A certain cookie recipe calls for 2 cups of flour to make one batch of cookies. Which graph best
represents the relationship between the amount of flour and the number of batches of cookies that
can be made using this recipe?

The probability that the Davis boys will occupy the first two seats in the row, the Jones boys will occupy the next three seats, and the Smith boys will occupy the last four seats is 7.937×\(10^{-4}\).

There are \(\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]\) potential arrangements for the nine boys if we do not make a distinction amongst boys with the same last name. We are curious in the likelihood of a specific one of these configurations.

Probability = \(\frac{1}{\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]}\)

                  = \(\frac{2!3!4!}{9!}\)

                 = 0.0007937

                = 7.937×\(10^{-4}\)

Hence, the probability is 7.937×\(10^{-4}\).

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Step-by-step explanation:

Let the amount of apples bought be x

Amount of strawberries bought be y and;

amount of oranges bought be z

If we buy 2 apples, 3 boxes of strawberry, and 4 oranges, the fruit would cost $15.30, then this will be expressed as;

2x+3y+4z = 15.30 ........... 1

If we buy 1 box of strawberry, 4 apples, and 2 oranges, the fruit would cost $10.90, this will be expressed as:

4x+y+2z = 10.90 ......... 2

If we buy 1 orange, 5 apples and 2 boxes of strawberry, the fruit would cost $13.70, this is expressed as:

5x+2y+x = 13.70 .......... 3

Solving the three equations simultaneously:

2x+3y+4z = 15.30 ........... 1

4x+y+2z = 10.90 ......... 2

5x+2y+z = 13.70 .......... 3

Reduce the number of equations

multiply equation 1 by 2 and subtract from equation 2

equation 1 * 2 will give:

4x+6y+8z = 30.6 ........... 4

eqn (4)-eqn(2)

6y-y + 8z-2z = 30.6-10.90

5y+6z = 19.7 ......... 5

Also multiply equation 2 by 5 and eqn 5 by 4 and subtract from each other.

eqn(2)* 5 will give:

20x+5y+10z = 54.5 .......... *

eqn(3) * 4 will give

20x+8y+4z = 54.8.......**

Subtsrct ** from *

8y-3y+(4z-10z)= 54.8-54.5

5y-6z = 0.3 .................. 6

Equate 5 and 6 and solve:

5y+6z = 19.7 ......... 5

5y-6z = 0.3 .................. 6

subtract:

6z+6z = 19.7+0.3

12z = 20

z = 20/12

z = 1.67

Substitute z = 1.67 into eqn 6

5y-6(1.67) = 0.3

5y - 10 = 0.3

5y = 10.3

y = 10.3/5

y = 2.06

Substitute z = 1.67 and y = 2.06 into equation 1

From 1:

2x+3y+4z = 15.30

2x+3(2.06)+4(1.67) = 15.30

2x+6.18+6.68 = 15.30

2x+12.86 = 15.30

2x = 15.30-12.86

2x = 2.44

x = 2.44/2

x = 1.22

Therefore 1 apple costs $1.22, 1 strawberry costs $2.06 and 1 orange costs $1.67

Explanation:

We'll let you draw the diagram. Here are some possible equations. We have listed the shortest sequence first.

(a) 24 = (10 + 10 + 4) = (8 + 8 + 8) = (10 + 8 + 4 + 2)

(b) 17 = (10 + 3 + 2 + 2) = (10 + 3 + 3 + 3 - 2) = (3 + 3 + 3 + 3 + 3 + 2)

(c) 15 = (11 + 4) = (6 + 6 + 3) = (4 + 4 + 4 + 3)

(d) 27 = (19 + 8) = (19 + 12 - 4) = (19 + 12 + 4 - 8)

Answer:

∡SRT

Step-by-step explanation:

angle which creates the longest side is the largest angle

Answer:

3.6

Step-by-step explanation:

Answer:

No real solutions.

Step-by-step explanation:

To solve this, we need to use Quadratic Formula.

Quadratic Formula:

\(x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ \)

in the form of:

\(a {x}^{2} + bx + c\)

Given information from the question, we can deduce:

a = -1

b = -2

c = 5

Let's substitute these values into the formula.

\(x = \frac{ - ( - 2) + - \sqrt{ {( - 2)}^{2} - 4( - 1)( -5)} }{2( - 1)} \\ = no \: real \: solutions\)

if you punch these into the calculator.

Answer:

sentences 3,4, and 5 elaborate on the changes but since only 4 is a possible answer it must be sentence 4.

Answer: Akhenaton dedicated that only the sun god Aten would be worshiped in Egypt.

Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

This polynomial does not have any rational roots. To find the rational roots of the polynomial P(x) = 2x³ - 5x² + x - 1, we can use the rational root theorem. According to the theorem, any rational root of the polynomial will be of the form p/q, where p is a factor of the constant term (-1) and q is a factor of the leading coefficient (2).

The factors of -1 are ±1, and the factors of 2 are ±1 and ±2. Therefore, the possible rational roots are:
p/q = ±1/1, ±1/2, ±1/(-1), ±1/(-2).

To determine if any of these possible rational roots are actual roots of the polynomial, we can substitute them into P(x) and see if the result is equal to 0.

Let's try them one by one:
- When we substitute x = 1, we get P(1) = 2(1)³ - 5(1)² + (1) - 1 = 2 - 5 + 1 - 1 = -3. Since P(1) ≠ 0, x = 1 is not a root.
- When we substitute x = 1/2, we get P(1/2) = 2(1/2)³ - 5(1/2)² + (1/2) - 1 = 1/4 - 5/4 + 1/2 - 1 = -1. Since P(1/2) ≠ 0, x = 1/2 is not a root.
- When we substitute x = -1, we get P(-1) = 2(-1)³ - 5(-1)² + (-1) - 1 = -2 - 5 - 1 - 1 = -9. Since P(-1) ≠ 0, x = -1 is not a root.
- When we substitute x = -1/2, we get P(-1/2) = 2(-1/2)³ - 5(-1/2)² + (-1/2) - 1 = -1/4 - 5/4 - 1/2 - 1 = -9/4. Since P(-1/2) ≠ 0, x = -1/2 is not a root.

None of the possible rational roots are actual roots of the polynomial P(x) = 2x³ - 5x² + x - 1. Therefore, this polynomial does not have any rational roots.

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A group contains n men and n women. 2n! number of ways are there to arrange these people in a row if the men and women alternate. Arrangement is known as permutation.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

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We  have expressed the limit as a definite integral on a given interval.

In order to express a limit as a definite integral on a given interval, we can use the Fundamental Theorem of Calculus. The theorem states that if f is a continuous function on the interval [a, b],

then the function F defined by F(x) = ∫a^x f(t) dt is differentiable on the interval (a, b) and F'(x) = f(x). Therefore, we can use this theorem to evaluate limits as definite integrals.

To express the limit as a definite integral on a given interval, we first need to find the antiderivative of the function that the limit is approaching. Once we have the antiderivative,

we can evaluate it at the endpoints of the interval and subtract the values to get the definite integral.Let's look at an example:lim x → 0 (sin x)/x

We can express this limit as a definite integral on the interval [0, 1] by using the following steps:

Step 1: Find the antiderivative of (sin x)/x.F(x) = ∫(sin x)/x dxWe can use integration by parts to find the antiderivative.

F(x) = ∫(sin x)/x dx= -cos x ln |x| + ∫cos x/x dxWe can use another integration by parts to evaluate the second integral.F(x) = -cos x ln |x| + sin x + C, where C is the constant of integration.

Step 2: Evaluate the definite integral.F(1) - F(0) = (-cos 1 ln |1| + sin 1) - (-cos 0 ln |0| + sin 0)= -cos 1 + sin 1This is the definite integral of (sin x)/x on the interval [0, 1].

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Explanation:

A function has each x value map to exactly one y value. Choice A demonstrates this, which is why it's a function. Note how none of the x values are repeated in this table.

Choices B, C and D have repeated x values, which in turn means that we have an x input lead to multiple y outputs. For instance, choice B says that the input x = -5 has the two outputs y = -5 and y = 5; this is sufficient to show that table B is not a function. Choices C and D are a similar story.

The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

As per the given,

Total songs = 53

Like songs = 14

Probability of selecting and liking the first song = 14/53

Now since repetition is not allowed and one like the song has been chosen out of 14 thus, the remaining songs = 13, and total songs = 43 - 1 = 52

Probability of selecting liking the second song = 13/52

Probability of selecting liking the third song = 12/51

Probability of selecting liking the fourth song = 11/50

a)

The probability of liking all songs will be 14/53 x 13/52 x 12/51 x 11/50 = 0.03418.

b)

The probability of not liking the next four songs =1 - The probability of liking all songs

The probability of not liking the next four songs = 1 - 0.03418 = 0.96582.

Hence "The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658".

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The relationship that is noted between two or more variables is termed a correlation. Correlation refers to the statistical association or relationship between two or more variables.

It indicates the degree to which the variables are related or how they are related to each other. Correlation can be positive, negative, or zero, depending on the direction and strength of the relationship between the variables.

A positive correlation indicates that as one variable increases, the other variable also increases. A negative correlation indicates that as one variable increases, the other variable decreases. Zero correlation indicates that there is no relationship between the variables.

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Answer:  42

Step-by-step explanation:

  6x7=42 ft

Answer:

- 8n + 9

Step-by-step explanation:

A - B

= - 3n + 2 - (5n - 7) ← distribute by - 1

= - 3n + 2 - 5n + 7 ← collect like terms

= - 8n + 9 → or 9 - 8n

If the person has same neighbor to the left and right , Seating is considered same. By using circular permutation, the answer is 2.

A conceivable order or arrangement for a group of items, especially one among several alternatives.

The formula for permutation is:

\(P(n,r)= \frac {n!}{(n-r)!}\) (Permutation)

\(P(n)=(n-1)!\) (Circular permutation)

Total number of people=5

Since the orientation with same neighbor to left and right is considered same. We consider 3 people as 1 which represent a person with neighbors.

Total people used in circular permutation=3

P(3)= (3-1)!

=2!

=2.

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Step-by-step explanation:

Slope:  −2

y-intercept:  (0,1)

Answer:

Answer:

The answer you selected is correct.

Step-by-step explanation:

Converse of corresponding angles theorem:

If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.

Answer:

3/2

Step-by-step explanation:

flip the second fraction so its 3/5 times 5/2

cross multiply to get rid of the 5s and get 3/2

Answer: The answer is 1.5!

Step-by-step explanation: hope I could help

Answer:

Who knows

Step-by-step explanation:

The question doesn't make sense so tell your teacher

CD = (1.328/Re^(1/2)) for laminar boundary layer flow.

a) The boundary conditions of the 3rd order polynomial is that the velocity at the edge of the boundary layer is zero and the velocity at the outer edge of the boundary layer is equal to the free stream velocity.

b)Using the above boundary conditions, C1, C2, and C3 can be determined as follows:

Applying n = 0 to the equation, we obtain u = 0, which is the velocity at the edge of the boundary layer.

Therefore, C1 = 0.

Applying n = 1 to the equation, we obtain u/u∞ = 0.99, which is the velocity at the outer edge of the boundary layer. Therefore, C3 = 0.99∞

Applying the continuity equation, we obtain C2 = C1/2

c)dp/dx = μ*d2U/dy2dp/dx is the pressure gradient, µ is the dynamic viscosity of the fluid.

d) The boundary layer thickness expressed in the form 8/x is given as,

δ = 8/ [2.45(C1/Cf)1/2]

∫0∞ [(u∞ - u)/u∞]1/2dy

Here, Cf = (τw)/(1/2ρu∞^2).

Thus, the boundary layer thickness expressed in the form 8/x is,

δ = 0.37xRe^(-1/5)

e)The momentum thickness expressed in the form 0/x is given as,

θ = ∫0∞ [(u∞ - u)/u∞](1/2)1/2dy

Thus, the momentum thickness expressed in the form 0/x is,

θ = (C2/10) x (Re)^(-1/2)

f) The displacement thickness expressed in the form 8*/x is given as,

δ* = ∫0∞ [(u∞ - u)/u∞]dy

Thus, the displacement thickness expressed in the form 8*/x is,

δ* = (C2/30) x (Re)^(-1/2)

g) The skin friction coefficient, Cf is given as,

Cf = τw/(1/2ρu∞^2)

Thus, Cf = (0.455/Re^0.5) for laminar boundary layer flow.

h)The drag coefficient, CD is given as,

CD = (2F)/(ρu∞^2L)

= 2Fd/(ρu∞^2L)

Therefore, CD = (1.328/Re^(1/2)) for laminar boundary layer flow.

i)The drag force on both sides of the plate is given as,

F = ∫0^L τw dx

= 2∫0^(L/2) τwdx.

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Given:

(sinx + 1)(2sin²x - 3sinx - 2) = 0

sinx + 1 = 0

sinx = -1

Take the arcsin of both-side

x = sin⁻' (-1)

x = -90= -90 + 360 = 270 = 3π / 2

x =3π / 2

Similarly,

2sin²x - 3sinx - 2 = 0

let y = sinx

2y² - 3y - 2 = 0

Factorising the above;

2y² - 4y + y - 2 = 0

2y(y-2) + 1(y-2) = 0

(2y+1)(y-2) = 0

Put sin x back in for y so we can see what it's really supposed to be.

(2sinx + 1 )(sinx -2) = 0

Either one of the terms 2sin x + 1 or sin x - 2 can be 0 for this equation to be true. Let's solve each of them separately.

2sinx + 1 = 0

2sinx = -1

sinx = -1/2

Take the arcsin of both-side.

x= sin⁻' (-1/2)

x = - 30 = -30+360 = 330 ,

x = 7π /6 or 11π/6

Therefore, the correct option is B. x= 3π / 2 , 7π /6 , 11π/6

To find the derivative of\(f(x) = 6x - 7x^(-7),\) we can apply the power rule and the constant multiple rule.

The power rule states that if we have a term of the form x^n, the derivative is given by \(nx^(n-1).\)

The constant multiple rule states that if we have a function of the form cf(x), where c is a constant, the derivative is given by c times the derivative of f(x).

Using these rules, we can differentiate term by term:

\(f'(x) = 6 - 7(-7)x^(-7-1) = 6 + 49x^(-8) = 6 + 49/x^8\)

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The number of people employed in the service industry in New York is 3,838,420.

Percentage is a measure of frequency that is used to determine the fraction of an amount as a number out of hundred. The sign that represents percentage is %.

In order to determine the number of people employed in the service industry, multiply the percentage of the people who work in the service industry by the number of people who had jobs in 2002.

Number of people employed in the service industry = 41% x 9,362,000

0.41 x x 9,362,000 = 3,838,420

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Answer: 0.6 or 60 cents.

Step-by-step explanation:

Answer:

I believe it is $1.7.

Step-by-step explanation:

I rounded it from 1.666666667. Something like that.

Answer:

Probability of a line living less than 10.1 years is 16%.

Step-by-step explanation:

It is given that, lifespan of lines in a particular zoo are normally distributed.

Mean =12.5

standard deviation= 2.4

We need to find the P(x<10.1)

So, let's use Empirical rule.

mean± standard deviation = 68%

Mean±2 standard deviation= 95%

mean ±3 standard deviation=99.7%

Now, let's use this rule to solve our problem.↑