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 :)

Step-by-step explanation:

a) 6400

b) 4800

c) 32000

hope this answer helps you dear!

Answer:

6

Step-by-step explanation:

2 x 3

The percentage of the fire fighters have moderate to severe risk for alcohol problems is 28%  

From the sample, we can get that number of fire fighters who participated in rescue of 9/11 attack and are under moderate to severe risk for alcohol problems is =309.

Total number of fire fighters participated in 9/11 attack is =1102

So, percentage of fire fighters have moderate to severe risk for alcohol problems are =(309/1102)×100

    percentage from the sample= 0.28×100=28%

Hence, 28% fire fighters are in  severe risk for alcohol problems

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(Complete question) is:

what percentage of the fire fighters in the sample have moderate to severe risk for alcohol problems?

The linear function represents the line is y = 1/2x + 6

These are functions that has a leading degree of 1. Given the function in slope-intercept form;

y - 8 = 1/2(x-4)

Make y the subject of the formula

y = 1/2(x - 4) + 8

Expand

y = 1/2x -4/2 + 8

y = 1/2x - 2 +8

y = 1/2x + 6

Hence the linear function represents the line is y = 1/2x + 6

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Answer:

Which subject is optional in the morning??

Answer: I know this is a bit late but for anyone looking the answer to this question, i got it right here :D.

Step-by-step explanation: I guessed and got it correct.

The graph representing Sondra's weekly earnings is plotted and attached.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Sondra receives an allowance of $10 per week, plus an additional $5 for each chore she completes.

Assume that her weekly earnings is $y. Assume she does [x] extra chores in a week. Then, we can model her earnings by the equation -

y = 5x + 10.

Refer to the graph attached.

Therefore, the graph representing Sondra's weekly earnings is plotted and attached.

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Answer:

$9.38

Step-by-step explanation:

First, we have to find how much a single pound of potato costs.

3.75 / 8 = 0.46875

Since we know the cost of one pound, simply multiply it by 20 to find the cost of 20 pounds of potatoes.

0.46875 * 20 = 9.375

Answer:

$15.20

Step-by-step explanation:

first you must find the cost of each potato per pound, which will be 76 cents per pound then you multiply by 20 and u get 15.2 which is the answer

pls brainelist if this helps

The maximum likelihood estimate for p is 1/2, as it maximizes the likelihood of observing the sequence.

What is algebra ?

Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. Algebraic concepts include operations such as addition, subtraction, multiplication, and division, as well as the manipulation of equations

The maximum likelihood estimate (MLE) for p is the value that maximizes the likelihood function, which represents the probability of observing a particular sequence of red and white chips given the assumed distribution of reds and whites. In this case, we have two options for the proportion of reds, either 1/3 or 1/2. To calculate the likelihood of observing the sequence red, white, white, red, and white given p = 1/3, we calculate (1/3)(2/3)(2/3)(1/3)(2/3) = 4/243. To calculate the likelihood of observing the sequence given p = 1/2, we calculate (1/2)(1/2)(1/2)(1/2)(1/2) = 1/32. As we can see, the maximum likelihood estimate for p is 1/2, as the likelihood of observing this sequence given p = 1/2 is greater than the likelihood of observing this sequence given p = 1/3.

The maximum likelihood estimate for p is 1/2, as it maximizes the likelihood of observing the sequence.

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Answer:

B) 7....................

answer: f=37

Step-by-step explanation:

9514 1404 393

Answer:

  x = 6

Step-by-step explanation:

Use -8 in place of f(x) and solve the resulting 2-step linear equation in the usual way.

  -8 = -3x +10

  -18 = -3x . . . . . . . . step 1, subtract 10

  6 = x . . . . . . . . . . . step 2, divide by the coefficient of x

Answer:

x² + 4 > 4x

x² - 4x + 4 > 0

(x - 2)² > 0 (true for all real x)

Answer:

<3, < 6, <7 are all 102,

<1, <4, <5 and <8 are all 78

Step-by-step explanation:

If you slide angles 1, 102, 3 qnd 4 down along p, they will fit perfectly over 5,6,7 and 8.  So if you find the top four angles, you have found the bottom 4 angles.

<3 is a vertical angle to 102 and vertical angles always have the same measurement.

Angles 1 and 4 are supplemental to 102.  That means that the two angles will add to 180.  180 - 102 = 78

Answer:

-7=11*-8+b

-7=-88+b

+88 both sides

81=b

y=11x+81

Answer:

m<ZA = 109

Step-by-step explanation:

Supplementary angles mean the angles add up to 180 so:

8x - 27 + 4x + 3 = 180

12x - 24 = 180

12x = 180 + 24

12x = 204

x = 17

m<ZA:

8x - 27

8(17) - 27

136 - 27

109

The measure of angle A is 38 degrees by angle sum property

Given that ∠B is 40 degrees

∠AEB is 102 degrees

Now let us find ∠A

By angle sum property the sum of three angles is 180 degrees in triangle

AEB is triangle

40+102+ ∠A=180

142+∠A=180

∠A=180 - 142

∠A= 38 degrees

Hence, the measure of angle A is 38 degrees.

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The calculation of (6 X 5) X 1 can be simplified as 30

The calculation of (6 X 5) X 1 can be simplified as follows:

(6 X 5) X 1 = 30 X 1 = 30

When you multiply 6 and 5, you get 30. And when you multiply 30 by 1, you get the same number, 30. So, (6 X 5) X 1 equals 30.

However, none of the options given in the question match the result of the calculation.

Option A suggests that (7 X 5) X 1 equals 35, but that's not correct.

Option B suggests that (6 X 6) X 1 equals 36, which is also not correct.

Option C suggests that (7 X 5) X 1 equals 35, which, as we know, is incorrect.

Therefore, the correct answer to the given calculation is 30, but it's not listed among the choices.

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Given :

A parallelogram has sides 8 ft and 14 ft the height corresponding to the 14 ft base is 4 ft.

To Find :

The height corresponding to the 8 ft base.

Solution :

Since, both parallelogram are similar. So, ratio of the sides of parallelogram is similar in both the cases.

\(\dfrac{h_1}{h_2}=\dfrac{b_1}{b_2}\\\\\dfrac{8}{14}=\dfrac{h_1}{4}\\\\h_1 = \dfrac{8\times 4}{14}\\\\h_1 = 2.285 \ ft\)

Therefore, the height corresponding to the 8 ft base parallelogram is 2.285 ft.

The distance between the automobile and the farmhouse is increasing at a rate of 43.684 km/h when the automobile is 4.1 km past the intersection of the highway and the road.

Let's consider a right-angled triangle formed by the automobile, the farmhouse, and the intersection point. The length of the base of the triangle is 4.1 km (the distance the automobile has traveled past the intersection), and the length of the hypotenuse is the distance between the automobile and the farmhouse (which we need to find).

Using the Pythagorean theorem, we can express the relationship between the base (4.1 km), the hypotenuse (the distance between the automobile and the farmhouse), and the perpendicular side (1.5 km):

hypotenuse^2 = base^2 + perpendicular^2

Let d be the distance between the automobile and the farmhouse, we have:

d^2 = (4.1 km)^2 + (1.5 km)^2

d^2 = 16.81 km^2 + 2.25 km^2

d^2 = 19.06 km^2

d = √19.06 km

d ≈ 4.365 km

To find how fast the distance between the automobile and the farmhouse is increasing, we differentiate the equation with respect to time (t):

2d(dd/dt) = 0 + 0

2d(dd/dt) = 0

dd/dt = 0 / (2d)

dd/dt = 0 km/h

Therefore, the distance between the automobile and the farmhouse is not changing at this particular moment.

The distance between the automobile and the farmhouse is not changing when the automobile is 4.1 km past the intersection of the highway and the road.

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Factors of 47 are 1 and 47 which implies that it can only be divided by one and itself.

The number 47 is a prime number, which implies that it can only be divided by one and itself. As a result, the components of 47 are 1 and 47.

Generally, a number's factors are the positive integers that divide it evenly with no residual. The factors of 12 are, for example, 1, 2, 3, 4, 6, and 12, since each of these numbers can be divided into 12 without leaving a leftover.

Yet, there are only two elements in the case of prime numbers, such as 47, which are always 1, and the number itself. This is because, by definition, prime numbers have no divisors other than 1 and themselves.

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Answer:

A. 60°

Step-by-step explanation:

∠BEC = 1/2 arc BC = 32°

∠CED = ∠BED - ∠BEC = 62° - 32° = 30°

arc CD = 2 x ∠CED = 2 x 30° = 60°

The measure of the arc CD of the circle is 60°

Given data:

The central angle is an angle with two arms and a vertex in the middle of a circle.

The central angle of a circle formula is as follows.

Central Angle = ( s x 360° ) / 2πr

And, Central Angle = 2 x Angle in other segment

So,

∠BEC = 1/2 arc BC = 32°

The measure of the angle ∠CED  is determined as:

∠CED = ∠BED - ∠BEC = 62° - 32° = 30°

So, the measure of the arc from the central angle is:

arc CD = 2 x ∠CED = 2 x 30° = 60°

Hence , the measure of arc CD = 60°

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Answer:

1.) Find the difference of arc measures.

mAC - mDE = 56

2.) Multiply the angle measure by 2.

2(mABC)= 56

3.) Moving points A and C to change

the angle and arcs and make a

conjecture.

The difference of arc measures

always equal 2 times the

angle measure.

The difference of arc measures is always equal to two times the angles measured at an external point of the circle.

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

The dimensions are given as

m∠ABC = 28°

mAC = 80

mDE = 24

The difference of arc measure will be

mAC - mDE = 80 - 24

mAC - mDE = 56

Multiply the measure of the angle m∠ABC by 2.

2 (m∠ABC) =  2 (28°)

2 (m∠ABC) =  56°

Moving points A and C to change the angle and arcs make a conjecture.

The difference of arc measures is always equal to two times the angles measured at an external point of the circle.

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Answer:

±√7 and ±√6

Step-by-step explanation:

Let's denote x^2 as y, then the equation becomes:

y^2 - 6y - 7y - 6 = 0

y(y - 6) - 7(y - 6) = 0

(y - 7)(y - 6) = 0

Substituting back y with x^2, we get:

(x^2 - 7)(x^2 - 6) = 0

Solving each factor separately:

x^2 - 7 = 0 or x^2 - 6 = 0

x^2 = 7 or x^2 = 6

x = ±√7 or x = ±√6

Therefore, the zeroes of the equation are ±√7 and ±√6.

The calculated value of the surface area of the cube is 294 mm^2

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

The cube

The side length of the cube is

Length = 7 mm

The surface area of the cube is calculated as

Surface area = 6 * Length^2

Substitute the known values in the above equation, so, we have the following representation

Surface area = 6 * 7^2

Evaluate

Surface area = 294 mm^2

Hence the surface area is 294 mm^2

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The total spending figures indicate that Joe's demand for pizza is elastic as his total spending decreases when the price decreases, suggesting he is responsive to price changes.

a. The demand curve for Joe's pizza can be plotted by using the equation Q = 30 - 2P, where Q represents the quantity of pizza consumed and P represents the price per slice.

On the graph, the vertical axis represents the price (P), and the horizontal axis represents the quantity (Q). The vertical intercept occurs when Q is 0, which corresponds to P = 15. The horizontal intercept occurs when P is 0, which corresponds to Q = 30.

b. The total spending on pizza at P = 5 is $100, and the total spending at P = 4 is $88. This information indicates that Joe's total spending decreases as the price of pizza decreases.

Based on this, we can infer that Joe's elasticity of demand for pizza between P = 5 and P = 4 is elastic. When the price decreases from $5 to $4, the total spending decreases, indicating that the demand is responsive to price changes.

c. When P = 9, we can substitute this value into the demand function to calculate the corresponding quantity: Q = 30 - 2(9) = 30 - 18 = 12. To calculate Joe's consumer surplus, we need to find the area of the triangle formed by the demand curve and the price line.

The consumer surplus is given by (1/2) ˣ  (9 - P) ˣ  Q = (1/2) ˣ (9 - 9) ˣ  12 = 0.d. If the price of pizza rises to $15 per slice, we can again substitute this value into the demand function to find the corresponding quantity: Q = 30 - 2(15) = 30 - 30 = 0.

Joe's consumer surplus at this new price would be zero since he is not consuming any pizza at that price, resulting in no surplus.

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The measure of angle x in the right triangle is approximately 14.6 degrees.

The figure in the image is that of two right angles.

First, we determine the hypotenuse of the left-right angle.

Angle θ = 30 degrees

Adjacent to angle θ = 10 cm

Hypotenuse = ?

Using the trigonometric ratio.

cosine = adjacent / hypotenuse

cos( 30 ) = 10 / hypotenuse

hypotenuse = 10 / cos( 30 )

hypotenuse = \(\frac{20\sqrt{3} }{3}\)

Using the hypotenuse to solve for x in the adjoining right triangle:

Angle x =?

Adjacent to angle x = \(\frac{20\sqrt{3} }{3}\)

Opposite to angle x = 3

Using the trigonometric ratio.

tan( x ) = opposite / adjacent

tan( x ) = 3 / \(\frac{20\sqrt{3} }{3}\)

tan (x ) = \(\frac{3\sqrt{3} }{20}\)

Take the tan inverse

x = tan⁻¹(  \(\frac{3\sqrt{3} }{20}\) )

x = 14.6 degrees

Therefore, angle x measures 14.6 degrees.

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The answer is 64 degrees