ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)

A scale has a percent error of 5%. The actual mass of a rock is 30 g.

The scale is likely to show the mass as either;


A: 25 g. or 30 g.

B: 25.5 g. or 30.5 g.

C: 28 g or 31.5 g.

D: 28.5 g. or 31.5 g.

Example: (2x - 4) x=7 so (2x (x=7) - 4) =18

Based on the information, we can infer that the correct answer is 90° clockwise (option A).

To identify the correct rotation of this figure we must perform the following procedure:

1. We must identify the reference figure.

2. We must identify the figure that expresses the rotation.

3. We must identify the angle of rotation of the figure.

4. Select the option that correctly expresses the sense of rotation.

Based on the above, we can infer that the correct answer is A. 90° Clockwise because the rotation is to the right.

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Answer: 626 yd^2

Step-by-step explanation: First you need to split the figure into 2 rectangular prisms (see attached image). The tallest rectangular prism has a length of 12 yd, a width of 3 yd, and a height of 11 yd. The shorter one has a length of 12yd, a width of 4 yd, and a height of 4 yd. The surface area equation is SA=2(wl+hl+hw). First solve for the taller rectangular prism. SA=2(3x12+11x12+11x3). SA=2(36+132+33). SA=2(201). SA=402 yd^2. Now solve for the smaller rectangular prism. SA=2(4x12+4x12+4x4). SA=2(48+48+16). SA=2(112). SA=224 yd^2. Lastly, add both values together. 402+224=626 yd^2.

The integer number that represents the situation running up 24 steps is given as follows:

+24.

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

For altitudes, the signs are given as follows:

In this problem, we have an increase of altitude of 24 steps, hence the integer number is given as follows:

+24.

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The standard deviation of the random variable x is 1.1145

Since the Probability distribution of a random variable is the collection of value and its probability pair for values of that considered random variable.

The probability of a value of x is never neg.

The sum of the probabilities is always 1.

The sum of all values of P(X = x) equals 1, which is, considering n values

There are no negative values of P(X = x).

Since we are given the probability distribution as below, we will go and calculate the mean and standard deviation using the formula:

E(X)= ∑xP(X=x)

Standard deviation = √Variance(x)

Var(x) = E(x²) - [E(x)]²

X           0          1            2        3        4          5

p(x=x)   0.032   0.152   0.316  0.316  0.152  0.032

First we have to find E(x)

E(x) = (0x0.032) + (1x0.152) + (2x0.316) + (3x0.316) + (0.152) + (5x0.032)

The mean E(x) = 2.5

To find variance, we use Var(x) = E(x²) - [E(x)]²

But we have to calculate E(x²) first, since we already have found E(x)

So,

E(x²) = (0²x0.032) + (1²x0.152) + (2²x0.316) + (3²x0.316) + (4²x0.152) + (5²x0.032)

therefore, E(x²) = 7.492

Now we have all the values we can find the variance:

Var(x) = E(x²) - [E(x)]²

=7.492 - [2.5]²

= 1.242

With variance now we can find the standard deviation;

S.D = √Var(x)

= √1.242

= 1.1145

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Answer:

y = 5x + 11

Step-by-step explanation:

Step 1:  When two lines are parallel, they have the same slope, as indicated by the following equation as m2 = m1, where

Thus, since the slope of line 1 is 5, the slope of line 2 is also 5.

Step 2:  Now we can plug in (-2, 1) for x and y and 5 for m to solve for b, the y-intercept of the other line:

1 = 5(-2) + b

1 = -10 + b

11 = b

Thus, the equation of the line parallel to y = 5x + 2 and passing through (-2, 1) is y = 5x + 11

The quadratic equation with the given roots is:

y = 0.5x² + 1.5x - 5

For a quadratic equation with a leading coefficient a, and roots:

x = h and x = k, we will get general formula:

y = a*(x - h)*(x - k)

Here we know that the roots are x = 2 and x = -5, replacing that we will get:

y = a*(x - 2)*(x + 5)

And we know that this quadratic passes through (1, -3), replacing these values:

-3 = a*(1 - 2)*(1 + 5)

-3 = a*(-1)*(6)

-3 = -6a

-3/-6 = a

0.5 = a

Replacing that:

y = 0.5*(x - 2)*(x + 5)

Expanding the quadratic we will get:

y = 0.5x² + 1.5x - 5

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Answer: x=15.6

Step-by-step explanation:

An isosceles triangle has two congruent sides. (1 pair). So, the other side (not x) must equal 11.

Using the Pythagorean Theorem; a^2+b^2=c^2, you can substitute the values in as follows

11^1+11^2=x^2

121+121=x^2

242=x^2

15.55634918610405=x

round to the nearest tenth as said in the question...

x=15.6

Answer:

The equation that models the relationship between the time x (in minutes) and the distance y (in feet) from the ground is:

y = 2000x

This is because for every 2 minutes that go by (i.e. for every increase of x by 1), the balloon rises by 2000ft (i.e. a constant rate of change). So, the equation y = 2000x represents a straight line with a slope (rate of change) of 2000, passing through the origin.

The identification of the polygon that are given in the diagram above would be =

Polygon 1 = Isosceles trapezoid

polygon 2 = parallelogram

polygon 3 = Rectangle

polygon 4 = Rhombus

polygon 5 = Square

polygon 6 = trapezoid

Isosceles trapezoid : This is the type that of polygon in which the the top and base are not equal in length, but they are parallel to each other.

Parallelogram : This is defined as the type of polygon that has two pairs of parallel sides.

Rectangle : This has two pairs of sides that are equal and opposite.

Rhombus: All the sides are equal in length with its opposite angles equal .

Square: All sides are equal in length but and all angles are equal to 90°.

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If Ivy had given 3 more people bonuses, Ivy would have rewarded 13 of the workforce, Ivy Corporation's workforce has 592 employees.

Let's assume that the total workforce at Ivy Corporation is represented by "x".

According to the problem statement, Ivy Corporation gave a bonus to 74 people. Therefore, the remaining non-bonus-receiving employees would be (x-74).

If Ivy had given 3 more people bonuses, then the number of employees that would receive the bonus would be (74+3)=77.

According to the problem, 77 is equal to 13% of the total workforce (x):

77 = 0.13x

We can solve for x by dividing both sides by 0.13:

x = 592

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The 10,100 cards will be necessary to build a 100-story card tower.

To build a 100-story card tower, we can use the triangular number formula to calculate the total number of cards needed. The formula is:

Triangular number = (n * (n + 1)) / 2

In this case, n represents the number of stories in the tower (100). Plug in the value for n:

Triangular number = (100 * (100 + 1)) / 2
Triangular number = (100 * 101) / 2
Triangular number = 10,100 / 2
Triangular number = 5,050

Additionally, each story requires two cards, so we multiply the triangular number by 2 to get the total number of cards:

Total cards = 5,050 * 2
Total cards = 10,100

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Answer:

the distance between the cities is 21.75 miles.

Step-by-step explanation:

1 inch = 8.7 miles.

2.5 inches x 8.7 miles/inch = 21.75 miles

Answer:

Step-by-step explanation:

area of a rectangular piece of cloth 3 1/4m by 25 cm

the area of ​​the rectangle is found by making the base by the height, we convert the meters into centimeters

3 1/4 m = 3.25m = 325 cm

we find the area

325 × 25 = 8125 cm² (or 0.8125 m²)

The system of equation of the tables used is 8x + 10y = 124 and x = y + 2

He used 8 round tables and 6 rectangular tables

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

8x + 10y = 124

Where

x = round tables

y = rectangular tables

We understand that

He uses 2 more round tables than rectangular tables

This means that

x = y + 2

So, the system of equations is 8x + 10y = 124 and x = y + 2

The graph of the system is attached, where we have x = 8 and y = 6  

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Answer:

1836.50 square inches of the bulletin board is NOT covered with art work.

Step-by-step explanation:

The question focuses on the area covered by the paintings and the board, since area is defined as:  the amount of space enclosed within the boundaries of a flat, two-dimensional shape, such as a square, circle, or rectangle.

Step 1:  First, we need to know the total area of the five paintings.  

A = lw, where

We can allow 8.5 to be the length and 11 to be the width:

A = 8.5 * 11

A = 93.5 square inches

Multiplying 93.5 by 5 shows us the the total area covered by the five pieces of artwork is 467.50 square inches as 93.5 * 5 = 467.50

Step 2:  Now we need to find the area of the bulletin board.

A = s^2, where

48 is s in the area formula:

A = 48^2

A = 2304 square inches

Thus, the area of the bulletin board is 2304 square inches.

Step 3:  Finally, subtracting the total area of the five pieces of artwork from the area of the bulletin board will tell us how much of the bulletin board is NOT covered with art work:

2304 - 467.50 = 1836.50 square inches

Thus, 1836.50 square inches of the bulletin board is not covered with art work.

The measure of an interior angle is 140°.

The number of sides that this polygon has is 9 sides.

In Mathematics and Geometry, the measure of the sum of the angles of a convex quadrilateral, pentagon, and a nonagon is equal to 360 degrees. This ultimately implies that, the sum of all the exterior angles of a regular polygon must add up to 360 degrees.

Mathematically, the exterior angle of a regular polygon can be calculated by using this mathematical equation:

Exterior angle = 360/number of sides

40 = 360/number of sides

Number of sides = 360/40

Number of sides = 9 sides.

Additionally, the measure of each interior angle of a regular polygon can be calculated by using this mathematical equation:

Interior angles = [180 × (n - 2)]/n

Interior angles = [180 × (9 - 2)]/9

Interior angles = 1,260/9

Interior angles = 140°

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Answer:

x+3x-4=2x+x+5

Step-by-step explanation:

=4x-4= 3x+5

=4x-3x=5+4

= x=9. Done

The percentage is given by the expression A = ( 7.2 % ) ( 8650.00 ) and the value of A = $ 622.80

Given data ,

Let the initial amount be represented as P

Now , the value of P is

P = $ 8,650.00

On simplifying the equation , we get

Let the percentage value be d = 7.2 %

On simplifying the percentage , we get d = 0.072

So , A = 0.072 ( 8,650.00 )

Multiplying the expression , we get

A = $ 622.80

Therefore , the value of A is A = $ 622.80

Hence , the expression is A = $ 622.80

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Answer:

Step-by-step explanation:

To determine the value of t if the three points A(7, 4), B(-1, -2), and C(3t, 5-4t) are collinear, we can use the concept of slope. If the points are collinear, the slopes between any two pairs of points should be equal.

The slope between points A and B is given by:

m₁ = (y₂ - y₁) / (x₂ - x₁)

= (-2 - 4) / (-1 - 7)

= (-6) / (-8)

= 3/4

Now, let's calculate the slope between points B and C:

m₂ = (y₂ - y₁) / (x₂ - x₁)

= (5 - (-2)) / (3t - (-1))

= (7) / (3t + 1)

Since the points are collinear, the slopes m₁ and m₂ should be equal. Therefore, we can set up the equation:

3/4 = 7 / (3t + 1)

To solve for t, we can cross-multiply and solve the resulting equation:

4(7) = 3(3t + 1)

28 = 9t + 3

25 = 9t

t = 25 / 9

Therefore, the value of t that makes the points A(7, 4), B(-1, -2), and C(3t, 5-4t) collinear is t = 25/9.

Answer:

6/7

Step-by-step explanation:

If the three points are collinear, then the slope of the line passing through any two of the points should be the same as the slope of the line passing through the other two points.

Let's find the slope of the line passing through points A and B:

slope AB = (y2-y1)/(x2-x1)

= (-2-4)/(-1-7)

= -6/-8

= 3/4

Now let's find the slope of the line passing through points B and C:

slope BC = (y2-y1)/(x2-x1)

= (5-4t-(-2))/(3t-(-1))

= (7-4t)/(3t+1)

Since the three points are collinear, slope AB = slope BC:

3/4 = (7-4t)/(3t+1)

Cross-multiplying and simplifying:

12t + 4 = 28-16t

28t = 24

t = 24/28

t = 6/7

Therefore, the value of t is 6/7 if the three points A, B, and C are collinear.

Both containers hold the same amount of water.

Given are two solid figures, we need to compare which of them holds more water,

The container one has a base dimension of 3 ft × 180 in with height 90 in. and the second container has base dimension of 3 ft × 180 in with height 90 in.

To compare which container holds more water, we can calculate the volume of each container.

For consistency, let's convert all measurements to a single unit.

1 foot is equal to 12 inches, so the base dimensions of both containers can be expressed as

3 ft × (180 in + 3 ft × 12 in/ft) = 3 ft × 216 in

= 648 in × 648 in.

The volume of a container is calculated by multiplying the base area by the height.

Therefore, the volume of each container can be determined as follows:

Container 1:

Volume = Base area × Height

Volume = (648 in × 648 in) × 90 in

Container 2:

Volume = Base area × Height

Volume = (648 in × 648 in) × 90 in

Since the base dimensions and the height are identical for both containers, their volumes will also be the same.

Therefore, both containers hold the same amount of water.

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Correct form of the area of compound shape is:

Given,

Compound shape including triangle and rectangle.

Firstly , calculate the area of rectangle:

Area of rectangle = l* b

l= length of rectangle

b =  breadth of rectangle

Thus,

Area of rectangle = 12*m

Secondly, area of triangle,

Area of triangle = 1/2 *b * h

b = base of triangle

h = height of triangle

Base of triangle = 12 - n

Then,

Area of triangle = 1/2* (12 - n) *m

Area of triangle = 6m - 0.5mn

Now to calculate the total area of the compound shape,

Total area = Area of rectangle  + Area of triangle

Total area = 12m + (6m - 0.5mn)

Total area = 18m - 0.5mn

Hence option 3 satisfies the area of the compound shape .

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Answer:3rd one

Step-by-step explanation:

Answer:

∆SMK is similar to ∆RMT by AA.

The amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

Recall the compounding formula:

A = P * [tex]e^{rt}[/tex]

Where:

A = Final amount in the account

P = Initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (as a decimal)

t = Time in years

Given:

Initial principal (P) = $16,000

Annual interest rate (r) = 2%  = 0.02

time (t) = 4 years.

Substitute these values into the formula, we get:

A = $16,000 * [tex]e^{0.02 * 4}[/tex]

Using a calculator, we can calculate:

A = $16,000 * [tex]e^{0.08}[/tex]

A = $16,000 * 1.0833

A = $17,332.8

Therefore, the amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

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Jorge's gross earnings for the week assembling 317 game boards would be $633.

To calculate Jorge's gross earnings for the week, we need to determine how many game boards fall into each pay rate category and then multiply the quantity by the corresponding pay rate. Let's break down the calculation step by step:

Determine the number of game boards that fall into each pay rate category:

First 100 boards: 100 boards (as the rate applies to the first 100 boards).

Next 200 boards: Since Jorge assembled 317 boards in total and the first 100 boards are already accounted for, we subtract 100 from 317 to get 217 boards that fall into this category.

Over 300 boards: We check if the total number of boards exceeds 300. In this case, since Jorge assembled 317 boards, we have

317 - 300 = 17

boards that fall into this category.

Calculate the earnings for each category by multiplying the number of boards by the corresponding pay rate:

Earnings for the first 100 boards:

100 boards * $1.82 per board = $182.

Earnings for the next 200 boards:

217 boards * $1.92 per board = $416.64.

Earnings for the over 300 boards:

17 boards * $2.08 per board = $35.36.

Sum up the earnings from each category to find the gross pay for the week:

Gross pay = Earnings for the first 100 boards + Earnings for the next 200 boards + Earnings for the over 300 boards

Gross pay = $182 + $416.64 + $35.36

Gross pay = $633.

Therefore, Jorge's gross earnings for the week assembling 317 game boards would be $633.

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a) The area formula for the rectangle is equal to A = r² · sin 2θ.

b) By derivative tests, the maximum possible area of the rectangle is 16 square centimeters.

c) The dimensions of the rectangle are: Width: 5.66 cm, Height: 2.83 cm

In this problem we must determine the maximum possible area of a rectangle inscribed in a semicircle by means of first and second derivative tests. First, derive the area formula of the rectangle:

A = w · h

A = (2 · r · cos θ) · (r · sin θ)

A = 2 · r² · sin θ · cos θ

A = r² · sin 2θ

Where:

Second, perform first derivative test: (r - Constant)

A = 2 · r² · cos 2θ

2 · r² · cos 2θ = 0

cos 2θ = 0

θ = 45°

Third, perform second derivative test: (θ = 45°)

A'' = - 4 · r² · sin 2θ

A'' = - 4 · r² (MAXIMUM)

Fourth, determine the maximum possible area of the rectangle:

A = 4² · sin 90°

A = 16 cm²

Fifth, determine the width and the height of the rectangle: (r = 4, θ = 45°)

w = 2 · r · cos θ

w = 2 · 4 · cos 45°

w = 8 · √2 / 2

w = 4√2 cm

w = 5.66 cm

h = r · sin θ

h = 4 · sin 45°

h = 4 · √2 / 2

h = 2√2 cm

h = 2.83 cm

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The values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

A theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.

(25). 2x - 1 = x + 1 {equal tangent segments}

2x - x = 1 + 1 {collect like terms}

x = 2

(26). 2x - 4 = x {equal tangent segments}

2x - x = 4 {collect like terms}

x = 4

Therefore, the values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

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