If 4x + 3y = 5 is a true equation, what would be the value of 4(4x + 3y)? ​

Using the translation vector of 3 units up and 1 unit right resulted to image coordinate of

(3, 7)

(3, 5)

(2, 5)

The image is attached

The translation vector is of the rule 3 units up and 1 unit to the right

The coordinate of the preimage are

(2, 4)

(2, 2)

(1, 2)

The translation is done as below

(2 + 1, 4 + 3) = (3, 7)

(2 + 1, 2 + 3) = (3, 5)

(1 + 1, 2 + 3) = (2, 5)

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Answer:

- The probability that a bolt is too large for its nut = 0.00621

- The image of the drawing of this combined distribution is shown in the attached file to this solution.

Step-by-step explanation:

When independent, normal distributions are combined, the combined mean and combined variance are given through the relation

Combined mean = Σ λᵢμᵢ

(summing all of the distributions in the manner that they are combined)

Combined variance = Σ λᵢ²σᵢ²

(summing all of the distributions in the manner that they are combined)

For this question, the first distribution is the size of a nut, with mean 10 mm and a variance of 0.02

Second distribution is the size of a bolt, with mean 9.5 mm and a variance of 0.02.

The combined distribution is [size of nut − size of bolt]

Hence, λ₁ = 1, λ₂ = -1

μ₁ = 10 mm

μ₂ = 9.5 mm

σ₁² = 0.02

σ₂² = 0.02

Combined Mean = (1×10) + (-1×9.5) = 0.5 mm

Combined Variance = [(1)² × 0.02] + [(-1)² × 0.02] = 0.04

So, the combined distribution is also a normal distribution with a Mean of 0.5 mm and a variance of 0.04.

Standard deviation = √variance = √0.04 = 0.2 mm

The probability that a bolt is too large for its nut, [size of nut − size of bolt] ≤ 0, P(X ≤ 0)

To obtain this required probability, we first normalize/standardize 0 mm

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (0 - 0.5)/0.2 = - 2.50

To determine the required probability

P(x ≤ 0) = P(z ≤ -2.50)

We'll use data from the normal probability table for these probabilities

P(x ≤ 0) = P(z ≤ -2.50) = 0.00621

The image of the drawing of this combined distribution is shown in the attached file to this solution.

Hope this Helps!!!

Answer:

2

Step-by-step explanation:

Answer:

x = 2 and y =16

Step-by-step explanation:

Method 1

Rewrite  -2x + y = 12  to make y the subject:

Add 2x to both sides:   y = 12 + 2x

Now substitute  y = 12 + 2x   into   7x - 7y = -49x and solve for x:

                                             7x - 7(12 + 2x) = -49x

Multiply out the brackets:     7x - 84 - 14x = -49x

Collect like terms:                 7x - 14x - 84 = -49x

Combine like terms:                     -7x - 84 = -49x

Add 7x to both sides:                          -84 = -42x

Divide both sides by -42:                         2 = x

Therefore, x = 2

Now we have found the value of x, substitute this into  y = 12 + 2x  to find y:

y = 12 + (2 x 2)

 = 12 + 4

 = 16

Therefore, x = 2 and y =16

Method 2

Rewrite  -2x + y = 12  to make y the subject:

Add 2x to both sides:   y = 12 + 2x

Rewrite  7x - 7y = -49x  to make y the subject:

Subtract 7x from both sides:   -7y = -56x

Divide both sides by -7:              y = 8x

Equate both equations and solve for x:

                                                            y = y

                                                   12 + 2x = 8x

Subtract 2x from both sides:             12 = 6x  

Divide both sides by 6:                       2 = x

Therefore, x = 2

Now substitute x = 2 into any of the two equations to find y:

y = 8x

y = 8 x 2

y = 16

Therefore, x = 2 and y = 16

Answer:

Step-by-step explanation:

a). Given expression in the question is,

   \(\frac{13822\times 623}{14}\)

   Exact value of the expression will be,

   \(\frac{13822\times 623}{14}=615079\)

b). By using approximations to 1 significant figure,

   13822 ≈ 10000

   623 ≈ 600

   14 ≈ 10

   615079 ≈ 60000

   Now use the expression,

   \(\frac{13822\times 623}{14}=\frac{10000\times 600}{10}\)

                  = 60000

Answer: 15

Explanation:

The length of the segment is 10 plus 5 which is fifteen because you need to know how long it is. Just ignore the negatives.

Answer:

Triangular prism

Step-by-step explanation:

Answer:9/41

SOH = opposite over hypotenuse

Step-by-step explanation:

Answer

Yes, zero is contained in the interval

Answer:

Amadi: 20 years old

Chima : 4 years old

Answer: 20%

Step-by-step explanation:

If we let the original amount be x, then after increasing it by 25%, we now have 1.25x

To get this back to x, we need to do 1.25x*(something) = x

this gives us that something = 1/1.25 = 0.8

meaning you need to decrease it by 100% - 80% = 20%

Answer:

2, 3

Step-by-step explanation:

When a point is reflected over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. Therefore, if you reflect the point (-2, 3) over the y-axis, it will become (2, 3).

(Sorry, I tried to provide a picture but I could not.)

Answer: assistant A earned a total of $550, assistant earned a total of $225 so in a total they earn a total of $775.

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

6.11/104

Answer: 290 beans

Step-by-step explanation:

You multiply 145 by 2 since 145 is half of the beans or do 145 divided by 1/2.

145 * 2 = 290.

145/.5 = 290

Hope this helps!!! :)

Answer:

6. The equation that models Mekhi's savings account is:

A = P(1 + r/n)^(nt)

Where:

A = the amount of money in the account after t years

P = the initial investment ($15,000 in this case)

r = the annual interest rate (3.25% or 0.0325 as a decimal)

n = the number of times interest is compounded per year (usually 12 for monthly compounding)

t = the number of years

7. To write the equation in slope-intercept form, we need to simplify it:

A = P(1 + r/n)^(nt)

A = $15,000(1 + 0.0325/12)^(12t)

A = $15,000(1.00271)^(12t)

A = $15,000(1.00271)^12 * (1.00271)^t

A = $15,000(1.34685)^(t)

This is in exponential form, so there is no y-intercept or slope.

8. y-value: A, the amount of money in the account after t years

slope: There is no slope in an exponential equation.

9. To find out how much money will be in the savings account after 30 years:

A = $15,000(1.34685)^30

A = $15,000(10.638)

A = $159,570

Therefore, if Mekhi saves $15,000 in a savings account with a 3.25% APR for 30 years, he will have $159,570 when he retires.

10. To find out how many years Mekhi would have to work to retire with $35,000:

$35,000 = $15,000(1.34685)^t

1.34685^t = 35,000/15,000

1.34685^t = 2.3333

t = log(2.3333) / log(1.34685)

t = 9.93

Therefore, Mekhi would need to work for approximately 9.93 years (or about 10 years) to retire with $35,000, assuming he does not make any other contributions to his savings account.

The total surface area of the tomato ketchup given in the diagram can be determined as follows:

The total surface area of a shape is the addition of the areas of its individual surface.

So that the questions can be answered as thus:

A. To find the area of the given circle;

i. Area of a circle = \(\pi r^{2}\)

where r is the radius of the circle.

area of the circle = π\((2.5)^{2}\)

                            = 6.25\(\pi\)

ii. There are two identical circles in the cylinder.

iii. The total area of all circles = 2(6.25\(\pi\))

                                                 = 12.5\(\pi\) square inches

B. To find the area of the rectangle;

i. one side of the rectangle is 5 inches.

ii. The other side of the rectangle = 2\(\pi\)r

                                     = 2(2.5)\(\pi\)

                                     = 5\(\pi\) inches

iii. The area of the rectangle = l x b

                             = 5\(\pi\) x 5

                             = 25\(\pi\) square inches

C. Total surfce area of the cylinder = 5\(\pi\) + 25\(\pi\)

                                         = 30\(\pi\) square inches

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Answer:

Step-by-step explanation:

First box

6.25

2

12.5

------

Second box

------

5

5

25

------

Last box

------

37.5

Answer:

The answer is cos B = 2/3

I hope it will help you :)

Answer:

The equation of line through (-3,1) and slope 2 in slope-intercept form is: y = 2x+7

Step-by-step explanation:

The slope-intercept form of an equation is given by:

\(y = mx+b\)

here m is the slope of the line and b is the y-intercept

Given

\(m = 2\)

Putting m=2 in the general form

\(y = 2x+b\)

In order to find the y-intercept, the given point (-3,1) will be substituted in the equation

So

\(1 = 2(-3)+b\\1 = -6+b\\b = 1+6\\b = 7\)

Putting the value of b

\(y = 2x+7\)

Hence,

The equation of line through (-3,1) and slope 2 in slope-intercept form is: y = 2x+7

A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.

To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.

For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:

150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms

Therefore, 150 pounds is approximately equal to 68.0388 kilograms.

In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.

It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.

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Answer:

UY = 90

GH = 4

Step-by-step explanation:

Given that FGHIJ ~ YUVWX, therefore, their corresponding side lengths would be proportional to each other. Thus:

UY/GF = VW/HI

UY/10 = 63/7 (Substitution)

UY/10 = 9

UY = 10*9

UY = 90

In the same vein, we have:

VW/HI = UV/GH

63/7 = 36/GH (Substitution)

9 = 36/GH

GH*9 = 36

GH = 36/9

GH = 4

The scale factor and the value of x for each figure is given as follows:

A) Scale factor of 1/3, x = 7 m.

B) Scale factor 0.4747, x = 4.5 in.

For Figure A, we have that the ratio between the areas is given as follows:

510/4590 = 1/9.

As the area is measured in square units, while the side lengths are measured in units, the scale factor is the square root of 1/9, hence it is given as follows:

1/3.

Then the value of x is obtained as follows:

x = 21 x 1/3

x = 7 m.

For Figure B, we have that the ratio between the areas is given as follows:

16/71 = 0.22535.

The scale factor is then the square root of 0.22535, which is given as follows:

0.4747.

Then the value of x is given as follows:

x = 9.5 x 0.4747

x = 4.5 in.

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Answer:

what exactly do i need to do ?????

Step-by-step explanation:

Answer:

(g ◦ f)(x) = g(f(x)) = cos(f(x)) = cos(7x2).

Answer:

he first is a numerical sentence and the second is an equation

Step-by-step explanation:

equation because there's "="

Answer:

OA

Step-by-step explanation:

The graph will move from right to left in ascending order

Answer:

Option B

Explanation:

From the given options:

Thus, the equivalent expression is Option B.