cookie monster makes the perfect cookies. he uses 2 cups of chocolate chips for every 3 dozen cookies. if he makes 54 cookies, how many cups of chocolate chips does he need?

Answer:

x = 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

(h, k ) are the coordinates of the vertex and a is a multiplier

h(x) = 19(x - 5)² + 6 ← is in vertex form

with vertex (h, k ) = (5, 6 )

The axis of symmetry is a vertical line passing through the vertex

with equation x = 5

Answer:

2

Step-by-step explanation:

If the parent function is y = 2, then the function of the graph would also be y = 2.

The parent function represents the simplest form of a function and serves as a reference for transformations. In this case, the parent function y = 2 is a horizontal line parallel to the x-axis, passing through the y-coordinate 2. Any transformations applied to this parent function would alter its shape or position, but the function itself remains y = 2.

The correct statement is that an approximately normal distribution with a mean of 42 and a standard deviation of 4.1.

The probabilities that a value will take one of two independent values given a certain set of conditions or hypotheses are quantified by the probability distribution known as the binomial distribution.

For the normal approximation of binomial distribution, the formula to calculate the mean is μ=np and the standard deviation is σ=√(npq). Here, n is the number of trials, p is the probability of a successful outcome, and q is the probability of failure outcome.

Given the probability of failure is q=40%=0.4. And the probability of success is, p=(1-q)=0.6.

Then, the mean is,

\(\begin{aligned}\mu&=np\\&=70\times0.6\\&=42\end{aligned}\)

The standard deviation is

\(\begin{aligned}\sigma&=\sqrt{npq}\\&=\sqrt{70\times0.6\times0.4}\\&=4.09\\&=4.1\end{aligned}\)

From the calculation, the mean is found to be 42 and 4.1.

Therefore, the third option is correct.

To know more about binomial distribution:

https://brainly.com/question/14565246

#SPJ4

Answer:

4

Step-by-step explanation:

Attached to this answer is an image with the work on how to find the number of sign changes in the polynomial.

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

This is not a polygon as it has a section (at the bottom) which is composed of non-straight segments.

Miss kito wins the 45 games and Mr. Fishman wins the 36 games.

(a) The setup of the equations is:

3.5%x + 5.75% ($ 780,000 - x) = $33,600

(b) The farmer invested $500,000 at 3.5% and $280,000 at 5.75%

Miss Kito and Mr. Fishman played 81 games of their favorite 2-player game, 7 Wonders Duel.

We have to find the how many games did they each win?

Let's Miss Kito wins 'x' games

So, the equation will be:

x + (x - 9) = 81

2x - 9 = 81

2x = 90

x = 45

And, Mr. Fishman = 45 - 9 = 36

Miss kito wins the 45 games and Mr. Fishman wins the 36 games.

(a) A farmer bought a scratch ticket and found out later that he won $1,200,000. After 35% was deducted for income taxes he invested the rest; some at 3.5% and some at 5.75% .

$1,200,000 × (1 - 3.5%)= $780,000

Suppose that he invested x at 35%

and ($ 780,000 - x) at 5.75%

3.5%x + 5.75% ($ 780,000 - x) = $33,600

(b) 3.5% + 5.75%($ 780,000 - x) = $33,600

3.5%x - 5.75% + 44,850 = 33,600

2.25%x = $11,250

x = $500,000

=> $780,000 - $500,000

= $280,000

So, the farmer invested $500,000 at 3.5% and $280,000 at 5.75%

Learn more about Investment at:

https://brainly.com/question/15353704

#SPJ4

The given question is incomplete, complete question is :

Miss Kito and Mr. Fishman played 81 games of their favorite 2-player game, 7 Wonders Duel. Miss KIto ultimately won 9 more games than Mr. Fish did. How many games did they each win?

A farmer bought a scratch ticket and found out later that he won $1,200,000. After 35% was deducted for income taxes he invested the rest; some at 3.5% and some at 5.75% . If the annual interest earned from his investments is $33,600 find the amount he invest at each rate.

a. Define variables to represent the unknowns and setup the necessary equations to answer the question.

b. [4 points] Algebraically solve the equation you created and express your final answer using a complete sentence and appropriate units. (You will not receive full credit if a trial and error method is used in place of an algebraic method.)

answer: x = 70 because of straight line theory. x+110=180

x=180-110

x= 70

Answer:

She lost $54

Step-by-step explanation: Just trust me

If it was right mark as Brainleist

Answer:

The answer is $54.00.

Step-by-step explanation:

To find the how much money, we just need to multiply 600 by 0.09.           600 x 0.09 = 54.

  600

x 0.09

------------

 5400      

Now you just move the decimal 2 places to the left, and you get 54.00! The answer is $54.00. Hope this helped! :]      

The dot product of two vectors ~u and ~v is defined as ~u · ~v = ||~u|| ||~v|| cosθ, where ||~u|| and ||~v|| are the magnitudes of ~u and ~v, respectively, The statement is false. It is not necessarily true that either ~u or ~v equals the zero vector if ~u · ~v = 0.

The dot product of two vectors ~u and ~v is defined as ~u · ~v = ||~u|| ||~v|| cosθ, where ||~u|| and ||~v|| are the magnitudes of ~u and ~v, respectively, and θ is the angle between ~u and ~v. If ~u · ~v = 0, then cosθ = 0, which means that θ = π/2 (or any odd multiple of π/2). This implies that ~u and ~v are orthogonal, or perpendicular, to each other.

In general, if ~u · ~v = 0, it only means that ~u and ~v are orthogonal, and there are infinitely many non-zero vectors that can be orthogonal to a given vector. Therefore, we cannot conclude that either ~u or ~v is the zero vector based solely on their dot product being zero.

However, it is possible for two non-zero vectors to be orthogonal to each other. For example, consider the vectors ~u = (1, 0, 0) and ~v = (0, 1, 0). These vectors are non-zero and orthogonal, since ~u · ~v = 0, but neither ~u nor ~v equals the zero vector.

Therefore, the statement that ~u · ~v = 0 implies ~u = ~0 or ~v = ~0 is false.

Learn more about dot product here:

https://brainly.com/question/30404163

#SPJ11

Answer:

DIMENSIONS:

THE DOUBLE: 42.6 m cubed on both the length, width, and height

THE HALF: 10.6 m cubed on both the length width and height

THE CUBE: 21.3 m cubedon both the lengrh, width, and height

MOST HEIGHT: The Double at 42.6 m cubed

Step-by-step explanation:

We know that we have 64 m cubed. First, we should find out the volume of each cube. 64 times 2 is 128. This means the Double equals 128 in volume and half of 64 is 32. this means the Half is 32 in volume. Since these are all cubes, every side is exactly the same(or else it would be a rectangle) the formula for finding volume is length times width times height, we would divide EACH of the volumes by 3. 128 divided by 3 is 42.6 meaning the doubles dimensions would be 42.6 on each part of the cube (the lenght width and height would all be 42.6) you can check this by multiplying 42.6 by 3 which takes us back to 128. For the cube we would do 64 divided by 3 which is 21.3 pn every side and 32 divided by 3 is 10.6. The one with the most height is the double. I am not sure how to find the floor space I am super sorry but I hope this helps :)

The correct option is b) 2. The maximum rank of the 8×8 matrix AB can be determined by considering the rank properties of matrix products.

The rank of a product of two matrices is at most equal to the minimum of the ranks of the individual matrices involved.
In this case, the matrix A is an 8×5 matrix with rank 4, and the matrix B is a 5×8 matrix with rank 2.
To find the maximum rank of the 8×8 matrix AB, we take the minimum of the ranks of A and B, which is 2.
Therefore, the maximum rank of the 8×8 matrix AB is 2.
So, the correct option is b) 2.

Learn more about the rank of a matrix:

https://brainly.com/question/32622591

#SPJ11

The maximum rank of the product of two matrices is equivalent to the minimum rank of its component matrices. So in this case, the maximum rank of the 8x8 matrix formed by multiplying the two given matrices is 2.

In the field of Mathematics, specifically Linear Algebra, the rank of a matrix product cannot exceed the minimum rank of its factors. In your case, you have an 8x5 matrix A with a rank of 4 and a 5x8 matrix B with rank 2. When you compute their product, yielding an 8x8 matrix AB, the maximum rank will be equal to the lesser rank of both component matrices A and B.

So, based on these facts, the answer to your question is that the maximum rank of the 8x8 matrix AB is 2, which corresponds to option b).

https://brainly.com/question/34235587

#SPJ2

Answer:

Not a Function

Step-by-step explanation:

The equation x^2 + y^2 = 9 is not a function because it does not pass the vertical line test

x2 + y2 = 9 is that function or not an function

its a function

The solution to the system of differential equations that satisfies the initial conditions x(0)=5 and y(0)=3 is:

x(t) = (29/3) \(e^{\frac{22t}{3} }\) - (4/3) \(e^{\frac{-16t}{3} }\)

y(t) = (-13/3) \(e^{\frac{22t}{3} }\) + (2/3) \(e^{\frac{-16t}{3} }\)

To solve the system of differential equations, we can use matrix exponential. The system can be written in matrix form as follows:

X' = AX, where X = [x y], A = [22 60; -6 -16]

The matrix exponential of A can be calculated as follows:

\(e^{(At)}\) = I + At + \(\frac{(At)^{2}}{2!}\) + \(\frac{(At)^{3}}{3!}\) + ...

where I is the identity matrix and t is the variable of integration.

We can substitute A and t = 1 into the formula to get:

\(e^{A}\)= I + A + \(\frac{(A)^{2}}{2!}\) + \(\frac{(A)^{3}}{3!}\)+ ...

= [1 0; 0 1] + [22 60; -6 -16] + [44 192; -36 -104]/2! + [ -256 -768; 96 272]/3! + ...

= [1 + 22 + \(\frac{44}{2!}\) - \(\frac{256}{3!}\)*60 + \(\frac{192}{2!}\) - \(\frac{768}{3!}\);

-6 + \(\frac{(-6)}{2!}\) + \(\frac{96}{3!}\) - 16 + \(\frac{(-104)}{2!}\)+ \(\frac{272}{3!}\)]

= [\(\frac{29}{3}\) \(\frac{102}{3}\);

\(\frac{-13}{3}\)  \(\frac{-4}{3}\) ]

Now we can use the initial conditions to find the constants of integration. We have:

X(0) = [x(0) y(0)] = [5 3]

So,

[\(e^{A}\)] [\(c_{1}\)] = [5]

[\(c_{2}\)] [3]

Multiplying both sides by the inverse of \(e^{A}\), we get:

[\(c_{1}\)] = [29/3 102/3]^(-1) [5]

[\(c_{2}\)] [-13/3 -4/3] [3]

Solving this system of linear equations, we get:

\(c_{1}\) = -4/3

\(c_{2}\) = 2/3

Therefore, the solution to the system of differential equations that satisfies the initial conditions x(0)=5 and y(0)=3 is:

x(t) = (29/3) \(e^{\frac{22t}{3} }\) - (4/3) \(e^{\frac{-16t}{3} }\)

y(t) = (-13/3) \(e^{\frac{22t}{3} }\) + (2/3) \(e^{\frac{-16t}{3} }\)

To learn more about differential equations:

https://brainly.com/question/14620493

#SPJ4

A possible second point which has a y-coordinate of 8 is 5.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following slope and data points on the line:

Substituting the given points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

3/2 = (8 - 2)/(x₂ - 1)

3/2 = 6/(x₂ - 1)

Cross-multiplying, we have:

3(x₂ - 1) = 12

x₂ - 1 = 12/3

x₂ - 1 = 4

x₂ = 4 + 1

x₂ = 5

In conclusion, the required second point (x₂) is equal to 5.

Read more on slope here: brainly.com/question/3493733

#SPJ1

Together, Lindsay and Lorraine needs to jump 21 more jumps in a row.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

Number of jumps got by Lindsay = 14

Number of jumps got by Lorraine = 13

Total number of jumps gotten by both = 27

Let j be the number of jumps they need to jump more.

j = 48 - 27

j = 21

Hence 21 more jumps would be needed.

Learn more about Addition here :

https://brainly.com/question/29464370

#SPJ1

Answer:

135 rats

Step-by-step explanation:

first do 5 x 3 (because it triples every week) that equals 15 then triple that witch is 45, then triple that one more time, 135 (because you are supposed to do 3 weeks) so its 135 rats! hoped this helped ;)

Answer:

(1,2), (2,4), (5,10), (8,16)

Step-by-step explanation:

For the time, the number it land on that would be you x axis and the distance would be your y axis

Answer:

should be C 8v3

Step-by-step explanation:

hope this helps you

Answer:

8V3

Step-by-step explanation:

Given functions \(g(x)=1/√x and p(x)=x^2 - 4,\) to state the domains of the following functions using interval notation:

\(Domain of g(x)/p(x) and Domain of g(p(x)).\)

Domain of g(x)/p(x):

We have to find the domain of the function g(x)/p(x).

For that, we need to consider the following points:

If

x = 0,

the denominator becomes zero and the function is undefined.

x ≠ 0.

The value under the square root in g(x) cannot be negative.

Hence,

x > 0.

Hence,

\(x^2 - 4 ≥ 0 ⇒ x^2 ≥ 4 ⇒ x ≤ −2 or x ≥ 2\)

the domain of g(p(x)) is.

\([−∞, −2] ∪ [2, ∞).\)

To know more about interval visit:

https://brainly.com/question/11051767

#SPJ11

Answer:

Step-by-step explanation:

77-31=46

46/2=23

since layla is 31 years older add the 31 to 23 to get her age which is 54.

julia =23

layla=54

to check add their ages: 23+54=77

yes thats right since they have a difference of 31 (54-23=31)

The statement that correctly compares the two functions include the following: D. They have different y-intercepts but the same end behavior.

In Mathematics and Geometry, the y-intercept is sometimes referred to as an initial value or vertical intercept and the y-intercept of any graph such as a linear equation or function, generally occur at the point where the value of "x" is equal to zero (x = 0).

By critically observing the graph and the functions shown in the image attached above, we can reasonably infer and logically deduce the following y-intercepts:

y-intercept of f(x) = (0, 4).

y-intercept of g(x) = (0, 8).

Additionally, the end behavior of both functions f(x) and g(x) is that as x tends towards infinity, f(x) and g(x) tends towards zero:

x → ∞, f(x) → 0.

x → ∞, g(x) → 0.

Read more on y-intercept here: brainly.com/question/28351981

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

A) 6cm

B) 2:3

C) 1:5

Step-by-step explanation:

A) area of rectangle = width × length

54cm^2 = x × 9

x = 54 ÷ 9

width = 6cm

B) the width = 6cm

the length = 9cm

the ratio between the width and the length

=》6cm : 9cm

if you simplify, it becomes 2: 3

C) the perimeter of the rectangle

= (2 × width) + (2 × length)

= (2 × 6) + (2 × 9)

= 12 + 18

= 30 cm

the ratio between the width and the perimetet

=》 6cm : 30 cm

if you simplify, it becomes 1 : 5

The equation of a parabola with a given focus and directrix is:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

In this equation, (a, b) represents the coordinates of the focus, and c represents the y-coordinate of the directrix. This equation describes a parabola where all points on the parabola are equidistant from the focus and the directrix.

To write the equation of a parabola with a given focus and directrix, we can use the geometric definition of a parabola. A parabola is the set of all points that are equidistant from the focus and the directrix.

Let's assume the focus is denoted as F(a, b) and the directrix is a horizontal line given by y = c. The vertex of the parabola is at the midpoint between the focus and the directrix, which is V(a, (b + c) / 2).

The distance from any point (x, y) on the parabola to the focus F(a, b) is given by the distance formula:

sqrt((x - a)^2 + (y - b)^2)

The distance from the point (x, y) on the parabola to the directrix y = c is given by |y - c|.

According to the definition of a parabola, these two distances are equal. Thus, we can set up the equation:

sqrt((x - a)^2 + (y - b)^2) = |y - c|

Squaring both sides of the equation eliminates the square root:

(x - a)^2 + (y - b)^2 = (y - c)^2

Expanding and rearranging the terms:

x^2 - 2ax + a^2 + y^2 - 2by + b^2 = y^2 - 2cy + c^2

Simplifying and canceling out the y^2 terms:

x^2 - 2ax + a^2 + b^2 - 2by = c^2 - 2cy

Rearranging the terms to obtain the standard form of the equation:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Thus, the equation of the parabola with focus F(a, b) and directrix y = c is given by:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Complete Question - Write the equation of a parabola with focus F(a, b) and directrix given by y = c.

To know more about equation of parabola, refer here:

https://brainly.com/question/11911877#

#SPJ11

Answer:

15 boys

Step-by-step explanation:

Whatever number one side of the ratio is multiplied by, the other side has to be multiplied by that same number. So, we have to find the number that 4 is multiplied by to get 20. We can represent this as an equation, where the unknown number is x:

4x = 20

Divide both sides of the equation by 4 to find the value of x:

x = 5

4 was multiplied by 5 to get 20.

To find the number of boys, multiply 3 by 5:

3 * 5 = 15

If there are 20 girls, there will be 15 boys.

16.3 degrees is the angle that the ramp makes with the ground.

Draw a diagram: Draw a right-angled triangle with the ramp as the hypotenuse, the height of the truck as one of the other sides, and the horizontal distance from the bottom of the ramp to the truck as the other side.

Use trigonometry: We can use the trigonometric function tangent to find the angle the ramp makes with the ground. tan(theta) = opposite/adjacent = height of truck/horizontal distance

Let's substitute the given values:

tan(theta) = 6/21

Solve for theta: We can use the inverse tangent function to solve for theta.

theta = tan^-1(6/21)

theta ≈ 16.3 degrees

Therefore, the angle that the ramp makes with the ground is approximately 16.3 degrees.

To know more about trigonometric function refer here:

https://brainly.com/question/6904750#

#SPJ11

Venn diagram:

The percentage of students that studied mathematics = 25%
The percentage of students that studied electronics = 20%
The percentage of students that studied Communications = 55%
The percentage of students that studied both electronics and Communications subjects = 10%

P(studied Communications or electronics or both subjects)
= P(studied Communications) + P(studied electronics) - P(studied both electronics and Communications subjects)
= 55% + 20% - 10%
= 65%

Therefore, the probability that a student studied Communications or electronics or both subjects is 65%.

P(studied mathematics and Communications subjects)
= P(studied mathematics) × P(studied Communications)
= 25% × 55%
= 13.75%

Therefore, the probability that a student studied mathematics and Communications subjects is 13.75%.

Drawing a Venn diagram, we have 25% studying Mathematics (M), 20% studying Electronics (E), and 55% studying Communications (C).10% studied both Electronics and Communications.

Therefore, the percentages become as follows: M = 25% - 10% = 15% E = 20% - 10% = 10% C = 55%.

Part 2 - To obtain the probability that a student studied Communications or Electronics or both subjects

P(Communication or Electronics) = P(Communication) + P(Electronics) - P(Communication and Electronics) = 55% + 20% - 10% = 65%.

The probability that a student studied Communications or Electronics or both subjects is 65%.

Part 3 -To obtain the probability that a student studied Mathematics and Communications subjects,

P(Mathematics and Communications) = P(Mathematics) * P(Communications) = 25% * 55% = 13.75%.

The probability that a student studied Mathematics and Communications subjects is 13.75%.

To know more about Venn diagram visit:

https://brainly.com/question/17041038

#SPJ11

Step-by-step explanation:

Volume of a sphere is given by

\(V = \frac{4}{3} \pi {r}^{3} \)

Where r is the radius of the sphere

From the question

radius = 41 in

Substitute the value into the above formula

We have

\(V = \frac{4}{3} \times {41}^{3} \pi\)

\( = \frac{275684}{3} \pi\)

= 288695.6097

We have the final answer as

Hope this helps you

The answer on deltamath is

288695.6 in³

Answer:

9 cm

Step-by-step explanation:

If the area is 81 cm², this means that the length is 9 cm as length² of a square equals its area.