Set up a system of equations for the given information by filling in the boxes with the coefficients of the variables and the constant values, where is the amount invested in stocks, is the amount invested in bonds, and is the amount invested in CD's.

If there is no visible coefficient, then enter

for the coefficient.

If a specific variable is not present in the equation, then enter

for the coefficient.



Country Day's scholarship fund receives a gift of $200000. The money is invested in stocks, bonds, and CDs. CDs pay 5% interest, bonds pay 2.9% interest, and stocks pay 10.9% interest. Country day invests $20000 more in bonds than in CDs. The total amount earned from the investments is $11165.

Total amount invested:
+ +

=

Total amount earned from investements:
+ +

=

Relation of bonds and CDs:
+ + =

Tomika and Mark claim a medical deduction in the amount of $1,839.8.

What is the percentage?

A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a part per hundred. Per 100 is what the word percent means. It is represented by the symbol “%

Given that the gross income is $101,598

Medical insurance = 7.5 % of $101,598

                              = 7.5% x $101,598

                             =  $7,619.88.

The insurance covered 60% of the medical expenses.

Medical deduction claim = $7,619.88 - (100% - 60%)x $3,800

                                       = $7,619.88 - 40% x $3,800

                                        = $7,619.88 - $1,520

                                        = $6,099.88

Therefore, they can claim a medical deduction in the amount of $1,839.8.

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Answer:

Step-by-step explanation:

First you go up to your y intercept which in your case would be (0,4) and plot a point.

From there you add your slope. From the point (0,4) go down 2 and left 5 and plot a point there. You do that one p=more time from the new point and then you draw your line.

Hope this helps :)

1. The union of set B and C, BUC using interval notation is (3, ∞) U (-∞, 5]

2. The intersection of set B and C, B∩C using interval notation is (4, 5]

We'll begin by obtaining the elements of set B and C. Details below:

With the above information we can determine BUC in interval notation as follow:

BUC = (3, ∞) U (-∞, 5]

We can obtain B∩C in interval notation as follow:

B∩C = (3, ∞) ∩ (-∞, 5]

B∩C = (4, 5]

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Complete question:

B and C are sets of real numbers defined as follows.

Write BUC and B∩C using interval notation.

If the set is empty, write Ø.

B= {x|x>3}

C= {x|x≤5}

Note that the rule that describes the transformation shown is: (x,y) → (x+7,-y)(Number 2)

A transformation is a broad phrase covering four distinct methods of changing the shape and/or location of a point, line, or geometric figure. The Pre-Image is the original shape of the item, and the Image is the final shape and location of the object after the transformation.

Thus, with regard to the transformation above,

At Point A: The original coordinate of point A was (-6,-6).

The coordinate after the transformation is A'(1,6), which eliminates option 3.

At Point B:

The original coordinate of point B was (-2,4).

After the transformation, we have B'(5,-4), which eliminates option 1 and option 4. It is therefore right to state that (x,y) → (x+7,-y) is the correct representation of the transformation.

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Full Question:

The missing options are:

Which rule describes the transformation shown?

1. (x,y) → (-y, x+7)

2. (x,y) → (x+7,-y)

3. (x,y) → (-x, y+7)

4. (x,y) → (y+7, -x)

Answer:1/3=22, 1=66, 1.5=99

Step-by-step explanation:

The range of scores that Steve needs to get an average of 70 to 79 is 66 to 87 Points.

To find the range of scores that Steve needs to have to stay in the 70 to 79 range we first need to define the variables that we need to find.

Let x = Score that Steve needs

Since the exam is worth 3 exams, we will then use 3x to denote the weight of the final exam.

Now we need to add all the other exams and divide it by the number of exams.

[tex]\frac{3x + 70+77+71+71}{7} = 70[/tex]

3x + 292 = 7 *70

3x = 490 -292

3x = 198

[tex]\frac{3x}{3} =\frac{198}{3}[/tex]

x = 66

Now let's look for the score that Steve needs to get to a 79 average.

[tex]\frac{3x + 70+77+71+71}{7} = 79[/tex]

3x + 292 = 7 * 79

3x + 292 = 553

3x = 553 - 292

3x = 261

x = 87

So the range of scores is 66 to 87 Points.

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The factored form of 26x^5 - 13x is 13x(2x^4 - 1).

What is the greatest common factor?

The greatest common factor (GCF), also known as the greatest common divisor (GCD) or highest common factor (HCF), is a concept in mathematics that refers to the largest positive integer that divides two or more integers without a remainder.

To factor 26x^5 - 13x using the greatest common factor, we need to find the greatest common factor of the two terms.

26x^5 = 213x^5

13x = 13*x

The greatest common factor of the two terms is 13x.

So we can factor it out:

26x^5 - 13x = (13x) (2x^4 - 1)

Hence, the factored form of 26x^5 - 13x is 13x(2x^4 - 1).

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The slope and the intercept of the linear function 6x - 3y = -6 are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

The function in this problem is given as follows:

6x - 3y = -6.

In slope-intercept form, we have that:

3y = 6x + 6

y = x + 2.

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The mass of the wine can be found by multiplying the density of the wine (0.8 kg/litre) by the volume of the wine (20 litres). The mass of the wine is 16 kg.

Its density is how much "stuff" can fit into a certain quantity of space. For instance, a block of the more resilient, lighter element gold (Au) will have a higher density than a block of the more substantial element lead (Pb) (Au). Styrofoam blocks are not as dense as bricks. Mass per unit volume serves as its definition.

We use the word "density" to indicate how much space (or "volume") an object or substance occupies in relation to the amount of matter contained therein (its mass). Density can also be defined as the quantity of mass per unit of volume.

mass = density x volume

mass = 0.8 kg/litre x 20 litres

mass = 16 kg

So, the mass of the wine is 16 kg.

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Answer: 12x + 15y = 4140, x+y = 300

Step-by-step explanation:

12x represents $12 tickets, 15y represents $15 tickets, x + y is total tickets

Answer:

that a huge prob but yeah

Chelsea wants to add one layer of 3 x 3 cubics and Stephen wants to add one layer of 3 x 6 cubics.

From given figure, the dimension of the rectangular prism are:

6 cm × 3 cm × 3 cm

The volume of the rectangular prism would be,

V = l × w × h

V =  6 × 3 × 3

V = 54 cm³

Stephen and Chelsea want to increase the volume of this prism by 72 cubic centimeters.

Chelsea wants to add eight layers.

This means 72 = 8 × 3 × 3 cubics, then one layer in this case consists of 3 x 3 cubics;

Whereas Stephen says they only need to add four layers.

This means 72 = 4 × 3 × 6 cubics, then one layer in this case consists of 3 x 6 cubics.

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Find the complete question below.

The number of laps swum by Rita: L

The number of laps swum by John: 3L

The number of laps swum by Rodell: 3L + 25

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

Explanation:

We'll use the pythagorean theorem converse.

Consider a triangle with sides a,b,c where c is the longest side.

There are 3 scenarios possible:

The middle or second scenario is probably what you're most familiar with. That's the famous pythagorean theorem without the term "converse" attached to it.

--------------

The two given sides are 8 inches and 10 inches.

Let's say the third side was 5 inches (choice F)

This means we have a triangle with sides a = 5, b = 8, c = 10

Then compute the following:

Since 89 < 100, we see that a^2+b^2 < c^2 is the case. Therefore the triangle with sides 5,8,10 is obtuse.

This will allow us to rule out choice F since we're looking for an acute triangle.

--------------

Now onto choice G.

This time the sides are: a = 6, b = 8, c = 10

Both results (a^2+b^2 and c^2) are the same at 100; so we see that a^2+b^2 = c^2.

Therefore we have a right triangle. We can rule out choice G.

--------------

Now onto choice H.

The triangle now has sides: a = 8, b = 10, c = 12

Since 164 > 144, we see that a^2+b^2 > c^2 is the case. Therefore the triangle with side lengths 8,10,12 is acute.

--------------

For the sake of completeness, let's go over choice J.

We find 164 < 169 which leads to the scenario a^2+b^2 < c^2. The triangle for choice J is obtuse. We can rule out choice J.

You can use something like GeoGebra to help visually verify these results.

Answer:

Option B: Target.

Step-by-step explanation:

Kohl's sale

1/3 × 100= 33.3% off

While,

Target sale

1/2 × 100 = 50% off

Answer:

Target (option b/second option)

Step-by-step explanation:

We have to first convert the fraction rates into percentage rates. To change a fraction to a percentage, you can divide the numerator by the denominator then multiply the result by 100. Alternatively, you can multiply the numerator by 100 first then divide the result by the denominator of the fraction.

1/2 = 50%

1/3 = 33.33%

Now reviewing this data, we see that a 50% decrease of a price is more than a 33.33% decrease.

The solution of the trigonometric function in the interval is x = 0

A trigonometric function is an equation that contains the trigonometric ratios.

Given the trigonometric function secx + tanx = 1, we proceed to solve it as  follows.

secx + tanx = 1

Using the trigonometric identity tan²x + 1 = sec²x

⇒ secx = √(1 + tan²x)

So, substituting this into the equation, we have that

secx + tanx = 1

√(1 + tan²x) + tanx = 1

√(1 + tan²x) = 1 - tanx

Squaring both sides of the equation, we have that

√(1 + tan²x) = 1 - tanx

√(1 + tan²x)² = (1 - tanx)²

1 + tan²x = 1 - 2tanx + tan²x

Substracting 1 from both sides, we have that

1 - 1 + tan²x = 1 - 1 - 2tanx + tan²x

0 + tan²x = 0 - 2tanx + tan²x

tan²x = - 2tanx + tan²x

Substracting tan²x from both sides, we have that

tan²x - tan²x= - 2tanx + tan²x - tan²x

0 = -2tanx + 0

0 = -2tanx

tanx = 0/-2

tanx = 0

taking inverse tan, we have that

x = tan⁻¹0

x = 0

So, the solution is x = 0

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Answer: m<1 refers to the measure of an angle in a plane. The symbol < indicates that it is a smaller angle than a right angle which has a measure of 90 degrees. The value of m<1 is the measure of that angle in degrees.

36°, 70 degree and 1 degree are all measures of angles, but they are not necessarily the measure of m<1. Without any further context or information, it is not possible to say what m<1 is equal to.

Step-by-step explanation:

The formula for the cost, C, of hiring a DJ for n hours is C = hn + e

a. The formula for the cost, C, of hiring a DJ for n hours is C = hn + e, where h is the hourly fee and e is the equipment setup fee.

b. To find the inverse of the formula, we can solve for n in terms of C and h:

n = (C - e) / h

The new formula represents the number of hours the DJ was hired for given the cost, C, and the hourly fee, h.

c. If the DJ charged $550, we can use the inverse formula to find the number of hours she was hired for.

n = (550 - e) / h

where e is equipment setup fee.

Since we are not given the equipment setup fee, we can't calculate the number of hours she was hired for.

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A) x²  - 2x - 13 in the form of (x + c)²  + d is (x - 1)²  - 15, and the value of

c = -1, d = -15

B) The solutions of the equation are 1+ √15 and 1- √15.

A quadratic equation is a type of polynomial equation that has the general form of ax² + bx + c = 0, where x is the variable, a, b, and c are constants, and a is not equal to zero.

a) To write x²  - 2x - 13 in the form (x + c)²  + d, we can complete the square.

First, we add and subtract (2/2)²  = 1 to get:

x²  - 2x - 13 = x²  - 2x - 13 + 1 - 1

Next, we group the terms:

(x²  - 2x) - 14 = (x²  - 2x + 1) - 15

Now, we can see that the left side of the equation is a perfect square trinomial. To complete the square, we add the square of half of the coefficient of the x term, which is (1)² = 1 to both sides:

(x - 1)²  - 15 = 0

So, x² - 2x - 13 = (x - 1)²  - 15

c = -1, d = -15

b) Using the answer from part a, we know that x² - 2x - 13 = (x - 1)² - 15

=0

so (x-1)² = 15

x-1 = ± √15

x = 1 ± √15

The solutions of the equation are 1+ √15 and 1- √15.

In the form a = fg, where f and g are integers:

a = 1, f = 1, g = √15

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Answer:

a= 3/

Step-by-step explanation:

2/3a-1/6=1/3

2/3a=1/3+1/6

2/3a=1/2

a=1/2×3/

a=3/

Answer:

-79.9

Step-by-step explanation:

-60.7-19.2=-79.9

Answer: -79.9

Step-by-step explanation:

Subtract 19.2 from both sides of the equation to isolate the X.

0 + X = -60.7 - 19.2

X = -79.9

You can also check your answer by plugging in X into the equation and seeing if it equals -60.7

Answer:

$20239.6

Step-by-step explanation:

The amount financed for the car is $25,800 - $8,000 = $17,800.

To find the monthly payment, you can use the formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

where M is the monthly payment, P is the amount financed, i is the monthly interest rate (3.99%/12), and n is the number of payments (60 months).

So,

i = 3.99%/12 = 0.00399

n = 60

M = $17,800 [ 0.00399(1 + 0.00399)^60 ] / [ (1 + 0.00399)^60 – 1]

M ≈ $337.31

So, Michelle will make monthly payments of $337.31 for 60 months.

To find the total amount that Michelle will pay for the car, you can multiply the monthly payment by the number of payments:

$337.31 x 60 = $20239.6

So, the total amount that Michelle will pay for the car is $20239.6

The length of the side XY taken out by using trigonometric formulas is 12.208 cm.

Now we know that ΔWXY is a right-angled triangle. With ∠XWY = 90°

Hence we see that we can use the trigonometric formulas to find the length of XY

Since ∠YWX = 35° with XW being the corresponding side and XY being the hypotenuse we can use the formula

cosx = base/hypotenuse

Now using a scientific calculator we can calculate

cos35 to be 0.81915

or, base/hypotenuse = 0.81915

or, WX/XY = 0.81915

or, 10/XY = 0.81915

or, XY = 10/0.81915

or, XY = 12.208 cm

Hence the length of side XY is 12.208 cm.

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Complete Question

(Image Attached)

The speed travelled by mars in miles per minutes is 900. As Given that the mars revolves around the sun at a rate of approximately 15 miles per second.

We know that , Speed = distance / time

Hence we have speed of the mars as  15 miles/sec.

To convert the rate from miles/sec to miles/ minute we have to multiply the given with minute i.e 60 sec.

                    miles x min    =   miles x 60 sec          

                     sec x min              sec x min

           since , 1 minute = 60 sec

 hence, new speed = 15 x 60 miles/ minute.

Therefore , the speed travelled by mars in miles per minutes is 900.

( a) In two minutes mars will travel 900 x 2 times with the same rate.

        i.e 1800 miles per minute.

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The complete question is:

as mars revolves around the sun, it travels at a rate of approximately 15 miles per second. convert this rate to miles per minute. at this rate, how many miles will mars travel in 2 minutes ?

Answer:

Answer

Step-by-step explanation:

you can answer these NUTS!!!

Answer:

x - 2/3 = 2/3

Answer: x-2/3=2/3

Step-by-step explanation:

g(x) is the vertical stretch and reflection about the x-axis. Hence option (B) is the correct answer.

Vertical compression by a factor M: g(x) = m*f(x)  (m<1)

m = -1.4

it means for given value of xg(x) < f(x)

Vertical stretch by a factor m: g(x) = (1/m)*f(x) (|m|>1)

hence given vlaue of x g(x) > f(x)

reflection about x axis : y = -f(x)

So, In the given plot, we can say that g(x) is a reflection of f(x) about the x-axis,

and g(x) > f(x) for any value of x it denotes stretch

Therefore, g(x) is the vertical stretch and reflection about the x-axis.

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The difference in temperature at 10 a.m. and 3:30 p.m. is -3.3 degree Fahrenheit

When the time was 10 in the morning the temperature was 1.2 degrees Fahrenheit

When it was 3.30 in the afternoon, the temperature was - 2.1 degrees fahrenheit

The difference that would be in the temperatures that we have here would be:

-2.1 - 1.2

= -3.3 degrees fahrenheit

This tells us that there is a decrease in temperature in this time frame

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complete question

shows the exact temperatures at three different times in Beltsville, Md., one day last

3.30 p.m.

-2.1° F

Noon

10 a.m.

1.2° F

Time

Temperature

winter.

0° F

What is the difference between the temperatures at 10 a.m. and 3:30 p.m.? Indicate whether the

Answer:

see below

Step-by-step explanation:

C; slope =1/5. The flame length will increase at 5x of the speed increase

or, the speed increase is 1/5 of the flame length increase.

F: Y intercept in the graph is 0, so nothing has happened yet.  no fire, no flame.