Question 4 of 10 What is the scale factor from ABC to DEF? A BO 72 42 35 65 B 66 O A. 2 OB. O O D. 6 Ico​

1) Let's set the system of linear equations:

x +2y -3z = a

-x -y +z = b

2x +3y -2z =c

2) Since the solution has already been given ( -1,2,-3) all that's left to do, is to plug it into each equation so that we can find a, b and c. Just like this:

x +2y - 3z = a ⇒ (-1) +2(2) -3(-3) = a ∴ a = 4

-x -y +z = b ⇒ -(-1) -(2) +(-3) = b ∴ b = 0

2x +3y -2z =c ⇒ 2(-1) +3(2) -2 (-3)=c ∴ c = -2

3) Hence, a = 4 b = 0 and c = -2

8 - 5(3 + 2x)

open the parenthesis

8 - 15 - 10x

-7 -10x

Given the following ingredients

Cups of flour = 14 1/8 = 113/8 cups

Cups of sugar = 6 3/8 cups = 51/8 cups

Cups of salts = 3/8 cups

Calculate the total cups of dry ingredients

Find the LCM

Therefore there are 19 15/8 cups of dry ingredients in this recipe

Answer: 3 times more

Step-by-step explanation:

In questions 16, 17 and 18 we have a right triangle and in the three cases you know the measues for 2 sides, except for hipotenuse.

We can use the following relation to solve the problem:

16)

17)

18)

Answer:

f

Step-by-step explanation:

For this problem we were given the distance to the moon and the width of a quarter in meters. We need to determine how many quarters we would need to stack in order to reach the moon.

In order to solve this problem, we need to divide the distance from the surface of the Earth to the moon by the width of each quarter. Notice that both numbers are presented in scientific notations, therefore we need to divide the coefficients and subtract the exponents. This is done below:

If Fin's claim were true, he'd need to stack a total of 2.2*10^11 quarters.

Answer:

The Answer is A

Step-by-step explanation: Edge

In a line plot the maximum value is the rightmost mark in the line plot; in this case the maximum capacity is 2 1/2. On the other hand the minimum value is the leftmost mark in the line plot, here the minimum is 1 1/2. Let's calculate the difference between them:

Therefore, the difference between the maxiimum and minimum capacity is 1.

Answer: 120

Step-by-step explanation:

All angles in a triangle add up to 180. The third angle in the triangle is 60. A straight line is always 180, and line TU intersects it. So, subtract 60 from 180 and you get 120.

Answer:

120 degrees

Step-by-step explanation:

70 + 50 = 120 (exterior angle of a triangle)

Given:

Find-: 12th term of the sequence is

Sol:

Where,

Put the value then:

So 12th term is -63

Answer:

-63

Step-by-step explanation:

The balance in the account after years of compound interest arrangement can be represented by the equation; Balance = 1,000 (1.03)^n.

It follows from the task content that the equation which represents the balance in the account after years is required to be determined.

It follows that the principal amount is; $1,000 while the interest rate is; 3%.

This indicates that after each year, the new balance is 103% of the preceding balance.

Hence, the exponential equation which correctly represents the balance at any point in time is;

Balance = 1,000 (1.03)^n.

Where n = number of years after.

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Here, we want to get the measure of the angle marked A

We are going to use the sides given

The trigonometric ratio that links the adjacent to the hypotenuse is the cosine

The cosine is the ratio of the adjacent to the hypotenuse

Mathematically;

we have that

Answer: B.

Step-by-step explanation: A function relates an input to an output.

The relation which is a function is: function 1.

Option A is correct.

A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).

A relation is a function when each input have only one output.

Function 1 have one output to each corresponding output.

Function 2 have two output for input x= 2.

Function 3 have two output for input x= 3.

Function 4 have two output for input x= 1.

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11 is the greatest number of bags that Jason can fill with equal number of raspberry and blackberry scones.

In this question we have been given Jason has 22 raspberry scones and 55 blackberry scones.

We need to find the maximum number of bags Jason can fill with equal number of raspberry scones and blackberry scones.

We will be using Greatest common factor (GCF) for knowing the number of bags.

22 = 2 × 11

and 55 = 5 × 11

So, the greatest common factor of 22 and 55 is 11

GCF(22, 55) = 11

Therefore, 11 is the greatest number of bags that Jason can fill with equal number of raspberry and blackberry scones.

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The number of graduates in the sample that came from University A is:

35 + 90 + 35 = 160 graduates

We want to proof for this case if there is enough evidence to conclude that the New York police are racially biased in terms of force

From the info given is possible to see that the proportion with High level of force used is higher for Black people compared to White people. A difference of 6.3-5.8% = 0.5%.

In the other hand, we can see that for the Hands up force level, there is a significant difference between the two proportions, higher for Black compared to White with a difference of 15.1-9.7%= 5.4%

And finally when we analyze the case for No force used, we can see that there is a higher percentage for White (84.4%) compared to Black (78.7%) with a difference of 5.7%.

Based on this results we can conclude that in general the New York police is partially biased since is possible to see that for any level of force used the records are in favor of the White people.

we know that

The reciprocal of a number is: 1 divided by the number

If you multiply a number by the reciprocal, the result is 1

so

we have

5/7

so

the reciprocal is 7/5

Verify

(5/7)(7/5)=1 -----> is ok

a)There is 160 grams of copper are in the resulting mixture

b) There is 61.5% percentage of the resulting mixture is copper.

What are mathematics operations?

• An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value.

• The operation's arity is determined by the number of operands.

• Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.

• A zero-arity operation, also known as a nullary operation, is a constant.

• The mixed product is an example of an arity 3 operation, also known as a ternary operation

From the question:

a) Suppose that a certain alloy is made by mixing 70 grams of an alloy that contains 12% copper with 90 grams of pure copper.

The number of grams of copper in the resulting mixture = 70 grams + 90 grams = 160 grams

b)  70 grams of an alloy that contains 12% copper = 70 × 12%

= 70 grams × 0.12

= 8.4 grams

The number of grams of copper in the resulting mixture = 160 grams

The percentage of the resulting mixture that is copper is

=( 8.4 grams + 90 grams of pure copper/160) × 100

= 98.4/160 × 100

= 61.5%

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Answer:

1 is the answer

Step-by-step explanation:

a-b+c       Substitute values into the equation

4-2+(-1)

2+(-1)

2-1

1 Answer

The value of: 1) a - b + c is, 1 is the solution.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

a=4 b=2 and C=-1

now,

a-b+c      

Substitute values into the equation

we get,

4-2+(-1)

=2+(-1)

=2-1

=1  (Answer)

Hence, The value of: 1) a - b + c is, 1 is the solution.

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The figure's perimeter and area would be as follows.

Perimeter = 21.19 cm

Area = 25.501 cm²

A Cartesian coordinate system in some kind of a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates, which are the signed distances from two fixed perpendicular lines that are aligned to the point and are both measured in the same length.

point of the coordinates are as follows:

A(2, 1)

B(8, 6).

C(10, 1)

We know that the formula for finding for the distance is:

d=√((x2 – x1)² + (y2 – y1)²).

For Point AB:

X₁ = 2

Y₁ = 1

X₂ = 8

Y₂ = 6

putting the values onto formula we get:

d=√((x2 – x1)² + (y2 – y1)²).

d=√((8 – 2)² + (6 – 1)²).

d=√((6)² + (5)²).

d=√(36 + 25).

d=√(61).

AB =7.81

For Point BC:

X₁ = 8

Y₁ = 6

X₂ = 10

Y₂ = 1

putting the values onto formula we get:

d=√((x2 – x1)² + (y2 – y1)²).

d=√((10 – 8)² + (1 – 6)²).

d=√((2)² + (-5)²).

d=√(4 + 25).

d=√(29).

BC = 5.38

For Point CA:

X₁ = 10

Y₁ = 1

X₂ = 2

Y₂ = 1

putting the values onto formula we get:

d=√((x2 – x1)² + (y2 – y1)²).

d=√((2 – 10)² + (1 – 1)²).

d=√((-8)² + (0)²).

d=√(64 + 0).

CA = 8

The perimeter of the given figure is:

Sum of all the sides.

AB + BC + CA

7.81 + 5.38 + 8

21.19 cm

Now finding the area of the tringle we use Pythagoras formula:

H² = P² + B²

P² = H²  - B²

P² = (7.81)²  - (5.38)²

P = 9.4837

We know that the area of the triangle is: = 1/2(base * Hight).

                                                                    = 1/2(5.38  * 9.48)

                                                                    = 25.501 cm²

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Answer:

Step-by-step explanation:

-2f

We want to find the following probability:

where X is a normal random variable with mean 13.3 and standard deviation 1.1. To find this probability let's normalize the random variable; to do this we use the z-score given by:

Then, in this case, we have:

Using the standard normal table, we have:

Therefore, the probability of purchasing an item with a lifespan greater than 10 years is 0.9987

The coordinates of the point P lying between AB is found as (7, -2/5).

For the given question;

The two end coordinates are;

(x₁, y₁) = (8, 0)

(x₂, y₂) = (3, -2)

The ratio of the division is;

AP/PB = 1/4

OR

m:n = 1:4

The Formula for finding the coordinates of P for internally crossing is;

x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

Put the values;

x = (mx₂ + nx₁)/(m + n)

x = (1×3 + 4×8)/(1 + 4)

x = (3 + 32)/5

x = 7

Now for y coordinates.

y = (my₂ + ny₁)/(m + n)

y = (1×(-2) + 4×0)/(1 + 4)

y = -2/5

Thus, the coordinates of the point P lying between AB is found as (7, -2/5).

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Consider the phase space that consists of elements of the form (boy, boy, boy, boy), (girl, boy, boy, boy),...,(girl, girl, girl, girl).

There is a total of 2*2*2*2=2^4=16 possible combinations and each of them has the same probability to happen. Only one element is the case we are interested in (girl, girl, girl, girl).

Therefore, the probability of a family having 4 girls is

The answer is false, the probability is 0.0625

The standard form is 6x⁴+5x³-2x-15.

Here the term polynomial is characterized as an expression that is composed of variables, exponents, and constants, that are combined utilizing numerical operations such as subtraction,  addition, division, and multiplication. the standard form of a polynomial is :

P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ +aₙ₋₂xⁿ⁻² + ………………. + a₁x + a₀  

Where aₙ, aₙ₋₁, aₙ₋₂, ……………………, a₁, a₀  are the coefficients of xⁿ, xⁿ⁻¹, xⁿ⁻², ….., x and are to a real number.

The polynomial given to us is (3x² + x − 5) (2x² + x + 3)

=3x²(2x² + x + 3) + x (2x² + x + 3) − 5 (2x² + x + 3)

= 6x⁴ + 3x³+9x²+2x³+x²+3x-10x²-5x-15

= 6x⁴+3x³+2x³+9x²+x²-10x²+3x-5x-15

= 6x⁴+5x³-2x-15

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Given:

Total invested amount = $9000

One account = 5%

Another account = 6%

Find-:

Invested amount of each equation

Explanation-:

Let in 5% account invested amount is x

then amount in 6% account is (9000-x)

Then,

Then the value of "x" is:

The "x" is:

The value of x is 3000 the mean amount in 5% invested amount is 3000.

6% invested amount is:

So each account invested amount is:

Solution

Complete the vertical algorithm to evaluate the product:

Therefore the product of the expression is

Given:

Adrian initially has $52,000 and n denotes the number of years

Required:

Adrian's annual income, /(7), as a function of

the year?

Explanation:

Initially has $52,000, therefore

The salary is 1.05 times the previous year's salary.

Required answer:

Option D