You are given the yearly interest earned from a total of $18,000 invested in two funds paying the given rates of simple interest. Write and solve a system of equations to find the amount invested at each rate. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.

Yearly Interest: $579
Rate 1: 2.75%
Rate 2: 4.75%

(dollars invested at 2.75%, dollars invested at 4.75%) =

Answer: The end behavior of a function is the behavior of the function as x approaches positive infinity or negative infinity.

For the function f(x) = -2√x + 5 + 1, as x approaches positive infinity, the square root of x approaches positive infinity as well. So, the function approaches negative infinity as x approaches positive infinity:

lim x → ∞ f(x) = lim x → ∞ -2√x + 5 + 1 = -∞

As x approaches negative infinity, the square root of x approaches 0, so the function approaches:

lim x → -∞ f(x) = lim x → -∞ -2√x + 5 + 1 = 7

Therefore, the end behavior of the function is that it approaches negative infinity as x approaches positive infinity, and it approaches 7 as x approaches negative infinity.

Step-by-step explanation:

Answer:

The answer is 112ft

Step-by-step explanation:

32+16+8+8+16+8+8+16 = 112ft

Answer:

112ft

Step-by-step explanation:

The length of the little rectangle jutting out is the only unmarked length, so once we find that we can just add up all the sides to find the perimeter.

We see the overall length of the shape is 24ft and the length of the top of the shape, minus the unmarked length, is 16ft. This means the unmarked length is 24ft-16ft=8ft

Now add up each side to get to the perimeter:

32ft + 16ft + 16ft + 8ft +8ft +8ft +8ft +16ft = 112ft

Answer:

-$48.39

Step-by-step explanation:

The correlation coefficient of the data-set in this problem is given as follows:

C. r² = 0.931.

The coefficient is obtained inserting the points in a data-set in a correlation coefficient calculator.

The points from the table in this problem are given as follows:

(3,2), (4,4), (5,5), (7,6), (10,20).

Inserting these points into a calculator, the correlation coefficient is obtained as follows:

r² = 0.931.

Meaning that the correct option is given by option C.

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Answer:

Step-by-step explanation:

For part a:

Mean: Use the AVERAGE function to find the mean of the "Number" column.

Median: Use the MEDIAN function to find the median of the "Number" column.

Mode: There is no built-in function to find the mode in Excel, but you can use a combination of the IF, COUNTIF, and MAX functions to find the most frequently occurring value.

Maximum: Use the MAX function to find the maximum value in the "Number" column.

Minimum: Use the MIN function to find the minimum value in the "Number" column.

For part b:

Mean: Use the AVERAGE function to find the mean of the "Percent" column.

Median: Use the MEDIAN function to find the median of the "Percent" column.

Mode: There is no built-in function to find the mode in Excel, but you can use a combination of the IF, COUNTIF, and MAX functions to find the most frequently occurring value.

Maximum: Use the MAX function to find the maximum value in the "Percent" column.

Minimum: Use the MIN function to find the minimum value in the "Percent" column.

For part c:

The statistics on children whose parents do not have secure employment provide important insights into the state of the economy. In this case, the mean and median of the number of children in each state seem to be around 450,000. The mode cannot be determined since there are no repeated values in the "Number" column. The maximum number of children is 678,000 in Ohio, while the minimum number is 141,000 in Iowa.

Comparing the states, Indiana has a slightly higher mean and median percent of children whose parents do not have secure employment at 27%, compared to the other surrounding states which range from 20% to 31%. However, there is no clear state with the best or worst data as the range of the percent values is not too wide.

In terms of comparison, the number of children may provide a more comprehensive understanding of the extent of the problem, as it gives a clearer picture of the actual number of children affected. However, the percentage provides a more relative comparison between the states, allowing for easier comparison and a clearer understanding of the proportion of children affected in each state.

The combined volume of a 4-foot cube and a 6-foot cube is not equal to the volume of a 10-foot cube.

The volume of a cube is calculated by cubing the length of its side.

here,

Let's denote the length of the sides of the 4-foot and 6-foot cubes as "a" and "b", respectively. Then the length of the side of the 10-foot cube is "c", and we know that:

a³ + b³ = c³

We want to confirm if the combined volume of a 4-foot cube and a 6-foot cube is equal to the volume of a 10-foot cube. We can calculate the volumes of the cubes as follows:

Volume of 4-foot cube: a³ = 4³ = 64 cubic feet

Volume of 6-foot cube: b³ = 6³ = 216 cubic feet

Volume of 10-foot cube: c³ = 10³ = 1000 cubic feet

The sum of the volumes of the 4-foot and 6-foot cubes is:

64 + 216 = 280

Therefore, the combined volume of a 4-foot cube and a 6-foot cube is not equal to the volume of a 10-foot cube.

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Answer:

Multiplied by -5

Step-by-step explanation:

-8 X -5 = 40

40 X -5 = -200

Answer:

-30

Step-by-step explanation:

The best way to figure out if there is a solution to the equation:

 --> solve this whole thing algebraically

Let's solve:

 [tex]-4x+7x=4(x+2)-(x+8)\\3x=4x+8-x-8\\3x=3x[/tex]

If we get this kind of circumstance:

 --> where the left/right part of the equation are equal and cannot be

      solved further

     ---> the solution is all real numbers

Answer: solution is all real numbers

The width of the rectangle is [tex]4x^8y^6[/tex]inches.

Option A is correct.

What is the area of the rectangle?

A rectangle is a four-sided polygon with two pairs of parallel sides, and all four angles are right angles (90 degrees). The area of a rectangle is the amount of two-dimensional space that it occupies and is given by the product of its length and width. In other words, the area A of a rectangle with length l and width w is given by the formula:

A = l x w

To find the width of the rectangle, we can use the formula for the area of a rectangle, which is:

Area = length x width

In this case, we are given the area and the length of the rectangle, so we can rearrange the formula to solve for the width:

width = Area / length

Substituting the given values, we have:

width = [tex]\frac{(32x^{12}y^{9})}{(8x^4y^3)}[/tex]

Simplifying the expression, we get:

width = [tex]4x^{8}y^{6}[/tex]

Therefore, the width of the rectangle is[tex]4x^8y^6[/tex]inches.

Option A is correct.

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Answer:

(3) 3

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which each of them can be defined by adding a common difference to a term to find the next term.

So for example, let the first term, or number be expressed as: [tex]a_1[/tex] and the common difference be expressed as: [tex]d[/tex] That means the second term, or number can be defined as: [tex]a_2=a_1+d[/tex]. If we now add the common difference to the second term, we would get the third term, and so on.

An arithmetic sequence can be compared to that of a linear equation, except it's a sequence of numbers... and also it's restricted to integers greater than zero (starts at first term, second term.... and so on)

So the common difference can be compared to the slope, and we can actually just use the slope formula! The "x" value being the term number, and the "y" value being the term. So the first term in the sequence is 5 can be expressed as: (1, 5) and the fifth term is 17 can be expressed as (5, 17). Now using the slope formula we would get: [tex]d=\frac{17-5}{5-1}=\frac{12}{4}=3[/tex]

Another way to think of it is the first term is 5, and if we add "d" or the common difference to it, we get the second term, if we add another "d" we get the third term, if we another "d" we get the fourth term and if add yet another "d" we get the fifth term. We add a total of four "d's" which can be expressed as: [tex]5+4d[/tex] and this equals the fifth term, but we also know this to be equal to 17, so we can set them equal to each other: [tex]5+4d=17[/tex] now just subtract 5 and divide by 4 to get: [tex]d=3[/tex]

Answer:B costs less than A

Step-by-step explanation:

i am not quite sure but i think,

A)8----2,89

  1------x

x=0.38

B)12----4,19

1---------y

y=0.35

Answer:

C. No real factors

Step-by-step explanation:

Not factorable

Answer: 54.54 mph

Step-by-step explanation: To calculate the average speed of a car that traveled 300 miles in 5.5 hours, you can divide the total distance traveled by the total time taken: Average speed = Total distance / Total time-average speed = 300 miles / 5.5 hours = 54.55 miles per hour (mph)So, the average speed of the car is 54.55 mph.

In the given figure angle CBF and angle CEF are supplementary angles. So Option C is correct.

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Given that,

A figure which contains one trapezium BCEF

And in this portion angle CBF and angle BCE are  opposite angles

and opposite angles are supplementary angles,

Hence, the pairs of angles are ∠CBF & ∠CEF

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The solutions of the quadratic equation are;

1) x = 1 or -1/2

2) x = 11 or -1

We know that the quadratic formula is one of the ways that we can use to solve for the variables that we have in a quadratic equation. We can be able to obtain x by using the formula;

x = -b ±√b^2 - 4ac/2a

To use the discriminant;

√b^2 - 4ac

√(-5)^2 - (4 * 4 * 10)

√-135

The roots are imaginary

√18^2 - 4(1 * 81)

= 0

The roots are equal

√(-4)^2 - (4 * 4 * -24)

=20

The equation roots are real and different

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[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

An equation in point-slope form for this line is y=6x+5.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Given that;

Point on a line (-1,-1)

Slope of the line 6

Now, substituting the values in the general formula of line

y+1=6(x+1)

y+1=6x+6

y=6x+5

Therefore, the equation with the given slope will be y=6x+5.

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Answer: TASK 1: The answer to how much more of the atmosphere is nitrogen than all other gases combined can be found by measuring the atmospheric composition. Nitrogen makes up the largest fraction of the Earth's atmosphere, at around 78%. Oxygen makes up around 21%, while all other gases make up the remaining 1%. So, nitrogen makes up around 77% more of the atmosphere than all other gases combined.

TASK 2: I'm sorry, but there seems to be a typo in your prompt. Can you please clarify what you meant by "in the Tronosphere was separated out from"?

Step-by-step explanation:

A graph of the solution to this inequality 2.45 < x ≥ 4.6 is shown in the image attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would translate the word problem into an algebraic equation as follows;

2.45 < x ≥ 4.6

By splitting, we have the following compound inequality:

x > 2.45

x ≥ 4.6

In this scenario, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the graph contains a dashed line because of the greater than (>) symbol.

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place g(x) as the value x, into p(x)

to gain p(g(x)) = (1 / SqrRt(x) )² - 4

simplify = ( 1 / x ) - 4

find domain

x =/= 0 (undefined) & (1/4)

The equations that explains the process to find the number of square yards of fabric she will use and the number of square yards of fabric she will have left, using the addition of fractions are;

(3/8) + (2/8) = 5/8 square yards of fabric will be used

1 - 5/8 = 3/8 square yard of fabric will be left

A fraction is a representation of a part of a whole, consisting of a number in the numerator divided by another number in the denominator expressed as a quotient.

The amount of fabric Diana has = 1 square yard

Amount of fabric to make one pillow = 3/8 square yard

Amount of fabric required to make the other pillow = 2/8 square yard

Therefore, the amount of fabric Diana will use can be found by adding the fractions of the areas of the fabric she uses for each pillow as follows;

The number of square yard of fabric Diana will have left can be found from the difference between the initial number of square yards of fabric Diana has and the amount of square yards of fabric she will use.

Initial number of square yards of fabric = 1

Number of square yards of fabric she will use = 5/8

Therefore;

Number of square yard of fabric Diana has left = (Initial number of square yards of fabric) - (Number of square yards of fabric she will use)

Number of square yard of fabric Diana has left = 1 - 5/8 = (8 - 5)/8 = 3/8

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The x-intercepts are (-2, 0), (-1, 0), (1, 0), and (2, 0).

What is meant by the x-intercept?

The value of the x coordinate at the point where the graph intersects the x-axis, or alternatively, the value of the x coordinate at the point where the value of the y coordinate equals zero, is the x-intercept for any curve.

The x-intercepts are the points where the graph meets the x-axis.

Which means that the coordinate of y will be zero.

It is given in the question that the graphed function will meet the x-axis at 4 points which are (-2, 0), (-1, 0), (1, 0), and (2, 0)

Therefore the x-intercepts of the function will be: (-2, 0), (-1, 0), (1, 0), and (2, 0).

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Answer: B)  (-1,0)

Step-by-step explanation:

Just took the test on edge

Answer:

Step-by-step explanation:

To determine which option is faster, we need to determine the total number of nights required for each option.

First, let's find the number of pages Nora still needs to read by subtracting the number of pages she's already read from the total number of pages: 280 pages * 30% = 84 pages

So, Nora still needs to read 280 pages - 84 pages = 196 pages.

For Option 1, Nora would read 25% of the remaining pages each night, so the number of pages she reads each night would be: 196 pages * 25% = 49 pages

The total number of nights required would be 196 pages / 49 pages/night = 4 nights.

For Option 2, Nora would read 28 pages each night, so the total number of nights required would be 196 pages / 28 pages/night = 7 nights.

Since 4 nights is less than 7 nights, Nora should choose Option 1 to finish reading the book in the least amount of time.

The new tuition 4 years from now is $6962.68.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Given that, principal =$6691, rate of interest=1% and time period=4 years.

Now, A=6691(1+1/100)⁴

=6691(1+0.01)⁴

=6691(1.01)⁴

= 6691×1.04060401

= $6962.68

Therefore, the new tuition 4 years from now is $6962.68.

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Answer:

Base: 8. Height: 3.

Step-by-step explanation:

Let the height be x. Then the base would be 2x+2. The formula for the area of a triangle is 1/2*base*height. We know the area, and we know the base and height in terms of x. Now you just solve for x. 1/2*x*(2x+2) = 12. x(2x+2) = 24. You could plug in factors of 24, but I used the quadratic formula to solve this equation. 2x^2 +2x -24 = 0. Plugging in these values into the quadratic formula, we get that x = 3. This means that the height is 3. Since the base is 2x+2 and x is 3, then the base is 8.

The vertex of the given function is (0,4)  

What is a quadratic equation?

A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.

identify the coefficients a and b of the quadratic function

y =ax² +bx+c-------(1)

a=2, b=0

x-coordinate of the vertex is x= -b/2a = -(0)/(2(2)) = 0

Substitute  x=0 into given equation  to get y-coordinate of the vertex

y= 2(0)² + 4 = 0+4 = 4

Vertex= (x,y) = (0,4)

The vertex of the given function is (0,4)

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By using the substitution method, the value of x is equal to -1.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

2y - 4x = 8                 .......equation 1.

3(x + 4) - 2y = 5          .......equation 2.

From equation 1, we have:

y = 2x + 4         .......equation 3.

By using the substitution method to substitute equation 3 into equation 2, we have the following:

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

3x + 12 - 4x - 8 = 5

-x + 4 = 5

x = 4 - 5

x = -1.

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The slope of the line on the graph will be a negative one. Then the correct option is A.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

From the graph, the two points are (-2, 2) and (2, -2). Then the slope is given as,

m = (- 2 - 2) / (2 + 2)

m = - 4 / 4

m = - 1

The slope of the line on the graph will be a negative one. Then the correct option is A.

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The complete question is attached below.