Beverly evenly shared a box of 24 cookies with three friends. Then, Beverly ate 5 of her cookies. Which equation shows how to find n, the number of cookies Beverly has left?

The population after 4 years is 1982.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have.,

Current population = 1652 people

The population triples every 10 years.

This means,

We can make a function for the number of population after m years.

y = 1652 x 3(m/10)

Where M is the number of years.

Now,

Substitute m = 4.

y = 1652 x 3(m/10)

y = 1652 x 3 (4/10)

y = 1652 x 3 x 2/5

y = 1982.4

y = 1982

Thus,

1982 is the population after 4 years.

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Answer:

Step-by-step explanation:

To obtain a polynomial of lowest degree with the given zeros and leading coefficient, we can use the fact that if a polynomial has a root of multiplicity m, then the factor (x - r)^m appears in the polynomial. Therefore, we can write:

f(x) = A(x + 1/4)^2(x - 2/3)

where A is a constant that we need to determine to satisfy the condition f(0) = 2.

To find A, we substitute x = 0 into f(x) and set the result equal to 2:

f(0) = A(0 + 1/4)^2(0 - 2/3) = -A/27 = 2

Solving for A, we find that A = -54.

Therefore, the polynomial f(x) is:

f(x) = -54(x + 1/4)^2(x - 2/3)

Step-by-step explanation:

classic Christian from x x + 4 + 8 is equal to 21 what is the answer

Answer:

The largest possible whole-number length for the third side of a triangle with two sides of length 7 and 10 is 13. This is due to the fact that the two given lengths must be added together, and then subtracted from the third side in order to create a valid triangle. Therefore, the third side must be at least 13 in order to create a triangle.

Answer:

n = 14

Step-by-step explanation:

Theorem:

In a triangle, the measure of an exterior angle equals the sum of the measures of the two remote interior angles.

12n - 8 = 8n - 4 + 52

4n = 56

n = 14

The placebo effect refers to an experiment where neither the participants nor the experimenters know who belongs to the treatment group and who belongs to the control group. As a​ result, it is impossible for the experiments to link certain effects to certain​ patients, which make the results difficult to interpret.

What is the placebo effect is an experimental study refers to the?

The placebo effect is a phenomenon where people report real improvement after taking a fake or nonexistent treatment, called a placebo. Because the placebo can't actually cure any condition, any beneficial effects reported are due to a person's belief or expectation that their condition is being treated.

Hence , The placebo effect refers to an experiment where neither the participants nor the experimenters know who belongs to the treatment group and who belongs to the control group. As a​ result, it is impossible for the experiments to link certain effects to certain​ patients, which make the results difficult to interpret.

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C. A placebo refers to a situation in which a patient improves simply because they believe they are receiving a useful treatment.

The volume of the sno-cone is approximately 774.9 cm³.

The volume of a hemisphere is the amount of space that a hemisphere (a half-sphere) takes up. A hemisphere is a three-dimensional shape that is half of a sphere, and it is created by cutting a sphere in half along a plane that passes through the center of the sphere.

The formula for the volume of a hemisphere is given by:

V = (2/3)πr³

Where V is the volume of the hemisphere, π is the mathematical constant pi (approximately 3.14), and r is the radius of the hemisphere.

To use this formula, you simply need to know the radius of the hemisphere. To find the radius, measure the distance from the center of the sphere to the edge of the hemisphere. Then, plug this value into the formula and simplify to find the volume.

The volume of the sno-cone can be calculated by finding the volume of the hemisphere and the volume of the cone separately and then adding them together.

Volume of the hemisphere = (2/3)πr³

where r is the radius of the hemisphere

Given r = 5 cm, the volume of the hemisphere is

(2/3)π(5)³ = (500/3)π ≈ 523.6 cm³

Volume of the cone = (1/3)πr²h

Given r = 5 cm and h = 9.6 cm, the volume of the cone is

(1/3)π(5)²(9.6) ≈ 251.3 cm³

The volume of the sno-cone is the sum of the volume of the hemisphere and the volume of the cone, which is

523.6 + 251.3 ≈ 774.9 cm³

Therefore, the volume of the sno-cone is approximately 774.9 cm³.

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Path z is the longest path that leads to the lake.

An algebraic expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It is a mathematical phrase that can contain one or more terms separated by mathematical operators.

For example, 3x + 4y - 2z is an algebraic expression that contains three terms: 3x, 4y, and -2z. Each term is made up of a coefficient and a variable, where the coefficient is the numerical value that multiplies the variable.

In algebraic expressions, variables are used to represent unknown values, and the expression can be evaluated by substituting known values for the variables. For instance, if x = 2, y = 3, and z = 1, then the expression 3x + 4y - 2z can be evaluated as 3(2) + 4(3) - 2(1) = 12.

Algebraic expressions can also include exponentiation, roots, and other advanced mathematical operations. They are widely used in mathematics and other fields, such as physics and engineering, to represent relationships between variables and to model real-world situations.

Let's start by assigning variables to each path:

Let x be the length of path x (in meters).

Then path y is 116 meters longer than path x, so its length is x + 116.

Path w is 51 meters shorter than path y, so its length is x + 116 - 51 = x + 65.

Path z is 85 meters longer than path w, so its length is x + 65 + 85 = x + 150.

To find the longest path, we need to compare the lengths of all four paths. We can do this by looking at the expressions we just derived:

Path x has length x.

Path y has length x + 116.

Path w has length x + 65.

Path z has length x + 150.

Since all four paths have a common component of x, the lengths of the paths can be compared by comparing the values of the expressions that add to x. We can see that x + 150 is the largest expression, which means that path z is the longest.

Therefore, path z is the longest path that leads to the lake.

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The domain are the possible input while the range are the possible output of a function.

(a) The domain = [-√2, √2], the range = [0, 2]

(b) The domain = [-1, 1], the range = [0, 1]

(c) The domain = [-1, 1], the range = [0, -1]

(d) The domain = [0, 2], the range = [0, 1]

(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]

Reasons:

The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1

Therefore, we have;

(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2

The x-intercept of the above function are, x = √2, and x = -√2

Which gives;

The domain = [-√2, √2]

The range = [0, 2]

(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3

At the x–intercepts, we have;

-3·x² + 3 = 0

x = ±1

The domain = [-1, 1]

The maximum value of y is given at x = 0, therefore;

= -3 × 0² + 3 = 3

The range = [0, 1]

(c) y = -f(x) = -(-x² + 1) = x² - 1

At the x–intercepts, x² - 1 = 0

x = ± 1

The domain = [-1, 1]

The minimum value of y is given at x = 0, which is y = -1

The range = [0, -1]

(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x

At the x–intercepts, we have;  -x² + 2·x = 0, which gives;

(-x + 2)·x = 0

Which gives, x = 0, or x = 2

The domain = [0, 2]

The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1

y = f(1) =  -1² + 2×1 = 1

Therefore;

The range = [0, 1]

(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2

At the x–intercepts, we have;  -x² - 4·x - 2 = 0, which gives;

x = -(2 + √2) or x = x = √2 - 2

The domain = [-(2 + √2), (√2 - 2)]

The maximum value of y is given when x = -4/(2)) = -2

Which gives;

-(-2)² - 4·(-2) - 2 = 2

The range = [0, 2]

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Answer:

25

Step-by-step explanation:

Let's assume the number of boys in the class is "x". Then, according to the problem, the number of girls in the class is 2.5 times the number of boys, which can be expressed as:

number of girls = 2.5 * number of boys

We also know that the total number of students in the class is 35. Therefore, we can write an equation in terms of "x" as follows:

x + 2.5x = 35

Simplifying the above equation, we get:

3.5x = 35

Dividing both sides by 3.5, we get:

x = 10

This means that there are 10 boys in the class. To find the number of girls, we can use the equation we derived earlier:

number of girls = 2.5 * number of boys

number of girls = 2.5 * 10 = 25

Therefore, there are 25 girls in the class.

Southeast Washington State has a long history of seasonal dust storms. In October 1991, levels of dust particles in the air were six times greater than the Environmental Protection Agency's standard.

Several researchers conducted studies at three community hospitals to examine the relationship between the amount of dust particles in the air during the storms and the number of emergency room visits for respiratory disorders. Using the methods of correlation and regression, they were able to determine the effect of these dust storms on local residents.

In this module, you will write a short statistical report based on your linear regression analysis of data collected for two interesting variables that you believe could be linearly correlated. Your report should be supported by a scatter plot of the data and a least squares regression line.

To begin, you should collect your own data or use data that has already been collected. You may find data in the exercises at the end of sections 10.2 and 10.3 of your course text. Use at least 5 pairs of data.

Once you have collected your data, you should create a scatter plot of the data and a least squares regression line. You should also calculate the correlation coefficient and the equation of the regression line.

In your report, you should discuss the relationship between the two variables and the strength of the correlation. You should also discuss the equation of the regression line and how it can be used to make predictions.

Finally, you should conclude your report by discussing the implications of your findings and any limitations of your study.

Overall, your statistical report should be factually accurate, professional, and concise. You should also be sure to cite any sources that you use in your report.

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Required probability P(A)= 0.46. The problem here is a Joint Probability Distribution exercise. See the answers and explanation below.

Joint Probability Distribution can be simply described as the likelihood of two events (variables) occurring at the same time. These two events are commonly referred to as event A and event B, and their formal names are: p (A and B).

here, we have,

What is the solution to the questions?

A - The likelihood that each line has exactly one customer: The probability relates to the associated row and column.

X₁ = 1  and X₂ = 1

P (X₁ = 1, X₂ =1) = 0.15

B - The sum of the diagonal elements of the joint pmf indicates the likelihood that the amount of clients in both lines is the same:

P(X₁ = X₂) =) p(0,0) + p (1,1) + p(2, 2) + p(3,3

= 0.08 + 0.15 + 0.10 + 0.07

= 0.4

Hence,

C - Let A represent the situation in which there are at least two more clients than the other line: The following are examples of variable combinations:

X₂ =0 ;   X₁ = 2,3, 4

X₂ =1  ;   X₁ = 3, 4

X₂ =2 ;   X₁ = 0, 4

X₂ =3 ;   X₁ = 0, 1

The probability is thus computed as follows:

P (A) = p(1, 3) + p (2,2) + p(2, 3) + p(3,1) + p(3,2) + p(3,3) + p(4,0) + p(4,1) + p(4,2) + p(4,3)

= 0.04 + 0.10 +0.06 + 0.03 + 0.04+ 0.07 + 0.00 + 0.01 + 0.05 + 0.06

= 0.46

Hence , P(A)= 0.46

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Answer:   3

Step-by-step exp lanation:

divided

Answer:

3.

a.4 feet

b.77 feet

c.8 seconds

Step-by-step explanation:

We can start by noting that the given equation, d(p) = 1/4p^2 - 2p, represents the depth (in feet) at a given point in time as you swim underwater, where p is the time in seconds since you started swimming.

a. To find the deepest point underwater, we need to find the maximum of the function d(p). We can do this by finding the vertex of the parabola. The formula for the x-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by x = -b/2a. In this case, a = 1/4 and b = -2, so the x-coordinate of the vertex is:

x = -b/2a = -(-2)/(2(1/4)) = 4

So the deepest point underwater occurs at p = 4 seconds. To find the depth at this point, we can substitute p = 4 into the equation:

d(4) = 1/4(4)^2 - 2(4) = -4 feet

Therefore, the deepest point underwater is 4 feet below the surface.

b. To find the depth when you have held your breath for 22 seconds, we need to evaluate the function d(p) at p = 22. We can round our answer to the nearest foot.

d(22) = 1/4(22)^2 - 2(22) = 77 feet

Therefore, the depth when you have held your breath for 22 seconds is approximately 77 feet below the surface.

c. To find how long you hold your breath to make the swim, we need to find the time it takes to swim from one side of the pool to the other. We can do this by finding the roots of the equation d(p) = 0, which represent the times when you reach the other side of the pool (i.e., when the depth is zero). We can use the quadratic formula to solve for p:

p = (-b ± sqrt(b^2 - 4ac))/2a

In this case, a = 1/4, b = -2, and c = 0, so the formula becomes:

p = (-(-2) ± sqrt((-2)^2 - 4(1/4)(0)))/(2(1/4)) = 8 or 0

The root p = 0 corresponds to the start of the swim, so the time it takes to make the swim is:

p = 8 - 0 = 8 seconds

Therefore, you hold your breath for 8 seconds to make the swim from one side of the pool to the other.

Answer:

Step-by-step explanation:

Pour trouver la forme standard de l'équation d'une ellipse à partir des extrémités des grands axes et des petits axes, nous pouvons utiliser les formules suivantes:

Le centre de l'ellipse est le point (h, k), où h est la moyenne des coordonnées x des extrémités des grands axes et k est la moyenne des coordonnées y des extrémités des petits axes. Donc,

h = (2 + 8) / 2 = 5

k = (3 + 1) / 2 = 2

Donc, le centre de l'ellipse est (5, 2).

La distance a est la moitié de la longueur du grand axe, donc

a = (8 - 2) / 2 = 3

La distance b est la moitié de la longueur du petit axe, donc

b = (3 - 1) / 2 = 1

Maintenant, nous pouvons utiliser ces valeurs pour écrire l'équation de l'ellipse en forme standard:

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

En substituant les valeurs trouvées précédemment, nous avons:

(x - 5)^2 / 3^2 + (y - 2)^2 / 1^2 = 1

Ce qui est la forme standard de l'équation de l'ellipse.

Answer:7 3/4

Step-by-step explanation:

(5*8+1)/8+(8*2+5)/8=41/8+21/8=62/8=7 6/8=7 3/4

The equations that determine the cost of each hamburger and each fries is 4x + 5y = 20 and 10x + 7y = 41.20

An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents

Let x represent the cost of each hamburger and y represent the cost of each fries.

She purchased 4 hamburgers and 5 fries for $20.00, hence:

4x + 5y = 20    (1)

She purchased 10 hamburgers and 7 fries for $41.20, hence:

10x + 7y = 41.20   (2)

From both equations, solving simultaneously:

x = 3; y = 1.6

The cost of each hamburger is $3 while the cost of each fries is $1.6

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The Total Surface area of cardboard in the box is 992 cm².

The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of the two areas.

Given:

length= 20 cm

width = 12 cm

height= 8 cm

So, the TSA of Cuboid

= 2(lw + wh + lh)

=2( 20 x 12 + 12 x 8 + 8 x 20)

=2( 240 + 96 + 160)

= 2(496)

= 992 cm²

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The measure of angle m2 is 65°, the reason is interior opposite angles.

For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).

Exterior angle is an measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended. Also, due to polygon being regular, let it be having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.

We are given that;

The measure of angle 1= 65°

Now,

By interior opposite angle property

Angle 1 = Angle 2

Substituting the value of angle 1

65°= angle 2

Therefore, by interior angle property the answer will be 65°.

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The area of the shaded region is 104 m².

What is a Triangle ?

The intersection of the two sides of a triangle's three sides, which are known as the vertex, is a sort of polygon. Between two sides, an angle forms. This is among geometry's crucial components.

We know that Area of a triangle = 1/2 × base × height

The area of Big triangle = 1/2 × 30 × 13

                                        = 15 × 13

                                       = 195 m²

Area of Small triangle = 1/2 × 14 × 13

                                    = 91 m²

So, Area of the shaded region

        =  Area of big triangle - Area of small triangle

        = 195 - 91

        =  104 m²

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Answer:

Find the ninth term rule for the sequence 3, 4, 7, 12, 19

28, 39, 52, 67

(the term number) nth term is +increasing odd numbers (+1, +3, +5, +7, etc)

Step-by-step explanation:

You're welcome.

Answer:

Step-by-step explanation:

line a is 5ft

The original number in the given question solved by algebra is 39/7.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

The number is divided 5 times by 7 more than that number.

Let the number be x

Then,

x+7/5x = 8

x+7=40x

7=39x

x=39/7

Therefore, by algebra the answer will be 39/7.

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The speed of the slower plane is 125 mph and the speed of the faster plane is 175 mph.

Let's call the speed of the slower plane "x" and the speed of the faster plane "x+50".

When two planes are flying in opposite directions, the distance between them increases at a rate equal to the sum of their speeds. So, we can set up the following equation:

2(x + x+50) = 600

Simplifying this equation, we get:

2(2x+50) = 600

4x + 100 = 600

4x = 500

Divide

x = 125

Therefore, the speed of the slower plane is 125 mph and the speed of the faster plane is x+50 = 175 mph.

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Multiplying a whole number by a proper fraction results in a product which is lesser than the whole number.

Proper fractions are fractions in which the value of the numerator is less than the value of the denominator.

For example, 1/4, 3/4, 3/8, are all proper fractions.

4/3, 5/2, are all improper fractions.

So, from the definition, it is clear that, proper fractions are all less than 1.

When a whole number is multiplied by 1, we get the number itself.

So logically, when we multiply an whole number with fractions less than 1, then the resulting number will always be less than the whole number.

For example, consider 3 × [tex]\frac{3}{4}[/tex]

Multiplication of fraction is by multiplying numerators together and the denominators together.

3 × [tex]\frac{3}{4}[/tex] = [tex]\frac{3}{1}[/tex] × [tex]\frac{3}{4}[/tex] = [tex]\frac{9}{4}[/tex] = 2.25 < 3

Hence the multiplication of a whole number with a proper fraction is always less than the whole number.

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Therefore , the solution of the given problem of  test statistic comes out to be  Using a t-table or calculator, with 66 degrees of freedom (df = n1 + n2 - 2), we find the p-value to be approximately 0.039.

The Z-statistic has been the test statistics for anything resembling a Z-test and it confirms that the ordinary standard neutral hypothesis is true. Consider doing two separate X-y tests with a 0.05 level of significance and getting a 2.5 R-t value from your data (also referred as a Z-value). The p-value associated with this Z-value is 0.0124.

Here,

The hypotheses are:

Null hypothesis: There is no significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.

Alternative hypothesis: There is a significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.

To test this claim, we can use a two-sample t-test since we are comparing the means of two independent samples.

The formula for the test statistic is:

t = (x1 - x2) / sqrt((s1² / n1) + (s2² / n2))

where:

x1 = sample mean of those who smiled

x2= sample mean of those who remained neutral

s1 = sample standard deviation of those who smiled

s2 = sample standard deviation of those who remained neutral

n1 = sample size of those who smiled

n2 = sample size of those who remained neutral

Substituting the given values, we get:

t = (4.9 - 4.1) / sqrt((1.7² / 34) + (1.5² / 34))

t ≈ 2.116

Using a t-table or calculator, with 66 degrees of freedom (df = n1 + n2 - 2), we find the p-value to be approximately 0.039.

Since the p-value (0.039) is less than the significance level (0.10), we reject the null hypothesis. Therefore, we have sufficient evidence to conclude that there is a significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.

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Answer:

f/ 3 4 5 6

b/ 8 10 12 14

Step-by-step explanation:

the 4th wall has 6×3-4=14

so the relationship is

f/ 3 4 5 6

b/ 8 10 12 14

The evaluation of the two more bids Bruno received, and the equations, table and graph obtained from the bids are as follows;

x = The number of books

y = The total charge based on the pricing

The equations are;

Bid 7: y = 15·x + 3

Bid 8: y = 10·x + 40

Please find the completed table in the following explanation part

Part B;

Please find attached the graph of the two equations, created with MS Excel

An equation is a mathematical statement indicating that the quantity, magnitude or values of two expressions are the same.

The amount Bid 7 charges per book = $15

Amount paid upfront for Bid 7 = $5

Amount Bid 8 charges upfront = $40

Amount Bid 8 charges per book = $10

The variables are;

The equations are;

The table of values can be presented as follows;

                   Bid 7               [tex]{}[/tex]        Bid 8

x             [tex]{}[/tex] y = 15·x + 5              y = 10·x + 40

0               [tex]{}[/tex]       5               [tex]{}[/tex]          40

3               [tex]{}[/tex]       50               [tex]{}[/tex]        70

5               [tex]{}[/tex]       80               [tex]{}[/tex]        90

7               [tex]{}[/tex]       110               [tex]{}[/tex]        110

10               [tex]{}[/tex]     155               [tex]{}[/tex]       140

Part B;

Please find attached the required graph of the two equations, showing the legend and the scale for the x and y axis created with MS Excel.

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