Laura Amalia ha comprado un equipo de musica y le han hecho un descuento de un 15%, lo que supone que ha pagado $ 825 menos que lo que marcaba. ¿Cuánto le ha costado el equipo de musica?

From the given conditions system of equations is

x + 6y &= 39

x + 9y &= 51

What is expression ?

Expressions can be evaluated or simplified using mathematical rules and operations to obtain a single value or a simpler form. Expressions are used in various mathematical contexts, including algebra, calculus, and geometry, to represent mathematical relationships and solve mathematical problems.

Let x be the cost of admission and y be the cost of a ride at the fair.

Katie's expenses can be represented by the equation:

39 = x + 6y

Alma's expenses can be represented by the equation:

51 = x + 9y

Thus, the system of equations is:

x + 6y &= 39

x + 9y &= 51

This system of equations can be used to find the values of x and y that satisfy both equations and give the cost of admission and rides at the fair.

Therefore, from the given conditions system of equations is

x + 6y &= 39

x + 9y &= 51

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The curve represented by the parametric equations x = t^2 + 1 and y = 7t + 1 is sketched, indicating the orientation of the curve. The corresponding rectangular equation is obtained by eliminating the parameter t, resulting in the equation y = 7√(x - 1) + 1.

To sketch the curve represented by the parametric equations x = t^2 + 1 and y = 7t + 1, we can analyze the behavior of x and y as t varies. Since x = t^2 + 1, we can see that x increases as t increases. This indicates that the curve moves in the positive x-direction. Similarly, since y = 7t + 1, we observe that y also increases as t increases. Therefore, the curve moves upward in the positive y-direction.

To obtain the corresponding rectangular equation, we can eliminate the parameter t by solving one of the equations for t and substituting it into the other equation. From the equation y = 7t + 1, we can solve for t as t = (y - 1)/7. Substituting this value of t into x = t^2 + 1, we get x = ((y - 1)/7)^2 + 1. Simplifying further, we have x = (y - 1)^2/49 + 1. Rearranging this equation, we obtain (y - 1)^2 = 49(x - 1). Taking the square root of both sides, we get y - 1 = 7√(x - 1). Finally, rearranging this equation, we arrive at the rectangular equation y = 7√(x - 1) + 1.

In conclusion, the curve represented by the parametric equations x = t^2 + 1 and y = 7t + 1 moves in the positive x-direction and upward in the positive y-direction. The corresponding rectangular equation is y = 7√(x - 1) + 1, which describes the relationship between x and y on the curve.

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Answer:A D  but not sure for b

Step-by-step explanation:

Answer: 176cm

Step-by-step explanation:  To find the circumference of the circle, we will use the circumference formula: 2πr = 2 × 22/7 × 28

The term you are looking for is the empirical rule, also known as the 68-95-99.7 rule. To determine the number of cycles a sine function has in the interval from 0 to 2π,

we need to look at the coefficient in front of the angle variable (in this case, ∅). This rule states that for data sets having a distribution that is approximately bell-shaped, about 68% of all data values fall within one standard deviation from the mean.

In other words, if the data follows a normal distribution, about 68% of the data points will fall within one standard deviation of the mean.

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For data sets having a distribution that is approximately bell-shaped, the Empirical Rule states that about 68% of all data values fall within one standard deviation from the mean.

Let's break it down step by step:

1. The Empirical Rule applies to data sets that have a bell-shaped distribution, also known as a normal distribution. This distribution is symmetrical and has a characteristic bell-shaped curve.

2. The Empirical Rule states that approximately 68% of the data values in a normal distribution fall within one standard deviation from the mean.

3. The mean is the average value of the data set, while the standard deviation measures the spread or dispersion of the data points around the mean.

4. To visualize this, imagine a bell-shaped curve. Approximately 68% of the data values lie within one standard deviation of the mean, which means they are relatively close to the average value.

5. The remaining percentage of data values, approximately 32%, is divided equally on both tails of the bell-shaped curve, beyond one standard deviation from the mean.

Overall, the Empirical Rule helps us understand the distribution of data in a normal distribution and provides valuable information about how data values are spread around the mean.

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The measure of center that would best summarize the plot is given as follows: Median of 11.

The measure of variability is given as follows: IQR of 1.5.

A box and whisker plots shows these five features from a data-set, listed as follows:

From the plot, these features are given as follows:

The median is the best measure of center of the data-set.

There is an outlier at 16, hence the best measure of variability is the IQR, given by the difference between the Q3 and the Q1, hence:

IQR = 11.5 - 10

IQR = 1.5.

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The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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Answer:

15 weeks.

Step-by-step explanation:

Answer: i tried to do this and the closes was to letter B i hope this helps

Step-by-step explanation:

Answer:

-6 and 2

Step-by-step explanation:

See attached worksheet.

The steady-state levels of consumption per worker are 0.9 for country A and 1.4 for country B.

a. To check if a production function has constant returns to scale, we need to examine if doubling both inputs results in a doubling of output. Let's try it out:

f(2K, 2L) = (2K)^(1/3) * (2L)^(2/3) = 2^(1/3) * K^(1/3) * 2^(2/3) * L^(2/3)

= 2 * (K^(1/3) * L^(2/3)) = 2f(K,L)

Since doubling the inputs results in a doubling of output, this production function has constant returns to scale.

b. The per-worker production function is obtained by dividing the production function by the labor input L:

f(K,L)/L = (1/32)^(1/3) * K^(1/3) * L^(-2/3)

c. The steady-state level of capital per worker is found by equating investment to depreciation:

sY = δK

where s is the saving rate, Y is output per worker, δ is the depreciation rate, and K is the capital per worker. Solving for K, we have:

K = sY/δ

For country A, s=0.1 and δ=0.2, so:

K_A = (0.1*(1/32)^(1/3)*K_A^(1/3)/(0.2)

Simplifying:

K_A^(2/3) = (0.1/(0.2*(1/32)^(1/3)))^3

K_A = ((0.1/(0.2*(1/32)^(1/3)))^3)^(3/2) = 4

Similarly, for country B, s=0.3 and δ=0.2, so:

K_B = (0.3*(1/32)^(1/3)*K_B^(1/3)/(0.2)

Simplifying:

K_B^(2/3) = (0.3/(0.2*(1/32)^(1/3)))^3

K_B = ((0.3/(0.2*(1/32)^(1/3)))^3)^(3/2) = 12

To find the steady-state levels of income and consumption per worker, we use the production function and the capital per worker found above:

Y_A = (1/32)^(1/3)*4^(1/3) = 1

Y_B = (1/32)^(1/3)*12^(1/3) = 2

The steady-state levels of consumption per worker are found by subtracting the investment per worker (sY) from the output per worker:

C_A = (1 - 0.1)*1 = 0.9

C_B = (1 - 0.3)*2 = 1.4

Therefore, the steady-state level of capital per worker for country A is 4, and for country B it is 12. The steady-state levels of income per worker are 1 for country A and 2 for country B. The steady-state levels of consumption per worker are 0.9 for country A and 1.4 for country B.

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Answer: y = 1.75x - 1

Step-by-step explanation: The slope of the line is 1.75

ANSWER:

-17/32, -18/32, -19/32, -20/32, -21/32, -22/32

EXPLANATION:

-4/8 and -3/4

-4*4/8*4 and -3*8/4*8

-16/32 and -24/32

There are 8 numbers between -16/32 and -24/32. You can write any six of it.

\(\huge\bold{Solution }\)

\(\large\mathfrak{given}\)

\( \large \: \mathfrak{ {formula}}\)

Let height be : x

\(\sf\Rightarrow{ \: 968 = 2\pi \: r(r \: + h) } \: \)

\(\sf\Rightarrow{968 = 2 \times \frac{22}{7} \times 7 \times (7 + x) }\)

\(\sf\Rightarrow{ 968 = 2 \times 22 \times(7 + x)}\)

\(\sf\Rightarrow{ 968 = 44(7 + x)}\)

\(\sf\Rightarrow{ \frac{968}{44} = 7 + x}\)

\(\sf\Rightarrow{22 = 7 + x }\)

\(\sf\Rightarrow{22 - 7 = x }\)

\(\sf\Rightarrow{x = 15 }\)

\(\bf\Rightarrow{ x = 15}\)

\(\sf\Rightarrow{ \underline{{ height \: = 15}}} \\ \\ \sf \: option \: A is \: correct \: \)

\( {\underline{ \rule {200pt}{6pt}}}\)

his loan will be $37,234 in the year 2022.

ax2+bx+c=0, with a not equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given, David took out a 20-year $70,000 loan from his bank in 2010.

The quadratic equation that approximates the year/loan balance relationship is y = -98*x^2 - 1,531x + 69,718,

where x is the number of years and

y is the balance

Since the Loan balance is given $37,234.

Thus to calculate the year

$37,234 = -98*x^2 - 1,531x + 69,718,

98 x² + 1534x - 32484 = 0

Comparing with the general form of the quadratic equation.

ax² + bx + c = 0

The discriminant b² - 4ac > 0 thus it has Two real roots.

using the Quadratic Formula

x = \(\frac{-b +- \sqrt{b^{2} - 4ac } }{2a}\)

x = -27.62

and

x = 12

Thus year = 2010 + 12 = 2022

Therefore, In the year 2022, his loan will be $37,234.

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Answer:

The carpenter had 4 \(\frac{1}{4}\) in the beginning

Before: x

Amount deducted: 3 \(\frac{3}{16}\)

After: 1 \(\frac{1}{16}\)

Equation:

x - 3 \(\frac{3}{16}\) = 1 \(\frac{1}{16}\)

x = 4 \(\frac{4}{16}\)

x = 4 \(\frac{1}{4}\)

Answer:

40%

Step-by-step explanation:

6.75 + 1.25 = 8 (Total she just spent)

8 (Total she just spent) + 12 (Total she had left) = 20 (Total she started with)

8/20 = 0.4 = 40%

(Total spent / total she started with = 40%)

Answer:

Hello!!

If Given drinks \(\frac{1}{3}\) liter of milk each day. He will drink...

a) \(2\frac{1}{3}\) liters of milk in a week.

Hope this helps

Answer: 62 degrees

Step-by-step explanation:

.130-180=50

.16x+4+14x+6+50=180

.180-4-6-50=120

.16x+14x=120

.30x=120

.x=4

.14(4)+6

.56+6

.62

Answer:

15 mm per case is the answer. The full answer is 195 mm.

Step-by-step explanation:

hope this helps:)

If the perimeter of the isosceles triangle is 12 cm, then the base of the triangle (x), as well as the length of the triangle leg (x) is 4 cm.

An isosceles triangle is a type of triangle in which two sides have the same length. These two equal sides are referred to as the legs of the triangle, while the remaining side is known as the base.

The perimeter of a triangle is the sum of the lengths of all its sides. In this case, since the triangle is isosceles, the base and one leg have the same length (x), and the other leg also has the same length (x). Therefore, the perimeter of the triangle is 2x + x = 3x. Given that the perimeter of the isosceles triangle is 12 cm, then:

3x = 12

 x = 12/3

 x = 4

So, the base and legs of the isosceles triangle each have a length of 4 cm.

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Your question seems to be missing the value for the perimeter of the triangle, but I suppose the complete question was:

"The length of the base of an isosceles triangle is x. The length of a leg is x. The perimeter of the triangle is 12 cm. Find x."

Answer:

It is a 67% decrease

Step-by-step explanation:

First subtract the new amount from the old one

\(15-5=10\)

Then divide the difference by the original amount.

\(10/15-0.67\)

Move the decimal point over two spots (multiply by 100) to get your percentage.

0.67=67%

Usando proporciones, hay que el auto puede viajar 30 km.

Una proporción es una fracción de la cantidad total, y puede ser encontrada por intermedio de una regla de tres.

En este problema, la regla de tres es dada por:

12 litros - 90 km

4 litros - x km

Aplicando multiplicación cruzada:

\(12x = 360\)

\(x = 30\)

El auto puede viajar 30 km.

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The equation of the line that contains (-4, 6) and (7, -5) in point slope form is y + 5 = - 1(x - 7).

The point slope form can be represented as follows:

y - y₁ = m(x - x₁)

where

Therefore, the equation of the line that contains (-4, 6) and (7, -5) can be found in point slope form as follows:

Hence,

m = -5 - 6 / 7 + 4

m = - 11 / 11

m = -1

Therefore, using (7, -5)

y + 5 = - 1(x - 7)

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a. The experimental probability of spinning a 5 was approximately 10% more than theoretically expected.

In terms of the experimental and theoretical probabilities of spinning a 5, the observed data indicates that the experimental probability was approximately 10% higher than the theoretical probability.

The theoretical probability of spinning a 5 on a spinner with 6 equal sections is 1/6 or approximately 0.1667.

Therefore, in 29 spins, the expected frequency of spinning a 5 would be 4.8353 (rounded to four decimal places).

However, the observed frequency from the data suggests that the number of times a 5 was spun was around 10% higher than the expected frequency.

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Answer: true

Step-by-step explanation:

Answer:

True, because when x is zero (which is greater than -2), y is 0 Which is also true.

Answer: 14

Step-by-step explanation:

P(6)- Q(2) = 4

Q(5) - R(2) = 3

R(6) - S(2) = 4

S(5) - P(2) = 3

4 + 3 + 4 + 3 = 14

Brainliest is appericiated!

Answer:

Perimeter = 14

Step-by-step explanation:

to find the perimeter first find the distance between the two points :

d=√((x2-x1)²+(y2-y1)²)

PQ:(2,2)(6,2)

d=√(6-2)^2+(2-2)^2

= √16=4

PQ=4

RS: (6,5),(2,5)

d=√(6-2)^2+(5-5)^2

d=4

RS=4

QR:(6,2),(6,5)

QR=3

SP(2,5),(2,2)

SP=3

perimeter=2length+2width

P=2l+2w

p=2(4)+2(3)

p=8+6=14