The larget taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. The total weight of thee two ingredient wa 617. 3 kg. How many kilogram of each ingredient were ued?

The interest rate on the loan is approximately 6.0%. Option a

To find the interest rate on the loan, we need to calculate the total amount repaid over the course of the loan and compare it to the amount borrowed.

The total amount repaid can be calculated by multiplying the monthly payment by the number of coupons in the passbook:

Total amount repaid = Monthly payment × Number of coupons

Total amount repaid = $463.27 × 50

Total amount repaid = $23,163.50

The interest paid can be found by subtracting the amount borrowed from the total amount repaid:

Interest paid = Total amount repaid - Amount borrowed

Interest paid = $23,163.50 - $7,302

Interest paid = $15,861.50

Now, we can calculate the interest rate using the formula:

Interest rate = (Interest paid / Amount borrowed) × 100

Interest rate = ($15,861.50 / $7,302) × 100

Interest rate ≈ 217.29%

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The unit rate of $68 dollars for 8 1/2 hour is 8 dollars/hour.

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one.

Now it is given that,

Number of dollars = $68

Number of hours = 8 1/2 hour

Converting hours into improper fraction we get

⇒ Number of hours = 17/2 hour

Thus, unit rate = Number of dollars / Number of hours

⇒ unit rate = 68/( 17/2 ) dollars/hour

⇒ unit rate = 8 dollars/hour

this is the required unit rate.

Thus, the unit rate of $68 dollars for 8 1/2 hour is 8 dollars/hour.

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Answer: The equation for the perpendicular bisector of line segment xy is .

Explanation:

It is given that the line segment xy has endpoints x(5,7) and y(-3,3).

The bisector divides the line segment xy in two equal parts, so the bisector must be passing through the midpoint of xy.

Midpoint of two points (x_1,y_1) and (x_2,y_2) is calculated as,

Midpoint of xy is,

So, the perpendicular bisector must be passing through the point (1,5).

The slope of line passing through the point (x_1,y_1) and (x_2,y_2) is calculated as,

Slope of line segment is . Therefore the slope of perpendicular bisector is -2 because the the product of slopes of two perpendicular lines is always -1.

The line passing through the point (x_1,y_1) with slope m is defined as,

Bisector passing through the point (1,5) with slope 2.

Therefore, the equation for the perpendicular bisector of line segment xy is .

Answer:

12 ×  25 or 12 ×  25  =   1 × 2   =   2

Hello there ☺️,

Please check the attached images of answer for explanation as well as answer.

✍️ By Benjemin ☺️

Answer:

a) 13

b) 1/3

c) -2

d) 1

Step-by-step explanation:

This is quite simple if you look at it from a different perspective. Imagine that when it says "f(2)" That you are plugging the number 2 in for every x on the right side of the equation:

For example:

f(x) = 3x + 7

f(2) = 3(2) + 7

f(2) = 6 + 7

f(2) = 13

________

f(-3) = 3x + 7

f(-3) = 3(-3) + 7

f(-3) = -9 + 7

f(-3) = 7 - 9 (This is just for those that hate negative values. You can rearrange the values as long as their sign is the same when you do move them. Ex: -14 + 6 - 4 + 9 == 9 + 6 - 14 - 4. I hope that makes sense.

f(-3) = -2

The other way is quite simple as well, if you look at it from a different perspective. Imagine that when it says "f(x) = 8" that you are changing the f(x) to the number 8:

For example:

f(x) = 8

f(x) = 3x + 7

8 = 3x + 7

8 - 7 = 3x

1 = 3x

x = 1/3

f(x)= 10

f(x) = 3x + 7

10 = 3x + 7

10 - 7 = 3x

3 = 3x

3/3 = x

1 = x

I hope this helps!

\((poq)^(-1)(U) = q^(-1)(p^(-1)(U)) = q^(-1)(A)\)is open in X. This shows that poq is a quotient map with respect to the topology on B induced by p.

poq is a quotient map, V = poq(p(V)) is open in B. p(V) is open in B, and this shows that p is a quotient map with respect to the topology on B that turns poq into a quotient map.

Let X be a topological space. Let q: X→ A be a quotient map and let p: A → B be a surjection onto the set B. To show that the topology that turns p into a quotient map is the same as the topology that turns poq into a quotient map, we need to prove that:

(i) The function poq is a quotient map with respect to the topology on B induced by p.

(ii) The function p is a quotient map with respect to the topology on B that turns poq into a quotient map.

1. Let U be an open subset of B. Then, since p is a surjection, we can write U = p(A) for some subset A of A. Since q is a quotient map, \(q^(-1)(A)\)is open in X.

2. Let V be an open subset of B that turns poq into a quotient map. Then, we need to show that p(V) is open in B.

Let\(U = q^(-1)(p(V))\). Since q is a quotient map, U is open in X.

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Answer:

Cone Volume = (PI * radius^2 * height) / 3

96 cc = (PI * radius^2 * 14) / 3

(96 * 3) / (PI * 14) = radius^2

radius ^ 2 = 6.5480890872

radius = 2.5589234235

diameter = radius *2 = 5.117846847  cm

diameter = 5.12 cm (rounded)

Step-by-step explanation:

Answer:

<1 and <2 - Corresponding angles

6 and <1, -Aternative exterior angles

<5 and <6-Corrosponding Angles

Answer:

Area = 5 × 8

= 40 square units

Answer:

40^2

Step by Step Solution:

I counted the difference between the length and the width, which was 5 and 8, then using the formula for area, lw=a^2, I did 5(8)=40^2.  Some people leave out the squared part of the area, but 40^2 would be the most correct option if they do not square any of the answers, just put 40 that'll probably be accepted too.

If A is a symmetric matrix, then A³ is also a symmetric matrix.

To prove this, we can use the definition of a symmetric matrix, which is a matrix that is equal to its transpose. In other words, if A is a symmetric matrix, then A = A^T.

Now, let's look at A³:

A³ = A * A * A

We can replace each A with A^T, since they are equal:

A³ = A^T * A^T * A^T

Now, we can use the property that the transpose of a product of matrices is equal to the product of their transposes in reverse order:

A³ = (A^T * A^T * A^T)^T

A³ = (A^T)^T * (A^T)^T * (A^T)^T

Since the transpose of a transpose is the original matrix, we can simplify:

A³ = A * A * A

Therefore, A³ is also a symmetric matrix.

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There will  total of 987 outcomes involving at least 8 heads when a coin is tossed ten times

We will be using the formula of combination for calculating the outcomes. Since we have tossed a coin 10 times , so total number of possible outcomes: 2¹⁰ = 1024 .Since at least 8 heads means we will get tail, exactly after two tosses exactly. we will find the outcomes for no head, one head, and 2 head .So, the number of outcomes involving will be 8 heads :

= 1024 - ⁸C₀ ( + ⁸C₁ + ⁸C₂ )

= 1024 - ( 1+8+28) = 1024 - 37

= 987

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Answer:

not similar

Step-by-step explanation:

hope it help

Answer: 38

Step-by-step explanation: (129-15) ÷ 3

The time required for the first unit is "x" hours, the time required for the eighth unit is "x + 35" hours, and the total amount of time required for building the eight units is "8x + 140" hours.

To determine the approximate amount of time required for building the remaining bikes, we need to consider the time spent on the first and second bikes as well as the number of remaining bikes. Let's denote the time required for building the first bike as "x" hours and the time required for building the second bike as "5" hours.

(a) To find the approximate time required for building the first unit, we already know that "x" hours spent on it.

(b) For the eighth unit, we can observe that a pattern is emerging. The time required for each unit is increasing by 5 hours. Therefore, for the eighth unit, we can calculate the time as follows:

Time for the eighth unit = Time for the first unit + (7 * 5) hours = x + 35 hours.

(c) To find the total amount of time required for building the eight units, we need to sum up the time required for each unit. Since each subsequent unit takes 5 hours longer than the previous one, we can use the arithmetic series formula to calculate the sum:

Total time for eight units = (Number of units / 2) * (Time for the first unit + Time for the last unit)

                            = (8 / 2) * (x + (x + 35))

                            = 4 * (2x + 35)

                            = 8x + 140 hours.

In summary, the time required for the first unit is "x" hours, the time required for the eighth unit is "x + 35" hours, and the total amount of time required for building the eight units is "8x + 140" hours.

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Using SAS, property of triangle congruency, ΔRTV ≅ ΔRTS.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.

The five congruent triangle theorems are therefore SSS, SAS, AAS, HL, and ASA.

Given,

Two triangles,

ΔRTV and ΔRTS,

RT = RT                                      (Side)    [Common side]

∠RTV = ∠RTS                            (Angle)    [Both are 90°]

VT = TS                                      (Side)   [As T is the mid - point of VS ]

Using SAS, property of triangle congruency,

ΔRTV ≅ ΔRTS

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Answer:

Step-by-step explanation:

1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Answer:

Step-by-step explanation:

The correct answer To find the orthogonal trajectories is (a) x² + y² = C ln |x|.

To find the orthogonal trajectories of a family of curves, we need to find a differential equation that satisfies the condition that the slopes of the curves and their orthogonal trajectories are negative reciprocals of each other.

The family of curves given is ellipses with centers at (0,0) and vertices at (1,0) and (-1,0). The equation of an ellipse with these characteristics is:

x²/a² + y²/b² = 1

where a is the distance from the center to one of the vertices along the x-axis, and b is the distance from the center to the corresponding point on the ellipse along the y-axis.

In this case, a = 1, and b = 0 since the vertices are located on the x-axis.

Substituting these values into the equation, we get:

x²/1² + y²/0² = 1

x² + y²/0 = 1

Since b is 0, the equation becomes x² = 1, which represents two vertical lines passing through (1,0) and (-1,0).

The slopes of these lines are undefined (vertical lines), so their orthogonal trajectories will be horizontal lines. The equation of a horizontal line is y = C, where C is a constant.

Therefore, the orthogonal trajectories of the family of ellipses with centers at (0,0) and vertices at (1,0) and (-1,0) are horizontal lines of the form y = C.

Among the given choices, the only option that represents a horizontal line is:

a. x² + y² = C ln |x|

Therefore, the correct answer is (a) x² + y² = C ln |x|.

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The probability of selecting a green baseball cap from the order of 64 caps is 0.25 or 25%.

To calculate the probability of selecting a green baseball cap from the order of 64 caps, we can use the concept of probability.

Given:

Total number of caps (n) = 64

Number of green caps (k) = 16

The probability (P) of selecting a green cap can be calculated as the ratio of the number of green caps to the total number of caps:

P(green cap) = k / n

Substituting the values:

P(green cap) = 16 / 64

P(green cap) = 0.25

Therefore, the probability of selecting a green baseball cap from the order of 64 caps is 0.25 or 25%.

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Trapezium

parallel sides = 18 cm, 12cm

Height = 8cm

Area of trapezium =

\( \frac{1}{2} \times (a + b) \times h\)

\( \frac{1}{2} \times (a + b) \times h\)

\( \frac{1}{2} \times (18 + 12) \times 8\)

\( \frac{1}{2} \times (30) \times 8\)

\( \frac{1}{1} \times (15) \times8\)

\(120 \: cm ^{2} \)

Therefore, Area of trapezium is \(120 \: cm {}^{2} \)

Answer:

Area of Trapezium = 120 cm³

Step-by-step explanation:

Trapezium = 1/2 * (a+b) * h [Formulae]

A & b = Sum of parallel sides

Given that,

Solved:

Therefore,the area of trapezium is 120 sq. cm or 120 cm².

The eigenvector of A⁶ is v and the associated eigenvalue is λ⁶ as A⁶ , eigenvector of A⁻¹ is v with associated eigenvalue λ⁻¹, eigenvector of 6A is v with associated eigenvalue 6λ.

Given that A is an invertible n × n matrix and v ― is an eigenvector of A with an associated eigenvalue -3. Let's find the eigenvalues of the following matrices:

(i) A⁶, (ii) A⁻¹, (iii) 6A.

For a matrix A, an eigenvector of A is a non-zero vector v such that

A v = λ v,

where λ is a scalar. This scalar is known as the eigenvalue associated with the eigenvector v.

i) Eigenvalues of A⁶:

Let λ be an eigenvalue of A with an eigenvector v.

Then the eigenvector of A⁶ is v and the associated eigenvalue is λ⁶ as A⁶

v = A.A.A.A.A.A v = A.A.A v.A.A v = A.A v.A.A.A v = A. v.A.A v = λ.A.A.A.A.A v = λ.A.A.A.A v.A.A.A.A.A v = λ⁶ v

Therefore, the eigenvector of A⁶ is v with associated eigenvalue λ⁶.

ii) Eigenvalues of A⁻¹:

Let λ be an eigenvalue of A with an eigenvector v.

Then the eigenvector of A⁻¹ is v and the associated eigenvalue is λ⁻¹ as A⁻¹ v = λ⁻¹. v

Therefore, the eigenvector of A⁻¹ is v with associated eigenvalue λ⁻¹.

iii) Eigenvalues of 6A:

Let λ be an eigenvalue of A with an eigenvector v.

Then the eigenvector of 6A is v and the associated eigenvalue is 6λ as 6A v = 6. λ. v = (6λ) v

Therefore, the eigenvector of 6A is v with associated eigenvalue 6λ.

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Expressing y in terms of x is as follows:

y = 25x

They wanted to cut exactly 160 meters of wire from a huge spool. They mistakenly measured mass instead of the length.

x = length of wire in meters

y = weight of wire in grams

Therefore, using proportion

Proportional relationship express values in ratios .Therefore,

3 meters wire = 75 grams of wire

x meters = y grams

cross multiply

75x = 3y

let's express y in terms of x as required

Therefore,

divide both sides by 3

y = 75x / 3

y = 25x

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Answer:

15

Step-by-step explanation:

because 35 divided by 5 is 7 and 15 divided by 15 is 3 making 7:3

hope it helps

The conditional expectation E[Y|X=2] is 11, and the variance of Y, var(Y), is 24, given the linear relationship Y = 15 - 2X and a variance of 6 for X.

The conditional expectation E[Y|X=2] represents the expected value of Y when X takes on the value 2.

Given the linear relationship Y = 15 - 2X, we can substitute X = 2 into the equation to find Y:

Y = 15 - 2(2) = 15 - 4 = 11

Therefore, the conditional expectation E[ Y|X=2] is equal to 11.

To calculate the variance of Y, var(Y), we can use the property that if X and Y are linearly related, then var(Y) = b^2 * var(X), where b is the coefficient of X in the linear relationship.

In this case, b = -2, and the variance of X is given as 6.

var(Y) = (-2)^2 * 6 = 4 * 6 = 24

Therefore, the variance of Y, var(Y), is equal to 24.

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Answer:

y=-4/3x-3

Step-by-step explanation:

The equation of the line that passes through the given point will be equal to (-4/3)x - 3.

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the given information in the question,

The given equation is,

4x + 3y = 15

And the point is (-3, 1)

3y = 15 - 4x

y = (-4/3)x + 15

The line has a slope, of -4/3.

Then, use the equation,

B = y - mx

B = 1 - (-4/3 × 3)

B = -3

So,

y = (-4/3)x - 3

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Answer:

C. 8

Step-by-step explanation:

Options

A. 5

B. 6

C. 8

D. Can't say without knowing the number of participants

Number of sweet distributed = Total number of sweets - left over sweets

= 1025 sweets - 1 left over sweet

= 1024 sweets

Number of participants = Number of sweets distributed / number of sweets given to each participant

A. 5

Number of participants = Number of sweets distributed / number of sweets given to each participant

= 1024 /5 Sweets

= 204.8 participant

B. 6

Number of participants = Number of sweets distributed / number of sweets given to each participant

= 1024/6

= 170.67 participant

C. 8

Number of participants = Number of sweets distributed / number of sweets given to each participant

= 1,024/8

= 128 participant

D. Can't say without knowing the number of participants

From the options given, the number of sweets given away to each participant could be 8

Number of sweets given to each participants is 32.

Since, A sports teacher had 1025 sweets and he had one sweet left after distributing.

So, number of sweets he distributing is, \(1025-1=1024\)

Since, distributing these equally amongst all the participants

Therefore, number of sweets given to each participants is, \(=\sqrt{1024}=32\)

So, total number of participants is 32 and number of sweets given to each participants is 32.

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The rate of change is obviously that term that describe the change over a certain period. In this problem, we are given with the condition that LaToya is able to burn 20 calories per minute. Therefore, the rate of change is 20 calories per minute.

\

Answer:B

Step-by-step explanation:20 calories per minute