Tickets for a school play cost $7 and $10 for the adults. The equation 7x+10y=80 represents the number of students(x) and the number of adults(y) who can attend the play for $80. If no students attend, how many adults can see the play for $80?

Answer:

27

Step-by-step explanation:

Convert the fraction in the exponent to a root, to simplify the expression and make the calculation easier.

[tex]9^{\frac{3}{2}}\\=\sqrt{9^{3} } \\=\sqrt{729} \\=27[/tex]

Therefore the integer which is equivalent to [tex]9^{\frac{3}{2} }[/tex] is 27.

we will proceed to verify each of the cases to determine the solution of the problem

we know that

The combination of raisins and chocolate chips that can the baker use, must be inside the triangular region

so

we're graphing each of the cases

Let

x--------> the number of possible raisins

y--------> the number of possible chocolate chips

case A

Let

[tex]A(28,20)[/tex]

using a graphing tool

see the attached figure

The point [tex]A(28,20)[/tex] is  include inside the triangular region

therefore

The case A is a solution

case B

Let

[tex]B(33,25)[/tex]  

using a graphing tool

see the attached figure

The point [tex]B(33,25)[/tex] is not include inside the triangular region

therefore

The case B is not a solution

case C

Let

[tex]C(45,10)[/tex]  

using a graphing tool

see the attached figure

The point [tex]C(45,10)[/tex] is not include inside the triangular region

therefore

The case C is not a solution

case D

Let

[tex]D(55,12)[/tex]    

using a graphing tool

see the attached figure

The point [tex]D(55,12)[/tex] is not include inside the triangular region

therefore

The case D is not a solution

the answer is the option A

[tex](28,20)[/tex]

Answer:

2nd Option is correct.

Step-by-step explanation:

We are given with four statements which describes a graph of a function.

We need to find the graph which represents the linear function.

Linear Function:

Linear functions are the functions whose graph are straight lines.

A linear function has the following form

y = f(x) = a + bx

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

So, In graphs of 1st , 3rd and 4th Options are curves not a straight line.

Only 2nd Option has graph which is straight as mentioned in it that a line passing through two points.

Therefore, 2nd Option is correct.

Answer

CD is 17,0

The point -2,19

Step-by-step explanation:

The dimensions of the right-circular cylinder, which has a volume of 1 liter and uses the least amount of material, are such that the radius and twice the height are equal to the cube root of the volume divided by π, i.e., (0.001/π)^(1/3).

In Mathematics, given the volume of a right-circular cylinder (an open top can), we can find its optimal dimensions that would use the least amount of material. These dimensions correspond to the minimum surface area of the cylinder, which includes its closed bottom but not the open top.

Since the volume V of a right-circular cylinder is given by V=πr²h, where r is the radius and h is the height. We know that the volume equals 1 liter or 0.001 m³. Rearranging the volume equation for h gives us h=V/(πr²).

Next, the surface area A of the cylinder with closed bottom is A=2πrh+πr². Substituting h=V/(πr²) into the surface area gives A=2r(V/r)+(πr²) which simplifies to A=2V/r+πr². For the surface area to be minimum, the derivative of A with respect to r must be equal to zero. The first derivative of A is A'=-2V/r²+2πr. Set A'=0 we solve for r we find r=(V/(π))^(1/3). Substituting this value back into the equation for h gives us h=2*(V/(π))^(1/3).

Hence, for a right-circular cylinder of 1 liter volume (0.001 m³) to use the least amount of material, it should have a radius and twice the height equal to the cube root of the volume divided by π, i.e., (0.001/π)^(1/3).

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Answer:

Option B is correct.    

Step-by-step explanation:

We have been given the different probabilities at different point we need to find the probability of not of 2

We know that sum of probabilities is 1

[tex]P(a_2)+P(not a_2)=1[/tex]

Here, the probability that is P(a 2)=0.40

Hence, the required probability is 1-0.40=0.60

Therefore, option B is correct.

Answer:

160g

Step-by-step explanation:

Comparing 59 pounds to 35 pounds shows a decrease of 24 pounds, which can be calculated by subtracting the smaller number from the larger number.

If we are considering the transition from 59 pounds to 35 pounds, we need to determine whether this change represents an increase or a decrease. Comparing the two numbers, we can observe that 35 pounds is less than 59 pounds. Therefore, moving from a higher number to a lower number indicates a decrease. To calculate the decrease, we subtract the smaller number (35 pounds) from the larger number (59 pounds) which equals 24 pounds. So, there is a decrease of 24 pounds.

Using the example parameters given in the hypothetical experiment on weight perception, we've applied similar reasoning. If someone in the experiment stepped down from lifting 20 pounds to lifting weights less than this, it would also be considered a decrease in weight. If they stepped up from lifting a weight of 20 pounds to a heavier weight, it would be termed an increase. This example underscores the importance of difference detection, which is often studied in sensory experiments within psychology.

Answer:

r ( common ratio) = 1.75

Step-by-step explanation:

Given : geometric sequence 4, 7, 12.25, 21.4375.

To find : What is the r value .

Solution : We have given

Geometric sequence 4, 7, 12.25, 21.4375.

r ( common ratio) = [tex]\frac{second\ term}{first\ term}[/tex].

r ( common ratio) = [tex]\frac{7}{4}[/tex] = 1.75

r ( common ratio) = [tex]\frac{12.25}{7}[/tex] = 1.75

Therefore, r ( common ratio) = 1.75

Answer:9

Step-by-step explanation:

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we know that

Probability is the giving the possibility of given outcome or any certain events.

Probability is the number of ways of achieving the success.

Probability of event that certain to happen is 1.

Probability of event that is impossible is 0.

Sum of probabilities of all likelihood occurring events is 1.

So, Probability of any event can exceed 1.

But,

[tex]\frac{5}{4}=1.25\text{ which is greater than 1}\\[/tex]

Hence, it is not possible value for a probability .

Therefore, Option 'D' is correct.

Final answer:

The value 5/4 is not a valid probability, as probabilities must be between 0 and 1 inclusive. The correct answer is D.

Explanation:

The question that needs assistance asks about which value is not a possible value for a probability. By definition, probabilities can range from 0 (the event will not occur) to 1 (the event is certain to occur). So, looking at the options given, A (0.001), B (1/16), and C (0.82) are all between 0 and 1, which means they are valid probabilities. However, option D (5/4) is greater than 1, which makes it an invalid probability. The correct answer is D: 5/4 is not a possible value for a probability.

Answer:  

$16.80

Step-by-step explanation:

The linear equation that models the growth of a tree that is 4 feet tall and grows 3 inches per year is y = 3x + 48.

The problem involves writing a linear equation in slope-intercept form to model the growth of a tree. The slope-intercept form is given by the equation y = mx + b, where 'm' represents the slope or the rate of change, and 'b' is the y-intercept or the initial value.

In the context of this problem, the tree's initial height is 4 feet and it grows at a rate of 3 inches per year. However, the units of the initial height and the yearly growth rate are different, so we need to convert 4 feet into inches. As 1 foot is equivalent to 12 inches, the initial height of the tree is 4 * 12 = 48 inches.

Therefore, the slope or rate of change 'm' is 3 inches per year and the y-intercept or initial value 'b' is 48 inches. Substituting these values into y = mx + b gives us the linear equation representing the growth of the tree: y = 3x + 48.

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Answer:

Step-by-step explanation:

(-)(-) = (+)

(-)(+) = (+)(-) = (-)

(+)(+) = (+)

2 - (-8) + (-3) = (*)

-(-8) = 8

+(-3) = -3

(*) = 2 + 8 - 3 = 10 - 3 = 7

Answer:

C. 17.0 feet

Step-by-step explanation:

We have been given that Jacob kicks a soccer ball off the ground and in the air with an initial velocity of 33 feet per second. We are asked to find the maximum height the soccer ball using formula [tex]H(t)=-16t^2+vt+s[/tex].

First of all, we will substitute [tex]v=33[/tex] in our given formula.

[tex]H(t)=-16t^2+33t+0[/tex]

Since our given parabola has a negative leading coefficient, so it will be downward opening parabola. The maximum height of the ball will be y-coordinate of the vertex of parabola.

Let us find x-coordinate of parabola as:

[tex]\frac{-b}{2a}=\frac{-33}{2\times -16}=\frac{-33}{-32}=\frac{33}{32}[/tex]

Now, we will substitute [tex]x=\frac{33}{32}[/tex] in our formula to find y-coordinate of vertex.

[tex]H(\frac{33}{32})=-16(\frac{33}{32})^2+33(\frac{33}{32})+0[/tex]

[tex]H(\frac{33}{32})=-16*\frac{1089}{1024}+\frac{1089}{32}[/tex]

[tex]H(\frac{33}{32})=-16*1.0634765625+34.03125[/tex]

[tex]H(\frac{33}{32})=-17.015625+34.03125[/tex]

[tex]H(\frac{33}{32})=17.015625[/tex]

[tex]H(\frac{33}{32})\approx 17.0[/tex]

Therefore, the ball reached the maximum height of 17.0 feet and option C is the correct choice.

yep 20.4 is the correct answer for plato!!

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=9\ years\\ P=\$2,136\\ A=?\\r=0.0536[/tex]

substitute in the formula above

[tex]A=2,136(1+0.0536*9)[/tex]

[tex]A=2,136(1.4824)[/tex]

[tex]A=\$3,166.41[/tex]  

Round to the nearest dollar

[tex]A=\$3,166[/tex]  

therefore

the answer is the option D

[tex]\$3,166[/tex]  

Transformation involves changing the position of a shape

The transformation rule is: [tex](x-10,y-3)[/tex]

From the attachment, we have:

[tex]A = (4,7)[/tex]

[tex]A' = (-6,4)[/tex]

The translation rule from ABCD to A'B'C'D' is calculated as follows:

[tex](x,y) = A' - A[/tex]

This gives:

[tex](x,y) = (-6,4) - (4,7)[/tex]

Rewrite as:

[tex](x,y) = (-6- 4,4-7)[/tex]

[tex](x,y) = (-10,-3)[/tex]

Hence, the transformation rule is:

[tex](x-10,y-3)[/tex]

Read more about transformations at:

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To find the measure of BE in rectangle ABCD, we can use the properties of a rectangle and similar triangles. By using the Pythagorean theorem, we find the length of the diagonal AC. Then, we use the properties of similar triangles to calculate the length of BE.

To find the measure of BE, we can use the properties of a rectangle. In rectangle ABCD, the diagonals are equal in length and bisect each other. Therefore, we can use the Pythagorean theorem to find the length of the diagonal AC: AC^2 = AB^2 + BC^2. Plugging in the values given, AC^2 = 40^2 + 30^2 = 2500, so AC = sqrt(2500) = 50. Since the diagonals bisect each other, we can conclude that AE = 50/2 = 25. Now, we can use the properties of similar triangles to find the length of BE. Triangle ABE is similar to triangle ACE, so we can set up the following proportion: AB/AC = BE/AE. Plugging in the values, 40/50 = BE/25. Solving for BE, we get BE = (40/50) * 25 = 20.

To find the measure of BE in rectangle ABCD, we use the Pythagorean Theorem. As the diagonals bisect each other, BE is half the length of diagonal AC, resulting in BE = 25.

In rectangle ABCD with BC=30 and AB=40, the diagonals bisect each other. That means E, the point of intersection, is the midpoint of both diagonals AC and BD. Since ABCD is a rectangle, its diagonals are equal, and AC = BD. To find BD, we use the Pythagorean Theorem in ΔABC:

Since E is the midpoint of BD, BE is half the length of BD: