The statement "The empirical rule assumes that the distribution of data follows a normal curve." is True.
The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that states that for a normal distribution, approximately 68% of the data will fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This implies that the distribution of data follows a normal curve.
A normal distribution is a type of probability distribution that follows a symmetrical bell-shaped curve. It is also known as the Gaussian distribution and is a continuous probability distribution. The normal distribution is defined by its mean, which is the average of the values, and its standard deviation, which is a measure of the spread of the values from the mean.
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For the following geometric sequence, find the next two terms, find the value
of r, and find the equation for the explicit rule.
2500, 1500, 900,
r=
Finally, using the first term a1 = 2500 and the common ratio r = 0.6, we can formulate the explicit rule for the sequence as follows: a = 2500 × 0.6^(n-1) (n-1)
What does equation mean in its simplest form?Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
Given :
We can use the fact that each word is produced by multiplying the previous term by the common ratio r to determine the value of r. Thus:
1500/2500 = 0.6 = r
We can keep adding r to the preceding term to find the next two terms:
900 × 0.6 = 540
540 × 0.6 = 324
540 and 324 are the next two terms as a result.
Finally, using the first term a1 = 2500 and the common ratio r = 0.6, we can formulate the explicit rule for the sequence as follows:
a = a1 × r^(n-1) (n-1)
The clear rule is as follows: a = 2500 × 0.6^(n-1) (n-1).
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Write the equation for a parabola with a focus at ( − 4 , 3 ) and a directrix at y=5 IN TERMS OF Y pls
pls answer asap
The equation for the parabola with a focus at (-4,3) and a directrix at y=5 in terms of y is y = (-1/8)x² - x/8 + 6.
The vertex of the parabola is the midpoint between the focus and directrix, which is (−4, 4).
Since the directrix is a horizontal line, the parabola will open downward.
Using the distance formula, the distance between a point (x, y) on the parabola and the focus (-4, 3) is equal to the distance between the point and the directrix y = 5.
√((x + 4)² + (y - 3)²) = |y - 5|
Squaring both sides yields:
(x + 4)² + (y - 3)² = (y - 5)²
Expanding the squares and simplifying, we get:
x² + 8x + 16 = -8y + 64
Rearranging terms, we have:
8y = -x² - 8x + 48
Dividing by 8, we get the equation of the parabola in terms of y:
y = (-1/8)x² - x/8 + 6
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Solve each question show solutions on the number line |x+8|=-2
On the number line, the empty set, denoted by an empty interval or a pair of crossed-out points, would be the solution set.
what is equation ?A mathematical assertion that establishes the equal of two expressions is called an equation. Variables, can serve as placeholders with unknowable values, and multipliers, and that are constants can multiply the variables, are frequently included. Determine you significance of the variables necessary make the answer true by solving the equation. The significant early (=), plus sign (+), and debit sign (-), among several other mathematical symbols, can be used to indicate equations. They are employed in many disciplines, such as mathematics, mathematics, chemistry, construction, and economics, to model the interactions between variables and to address issues.
given
Due to the fact that a real number's absolute value is never negative, the equation |x+8|=-2 has no solutions.
As a result, it is impossible for x+8 to have an absolute value of -2, which is a negative number.
On the number line, the empty set, denoted by an empty interval or a pair of crossed-out points, would be the solution set.
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PLEASE HELP will give brainliest
The provided arithmetic expression's explicit and recursive formulas are as follows:
Recursive formula = [tex]a_{n+1}=a_{n-7}[/tex]
Explicit formular is Tn = 22 - 7n
Distinguish between explicit formula and recursive formula?An explicit formula can be used to determine the value of any phrase in a sequence. The natural numbers 1, 2, 3, 4, and so on make up the integers. If you have a recursive formula for the sequence and know the value of the (n-1)th term in the series, you can use it to calculate the value of the nth term. While explicit formulae provide the value of a specific term depending on the location, recursive formulas supply the value of a specific phrase based on the preceding term. This is the primary difference among recursive and explicit formulations.
Given:
[tex]a_1[/tex] = 15
[tex]a_2[/tex] = 22 = 15 - 7 = [tex]a_1[/tex] - 7
Recursive formular = [tex]a_{n+1}=a_{n-7}[/tex]
a = 15, d = -7
Fn = a + (n - 1)d = 15 + (n - 1)-7 = 15 - 7n + 7 = 22 - 7n
Explicit formular is Tn = 22 - 7n
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Graph attached below,
A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the height, to the nearest foot, at a time of 7.8 seconds.
1.1 308
1.8 489
3.1 761
3.7 891
4.8 1070
The height of the rocket at a time of 7.8 seconds is approximately 2,254 feet.
To find a quadratic regression equation, we need to fit a quadratic function of the form [tex]y = ax^2 + bx + c[/tex]to the data.
Using a calculator or spreadsheet software, we can find the coefficients that minimize the sum of the squared errors between the predicted values of y and the actual values of y.
The resulting quadratic regression equation is:
[tex]y = 88.6x^2 + 2.9x + 196.5[/tex]
To find the height of the rocket at a time of 7.8 seconds, we simply substitute x = 7.8 into the equation and evaluate:
[tex]y = 88.6(7.8)^2 + 2.9(7.8) + 196.5[/tex]
y ≈ 2,253.6
Rounding to the nearest foot, we get:
y ≈ 2,254 feet
Therefore, the height of the rocket at a time of 7.8 seconds is approximately 2,254 feet.
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in july 2005, the internet was linked by a global network of about 352.1 million host computers. the number of host computers has been growing approximately exponentially and was about 35.3 million in july 1998. (a) find a formula for the number, n, of internet host computers (in millions of computers) as an exponential function of t, the number of years since july 1998, using exponential function of the form . what are the values of a and k in your model?
Answer:
a=671000
Step-by-step explanation:
woah
The formula for the number of internet host computers as an exponential function of t is: n(t) = 35.3 × e^((1/7) × ln(n(7) / 35.3) × t) and the values of a and k in the model are k = (1/7) × ln(n(7) / n(0)) and a = n(0) = 35.3 million
a. To find the values of a and k, we can use the information given in the question. Let n(0) be the number of host computers in July 1998, which is 35.3 million. Let n(7) be the number of host computers in July 2005, which is 352.1 million. We can use these values to solve for a and k.
n(0) = a × e^(k0) = a
n(7) = a × e^(k7)
Dividing the second equation by the first equation, we get:
n(7) / n(0) = e^(k×7)
Taking the natural logarithm of both sides, we get:
ln(n(7) / n(0)) = k×7
Therefore, k = (1/7) × ln(n(7) / n(0)) and a = n(0) = 35.3 million.
Therefore, the formula for the number of internet host computers as an exponential function of t is:
n(t) = 35.3 × e^((1/7) × ln(n(7) / 35.3) × t)
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Anyone help in number 5?
Answer:
Step-by-step explanation:
5)
Draw a right triangle with a hypotenuse of 60 km, a base angle of 60°, and the base leg of x.
Find x, the distance it traveled to the east:
cos60° = x/60
x = 60(cos60) = 30 km
Please someone help me I need to find the answer and the solution
Answer:
12.7
Step-by-step explanation:
3x+10x-15=180
13x=165
x=12.69.....
x=12.7
Mrs Smith paid R13 450.00 for a couch after a 25% discount. What was the
original price of the couch?
Mrs. Smith paid R13 450.00 for a couch that originally cost R17 933.33. This means that she received a discount of R4 483.33, which is 25% of the original price.
To find the original price of the couch, we need to first understand what a 25% discount means.
A discount is a reduction in price from the original or regular price of an item. A discount is usually given as a percentage of the original price. For example, a 25% discount means that the price of an item has been reduced by 25% of its original price.
Let's use this information to solve the problem at hand.
Let x be the original price of the couch. The discount given is 25%, which means that the price paid by Mrs. Smith is 75% of the original price. Mathematically, we can write this as:
75% of x = R13 450.00
To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 75% or 0.75 (which is the decimal equivalent of 75%).
75% of x / 0.75 = R13 450.00 / 0.75
x = R17 933.33 (rounded to the nearest cent)
Therefore, the original price of the couch was R17 933.33.
In conclusion, Mrs. Smith paid R13 450.00 for a couch that originally cost R17 933.33. This means that she received a discount of R4 483.33, which is 25% of the original price.
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The Area of a Rectangle is 56. The width is 2 more than 3
times the length. Find the width.
O 15
O 14
08
06
Answer:
14
Step-by-step explanation:
A = length x width
l = length
w = 3l + 2
A = l(3l + 2) = 56
3l² + 2l - 56 = 0
Now you have a polynomial you can solve by factoring or using the quadratic equation to find the 2 roots of l:
using the quadratic equation with a = 3, b = 2, c = -56
l = 4, -14/3
Disregarding the negative root,
l = 4
Therefore, w = 3(4) + 2 = 14
After the cataract took Euler's sight, he
john and jane are married. the probability that john watches a certain television show is .5. the probability that jane watches the show is .3. the probability that john watches the show, given that jane does, is .5. (a) find the probability that both john and jane watch the show. (round your answer to 2 decimal places.) (b) find the probability that jane watches the show, given that john does. (round your answer to 3 decimal places.) (c) do john and jane watch the show independently of each other? multiple choice yes no
(a) The probability that both John and Jane watch the show is 0.15 or 15% (rounded to 2 decimal places).
(b)The probability that Jane watches the show, given that John does, is 0.3 or 3.
(c) Since these probabilities are equal, John and Jane watch the show independently of each other.
The answer is Yes.
John and Jane watch the show independently of each other if
(a) To find the probability that both John and Jane watch the show, we can use the conditional probability formula:
P(A and B) = P(A|B) * P(B),
where A represents John watching the show and B represents Jane watching the show.
Given, P(A|B) = 0.5 and P(B) = 0.3.
P(A and B) = 0.5 * 0.3 = 0.15.
Therefore, the probability that both John and Jane watch the show is 0.15 or 15% (rounded to 2 decimal places).
(b) To find the probability that Jane watches the show, given that John does, we can use the conditional probability formula: P(B|A) = P(A and B) / P(A).
Given, P(A and B) = 0.15 and P(A) = 0.5.
P(B|A) = 0.15 / 0.5 = 0.3.
Therefore, the probability that Jane watches the show, given that John does, is 0.3 or 30% (rounded to 3 decimal places).
(c) John and Jane watch the show independently of each other if P(A and B) = P(A) * P(B).
In this case, P(A and B) = 0.15 and P(A) * P(B) = 0.5 * 0.3 = 0.15.
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A queen bee has a colony of 2,000 drones and 18,000 worker bees.6,000 of the worker bee forage for pollen and nectar. What part of the worker bees forage for pollen and nectar?
One-third of the worker bees forage for pollen and nectar.
What is percentage?
Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, 50% means "50 out of 100" or "50/100" or "0.5 as a decimal". Percentages are commonly used to express the proportion or relative size of a quantity with respect to another quantity. They can be used in a wide range of contexts, including finance, statistics, science, and everyday life.
Here out of the 18,000 worker bees, 6,000 forage for pollen and nectar.
To calculate the part of worker bees that forage for pollen and nectar, we can use the following formula:
Part = (Number of bees foraging / Total number of worker bees) x 100
Plugging in the numbers, we get:
Part = (6,000 / 18,000) x 100
Part = 0.333 x 100
Part = 33.3%
Therefore, 33.3% or approximately one-third of the worker bees forage for pollen and nectar.
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Find the distance, d, of AB.
A = (-2,-10) B = (-6,0)
-12-10 - B
A
-2
-B
-10
d = √(x2-x₁)² + (y2 - Y₁)²
d = [?]
Round to the nearest tenth.
Help Re
Skip
The calculated value of the distance between points A and B is 2√29 units.
Finding the distance, d, of AB.We can use the distance formula to find the distance between points A and B:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
where (x₁, y₁) = A = (-2, -10) and (x₂, y₂) = B = (-6, 0).
Substituting these values into the formula, we get:
d = √[(-6 - (-2))² + (0 - (-10))²]
d = √[(-4)² + 10²]
d = √(16 + 100)
d = √116
d = 2√29
Therefore, the distance between points A and B is 2√29 units.
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What is the greatest common factor of 42 and 56?
Answer: 14
Step-by-step explanation: you need to start by finding the factors of them and then what ever the biggest number is in both of them has to match but i got 14.
Newton bounces a ball off of a wall to Descartes. Find the value of x
The value of x is 45° for the Newton bounces a ball off of a wall to Descartes as shown in figure.
Define a right angle?An angle that is exactly 90 degrees, or a quarter turn, is called a right angle. It is made up of two lines that are perpendicular to one another or line segments that cross at a point, forming four equal angles.
If we consider the figure below we can find some angles and AD is a Straight line; (Refer the below figure 2)
⇒ ∠AOB + ∠BOC+ ∠DOC = 180°
⇒ x° + 90° + x° = 180°
⇒ 2x° = 180° - 90°
⇒ x° = 90°/ 2
⇒ x° = 45°
Therefore, the value of x is 45°
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Complete question-
According to the figure, x is 45° when Newton bounces a ball off of a wall and Descartes.
Define a right angle?Right angles are angles that are exactly 90 degrees, or a quarter turn. It is composed of two parallel lines or line segments that cross at a place to produce four equal angles. It is referred to as a right angle if the angle formed by two rays exactly equals 90 degrees, or π/2.
If we look at the graphic below, we can see that AD is a straight line and there are certain angles;
∠AOB + ∠BOC+ ∠DOC = 180°
x° + 90° + x° = 180°
2x° = 180° - 90°
x° = 90°/ 2
x° = 45°
Therefore, the value of x is 45°
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The complete question is attached below,
please find the answer
the equation y=1 does not represent a direct variation, whereas the other three equations given do represent direct variation.
What is Direct variation?
Direct variation is a relationship between two variables in which one is a constant multiple of the other. This means that if one variable increases, the other variable will also increase by a proportional amount. In other words, direct variation can be represented by the equation y=kx, where k is the constant of variation.
Out of the four equations given, the equation y=1 does not represent a direct variation. This is because the equation is not a function of x. In other words, no matter what value of x we choose, y will always be equal to 1. This means that the two variables, x and y, are not related to each other in any way. Therefore, there is no constant k that can be multiplied by x to get y.
On the other hand, the other three equations do represent direct variation. For example, in the equation y=x, y is equal to x multiplied by the constant k=1. Similarly, in the equation y=-5x, y is equal to x multiplied by the constant k=-5. Finally, in the equation y=0.9x, y is equal to x multiplied by the constant k=0.9.
In summary, the equation y=1 does not represent a direct variation, whereas the other three equations given do represent direct variation.
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In circle QQ, the length of \overset{\LARGE\frown}{RS} = \frac{4}{3}\pi RS ⌢ = 3 4 π and m\angle RQS=120^\circ∠RQS=120 ∘ . Find the area shaded below. Express your answer as a fraction times \piπ.
We can start by finding the length of the arc \overset{\LARGE\frown}{TS} using the fact that the length of the arc \overset{\LARGE\frown}{RS} is \frac{4}{3}\pi times the radius of the circle. Since angle RQS is 120 degrees, arc \overset{\LARGE\frown}{TS} is \frac{1}{3} of the circumference of the circle:
arc \overset{\LARGE\frown}{TS} = \frac{1}{3} (2\pi R) = \frac{2}{3}\pi R
Next, we can find the length of the chord TS using the Law of Cosines:
TS^2 = TR^2 + RS^2 - 2(TR)(RS)\cos(\angle TRS)
Since \angle TRS is 120 degrees, we have:
TS^2 = R^2 + (4/3)^2R^2 - 2(R)(4/3)R(-1/2)
Simplifying this expression, we get:
TS^2 = \frac{25}{9}R^2
Taking the square root of both sides, we get:
TS = \frac{5}{3}R
Now we can find the height of the shaded region by drawing the altitude from the center of the circle to chord TS. This altitude bisects chord TS and is also perpendicular to it, so it divides TS into two segments of equal length:
Height = \frac{1}{2}(TS) = \frac{5}{6}R
Finally, we can find the area of the shaded region by subtracting the area of triangle RST from the area of sector RQS:
Area of sector RQS = (120/360)\pi R^2 = \frac{1}{3}\pi R^2
Area of triangle RST = (1/2)(RS)(height) = (1/2)(4/3)R(\frac{5}{6}R) = \frac{5}{9}R^2
Area of shaded region = Area of sector RQS - Area of triangle RST = \frac{1}{3}\pi R^2 - \frac{5}{9}R^2 = \frac{2}{9}\pi R^2
Therefore, the area shaded below is \frac{2}{9}\pi times the square of the radius R of the circle.
As per the given data, in circle QQ, the area shaded below is (1/27)π.
What is circumference?The circumference is the perimeter of a circle or ellipse in geometry. That is, the circumference would be the circle's arc length if it were opened up and straightened out to a line segment.
To find the area shaded below, we need to first find the area of sector RQS and then subtract the area of triangle RQS to get the shaded area.
The length of arc RS is given as 4/3π. Since the circumference of the circle is 2πr, where r is the radius, we have:
2πr = 4/3π
r = 2/3
So, the radius of the circle is 2/3.
Next, we can use the formula for the area of a sector, which is given as:
A = [tex](1/2)r^2\theta[/tex]
where r is the radius of the sector and θ is the central angle in radians.
In this case, θ is 120 degrees or 2/3π radians, so we have:
A(sector RQS) = [tex](1/2)(2/3)^2(2/3\pi)[/tex] = 4/27π
Now, we need to find the area of triangle RQS. To do this, we can use the formula for the area of a triangle, which is given as:
A = (1/2)bh
Where b is the base of the triangle and h is its height.
Since RQ is the base of triangle RQS and is also a radius of the circle, its length is 2/3. To find the height of the triangle, we can draw a perpendicular from point S to line QR and call the point of intersection T.
Since angle RQS is 120 degrees, angle RQT is 30 degrees (since the sum of the angles in a triangle is 180 degrees), and we have:
sin 30 = h/2/3
h = 1/3
So, the area of triangle RQS is:
A(triangle RQS) = (1/2)(2/3)(1/3) = 1/9
Finally, we can find the shaded area by subtracting the area of triangle RQS from the area of sector RQS:
A(shaded) = A(sector RQS) - A(triangle RQS) = (4/27π) - (1/9) = (1/27)π
Therefore, the area shaded below is (1/27)π.
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A motorcycle 500 feet from your current position is driving toward you at a constant rate of 50 feet per second. The distanced (in feet) of the motorcycle from you
you after t seconds is given by the equation |500 - 50t| - d = 0. At what times is the car 75 feet from you?
Answer:
Step-by-step explanation:
Step 1: Substitute d for 75
|500-50t| - 75 = 0
Step 2: Move the constant to one side
|500-50t| = 75
Step 3: Separate the equation into two possible cases
500−50t=75
500−50t=−75
Step 4: Solve the equation for t
t = 17/2 = 8.5
t = 23/2 = 11.5
Solution:
D: 8.5 seconds and 11.5 seconds
Solutions that represent x > - 5
Answer:
x∈( -5; +∞)
Step-by-step explanation:
[tex]x > - 5[/tex]
[tex]x∈( - 5;+ ∞)[/tex]
degree of the polynomial p(x) = 5 options
A)1
B)2
C)0
D)NOT DEFINED
Answer: (c) 0
Step-by-step explanation:There is no variable x involved, so we can say that this polynomial is of degree 0.
Polynomial as having a constant term of 5 and no other terms involving x.
If p(x)=x^5 then degree of polynomial is 5
degree of polynomial = highest degree of x
A cylinder with diameter 3 centimeters and height 8 centimeters is filled with water. Decide which figures described here, if any, could hold all of the water from the cylinder. Explain & show your reasoning. 4.) Sphere with a radius of 2 centimeters.
Therefore, the sphere described here cannot hold all of the water from the cylinder.
What is diameter?Diameter is a straight line passing through the center of a circle or a sphere, and connecting two points on its circumference. It is the longest distance between any two points on a circle or a sphere, and it is equal to twice the radius. In other words, if you know the diameter of a circle or a sphere, you can find its radius by dividing the diameter by 2, and vice versa, if you know the radius, you can find the diameter by multiplying the radius by 2.
The volume of the cylinder can be calculated as follows:
Radius of cylinder = Diameter[tex]/2 = 3/2 = 1.5 cm[/tex]
Volume of cylinder[tex]= \pi r^2h = \pi (1.5)^2(8) = 56.55 cm^3[/tex]
To determine if a sphere with a radius of 2 cm can hold all of the water from the cylinder, we can calculate its volume as follows:
Volume of sphere [tex]= 4/3\pi r^3 = 4/3\pi (2)^3 = 33.51 cm^3[/tex]
Since the volume of the cylinder is greater than the volume of the sphere, the sphere cannot hold all of the water from the cylinder. Therefore, the sphere described here cannot hold all of the water from the cylinder.
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what is the difference between t0 and t0? select the correct answer. select answer from the options below t0 is a numerical value and t0 is a random variable. they are the same thing. they are both probabilities. t0 is a random variable and t0 is a numerical value.
The difference between t-distribution T0 and t0 is nothing, They are the same thing option B.
The central limit theorem explains the connection between the original population and the sampling distribution of means. Keep in mind that we must first determine the variance of the original population if we are to determine the variance of the sampling distribution.
A point estimate of the mean may be calculated without knowing the variance of the sampling distribution, but other, more complex estimation methods demand that you either know or estimate the variance of the population.
If you stop and think for a second, you'll see that it seems bizarre to know the population's variance when you don't know the mean. As the population variance and standard deviation must be calculated, it is necessary to know the population mean.
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Leon is interested in the relationships among geographic region and
political affiliation. Leon collected data about the political parties of US
senators at that time and the regions of the US that they represent. His
results are in the table below.
His results are in the table are-
Southeast = 36.4%
Southwest = 9.1%
West = 18.2%
Midwest = 20%
What is arithmetic?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Here, we have
: Leon is interested in the relationships between geographic region and political affiliation. Leon collected data about the political parties of US senators at that time and the regions of the US that they represent.
Southeast = 20/55 = 36.4%
Southwest = 5/55 = 9.1%
West = 10/55 = 18.2%
Midwest = 11/55 = 20%
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Three dogs can eat 3 bones in 3 days. If this efficiency is followed, how many bones can 9 dogs eat in 9 days?
Answer:
If three dogs can eat three bones in three days, we can assume that each dog eats one bone in three days. Therefore, in one day, one dog can eat one-third of a bone.
If nine dogs were to eat in the same efficiency, we can multiply the number of dogs by the fraction of bones each can eat per day. So, nine dogs can eat 3 times more than 3 dogs in a day, which is 3 x 3 = 9 bones. In one day, each dog can eat one-third of the bone, and therefore nine dogs will eat 9 x 1/3 = 3 bones.
This means that in nine days, nine dogs can eat 9 x 3 = 27 bones.
(PLEASE HELP) A ball is thrown into the air. The height, h(t), of the ball, in metres, after t seconds is
modelled by the equation:
h(t) = -4.9(1-1.39)² + 11
1) How high off the ground was the ball when it was thrown? (/2) For full marks,
include the units(/0.5) and you must include two decimal places (/0.5)
2) What was the maximum height of the ball? (/1) For full marks, include the
units(/0.5).
3) How high was the ball at 2.5s? (/2) For full marks, include the units(/0.5) and you
must include two decimal places (/0.5)
4) is the football in the air after 6 s? (/1)
5) When does the ball hit the ground? For full marks, include the units(/0.5) and you
must include two decimal places (/0.5)
The ball was thrown 11 m off the ground. The maximum height of the ball was 11 m. The height of the ball at 2.5s was 9.07 m. Yes, the football is in the air after 6s and the ball hits the ground at 8.67 s.
What is height?Height is the measure of vertical distance or the vertical extent of an object, person, or other thing from top to bottom. It is typically measured in units of meters or feet. Height is a measure of vertical distance or elevation above a given level, most commonly sea level. Height can also be determined by measuring the altitude of an object or location. Height is an important factor in many everyday contexts, such as architecture and sports.
To calculate the answers, we must first solve for the equation of the height of the ball h(t).
h(t) = -4.9(1-1.39)² + 11
1) The ball was thrown 11 m off the ground.
To calculate this, we set t = 0.
h(0) = -4.9(1-1.39)² + 11
h(0) = 11
Therefore, the ball was thrown 11 m off the ground.
2) The maximum height of the ball was 11 m.
To calculate this, we set the derivative of the equation, h'(t) = 0 and solve for t.
h'(t) = -9.8(1-1.39)
h'(t) = 0
1-1.39 = 0
1 = 1.39
Therefore, t = 1.
Substituting t = 1 into the equation for h(t), we get:
h(1) = -4.9(1-1.39)² + 11
h(1) = 11
Therefore, the maximum height of the ball was 11 m.
3) The height of the ball at 2.5s was 9.07 m.
To calculate this, we substitute t = 2.5 into the equation for h(t).
h(2.5) = -4.9(1-1.39)² + 11
h(2.5) = 9.07
Therefore, the height of the ball at 2.5s was 9.07 m.
4) Yes, the football is in the air after 6s.
To calculate this, we substitute t = 6 into the equation for h(t).
h(6) = -4.9(1-1.39)² + 11
+ 11
h(8.67) = 0
Therefore, the ball hits the ground at 8.67 s.
In conclusion, the ball was thrown 11 m off the ground. The maximum height of the ball was 11 m. The height of the ball at 2.5s was 9.07 m. Yes, the football is in the air after 6s and the ball hits the ground at 8.67 s.
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Dylan has a part-time job at an ice skating rink selling hot cocoa. He decided to plot the number of hot cocoas he sold relative to the day's high temperature and then draw the line of best fit. Based on the line of best fit, how many hot cocoas would you predict Dylan to sell if the day’s high temperature were 25
F?
We predict that Dylan will sell 114.79 hot cocoas if the day's high temperature is 25°F on the basis of the line of best fit.
What is intercept?Intercept is the point on the graph where the line crosses the x-axis or the y-axis. This point is calculated by solving the equation of the line for the given axis. It is used to determine the relationship between two variables.
To predict the number of hot cocoas to be sold at 25° Fahrenheit, we need to use the line of best fit equation.
The equation of the line of best fit can be determined by calculating the slope and y-intercept of the line and then using the point-slope form of a line.
The slope of the line can be calculated using the formula
m = (y₂-y₁) / (x₂-x₁)
For this graph, the slope can be calculated as
m = (104-94) / (12-0)
= 10/12
= 0.83
The y-intercept of the line can be calculated using the formula y = mx + b, where m is the slope and b is the y-intercept.
For this graph, the y-intercept can be calculated as
b = 104 - 0.83(12)
= 94.04
Therefore, the equation of the line of best fit is y = 0.83x + 94.04
Substituting the given temperature, 25°F into the equation, we get
y = 0.83(25) + 94.04
= 114.79 hot cocoas
Hence, based on the line of best fit, we predict that Dylan will sell 114.79 hot cocoas if the day's high temperature is 25 degree Fahrenheit.
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~~BRAINILY~~
The functions f(x) = x2 – 2 and g(x) = –x2 + 5 are shown on the graph.
To graph the solution set of the system of inequalities y>x²-2 and y ≥ -x²+5, which is the area between the two curves, above the curve of f(x) = [tex]x^2 - 2[/tex]and above or on the curve of g(x) = [tex]-x^2 + 5[/tex].
To graph the solution set to the system of inequalities y>x²-2 and y ≥ -x²+5, you can follow these steps:
Graph the functions f(x) = x² - 2 and g(x) = -x² + 5 on the same coordinate plane.
Shade the region above the curve of f(x) = x² - 2 since the inequality y > x² - 2 indicates that the values of y are greater than the corresponding values of x² - 2.
Shade the region above or on the curve of g(x) = -x² + 5 since the inequality y ≥ -x²+5 indicates that the values of y are greater than or equal to the corresponding values of -x² + 5. This region can be represented as the area bounded by the curve of g(x) and the x-axis.
This shaded region is the area between the two curves, above the curve of f(x) = x² - 2, and above or on the curve of g(x) = -x² + 5. This region can be described as the set of all points (x, y) in the coordinate plane that satisfy the two inequalities simultaneously.
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The functions f(x) = x2 – 2 and g(x) = –x2 + 5 are shown on the graph.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities How can the solution set be identified?
y>x²-2
y ≥ -x²+5
Lesson
6-10
Find the values of x and y,
given that AABC ~ AMNC.
B
Sy
A
Lv=600
4x/2x
C
M
60
N
We can find y by solving for the length of CN: CN = Sy - BC = 600 - 0 = 600 So the values of x and y are:
x = 0 , y = 600
First, we can look at the corresponding sides of triangle ABC and triangle MNC. Since we know that these triangles are
similar (as indicated by the ~ symbol), we can set up the following proportion:
AB/AM = BC/CN
We can substitute in the given values for these lengths:
4x/2x = (Lv + Sy)/Sy
Simplifying this equation, we can cancel out the common factor of 2x on the left side:
2 = (Lv + Sy)/Sy
Multiplying both sides by Sy, we can isolate the sum of Lv and Sy:
2Sy = Lv + Sy
Combining like terms, we get:
Sy = Lv
So we now know that Sy is equal to Lv, which is 600.
To solve for x and y, we can use the fact that corresponding sides are in proportion. Specifically, we can look at the ratio of the length of AB to the length of AM:
AB/AM = 4x/Lv
Substituting in the values we know, we get:
AB/AM = 4x/600
We can also look at the ratio of the length of BC to the length of CN:
BC/CN = 2x/Sy
Substituting in the values we know, we get:
BC/CN = 2x/600
Since AB and BC are corresponding sides in triangle ABC and AM and CN are corresponding sides in triangle MNC, we
know that these ratios must be equal:
4x/600 = 2x/600
Simplifying this equation, we get:
4x = 2x
Subtracting 2x from both sides, we get:
2x = 0
Dividing both sides by 2, we get:
x = 0
Since x is 0, we can't solve for it any further. However, we can solve for y by using the ratio we found earlier:
AB/AM = 4x/600 = 0/600 = 0
Since AB is 0, we know that BC is also 0 (since the sum of the lengths of the sides of a triangle must be greater than 0).
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What is the area of section A? OA. 49 square inches OB. 28.5 square inches OC. 14 square inches OD. 24.5 square inches Section A 7 inches 7 inches *Picture not drawn to scale
the area of section A, which has side lengths of 7 inches each.
To determine the area, we will use the following terms:
area, square inches, and side lengths.Area = Side length × Side length
Area = 7 inches × 7 inches
7 inches × 7 inches = 49 square inches
So, the area of section A is 49 square inches (OA).
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