write 12 as a product of its prime factors ​

The amount of each trail mix that should be combined to create the special order trail mix are:

6.25 pounds of the trial that contains 75% nuts.

3.75 pounds of the trial that contains 35% nuts.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

Trial mix A = x

= 75% nuts.

Trial mix B = y

= 35% nuts

Now,

Two equations are:

x + y = 10 _____(1)

x = 10 - y _____(2)

0.75x + 0.35y = 10 x 0.60 ______(3)

Substituting (2) in (3)

0.75 (10 - y) + 0.35y = 6

7.5 - 0.75y + 0.35y = 6

7.5 - 6 = 0.75y  - 0.35y

1.5 = 0.40y

y = 1.5/0.40

y = 3.75

Now,

x = 10 - 3.75

x = 6.25

Thus,

6.25 pounds of the trial that contains 75% nuts.

3.75 pounds of the trial that contains 35% nuts.

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Radius = 35 m 

Cost of fencing circular field is Rs 2640 at rate of Rs 12 per metre.

What is the radius of the circular field ?

 Let the radius of circular field be r metre.

Here , if we'll divide the total cost by per metre cost of fencing then we'll get circumference of the circular field.

➯ Circumference = 2640/12

➯ 220 m

As we know that , formula of circumference is

★ Circumference = 2πr ★

Hence, the radius of circular field is 35 metre.

Answer:

Solution given:

total cost =Rs 2640

rate=Rs 12/metre

We have

circumference of circle =\( \frac{total cost}{rate} = \frac{2640}{12} \)

2πr=220m

r=\( \frac{220}{2π} \)=35.01

r=35m(approximately)

the radius of the field is 35m.

Answer:

it is 752 hope this helped

Given the equation that represents pH level.

The pH level measures the concentration of hydronium ions and can be modeled by the function p(t)

The variable t represents the amount of hydronium ions, and p(t) gives the resulting pH level.

a. we will find pH when t = 0.45

so, substitute t = 0.45 and find the value of p

b. We will convert the logarithmic function into an exponential function using y for the рН.

So, the process will be as follows:

So, the answer will be, the equation will be as follows:

Answer:

I don't know where the equal sign us but here you go

6x-15+8x+4

14x-11

Answer:

=14x - 11

Step-by-step explanation:

1.)expand the bracket

3(2x -5) +4(2x+1)

=6x -15 +8x +4

2.)collect the like terms and simplify

=6x +8x -15 + 4

=14x -11

The solution of expression is,

⇒ 2 (x - 3) / (x + 1)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (x² - 6x + 9) / (2x³ + 5x) ÷ (x² - 2x - 3) / (4x² + 10)

Now, We can simplify the expression as;

⇒ (x² - 6x + 9) / (2x³ + 5x) ÷ (x² - 2x - 3) / (4x² + 10)

⇒ (x² - 6x + 9) / (2x³ + 5x) × (4x² + 10) / (x² - 2x - 3)\

⇒  (x² - 6x + 9) × 2 (2x² + 5) / x (2x²+ 5) (x² - 2x - 3)

⇒  2 (x² - 6x + 9) / (x² - (3 - 1)x - 3)

⇒ 2 (x² - (3 + 3)x + 9) / (x² - 3x + 1x - 3)

⇒ 2 (x² - 3x - 3x + 9) / (x (x - 3) + 1(x - 3)

⇒ 2 (x (x - 3) - 3 (x - 3) ) / (x - 3) (x + 1)

⇒ 2 (x - 3)² / (x - 3) (x + 1)

⇒ 2 (x - 3) / (x + 1)

Thus, The solution of expression is,

⇒ 2 (x - 3) / (x + 1)

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Functions (c) L(1) = C1 + AC and (d) L(1) = C°1 are linear operators on R^n, while functions (a), (b), and (e) do not satisfy the properties of linearity and therefore are not linear operators.

a) L(A) = 1 - 1: This function is not a linear operator because it does not preserve scalar multiplication. Multiplying A by a scalar c would yield L(cA) = c - c, which is not equal to cL(A) = c(1 - 1) = 0.

b) L(A) = 1 + 17: Similar to the previous case, this function is not linear since it fails to preserve scalar multiplication. Multiplying A by a scalar c would result in L(cA) = c + 17, which is not equal to cL(A) = c(1 + 17) = c + 17c.

c) L(1) = C1 + AC: This function is a linear operator since it satisfies both the preservation of addition and scalar multiplication properties. Adding matrices A and B and multiplying the result by scalar c will yield L(A + B) = C(1) + AC + C(1) + BC = L(A) + L(B), and L(cA) = C(1) + cAC = cL(A).

d) L(1) = C°1: This function is a linear operator since it satisfies the properties of linearity. Addition and scalar multiplication are preserved, and L(cA) = C(0)1 = c(C(0)1) = cL(A).

e) L(1) = 1?C: This function is not a linear operator as it does not preserve scalar multiplication. Multiplying A by a scalar c would give L(cA) = 1?(cC), which is not equal to cL(A) = c(1?C).

In summary, functions (c) L(1) = C1 + AC and (d) L(1) = C°1 are linear operators on R^n, while functions (a), (b), and (e) do not satisfy the properties of linearity and therefore are not linear operators.

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Answer:

um all you do is multiply 21 as the length by 14 was the width (LxW)  

Step-by-step explanation:

=294 is your answer    I think ...

This equation relates the rectangular coordinates x and y to the polar angle theta, and describes the curve traced out by the polar equation in the x-y plane.

To convert the polar equation \(r = 4 /cos (\theta) - sin (\theta)\) to rectangular coordinates, we can use the following trigonometric identities:

\(cos(\theta) = x/r\)

\(sin(\theta) = y/r\)

where x and y are the rectangular coordinates of the point.

Substituting these values in the given equation, we get:

r = 4 / (x/r) - y/r

\(r^2 = 4r/x - y\)

\(x^2 + y^2 = 4r - ry\)

Now, we can use the identity \(r^2 = x^2 + y^2\) to substitute for r in the above equation and simplify:

\(x^2 + y^2 = 4(4/cos(\theta) - sin(\theta)) - y(4/cos(\theta) - sin(\theta))\)

\(x^2 + y^2 = (16 - 4sin(\theta))/cos(\theta) - y(4/cos(\theta) - sin(\theta))/cos(\theta)\)

Multiplying both sides by cos(theta), we get:

\(x^2cos(\theta) + y^2cos(\theta) = 16 - 4sin(\theta) - y(4 - sin(\theta))\)

\(x^2cos(\theta) + y^2cos(\theta) + ysin(\theta) = 16 - 4sin(\theta)\)

Therefore, the equation in rectangular coordinates is:

\(x^2cos(\theta) + y^2cos(\theta) + ysin(\theta) = 16 - 4sin(\theta)\)

This equation relates the rectangular coordinates x and y to the polar angle theta, and describes the curve traced out by the polar equation in the x-y plane.

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Answer:

I THINK A AND E

Step-by-step explanation:

The probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur is 1/6.

To find the probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur, we need to determine the individual probabilities of each event and then multiply them together since the events are independent.

Event A: The coin lands on heads

A fair coin has two equally likely outcomes, heads or tails. Since we are interested in the probability of heads, there is only one favorable outcome out of two possible outcomes.

P(A) = 1/2

Event B: The die is 5 or greater

A fair six-sided die has six equally likely outcomes, numbers 1 through 6. Out of these six outcomes, there are two favorable outcomes (5 and 6) for Event B.

P(B) = 2/6 = 1/3

To find the probability of both events occurring (A and B), we multiply the individual probabilities:

P(A and B) = P(A) * P(B) = (1/2) * (1/3) = 1/6

Therefore, the probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur is 1/6.

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(a) The volume V of the box as a function of x is V = 4x^3-60x^2+200x

(b) The domain of V in interval notation is 0<x<5,

(c) The length L , width W, and height H of the resulting box that maximizes the volume is H = 2.113, W = 5.773, L= 15.773

(d) The maximum volume of the box is 192.421 cm^2.

In the given question,

A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.

(a) We have to express the volume V of the box as a function of x.

If we cut out the squares, we'll have a length and width of 10-2x, 20-2x respectively and height of x.

So V = x(10-2x) (20-2x)

V = x(10(20-2x)-2x(20-2x))

V = x(200-20x-40x+4x^2)

V = x ( 200 - 60 x + 4x^2)

V = 4x^3-60x^2+200x

(b) Now we have to give the domain of V in interval notation.

Since the lengths must all be positive,

10-2x > 0 ≥ x < 5 and x> 0

So 0 < x < 5

(c) Now we have to find the length L , width W, and height H of the resulting box that maximizes the volume.

We take the derivative of V:

V'(x) = 12x^2-120x+200

Taking V'(x)=0

0 = 4 (3x^2-30x+50)

3x^2-30x+50=0

Now using the quadratic formula:

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

From the equationl a=3, b=-30, c=50

Putting the value

x=\(\frac{30\pm\sqrt{(-30)^2-4\times3\times50}}{2\times3}\)

x= \(\frac{30\pm\sqrt{900-600}}{6}\)

x= \(\frac{30\pm\sqrt{300}}{6}\)

x= \(\frac{30\pm17.321}{6}\)

Since x<5,

So x= \(\frac{30-17.321}{6}\)

x= 2.113

So H = 2.113, W = 5.773, L= 15.773.

d) Now we have to find the maximum volume of the box.

V = HWL

V= 2.113*5.773*15.773

V = 192.421 cm^3

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The value of 'a' in the equation is 4.

The equation given represents a parabola in factored form. It states that the zeros (or x-intercepts) of the parabola are -5 and -3. We can rewrite the equation in factored form as follows:

y = a(x - (-5))(x - (-3))

Simplifying the equation, we have:

y = a(x + 5)(x + 3)

The equation also states that the point (0, 60) lies on the graph of the parabola. To find the value of 'a', we substitute the x and y coordinates into the equation:

60 = a(0 + 5)(0 + 3)

60 = a(5)(3)

60 = 15a

Dividing both sides of the equation by 15, we get:

4 = a

Therefore, the value of 'a' in the equation is 4.

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Answer:

not sure what you were asking, but its 15 cups of purple paint

Annie is incorrect in her measurement of the diameter of the circle, which should be greater than 3 cm if measure correctly placing the ruler at the center point.

Measuring the diameter of a circle with a ruler is a simple process. The diameter of a circle is the distance across the circle that passes through the center.

To measure the diameter of a circle with a ruler, you will need to follow these steps:

The issue here is that Annie did not place her ruler at the center of the circle. Thus, she obtained a wrong result which is smaller than the diameter should be.

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Answer:

1. Yes

2. 9 & 13

3. 9+13=22

4. 23

5. no

6. yes same as 1.

7. ????????????????????

the second q.

1.??? tried my best sry

Step-by-step explanation:

Answer: the answer is : you write a compound inequality for the amount of money she would spend, subtract the money she did spend and divide by the cost of what she has yet to buy she can buy between 1-7 shirt

Step-by-step explanation:

I took quiz

Answer:

36

Step-by-step explanation:

MC : BC : MB = 1 : √3 : 2

MC : BC = 1 : √3

12 : BC = 1 : √3

BC = 12 : 1/√3

BC = 12 × √3/1

BC = 12 × √3

BC = 12√3

MC : MB = 1 : 2

12 : MB = 1/2

MB = 12 : 1/2

MB = 12 × 2/1

MB = 12 × 2

MB = 24

AB = 2BD

AB = 2CD√3

AB = 2(½BC)√3

AB = 2(½ × 12√3) √3

AB = 2 × 6√3 × √3

AB = 12 × √9

AB = 12 × 3

AB = 36

By SAS similarity, ΔKML and ΔRTL are similar triangles. Therefore, option A is the correct answer.

From the given figure, KR=9 units, RL=15 units, MT=7.5 units and TL=12.5 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Consider ΔKML and ΔRTL, we get

RL/KL =15/(15+9)

= 15/24

= 5/8

TL/ML =12.5/(12.5+7.5)

= 12.5/20

= 5/8

Here, RL/KL=TL/ML

Here, ∠KLM≅∠RLT

By SAS similarity, ΔKML and ΔRTL are similar triangles

So, ∠KMT≅∠RTL

By SAS similarity, ΔKML and ΔRTL are similar triangles. Therefore, option A is the correct answer.

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Answer:

a

Step-by-step explanation:

got it right in edmentum

That depends on the function in question.

If f(x) is integrable and non-decreasing, then the right Riemann sum overestimates the integral of f.

If f is non-increasing, the right Riemann sum underestimates the integral.

Answer:

-5

Step-by-step explanation:

Answer:

x = -3

Step-by-step explanation:

-15x + 20 + 4 = 69

-15x + 24 = 69

-15x = 69 - 24

-15x = 45

x = 45/-15

× = -3

Answer:

Girls = 16

Total students = 40

Step-by-step explanation:

40% of the students are girls, this means 60% of the students are boys.

To find the number of girls, setup a proportion using the percentages and actual number of students in the class. I am going to make the numerator the numbers that go with the girls and the denominator will be the numbers that go with the boys.

Also let's convert the percentages to decimals by moving the decimal two places left.

40% = 0.4 and 60% = 0.6

\(\frac{.4}{.6} =\frac{g}{24} \\.6g=9.6\\\frac{.6g}{.6} =\frac{9.6}{.6} \\g=16\)

Now let's find the total number of students by adding the number of girls to the number of boys.

16 + 24 = 40

The given statement " If A and B are n x n and invertible, then A⁻¹B⁻¹ is the inverse of AB." is true because  A and B are invertible matrices, it means that they both have an inverse (A⁻¹and B⁻¹, respectively). The product of A and B, represented by AB, is also an n x n matrix.

To show that A⁻¹B⁻¹is the inverse of AB, we must demonstrate that the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix, which is an n x n matrix with 1s along the diagonal and 0s elsewhere.
To verify this, we'll multiply (AB) with (A⁻¹B⁻¹) and check if the result is the identity matrix:
(AB)(A⁻¹B⁻¹) = A(BA⁻¹)B⁻¹ (associative property of matrix multiplication)
Since B and A^-1 are inverses of each other, their product equals the identity matrix:

A(BA⁻¹)B⁻¹= AI B⁻¹(where I is the identity matrix)
Multiplying A and I doesn't change A:
AI B⁻¹= A B⁻¹
Now, A and B⁻¹are inverses of each other as well, so their product also equals the identity matrix:
A B⁻¹= I
Thus, A⁻¹B⁻¹ is indeed the inverse of AB, as the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix.

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Answer:

Clarify first which one you want to be solved. a or b?

Answer:

uwu

Step-by-step explanation:

Stan enhypen

for better future, follow me

\(\qquad\) ☀️So First – we have to find the perimeter of the frame on which the glue is applied and the length of the ribbon used by Miguel. The perimeter of the frame is the total length of ribbon Miguel uses.

\(\qquad\)____________________

According to the question:-

\(\qquad\)\( \pink{\bf\longrightarrow Perimeter _{(The \:frame) }= The\: total\: length\: of \:ribbon}\)

\(\qquad\)\( \purple{\bf \longrightarrow Perimeter _{(The \:frame) } = 2 ( length\: of\: the \:frame + breadth \:of \:the\: frame )}\)

\(\qquad\)\( \sf \longrightarrow Perimeter _{(The\: frame) } = 2 ( 5 + 8 ) \)

\(\qquad\)\( \sf \longrightarrow Perimeter _{(The \:frame) }= 2 ( 5 ) + 2 ( 8 ) \)

\(\qquad\)\( \sf \longrightarrow Perimeter _{(The\: frame) }= 10 + 16 \)

\(\qquad\)\( \purple{\bf \longrightarrow Perimeter _{(The \:frame) }= 26\: inch} \)

Therefore,

\(\qquad\)____________________

The Answer will be 26 inch

In Mary Shelley's "Frankenstein," there are many instances where the creature expresses his despair and loneliness. However, one detail that particularly highlights his despair is when he says, "I am alone and miserable; man will not associate with me; but one as deformed and horrible as myself would not deny herself to me."

This quote shows how the creature feels completely isolated and rejected by humanity. He longs for companionship and acceptance, but he is unable to find it because of his appearance. The fact that he even mentions that someone as deformed as himself would not deny him shows how desperate and hopeless he feels about ever finding companionship. This quote emphasizes the creature's deep sense of despair and loneliness that he experiences throughout the novel.

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Answer:

median=mode

Step-by-step explanation: