Heyy
please can i have help on these two questions and please can i have an explanation for how to work them out too!

1. the price of an mp3 player is increased by 8% to £52.92.
what was the original price?

2. the population of blackbirds in a park is counted every year.
the population decreases by 24% to 323.
what was the original population?

3. marcia bought a car for £34 500 and sold it for £29 700.
what was a percentage loss?

thank you soo much :)

Answer:

5.667

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :  3*x-(17)=0

Solve  :    3x-17 = 0  

Add  17  to both sides of the equation :   3x = 17

Divide both sides of the equation by 3: x = 17/3 = 5.667

So,  x = 17/3 = 5.667

Answer:

17/3

Step-by-step explanation:

3x=17

x=17/3

The number of jobs that he could he do if the cost was $four thousand, one hundred twenty five will be 25.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

When a man does job at the rate of $165 per job, the number of jobs that he could he do if the cost was $four thousand, one hundred twenty five will be:

= Amount / Rate

= $4125 / $165

= 25

Learn more about word problem on:

brainly.com/question/21405634

#SPJ1

A man does job at the rate of $165 per job. How many jobs could he do if the cost was $four thousand, one hundred twenty five?

The formula of the iteration function for Newton's method is given by g(x) = x - f(x) / f'(x).

The graph of g(x) and g'(x) shows convergence of Newton's method on [-1, 0] as a Fixed-Point Iteration technique. Applying Newton's method to find an approximation of the root of the equation x + e^(-0.812x) = 0 in [-1, 0], with an initial approximation of p0 = -1, gives an approximation of p_n = -0.567143. The standard output table for this method is: TLP_nP_n-1RE(P_nP_n-1) 0-1.00000000000.1559875219 1-0.4801700174-1.00000000000.4801700174 2-0.5889524214-0.4801700174 0.1087824049 3-0.5671941668-0.5889524214 0.0217582546 4-0.5671432850-0.5671941668 0.0000508818. The conclusion is that the Newton's method converges to a root of the equation x + e^(-0.812x) = 0 in [-1, 0] with a tolerance of 10^-5.

Know more about iteration here:

https://brainly.com/question/31377097

#SPJ11

If the researchers select a sample of 100 participants then the degree of freedom for a one sample t test is 99 .

In the question ,

it is given that ,

the number of participants that researcher select = 100 participants ;

we know that the formula for degree of freedom is = sample - (number of parameter)

Since we have to find degree of freedom for one sample test ,

So , number of parameter is = 1 .

the degree of freedom = 100 - 1

= 99

Therefore , the degree of freedom for a one sample t test is 99 .

Learn more about Degree Of Freedom here

https://brainly.com/question/28215112

#SPJ4

Answer:

A

Step-by-step explanation:

if you did 6+3=9

8x(9)=72

"27+45=72"

Answer:

C

Step-by-step explanation:

27 + 45 = 72

9(3 + 5)

9 x 3 = 27

9 x 5 = 45

27 + 45

Answer:

X=4,y=30

Step-by-step explanation:

given,

y=8x-2 ....(i)

3x+y=42...(ii)

now,

putting value of y in equation ii

we get,

3x+y=42

3x+(8x-2)=42

or,3x+8x=42+2

or,11x=44

or,X=4

again,

putting value of X in equation i

y=8x-2

=8×4-2

=30

Answer:

Ricky get $4 than Sam.

Step-by-step explanation:

.25x80=20

80-20=60

.30×80=24

80-24=56

Samantha needs to mix 10 milliliters of the 40% alcohol solution with 90 milliliters of the 60% alcohol solution to create 100 milliliters of a 58% solution.

Let x be the number of milliliters of the 40% alcohol solution that Samantha needs to mix, and let y be the number of milliliters of the 60% alcohol solution. Since Samantha needs to create 100 milliliters of a 58% solution, we can write the following system of equations:

x + y = 100 (equation 1: total volume)

0.4x + 0.6y = 0.58(100) (equation 2: alcohol concentration)

In equation 1, we see that the total volume of the resulting mixture must be 100 milliliters. In equation 2, we convert the concentration of the 58% solution into a decimal and set it equal to the weighted average of the concentrations of the two solutions.

We can solve this system of equations to find the values of x and y:

x + y = 100

0.4x + 0.6y = 58

Multiplying the first equation by 0.4, we get:

0.4x + 0.4y = 40

Subtracting this equation from the second equation, we get:

0.2y = 18

y = 90

Substituting y = 90 into equation 1, we get:

x + 90 = 100

x = 10

To learn more about quantity click on,

https://brainly.com/question/28914619

#SPJ4

By the Comparison Test, we can conclude that Σ (4sin(n))/(\(n^2\) - 1) converges.

We can use the Limit Comparison Test to determine the convergence or divergence of the series:

∑(4 sin(n))/n

To do this, we need to find a series whose convergence is known and which can be compared to the given series. Let's choose the series ∑(1/n) since we know that it diverges.

We take the limit of the ratio of the nth term of each series as n approaches infinity:

lim n→∞ (4 sin(n)/n)/(1/n) = lim n→∞ 4 sin(n) = DNE

Since the limit does not exist, we cannot apply the Limit Comparison Test. Therefore, Therefore, by the Comparison Test, we can conclude that Σ (4sin(n))/(\(n^2\) - 1) converges.

Learn more about Limit Comparison Test

https://brainly.com/question/31362838

#SPJ4

The equation of the line of best fit is ŷ = 0.06x + 2.57

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

Years Since 2000 0 1 2 3 4 5 6 7 8 9

Average Cost ($) 2.59 2.81 2.65 2.67 2.88 2.70 2.85 2.88 3.17 3.24

Next, we enter the above values in a graphing tool;

The calculation summary are as follows

The regression equation is represented as

ŷ = bx + a

Where

b = SP/SSX = 4.94/82.5 = 0.06

a = MY - bMX = 2.84 - (0.06*4.5) = 2.57

So, we have

ŷ = 0.06x + 2.57

Hence, the equation of the line of best fit is ŷ = 0.06x + 2.57

Read more about line of best fit at

https://brainly.com/question/30668844

#SPJ1

The average rate of change of y with respect to x over the interval [1, 5] for function \(y=4x^{2}\) is 24.

To find the average rate, follow these steps:

Therefore, the average rate of change of y with respect to x over the interval [1, 5] for the function \(y=4x^{2}\)  is 24.

Learn more about average rate of change:

brainly.com/question/8728504

#SPJ11

Answer:

division

Step-by-step explanation:

For the division of bases, use the division rule of exponents, where the exponents are subtracted. Combine the result of coefficients by the new power of 10. If the quotient from division of coefficients is not less than 10 and greater than 1, convert it to scientific notation and multiply it by the new power of 10.

Check the picture below.

\(\stackrel{\textit{\large Perimeter}}{6+3+3\sqrt{3}\implies 9+3\sqrt{3}~~\approx~~14.2}\)

Answer:

Step-by-step explanation:

14.2

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

According to the statement seen in this question, the line segments RT and  ST are collinear to each other. Mathematically speaking, the length of the line segment ST can be found by using the following formula:

RT = RS + ST

ST = RT - RS

ST = 19 - 6

ST = 13

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

To learn more on line segments: https://brainly.com/question/25727583

#SPJ1

To calculate the ocean freight charges in Canadian dollars, we need to determine the volume of each cargo and convert the volume to cubic meters (m³) since the ocean freight rate is given in USD per m³.

Calculate the volume of each cargo: Skid of Apple: Volume = length x width x height = 100 cm x 100 cm x 150 cm = 1,500,000 cm³. Box of Orange: Volume = length x width x height = 35" x 25" x 30" = 26,250 in³. Convert the volumes to cubic meters: Skid of Apple: 1,500,000 cm³ ÷ (100 cm/m)³ = 1.5 m³. Box of Orange: 26,250 in³ ÷ (61.0237 in/m)³ ≈ 0.43 m³. Calculate the total volume of both cargos: Total Volume = (2 skids of Apple) + (3 boxes of Orange) = 1.5 m³ + 0.43 m³ = 1.93 m³. Convert the ocean freight rate from USD to CAD:  Ocean Freight Rate in CAD = $250 USD/m³ × (1.25 CAD/USD) = $312.50 CAD/m³.

Calculate the ocean freight charges in Canadian dollars: Ocean Freight Charges = Total Volume × Ocean Freight Rate = 1.93 m³ × $312.50 CAD/m³. Therefore, the ocean freight charges for the given shipment in Canadian dollars will be the calculated value obtained in step 5.

To learn more about volume click here: brainly.com/question/28058531

#SPJ11

The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

For more such information on Algebra and Geometry:
https://brainly.com/question/24696219

#SPJ8

In scientific practice, we often use statistical inference to make conclusions about a population based on a sample. The use of confidence intervals is one method of making these inferences. A single 95% confidence interval can be interpreted as follows: we are 95% confident that our interval is one that contains the true population parameter.

This means that if we were to repeat the study many times, we would expect the true population parameter to be within our interval 95% of the time.
It is important to note that this interpretation assumes that the sample was selected randomly and that the assumptions for the statistical test used to construct the interval were met. Additionally, it is important to recognize that the interval is not a guarantee of the true population parameter being within it, but rather a range of values that is likely to contain the true parameter.

Overall, a single 95% confidence interval is a useful tool for making inferences about a population based on a sample, and it provides a range of values that we can be reasonably confident contains the true parameter.

To learn more about statistical interference : brainly.com/question/30214666

#SPJ11

The equation which models the relationship expressed in slope intercept form ls y = 45x

What is  linear equation?

An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a  linear equation.

                         The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.

Expressing the equation in the form :

y = bx + c

Slope, b = (900 - 225) / (20 - 5) = 45

Using any (x, y) points on the table given to find the value of c :

225 = 45(5) + c

225 = 225 + c

c = 0

Hence, the equation which models the relationship is y = 45x

Learn more about Linear equation

brainly.com/question/11897796

#SPJ1

The sum of the series ∑n=1[infinity]6n(n + 2) is ∞.

To find the sum of the series ∑n=1[infinity]6n(n + 2), we can use the formula for the sum of a series of the form ∑n=1[infinity]an = ∞∑n=1(an − an−1), where a0 = 0.

First, we need to find an expression for the nth term of the series, an. Using the formula for the product of two consecutives integers, we can write:

an = 6n(n + 2) = 6n^2 + 12n

Next, we can compute the difference between consecutive terms:

an - an-1 = [6n^2 + 12n] - [6(n-1)^2 + 12(n-1)]

= 6n^2 + 12n - 6(n^2 - 2n + 1) - 12(n - 1)

= 6n^2 + 12n - 6n^2 + 12n - 6 - 12n + 12

= 6

Therefore, we have:

∑n=1[infinity]6n(n + 2) = ∞∑n=1(6) = ∞

The series diverges to infinity.

Learn more about integers at:

brainly.com/question/15276410

#SPJ4

a) The 90% confidence interval for the population mean is approximately (21.52, 23.48).

b) The 95% confidence interval for the population mean is approximately (21.322, 23.678).

c) The 99% confidence interval for the population mean is approximately (20.926, 24.074).

To develop confidence intervals for the population mean, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

where the standard error is equal to the sample standard deviation divided by the square root of the sample size.

a) For a 90% confidence interval, we need to find the critical value corresponding to a confidence level of 90%. The critical value can be obtained from the t-distribution table with (n-1) degrees of freedom. Since the sample size is 56, the degrees of freedom is 56-1 = 55.

From the t-distribution table, the critical value for a 90% confidence interval with 55 degrees of freedom is approximately 1.671.

The standard error can be calculated as:

Standard Error = sample standard deviation / sqrt(sample size)

Standard Error = 4.4 / sqrt(56)

Standard Error ≈ 0.5882

Now we can calculate the confidence interval:

Confidence Interval = 22.5 ± (1.671 * 0.5882)

Confidence Interval = 22.5 ± 0.9816

Confidence Interval ≈ (21.52, 23.48)

b) For a 95% confidence interval, the critical value for 55 degrees of freedom is approximately 2.004 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.004 * 0.5882)

Confidence Interval = 22.5 ± 1.178

Confidence Interval ≈ (21.322, 23.678)

c) For a 99% confidence interval, the critical value for 55 degrees of freedom is approximately 2.678 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.678 * 0.5882)

Confidence Interval = 22.5 ± 1.574

Confidence Interval ≈ (20.926, 24.074)

For more such question on mean visit:

https://brainly.com/question/1136789

#SPJ8

Answer:

B

Step-by-step explanation:

Hope this helps!!!

Answer:

B. Math , Social Studies , Reading is the answer.

I think this helps you ☺️☺️.

Thank you ☺️☺️☺️

You have the following function:

As you can notice, the function does not have exponentials, logarithms, denominators and roots. Then there are no restrictions to the domain of the function neither the range of the function.

The range are all real numbers. In interval notation is:

(-∞,∞)

answer: (-∞,∞)

the value of P(A∩B) in terms of x and y is xy.

The correct option is D. xy.

To determine the value of P(A∩B) in terms of x and y, we can use the definition of conditional probability and the fact that P(A∩B) = P(A|B) * P(B).

Given that P(A|B) = x and P(B) = y, we can substitute these values into the equation:

P(A∩B) = P(A|B) * P(B)

        = x * y

To know  more about probability visit:

brainly.com/question/31828911

#SPJ11

Producing rDNA involves isolating and cleaving DNA, inserting fragments into a vector, and transforming host cells. rDNA can be introduced via transformation, transfection, or viral vectors. Clinical applications include protein production, gene therapy, vaccines, and diagnostics.

Producing a recombinant DNA (rDNA) vector involves several general steps. Here are the three main steps involved in the process:

Isolation and Cleavage of DNA:

The first step is to isolate the desired DNA fragments from the source organism. This can be done using various techniques such as PCR (Polymerase Chain Reaction) or restriction enzyme digestion. Restriction enzymes are enzymes that cut DNA at specific recognition sites. By using the appropriate restriction enzymes, the desired DNA fragment and a vector DNA can be cut at specific sites. The vector is usually a plasmid, which is a small circular DNA molecule.

Insertion of DNA Fragments into the Vector:

Once the DNA fragments and vector have been cut, they are mixed together and joined through a process called ligation. DNA ligase is used to catalyze the formation of covalent bonds between the ends of the DNA fragments and the vector. This creates a recombinant DNA molecule containing the desired DNA fragment within the vector. The recombinant DNA molecule is then introduced into host cells for replication.

Transformation of Host Cells:

The recombinant DNA molecules need to be introduced into host cells to produce multiple copies of the recombinant DNA. This is typically done using a process called transformation. Host cells, such as bacteria or yeast, are treated in a way that makes them more receptive to taking up the recombinant DNA. Methods for transformation include heat shock, electroporation, or using chemical agents. Once the host cells have taken up the recombinant DNA, they can be grown in culture to produce large quantities of the desired DNA fragment.

Introduction of rDNA into Cells:

Recombinant DNA can be introduced into cells using various methods, depending on the type of cells being targeted. Some common techniques include:

Transformation: As mentioned earlier, host cells, such as bacteria or yeast, can be treated to make them receptive to taking up the recombinant DNA. This can be achieved by exposing the cells to heat shock, electroporation, or using chemical agents.

Transfection: This method is used for introducing rDNA into eukaryotic cells, including animal cells. It involves the use of techniques such as calcium phosphate precipitation, liposome-mediated transfection, or electroporation.

Viral Vectors: Certain viruses, such as retroviruses, adenoviruses, or lentiviruses, can be modified to carry the recombinant DNA. These viral vectors can then infect target cells and deliver the rDNA into the host genome.

Clinical Applications of rDNA:

Recombinant DNA technology has revolutionized biomedical research and has led to numerous clinical applications. Some important applications include:

Production of Therapeutic Proteins: rDNA technology allows for the production of large quantities of therapeutic proteins, such as insulin, growth factors, clotting factors, and monoclonal antibodies. These proteins can be used to treat various diseases, including diabetes, cancer, and genetic disorders.

Gene Therapy: rDNA vectors can be used to deliver functional copies of genes into target cells to correct genetic defects. This holds promise for the treatment of inherited diseases caused by single gene mutations, such as cystic fibrosis and muscular dystrophy.

Vaccine Development: Recombinant DNA technology has been instrumental in the development of vaccines. By expressing specific antigens from pathogens, recombinant vaccines can be created to stimulate an immune response without causing disease.

Diagnostic Tools: Recombinant DNA techniques are used to produce specific DNA or RNA probes for diagnostic purposes. These probes can detect the presence of specific genes or mutations associated with diseases, aiding in early detection and personalized medicine.

for such more question on isolating

https://brainly.com/question/27746495

#SPJ8

Answer:

6.23yx-8y

Step-by-step explanation:

simplified answer!

Sum of the interior angle of any triangle must equal to 180 degrees thus :

\(53 + 90 + t = 180\)

\(143 + t = 180\)

\(t = 37\)

Thus angle T has a measure of 37° .

Answer: 37

Explanation: Angle S is a right triangle because ST is tangent to circle Q.
180 - 90 - 53 = 37

Answer:

c.

Step-by-step explanation:

Flip it across the x axis

x axis: ______________, horizontal . which would be c because its being flipped

The jet has a speed of 770 mi/h relative to the air, and the pilot heads the jet in the direction N 30° W. Z+ 2 A. Find the true speed of the jet: ⇒ x = 744.02 mph

let the speed of the jet be x

x sinθ - 55 sin30 = 770 sin30 .......(1)

&  x cosθ + cos30 = 770 cos30.......(2)

from (1) x sinθ = 412.5

from (2) x cosθ = 619.2

⇒ tanθ = 412.5 / 619.2 ≈ 0.666 ⇒ θ = tan(0.666)

                                                          ≈ 33.66°

                                                            33. 7°

⇒ x = 744.02 mph

Speed lets us know how quickly a person or thing is voyaging. You can track down the normal speed of an article assuming you realize the distance voyaged and the time it took. The equation for speed will be speed = distance ÷ time.

to know more about speed click here:

https://brainly.com/question/3004254

#SPJ4

the complete question is:

A jet is flying through a wind that is blowing with a speed of 55 mi/h in the direction N 30° E (see the figure). The jet has a speed of 770 mi/h relative to the air, and the pilot heads the jet in the direction N 30° W. Z+ 2 A Find the true speed of the jet. (Round your answer to the nearest integer.) 744 x mi/h Find the direction of the jet. (Round your answer to one decimal place.)