Help me PLEASE ixlllll

Answer:

Lawrence was incorrect.

Step-by-step explanation:

Amy: 2(3x) +2(4x + 3)

= 14x + 6 ✓

Kaye: 3x + 3x + 4x + 3 + 4x + 3

= 14x + 6 ✓

Lawrence: 4(3x) + 2(4x)

= 20x Ø

Sufjan: 6 + 3x + 3x + 4x + 4x

14x + 6 ✓

Answer:

\(x=-2\)

Step-by-step explanation:

In this case, our slope is undefined. We know this because the slope never changes in the x direction:

\(m=\frac{x}{0}\)

Thus, we can only conclude that the equation is simply \(x=-2\) since a y component is not possible.

Answer:

The correct option is c.

Step-by-step explanation:

Given that,

u = 7i+4j and v = 2i-3j

We need to find the product of u and v. The dot product of two vectors is given by :

\(u{\cdot}v=(7i+4j){\cdot} (2i-3j)\\\\=(7i)(2i)+(4j)(-3j)\\\\=14-12\\\\=2\)

So, the dot product of u and v is equal to 2.

Answer:a. Y=15+.20x

B. Y=25+.10x

C. (100, 35)

Step-by-step explanation:

The wide is the gym in the drawing is 5

In the given statement is

Cassie measured the middle school and made a scale drawing. The scale of the drawing was 1 inch : 9 feet. the actual width of the gym is 45 feet.

To find how wide is the gym in the drawing

Now, According to the question

and, Based on the given conditions

=45 x1/9

=45/9

=5

Thus, The wide is the gym in the drawing is 5

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Each Bj is an open interval or a set of the form (a,b) ∩ K, each Bj is open in the topology generated by B. Hence, U is a union of open sets in the topology generated by B and the topology generated by B is finer than the standard topology.

Given that K = {x : x is not a positive integer}. Also, B is the collection of open intervals (a,b) along with all sets of the form (a,b) ∩ K. We need to prove that the topology on R generated by B is finer than the standard topology on R.

Let's start with the following lemma:

Lemma: Every open interval in the standard topology is a union of elements of B.

Proof: Let (a,b) be an open interval in the standard topology. If (a,b) ∩ K = ∅, then (a,b) ∈ B and we are done. Otherwise, we can write(a,b) = (a,c) ∪ (c,b)where c is the smallest positive integer such that c > a and c < b.

Now, (a,c) ∩ K and (c,b) ∩ K are both in B. Therefore, (a,b) is a union of elements of B.

Now, let's prove that B generates a finer topology on R than the standard topology.

Let U be an open set in the standard topology and x be a point in U. Then there exists an open interval (a,b) containing x such that (a,b) ⊆ U. By the above lemma, we can write (a,b) as a union of elements of B.

Therefore, there exist elements B1, B2, ..., Bn of B such that (a,b) = B1 ∪ B2 ∪ ... ∪ Bn.

Since each Bj is an open interval or a set of the form (a,b) ∩ K, each Bj is open in the topology generated by B. Therefore, (a,b) is a union of open sets in the topology generated by B.

Hence, U is a union of open sets in the topology generated by B. Therefore, the topology generated by B is finer than the standard topology.

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(a) Taking the reciprocal, we get 1/(1/A) = A⁻¹. Thus, A⁻¹ is an eigenvalue of A⁻¹. (b) The eigenvalues and eigenvectors of matrix A are: Eigenvalue λ₁ = 1 with eigenvector v₁ = [1; 1] and Eigenvalue λ₂ = -3 with eigenvector v₂ = [1; 1]

(a) If A is an invertible matrix and A is an eigenvalue of A, we need to show that A = 0 and that A⁻¹ is an eigenvalue of A⁻¹.

To prove A = 0, we start by assuming that A is an eigenvalue of A. Then, by the definition of eigenvalues, we have A * v = A * v, where v is the eigenvector corresponding to A.

Multiplying both sides by A⁻¹ on the right, we get A * v * A⁻¹ = A * v * A⁻¹. Since A is invertible, we can cancel out A and A⁻¹, giving us v = v. This implies that the eigenvector v must be the zero vector. Therefore, A = 0.

To show that A⁻¹ is an eigenvalue of A⁻¹, we can use the fact that the eigenvalues of the inverse of a matrix are the reciprocals of the eigenvalues of the original matrix.

Since A = 0, the eigenvalue of A⁻¹ is 1/A.

(b) To find the eigenvalues and eigenvectors of matrix A, which is given as:

\(\left[\begin{array}{cc}-1 & 4 \\ 1 & -1 \end{array}\right]\)

Let's begin by finding the eigenvalues λ. We'll solve the characteristic equation |A - λI| = 0, where I is the identity matrix.

Setting up the characteristic equation for matrix A:

|A - λI| = |[-1-λ, 4; 1, -1-λ]| = 0

Expanding the determinant:

(-1-λ)(-1-λ) - (4)(1) = 0

(λ+1)(λ+1) - 4 = 0

(λ+1)² - 4 = 0

(λ+1)² = 4

λ+1 = ±√4

λ+1 = ±2

λ = -1±2

λ₁ = 1

λ₂ = -3

So, the eigenvalues of matrix A are λ₁ = 1 and λ₂ = -3.

To find the corresponding eigenvectors, we need to solve the system of equations (A - λI)v = 0 for each eigenvalue.

For λ₁ = 1:

(A - λ₁I)v₁ = (A - I)v₁ = 0

Substituting λ₁ = 1 and I into the equation:

|(-1-1) 4; 1, (-1-1)|v₁ = 0

|-2 4; 1, -2|v₁ = 0

Row reducing the matrix:

|-2 4; 1, -2| ≈ |1 -2; 0, 0|

The reduced row-echelon form indicates that v₁ is a free variable, so we can choose any non-zero value for v₁. Let's set v₁ = 1 for simplicity.

Thus, the eigenvector corresponding to λ₁ = 1 is v₁ = [1; 1].

For λ₂ = -3:

(A - λ₂I)v₂ = (A + 3I)v₂ = 0

Substituting λ₂ = -3 and I into the equation:

|(-1+3) 4; 1, (-1+3)|v₂ = 0

|2 4; 1, 2|v₂ = 0

Row reducing the matrix:

|2 4; 1, 2| ≈ |1 2; 0, 0|

Again, the reduced row-echelon form indicates that v₂ is a free variable, so we can choose any non-zero value for v₂. Let's set v₂ = 1 for simplicity.

Thus, the eigenvector corresponding to λ₂ = -3 is v₂ = [1; 1].

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Answer:

9 pencils were sharp

Step-by-step explanation:

3*4=12 so if three fourths were sharp then 9 were

Answer:

B

Step-by-step explanation:

Look for the exponets that are in decending order such as 5 2 1

Answer:x= 45°

Step-by-step explanation:

The value of angle LKN is 75°becausw the theorem vertically oposite angles

Then the value of angle LPN is 45° because figure LKNP is a rectangle so the sum of the angles should be 360°so 120°+120°+75°+angle LPN is 360°so the value of angle LPN is 45°

The value of x is also 45° because of vertically oposite angles theorem

Given:

A new four way intersection is being constructed in New York Hyde park through point P(-3,-15).

Equation of line of one road : \(y=-\dfrac{3}{4}x+7\).

New road that will run perpendicular to the first road

To find:

The equation of line for the new road.

Solution:

The slope intercept form of a line is

\(y=mx+b\)

where, m is slope and b is y-intercept.

We have,

\(y=-\dfrac{3}{4}x+7\)

Slope of this line is \(-\dfrac{3}{4}\) and y-intercept is 7.

Product of slopes of two perpendicular line is -1.

\(m_1\times m_2=-1\)

\(-\dfrac{3}{4}\times m_2=-1\)

\(m_2=\dfrac{4}{3}\)

The point slope form of a line is

\(y-y_1=m(x-x_1)\)

where, m is slope.

The slope of new line is \(\dfrac{4}{3}\) and it passes through P(-3,-15). So, the equation of line of new road is

\(y-(-15)=\dfrac{4}{3}(x-(-3))\)

\(y+15=\dfrac{4}{3}(x+3)\)

\(y+15=\dfrac{4}{3}x+4\)

Subtract 15 from both sides.

\(y=\dfrac{4}{3}x+4-15\)

\(y=\dfrac{4}{3}x-11\)

Therefore, the equation of the line representing the new road is \(y=\dfrac{4}{3}x-11\).

The dealer's estimated cost of the car is $742.13.

The given parameters:

The total offer price of the car is calculated as follows;

Base and option cost = (0.897 x $24.495) + (0.1 x 1.6)

                                    = $22.13

The total offer price = Base and option cost + destination charge

                                 = $22.13 + $720

                                 = $742.13

Thus, the dealer's estimated cost of the car is $742.13

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Answer:

Option D is your answer.

Step-by-step explanation:

Remember that the x-values are the x coordinates and the y-values are the y coordinates in an ordered pair. Ordered pairs are written like this (x,y).

So for line r, you got (-6,4), (-3,0), and (0,-4).

But you only need two of these pairs to determine slope. Let's do that real quick, by using this formula. (Sorry if it's small)⤵⤵⤵

\( \frac{y _{2} - y _{1} }{x _{2} - x _{1} } \)

We'll use (-6,4) and ( -3,0).

0 - 4 = -4

-3 - (-6) = -3 + 6 = 3

So slope of line r is -4/3.

Now we'll do the same for line s:

Ordered pairs = (-5,-4), (5,0), and (20,6)

We'll use (-5,-4) and (5,0).

0 - (-4) = 0 + 4 = 4

5 - (-5) = 10

So slope of line s is 4/10 or 2/5.

Now we got to find the option choice that has these as the slopes.

We'll turn each into slope-intercept form.

A)

- Subtract 4x on both sides to get

3y = -4x - 12, then divide 3 on both sides to get y = -4/3 x - 4.

- Subtract 2x on both sides to get

-5y = -2x + 10, then divide -5 on both sides to get y = 2/5 x - 2.

B)

- Add 4x on both sides to get

3y = 4x + 12, the divide 3 on both sides to get y = 4/3 x + 4.

- Subtract 2x on both sides to get

-5y = -2x - 10, divide -5 on both sides to get y = 2/5 x + 2.

C)

- Subtract 4x on both sides to get

-3y = -4x - 12, then divide -3 on both sides to get y = 4/3 x + 4.

- Add 2x on both sides to get

-5y = 2x + 10, then divide -5 on both sides to get y = -2/5 x -2.

D)

- Add 4x on both sides to get

-3y = 4x - 12, then divide -3 on both sides to get y = -4/3 x + 4.

- Add 2x on both sides to get

5y = 2x + 10, then divide 5 on both sides to get y = 2/5 x + 2.

After all that writing we can tell that D is our answer, because both -4/3 and 2/5 appear as slopes.

Sorry this may seem like a lot, but the process really isn't that hard. Hope this helps :)

The numerator degree of freedom for the F test statistic to determine if the factor bread was significant would be 3.

This is because there are 4 different kinds of bread, but when conducting a two-way ANOVA test, one of the groups is always used as the reference group. Therefore, there are only 3 groups of bread that are being compared to each other. The denominator degree of freedom would be 56 (60 total samples minus 4 groups of bread and 5 groups of meat).

The F test statistic would determine if there is a significant difference in revenues between the different kinds of bread, while also controlling for the effect of the different kinds of meat.

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The ratio of the volume of cylinder C to the volume of cylinder D is ∛6:1.

To determine the ratio of the volume of cylinder C to the volume of cylinder D, we need to consider the relationship between the scale factors of the cylinders.

Given that the ratio of the volume of cylinder A to the volume of cylinder B is 5:1, we can infer that the scale factor between A and B is the cubic root of the volume ratio, which is ∛(5/1) = ∛5.

Similarly, the scale factor between cylinder B and cylinder D is 3:1, which implies that the cubic root of the volume ratio is ∛(3/1) = ∛3.

Now, we know that cylinder A is similar to cylinder C with a scale factor of 2:1. This means that the scale factor between A and C is 2:1, and the cubic root of the volume ratio is ∛(2/1) = ∛2.

By combining the scale factors, we can find the ratio of the volume of cylinder C to the volume of cylinder D:

Ratio of C to D = (Ratio of A to C) * (Ratio of B to D)

= ∛2 * ∛3

= ∛(2*3)

= ∛6

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Answer:

22

Step-by-step explanation:

just subtract 55-33

Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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Answer:

15 1/8 cups of oatmeal will be used

Step-by-step explanation:

Firstly, we shall be calculating the total number of dozens of muffin made

That would be the addition of the dozens of muffin made for the family reunion and that made for the club meeting = 3 + 2 1/2 = 5 1/2 or simply 5.5 dozens

Now, from the question initially, 2 3/4 or simply 2.75 cups of oatmeal makes 1 dozen muffins

x cups of oatmeal = 5.5 dozens of muffin

x * 1 = 2.75 * 5.5

x = 15.125 cups of oatmeal or simply 15 1/8 cups of oatmeal

The dimensions of the dumpster that will minimize its surface area

Length = 4.37 yds

Width  = 2.185 yds

Height  = 2.93 yds

What is Surface Area?

An object's surface area is the total area that all of its surfaces occupy. The formulas we will learn in this post make it simple to determine the various surface areas that various 3D shapes in geometry have. There are two groups for the surface area:

1) Curved surface area or Lateral surface area

2) Surface area overall

The length is said to be twice as long as the width.

So, l = 2w.

Now, the formula for a cube's surface area is;

S = 2lw + 2lh + 2wh.

Changing 2w to l yields;

S = 4wh + 4w² + 2wh.

S = 4w² + 6wh

In the meantime, the formula for a cube's volume is;

V = lwh

add 2w for l to receive;

V = 2w²h

h = V/2w²

In the SA equation, substitute V/2w² for h to get;

SA = 4w² + 6w(V/2w²)

SA = 4w² + 3V/w

V is stated to equal 28 yd3.

Thus;

S = 4w² + 84/w

Let's find the first derivative of S as we want to reduce the surface area;

S' = 8w - 84/w²

At S' = 0;

8w - 84/w² = 0

8w = 84/w²

w³ = 84/8

w = ∛(84/8)

w = 2.185 yds

L = 2 x 2.185

since, l = 2w.

l = 4.37 yds

h = V/2w²;

h = 28/(2 × 2.185²)

h = 2.93 yds

Hence, The dimensions of the dumpster that will minimize its surface area is l = 4.37 yds, w = 2.185 yds and h = 2.93 yds

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The variance of the scores in a sample tends to be less than or equal to the variability of the scores in the population from which the sample was obtained.

When we take a sample from a population, it is expected that the variability within the sample will be somewhat representative of the variability in the population. However, due to the random nature of sampling, there is a chance that extreme scores or outliers in the population may not be fully captured in the sample, resulting in slightly reduced variability. Therefore, the sample variance typically provides an estimate that is close to the population variance but is generally smaller due to the potential sampling variability.

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Answer:

-3x + 10

Step-by-step explanation:

you add like terms of 20 and negative 10 to simplify to -3x +10

The quotient to the expression is 1/64

Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.

Given here: The expression 4⁻⁵ / 4⁻²

When multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.

Thus simplifying the expression we get

4⁻⁵ / 4⁻²

4⁻⁵× 4²

4⁻⁵ ⁺ ²

4⁻³

1/64

Thus the quotient is 4⁻³

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Option A. The expression 4.4−3(34+1.125) is equivalent to -101.975.

We can simplify the expression using the order of operations (also known as PEMDAS), which tells us to perform the operations inside the parentheses first, then any multiplication or division, and finally any addition or subtraction.

Starting with the expression:

4.4 − 3(34 + 1.125

We can simplify the expression inside the parentheses first:

= 4.4 − 3(35.125)

Next, we can multiply 3 by 35.125:

= 4.4 − 105.375

Finally, we can subtract 105.375 from 4.4:

= -101.975

Therefore, the number -101.975 is the same as the formula 4.43(34+1.125).

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Checking the answer choices, we can see that option A is 4.4−3(2) = -1

The predicted weight of a girl who is 11 years old, if B0 equals 3, and B1 equals 7, is 80. The correct option is 80.

To find the predicted weight of an 11-year-old girl using the given model, follow these steps:

1. Plug in the given values for B0, B1, and Age into the equation: Weight = B0 + B1*Age + E
2. In this case, B0 = 3, B1 = 7, and Age = 11: Weight = 3 + 7*11 + E
3. Calculate the product of B1 and Age: 7 * 11 = 77
4. Add the result to B0: 3 + 77 = 80
5. Since E represents the error term and is not provided, we will assume it to be zero for this prediction. Thus, the predicted weight is 80.

So, the predicted weight of an 11-year-old girl is 80 (choice A).

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Answer:

7

Step-by-step explanation:

First, plug-in f(-3) into t in the function:

\(f(-3)=-2(-3) +1\)

Second, multiply -2 and -3 to get 6:

\(f(-3)=-2(-3)+1\)⇒\(f(-3)=6+1\)

Third, add 6 and 1 to get your answer:

\(f(-3)= 6+1\)⇒\(f(-3)=7\)