Solve the inequality:
-3t+9 > -21
O t< -10
o t < 10
O t> -10
O t > 10

The mass that would remain after 50 years is 48. 79 kilograms

It is important to note that half - life is the time it takes for amount of a substance to reduce to half of its initial value.

Given the equation

m(t)=120e−0.018t

Where

m(t) is the amount = unknown

t = time = 50 years

[tex]m(t) = 120e^0^.^0^1^8^t[/tex]

Substitute the value into the equation

[tex]m(t) = 120e^0^.^0^1^8^(^5^0^)[/tex]

[tex]m(t) = 120e^-^0^.^9[/tex]

Find the exponential value

[tex]m(t) = 48.788399[/tex]
m(t) = 48. 79 kilograms in 2 decimal places

Thus, the mass that would remain after 50 years is 48. 79 kilograms

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Answer:

1/6

Step-by-step explanation:

1/15 yellow, 1/10 green, and 1/20 white

1/15 + 1/10 is the probability for yellow or green.

2/30 + 3/30 = 5/30 = 1/6

Brainliest, please :)

The probability of landing on the shaded region of the figure is 0.10

The probability of landing on the shaded region can be calculated as follows;
area of the bigger circle = πr² = 3.14 × 25² = 1962.5 cm²

area of the smaller region = πr² = 3.14 × 8²  = 200.96 cm²

Therefore,

the probability of landing on the shaded region of the figure = 200.96 / 1962.5

the probability of landing on the shaded region of the figure = 0.10

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The equation of the line in standard form is 6x - 7y = - 11

The standard form for linear equations in two variables is Ax + By = C.

Therefore, using (-3, -1)(1 / 2, 2)

y = mx + b

where

Hence,

m = 2 + 1 / 1  /2 + 3 = 6 / 7

Hence,

-1 = 6 / 7(-3) + b

- 1 = - 18 / 7 + b

-1 + 18 / 7 = b

b =  -7 + 18/ 7

b = 11 / 7

Therefore,

y = 6 / 7 x + 11 / 7

Using the standard form,

6 / 7 x - y = - 11 / 7

6x - 7y = - 11

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The linear equation in standard form is:

6x - 7y = -11

Which is the last option.

The line in slope-intercept form is written as:

y = a*x + b

We can see that the line passes through the points (-3, -1) and (1/2, 2), then the slope is:

[tex]a = \frac{2 - (-1)}{1/2 - (-3)} = \frac{3}{3.5} = \frac{6}{7}[/tex]

Then we can write:

y = (6/7)*x + b

To find the value of b, we use the first point. It means that when x = -3, the value of y is -1, then we get:

-1 = (6/7)*-3 + b

-1 + 18/7 = b

-7/7 + 18/7 = b

11/7 = b

Then the equation is:

y = (6/7)*x + 11/7

If we multiply both sides by 7 we get:

7y = 6x + 11

Now we move the term with "x" to the left:

7y - 6x = 11

That is the line in standard form.

If we multiply both sides by -1, we get the last option:

6x - 7y = -11

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Answer:

l dont know l am not studying it sorry

Answer:

hey what was the answer?

Step-by-step explanation:

I need help im going to failllll!!!!!!

The volume of the rectangular prism is of 28.6875 mm³.

The volume of rectangular prism of length l, width w and height h is given by:

V = lwh.

For this problem, the dimensions are:

Hence the volume is:

V = 2.125 x 6.75 x 2 = 28.6875 mm³.

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The solutions of the equation 2cos(2x) = x are (0.626, 0.626), (-1.607,-1.607) and (-1.798,-1.798)

The equation is given as:

2cos(2x) = x

Split the equation as follows:

y = 2cos(2x)

y = x

Next, we plot the graph of y = 2cos(2x) and y = x (see attachment)

From the attached graph, y = 2cos(2x) and y = x intersect at the following points

(x, y) = (0.626, 0.626), (-1.607,-1.607) and (-1.798,-1.798)

Hence, the solutions of the equation 2cos(2x) = x are (0.626, 0.626), (-1.607,-1.607) and (-1.798,-1.798)

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The attached line is a parallel line that goes through C and parallel to AB

Parallel lines are lines on the same plane that have the same slope, they do not intersect even when they are extended indefinitely

From the question, we have the following points and line:

The following steps would create the parallel line that goes through C and parallel to AB

See attachment for the parallel line that goes through C and parallel to AB

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The 4 reasons for the Algebra proof are respectively;

Given; Distributive property; Addition Property; Division Property

We want to use algebra properties to find the value of x in the expression; -5(x + 4) = 90

Statement 1;  -5(x + 4) = 90

Reason 1; Given

Statement 2; -5x - 20 = 90

Reason 2; Distributive property of Algebra because we distributed -5 into the bracket terms.

Statement 3; -5x = 110

Reason 3; Addition property of equality because we added 20 to both sides to achieve that.

Statement 4; x = -22

Reason 4; Division property of equality because we divided both sides by -5 to obtain x = -22.

Thus, the 4 reasons are respectively;

Given; Distributive property; Addition Property; Division Property

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The graph of the parabola g(x) is (x+2)^2 + 3

Given the following parent function of the parabola expressed as;

f(x) = x^2

The function g(x) shows a horizontal translation to the left by 2 units and vertical translation up by 3 units to have the equation;

g(x)  = (x+2)^2 + 3

Hence the graph of the parabola g(x) is (x+2)^2 + 3

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Option D, 4.1 is the correct answer. The mean baseball score is 4.1 given the table of values of baseball scores and score number of students. This can be obtained by using the formula for mean.

Mean can be obtained by the formula,

Mean = [tex]\frac{sum\ of\ observations}{total\ number\ of\ observations}[/tex]

Sum of basketball scores = 0×1 + 1×2 + 2×5 + 3×3 + 4×6 + 5×7 + 6×9

= 0 + 2 + 10 + 9 + 24 + 35 + 54

total number of basketball scores =  1 + 2 + 5 + 3 + 6 + 7 + 9 = 33

Mean = [tex]\frac{0+2+10+9+24+35+54}{33}[/tex] = 4.06 ≈ 4.1

Hence the mean baseball score is 4.1 given the table of values of baseball scores and score number of students. Option D, 4.1 is the correct answer.

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Using the given frequencies, the probabilities for the next color chosen is:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

There were 50 markers, of which 12 were yellow, 37 blue and 1 red, hence the probabilities for each are given as follows:

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Answer:

$19.50

Step-by-step explanation:

Dividing both sides by 32, we get $19.50.

Answer:

D. 6

Step-by-step explanation:

Let's first find x :-

[tex]\sf 3 + 2x + 22 = x + 17[/tex]

Now that we found x, let's find QR :-

QR = 2x + 22

Therefore, QR = 6 !!!

The equation y = -0.5x +45 represent the linear relationship.

According to the statement

We have given that the When she plants 30 stalks, each plant yields 30 oz of beans and When she plants 33 stalks, each plant produces 29 oz of beans.

And we have to find the linear relationship between the plants which are stalks.

So, For this purpose,

When we consider this graph as a straight line, the two points lying on the line would be

(30, 30) and (34, 28) taking n as horizontal and y vertical

Using two point equation we find that

the equation of the line is

y-y1 / y2-y1 =  x-x1 / x2-x1

Substitute the points as x =n and put the other values in it then

y-30 / 28-30 =  x-30 / 34-30

Then

y = -0.5x +45

This represent the relationship.

So, The equation y = -0.5x +45 represent the linear relationship.

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Answer:-8.5714285714 × 10-1

Step-by-step explanation:

-101/119=-0.85714285714

remember Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.

so -0.85714285714 in standard form is -8.5714285714 × 10-1

The third graph represents a function.

In a function, every input (x value) has exactly one output (y value). If even a single input has zero or two outputs, the graph does not represent a function.

A good way of testing this is using a vertical line. As you move a vertical line from left to right across a graph, it should always be touching exactly one point on the graphed line.

In this case, every graph fails this vertical line test except for the third graph, so the third graph represents a function.

The graph is shown in the attached image.

7. D. Arc JK = 124°

8. Applying the angle of intersecting chords theorem, m∠1 = 115°.

The angle of intersecting chords theorem states that the angle (∠1) formed by two chords in a circle, equals half of the sum of the intercepted arcs (arcs ML and JK).

Arc JMK = 2(118) = 236° [inscribed angle theorem]

Arc JK = 360 - arc JMK = 360 - 236

Arc JK = 124°

Arc ML = 236 - 70 - 60 = 106°.

m∠1 = 1/2(arc JK + arc ML)

m∠1 = 1/2(124 + 106)

m∠1 = 115°.

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Answer:

Angle is measured in degrees (°) and radians. It is formed between the two adjacent sides of a polygon. Every polygon has different sides and different numbers of angles. The formula to find the angles in degrees is useful in geometry and trigonometry. It is essential to understand other concepts of mathematics, such as arc, a central angle of the circle, etc.  

A full circle = 360°

A straight line = 180°

A semicircle= 180°

A Quarter circle = 90°

Given: Hypotenuse = 12

Perpendicular = 6

The trigonometry function to calculate the angle is given by:

sinA = 6/12

A = 30°

Using a system of equations, the translated expression is:

P - 32.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variable is the number of dollars Paul owes, which is P. That amount minus 32 is represented by:

P - 32.

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Answer:

D.{15,23,25,38,53}

Step-by-step explanation:

Replace f(x) with any other variables of your choice.

Substitute the value of the variable for the given set of hits

that is {4,12,14,27,42}

Solve for x for each value of the variable from the above set

Put all the solution for x in a set that is inside {,} brackets.

The correct option should be D

As k₁ = k₂ = k₃, the table represents a linear relation whose constant of variation is - 4.

A table between two variables represents a linear relation if and only if every pair of values (x, y) have the same constant:

k = y/x     (1)

Now we proceed to check the existence of the constant of variation:

k₁ = 8/(- 2) = - 4

k₂ = (- 16)/4 = - 4

k₃ = (- 36)/9 = - 4

As k₁ = k₂ = k₃, the table represents a linear relation whose constant of variation is - 4.

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Answer: 54

Step-by-step explanation:

So I helped 54 customers in 7.5 hours yesterday.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

You helped 3.6 customers per half hour yesterday.

That means,

for one hour:

Using multiplication

(3.6) x 2 per 1/2 x 2 hours

7.2 per hour.

Therefore,

if n hours so,

(7.2) per n hours

Here, n = 7.5

(7.2) x (7.5) per 7.5 hours

54 customers per 7.5 hours.

Therefore, I helped 54 people in 7.5 hours.

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The blanks are as follows:

Answer:

(-oo, -8/3) U (-8/3, oo)

Step-by-step explanation:

Hope this helps.

The domain of the equation f(x) = 2/(3x + 1) is (-∝, -8/3) U (-8/3, ∝)

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

f(x) = 2/(3x + 1)

The above equation is a rational function

The rule of a function is that

The domain is the set of all input numbers

For the domain, we set the denominator not equal to 0

So, we have

3x + 8 ≠ 0

Evaluate

x ≠ -8/3

When represented as interval notation, we have

Domain = (-∝, -8/3) U (-8/3, ∝)

Hence, the domain is (-∝, -8/3) U (-8/3, ∝)

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Answer:

x=6

Step-by-step explanation:

This is a vertical line going through (6,0).  If you take this point and the point given and calculate the slope you find the change in y over the change in x.  

0-(-3)/6-6  The slope is undefined because the denominator of the slope would be zero.

The exponential growth formula is 3,400,000 x (1.09^t).

The year in which the grove would reach one billion board feet is  63.16 years.

The exponential growth formula usually has this form:

FV = P (1 + r)^n

3,400,000 x (1.09^t).

The year in which the grove would reach one billion board feet  = (In 1,000,000,000 / 3,400,000) / 0.09 = 63.16 years

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