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Each egg carton holds 12 eggs. The number of eggs is proportional   to the number of egg cartons.

What does the word "proportional" mean?

Comparing the quantity of eggs and egg cartons is what we're attempting to do.

Since each carton contains 12 eggs, we can be certain that there will be 12 times as many eggs as there are cartons. Increases in egg production will follow increases in carton production, and vice versa.

Equal or having the same value are definitions of equivalent. Because 1/4, 2/8, and 0.25 all have the same value, they are all comparable. They are not equal because we only have 12 eggs in a carton.

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Given:

Points: (3, -9) and (6, -2) on a coordinate plane

To find:

The distance between the two points

To determine the distance between the points, we will apply the formula:

Given

defect rate = 3%

Number of items chosen at random = 6

Find

probability that at least one will have a defect

Explanation

Probability of defective items = 3% = 0.03

Probability of non defective items = 1 - 0.03 = 0.97

so ,

probability that at least one will have a defect = 1 - Probability of 0 defects

Final Answer

Hence , the probability that at least one will have a defect is 0.167(approx)

The inverse property of multiplication states that the product of a number and its inverse is one. (a/b)*(b/a) = 1.

In the question, the numer is 14, its inverse is 1/14, and their multiplication is equal to 1.

Given:

There are given the function:

And,

The transferred function is:

Explanation:

According to the question:

We need to describe the transformation:

So,

We can see that in the transfer function, there is given that a negative sign.

So,

The transformation is:

Reflection on the x-axis: reflected:

Final answer:

Hence, the correct option is A.

To translate a point given its coordinate and a vector to translate by, we can simply add each value of the vector to the corresponding x and y coordinates of the point, so:

So, the image of the translations is (2, -7).

we know that the endpoints of AB are

and the distance formula is given by

By substituying these points, we have that

which is equal to

then

On the other hand, if

similarly to the previous case, the distance between the endpoint for A'B' is

which is equal to

Now, by comparing equation A and equation B, we can see that, the scale factor is 1/3.

Then, the answer is B.

Answer:  she will need about 2 gallons of juice

Step-by-step explanation:

Using the law of indices

This can further be simplify into;

Answer:

m^8a+8m^6a+24m^4a+32m^2a+16

Step-by-step explanation:

Simple binomial theorem.

(x+y)n = nC0 xny0 + nC1 xn-1y1 + nC2 xn-2 y2 + ... + nCn-1 x1yn-1 + nCn x0yn

OR

(x+y)n = ∑nk=0nCk xn-kyk = ∑nk=0nCk xkyn-k

plugging the numbers into this theorem yields that answer.

function y = 3.75 + 2.5(x - 3)

dy/dx = 0 + 2.5 - 0

dy/dx = 2.5

The rate of change of the cost in dollars = 2.5

Answer:

3x=14

Explanation:

Given the two equations:

Adding the two equations gives:

Part A:

By Angle-Angle Theorem,

Triangle BCA is similar with triangle BDC (∠B ≅ ∠B, and ∠C ≅ ∠D)

Triangle CDA is similar with triangle BCA (∠CBA ≅ ∠DCA, and ∠BCA ≅ ∠CDA)

By transitive property

ΔBCA ~ ΔCDA ~ BDC

Part B:

Part C:

Cross multiplying the proportions we have

Solution:

The statement is given below as

From the image in the question, we can see that

Concept:

If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of a second triangle, then the triangles are congruent.

Hence,

With the statements above, the final answer is

OPTION B is the right answer

The ratio of height of the building to the number of floors is 119/7 and the unit ratio is 17 which means that the height of each floor is 17 ft.

In the given question,

The height of a building is proportional to the number of floors.

In the building have 7 floors.

That means, n = 7

the height of building H = 119 ft.

Since the height of a building is proportional to the number of floors.

So [tex]\frac{H}{n}=k[/tex] where k = constant.

Firstly we have to find the ratio of height of the building to the number of floors.

As we know, H = 119 ft, n = 7

So the ratio,

[tex]\frac{H}{n}=\frac{119}{7}[/tex]

The ratio of height of the building to the number of floors is 119/7.

Now we have to find the unit rate.

To find the unit rate we have to divide the height of building to the number of floors.

As we know,

[tex]\frac{H}{n}=\frac{119}{7}[/tex]

now simplifying the ratio by dividing the both number by 7

Unit ratio [tex]=\frac{H}{n}[/tex]

Unit ratio [tex]=\frac{119/7}{7/7}[/tex]

Unit ratio [tex]=\frac{17}{1}[/tex]

Unit ratio = 17

Hence, the unit ratio is 17 ft which means that the height of each floor is 17 ft.

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Answer:

166.07

Step-by-step explanation:

The discriminant and the point of tangency are used to find the values of the variables as follows;

7. The line y = m·x is tangent to the curve x² + 2·x·y + 2·x = 1 when m = 1

8. The line y = 2·x - k is tangent to the curve x² + y² = 5, when k = ±5

Exercise 11.

1. The discriminant of the equation x² - 6·x + y² - 2·y + 2 = 0 is zero when y = x - 6, therefore the line x - y = 6 is tangent to the curve x² - 6·x + y² - 2·y + 2

2. The exact values of k for which the line 2·x + 3·y = k is tangent to the curve C = 4·x² + 9·y² = 36 is k = ±6·√2

The discriminant is the values which are within the radical sign of the quadratic formula.

7. At the point of tangency, the discriminant is 0

The equation is; x² + 2·x·y + 2·x = 1

The equation of the line is; y = m·x

Rewriting the equation of the curve, we get;

x² + 2·x·y + 2·x = 1

2·x·y = 1 - x² - 2·x

[tex]y = \dfrac{1 - x^2 - 2 \cdot x}{2\cdot x}[/tex]

At the point of tangency, we have;

[tex]y = \dfrac{1 - x^2 - 2 \cdot x}{2\cdot x} = m\cdot x[/tex]

1 - x² - 2·x - 2·m·x² = 0

1 - x² - 2·m·x² - 2·x  = 0

1 - x²·(1 - 2·m) - 2·x  = 0

The discriminant is zero at the point of tangency, which gives;

((-2²) - 4× (-(1 - 2·m)) × 1) = 0

8 - 8·m = 0

8 = 8·m

m = 8 ÷ 8 = 1

8. The line y = 2·x - k is tangent to the curve, x² + y² = 5 where we have;

y² = 5 - x²

y² = (2·x - k)²

5 - x² = (2·x - k)²

Which gives;

k² - 4·k·x + 5·x² - 5

5·x² - 4·k·x + k² - 5

At a tangent point the discriminant is therefore;

(-4·k)² - 4 × 5 × (k² - 5) = 100 - 4·k² = 0

100 - 4·k² = 0

4·k² = 100

k² = 100 ÷ 4 = 25

k = √(25) = ±5

Exercise 11

1. The equation of the line is; x - y = 6

The equation of the curve is; x² - 6·x + y² - 2·y + 2 = 0

From the equation, x - y = 6, we get; y = x - 6

Which gives; x² - 6·x + (x - 6)² - 2·(x - 6) + 2 = 0

x² - 6·x + (x - 6)² - 2·(x - 6) + 2 = 2·x² - 20·x + 50 = 0

2·x² - 20·x + 50 = 0

x² - 10·x + 25 = 0

The discriminant is; (-10)² - 4 × 1 × 25 = 0

Therefore;

3. The curve 4·x² + 9·y² = 36 has the tangent line 2·x + 3·y = k, when we have;

4·x² + 9·y² = 36

9·y² = 36 - 4·x²

y² = (36 - 4·x²)/9 = 4 - (4/9)·x²

y² = 4 - (4/9)·x²

2·x + 3·y = k

3·y = k - 2·x

y = (k - 2·x)/3

y² = ((k - 2·x)/3)²

4 - (4/9)·x² = ((k - 2·x)/3)²

4 - (4/9)·x² - ((k - 2·x)/3)² = 0

8·x² - 4·k·x + k² - 36 = 0

(-4·k)² - 4 × 8 × (k² - 36) = 0

1152 - 16·k² = 0

16·k² = 1152

k² = 1152 ÷ 16 = 72

k = √(72) = ±6·√2

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If the Busy Bee store bottles fresh jars of honey at a constant rate and In 3 hours, it bottles 36 jars, and in 7 hours, it bottles 84 jars of honey, then the constant of  proportionality is 12

The Busy Bee store bottles fresh jar of honey at a constant rate.

That means number of bottle is directly proportional to the time taken

Number of bottle they bottles =  k × Time taken

Where k is the constant of proportionality

In 3 hours, it bottles 36 jar

36 = k ×3

k = 36/3

k = 12

In 7 hours, it bottles 84 jar

84 = k × 7

k = 84/7

k = 12

Hence, if the Busy Bee store bottles fresh jars of honey at a constant rate and In 3 hours, it bottles 36 jars, and in 7 hours, it bottles 84 jars of honey, then the constant of  proportionality is 12

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[tex]\begin{cases} f(x)=5x-2\\\\ g(x)=x^2-5x+11\\\\ (f\circ g)(x)=f(~~g(x)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ g(1)=(1)^2 -5(1)+11\implies g(1)=7 \\\\\\ f(~~g(1)~~)\implies f(~~7~~)=5(7)-2\implies \stackrel{(f\circ g)(1)}{f( ~~ 7 ~~ )}=33[/tex]

Answer: $17, 535

Evaluate the value of expression.

Answer is - 2.

Answer: х=-8  gooood luck

Step-by-step explanation:

This is a linear function whose graph cuts the origin.

Therefore, any increase in the x axis will lead to a corresponding increase in the y axis by the same factor.

Thus, C is the answer

Answer:

Step-by-step explanation:123123km equals to 110m

Note:

Multiplication of a positive and negative number gives a negative number as the product.

+ve x -ve = +ve

Part A:

Devon's statement is always true

For example,

-12 x 11 = -132

-7 x 16 = -112

Part B:

Rule: Multiplication of a positive integer with a negative integer gives a negative integer as the result

Answer:

b)

Step-by-step explanation:

this is so becuz a fair die contains or has six parts meaning if its rolled once there are 6 probabilities so if its rolled twice the probabilities increase the chances are (1,1),(1,2),(1,3)... to (1,6) there is only one probability that its(3,3) so giving u 1/12 which when divided hives u b)

The question asks us to find the vertex of the equation below:

The question asks us to find the vertex using two methods.

For the first method, we will use is to plot the graph of the equation and highlight the coordinate of the vertex on the graph.

The second method will employ completing the square method to find the vertex of the equation.

Method 1:

Plotting the graph of the equation, we have:

From the plot above, we can see that the vertex is: (31.765, 22.953)

The next method must get the same values for the vertex coordinates.

Method 2:

This method is the completing the square method. It converts quadratic equations into their vertex forms.

The general equation for a vertex form of a quadratic equation is:

In order to apply "completing the square" method, we need to complete the following steps:

1. Factor out the coefficient of x-squared

2. Divide the coefficient of x by 2 and square the result

3. Add and subtract the answer from step 2 to the equation; then factorize to get the quadratic equation

in its vertex form.

Now, let us proceed to find this vertex form:

1. Factor out the coefficient of x-squared

2. Divide the coefficient of x by 2 and square the result

3. Add and subtract the answer from step 2 to the equation; then factorize to get the quadratic equation

in its vertex form.

Now that we have the equation in vertex form, we just need to compare the equation with the general formula for the vertex form, to get the coordinates of the vertex.

Therefore, the final answer is: (31.7647, 22.9529)

Value of m for which the graph of y = 3x² + 7x + m have two

x- intercepts is equal to m < 49 /12.

As given in the question,

Given graph equation:

y = 3x² + 7x + m

Graph y = 3x² + 7x + m has two x-intercepts if and only if

3x² + 7x + m<0 __(1)

Formula used to calculate x value is x = -b/2a

Compare with the standard form:

a= 3

b=7

c=m

x= -7/ 2(3)

  = -7/6

Substitute x=-7/6 in (1)

3(-7/6)² + 7(-7/6) +m<0

⇒49/12 -49/6 +m <0

⇒-49/12 +m<0

⇒m< 49/12

Therefore, Value of m for which the graph of y = 3x² + 7x + m have two

x- intercepts is equal to m < 49 /12.

The complete question is:

For what values of m does the graph of y = 3x²+ 7x + m have two x-intercepts?

a. m > 25/3

b. m < 25/ 3

c. m < 49 /12

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The expression representing the time Philip spent in the challenge is 30x+750.

If an expression was created utilizing integer variables, constants, and algebraic operations, it is said to be algebraic (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

Transcendental numbers, like such and e, are not algebraic, though, as they are not produced by the application of algebraic operations and numerical constants.

While it is common to produce with Euclidean expressions, the definition of e requires an unlimited number of algebraic operations.

An expression is considered to be rational if it can be completely reduced to a reasonable fraction using the principles of arithmetic operations ( associative properties and commutative properties of multiplication and addition, distributive property and rules for the operations on the fractions).

For the first 10 days:

read =10 x wrote 15 × 10 = 150

For the last 20 days

read =20 x

wrote = 30×20 = 600

Hence the total expression is 30x+750.

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Given:

P(A) = 0.31

P(B) = 0.5

P(A or B) = 0.585

To find:

P(A and B)

To determine P(A and B), we will apply the formula: