paige and her family went to the movies. They bought 4 tickets and paid $12 for popcorn. They spent $40. How much did each ticket cost?

For this case we must simplify the following expression:[tex](x ^ {\frac {3} {2}}) ^ 6[/tex]

We have that by definition of properties of powers that is fulfilled:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Then, rewriting the expression:

[tex]x ^ {\frac {3 * 6} {2}} =\\x ^ {\frac {18} {2}} =\\x ^ 9[/tex]

ANswer:

Option D

Answer:

10 degrees

Step-by-step explanation:

Answer: OPTION C

Step-by-step explanation:

Given the quadratic equation [tex]x^2 - 7x + 10[/tex] and the value of the variable "x" [tex]x = -2[/tex], you need to substitute the given value of the variable. Then:

[tex]=(-2)^2 - 7(-2) + 10[/tex]

And finally, you need to evaluate.

Remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]

Therefore, you get the following result:

[tex]=4+14 + 10[/tex]

[tex]=28[/tex]

This matches with the option C.

Answer:

Discount Rate=17%

Step-by-step explanation:

We know the price and discount of the car. The formula for calculating the discount when rate is given is:

[tex]Discount=Listed\ price*discount\ rate[/tex]

We know two quantities out of three, so putting in the known values:

[tex]3000=18000*rate\\rate=\frac{3000}{18000}\\Rate=16.67%[/tex]

The rate rounded off to nearest percent will give us:

17 percent.

So the discount rate is 17% ..

When rounded to the nearest whole percent, the discount rate is 17%.

To calculate the rate of the discount for the Bucio family's new car purchase, we will use the formula for finding the percentage rate of a discount, which is:

Discount Rate = (Discount Amount / Original Price) x 100.

In their case, the car has an original list price of $18,000, and they are offered a discount of $3,000. Plugging these values into the formula gives us:

Discount Rate = ($3,000 / $18,000) x 100

Discount Rate = 0.1667 x 100

Discount Rate = 16.67%

When rounded to the nearest whole percent, the discount rate is 17%.

Answer:

[tex]y=6\sqrt{3}[/tex]

Step-by-step explanation:

Using the Pythagoras theorem for triangle MTU,

[tex]TU^2+3^2=6^2[/tex]

[tex]TU^2+9=36[/tex]

[tex]TU^2=36-9[/tex]

[tex]TU^2=27[/tex]

[tex]TU^2=27[/tex]

From, triangle NTU,

[tex]y^2=TU^2+NU^2[/tex]

This implies that:

[tex]y^2=27+9^2[/tex]

[tex]y^2=27+81[/tex]

[tex]y^2=108[/tex]

[tex]y=\sqrt{108}[/tex]

[tex]y=6\sqrt{3}[/tex] units.

Answer:

The value of y=6√3 units.

Step-by-step explanation:

edge2020

Answer:

The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)

The minimum value of the objective function C is 125

Step-by-step explanation:

* Lets look to the graph to answer the question

- There are 3 inequalities

# y ≤ 15 represented by horizontal line (purple line) and cut the

  y-axis at point (0 , 15)

# x + y ≤ 25 represented by a line (green line) and intersected the

  x-axis at point (25 , 0) and the y- axis at point (0 , 25)

# x + 2y ≥ 30 represented by a line (blue line) and intersected the

  x-axis at point (30 , 0) and the y-axis at point (0 , 15)

- The three lines intersect each other in three points

# The blue and purple lines intersected in point (0 , 15)

# The green and the purple lines intersected in point (10 , 15)

# The green and the blue lines intersected in point (20 , 5)

- The three lines bounded the feasible region

∴ The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)

- To find the minimum value of the objective function C = 4x + 9y,

  substitute the three vertices of the feasible region in C and chose

  the least answer

∵ C = 4x + 9y

- Use point (0 , 15)

∴ C = 4(0) + 9(15) = 0 + 135 = 135

- Use point (10 , 15)

∴ C = 4(10) + 9(15) = 40 + 135 = 175

- Use point (20 , 5)

∴ C = 4(40) + 9(5) = 80 + 45 = 125

- From all answers the least value is 125

∴ The minimum value of the objective function C is 125

The vertices of the feasible region are (0, 15), (10, 15), and (20, 5). The minimum value of the objective function C = 4x + 9y is 190 at the vertex (10, 15).

The feasible region is the area on a graph where all the constraints of a system of inequalities are satisfied. To find the vertices of the feasible region, we need to find the intersection points of the lines formed by the given constraints. By solving the system of equations, we find that the vertices of the feasible region are (0, 15), (10, 15), and (20, 5).

To find the minimum value of the objective function C = 4x + 9y, we substitute the x and y values of each vertex into the objective function and determine which vertex gives the smallest value. By evaluating the objective function at each vertex, we find that the minimum value is obtained at the vertex (10, 15) with a value of 4(10) + 9(15) = 190.

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B is the correct answer

The solutions of the equation 2x² = 18 are x = 3 and x = -3.

To find the solutions of the equation 2x² = 18, we need to solve for x.

We can start by dividing both sides of the equation by 2, which gives us x² = 9.

Next, we can take the square root of both sides to find the solutions. The square root of 9 is 3, so the solutions are x = 3 and x = -3.

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The equation 2x² = 18 has two solutions, x = 3 and x = -3, which can be determined both algebraically and graphically by observing the points where the parabola f(x) = 2x² - 18 intersects the x-axis.

The solutions of the equation 2x² = 18 can be found by first dividing both sides of the equation by 2, which simplifies to x² = 9. This is a standard quadratic equation which can be further solved by taking the square root of both sides. The solutions are x = 3 and x = -3. If we graph the related function, which is f(x) = 2x² - 18, we will see a parabola opening upwards with its vertex at the origin (0,0), and it will intersect the x-axis at the points (3,0) and (-3,0), representing our solutions.

To use a graph of the related function, we can plot the equation 2x² - 18 = 0 on a graph and find the x-values where the graph intersects the x-axis. These x-values correspond to the solutions of the equation.

Answer:

30°

Step-by-step explanation:

Given

BC=30°

Central abgle is equal to its arc

so <3=30°

Answer:

The answer is 30

Step-by-step explanation:

If P(3) stands for the probability of the number 3 getting rolled, since 3 was rolled 5 times (as shown on the graph) out of 50 (as mentioned in the question), the experimental probability would be: 5/50, which when simplified, is 1/10

The student is asked to calculate the experimental probability of rolling a 3, but the specific frequency Sarah rolled a 3 is not provided. Without this, we cannot compute the experimental probability. Generally, the method involves dividing the number of times a 3 was rolled by the total number of rolls.

The question asks for the experimental probability of rolling a 3 on a six-sided die based on the results Sarah obtained from her 50 rolls. However, the provided information does not include the actual frequency of rolling a 3 in her experiment. If we had that data, the experimental probability P(3) would be the number of times a 3 was rolled divided by the total number of rolls (50 in Sarah's case).

For example, if Sarah rolled a 3 ten times out of 50, then the experimental probability of rolling a 3 would be calculated as follows: P(3) = 10/50 = 1/5. Without the specific results of Sarah's rolls, we cannot determine the experimental probability from the information given in the question.

Answer:

D) cylinder; radius = 6in.; height = 5 in.

The solid  produced if rectangle ABCD is rotated around line m is a cylinder with radius of 6 in and height of 5 in.

A solid figure is a three dimensional shape having length, width and height. Examples of three dimensional figures are prism, pyramid, cone, cylinder and so on.

The solid  produced if rectangle ABCD is rotated around line m is a cylinder with radius of 6 in and height of 5 in.

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Answer:

interest earned= 12.47

the future value of an annuity= 162.47

Step-by-step explanation:

Given Data:

Interest rate,r= 4%

time,t = 2 years

monthly payment, P= 150

n= 12 as monthly

At the end of 2 years, final investment A= ?

As per the interest formula for compounded interest

A= P(1+r/n)^nt

Putting the values in above equation

= 150(1+0.04/12)^24

 = 162.47

Interest earned = A-P

                          = 162.47-150

                           = 12.47 !

Answer:

B. y=sin(x) and y=-1/2

Step-by-step explanation:

We have been given the following trigonometric inequality;

2sin(x)=>-1

The above inequality can be re-written as;

sin(x)=>-1/2

after dividing both sides by 2.

We can then formulate two separate equations, one containing the expression on the right hand side and the other containing the expression on the left hand side;

From the left hand side we form the following equation;

y = sin(x)

From the right hand side we form the following equation;

y = -1/2

Therefore, the above two equations can be graphed to help solve the given trigonometric inequality

Answer: B

y=sin(x) and y=-1/2

Step-by-step explanation:

Answer:

each slice will be 1/36

Step-by-step explanation:

1/4 • 1/9 equals 3/36

Final answer:

Rebecca can divide ¾ of a cake into 9 pieces by finding the fraction of each piece relative to the whole cake, which is ⅛ or one-twelfth of the whole cake.

Explanation:

How to Divide a Cake into Equal Pieces

To divide ¾ of a cake into 9 equal pieces, Rebecca must consider how many pieces the whole cake can be divided into first. Since she has three-quarters of a cake, and she wants to make 9 pieces out of it, each piece will be one-ninth of the three-quarters of a cake. To find out the size of each piece relative to the whole cake, she divides ¾ by 9. This can be calculated as ¾ × ⅟, which simplifies to ⅛. This means that each piece of cake will be one-twelfth of the whole cake.

Understanding fractions such as halves, thirds, and quarters is useful in daily life and in solving problems like these. Knowing that a quarter is 25 cents makes it easier to grasp a quarter of a pie or cake. If you can visualize that two-thirds of a pie is more than half a pie, it helps when dividing portions or budgeting resources.

4y-7=2y-1

Subtract 2y from both sides

2y-7=-1

Add 7 to both sides

2y=6

Y=3

Answer:

D. h=7

Step-by-step explanation:

1               2            16

------ + ------------ = ----------

h-5        h+5          (h^2 -25)

1               2            16

------ + ------------ = ----------

h-5        h+5          (h-5)(h+5)

Since h^2 -25 factors in (h-5) (h+5)  ( it is the difference of squares)

We will multiply both sides by  (h-5) (h+5)  to clear the fractions

(h-5) (h+5)              2 (h-5) (h+5)            16 (h-5) (h+5)

------              + ------------                     = ----------

h-5                   h+5                                (h-5)(h+5)

Canceling like terms

 (h+5)              2 (h-5)             16

------              + ------------      = ----------

1                         1                          1

h+5 + 2(h-5) = 16

Distribute

h+5 + 2h -10 = 16

Combine like terms

3h-5=16

Add 5 to each side

3h-5+5 =16+5

3h =21

Divide each side by 3

3h/3 = 21/3

h = 7

A ratio is the part divided by the whole. Johnny took 3 pieces of pizza when the whole pizza had 8. Johnny has 3/8 (3 out of 8) pieces of pizza, or .375 parts. To find that number, literally divide your part from your whole to get the decimal form.

Answer:

7

Step-by-step explanation:

Given:

Simulation of randomly checking 25 vans, with over 100,000 miles=

                                                96408 03766 36932 41651 08410

Here  the digits 1, 2, and 3 represent a van with check engine light that turn on.

Approximately how many vans will have check engine lights come on?

From the above given data the digits 1, 2 and 3 that represented the particular model of van having check engine lights on are repeated 7 times in the simulation of randomly checking 25 vans, with over 100,000 miles

Hence 7 vans will have check engine lights come on!

In a simulation using the provided set of digits, we find that out of 25 vans, approximately 6 have check engine lights that turn on.

To solve this problem, we'd first identify all the digits that are either 1, 2, or 3 within the provided sequence of randomly generated digits. These digits, according to your problem, represent vans with check engine lights that turn on. The string you provided is 96408, 03766, 36932, 41651, and 08410.

Upon counting, the following digits in the string are 1, 2, or 3: '3', '2', '3', '1', '1', and '1'. This gives us a total of 6 occurrences.

Therefore, based on this simulation, if we were to randomly check 25 vans with over 100,000 miles, approximately 6 of them would have check engine lights that come on.

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Answer:

Two distinct real solutions.

Step-by-step explanation:

Given the equation in the form [tex]ax^2+bx+c=0[/tex], you need to find the Discriminant with this formula:

[tex]D=b^2-4ac[/tex]

For the equation [tex]-2x^2+5x-3=0[/tex] you can identify that:

[tex]a=-2\\b=5\\c=-3[/tex]

Then, substituting these values into the formula, you get that the Discriminant is:

[tex]D=5^2-4(-2)(-3)[/tex]

[tex]D=1[/tex]

 Since [tex]D>0[/tex], then [tex]-2x^2+5x-3=0[/tex] has two distinct real solutions.

13 x 8= 104

hope this helps!

Answer:

Step-by-step explanation:

Problem One

Blue =   5

Black  =2

Red    = 3

First of all there are 10 marbles, 2 of which are black.

That means that 8 others are not black

You can draw any one of the 8.

P(not black) = 8/10 = 4/5

Problem Two

There are 10 marbles in all

3 of them are red.

P(Red) = 3/10  

Answer:

See image

Step-by-step explanation:

Palto

ANSWER

[tex](x + 5i)(x - 5i) = 0 [/tex]

EXPLANATION

The given function is

[tex] {x}^{2} + 25 = 0[/tex]

The zeros of this function are;

[tex]x = \pm5i[/tex]

Or

[tex]x = - 5i \: and \: x = 5i[/tex]

[tex]x + 5i = 0\: and \: x - 5i = 0[/tex]

Hence the factored form is:

[tex](x + 5i)(x - 5i) = 0 [/tex]

If the equation were:

[tex] {x}^{2} - 25 = 0[/tex]

Then the factored form is

[tex](x + 5)(x - 5) = 0 [/tex]

For this case we have that by definition, the density is given by:

ρ =[tex]\frac {M} {V}[/tex]

Where:

M: It's the mass

V: It's the volume

The volume of a solid cone is given by:

[tex]V = \frac {1} {3} \pi * r ^ 2 * h[/tex]

Where:

A: It's the radio

h: It's the height

Substituting the data we have:

 [tex]V = \frac {1} {3} \pi * (4) ^ 2 * 21\\V = \frac {1} {3} \pi * 16 * 21\\V = 401.92 \ cm ^ 3[/tex]

On the other hand, we have that by definition, the density of the platini is given by:

[tex]21.45 \frac {g} {cm ^ 3}[/tex]

Substituting in the initial formula, we look for the mass:

[tex]M = 401.92 \ cm ^ 3 * 21.45 \frac {g} {cm ^ 3}\\M = 8621.184 \ g[/tex]

ANswer:

The mass of the platinum cone is 8621.2 grams.

To find the mass of a solid platinum cone with a height of 21 cm and a diameter of 8 cm, calculate the volume using the formula for a cone (⅓πr²h) and then multiply by platinum's density (21,450 kg/m³) to get approximately 30.342 kg.

Calculate the Mass of a Platinum Cone

To determine the mass of a solid cone made of platinum with a given height and diameter, we must first calculate its volume and then use the density of platinum to find its mass. The density of platinum is approximately 21,450 kg/m³. The volume of a cone is given by the formula ⅓πr²h, where r is the radius and h is the height. For our cone with a height (h) of 21 cm and a diameter of 8 cm, the radius (r) would be half of the diameter, so r = 4 cm = 0.04 m. Plugging the values into the formula, we get:

Volume (V) = ⅓π(0.04 m)²×21 cm = ⅓π(0.0016 m²)× 0.21 m = 0.0014136 m³.

To find the mass (m), we multiply the volume by the density of platinum (ρ):

Mass (m) = Density (ρ) × Volume (V) = 21,450 kg/m³ × 0.0014136 m³ = 30.342 kg.

Therefore, the mass of the solid platinum cone is approximately 30.342 kilograms.

Answer:

The correct options are 1 and 3.

Step-by-step explanation:

From the given box plot it is clear that

[tex]\text{Minimum values}=34[/tex]

[tex]Q_1=42[/tex]

Q₁ is 25% of a data.

[tex]Median=46[/tex]

Median is 50% of a data.

[tex]Q_3=70[/tex]

Q₃ is 75% of a data.

[tex]\text{Maximum values}=76[/tex]

34 is minimum value of the data and 46 is median it means 50% of the data values lies between 34 and 46. Therefore option 1 is correct.

42 is first quartile and and 70 is third quartile. it means 50% of the data values lies between 42 and 70. Therefore option 2 is incorrect.

The difference between Minimum value and first quartile, Maximum value and third quartile is less than 1.5×(IQR), therefore it is unlikely to have any outliers in the data.

Hence option 3 is correct.

The interquartile range of the data is

[tex]IQR=Q_3-Q_1[/tex]

[tex]IQR=70-42=28[/tex]

The interquartile range is 28. Therefore option 4 is incorrect.

Range of the data is

[tex]Range=Maximum-Minimum[/tex]

[tex]Range=76-34=42[/tex]

The range is 42. Therefore option 5 is incorrect.

Answer:

A,C

Step-by-step explanation:

got it right on edge 2021

    have a wonderful day

Answer:

the answer is D (4,3)

Step-by-step explanation:

Answer:

6 ft^2 and 2ft^2

Step-by-step explanation:

Multiply the height and length of each hole to get the answers. Not sure if you wanted both or not.

Answer:

im on the same question but i think u just have to multiply length times width for all of them then u subtract. hope it helps

Step-by-step explanation:

Answer:

a segment cd only

Step-by-step explanation:

segment cd is the only line that passes through segment ab at a right angle

Answer: 3,658 miles

Step-by-step explanation:

118 x 31 = 3,658 miles

Multiply the daily value by the number of days to find the total.

Answer:

3,658

Step-by-step explanation:

So if Kellianna drives 118 Miles each day you would simply multiply the 118 x 31 (Days) = 3,658

The value of the integral ∫ ln(x)/x dx is  ln²(x)/2 + c

From the question, we have the following parameters that can be used in our computation:

S lnx/x dx

Express properly

So, we have

∫ ln(x)/x dx

The above expression can be integrated using substitution method

Let u = ln(x)

So, we have

du/dx = 1/x

Make dx the subject

du = dx/x

So, we have

∫ u du

Apply the power rule to integrate

∫ u du = u²/2

Substitute u = ln(x)

When integrated, we have

∫ ln(x)/x dx = ln²(x)/2 + c

Where c is a constant

Hence, the value of the integral is ln²(x)/2 + c

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Answer:

C ≈ 87.96in

Step-by-step explanation: