Jeremiah and his children went into a bakery and he bought $20 worth of cupcakes and cookies. Each cupcake costs $5 and each cookie costs $1.25. He bought 4 times as many cookies as cupcakes. Graphically solve a system of equations in order to determine the number of cupcakes, x,x, and the number of cookies, y,y, that Jeremiah bought.

(a) The exact value of sinh(log(6) - log(5)) is 11/60.

To calculate sinh(log(6) - log(5)), we can use the identity: sinh(x) = ([tex]a^n[/tex] - [tex]e^-x[/tex])/2

So, substituting x = log(6) - log(5), we get:

sinh(log(6) - log(5)) = ([tex]e^(log(6)[/tex] - log(5)) - [tex]e^-(log(6)[/tex] - log(5)))/2

= (([tex]e^log(6)[/tex])/([tex]e^log(5)[/tex]) - ([tex]e^-log(6)[/tex])/([tex]e^-log(5)[/tex]))/2

= ((6/5) - (5/6))/2

= (36/30 - 25/30)/2

= 11/60

Therefore, sinh(log(6) - log(5)) = 11/60.

(b) The exact value of sin(arccos(76)) is undefined.

To calculate sin(arccos(76)) exactly, we can use the Pythagorean identity [tex]sin^2[/tex](x) + [tex]cos^2[/tex](x) = 1.

Let's assume arccos(76) = x. Applying the cosine function to both sides, we have cos(arccos(76)) = cos(x).

Since arccos and cosine are inverse functions, cos(arccos(76)) simplifies to 76.

Now, using the Pythagorean identity, we can calculate sin(x):

sin(x) = sqrt(1 - [tex]cos^2[/tex](x)) = sqrt(1 - 76^2) = sqrt(1 - 5776) = sqrt(-5775).

The square root of -5775 is an imaginary number, which cannot be expressed exactly without using complex numbers or numerical methods.

Therefore, the exact value of sin(arccos(76)) cannot be determined without using a calculator or numerical methods.

To know more about exact value refer here:

https://brainly.com/question/28209768#

#SPJ11

Answer:

114

Step-by-step explanation:

To find - Find the sum of all the two-digit numbers that divide 170 with a remainder of 5.

Proof -

The 2 digit number is 11

170 = 11(15) + 5

The two digit number is 15

170 = 15(11) + 5

The two digit number is 33

170 = 33(5) + 5

The two digit number is 55

170 = 55(3) + 5

∴ we get

The two digit numbers are

11, 15, 33, 55

Their sum is equals to

11 + 15 + 33 + 55 = 114

Answer: 424

Step-by-step explanation:

To find out the single payment that is economically equivalent to the payment stream of $2,500 due today, $3,000 due 100 days from today, and $3,500 due 240 days from today, we have to follow the below-given steps:

Step 1: Calculate the Future Value (FV) of each payment. Let's assume that "P" is the single payment we need to find out and "i" is the annual interest rate (5%)P = FV × [1 / (1 + i/365)^n] where n is the number of days between today and the payment date. For the first payment of $2,500 that is due today, the future value is $2,500 because it is already available today. Hence, no calculation is required for it. For the second payment of $3,000 that is due 100 days from today, Future Value (FV) = $3,000 × [1+(0.05/365)]^100 ≈ $3,093.29For the third payment of $3,500 that is due 240 days from today, Future Value (FV) = $3,500 × [1+(0.05/365)]^240 ≈ $3,701.85

Step 2: Calculate the Present Value (PV) of the payment stream by discounting each FV to 80 days from today. The formula for the present value of a future amount is PV = FV × [1 / (1 + i/365)^n] where "n" is the number of days between the date of the future amount and the date on which it is to be discounted. Here, we need to discount all three payments to 80 days from today. The number of days between today and 80 days from today is 80. So, we put n = 80 in the above formula.

For the first payment of $2,500 that is already available today, there is no need for any discounting. Hence, its present value is the same as its future value, i.e., $2,500.For the second payment of $3,093.29 that is due 100 days from today, Present Value (PV) = $3,093.29 × [1 / (1 + 0.05/365)^80] ≈ $2,893.16For the third payment of $3,701.85 that is due 240 days from today, Present Value (PV) = $3,701.85 × [1 / (1 + 0.05/365)^80] ≈ $3,243.11

Step 3: Add up the present values of all three payments to find the present value of the payment stream Present Value of the payment stream = $2,500 + $2,893.16 + $3,243.11 = $8,636.27

Step 4: Calculate the single payment that is economically equivalent to the payment stream by calculating its future value at the end of 80 days. FV = PV × (1 + i/365)^n where n = 80, i = 0.05, and PV = $8,636.27FV = $8,636.27 × (1 + 0.05/365)^80 ≈ $9,040.07Therefore, the single payment that is economically equivalent to the payment stream is $9,040.07.

Learn more about economically equivalent:

https://brainly.com/question/2599759

#SPJ11

1. She would use Facial electromyography

2. She would use smiling

3. She would use  Subjective Happiness Scale

It is common practice to evaluate subjective experiences, including happiness, using self-report measures. The Subjective Happiness Scale (SHS) is a popular tool for gauging happiness.

The SHS is a self-report survey that asks participants to rate how much they agree with statements about their personal experiences of happiness. It consists of four things and is frequently utilized in studies.

Learn more about happiness:https://brainly.com/question/28315652

#SPJ4

side length of square=10

Now,

perimeter of square =4l

=4×10

=40m

Answer:

Step-by-step explanation:

Sum of the interior angles of a regular polygon:

Pentagon has sum of angles:

Sum the given angles and find x:

Hexagon has sum of angles:

Sum the given angles and find x:

Value of y[1] = 0.5 and y[2] = 0.5.

The given discrete-time system is:

y[k-1] + 2y[k] = [k]with y(0) = 0.

Substituting k = 0 in the above equation:

y[-1] + 2y[0] = [0] y[-1] = 0

Substituting k = 1 in the given equation:

y[0] + 2y[1] = [1]

Substituting the value of y[0] from the above equation in this equation, we get:

2y[1] = [1] - y[0]

Substituting the value of y[0] = 0 in the above equation:

2y[1] = [1]y[1] = [1]/2 = 0.5

Substituting k = 2 in the given equation:

y[1] + 2y[2] = [2]

Substituting the value of y[1] from the above equation in this equation, we get:

2y[2] = [2] - y[1]

Substituting the value of y[1] = 0.5 in the above equation:

2y[2] = [2] - 0.5y[2] = [2]/2 - 0.5 = 0.5

Therefore, y[1] = 0.5 and y[2] = 0.5.

To learn more about discrete-time

https://brainly.com/question/14863625

#SPJ11

Answer:

 25

Step-by-step explanation:

Answer:

2b^2 + 22

Step-by-step explanation:

2b(b + 11)

2b ×b + 2 × 11

2b^2 + 22

Answer:

-6

Step-by-step explanation:

Answer:

No -6

Step-by-step explanation:

Answer: b

Step-by-step : not needed

Felipe's age is ≥ 5

Step-by-step explanation:

Difference of F's age and 4: f - 4

Twice: 2 (f -4) ≥ 2

2f - 8 ≥ 2

2f ≥ 10

f ≥ 5

Answer:

Step-by-step explanation:

(a) Using the method of maximum likelihood, the estimated parameter of the exponential distribution is λ = 0.050.

(b) Comparing the estimators obtained by the method of moments (L) and the method of maximum likelihood (M), we have L < M.

(a) The maximum likelihood estimation involves finding the parameter that maximizes the likelihood function based on the given data. In this case, using the sample of replacement times (19, 23, 21, 22, 24), the estimated parameter λ of the exponential distribution is calculated to be 0.050.

(b) Comparing the estimators obtained by the method of moments (L) and the method of maximum likelihood (M), we can determine the relationship between them. In general, the method of maximum likelihood tends to provide more efficient and precise estimators compared to the method of moments. Therefore, we have L < M, indicating that the estimator obtained by the method of maximum likelihood (M) is expected to be greater than the estimator obtained by the method of moments (L) in this situation.

To learn more about maximum likelihood (M), click here: brainly.com/question/30625970

#SPJ11

The number of pizzas the people of the town will produce in a year, obtained using the simple mathematical operations, is 120 pizzas.

Mathematical operations include operations of additions, subtraction, division, and multiplication.

The number of pizzas produced in a year can be obtained using mathematical operations as follows;

The number of people required to produce one pizza in a month = 10 people

The number of people in the town = 100 people

The number of pizza'a that the people in the town can produce in a month is therefore;

Number of pizza's produced in a month  = 100/10 = 10

The number of months in a year = 12 months

The number of pizzas the people in the town can produce in a year = 10 × 12 = 120 pizzas

Learn more on mathematical operations here: https://brainly.com/question/1794851

#SPJ1

Answer:

The equation of the circle is;

(x - 2)² + (y - 4)² = 5²  

Step-by-step explanation:

We note that the general equation of a circle is given as follows;

(x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

The given parameters are;

The location of the center of the pool to the center of their formation = 2 feet to the right and 4 feet up from the center of the pool

The point through which the circle which they form goes through = A point 3 feet to the left and 4 feet up from the center of their formation

Taking the center of the pool as the origin of the coordinate plane system, we have;

The coordinate of the center of the circle = The coordinate of their motion from the center of the circle

∴ The coordinate of the center of the circle = (2, 4)

∴ (h, k) = (2, 4)

h = 2, k = 4

The coordinate of the point through which the circle passes = (2 - 3, 4 + 4) = (-1, 8)

∴ The length of the radius, 'r', can be found as, r = √((-3)² + 4²) = 5 or r = √((-1 - 2)² + (8 - 4)²) = 5

r = 5

The equation of the circle is therefore presented by substituting the values of 'h', 'k', and 'r', as follows;

(x - 2)² + (y - 4)² = 5².

Answer:

A. 261.8

Step-by-step explanation:

espero ayudar sorry

Answer:

the jacket price was reduced by 40%.

Step-by-step explanation:

if $50 is 100% then every one dollar is 2%.

Percentage of the reduction of price of the jacket is 40%.

Percentage is defined as the parts of a number per fraction of 100.

Percentage is usually denoted by the symbol '%'.

We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Given that,

Original price of the jacket = $50

Let x be the percentage of reduction of the price of the jacket.

50 - (x × 50) = 30

50x = 50 - 30

50x = 20

x = 20 / 50

x = 0.4

Percentage = 0.4 × 100 = 40%

Hence the percentage reduction is 40%.

Learn more about Percentage here :

https://brainly.com/question/15308590

#SPJ6

Answer:

2/4 quarts of juice is 0.125 Gallons of juice for

Step-by-step explanation:

Please Give Brainliest

Answer:

He divided instead of using multiplication

Step-by-step explanation:

Given:

The figure of a parallelogram.

To find:

The measure of angle Z.

Solution:

We know that, the consecutive interior angles of a parallelogram are supplementary angles, it means there sum is 180 degrees.

In the given figure angle W and angle Z are supplementary angle. So,

[tex]m\angle W+m\angle Z=180^\circ[/tex]

[tex](18b-11)^\circ+(9b+2)^\circ=180^\circ[/tex]

[tex](27b-9)^\circ=180^\circ[/tex]

[tex](27b-9)=180[/tex]

Adding 9 on both sides, we get

[tex]27b=180+9[/tex]

[tex]27b=189[/tex]

[tex]b=\dfrac{189}{27}[/tex]

[tex]b=7[/tex]

Now,

[tex]m\angle Z=(9b+2)^\circ[/tex]

[tex]m\angle Z=(9(7)+2)^\circ[/tex]

[tex]m\angle Z=(63+2)^\circ[/tex]

[tex]m\angle Z=65^\circ[/tex]

Therefore, the correct option is C.

Consider the inequality -20.2 > 0y. Which of the following must be true? Check all that apply.

You cannot divide by zero.

The inequality is equivalent to -20.2 > 0, which is false.

The solution is y > 0.

The solution is 0 > y.

The solution is y = 0.

All interior angle degrees must add up to 180 degrees.

the little square means that it is a right angle (90 degrees)

30 + 90 = 120

Y = 60

Answer:

15.46 gallons per minutes

Step-by-step explanation:

Garden hose was running for 1000 minutes

Volume of the pool = 15,460 gallons

What is the approximate rate at which water leaves the garden hose?

Rate at which water leaves the garden hose = Volume of the pool / running time of the hose

= 15,460 gallons / 1000 minutes

= 15.46 gallons per minutes

Rate at which water leaves the garden hose = 15.46 gallons per minutes

The dispersion of a Normal distribution is less dispersed than the T-distribution.

The dispersion of a distribution is measured by the standard deviation (or variance) of the distribution.

For a Normal distribution, the standard deviation is always known.

On the other hand, for a t-distribution, the standard deviation of the population is not known and is estimated using the sample standard deviation.

This means that the t-distribution has more uncertainty, which leads to more dispersion compared to the Normal distribution.

The t-distribution is often used when the sample size is small or when the population standard deviation is unknown. As the sample size increases, the t-distribution approaches the Normal distribution.

Therefore, for large sample sizes, both distributions become more or less similar.

In conclusion, the Normal distribution is less dispersed than the t-distribution.

To learn more about Normal distribution

https://brainly.com/question/12892403

#SPJ11

The integral of 8(3x - 2)³ dx is 2(3x - 2)⁴ + C, where C is the constant of integration.

To find the integral of 8(3x - 2)³ dx, we can apply the power rule of integration. According to the power rule, the integral of xⁿ dx is (xⁿ⁺¹ / (n + 1)) + C, where n is a constant and C is the constant of integration.

In this case, we have (3x - 2)³ as the integrand. We can rewrite it as 8(3x - 2)³ to simplify the expression. Since 8 is a constant multiplier, it can be factored out of the integral.

Using the power rule, we integrate each term separately. The integral of (3x - 2)³ is [(3x - 2)⁴ / 4] + C, where C is the constant of integration. Multiplying by the constant 8, we get 8[(3x - 2)⁴ / 4] + C.

Simplifying further, we can simplify the expression to 2(3x - 2)⁴ + C, where C is the constant of integration.

Therefore, the integral of 8(3x - 2)³ dx is 2(3x - 2)⁴ + C.

Learn more about integration here:

https://brainly.com/question/31744185

#SPJ11

Answer:

z= 4-x-y

z= -1+4x-y

z= 2-x

Step-by-step explanation:

z = 2-x

y = -1-z +4x

substitute

x -1 -2+x +4x + 2 -x = 4

-1 + 5x = 4

5x = 5

x = 1

z = 1

1+y+1 = 4

y = 2

Answer:

A

Step-by-step explanation:

Think about the square root of 64, which is 8. It will only be slightly higher than 8, which will not even be .5, so 8 is the closest number.

Answer:

Side x = 2.12132 = 3√2/2

Step-by-step explanation:

I used a triangle calculator to find side x

Answer: 140cm^3

Step-by-step explanation:

Based on the given options, the additional information that could be used to prove congruence using AAS or ASA is:

Option 1: B ≅ P and BC ≅ PQ

To prove that two triangles are congruent using AAS (Angle-Angle-Side) or ASA (Angle-Side-Angle) postulates, we need specific conditions met. Let's examine the given options:

1. B ≅ P and BC ≅ PQ:

This condition satisfies the AAS postulate since we have two angles and a corresponding side that are congruent.

2. A ≅ T and AC = TQ = 3.2 cm:

This condition satisfies the ASA postulate since we have two angles and the included side that are congruent.

3. A ≅ T and B ≅ P:

This condition alone does not satisfy either the AAS or ASA postulate, as we need to have at least one side congruent or an included side congruent to prove congruence.

4. AC = TQ = 3.2 cm and CB = QP = 2.2 cm:

This condition alone does not satisfy either the AAS or ASA postulate, as we need to have congruent angles as well.

Based on the given options, the additional information that could be used to prove congruence using AAS or ASA is:

- Option 1: B ≅ P and BC ≅ PQ

This satisfies the AAS postulate, and with the given information, we can conclude that the triangles are congruent.

For more questions on congruence

https://brainly.com/question/29789999
#SPJ8