Alex Murphy purchased a TV with surround sound and remote control on an installment plan with a 60 down payment and 12 payments of $104.63. Find the installment price of the TV.

Answer:

In order: 18, 24, 48

Step-by-step explanation:

Let the number on the three evenings be a, b, and c, in order.

a + b + c = 90

a = b - 6

c = 2b

b - 6 + b + 2b = 90

4b - 6 = 90

4b = 96

b = 24

a = b - 6 = 24 - 6 = 18

c = 2b = 2(24) = 48

In order: 18, 24, 48

a. The probability of a pregnancy lasting 309 days or longer is approximately 0.0021, or 0.21%.

b. The length that separates premature babies from those who are not premature is approximately 235.25 days.

a. To find the probability of a pregnancy lasting 309 days or longer, we need to calculate the area under the normal distribution curve to the right of 309 days.

Using the z-score formula: z = (x - μ) / σ, where x is the value of interest, μ is the mean, and σ is the standard deviation, we can calculate the z-score for 309 days:

z = (309 - 266) / 15 = 43 / 15 ≈ 2.87

Now, we can use a standard normal distribution table or a calculator to find the probability associated with the z-score of 2.87. From the standard normal distribution table, we find that the area to the right of 2.87 is approximately 0.0021.

Therefore, the probability of a pregnancy lasting 309 days or longer is approximately 0.0021, or 0.21%.

b. To find the length that separates premature babies from those who are not premature, we need to determine the z-score corresponding to the lowest 2% of the normal distribution.

From the standard normal distribution table, we find the z-score associated with the lowest 2% to be approximately -2.05.

Now, we can use the z-score formula and solve for x to find the corresponding length:

-2.05 = (x - 266) / 15

Solving for x:

x - 266 = -2.05 * 15

x - 266 = -30.75

x = -30.75 + 266

x ≈ 235.25

Therefore, the length that separates premature babies from those who are not premature is approximately 235.25 days.

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The required expression is

[tex]( 10x^{6}) \sqrt7[/tex]

Radical expressions are algebraic expressions involving radicals. The radical expressions consist of the root of an algebraic expression (number, variables, or combination of both).

The root can be a square root, cube root, or in general, nth root.

Simplifying radical expressions implies reducing the algebraic expressions to the simplest form and, if possible, completely eliminating the radicals from the expressions.

Given the radical expression

[tex]13x^{2} \sqrt7x^{8}-3\sqrt7x^{12}[/tex]

Take the square root of x⁸ and x¹²

[tex]13x^{2} \sqrt7x^{4}-3\sqrt7x^{6}[/tex]

Factor out √7 which is common to both terms

[tex]\sqrt7(13x^{6} -3x^{6})[/tex]

Simplify the terms in the bracket

[tex] \sqrt7( 10x^{6} )[/tex]

Rewrite the expression

[tex]( 10x^{6}) \sqrt7[/tex]

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Answer:c

Step-by-step explanation:

The congruence theorems or postulates that are taken to be reasons why ABV≈ XYZ are SSS and SAS. That is option A and C.

The congruence theorem of triangle consist of various theorem that shows how two triangles are similar. They include the following:

Side side side theorem(SSS): This states that triangles are congruent if the three sides of one are equal to the three sides of another one.

Side angle side theorem(SAS): This states that triangles are congruent if two sides and one angle (between the sides) of one triangle are equal to two sides and one angle of another triangle.

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The amount of medicine to be taken in each dose is 13/20 tablespoons.

To find the amount of medicine to be taken in each dose, we need to divide the total amount of medicine (2 3/5 tablespoons) by the number of doses (4).

First, let's convert the mixed number 2 3/5 into an improper fraction:

2 3/5 = (2 * 5 + 3)/5 = 13/5

Now, we can divide 13/5 by 4 to find the amount of medicine per dose:

(13/5) / 4 = 13/5 * 1/4 = 13/20

Therefore, 13/20 teaspoons of the medication should be consumed for each dose.

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Answer:

Step-by-step explanation:

101.50 x 28 = 2,842.00

Price of TV = 2,499.00

2,842.00 - 2,499.00 = 343.00

$343.00 was paid in finance charges

Picture it like this! Imagine you're running an extraordinary and magical Soup Express, a unique train that only serves delicious soup. Now, this peculiar train only has 144 seats available for each journey, and the moment has come when a bustling crowd of 1990 hungry passengers are waiting eagerly at the platform to board the Soup Express.

So, how many trips must your Soup Express make to serve all the soup-loving travelers?

To find that out, you'll divide the total number of passengers by the number of seats available on your train. That's 1990 passengers divided by 144 seats, which gives you about 13.82 trips. But, oh, the Soup Express can't very well make .82 of a trip, now can it? Your train must make full trips! So, you'll need to round up because even if there is just one passenger left, your train must still make the journey.

So, it turns out your Soup Express will need to make 14 full trips!

Now, let's find out how many passengers will be riding the final journey of the Soup Express. It's like having the leftovers after a grand feast! You've already served 13 full train journeys, each carrying 144 passengers. That's 13 journeys times 144 passengers, which equals 1872 satisfied soup enthusiasts!

But remember, you started with 1990 hungry passengers. So, to find out how many are left for the final trip, subtract the number of passengers already served from the total. That's 1990 minus 1872, which equals 118 passengers.

So, there you have it! The Soup Express will make 14 marvelous soup-serving trips, and the final journey will have 118 content passengers sipping on their favorite soup as they ride off into the sunset!

Alright, let's solve this system of equations whimsically, shall we?

First, imagine these lines as threads of destiny. Each equation is like a thread weaving through the vast fabric of the cosmos, plotted on the 2D plane of our imagination.

So let's embark on this mathematical journey together!

Our first traveler is Line 1, or as we'll call him, "Sir L1." He struts along with the equation y = 3x + 1. His path is clear: for every step he takes in the x direction, he ascends 3 steps in the y. He's quite the climber!

Next, we meet Lady L2 with the equation y = 2x - 3. A bit more relaxed than Sir L1, she ascends 2 steps in the y direction for every step in the x. They clearly don't cross paths—they're too different in their inclinations. This means that Sir L1 and Lady L2 are consistent and independent.

Our third traveler is the mysterious Master L3. His equation is slightly different, written as 3y + x = 6. Let's write this in y = mx + c form to match our other travelers. With a little rearranging, we get y = -1/3x + 2. He's a bit of a downer, descending 1 step in y for every 3 steps in x. Observing him from afar, it's clear he never intersects with Lady L2 or Sir L1. They're all leading their independent lives.

Lastly, we have the young Miss L4, with her equation y = 1/3x - 1. She's a gentle traveler, ascending only a third of a step in y for every step in x. However, like the others, she doesn't cross paths with any of our other travelers.

So, in this whimsical world of equations, it appears that none of our travelers cross paths. Each one treads their own unique path. This means our system of equations is indeed consistent, but each line is independent, meaning they don't intersect, and each has a unique solution. There are no shared points of intersection. It seems our travelers are lone wolves in this cosmos of coordinates!

The equation for the total value is 0.01p + 0.25q = 3.90

The equation for the total number of coins is p + q = 54

Let p represent the number of pennies and q represent the number of quarters in the jar.

The total value of the coins can be expressed as the sum of the values of the pennies and quarters.

Since each penny is worth $0.01 and each quarter is worth $0.25, the equation for the total value can be written as:

0.01p + 0.25q = 3.90

Additionally, we know that there are a total of 54 coins in the jar, so the equation for the total number of coins can be written as:

p + q = 54

These two equations form a system that can be solved simultaneously to find the values of p and q.

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Answer:

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

[tex]f(g(2))=f(6\cdot2-8)=f(12-8)=f(4)=2(4)^2+1=2(16)+1=32+1=33[/tex]

[tex]f(g(x))=f(6x-8)=2(6x-8)^2+1[/tex]

[tex]g(f(x))=g(2x^2+1)=6(2x^2+1)-8=12x^2+6-8=12x^2-2[/tex]

[tex](g\circ g)(x)=g(g(x))=g(6x-8)=6(6x-8)-8=36x-48-8=36x-56[/tex]

[tex](f\circ f)(-2)=f(f(-2))=f(2(-2)^2+1)=f(9)=2(9)^2+1=2(81)+1=163[/tex]

Answer: 0.4714

Step-by-step explanation: square root of 8 is 2.8284 divided by 6 = 0.4714.

[tex] \frac{6}{ \sqrt{8x} } \\ \frac{ {6}^{2} }{ {( \sqrt{8x)} }^{2} } \\ \\ \frac{36}{8x} \\ \ \\ \frac{36 \div 4}{8x \div 4} \\ \\ \frac{9}{2x} [/tex]

this is one of the ways to simplify it

you can divide 9 by 2 the answer will be 4.5x

Answer: 8

Step-by-step explanation:

From the circle.

CF . BF = EF . DF

9.6 = 3. (10+x)

54= 30+3x

3x = 24

x = 8

The sin(14°) = opp/1opp = sin(14°)The exact value of x in M194° is therefore x = sin(14°) or approximately 0.2419 (rounded to four decimal places).

To solve for x in M194°, we first need to understand the concept of reference angles.A reference angle is the acute angle formed between the terminal side of an angle and the x-axis in standard position.

To find the reference angle of M194°, we subtract 180° from 194°:

Reference angle = 194° - 180° = 14°We can use this reference angle to determine the quadrant in which M194° lies and find the exact value of x using trigonometric ratios.

The angle M194° is in the third quadrant since it is greater than 180° but less than 270°.

In the third quadrant, sine and cosecant are positive. Therefore, we can use the sine ratio to solve for x.sin(14°) = opp/hypwhere opp is the opposite side and hyp is the hypotenuse. Since the hypotenuse is not given, we can assume it to be 1.

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The log expression that is equivalent to [tex]\log_8 4a[ \frac{b - 4}{c^4} ][/tex] is log₈4 + log₈a + (log₈(b - 4)) - 4log₈C.

The equivalent log expression is determined by applying the rules of logarithm as follows;

The given logarithm expression;

[tex]\log_8 4a[ \frac{b - 4}{c^4} ][/tex]

This expression is expanded as follows; we will use the equal base of 8;

[tex]\log_8 4a[ \frac{b - 4}{c^4} ][/tex] = log₈4 + log₈a + (log₈(b - 4)) - 4log₈C

Note: when we write the division of a log in a linear, we use the operator (-), that is negative sign. Also, the power becomes the coefficient (c⁴ = 4C).

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The complete question is below:

Which expression is equivalent to [tex]\log_8 4a[ \frac{b - 4}{c^4} ][/tex]?

Answer:

67/100

Step-by-step explanation:

Percent means out of 100.

67% = 67/100

Answer:

67/100

Step-by-step explanation:

Rounded to the nearest square kilometer, the area of the forest after 8 years will be approximately 2773 km².

To find the area of the forest after 8 years, we need to calculate the successive decreases in area over each year.

Let's denote the initial area of the forest as A₀ = 5000 km².

Each year, the area decreases by 7.5%, which means it remains at 92.5% of the previous year's area.

After 1 year, the area will be:

A₁ = A₀ - 0.075 * A₀ = 0.925 * A₀

After 2 years, the area will be:

A₂ = 0.925 * A₁ = 0.925 * (0.925 * A₀) = (0.925)² * A₀

Similarly, we can continue this process for 8 years:

A₈ = (0.925)⁸ * A₀

Now, let's calculate the final area after 8 years:

A₈ = (0.925)⁸ * A₀

≈ 0.55465 * A₀ (rounded to 5 decimal places)

To find the area in square kilometers, we multiply this value by the initial area A₀:

A₈ ≈ 0.55465 * 5000 km²

≈ 2773.25 km²

Rounded to the nearest square kilometer, the area of the forest after 8 years will be approximately 2773 km².

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Answer:375<52m

Step-by-step explanation:

jennifer will want at least 375 so you could get more and 52 is about per month m so 375<52m

Answer:

4. 375 < 52m

Step-by-step explanation:

In this inequality, "m" represents the number of months Jennifer will need to save in order to afford the party. The left side of the inequality, 375, represents the cost of the party, which Jennifer wants to be able to afford. The right side of the inequality, 52m, represents the amount of money Jennifer saves per month multiplied by the number of months, which should be more than or equal to the cost of the party for her to afford it!

Hope this helps, thank you.

Answer: 127

Step-by-step explanation:

Vertical Angles mean that those 2 angles are equal.

Thus,

You set the two equations equal to each other and solve for the value of x.

5x+12 = 6x-11

x = 23

Next

Once you find the value of x you need to plug in 23 back into any equation to get the value of your angle.

5(23) + 12 = 127

Answer:

To find the monthly payment for a 3-year auto loan at 4% annual interest compounding monthly, we can use the formula for **monthly payment for a loan**:

```

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

```

where:

- M is the monthly payment

- P is the principal or amount borrowed

- i is the monthly interest rate

- n is the number of months

In this case, the principal or amount borrowed is $18,000 and the down payment is $2,000. Therefore, the principal amount that needs to be financed is $16,000.

The monthly interest rate can be calculated by dividing the annual interest rate by 12. In this case, the annual interest rate is 4%, so the monthly interest rate is 4% / 12 = 0.00333333.

The number of months can be calculated by multiplying the number of years by 12. In this case, the number of months is 3 years x 12 months/year = 36 months.

Now we can substitute these values into the formula:

```

M = $16,000 [ 0.00333333(1 + 0.00333333)^36 ] / [ (1 + 0.00333333)^36 – 1]

```

Simplifying this expression gives us:

```

M = $468.43

```

Therefore, Carmen's monthly payment will be **$468.43** .

The perimeter of the triangle ABC is 60units

A triangle is a polygon with three sides having three vertices.

Perimeter is a math concept that measures the total length around the outside of a shape.

Since the radius of the circle is 4,

The hypotenuse = 6+x

base = 4+x

Using Pythagorean theorem

(6+x)² = 10² + (4+x)²

36+12x +x² = 100+ 16 + 8x + x²

collecting like terms

116-36 = 12x -8x

80x = 4x

x = 80/4

x = 20

Therefore ;

hypotenuse = 20+6 = 26

base = 20+4 = 24

Perimeter of the triangle = 26+24+10

= 60 units

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The sequence of transformations that proves that the shapes are similar is given as follows:

B. a reflection across the x-axis, and then a dilation by a scale factor of 1.5

First, we have that the orientation of the figure, hence it was reflected.

The figure was reflected from the second quadrant to the third quadrant, hence the figure was reflected over the x-axis.

The base segment changes from a length of 2 units to a 3 units, hence the scale factor of the dilation is given as follows:

3/2 = 1.5.

Hence option B is the correct option for this problem.

The missing parts of the problem are given by the image presented at the end of the answer.

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Answer:

26

Step-by-step explanation:

Since 2 teachers have 40 students together, we have to divide 40 by 2:

40÷2=20

Now the new information is "Ms. fielder has 6 more students than Mr. Pearce." So we minus 6 from one side and add it to 5 the other:

20-6=14

20+6=26

So Ms. Felder has 26 students in all.

I hope this helps...

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Have a nice day!

Pi is an irrational number and belongs to the set of real numbers. It is not part of the sets of natural numbers, whole numbers, integers, or rational numbers due to its non-integer and non-fractional nature. Pi is a unique and fundamental mathematical constant with significant applications in various fields of mathematics and science.

Pi, denoted by the Greek letter π, is a mathematical constant that has been widely used throughout history. It is a transcendental number, which means it is not the root of any non-zero polynomial equation with rational coefficients. Pi is approximately equal to 3.14159, but its decimal representation continues infinitely without repetition.

Let's examine each set and determine if pi belongs to them:

1. Natural numbers: Natural numbers are positive integers starting from 1. Since pi is not an integer, it does not belong to the set of natural numbers. Pi represents a ratio of a circle's circumference to its diameter, and it cannot be expressed as a whole number.

2. Whole numbers: Whole numbers include non-negative integers, including zero. Similar to the natural numbers, pi is not a whole number as it is not an integer. Therefore, pi is not part of the set of whole numbers.

3. Integers: Integers consist of positive and negative whole numbers, including zero. Since pi is not an integer, it is not an element of the set of integers. Pi's decimal expansion goes beyond any finite integer value.

4. Rational numbers: Rational numbers are numbers that can be expressed as a fraction of two integers. However, pi is not a rational number. Its decimal representation is non-terminating and non-repeating, which means it cannot be expressed as a fraction of two integers.

5. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction. Pi falls into this category, as it has an infinite and non-repeating decimal expansion. Pi is a famous example of an irrational number, and it cannot be expressed as a simple fraction.

6. Real numbers: Real numbers encompass both rational and irrational numbers. Pi is an irrational number, and therefore, it is included in the set of real numbers. Real numbers represent all possible points on the number line, including both rational and irrational numbers.

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The question probable may be:

Choose all the sets containing the number Pi:

natural numbers

whole numbers

integers

rational numbers

irrational numbers

real numbers  

The reflection of the point (–4, 6) across both axes is (b) (4, -6)

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

Point = (-4, 6)

The rule of reflections across both axes is

(x, y) = (-x, -y)

Using the above as a guide, we have the following:

Image = (4, -6)

Hence, the reflection of the point (–4, 6) across both axes is (b) (4, -6)

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Expert needed for this one

The monthly earnings are less than the amount needed to pay the monthly car insurance bill of $200, the answer is no, the car insurance bill cannot be afforded.

Calculation of bi-weekly paycheck based on 20 hour weeks at a rate of $9.00 per hour is done below:

Earnings before deductions = $9.00 x 20 = $180.00

Now, we will calculate the total amount of deductions made from the earnings.

Total deductions = Federal Income Tax (11.9%) + State Income Tax (3.6%) + F.I.C.A (7.65%) + professional dues

= 11.9% + 3.6% + 7.65% + professional dues

= 23.15% + professional dues

Since the amount of professional dues is not given, we will assume it to be 2%.

Total deductions = 23.15% + 2% = 25.15% of earnings.

Now, we will calculate the amount of deductions made from the earnings.

Amount of deductions = 25.15% x $180.00

= $45.27

Thus, total earnings after deductions = $180.00 - $45.27

= $134.73

Now, we will determine whether or not the monthly car insurance bill of $200 can be paid from the bi-weekly paycheck.

Bi-weekly earnings = $134.73 x 2

= $269.46

Monthly earnings = $269.46 x 2

= $538.92

Since the monthly earnings are less than the amount needed to pay the monthly car insurance bill of $200, the answer is NO.

Therefore, the car insurance bill cannot be afforded.

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a) Account 2 with compound interest at a rate of 6% per year will pay Vinnie more interest after 11 years.

b) Account 2 will pay £221.60 less interest compared to Account 1 after 11 years.

a) For Account 1 with a simple interest at a rate of 8% per year:

Interest = Principal * Rate * Time

We are given:

Principal = £2800

Rate = 8% = 0.08

Time = 11 years

Thus:

Interest = £2800 * 0.08 * 11

Interest = £2464

For Account 2 with compound interest at a rate of 6% per year:

Interest = Principal * [(1 + Rate)^{Time}] - Principal

Interest = £2800 * (1 + 0.06)¹¹ - £2800

Interests = £3042.40 - £2800

Interest = £242.40

b) The difference in interest earned by the two accounts is:

Difference = Interest in Account 2 - Interest in Account 1

Difference = £242.40 - £2464

Difference = -£221.60

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The new function g(x) after shifting upward 66 units and shifting 19 units to the right is g(x) = (x - 19)^2 + 66.

After performing the described transformations on the function f(x) = x^2, the new function g(x) can be determined.

Shift upward 66 units:

To shift the graph of f(x) upward by 66 units, we add 66 to the original function:

f(x) + 66 = x^2 + 66

Shift 19 units to the right:

To shift the graph of f(x) 19 units to the right, we replace x with (x - 19):

f(x - 19) = (x - 19)^2

Combining both transformations, the new function g(x) is:

g(x) = (x - 19)^2 + 66

As a result, the new function g(x) is now g(x) = (x - 19)2 + 66 after being shifted up 66 units and 19 units to the right.

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