Tamara has $30,000, part or all of which she wants to invest into a combination of corporate bonds and municipal bonds. She wants to invest no less than $8,000 into corporate bonds, and at least three times as much into corporate bonds than into municipal bonds.

Let x be the amount invested in corporate bonds, and let y be the amount invested in municipal bonds.

Which system of inequalities describes Tamara’s investment options?


x + y ≤ 30,000
x ≤ 8,000
x ≥ 3y


x + y ≤ 30,000
x ≥ 8,000
x ≥ 3y


x + y ≤ 30,000
x ≥ 8,000
x ≤ 3y


x + y ≤ 30,000
x ≤ 8,000
x ≤ 3y

The domain and range are (0 , ∞) and (0 , ∞).

What is domain ?

The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

The set of all initial elements in ordered pairs constitutes the domain (x-coordinates). The set of all second items in ordered pairs is the range (y-coordinates).

Given

y = 80 / x

As per the graph the domain and range are

domain : (0 , ∞)

{depth of the diamond > 0 }

range : (0 , ∞)

{ratio > 0}

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Answer: Each roll of fabric had 86.4 inches of fabric.

Step-by-step explanation:

Each roll of fabric used in the annual school play had a length of 14.4yd / 6 rolls = 2.4 yards of fabric.

1 yard = 36 inches

so, 2.4 yards = 2.4 x 36 inches = 86.4 inches

Each roll of fabric had 86.4 inches of fabric.

Explanation: The problem states that Chau used 6 rolls of blue fabric, and the total length of fabric used was 14.4 yards. Dividing the total length of fabric by the number of rolls gives the length of each roll, which is 2.4 yards or 86.4 inches.

Answer:

The annual passenger revenue of the rail transport corporation was $930 million when:

R = 930

-20|t-15| + 1,010 = 930

-20|t-15| = 80

|t-15| = 4

So, we can see that t-15 = 4 and t-15 = -4 both lead to an annual revenue of $930 million dollars.

To find the values of t, we add 15 to both sides of the equation:

t-15 = 4 => t = 19

t-15 = -4 => t = 11

So, the years where the passenger revenue was $930 million are:

2011

2019

Answer:

Step-by-step explanation:

a. To minimize the average cost, we need to find the value of x that minimizes the cost function C(x) = x² - 40x + 500.

This is the same as finding the minimum value of the parabola represented by the function. The vertex of the parabola is the point at which the parabola reaches its minimum or maximum value. The vertex form of a parabola is given by C(x) = a(x - h)² + k, where (h, k) is the vertex.

By comparing the given function with the vertex form of a parabola, we can find the vertex:

C(x) = x² - 40x + 500

= a(x - h)² + k

= (x - h)² + k

The x-coordinate of the vertex h = 40/2 = 20

So the minimum average cost occurs when 20 televisions are made per week.

b. To find the minimum average cost, we need to substitute the value of x = 20 into the cost function:

C(x) = x² - 40x + 500

= 20² - 40*20 + 500

= 400 - 800 + 500

= 100

So the minimum average cost is $100 per television.

If the average cost is $200 per television, we can set C(x) = 200 and solve for x:

200 = x² - 40x + 500

0 = x² - 40x + 300

This is a quadratic equation that can be solved by factoring or by using the quadratic formula.

we can factor it as

0 = (x-50)(x-6)

x = 50 or x = 6

The number of televisions made per week if the average cost is $200 per television is 50 or 6. Since 50 is much higher than 20, the minimum average cost, it is not physically possible to make 50 televisions with the average cost of $200 per television. So the answer is 6 televisions per week.

The table that represents the equation and the graph is

(-1, 7.5). (1, 4.5), (3, -1.5), and (5, 1.5)

This can be found by tracing the points on the graph or substituting into the equation

The equation is 3x − 2y = 12, rearranging will result to 1.5x - 6 = y

substituting the values of x into y = 1.5x - 6

for x = -1, y = 1.5 * -1 - 6 = -7.5

for x = 1, y = 1.5 * 1 - 6 = -4.5

for x = 3, y = 1.5 * 3 - 6 = -1.5

for x = 5, y = 1.5 * 5 - 6 = 1.5

Hence the third option while counting from top id the correct option

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The ordered pairs for the equation 3x - 2y = 12 is (-1, -7.5), (1, -4.5), (3, -1.5) and (5, 1.5)

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

Given the equation:

3x - 2y = 12

2y = 3x - 12

y = (3/2)x - 6

When x = -1; y = (3/2)(-1) - 6 = -7.5

When x = 1; y = (3/2)(1) - 6 = -4.5

When x = 3; y = (3/2)(3) - 6 = -1.5

When x = 5; y = (3/2)(5) - 6 = 1.5

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Using substitution method to solve the system of linear equations, the value of x and y are 4 and -24 respectively.

A system of linear equations is a set of two or more linear equations that contain two or more variables. The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system simultaneously. Linear equations are equations that can be written in the form of ax + by = c, where a, b, c, x and y are constants.

In this problem, the equations are

Using substitution method;

Put the value y in eq(i) into eq(ii)

-2x - (-6x) = 16

-2x + 6x = 16

4x = 16

x = 4

Put x = 4 into equ(i)

y = -6(4)

y = -24

The value of x and y are 4 and -24

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Answer:

Step-by-step explanation:

Assuming that the same ratio of invitees to respondents holds true for the 30 additional HRDs, the best estimate of the number of people employed by the 30 organisations is 67.5 (30/45*100). This means that the total number of people employed by the 363 organisations represented by the 333 invited HRDs and the 30 additional HRDs is 5,475 (5,407.5 + 67.5).

Answer:

this statement is true .............

Answer:

8232 South African Rand

Step-by-step explanation:

The question cuts off at "if the current exchange" so the exchange rate is not specified. At the time of writing this answer, the echnage rate from one sterling pound to South African Rand is 1=20.58. So, we just need to multiply 20.58*400 to get 8232.

The fraction is 0.001545/5 =0.00309/1 .

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

2 in² and 5 yd²

now,

1 inch =0.0278yard

so, we get,

2in^2=0.001545 yd^2

i.e. 0.001545/5

=0.00309/1

hence, The fraction is 0.001545/5 =0.00309/1 .

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Answer:

Hi!

0 is basically inverse 0

any integer Inverse change the function

Answer:

this is very big question and the answer I think so is 11474

So on solving the provided question we can say that here in both triangles are similar, y = 10; x = 12

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here in both triangles are similar,

y = 10

x = 12

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the photo is not loading ok this is your photo open this and see now that address now because you are so

Answer:

Ms. Nahar is 7 years old.

Step-by-step explanation:

21/7 =3

Answer:

She is 7 years old if he is 21

Step-by-step explanation:

21/3

Answer: We can set up a system of equations to solve this problem. Let x be the number of quarters and y be the number of nickels. We know that:

x + y = 20 (the total number of coins)

0.25x + 0.05y = 4.20 (the total value of the coins in dollars)

We can use the first equation to solve for one variable in terms of the other, and then substitute that into the second equation to get a single equation with one variable.

For example:

x = 20 - y

0.25(20-y) + 0.05y = 4.20

5-0.25y + 0.05y = 4.20

5= 4.20

y = 20 - 5

y = 15

x = 20 - 15

x = 5

So Jada has 5 quarters and 15 nickels in her pocket.

Step-by-step explanation:

The final answer is N * 58 + 64.

What is the PEMDAS?

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction (from left to right).

The order of operations (PEMDAS) tells us to perform the following steps:

Parentheses: (4 x 12 - 40) to the power of 2 = (-8)^2 = 64

Exponents: N * 58 + 64

Multiplication and Division: from left to right

Addition and Subtraction: from left to right

Hence, the final answer is N * 58 + 64, since we do not know the value of N we can't solve it.

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Answer:

g(x) is translated 2 units up from f(x).

Step-by-step explanation:

f(x) = 4x

g(x) = 4x+2

g(x) = f(x) + d  where d is an upwards translation from f(x)

Adding 2 is a vertical translation up 2 units

The savings before he purchased the radio is

A percentage is a figure or ratio that can be stated as a fraction of 100.

If we need to determine the percentage of the given number, we divide the number by its whole number and multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".

Given cost of radio = $109.65

and $109.65 is 43% of his savings,

let saving be  x

according to conditions,

43% of x = 109.65

43x/100 = 109.65

43x = 109.65 × 100

x = 10965/43

x = $255

Hence the saving of George is $255.

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Answer: -32

Step-by-step explanation:

The domain and range of the function y = 1/2 - 1 lies on  (-∞, ∞)

The collection of all input values (sometimes referred to as independent variables) for which a function is defined and yields a valid output is known as the domain of the function. It is the collection of all possible values that can be entered into a function.

All real numbers, for instance, fall inside the domain of the function        f(x) = x², since any real number may be squared to yield an accurate result.

On the other hand, a function's range is the collection of all feasible output values (also known as the function's dependent variable) that it can generate. It is the collection of all outcomes that the function is capable of producing.

For instance, since squaring real numbers makes the range of the function f(x) = x² all non-negative values.

It's vital to remember that not all functions have the same range or are defined for all conceivable input values. For instance, because the square root function x is not defined for negative numbers, all real numbers that are not negative fall within its domain.

In conclusion, the collection of all input values for which a function is defined and yields a valid output is known as the domain of the function. The collection of all potential output values that a function may produce is known as its range.

In the given function;

y = 1/2x - 1

The domain of this function is (-∞, ∞)

The range of the function f(x) = 1/2x - 1 is (-∞, ∞)

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Answer: 0.515

Step-by-step explanation:

Since our angle is between 0 and 90 degrees, it is located in Quadrant I

In the first quadrant, the values for sin, cos and tan are positive.

Since 31° is less than 90, we can express this in terms of a cofunction

sin(θ) = cos(90 - θ)

sin(31) = cos(90 - 31)

sin(31) = cos(59)

hope this helps!

The value of sin 31° is 0.51504.

Sin 31 degrees is the value of the sine trigonometric function for an angle equal to 31 degrees.

The sin of 31 degrees is 0.51504, but the sin of 31 degrees can also be expressed in radians. To obtain 31 degrees in radian multiply 31° by π/ 180° = 31/180π. Sin 31degrees = sin (31/180 ×π)

The results of sin31° are rounded to five decimal places.

The following are identities of sine 31° :

sin31°

= cos (90°-31°) = cos 59°

= sin (180°-31°) = sin 149°

-sin31°

= cos (90°+31°) = cos 121°

= sin (180°+31°) = sin 211°

Therefore, The value of sin 31° is 0.51504.

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Answer: I believe the answer is A; 0.72

Answer: The largest marginal relative frequency is 0.90 and it represents the probability of an individual having brown hair given that they have brown eyes.

Step-by-step explanation:

The reason why 0.90 represents the probability of an individual having brown hair given that they have brown eyes is because the study shows that 90% of the people who have brown eyes also have brown hair. This is a conditional probability, which means that it is the probability of one event happening given that another event has already happened. In this case, the event of having brown hair is conditional on the event of having brown eyes. The probability of 0.90 is calculated by taking the total number of individuals with brown eyes and brown hair and dividing it by the total number of individuals with brown eyes. The number is large because 90% of the individuals with brown eyes have brown hair, it is the largest because it is the highest probability among the other marginal relative frequencies. This indicates that the majority of people with brown eyes also have brown hair

The system of inequalties on the graph is:

x  + 4y ≤ 15

y ≥ 0

First, we can see a solid line at y = 0 and we have the region above that line shaded, so one of the inequalities is:

y ≥ 0.

The other inequality is a solid line with a negative slope and the shaded region is below the line.

The only option that has these characteristics is:

x  + 4y ≤ 15

4y ≤ - x + 15

y ≤ (-1/4)x + 15/4

Then the system of inequalities is:

x  + 4y ≤ 15

y ≥ 0

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I hope this helped you

Answer:

a = 3

Step-by-step explanation:

24 x 2ªx 3

8= 2ª

a= 3

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{24 = 2a \times 3}\\\mathsf{\rightarrow 2a \times 3 = 24}\\\mathsf{\rightarrow 2(3)(a) = 24}\\\mathsf{\rightarrow 6(a) = 24}\\\mathsf{\rightarrow 6a = 24}\\\\\text{DIVIDE 6 to BOTH SIDES}\\\\\mathsf{\rightarrow\dfrac{6a}{6} = \dfrac{24}{6}}\\\\\text{SIMPLIFY it}\\\\\mathsf{\rightarrow a = \dfrac{24}{6}}\\\\\mathsf{\rightarrow a = 4}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{a = 4}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: a. The value of n is 10, as there are 10 tosses of seven coins.

b. The value of Y2 is 6, as the number of heads in the second toss is 6.

c. The value of Y7 is 3, as the number of heads in the seventh toss is 3.

d. For i = 1, 2, 3, 4, the value of Y is 2. For i = 5, 8, the value of Y is 3. For i = 6, 9, 10, the value of Y is 4.

e. Yi-1 refers to the observation made in the previous toss (i-1), whereas Yi – 1 refers to the observation made in the current toss (i) minus 1.

f. Yi-1 = Y1 = 2 and Yi – 1 = Y2 – 1 = 6 – 1 = 5 for i = 2

g. The observations can be written as a vector Y = (2, 6, 2, 2, 5, 3, 5, 3, 3, 4)

Step-by-step explanation:

Answer:

You can find the value of the tangent of any angle on a unit circle. Just draw a vertical line from the x-axis at either zero or pi until it intersects what is the extension of the radius through the angle. The length of that vertical line is the value of the tangent at the angle in question.

Step-by-step explanation:

In any right triangle, the tangent of an angle is the length of the opposite side (O) divided by the length of the adjacent side (A).

Helpful Tip!:)