A system of equations is shown.
{ x= = 10
3x + 5y = 20
What is the solution x of the system of equations?

The statement that "if you took a true "if-then' statement and reversed the clauses, the new statement would also be true" is False.

By reversing the clauses within an accurate "if-then", one will manifest a new statement known as the "converse" of the initial formula. Though, it is not inevidably true.

For instance, if the original expression was "If it rains, then the ground gets wet", its converse is "If the ground gets wet, then it rains". Unfortunately, that specific converse has the potential to be incorrect since there are several other methodologies from which the land can gain moisture beside rain (e.g. sprinkler system, someone unintentionally pouring water, etc.).

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Answer: According to the problem, N Heracio used the computer for 40 hours last week. We are asked to find the difference between the time spent on shopping online and doing homework.

To do this, we first need to find the amount of time spent on each activity. We can do this by multiplying the total computer time by the percentage of time spent on each activity:

Time spent on videos = 10% of 40 hours = 4 hours

Time spent on homework = 15% of 40 hours = 6 hours

Time spent on games = 20% of 40 hours = 8 hours

Time spent on social media = 25% of 40 hours = 10 hours

Time spent on shopping online = 20% of 40 hours = 8 hours

Therefore, Heracio spent 6 hours on homework and 8 hours on shopping online.

The difference between these two amounts is:

6 hours - 8 hours = -2 hours

This means that Heracio spent 2 hours more on shopping online than on doing homework.

Step-by-step explanation:

The solution is: the area of the shaded base in square centimeters is:

B= 15 cm²

Here, we have,

The base of the triangular shaped wedge of cheese is a right-triangle.To find the area of a right-triangle you apply the formula for half base by height.

A=1/2*b*h

 = base area

 = B

In this case, assume the sides of the triangle given are;

a=5 cm and b=6 cm,

thus area will be 1/2*6*5 =15 cm²

Hence, the area of the shaded base in square centimeters is :

B= 15 cm²

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complete question:

Evelyn cut a wedge of cheese into the shape of a triangular prism-like the one shown below. The shaded part represents one of the bases of the prism.

A formula for the volume of a triangular prism is v=Bh . Which equation can be used to find B , the area of the shaded base in square centimeters?

Answer:

B. Y= 5x - 2

Step-by-step explanation:

The Y is negative, you can see the number -5 below the point, if you go to the top, that is, to 0 and count down, the lines are two and the X is positive 5, you can see where the number 5 is and the point is above.

Answer:

Step-by-step explanation:

8+(6-3)-9

The first action is addition in parentheses

(6-3) = 3

The second action is addition and then subtraction, you can subtract first and then add, it makes no difference because the answer will be the same in all cases

8 + 3 - 9 = 11 - 9 = 2

Answer:

it's an easy one

Step-by-step explanation:

1. combine those -->4v+4=16

2. subtract the like terms--> 4v=16-4--> 4v=12

3. divide--> v=12/4-->3

4. Answer--> v=3

Answer:

x = - 9

Step-by-step explanation:

-48 - x = -39

Add 48 on both sides

-x = 9

Divided both sides by -1

x = - 9

So, the answer is x = - 9

Answer:

V ≈ 1809 ft^3

Step-by-step explanation:

Given:

r (radius) = 6ft

h (height) = 16ft

π = 3,14

Find: V (volume) - ?

[tex]v = \pi {r }^{2} \times h[/tex]

[tex]v = 3.14 \times {6}^{2} \times 16 ≈1809 \: {ft}^{3} [/tex]

Answer:

1. $990

2. Sn = Sn-1 + (r/100) * Sn-1

3. $27,037.44

Step-by-step explanation:

1. The interest earned each year can be calculated using the simple interest formula:

Simple Interest = (Principal * Rate * Time) / 100

Here, Principal = $22,000, Rate = 4.5%, and Time = 1 year

So, the interest earned each year would be:

= (22,000 * 4.5 * 1) / 100

= $990

Therefore, the interest earned each year would be $990.

2. The recurrence relation to model the value of investment from year to year is:

Sn = Sn-1 + (r/100) * Sn-1

where Sn represents the value of the investment after n years, Sn-1 represents the value after n-1 years, and r represents the annual interest rate.

Using this recurrence relation, we can calculate the value of the investment for different years:

- S1 = 22,000 + 990 = 22,990

- S2 = 22,990 + (4.5/100) * 22,990 = 24,026.55

- S3 = 24,026.55 + (4.5/100) * 24,026.55 = 25,103.46

And so on...

3. To determine the value of the investment after 5 years, we can simply substitute n = 5 in the recurrence relation:

S5 = S4 + (r/100) * S4

= S3 + (r/100) * S3 + (r/100) * S3

= S2 + (r/100) * S2 + (r/100) * S2 + (r/100) * S2

= S1 + (r/100) * S1 + (r/100) * S1 + (r/100) * S1 + (r/100) * S1

Substituting values from previous calculations:

S1 = 22,000 + 990 = 22,990

So,

S5 = 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990

= $27,037.44

Therefore, the value of the investment after 5 years would be $27,037.44.

Answer:

I can tell

Step-by-step explanation:

Ok so to help you understand it do you see the button that says video? Yeah, click it. A video will pop up and explain it to you! :)

The percentage rate of change per minute is approximately 0.98%

The mass of the sample decreases by 59% every hour, so we can write the following differential equation:

dm/dt = -0.59m

Rate of change of the mass (dm/dt) is equal to the mass (m) multiplied by the constant -0.59.

We can solve this differential equation using separation of variables:

dm/m = -0.59 dt

Integrating both sides, we get:

ln|m| = -0.59t + C

where C is the constant of integration.

To find C, we can use the initial condition that the mass of the sample is 530 grams at t=0:

ln|530| = C

C = ln(530)

So the solution to the differential equation is:

ln|m| = -0.59t + ln(530)

[tex]m(t) = 530 e^(^-^0^.^5^9^t^)[/tex]

This function represents the mass of the sample after t hours, where the rate of change per minute is given by the constant

k = -0.59/60 = -0.00983 (rounded to 5 decimal places).

To find the percentage rate of change per minute, we can multiply k by 100 to convert it to a percentage:

-0.00983 × 100 = -0.983%

Therefore, the percentage rate of change per minute is approximately 0.98%

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The probability that a single randomly selected value is greater than 31.9 is 0.511.

The probability that a sample of size 66 is randomly selected with a mean greater than 31.9 is 0.641.

Probability that a single randomly selected value is greater than 31.9:

z = (31.9 - 32) / 3.9 = -0.026

We can find the probability:

P(X > 31.9) = P(Z > -0.026) = 0.511

Also, μ = 32, σ = 3.9, n = 66

z = (31.9 - 32) / (3.9 / √66) = -0.363

Using a standard normal distribution table or calculator, we can find the probability:

P(M > 31.9) = P(Z > -0.363) = 0.641

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The baker should use 24kg amount of flour when making the biscuits. The correct answer is (b) 24kg.

To determine the amount of flour the baker should use when making biscuits, we can use the given ratio of flour to sugar, which is 4:1.

Since the ratio is 4:1, for every 4 parts of flour, there is 1 part of sugar. Therefore, the ratio of flour to sugar can be expressed as 4/1.

If the baker uses 6kg of sugar, we can set up a proportion to find the corresponding amount of flour:

4/1 = x/6

Cross-multiplying, we get:

4 * 6 = 1 * x

24 = x

Therefore, the baker should use 24kg of flour when making the biscuits.

In summary, the correct answer is (b) 24kg.

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The population of Greensville 10 years from now will be approximately 13,184.

To find the population of Greensville 10 years from now, we need to use the formula for compound interest:

A = P(1 + r)ᵗ

Where A is the future value, P is the present value, r is the annual interest rate as a decimal, and t is the number of years.

In this case, the present value (P) is 8,000, the annual interest rate (r) is 5.6% or 0.056 as a decimal, and the time (t) is 10 years. Plugging these values into the formula, we get:

A = 8,000(1 + 0.056)¹⁰

A = 8,000(1.648)

A = 13,184

This calculation assumes that the population growth rate remains constant at 5.6% per year.

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Answer:

[tex]A_{\text{red}} = 1766.25 \text{ in}^2[/tex]

Step-by-step explanation:

We can see that there are four bands total on the target, two of which are red bands. With this information, we can solve for the radius of the circle within each band, since we know that each band is the same width:

[tex]r_1 = \dfrac{1}{4} \cdot 30 = 7.5\\[/tex]

[tex]r_2 = \dfrac{2}{4} \cdot 30 = 15\\[/tex]

[tex]r_3 = \dfrac{3}{4} \cdot 30 = 22.5\\[/tex]

[tex]r_4 = 30[/tex]

We can now find the area of each red band by subtracting:

the area of the circle within the white band just inward of the red band

-- from --

the area of the circle within the red band.

Finding the area of the outer red band:

[tex]A_{\text{outer red}} = A(\text{circle within outer red}) - A(\text{circle within outer white})[/tex]

[tex]A_{\text{outer red}} = A(\odot \text{ with radius }r_4) - A(\odot \text{ with radius } r_3)[/tex]

↓ substituting the radius values into the circle area formula ([tex]\pi r^2[/tex])

[tex]A_{\text{outer red}} = (\pi \cdot 30^2) - (\pi \cdot 22.5^2)[/tex]

↓ using 3.14 for [tex]\pi[/tex]

[tex]A_{\text{outer red}} = (3.14 \cdot 30^2) - (3.14 \cdot 22.5^2)[/tex]

↓ evaluating the right side

[tex]A_{\text{outer red}} = 2826 - 1589.625[/tex]

[tex]A_{\text{outer red}} = 1236.375 \text{ in}^2[/tex]

Finding the area of the inner red band:

[tex]A_{\text{inner red}} = A(\text{circle within inner red}) - A(\text{circle within inner white})[/tex]

[tex]A_{\text{inner red}} = A(\odot \text{ with radius }r_2) - A(\odot \text{ with radius } r_1)[/tex]

↓ substituting the radius values into the circle area formula ([tex]\pi r^2[/tex])

[tex]A_{\text{inner red}} = (\pi \cdot 15^2) - (\pi \cdot 7.5^2)[/tex]

↓ using 3.14 for π

[tex]A_{\text{inner red}} = (3.14 \cdot 15^2) - (3.14 \cdot 7.5^2)[/tex]

↓ evaluating the right side

[tex]A_{\text{inner red}} = 706.5 - 176.625[/tex]

[tex]A_{\text{inner red}} = 529.875 \text{ in}^2[/tex]

Finally, we can find the area of all of the red on the target by adding the area of the outer and inner red bands.

[tex]A_{\text{red}} = A_{\text{outer red}} + A_{\text{inner red}}[/tex]

[tex]A_{\text{red}} = 1236.375 \text{ in}^2 + 529.875 \text{ in}^2[/tex]

[tex]\boxed{A_{\text{red}} = 1766.25 \text{ in}^2}[/tex]

The value of correct Set-builder form is,

⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }

We have to given that;

The set is,

⇒ {4, 5, 6, 7, 8}

Thus, We can write correct Set-builder form as,

⇒ {4, 5, 6, 7, 8}

⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }

So, The value of correct Set-builder form is,

⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }

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An inequality to show the number of people  is  p ≥ 12

Let p be the number of people on the bus. We know that there are at least 12 people on the bus, so we can write:

p ≥ 12

This inequality means that the number of people on the bus, p, must be greater than or equal to 12.

To graph this inequality, we can draw a horizontal line at y = 12 on the y-axis, and shade the area above the line, since any value of p that is greater than or equal to 12 satisfies the inequality.

Here's a graph of the inequality attached

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Answer: 0.12

Step-by-step explanation:

just divide whatever is under 5 with the total amount of frequency

so then you do 12/100 which is 0.12

Answer:

Step-by-step explanation:

The resulting matrix after row 1 is multiplied by 2 is given as follows:

[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

The first row is given as follows:

7, -4 and 8.

Multiplying the first row by two, we have that:

(when we multiply a matrix by a constant, each element of the matrix is multiplied by the constant).

Hence the resulting matrix is given as follows:

[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]

(the second row was kept constant, while the first row was multiplied by 2).

The matrix is:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

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Answer:

Set your calculator to degree mode.

2) tan(43°) = x/8.2

x = 8.2tan(43°) = 7.6

3) sin(29°) = 3.5/x

x sin(29°) = 3.5

x = 3.5/sin(29°) = 7.2

The amount it would cost to paint the wall, given the cost of paint and the area covered is $ 56 .

The surface area of the circular wall would be :

A = 2 x π x r x h

The area is therefore:

= 2 x π x r x h

= 2 x 3. 14 x 15 x 4

= 376. 8 square feet

The number of gallons needed is therefore:

= 376. 8 / 225

= 1. 674

= 2 gallons

The cost of two gallons is:

= 2 x 28

= $ 56

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The side length x of the given right angle triangle is: 14.97

When two sides of a right-angled triangle are given and one side is to be found, we can do so using the Pythagoras theorem. In the given triangle the base is x, the perpendicular is 10 and the hypotenuse is 18.

According to the Pythagoras Theorem, the following equation can be written as:

x² = 18² - 10²

x = √224

x = 14.97

Thus, that is the missing length of the given right triangle

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Answer:

Step-by-step explanation:

C (Wait for another defendant, check with him and write this answer)

Answer: Let's start by using algebra to represent the problem.

Let X be the amount of money that Kyle started with.

Then we can create the following equations:

And we know that he's out of money, so:

Substitute the first equation into the second equation to get:

Substitute the first two equations into the third equation to get:

Substitute all three equations into the fourth equation to get:

(0.5X + 36.50) + (0.25X + 9.25) + (0.25X + 4.75) = X

Simplify and solve for X:

Therefore, Kyle started with $101.

The equation that can be used to determine the cost of each admission ticket is 4x + $25.00 = $175.00.

The cost in dollars of the admission ticket is $ 37.50.

Let x be the cost, in dollars, of each admission ticket, including tax.

The total cost of 4 admission tickets can be expressed as 4x, since the cost of each ticket is the same.

The total cost of 4 admission tickets and parking is given as $175.00, so we can write:

4x + $25.00 = $175.00

Simplifying the equation, we can solve for x:

4x = $175.00 - $25.00

4x = $150.00

x = $37.50

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