Tory is going to the fair with four of her friends. The entrance fee per person is $7.50. They plan to go together on all the rides. The cost of each ride is $3.00. Write an expression to represent the cost of the group to go to the fair for any number of rides.

Answer:

Explanation:

So you want to start by finding the area of the big square.

We know the width of the big square is 60cm. The length of the big square is

19

+

24

+

13

=

56

Big square

A

r

e

a

=

L

⋅

W

=

56

⋅

60

=

3360

Now let’s find the little square inside the bigger square. We see from the picture that the width is 34 and the length is 24cm. Using the same formula, we can find the area of the little square.

Little square

A

r

e

a

=

L

⋅

W

=

24

⋅

34

=

816

The area enclosed in the area of the big square minus the area of the little square.

3360

−

816

=

2544

So the area enclosed is

2544

c

m

2

Step-by-step explanation:

Hi 

let call "a number" X.

then we have: 4-13X = X + 8 ..

The logarithmic function f(x) = a·log₃(x - 4), passing through the points (13, 7), has the values;

5 a. The value of a is 3.5

b. Please find attached the graph of the function, f(x) = 3.5·log₃(x - 4), created with MS Excel

A logarithmic function is a function that contain and involves logarithm operation and it is the inverse of an exponential  function

The function is f(x) = a·log₃(x - 4),

x > 4 and a > 0

The coordinates of a point on the graph of the function, f is A(13, 7)

5 a. The value of a can be found by plugging in the value of (13, 7) = (x, f(x)), as follows

f(13) = 7 = a·log₃(13 - 4) = a·log₃9 = a·log₃3²

7 = a·log₃3²

7 = 2·a·log₃3 = 2·a·1 = 2·a

2·a = 7

a = 7 ÷ 2 = 3.5

a = 3.5

5 b. The coordinates of the x-intercept of the graph = (5, 0)

The equation of the function is;

f(x) = 3.5·log₃(x - 4)

A third point on the graph is given when f(x) = 14 as follows;

f(x) = 14 = 3.5·log₃(x - 4)

log₃(x - 4) = 14 ÷ 3.5 = 4

3⁴ = x - 4

x = 3⁴ + 4 = 85

Which gives the point, (85, 14)

Similarly, we have the point (31, 10.5), (7, 3.5)

Please find attached the graph of f(x) created with MS Excel

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Answer:

Its option D. 9

mark me as brainlist

The minimum essay score that the student received from the dot plot is given by A = 2

Dots are used in a scatter plot to show the values of two different numerical variables. Each dot's location on the horizontal and vertical axes represents a data point's values. To view relationships between variables, utilize scatter plots.

The closer the data points come to forming a straight line when plotted, the higher the correlation between the two variables, or the stronger the relationship. If the data points make a straight line going from near the origin out to high y-values, the variables are said to have a positive correlation.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

Given data ,

Let the dot plot represent the essay score for each student in Mr. Ji's class

And , each dot represents a different student

Now , the test scores varies from 1 , 2 , 3 , 4 , 5 and 6

The student which receives the lowest score would be 1

But no student has scored a point 1 , and the student with 2 point is applicable

Hence , the minimum essay score that the student received from the dot plot is 2

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Answer:

To mathematically prove that Marc hit the ball near the top of the tower, he could use the equation h(x) = -16x^2 + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air.

First, Marc would need to determine the maximum height the ball reached during its flight. This can be found by using the vertex formula, which is x = -b/2a. In this case, a = -16 and b = 120, so x = -120/(2*-16) = 3.75 seconds.

Next, Marc can substitute this value back into the original equation to find the maximum height the ball reached. h(3.75) = -16(3.75)^2 + 120(3.75) = 135 feet.

Since the tower is 300 feet tall, Marc could conclude that if the ball hit near the top of the tower, it would have reached a height close to 300 feet. Since the ball reached a maximum height of 135 feet, it is unlikely that it hit the top of the tower.

However, this calculation assumes that the tower is directly in line with Marc's shot and that the ball did not have any horizontal movement. In reality, the tower could have been to the left or right of the shot, and the ball could have had some horizontal movement, which would affect its height at impact. Therefore, this calculation can only provide a rough estimate and cannot definitively prove whether or not the ball hit near the top of the tower.

Ok let's begin

These are adjacent complementary angles, these two guys together equal 90 degrees.

so we line them up into an equation

5x-18+4x+45 = 90

9x = 90 - 27

9x = 63

x = 7

Hope this helps

Answer:

X(s) = 2/[s³(s + 9)]

Step-by-step explanation:

Here is the complete question

Solve for the function X(s) in the Laplace domain by taking the Laplace transform of the following differential equations with given initial conditions.

dx/dt + 9x = 16t²     x(0) = 0 and dx(0)/dt = 5

Solution

dx/dt + 9x = 16t²

Taking the Laplace transform of the differential equation, we have

L{dx/dt + 9x} = L{16t²}

L{dx/dt} + L{9x} = L{16t²}

L{dx/dt} + 9L{x} = 16L{t²}

sL{x} - x(0) + 9L{x}  = 16L{t²}

L{x} = X(s)

L{t²} = 2!/s³

Substituting X(s) and L{t²} into the equation above, we have

sX(s) - x(0) + 9X(s) = 2!/s³

Substituting x(0) = 0 into the equation above, we have

sX(s) - x(0) + 9X(s) = 2!/s³

sX(s) - 0 + 9X(s) = 2!/s³

sX(s) + 9X(s) = 2!/s³

Factorizing X(s), we have

(s + 9)X(s) = 2!/s³

X(s) = 2/[s³(s + 9)]

So X(s) in the Laplace domain is

X(s) = 2/[s³(s + 9)]

Step-by-step explanation:

the expected value is calculated by multiplying each of the possible outcomes by their probability, and then summing up all these results.

tossing a coin 2 times gives us 4 possible different outcomes (all with the same probability of 0.25) :

head - tail

head - head

tail - head

tail - tail

to have exactly one head is 2 out of these 4 possible outcomes, and the probability is 0.5.

everything else is also 2 out of these 4 possible outcomes, and the probability for that is therefore 0.5 too.

the expected value (from your point of view) is

9×0.5 - 15×0.5 = -$3.00

Given:

with domain x={-4,-2,0,3}

Find: the range of the function for the given domain.

Explanation:

so the range of function for the given domain is {25,1,-7,11}.

Final answer: the required answer will be {25,1,-7,11}.

The additional 60 men, the provisions will last for approximately 20 weeks.

To determine how long the provisions will last with the additional 60 men, we need to consider the total number of people and the original duration the provisions were meant to last.

Originally, the provisions were intended to sustain 400 men for 23 weeks. This means that the provisions were estimated to be sufficient for a total of 400 * 23 = 9200 person-weeks.

Now, with the additional 60 men, the total number of men becomes 400 + 60 = 460.

To calculate how long the provisions will last with the increased number of men, we divide the total person-weeks by the new number of men:

Provisions last = Total person-weeks / Number of men

= 9200 / 460

≈ 20 weeks (rounded to the nearest whole number)

The additional 60 men will extend the supply's shelf life to around 20 weeks.

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Answer: V≈508.94m³

Step-by-step explanation:

V=π(d

2)2h=π·(18

2)2·2≈508.93801m³

V= 508.9m^3

Step-by-step explanation:

Use the equation for the volume of a cylinder which is \(V=\pi r^{2} h\)

r = 18/2 = 9m and h = 2m so \(V=\pi 81*2=162\pi =508.9380m^{3}\)

Answer:

34 div 68m??

Step-by-step explanation:

Answer:

answer = 34 / m

Step-by-step explanation:

Usually there would be another number or variable to write an algebraic expression, but if this is the only information given, then this would be the answer

Answer:

the answer is here.

Step-by-step explanation:

hope it will helps you

ACF is a 30º-60º-90º triangle because of the following:

1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : \(\sqrt{3}\)

1 → short leg

2 → hypotenuse

\(\sqrt{3}\) → long leg

Side length of the hexagon is the short leg of the triangle. It is 1.

r1 is the radius of the incircle in a regular hexagon. 2(r1) is the diameter of the incircle. It is also the hypotenuse of the right triangle. It is 2.

Using Pythagorean theorem.

\(a^2 + b^2 = c^2\)

\(1^2 + b^2 = 2^2\)

\(b^2 = 2^2 - 1^2\)

\(b^2 = 4 - 1\)

\(b^2 = 3\)

\(\sqrt{b^2} = \sqrt{3}\)

\(b = \sqrt{3}\)

The total amount that the person with base salary 42000; total sales 175000; commission 4% gets is $51000.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. In this case, the percentage of commission is given as 4%.

The commission will be:

= Percentage × Amount

= 4% × 175000

= 7000

Therefore, the total amount that the person gets will be:

= Salary + Commission

= 42000 + 7000

= $51000

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Answer:

The answer is below

Step-by-step explanation:

The complete question is:

In 1960​, there were 237,794 immigrants admitted to a country. In 2001, the number was 1,150,729.

a. Assuming that the change in immigration is​ linear, write an equation expressing the number of​ immigrants, y, in terms of​ t, the number of years after 1900.

b. Use your result in part a to predict the number of immigrants admitted to the country in 2013.

c. Considering the value of the​ y-intercept in your answer to part a​, discuss the validity of using this equation to model the number of immigrants throughout the entire 20th century.

Answer:

a) From the question, we can get two ordered pairs which are \((t_1,y_1)=(60,237794)\ and\ (t_2,y_2)=(101,1150729)\)

Using the equation of a line given two points:

\(y-y_1=\frac{y_2-y_1}{t_2-t_1}(t-t_1)\\ \\y-237794=\frac{1150729-237794}{101-60}( t-60)\\\\y-237797=22266.71(t-60)\\\\y=22266.71t-1098205.44\)

b) In 2013, t = 2013 - 1900 = 113.

Hence:

\(y=22266.71t-1098205.44\\\\y=22266.71(113)-1098205.44\\\\y=1417932.488\\\\y=1417933\)

c)

\(y=22266.71t-1098205.44\\\\the\ y\ intercept\ is\ at\ t=0,hence:\\\\y=22266.71(0)-1098205.44\\\\y=-1098205.44\)

Since the y intercept is negative, that is in 1900 the number of immigrants was -1098206 which can not be possible. Hence this equation is not valid and the growth may or may not be linear.

The graph of y = x^2 should be translated by 1 unit to the right and 3 units up.

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics, a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

Therefore, we have the following:

f(x) = x^2

g(x) = f(x - 1) + N

g(x) = (x - 1)^2 + 3

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Answer:

Discriminant = 9.

Step-by-step explanation:

Discriminant

\(\boxed{b^2-4ac}\quad\textsf{when}\;ax^2+bx+c=0\)

\(\textsf{when $b^2-4ac > 0 \implies$ two real roots}.\)

\(\textsf{when $b^2-4ac=0 \implies$ one real root}.\)

\(\textsf{when $b^2-4ac < 0 \implies$ no real roots}.\)

Given function:

\(x^2+x-2=0\)

Therefore:

Substitute the values of a, b and c into the discriminant formula:

\(\begin{aligned} \implies b^2=4ac&=(1)^2-4(1)(-2)\\&=1-4(-2)\\&=1+8\\&=9\end{aligned}\)

Therefore, the discriminant of the given function is 9.

As the discriminant is greater than zero, this implies that there are two real roots.

Answer:

x = 1

Step-by-step explanation:

given 2 secants to a circle from an external point , then

the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant, that is

8(8 + 10x) = 9(9 + 7x) ← distribute parenthesis

64 + 80x = 81 + 63x ( subtract 63x from both sides )

64 + 17x = 81 ( subtract 64 from both sides )

17x = 17 ( divide both sides by 17 )

x = 1

Answer:

The length of the third side is approximately ≈ 14.79 inches

Step-by-step explanation:

A piece of wire is bent into the shape of a triangle. Two sides have lengths of 16 inches and 23 inches. The angle between these two sides is 40°. What is the length of the third side to the nearest hundredth of an inch?

Use the law of cosines to find the length of the missing side.

Let C be the third side.

A = 18

B = 23

Angle C = 40^∘

c^2  =  a^2  +  b^2 - 2ab  cos C

c =  √a^2 + b^2 - 2ab cos C

c =  √18^2 + 23 ^2 - 2 (18) (23) cos 40^∘

c = √583 - 828 cos40^∘

≈ 14.79

Thus, The length of the third side is approximately  14.79 inches.

Hope this helps!

Answer:

Hint: everything in that big [] is to the power of zero. anything to the power of zero is one. so

1+(6-8)=?

Answer:

s>1 or 1<s

Step-by-step explanation:

-2(6+s)<-16+2s

-12-2s<-16+2s

4<4s

1<s

Answer:

first you have to divide 2 - 1 then 1 2 3

Step-by-step explanation:

156

Answer:

B. new elements are created when uranium breaks apart

Explanation:

Fission is the breaking apart of an atom.

The other choices are fusion, where atoms fuse together.

Answer: choice A

Step-by-step explanation:

the transposed matrix would be

5 3

2 -1

so

5*5+2*2=29

3*5+2*-1=13

5*3-2*-1=13

3*3+-1*-1=10

which gives us the answer

29 13

13 10

Answer:

\((-5,-4)\)

Step-by-step explanation:

Given

\(P = (5,4)\)

Rotation: 180 degrees counterclockwise

Required

P'

Rotation: 180 degrees counterclockwise

The rule is:

\((x,y) \to (-x,-y)\)

So: \(P = (5,4)\) becomes

\((5,4) \to (-5,-4)\)

Answer:

A'(0,4)
B'(6,-4)
C'(-2, -8)

Step-by-step explanation:

In order to scale a figure by a factor all you have to do is multiply each coordinate by the scaled number.
So in this case we'd take A(0,2) and then multiply the x-value and y-value by 2 to get A'(0,4).
Repeat this for each coordinate to get the answer!

Answer:

2 cm

Step-by-step explanation:

If x is the length of the sides of the squares, then the height of the box is also x.  The length and width of the base are 10−2x and 20−2x.  The area of the base is the length times the width.

96 = (10 − 2x) (20 − 2x)

96 = 200 − 20x − 40x + 4x²

0 = 4x² − 60x + 104

0 = x² − 15x + 26

0 = (x − 2) (x − 13)

x = 2 or 13

Since x < 5, x = 2.

So the length of the sides of the squares is 2 cm.