M and N, and radius equal to half the distance between the two points.
How do we determine the value?The midpoint of M and N is given by:
((-4+1)/2, (3+0)/2) = (-1.5, 1.5)
The distance between M and N is given by the distance formula:
√((1-(-4))^2 + (0-3)^2) = sqrt(25 + 9) = √(34)
So, the radius of the circle is √(34)/2.
Hence, the equation of the locus of point P is given by:
(x-(-1.5))^2 + (y-1.5)^2 = (√(34)/2)^2
or
(x+1.5)^2 + (y-1.5)^2 = (√(34)/2)^2
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Sandra has a savings account which gathers compound interest each year. She opened the account with a deposit of £2500. After 4 years there is £2937.91 in the account. Work out the annual interest rate of the savings account. Give your answer as a percentage to 1 d.p.
The annual interest rate of the savings account is 0.04%
What is compound interest?Compound interest refers to the interest added to a loan or deposit. Compound interest is the type of interest that is calculated using both the principal and the interest that has accumulated over the preceding period. In contrast to simple interest, compound interest does not factor in the principal when calculating the interest for a subsequent period.
We have the formula
Amount, A = P [1 + (r/t)]ⁿ
where P = principal, r = rate of interest, t = number of times interest is compounded per year, n = time (in years)
Given:
principal = 2500
Amount = 2937.91
t = 1
n = 4
So, 2937.91 = 2500 [1 + (r/1)]⁴
[tex](1.175)^{(1/4)[/tex] = 1 + r
1.041 = 1 + r
r = 0.04
Thus, the annual interest rate is 0.04% .
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Answer:
4.1%
Step-by-step explanation:
You want the annually compounded interest rate that results in £2500 growing to £2937.91 in 4 years.
Compound interest
The amount in an account earning compound interest is ...
A = P(1 +r)^t
where P is the principal invested at rate r for t years.
RateSolving for r, we find ...
(A/P)^(1/t) = 1 +r
r = (A/P)^(1/t) -1 = (2937.91/2500)^(1/4) -1 ≈ 0.0412 ≈ 4.1%
The annual interest rate of the savings account is about 4.1%.
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please help asap, show your work then choose an answer
Note that where the figure below contains two semi-circles that are tangent to each Other at point B and ray DE is tangent to both semicircles at points E and F, it is correct to state that ED = 6√2 (Option A).
What is a Semi Circle?A semicircle is a one-dimensional point collection that forms half of a circle in mathematics. It is a circular arc with a circumference of 180°. It just has one symmetry line.
Solving the ED, we have:
ΔDEM ~ ΔDFP
This means that MD/PD = EM/FP
MD/(MD + 9) = 3/6
6MD = 3MD + 27 (Collect like terms over the equation)
3MD = 27
MD = 9 (If both sides are divided by 9)
Note that
ED = √[MD²-EM²]
ED = √9²-3²]
ED = 6√2
Thus, it is correct to state that ED = 6√2
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2,300 = 23 x10^2 or 2.3 x 10^3. How would you describe the relationship between the two representations?
Answer:
identical
Step-by-step explanation:
23 * 100 = 2.3 * 1000
they are the same
an anchor weighing 100 lbs in water is attached to a chain weighing 3 lb/ft in water. find the work done to haul the anchor and chain to the surface of the water from a depth of 25 ft.
In linear equation, 3437.5 feet - lbs is the work done to haul the anchor .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Anchor weighing = 100 lbs
given 3 lb/ft
the combined weight = 3( 25 -y ) + 100
= 175 - 3y
the workdone on small solution is = (175 - 3y)Δy
w = ∫₀²⁵ (175 - 3y) dy
= 175[y]²⁵₀- 3/2[y²]²⁵₀
= 175 [ 25 - 0 ] - 3/2 [ 25²- 0²]
= 3437.5 feet - lbs
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x=5-2y
3x+2y=17
solve the system of equations!!
show your work!! :)
Answer: (x = 6, y = -0.5)
Step-by-step explanation:
Substitute into one of the equations: 3(5 - 2y) + 2y = 17
Apply Multiplicative Distribution Law: 15 - 6y + 2y = 17
Rearrange unknown terms to the left side of the equation: -6y + 2y = 17 - 15
Combine like terms: -4y = 2
Divide both sides of the equation by the coefficient of variable: y = 2 / (-4)
Remove the parentheses: y = -2 / 4
Calculate the product or quotient: y = -0.5
Substitute into one of the equations: x = 5 - 2 * (-0.5)
Remove the parentheses: x = 5 - 2 * -0.5
Calculate the product or quotient: x = 5 + 1
Calculate the sum or difference: x = 6
The solution of the system is: {x = 6, y = -0.5}
Hope this helps!
In the graph shown, which of the following values represents the x-value where line l and
the line y = 2x - 1 intersect?
-1
0
1
2
Answer:
2 or -1
Step-by-step explanation:
[tex]1. \: y + 1 = 2x \\ 2. \: \frac{y + 1}{2} = x \\ 3. \: x = \frac{y + 1}{2} [/tex]
[tex]1. \: y = 2 \times 0 - 1 \\ 2. \: y = - 1[/tex]
Two families attend a performance of the Circus Mage. The cost of a ticket for adult is
1.5 times higher than that of a child ticket. Clothilde buys a ticket for her, for her
husband and for her 2 children. She pays $90 in all, taxes included. Her friend Naomie
buys tickets for her 4 children and herself. Clothilde thinks that going to the circus
costs her less than Naomie. Is she right?
Answer: NO
Step-by-step explanation:
Adult tickets cost $27
Child tickets cost $18
$18 x 4 child tickets = $72 + $27 adult ticket = $99
5 men have been hired to paint a house. If an additional man is hired, the painting will be completed 2 days earlier. How many men will be required to finish painting the house in 5 days?
The number of men required to finish the house in 5 days is 9 men.
What is the number of men needed?The number of men required to finish the house in 5 days can be found using the following formula.
Number of men = 5 x Number of days / (Number of days - 2)
Substituting the given values:
Number of men = ( 5 x 5 )/ (5 - 2)
Number of men = ( 5 x 5 ) / 3
Number of men = 25 / 3
Number of men = 8.33
Since the number of men has to be a whole number, the answer is 9 men.
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The Energy Information Administration reported that the mean retail price per gallon of regular grade gasoline was. Suppose that the standard deviation was and that the retail price per gallon has a bell-shaped distribution
2.5% of regular grade gasoline sold for more than $3.71 per gallon.
The empirical rule states that for a normal distribution:
68% of the data will fall within one standard deviation of the mean.
95% of the data will fall within two standard deviations of the mean.
Almost all (99.7%) of the data will fall within three standard deviations of the mean
a) 3.31 and 3.71 are 2 standard deviations below and above the mean respectively.
So,
95.0% of regular grade gasoline sold between $3.31 and $3.71 per gallon.
b) 3.31 and 3.61 are 2 standard deviations below and one standard deviation above the mean respectively.
percentage of regular grade gasoline sold between $3.31 and $3.61 per gallon
=(0.95/2)+(0.68/2)
=0.475+0.34=0.815 or 81.5%
c)2.5% of regular grade gasoline sold for more than $3.71 per gallon.
The complete question is:
The Energy Information Administration Reported That The Mean Retail Price Per Gallon Of Regular Grade Gasoline Was $3.51 . Suppose That The Standard Deviation Was $0.10 And That The Retail Price Per Gallon Has A Bell-Shaped Distribution. (Hint: You Must Use The Empirical Rule For This Problem. ) A. What Percentage Of Regular Grade Gasoline Sold Between
The Energy Information Administration reported that the mean retail price per gallon of regular grade gasoline was $3.51 . Suppose that the standard deviation was $0.10 and that the retail price per gallon has a bell-shaped distribution. (Hint: You must use the empirical rule for this problem. )
a. What percentage of regular grade gasoline sold between $3.31 and $3.71 per gallon (to 1 decimal)?
b. What percentage of regular grade gasoline sold between $3.31 and $3.61 per gallon (to 1 decimal)?
c. What percentage of regular grade gasoline sold for more than $3.71 per gallon (to 1 decimal)?
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Which figure would best model the sandbox to help determine the amount of sand needed?
You need to buy 80 cubic feet of sand to fill the sandbox.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The sandbox is a rectangular prism.
Length is 10 feet.
Width is 8 feet
Height is 1 feet.
Volume of prism=Length×Width×Height
=10×8×1
=80 cubic feet.
Hence, you need to buy 80 cubic feet of sand to fill the sandbox.
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The complete question is given in the attachment.
Archive invested an amount of money in a savings account that pays compound interest at a rate of 6% per annum. After 11 years there is £13,288.09 in the savings account (rounded to the nearest 1p). How much did Archive initially invest?
Answer: 7000 (4 s.f)
Step-by-step explanation:
[tex]x[/tex] x [tex]1.06^{11} = 13,288.09[/tex]
[tex]x = \frac{13,288.09}{1.06^{11} }[/tex]
[tex]x = 7000[/tex] (4 s.f)
This is a question where you make the equation by yourself using compound interest. If you have any further questions, feel free to ask me :)
Help……………………………………..
The correct option is the third one. The statement "The [tex]\lim_{x \to \0} f(x)=4[/tex] because both the left hand and the right hand limit is equal to 4" identifies and explains the function of limit.
What is a limit?The limit function in mathematics is a way of finding the value that a function or sequence approaches as the input values approach a certain point. It is used to determine the behavior of a function as the input values approach a certain point or their maximum or minimum values.
Where the above two limits say that when we approach zero from the negative side (the first one) and from the positive side (the second one), we must get the same value.
Remember that the limit is an approximation through near points.
Then, regardless the fact that f(0) = -2, we can see that as x approaches 0 from both sides, the value of the function approaches 4.
Thus, we can conclude that the limit of f(x) when x tends to zero is equal to 4.
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Norachai and Rain each improved their yards by planting rose bushes and grass. They bought their supplies from the same store. Norachai spent $209 on 11 rose bushes and 11 bunches of grass. Rain spent $40 on 3 rose bushes and 2 bunches of grass. What is the cost of one rose bush and the cost of one bunch of grass?
The cost of one rose bush is $2 and the cost of one bunch of grass is $17.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, Norachai and Rain each improved their yards by planting rose bushes and grass.
Let the cost of rose bushes be x and the cost of bunches of grass be y.
Norachai spent $209 on 11 rose bushes and 11 bunches of grass.
Now, 11x+11y=209
x+y=19 --------(i)
Rain spent $40 on 3 rose bushes and 2 bunches of grass.
3x+2y=40 --------(ii)
Substitute x=19-y in equation (ii), we get
3(19-y)+2y=40
57-3y+2y=40
57-40=y
y=17
Substitute y=17 in equation (i), we get
x=2
Therefore, the cost of one rose bush is $2 and the cost of one bunch of grass is $17.
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What is the slope of the line below?
Answer:
-1/2 is the answer of this question
Summary consider the exponent properties (a^n)^m=a^nm and a^nb^n=(ab)^n. what is the main difference in these properties? when simplifying an expression, how would you decide which one to use?
The main difference between these exponential properties is that for (a^n)^m=a^(nm) we have the same base, hence we just just multiply the powers, applying the power of power rule. For a^nb^n=(ab)^n, we have different bases, hence the exponent is just a common factor.
What is the power of a power rule?The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
It can be applied if the bases are the same, that is:
(a^n)^m = a^(n x m) = a^(nm).
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