Theodore invests a total of $11,000 in two accounts paying 8% and 4% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $780.00.

________ was invested at 8% and

______ was invested at 4%.

1) Between the years 2003 and 2009, 768 students joined the school.

2) It took 6 years for the population to grow from 1219 students to 1987 students.

3) The average population growth per year is 128 students per year.

P = 128 students per year

4) The population of students in the year 2000 was a total of 835 students.

5) 1219 + (p3) = 1987

6) 1987 + (p3) = 2371

P3 = 384

Answer:

[tex]g(x)= -3x^{2} +4x +5[/tex]

Step-by-step explanation:

Five more = Addition of 5

Opposite = (-)

3 times = Multiplication by 3

Square = To the power (exponent) of two

4 times the number = Multiplication by 4

The number = unknown number = x

This value is approximate

=======================================================

Work Shown:

[tex]\log_{10}(2) \approx 0.301\\\\\log_{10}(3) \approx 0.477\\\\\log_{10}(6) = \log_{10}(2*3)\\\\\log_{10}(6) = \log_{10}(2)+\log_{10}(3) \ \text{ see note below}\\\\\log_{10}(6) \approx 0.301 + 0.477\\\\\log_{10}(6) \approx 0.778\\\\[/tex]

Note: I used the rule that log(A*B) = log(A)+log(B) which works for any valid log base.

Step-by-step explanation:

Since the question has already been answered, I'd like to add something new, and explain why: [tex]log_b(a*c)=log_ba+log_bc[/tex]

So let's just say that:

[tex]x=log_ba[/tex] and that [tex]y=log_bc[/tex]

This means that: [tex]b^x=a[/tex] and that [tex]b^y=c[/tex].

So if we were to multiply the two, a and c. You get

[tex]a*c=b^{x+y}[/tex]

This is due to the exponent identity that: [tex]b^a*b^c=b^{a+c}[/tex]

So if you rewrite this in logarithmic form you get:

[tex]log_b{ac}=x+y[/tex]

and remember what x and y are equal to? that's right, it's the logarithms

so now you substitute the logarithms back in and get

[tex]log_b{ac} = log_ba+log_bc[/tex]

Answer:

Proof:

By the inscribed angle theorem, we know that angle BAC is equal to angle DEC. By the second corollary to the inscribed angle theorem, we know that line segment AE is perpendicular to line segment AC. Therefore, line segment AE is tangent to circle C.

Step-by-step explanation:

Analyze and ensure the answer is correct.

Answer:

Step-by-step:

By the inscribed angle theorem, we know that angle BAC is equal to angle DEC. By the second corollary to the inscribed angle theorem, we know that line segment AE is perpendicular to line segment AC. Therefore, line segment AE is tangent to circle C.

Answer:

8

Step-by-step explanation:

12+4=16

16 divided by 2= 8

Based on the conditional statement given, the truth value can be found to be T T → T.

The truth value can be found by using the Boolean Table which is shown as:

p        q        p → q

T         T        T

T         F        F

F         T        T

F         F        T

From the table, we can then see that if both p and q are true, then p → q is true as well.

We will then have a truth value of T T → T.

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Answer:The answer is 27.04

Step-by-step explanation:

The solution is in the attached

Answer:

35

Step-by-step explanation:

28 Orange Marbles divided by 4 Orange Marbles =

7

5 Blue Marbles for every 7 Orange Marbles =

35

The equation solved for w is w = 6g - 40

The complete question is in the attached image

The equation is given as:

g = 1/6(w + 40)

Multiply both sides by 6

6g = w + 40

Subtract 40 from both sides

w = 6g - 40

Hence, the equation solved for w is w = 6g - 40

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Answer:

f-(g/h) is an algebraic expression of the difference of f and the quotient of g and h.

Step-by-step explanation:

[tex]f - ( \frac{g}{h} )[/tex]

I hope it was helpful for you..m

The requried algebraic expression of English phrase is given as f - g/h.

The algebraic expression consists of constants and variables. eg x, y, z, etc.

the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
The difference between f and the quotient of g and h.
The difference represents the subtraction of values, and the quotient can be obtained by division of g by h.
So,
Required algebraic expression,
= f - g/h

Thus, the required expression is given as f - g/h.

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Answer:

  B.  360 meters

Step-by-step explanation:

The triangles shown are similar, so their corresponding parts are proportional.

There are a couple of useful proportions here. We can equate the ratio of horizontal segments to the ratio of diagonal segments:

  (600 m)/(250 m) = ??/(150 m)

Or, we can equate the ratios of the diagonal segment to the corresponding horizontal segment:

  ??/(600 m) = (150 m)/(250 m)

Either way, when we multiply the equation by the denominator of ??, we get the result ...

  ?? = (600)(150/250) m = 360 m

The distance from F to G is 360 meters.

Answer:

Step-by-step explanation:

This problem is similar to many others in which the sum of two quantities and their difference are given. The solution can be found easily when the equations for the relations are written in standard form.

Let s and h represent numbers of sodas and hot dogs sold, respectively. The given relations are ...

Adding the two equations eliminates one variable.

  (s +h) +(s -h) = (235) +(59)

  2s = 294 . . . . simplify

  s = 147 . . . . . .divide by 2

  h = 147 -59 = 88 . . . . h is 59 less

147 sodas and 88 hot dogs were sold.

__

Additional comment

The solution to a "sum and difference" problem is always the same. One of the numbers is half the sum of those given, and the other is half their difference. ((235-59)/2 = 88)

The mean of the data about students size of Mr. Sirac classes is 24.

Given students size of each of Mr. Sirac'sclasses 21,20,22,23,24,25,26,28,27 and we have to find the mean of the data.

We know that mean is the basically sum of numbers divided by the number. It is also known as average.

Mean =∑X/n where n is number of values and ∑X is sum of all the values.

∑X=21+20+22+23+24+25+26+28+27

=216

n=9

Mean is calculated by dividing sum by n.

Mean =216/9

=24

Hence the mean of the data about students size of each of Mr. Sirac classes is 24.

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Answer:

our volume is 4500cm³

Step-by-step explanation:

note: the following will be assuming that this fish tank is rectangular, as most fish tanks are

To find the volume of a rectangular structure, we multiply :

length × width × height

here, we know our

length to be 12 cm

width to be 15 cm

and height/depth to be 25 cm

so, we can follow our volume formula (length × width × height) using these values

length × width × height = volume

12 × 15 × 25 = 4500

so, our volume is 4500cm³

(also called 4500cubic centimeters)

(we write volume as cubed--units³)

hope this helps! have a lovely day :)

The product is equal to:

[tex]\frac{18}{25}(cos(165) + i*sin(165))[/tex]

Remember that we can write a complex number in polar form as:

[tex]R*e^{i*a} = R*(cos(a) + i*sin(a))[/tex]

Then the given product:

[tex]\frac{6}{5}*(cos(120) + i*sin(120))*\frac{3}{5}*(cos(45) + i*sin(45))[/tex]

can be rewritten to:

[tex](\frac{6}{5}*e^{i*120})*(\frac{3}{5}*e^{i*45})[/tex]

Now is easier to solve the product:

[tex](\frac{6}{5}*e^{i*120})*(\frac{3}{5}*e^{i*45})\\\\= \frac{6}{5} *\frac{3}{5} *e^{i*(120 + 45)}\\\\= \frac{18}{25}*e^{i*165}\\\\= \frac{18}{25}(cos(165) + i*sin(165))[/tex]

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Answer:

Step-by-step explanation:

x=40

Answer:

here is

Step-by-step explanation:

5x-20=180

5x=180+20

=200

X=200/5

40

Answer:

4

Step-by-step explanation:

The common difference is found by subtracting the 2nd term from the 1st term. In this example we can say 11 is the 2nd term and 7 is the 1st term. 11 - 7 = 4.

Answer:

0.36ml

Step-by-step explanation:

Note: micrograms = [tex]10^{-6} g[/tex]

Given the concentration,

[tex]500*10^{-6} g = 1ml\\1*10^{-6}g =\frac{1}{500} ml\\180*10^{-6} g=(\frac{1}{500} *180)ml\\180micrograms = 0.36ml[/tex]

The range of the given relation is:   range = { 3, 9, 10}

Range is the out come of the event is know as y.

Here, the given relation:

               R = {(0,3), (8,9), (16,10)

Now, range = { 3, 9, 10}

Thus, the range of the given relation is: range = { 3, 9, 10}

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By using the table, we see that the correct options are:

a) f(2) = 7

b) f(x) = 3 when x = 8.

c) f⁻¹(7) = 2

d) f⁻¹(x) = 8 when x = 3.

Here we have a table of x and f(x).

First, we want to find f(2). To get that, we need to go to the row where we have x = 2.

In that same row we can see that f(x) = 7.

Then f(2) = 7.

Then it says:

"if f(x) = 3, then x = ?"

This time we do the opposite. We find the row where f(x) = 3, and then we see the value of x in that row.

In the second row (counting from the bottom) we can see that when x = 8, f(x) = 3.

Then:

"if f(x) = 3, x = 8"

Then we want to get the inverse of f(x) evaluated in 7.

Here we use the rule:

[tex]f(x) = y\\f^{-1}(y) = x[/tex]

Then

[tex]f(2) = 7\\f^{-1}(7) = 2[/tex]

The answer here is 2.

Finally:

"if the inverse evaluated in x si 8, then what is the value of x"

Similar to before, we know that when we evaluate f(x) in 8, the outcome is 3.

Then when we evaluate the inverse in 3, the outcome is 8.

So here we must have x = 3.

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The equation of the line through the points is y = 3/5 + 1/5.

First, we find the Slope using the formula: m = y2 - y1/x2 - x1

You may choose any two points but I will use these two for no reason at all.)

Points: (3,2) and (8,5)

m = y2 - y1/x2 - x1

m = 5 - 2/8 - 3

m = 3/5

Now that we have the slope, we can now find the Slope-Intercept Form by using the Slope Form Formula. (need at least one point and slope.)

Formula: y - y1 = m(x - x1)

Point: (3,2)

y - y1 = m(x - x1)

y - 2 = 3/5(x - 3)

y - 2 = 3/5x - 9/5

y - 2 = 3/5x - 9/5

y = 3/5x - 9/5 + 10/5 (2 can be is any fraction that consists of the numerator multiplied twice by the denominator, such as 2/1, 4/2, 8/4, etc.)

y = 3/5 + 1/5

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The graph which has the same end behaviour as the function given; f(x) = (10x³+x² +3)/(2x²+1) is; a linear graph whose slope is 5.

The function given can further be simplified by means of polynomial division in which case;

although not a perfect division; the quotient of the division is; (5x-0.5) and evidently, the function which would have the same end behaviour as the given function is a linear function whose slope is 5.

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Answer:

C

Step-by-step explanation:

it just is

A) A parallelogram has 4 sides.

B) The opposite angles of parallelogram are congruent.

C) [tex]\angle A \cong \angle C, \angle B \cong \angle D\\\\\implies m\angle C=115^{\circ}, m\angle D=65^{\circ}[/tex]

The slope m = 3/2 and the y-intercept = ( 0, -6 ).

The graph is a solid line and shaded area below the boundary line since y is less than (3/2)x - 6.

Given that:

3x -2y ≥ 12

First we write the inequality in slope intercept form y = mx + b.

Solve for y

3x -2y ≥ 12

-2y ≥ 12 - 3x

Now, divide each term by -2

y ≤ -6 + 3x/2

We re-arrange

y ≤ (3/2)x - 6

Using the slope intercept form y = mx + b. we can see that;

m = 3/2

b = -6

Hence, the slope m = 3/2 and the y-intercept = ( 0, -6 ).

The graph is a solid line and shaded area below the boundary line since y is less than (3/2)x - 6.

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Answer:

Step-by-step explanation:

The attached graph shows the graph opens downward, so the vertex at (-2, 6) is a maximum. The y-intercept is the constant, +2.

The range is the vertical extent of the function. Its upper limit is the maximum value of the function (6), and its lower limit is negative infinity.

  The range is {y l y ≤ 6}.

The graph opens downward, so it is increasing to the left of its maximum value, and decreasing to the right of its maximum. The x-coordinate of the maximum (-2) defines the upper limit of the increasing interval.

  The function is increasing over the interval (-∞, -2).

The y-intercept of the graph is where it crosses the y-axis. The value of x is zero there, so the value of the function is the value of its constant, +2.

  The function has a positive y-intercept.

Answer:

4² + b² = 12²

16 + b² = 144

b² = 144 - 16

b² = 128

b = √128

b = 11.3 feet

Step-by-step explanation: