Can you help me with all of them so 1-6 for them please

Factor by grouping: 16x³ +28x² - 28x - 49 = 0 is  (4x² - 7) (4x - 7) = 0

Large polynomials can be divided into groups based on a common factor. As a result, we may factor each distinct group and then merge like words. We refer to this as factoring by grouping.

We have the equation,

16x³ +28x² - 28x - 49 = 0

In order to solve the equation by using factor by grouping:

We find common terms in between,

So, we arrange the terms,

16x³ +28x² - 28x - 49 = 0

4x² (4x - 7) -7 (4x - 7) = 0

Here, we have common term (4x-7).

Factor out the common binomial.

(4x² - 7) (4x - 7) = 0

Therefore, (4x² - 7) (4x - 7) = 0 is the factor.

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Answer:

19c + 30

Step-by-step explanation:

Distributive property : a(b+c) = ab + ac

Explanation : simply multiply the value on the outside of the parenthesis by both the values on the inside of the parenthesis.

Here we have 1(19c + 30)

To distribute, we multiply 1 by both 19c and 30

1 x 19c = 19c

1 x 30 = 30

We're left with 19c + 30

Step-by-step explanation:

just think calm and logically.

what are the parts of the surface area ?

rest assured, there is no such thing like a general equation for the surface area of a prism.

well sure, there could be, but there are so many different variations, to describe them would be more complicated than the formula. so, we only have a general approach for the volume of such regular prisms (ground area × height).

but for the surface area we just have to break this problem into smaller problems we can easily solve and then add the results together.

so,

we see, there are 5 sides of this special prism.

top, bottom, left, right and front.

so, we need to calculate these 5 areas and simply add them up.

left and right are rectangles. one is

11×18 = 198 in²,

the other is

12×18 = 216 in², together they are 414 in².

the front is a rectangle

8×18 = 144 in²

top and bottom are equal triangles. each is

8 × height / 2

or per Heron's formula

A = sqrt(s(s -a)(s - b)(s -c)) where s = (a + b + c)/2

our s here is

s = (8 + 11 + 12)/2 = 15.5

A = sqrt(15.5×7.5×4.5×3.5) = sqrt(1830.9375) =

= 42.78945548... in²

both together are 85.57891095... in²

so, the total surface area is

414 + 144 + 85.57891095... = 643.578911... in²

if we need to round to e.g. whole square inches, this would be

644 in²

Given this minitab printout, the response variable in this multiple regression equation is a numerical variable. Multiple regression is a statistical method used to examine the relationship between a dependent variable (also known as the response variable) and two or more independent variables (also known as predictors or explanatory variables).The minitab printout typically shows the coefficient estimates of the regression equation, along with various other statistics such as the R-squared value, standard error, etc. However, it doesn't indicate whether the response variable is categorical or numerical.A response variable is categorical if it can only take on a limited number of discrete values or categories. Examples of categorical variables include gender, occupation, marital status, etc. A response variable is numerical if it can take on any value within a certain range. Examples of numerical variables include age, income, height, etc.In the given minitab printout, the response variable is the variable labeled "Cust_Satisfaction." This variable is measured on a scale from 1 to 100, and therefore, it can take on any numerical value within that range. Hence, we can conclude that the response variable in this multiple regression equation is a numerical variable.

Answer:

17/ 30 ???

Step-by-step explanation:

.....................

Answer:

17/30

Step-by-step explanation:

2          1                   =            17

5          6                  =            30

The Laplace transform of L{t²e^(-at)} is (2!)/(s^(3+1)) * a^(-3-1)

To calculate the Laplace transform of t²e^(-at).

We can utilize the property of the Laplace transform that states:

L{t^n} = n!/(s^(n+1))

Applying this property to t², we have:

L{t²} = 2!/(s^(2+1)) = 2!/(s^3)

Next, we need to consider the Laplace transform of e^(-at). It is given by:

L{e^(-at)} = 1/(s + a)

To find the Laplace transform of t²e^(-at), we can multiply the Laplace transforms of t² and e^(-at):

L{t²e^(-at)} = L{t²} * L{e^(-at)} = (2!/(s^3)) * (1/(s + a))

Simplifying further:

L{t²e^(-at)} = (2!/(s^3)) * (1/(s + a)) = (2!/(s^3)) * (1/(s + a)) = (2!/(s^(3+1))) * a^(-3-1)

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Answer:

GEOMETRY

Step-by-step explanation:

In a heap, the height is defined as the number of edges on the longest path from the root to a leaf node. The height of a heap with n elements is at most log₂(n+1).

To find the minimum and maximum numbers of elements in a heap of height h, we can use the formula:

The minimum number of elements in a heap of height h is 2^h (a complete binary tree of height h with the minimum number of nodes).

The maximum number of elements in a heap of height h is 2^(h+1) - 1 (a complete binary tree of height h with the maximum number of nodes).

Therefore, the minimum and maximum numbers of elements in a heap of height h are:

Minimum: 2^h

Maximum: 2^(h+1) - 1

Note that not all values of h are valid heap heights. A heap must be a complete binary tree, so its height can only take on values that satisfy the formula: \(h < = log₂(n+1),\)where n is the number of elements in the heap.

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Answer:

1

the equation (x-4)^2-17=8 has two solutions because it is in a quadratic form.

(x-4)^2-17=8

x²-8x+16-17-8=0

x²-8x-9=0

Doing middle term factorization

x²-9x+x-9=0

x(x-9)+1(x-9)=0

(x-9)(x+1)=0

either

x=9

x=9or

x=9orx=-1

2.

x^2+4x+3=0:

Doing middle term factorization

x²+3x+x+3=0

x(x+3)+1(x+3)=0

(x+3)(x+1)=0

either

x=-3

or

x=-1

Josh’s solution is incorrect because he missed x=-3.

3.

x^2-6x+7=0

By using quadratic equation formula:

Comparing above equation with ax²+bx+c=0

we get

a=1

b=-6

c=7

Now

we have

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

x=\( \frac{ 6± \sqrt{ {-6}^{2} - 4*1*7} }{2} \)

x=\( \frac{ 6±2\sqrt{ 2}}{2} \)

x=\( { 3±\sqrt{ 2}} \)

Taking positive

x=\( { 3+\sqrt{ 2}} \)

taking negative

x=\( { 3-\sqrt{ 2}} \)

Answer:

66

Step-by-step explanation:

The recipe states that a 4 egg cake mixture will serve 12 people.

To find the number of people a 1 egg cake mixture will serve: 12 ÷ 4 = 3  ⇒  1 egg will make a cake big enough to serve 3 people.

If Gareth has 22 eggs, then 22 x 3 = 66

So a 22 egg mixture will be able to serve 66 people.

Answer:

About 60 people

Step-by-step explanation:

1.) Garret has 22 eggs and the recipe calls for four eggs to serve 12.

2.) Garret Can make this cake 5 times with 22 eggs (4 x 5=20)

3. Thus his cake can serve about 60 people

12 (people fed per cake) x 5 (cakes he could make) = 60 people

Answer:

2y - 13

Step-by-step explanation:

y - 9 + y - 4

2y - 9 - 4

2y - 13

Answer:

Step-by-step explanation:

Here, "combining like terms" would require y + y -9 - 4, or 2y - 13.  Order is unimportant here.

Answer:

B. \(T=h\)

*Sorry, I'm probably too late

Step-by-step explanation:

If the answer was \(T=h\), the starting temperature would be \(0\). This is wrong because the starting temeperature is supposed to be \(70\).

Answer:

85°C

Step-by-step explanation:

F = 185

Substitute the value of F in the formula.

C = \(\frac{5}{9}\) × (185 - 32)

C = \(\frac{5}{9}\) × 153

C = 85

∴ 185°F = 85°C

The answer is A intersection B = {v, z}.

The intersection of two sets is the set of all elements that are in both sets. In this case, the elements that are in both sets A and B are v and z. Therefore, the intersection of A and B is {v, z}.

To find the intersection of two sets, we can use the following steps:

List all of the elements in the first set.

List all of the elements in the second set.

For each element in the first set, check if it is also in the second set. If it is, add it to the set of the intersection.

The set of the intersection is the set of all elements that were added in step 3.

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Answer:

The answer is 900

good luck

Answer:

\(0 < \text{x} \le 4\)

If x is an integer, then x is any value in the set {1,2,3,4}

======================================================

Work Shown:

x = length of each side

6x = perimeter of the regular hexagon

The perimeter must be greater than 0.

Also, the perimeter must be less than or equal to 24. This is because of the phrasing "perimeter is at most 24 inches".

In other words, the perimeter is between 0 and 24, excluding 0 and including 24.

\(0 < \text{ perimeter } \le 24\\\\0 < 6\text{x} \le 24\\\\0/6 < 6\text{x}/6 \le 24/6\\\\0 < \text{x} \le 4\\\\\)

If x is an integer, then x can be any value in the set {1,2,3,4}

Examples:

The basis for W is {x - 1, x^2 - 1}, and since there are two linearly independent polynomials, the dimension of W is 2, which confirms our conjecture.

a) To show that the set W of polynomials in P2 such that p(1) = 0 is a subspace of P2, we need to verify the three conditions for a subset to be a subspace:

The zero polynomial, denoted as 0, must be in W:

Let p(x) = ax^2 + bx + c be the zero polynomial. For p(1) = 0 to hold, we have:

p(1) = a(1)^2 + b(1) + c = a + b + c = 0.

Since a, b, and c are arbitrary coefficients, we can choose them such that a + b + c = 0. Thus, the zero polynomial is in W.

W must be closed under addition:

Let p(x) and q(x) be polynomials in W. We need to show that their sum, p(x) + q(x), is also in W.

Since p(1) = q(1) = 0, we have:

(p + q)(1) = p(1) + q(1) = 0 + 0 = 0.

Therefore, p(x) + q(x) satisfies the condition p(1) = 0 and is in W.

W must be closed under scalar multiplication:

Let p(x) be a polynomial in W and c be a scalar. We need to show that the scalar multiple, cp(x), is also in W.

Since p(1) = 0, we have:

(cp)(1) = c * p(1) = c * 0 = 0.

Thus, cp(x) satisfies the condition p(1) = 0 and is in W.

Since W satisfies all three conditions, it is indeed a subspace of P2.

b) Conjecture about the dimension of W:

The dimension of W can be conjectured by considering the degree of freedom available in constructing polynomials that satisfy p(1) = 0. Since p(1) = 0 implies that the constant term of the polynomial is zero, we have one degree of freedom for choosing the coefficients of x and x^2. Therefore, we can conjecture that the dimension of W is 2.

c) Confirming the conjecture by finding the basis for W:

To find the basis for W, we need to determine two linearly independent polynomials in W. We can construct polynomials as follows:

Let p1(x) = x - 1.

Let p2(x) = x^2 - 1.

To confirm that they are in W, we evaluate them at x = 1:

p1(1) = (1) - 1 = 0.

p2(1) = (1)^2 - 1 = 0.

Both p1(x) and p2(x) satisfy the condition p(1) = 0, and they are linearly independent because they have different powers of x.

Therefore, the basis for W is {x - 1, x^2 - 1}, and since there are two linearly independent polynomials, the dimension of W is 2, which confirms our conjecture.

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The sample regression equation is Earnings = 10,004.9665 + 0.4349Cost + 178.0989Grad + 141.4783Debt(A).

The sample regression equation represents the relationship between the dependent variable (Earnings) and the independent variables (Cost, Grad, and Debt). In this equation, the intercept is 10,004.9665, and the coefficients for Cost, Grad, and Debt are 0.4349, 178.0989, and 141.4783, respectively.

The equation shows that for every unit increase in Cost, Grad, and Debt, the Earnings are expected to increase by the corresponding coefficients. So the correct option is A.

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Answer:

210

Step-by-step explanation:

6 times 3.5=210

Give the following equation:

1.09 represents the growth rate. It means that the population increases by 9% each hour, (1 + r).

The answer is 9%.

The three numbers are 4, 6, and 9.

Three numbers form a geometric progression.

Three numbers in a geometric progression can be written in terms of the first term (a) and the common ratio (r) as a, ar, ar². The second term is increased by 2, so the new terms are a, ar+2, ar².

Then the progression will become arithmetic: ar^2 - (ar+2) = (ar+2) - a

ar² - ar - 2 = ar + 2 - a

ar² - 2ar - a - 2 = 0 ...(1)

On solving equation (1), we get (r-1)(ar+2) = 0

If r = 1, then a, a+2, a+4 are in an arithmetic progression.

ar² + (ar+2+9) = (ar+2+9)²

ar² + ar + 11 = 0

On solving the above equation, we get:

r = (-1 ± √(1-4(11)a))/2a

As r ≠ 1, we have:

r = (-1+√(1-4(11)a))/2a

Substituting the value of r in equation (1), we get:

a = 4

Therefore, the three numbers are 4, 6, 9.

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Any piece of luggage must have a length, width, and height combined that is less than or equal to 150 cm. A traveler requests to take a package with the maximum permitted volume. if the length and width are to be equal, then the dimensions would be 48*96*72

Any piece of luggage must have a length, breadth, and height combined that is 216 cm or less.

L+W+H=216 (because we want the max volume, we may ignore the "less than part" and set them equal) (since we want the max volume, we can ignore the "less than part" and set them equal)

L = W if the length and width are equal.

Let's construct this new equation by swapping L for W.

Arrange H to the left so that H=216-2W when 2W+H = 216

Consequently, what is volume V=L*W*H=W=W2*(216-2W) =216W2-2W3 div./dW=432W-6W?

2\s432W-6W^2=0

72w-w2=0 divided by 6 on both sides.

W = 72 L H = 72 cm

L=2W is the only item that has altered.

Given that L+W+H=216 and that V=L*W*H=2W*W*(216-3W) =432W2-6W, 3W+H=216

864W-18W2 x 3 V prime

Set V prime to 0, solve it by dividing both sides by 18, and you'll get W = 48. dimensions will be

48, 96, and 72 cm in width ,lenght and height

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Answer:

The Correct Answer is option C.)  \(3052.1 km^{3}\)

Probability that exactly 33 buyers would prefer blue:

P(33) = 8.59\(exp^{-243}\)

Given,

Study of color preference of new car .

We will use the Binomial probability formula to find the answer

The formula is given by ⁿCₓ (p)ˣ (1-p)ⁿ-ˣ

We have

n, the number of trial = 1010

x, the sample we aim to try = 33

p, the probability of success = 0.5

Substitute these values into the formula

P(33) = \(1010_{C}{33} (0.5)^{33}(1 - 0.5)^{1010 - 33}\)

Hence the probability is,

P(33) = 8.59\(exp^{-243}\)

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Answer:

9 shirts and 10 caps

Step-by-step explanation:

Buying one t shirt costs 20 dollars, and one cap would cost 12 dollars. If Paxton bought one cap and one shirt, that would cost 32 dollars. If we multiply that by 9, we get 288. So Paxton can buy 9 shirts and 9 caps with 288 dollars. Paxton has 12 dollars left, so Paxton can buy one more cap to entirely spend the budget.

Answer:

Perimeter = \(34\sqrt{2}\) feet

Area = 60 feet²

Step-by-step explanation:

Let us revise the rules of perimeter and area of a rectangle

→ From the given figure

∵ The length = \(\sqrt{8}\) feet

∵ The width = 5\(\sqrt{18}\) feet

→ Simplify the roots

∵ \(\sqrt{8}=\sqrt{(2)(2)(2)}\)

∴ \(\sqrt{8}=2\sqrt{2}\)

∴ The length = \(2\sqrt{2}\) feet

∵ \(5\sqrt{18}=5\sqrt{(3)(3)(2)}\)

∴ \(5\sqrt{18}=5(3)\sqrt{2}=15\sqrt{2}\)

∴ The width = \(15\sqrt{2}\) feet

→ Perimeter = 2(Length + width)

∵ Perimeter = \(2[2\sqrt{2}+15\sqrt{2}]\)

∴ Perimeter = \(2[17\sqrt{2}]\)

∴ Perimeter = \(34\sqrt{2}\) feet

→ Area = Length × Width

∵ Area = \(2\sqrt{2}\) × \(15\sqrt{2}\)

∴ Area = \((2)(15)(\sqrt{2})(\sqrt{2})=(30)(2)=60\)

∴ Area = 60 feet²

The resulting formulas after the first three iterations are: Iteration 1: p ∧ (¬p ∨ ¬q) ∧ (¬q ∨ r) ∧ (q ∨ ¬r), Iteration 2: (True ∨ ¬q) ∧ (¬q ∨ r) ∧ (q ∨ ¬r), Iteration 3: (True ∨ True) ∧ (True ∨ r) ∧ (q ∨ ¬r)

Applying unit propagation on the given formula with an empty set of literals, the resulting formulas after the first three iterations are:

Iteration 1: p ∧ (¬p ∨ ¬q) ∧ (¬q ∨ r) ∧ (q ∨ ¬r)

Since there are no assigned literals yet, no unit clauses are present. No changes occur in this iteration.

Iteration 2: (¬p ∨ ¬q) ∧ (¬q ∨ r) ∧ (q ∨ ¬r)

In this iteration, the literal 'p' is assigned the value true to satisfy the unit clause 'p'.

The formula becomes:

(True ∨ ¬q) ∧ (¬q ∨ r) ∧ (q ∨ ¬r)

Iteration 3: (True ∨ ¬q) ∧ (¬q ∨ r) ∧ (q ∨ ¬r)

In this iteration, the literal '¬q' is assigned the value true to satisfy the unit clause '¬q'.

The formula becomes:

(True ∨ True) ∧ (True ∨ r) ∧ (q ∨ ¬r)

Unit propagation is a process in propositional logic where unit clauses, which are clauses containing only one unassigned literal, are identified and assigned a truth value to satisfy them.

The process continues iteratively until no more unit clauses remain.

In the given formula, the first iteration does not result in any changes since there are no unit clauses present.

In the second iteration, the unit clause 'p' is identified, and we assign it the value true. This assignment satisfies the unit clause, and the formula is modified accordingly.

In the third iteration, the unit clause '¬q' is identified, and we assign it the value true. This assignment satisfies the unit clause, and the formula is modified again.

It is important to note that the given formula is not yet in its simplified or final form, as there may be further iterations of unit propagation or other simplification rules to apply.

The process of unit propagation continues until no more unit clauses can be satisfied.

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Answer:

\(n = 144m^2 - 1\)

Step-by-step explanation:

__________________________________________________________

FACTS TO KNOW BEFORE SOLVING :-

__________________________________________________________

According to the question ,

\(3m = \frac{(n + 1)^{\frac{1}{2} }}{4}\)

Lets multiply both the sides by 4.

\(=> \frac{(n + 1)^{\frac{1}{2} }}{4} \times 4 = 3m \times 4\)

\(=> (n + 1)^{\frac{1}{2} } = 12m\)

It can be also written as :-

\(=> \sqrt{(n + 1)} = 12m\)

Lets square both the sides.

\(=> [\sqrt{(n + 1)} ]^{2} = (12m)^{2}\)

\(=> n + 1 =144m^2\)

\(=> n = 144m^2 - 1\)