Work out the percentage change to 2 decimal places when a price of £60 is increased to £89.99

Answers

Answer 1

Answer:

that is the solution to the question

Work Out The Percentage Change To 2 Decimal Places When A Price Of 60 Is Increased To 89.99
Answer 2

The percentage change to 2 decimal places when a price of £60 is increased to £89.99 is 49.98%.

Given that, a price of £60 is increased to £89.99.

What is percentage?

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, old price =£60 and new price =£89.99

Change in price = 89.99-60

= 29.99

Percentage = Change in price/Old price ×100

= 29.99/60 ×100

= 0.4998 ×100

= 49.98%

Therefore, the percentage change to 2 decimal places when a price of £60 is increased to £89.99 is 49.98%.

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Related Questions

How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 41 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold: x = 35, s = 18.

Answers

Answer:

7

Step-by-step explanation:

67ururiierururf8fucicififfifig

I’m sorry but this is all I could find ma’am or sir

This net consists of a square and 4 identical triangles. What is the surface area of the sold this net can form?

Not drawn to scale

Answers

Final answer:

The surface area of a square pyramid is found by adding the area of the square base to the area of the four triangular faces. If the side of the square base is 's' and the length of the slant height of the triangles is 'l', the formula is: Surface [tex]Area = s^2 + 2 * s * l.[/tex]

Explanation:

The net described in the question would form a square pyramid. To calculate the surface area of a square pyramid, you add the area of the square base to the combined areas of the four triangular faces. If the side of the square is 's' and the length of the slant height of the triangular faces is 'l', the formula is: Surface [tex]Area = s^2 + 2 * s * l.[/tex] The surface area is expressed in square units. For example, if the side of the square is 4 units and the slant height is 6 units, the surface area of the pyramid is [tex]4^2 + 2 * 4 * 6 = 16 + 48 = 64[/tex] square units.

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A builder makes all of their ramps with a base to height ratio of 12:112:112, colon, 1 to be wheelchair-accessible. See the diagram below, which is not drawn to scale:

A certain ramp needs to cover a height of 0.80.80, point, 8 meters.

What is the length \ellℓell of this ramp?
Round your answer to the nearest hundredth of a meter.

Answers

The length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.

Pythagoras theorem states that, right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

A builder makes all the ramps with a base to height ratio of 12 to 1 to be wheelchair accessible.

Let p is the factor of ratio. Thus, the height and base is,

h = p

b = 12p

According to Pythagoras theorem,

unknown side (say l) is hypotenuse

l² = (12p)² + p²

[tex]l^2=144p+p^2[/tex]

[tex]l = \sqrt{144p+p^2}[/tex]

[tex]l = \sqrt{145} p[/tex]

A ramp needs to cover a height of 0.8 m. Height is equal to the factor p.

Thus, the value of p is,

p = h

p = 0.80

Thus, the length of the l is,

[tex]l = \sqrt{145} p[/tex]

[tex]l = \sqrt{145} {(0.8)}[/tex]

[tex]l=(12.041)(0.8)[/tex]

[tex]l=9.63m[/tex]

Hence, the length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.

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The correct question has in the image below

A random sample of n = 16 professors from a university has been selected; salaries have been plotted on the following Q-Q plot. qqplot If we created a 95% confidence interval for salaries to be ($99,881, $171,172), how would we interpret that interval? Since n = 16 > 15, we can use the CLT to say we are 95% sure that all professors' salaries at this university are between $99,881 and $171,172. Since n = 16 > 15, we can use the CLT to say we are 95% sure the average of all professors' salaries at this university is between $99,881 and $171,172. We actually can't be 95% sure the average professor salary is in the interval, since the salaries are right-skewed and n = 16 < 30.

Answers

Answer:

The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance.

The conclusion we can make is that there is 95% of probability that the mean of the population (professor's average salary) is within $99,881 and $171,172.

Step-by-step explanation:

This is a case in which, from a sample os size n=16, a confidence interval is constructed.

The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance. In this case, the probability that the real mean is within the interval is 95%.

Identify the domain of the function shown in the graph.

Answers

D. All real numbers
The domain is all possible values of x, and since the graph seemingly stretches forever, the domain is all real numbers.

What do 2+e(6-7)? Everybody is saying it’s 2 but idk

Answers

Answer:

-0.71828

Step-by-step explanation:

2 + e(6-7)

2 + e(-1)

2 -e

e is approximately 2.718281828459045235360287471352662497757247093699959574966

2 - 2.71828.....

-0.71828

Answer:

2.37 (3 sf)

Step-by-step explanation:

2 + e^(6-7)

2 + e^(-1)

2 + 1/e (exact)

Roughly, 2.367879441

NO CALCULATOR IS ALLOWED FOR THIS QUESTION.

Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit.

Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point.

Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.

A particle moves along the l-axis so that its position at time t>0 is given by x(t)= (t^2 - 9)/(3t^2 + 8)

Show that the velocity of the particle at time t is given by v(t)=70t/(30t^2 + 8)^2

Answers

Answer:

We showed that if we have the position of the particle [tex]x(t)= \frac{t^2 - 9}{3t^2 + 8}[/tex] the velocity of the particle at time t is given by [tex]v(t)=\frac{70t}{\left(3t^2+8\right)^2}[/tex].

Step-by-step explanation:

Velocity is defined as the rate of change of position with respect to time.

                                                  [tex]v(x)=\frac{dx}{dt}[/tex]

To find velocity, we take the derivative of the position function [tex]x(t)= \frac{t^2 - 9}{3t^2 + 8}[/tex]

[tex]\mathrm{Apply\:the\:Quotient\:Rule}:\quad \left(\frac{f}{g}\right)'=\frac{f\:'\cdot g-g'\cdot f}{g^2}[/tex]

[tex]\frac{d}{dt}\left(\frac{t^2-9}{3t^2+8}\right)=\frac{\frac{d}{dt}\left(t^2-9\right)\left(3t^2+8\right)-\frac{d}{dt}\left(3t^2+8\right)\left(t^2-9\right)}{\left(3t^2+8\right)^2}[/tex]

Next, we find the values of [tex]\frac{d}{dt}\left(t^2-9\right)[/tex] and [tex]\frac{d}{dt}\left(3t^2+8\right)[/tex]

[tex]\frac{d}{dt}\left(t^2-9\right)=\frac{d}{dt}\left(t^2\right)-\frac{d}{dt}\left(9\right)=2t-0=2t[/tex]

[tex]\frac{d}{dt}\left(3t^2+8\right)=\frac{d}{dt}\left(3t^2\right)+\frac{d}{dt}\left(8\right)=6t+0=6t[/tex]

So,

[tex]\frac{d}{dt}\left(\frac{t^2-9}{3t^2+8}\right)=\frac{2t\left(3t^2+8\right)-6t\left(t^2-9\right)}{\left(3t^2+8\right)^2}[/tex]

Next, we expand [tex]2t\left(3t^2+8\right)-6t\left(t^2-9\right)[/tex]

[tex]2t\left(3t^2+8\right)-6t\left(t^2-9\right)=6t^3+16t-6t\left(t^2-9\right)=6t^3+16t-6t^3+54t=70t[/tex]

Therefore,

[tex]v(t)=\frac{d}{dt}\left(\frac{t^2-9}{3t^2+8}\right)=\frac{70t}{\left(3t^2+8\right)^2}[/tex]

Final answer:

This question lies in high school level Mathematics, more specifically in calculus. The process includes finding the derivative of a function x(t) to get v(t), which is the velocity of the particle. There appears to be an error in the provided equations in the question.

Explanation:

The subject of this question falls under calculus, a branch of Mathematics, and the grade level would most likely be High School. The equation for the particle's position in terms of time x(t)=(t^2 - 9)/(3t^2 + 8) indicates the focus is on particle motion.

To find the velocity of a particle moving along a line at a given time, we find the derivative of the position function. This principle comes from the fact that velocity is the rate of change of position with respect to time. In this case, the derivative of the position function x(t) gives the velocity function v(t).

However, it seems there might be a mistake in the question because the derivative of x(t) is not v(t)=70t/(30t^2 + 8)^2. Please double-check the original problem to ensure the equations are correctly provided.

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Select three ratios that are equivalent to 8:20
A: 1:4
B: 4:10
C: 24:60
D: 2:5
E: 10:24

Answers

B, c, d all can be multiplied or divided by 3

Answer:

8 to 20 1 to 4 4 to 10

Step-by-step explanation:

it was easy

PLEASE HELP!!!!!!Dimensions of the triangular prism
Base - 20 feet by 20 feet
Height - 40 feet
Dimensions of the rectangular prism
Base - 15 feet by 40 feet
Height - 20 feet
What is the total amount of volume inside the parking
garage?
16.000
18.000
24.000

Answers

Answer:20000ft^3

Step-by-step explanation:

volume of triangular prism:

Base area x height

1/2 x 20 x 20 x40

(1x20x20x40) ➗ 2

16000 ➗ 2=8000ft^3

Volume of rectangular prism:

Length x width x height

40 x 15 x 20=12000ft^3

Total volume=8000+12000

Total volume=20000ft^3

The total amount of volume inside the parking garage = 20,000 cu. ft.

What is the volume of the triangular prism?

The volume of the triangular prism = base area × height

What is the volume of the rectangular prism?

V = l × b × h, where 'l' represents the length, 'w' represents the width and 'h' represents the height of the rectangular prism

For given example,

Let V1 represents the volume of the triangular prism and V2 represents the volume of the rectangular prism.

Dimensions of the triangular prism are:

Base - 20 feet by 20 feet and Height - 40 feet

The base of the triangular prism is a triangle.

So, the area of the base would be,

⇒ A = 1/2 × 20 × 20

⇒ A = 200 sq. ft.

The volume of the triangular prism would be,

⇒ V1 = base area × height

⇒ V1 = 200 × 40

⇒ V1 = 8,000 cubic feet

Now, the dimensions of the rectangular prism are:

Base - 15 feet by 40 feet and Height - 20 feet

⇒ l = 40ft., w = 15 ft., h = 20 ft.

The volume of the rectangular prism would be,

⇒ V2 = l × w × h

⇒ V2 = 40 × 15 × 20

⇒ V2 = 12,000 cu. ft.

So, the total amount of volume inside the parking garage would be,

⇒ V = V1 + V2

⇒ V = 8000 + 12000

⇒ V = 20,000 cu. ft.

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Coach Riley needs eight new volleyballs. If the retail price for one ball is $20 at ALL SPORTS and the SPORT SHACK, which store should he buy from in order to pay the least amount? How much will he save?

Answers

Answer:

The way you worded this he should buy at either store because the price is 20 at both and he won't have any savings because they have the same price.

Step-by-step explanation:

Answer:

Well correct me if I am wrong but I think something is missing in this problem because I do not see another number to compare $20 to...

XYZ has been rotated 90°, as shown in the diagram. What is the length of
Y'Z?
Help Idk the answer ​

Answers

Answer:

7

Step-by-step explanation:

The Eastside High School marching band is made up of the instrument players and the percussion. If there are 245 members who play instruments and 35 percussion members, then what percent of the marching band is percussion?

Answers

Answer:

14%

Step-by-step explanation:

you divide 35 by 245 to get 0.14285714285 than you round

The correlation analysis assumes that the measurements have a bivariate normal distribution in the population. Select all of the features that define a bivariate normal distribution.
A) A cloud of points that is funnel shaped (wider at one end than the other)
B) A relationship between X and Y that is not linear
C) The frequency distributions of X and Y separately are normal
D) Either X or Y has a decidedly skewed distribution
E) The presence of outliers Bell-shaped probability distribution in two dimensions rather than one
D) A relationship between X and Y that is linear

Answers

Answer:

Bruh i got correlation hw that i posted on here too and nobody helped lol.

Step-by-step explanation:

This table gives a few (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane. -28 -54 -21 -40 -14 -26 What is the y-intercept of the line?

Answers

Answer:

The y-intercept is y = 2

Step-by-step explanation:

A linear function has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept, which is the value of y when x = 0.

We are given these three points:

(-28, -54)

(-21, -40)

(-14, -26)

We use two of them to build a system, to find values for m and b.

(-28, -54)

This means that when [tex]x = -28, y = -54[/tex]

So

[tex]y = mx + b[/tex]

[tex]-54 = -28m + b[/tex]

[tex]28m = b + 54[/tex]

[tex]m = \frac{b + 54}{28}[/tex]

(-21, -40)

This means that when [tex]x = -21, y = -40[/tex]

So

[tex]y = mx + b[/tex]

[tex]-40 = -21m + b[/tex]

[tex]-40 = -21\frac{b + 54}{28} + b[/tex]

[tex]-40 = \frac{-21b - 1134 + 28b}{28}[/tex]

[tex]7b - 1134 = -40*28[/tex]

[tex]7b = 14[/tex]

[tex]b = \frac{14}{7}[/tex]

[tex]b = 2[/tex]

The y-intercept is y = 2

Answer:

y = (0,2)

Step-by-step explanation:

Find the point estimate for the true difference between the given population means. Round your answer to three decimal places.

(HINT: The point estimate for the difference between the population means is found by simply subtracting one sample mean from the other.)


Sample 1: Weights (in Grams) of Soap Bar A:

129, 127, 129, 129, 128, 130, 127, 129, 128, 131, 127

_____________________________________________________________

Sample 2: Weights (in Grams) of Soap Bar B:

131, 126, 132, 129, 128, 131, 131, 130, 128, 129, 126, 132, 131

Answers

Answer:

Point Estimate for different between population means = - 0.99

Step-by-step explanation:

We are given data of two samples and we have to find the best point estimate of the true difference between two population means. Remember that in absence of data about population the best estimator is the sample data. So, we will find the means of both sample data and find the difference of that means. This difference between the means of sample data will be the best point estimate for the true difference between the population means.

Formula to calculate the mean is:

[tex]Mean=\frac{\text{Sum of Values}}{\text{Number of Values}}[/tex]

Mean of Sample 1:

[tex]Mean=\frac{1414}{11}=128.55[/tex]

Mean of Sample 2:

[tex]Mean=\frac{1684}{13}=129.54[/tex]

Therefore the best point estimate for difference between two population means would be = Mean of Sample 1 - Mean of Sample 2

= 128.55 - 129.54

= - 0.99

Final answer:

The point estimate for the true difference between the given population means is -1.028.

Explanation:

The point estimate for the true difference between the given population means can be found by subtracting one sample mean from the other. Let's calculate it:

Sample 1: 129, 127, 129, 129, 128, 130, 127, 129, 128, 131, 127
Sample 2: 131, 126, 132, 129, 128, 131, 131, 130, 128, 129, 126, 132, 131

Sample mean of Sample 1 = (129+127+129+129+128+130+127+129+128+131+127)/11 = 128.818

Sample mean of Sample 2 = (131+126+132+129+128+131+131+130+128+129+126+132+131)/13 = 129.846

Point estimate for the difference = Sample mean of Sample 1 - Sample mean of Sample 2 = 128.818 - 129.846 = -1.028

The amount of soda in a 16-ounce can is normally distributed with a mean of 16 ounces and a standard deviation of .5 ounce. What is the probability that a randomly selected can will have less than 15.5 ounces? Round your answers to four decimal places.

Answers

Final answer:

Under a normal distribution with a mean of 16 ounces and a standard deviation of 0.5 ounce, there's a 15.87% probability that a randomly selected can will have less than 15.5 ounces of soda.

Explanation:

This question is related to probability within the field of statistics. Particularly, it's about the normal distribution, a common statistical distribution that shows the spread of data around the mean. In this specific case, the amount of soda in a 16-ounce can is normally distributed with a mean (µ) of 16 ounces and a standard deviation (σ) of 0.5 ounce.

We're asked to calculate the probability that a randomly selected can will have less than 15.5 ounces. This requires us to standardize the score of 15.5, meaning we use the formula (X - µ) / σ, where X is the value we are assessing. So, (15.5 - 16) / 0.5 equals -1.

This standardized score is known as a z-score, and tells us how many standard deviations a value is from the mean. In this case, 15.5 is one standard deviation below the mean. We then look up this z-score in a z-table, which gives us the probability associated with this z-score. For a z-score of -1, the probability is 0.1587, or 15.87%.

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The probability that a randomly selected can will have less than 15.5 ounces is approximately 0.1587.

To find the probability that a randomly selected can will have less than 15.5 ounces, we can use the standard normal distribution.

First, we need to calculate the z-score for 15.5 ounces using the formula:

[tex]\[ z = \frac{{X - \mu}}{{\sigma}} \][/tex]

where:

X is the value we're interested in (15.5 ounces), [tex]\( \mu \)[/tex]is the mean (16 ounces), [tex]\( \sigma \)[/tex] is the standard deviation (0.5 ounce).

Plugging in the values:

[tex]\[ z = {{15.5 - 16}}/{{0.5}} \][/tex][tex]\[ z = {{-0.5}}/{{0.5}} \][/tex]z = -1

Next, we look up the z-score of -1 in the standard normal distribution table to find the probability. The probability that a randomly selected can will have less than 15.5 ounces is the area to the left of the z-score of -1.

Using the standard normal distribution table, the area to the left of -1 is approximately 0.1587.

Therefore, the probability that a randomly selected can will have less than 15.5 ounces is approximately 0.1587.

Katelyn did a survey of 200 randomly selected gym members, and found that 72 of them are interested in yoga classes. The gym has 1,000 members. About how many gym members would be interested in yaga?

Answers

Katelyn did a survey of 200 randomly selected gym members, and found that 72 of them are interested in yoga classes. The gym has 1,000 members. About how many gym members would be interested in yaga?

Answer:

360

Step-by-step explanation:

Divide by two on both numbers to get how many out of 100, or a percentage.

72 / 2 = 36

200 / 2 = 100

Multiply times ten to get 1000

100 x 10 = 1000

36 x 10 = 360

A cell phone weighs about 2.8 times 10 Superscript n pounds. Which value of n is most reasonable? Negative 3 Negative 1 0 1

Answers

Answer:

-1

Step-by-step explanation:

The weight of the cell phone is given by:

[tex]W=2.8*10^n[/tex]

The options provided for 'n' are:

a. -3

b. -1

c. 0

d. 1

Applying the possible values:

[tex]W_a=2.8*10^{-3}\\W_a = 0.0028\ pounds\\\\W_b=2.8*10^{-1}\\W_b = 0.28\ pounds\\\\W_c=2.8*10^{0}\\W_c = 2.8\ pounds\\\\W_d=2.8*10^{1}\\W_d = 28\ pounds[/tex]

A cellphone could not possibly weigh as little as 0.0028 or as much as 2.8 or 28 pounds. Therefore, the most reasonable value for n is -1.

Answer:

(B)-1

Step-by-step explanation:

Let us plug in the given values into [tex]2.8X10^n[/tex][tex]2.8X10^{-3}=2.8X 0.001=0.0028\:Pounds\\2.8X10^{-1}=2.8X 0.1=0.28\:Pounds\\2.8X10^{0}=2.8X 1=2.8\:Pounds\\2.8X10^{1}=2.8X 10=28\:Pounds[/tex]

A reasonable value for the weight of a cell phone will be 0.28 Pounds.

Therefore, n=-1

An angle measures 30° more than the measure of its complementary angle. What is the measure of each angle?

Answers

Angle: [tex]\( 60^\circ \)[/tex], complementary angle: [tex]\( 30^\circ \)[/tex]. Angle is 30° more than its complementary angle.

Let's denote the measure of the angle as [tex]\( x \)[/tex] degrees.

The complementary angle would be [tex]\( 90^\circ - x \)[/tex] degrees.

Given that the angle measures 30° more than its complementary angle, we can write the equation:

[tex]\[ x = (90^\circ - x) + 30^\circ \][/tex]

Now, let's solve for [tex]\( x \)[/tex]:

[tex]\[ x = 90^\circ - x + 30^\circ \][/tex]

[tex]\[ 2x = 90^\circ + 30^\circ \][/tex]

[tex]\[ 2x = 120^\circ \][/tex]

Dividing both sides by 2:

[tex]\[ x = \frac{120^\circ}{2} \][/tex]

[tex]\[ x = 60^\circ \][/tex]

So, the angle measures [tex]\( 60^\circ \)[/tex] and its complementary angle measures:

[tex]\[ 90^\circ - 60^\circ = 30^\circ \][/tex]

Therefore, the measure of the angle is [tex]\( 60^\circ \)[/tex] and the measure of its complementary angle is [tex]\( 30^\circ \)[/tex].

In November 2010, an article titled "Frequency of Colds Dramatically Cut with Regular Exercise" appeared in Medical News Today. The article was based on the findings of a study by researchers Nieman et al. (British Journal of Sports Medicine, 2010) that followed 1,002 people aged 18–85 years for 12 weeks, asking them to record their frequency of exercise (5 or more days a week? Yes or No) as well as incidences of upper respiratory tract infections (Cold during last week? Yes or No.)

Answers

Answer:

Part a

For the given study, the explanatory variable or independent variable is given as regularity or frequency of exercise. This variable is classify as categorical variable because variable is divided into two categories such as whether participant exercise 5 or more days a week or not.

Part b

For the given study, the response variable or dependent variable is given as frequency of colds. This variable is classified as quantitative variable because we measure the quantities or frequency of number of colds.

Part c

A confounding variable for this research study is given as incidence of upper respiratory tract infections that provides an alternative explanation for the lower frequency of colds among those who exercised 5 or more days per week, compared to those who were largely sedentary. This confounding variable is categorical in nature.

Find the volume of this prism.
Image attached ​

Answers

Answer:

840cm³

Step-by-step explanation:

devide them into 2 shapes.

the shape at the bottom

a×b×h

15cm×6cm×8cm=720cm³

the shape at the top

a×b×h

a: 5 cmb: 6 cmh: 12-8=4 cm5cm×6cm×4cm=120cm³

V=720cm³+120cm³=840cm³

Answer:

840 cm^3

Step-by-step explanation:

L x W x H = V

Split the prism into 2 different prisms.

6 is constant throughout the figure, so all we have to do is find the L and H of the two prisms and multiply them by 6.

15 x 8 = 120

The height of the higher prism can be determined by subtracting the bottom height from the total height.

12 - 8 = 4

5 x 4 = 20

Add the two side areas together.

20 + 120 = 140

Multiply by the width, 6.

140 x 6 = 840

A manufacturer of a new medication on the market for Parkinson's disease makes a claim that the medication is effective in 75% of people who have the disease. One hundred fifty individuals with Parkinson's disease are given the medication, and 100 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 75% claim the company made? Make sure to include parameter, conditions, calculations, and a conclusion in your answer.

Answers

Answer:

Claim is rejected

Step-by-step explanation:

Solution:-

- The claim was made on the effectiveness of medication on the market of Parkinson's disease to be p = 75%.

- A random sample was taken of N = 150 individuals and n = 100 number of people reported that it was effectively.

- We are to test the claim made by the manufacturer of the medication based on the statistics available for the sample N.

- State the hypothesis for the effectiveness of medication:

          Null Hypothesis: p = 0.75   ... Claim

          Alternate hypothesis: p < 0.75   .... Test

- The conditions of standard normality:

n*p > 5 , 150*0.75 = 112.5   .. ( Check )

n*(1-p) > 5 , 150*0.25 = 37.5  .. ( Check )

Hence, the standard normal test is applicable. Assuming the population proportion to be normally distributed.

- We will estimate the population proportion with the sample proportion ( p* ):

                          p* = n / N

                          p* = 100 / 150

                          p* = 2/3 = 0.667

- Testing against the claimed population proportion ( p ) = 0.75. The standard normal statistic value is given by:

                         [tex]Z-test= \frac{(p^* - p)}{\sqrt{p(1-p) / N} } \\\\Z-test= \frac{(0.6667 - 0.75)}{\sqrt{0.75(0.25) / 150} } \\\\Z-test= \frac{-0.0833}{\sqrt{0.00125} } \\\\Z-test= -2.35607 \\[/tex]

- We will see whether the Z-test statistic falls in the rejection region defined by the critical value of Z at significance level ( α ) of 0.05.

- The rejection region is defined by the Alternate hypothesis which is less than the claimed value. So, the rejection region defined by the lower tail of the standard normal.

- So for lower tailed test the critical value of statistics is:

                       P ( Z < Z-critical ) = α = 0.05

                       Z-critical = - 1.645

- The rejected values all lie to the left of the Z-critical value -1.645          

- The claim test value is compared the rejection region:

                      -2.35607 < -1.645

                       Z-test < Z-critical

Hence, Null hypothesis rejected because test lies in the rejection region.

Conclusion:

The Null hypothesis or claim made by the manufacturer of Parkinson's disease medication of 75% effectiveness is without sufficient evidence. Hence, the claim made is false or has no statistical evidence.

Final answer:

By calculating the Z-score and corresponding p-value for the statistical test, we found that there is significant evidence at the 0.05 level to suggest that the medication's effectiveness is less than the 75% claimed.

Explanation:

The subject we're dealing with here is hypothesis testing in statistics, where we have a claim (the effectiveness of the medication is 75%) and we are testing whether the observations (effectiveness in 100 out of 150 individuals) support this claim.

Firstly, the parameter of interest here is the proportion (p) of individuals for whom the medication is effective. Our null hypothesis (H0) is that p = 0.75 and our alternate hypothesis (Ha) is that p < 0.75.

To conduct the hypothesis test, let's check the conditions:

Random: It's not mentioned, but assuming these 150 individuals were chosen randomly, this condition is met.Normal: Since both np (150 * 0.75 = 112.5) and n(1-p) (150 * 0.25 = 37.5) are greater than 10, the sampling distribution will be approximately normal.Independent: Again, this is not stated, but let's assume the responses from the individuals are independent.

The sample proportion (p-hat) = 100/150 = 0.67

Next, we calculate the Z score, which is (p-hat - p) / sqrt[p(1-p)/n] = (0.67 - 0.75) / sqrt[0.75 * (0.25) / 150] = -1.65. The p-value associated with a Z score of -1.65 is 0.0495.

Since the p-value is less than the significance level of 0.05, we reject H0 and conclude that there is statistically significant evidence at the 0.05 level that the effectiveness of medication is less than 75% as claimed by the manufacturer.

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The Martin family's truck gets an average of 35 miles per gallon. Predict how many miles they can drive
using 4 gallons of gas.

Answers

Answer:

25 miles per gallon x 7 gallons used=175 miles driven

175/7=25

NOTE: THIS IS AN EXAMPLE

A production process manufactures electronic components with timing signals whose duration follows a normal distribution. A random sample of 55 components was​ taken, and the durations of their timing signals were measured.a. The probability is 0.01 that the sample variance is bigger than what percentage of the population​ variance?


b. The probability is 0.05 that the sample variance is less than what percentage of the population​ variance?

Answers

Answer:

Check the explanation

Step-by-step explanation:

b ) [tex]P(s^2<p\sigma^2)=0.05[/tex]

or , [tex]P\left (\frac{(n-1)s^2}{\sigma^2}<(n-1)p \right )=0.05[/tex]

or , [tex]P\left (\chi^2_5<5p \right )=0.05=P(\chi^2_5< 1.145476 )[/tex]

or , 5p =1.145476

or , [tex]p =\frac{1.145476}{5}= 0.2290952[/tex]

Required percentage = 22.91

PLEASE HELP !!!! What happens to the value of the expression 20+a20+a20, plus, a as a increases?
Choose 1 answer:

(Choice A)
A
It increases.

(Choice B)
B
It decreases.

(Choice C)
C
It stays the same.

Answers

Answer:

the answer is a it increases

Step-by-step explanation:

Answer:

(A)-  It increases

Step-by-step explanation:

Good luck with your unit test for Kahn!!

A rhombus TEMPhas coordinates A(-6, 3)
B(-4, 4)
C(-2, 3)
D(-4, 2).
What are the coordinates of rhombus A'B'C'D' AFTER A 90° COUNTERCLOCKWISE ROTATION ABOUT THE ORIGIN FOLLOWED BY A TRANSLATION 3 UNITS TO THE LEFT AND 2 UNITS DOWN ?

Answers

Answer:

A'(-6, -8)B'(-7, -6)C'(-6, -4)D'(-5, -6)

Step-by-step explanation:

A 90° CCW rotation makes the transformation ...

  (x, y) ⇒ (-y, x)

A translation 3 left and 2 down makes the transformation ...

  (x, y) ⇒ (x -3, y-2)

The two transformations together are ...

  (x, y) ⇒ (-y-3, x -2)

Then the given points are transformed to ...

 A'(-6, -8)

  B'(-7, -6)

  C'(-6, -4)

  D'(-5, -6)

The two graphs below compare the gallons of gasoline used and the total distance traveled for two different cars.

Car 1
A graph has gallons of gasoline used on the x-axis and miles traveled on the y-axis. A line goes through points (2, 50) and (4, 100).
Car 2
A graph has gallons of gasoline used on the x-axis and miles traveled on the y-axis. A line goes through points (2, 40) and (4, 80).

Which comparison of the slopes of the two lines is accurate?

Answers

The comparison of the slopes is accurate: the slope of the line for Car 1 is greater than the slope of the line for Car 2.

Step 1:

The comparison of the slopes of the two lines can be made by calculating the slope of each line. Let's calculate the slopes:

For Car 1:

The coordinates are (2, 50) and (4, 100).

Using the slope formula [tex]\( m = \frac{y_2 - y_1}{x_2 - x_1} \)[/tex]:

[tex]\[ m = \frac{100 - 50}{4 - 2} = \frac{50}{2} = 25 \][/tex]

For Car 2:

The coordinates are (2, 40) and (4, 80).

Using the slope formula:

[tex]\[ m = \frac{80 - 40}{4 - 2} = \frac{40}{2} = 20 \][/tex]

Step 2:

Comparing the slopes:

- The slope of the line for Car 1 is 25.

- The slope of the line for Car 2 is 20.

Therefore, the comparison of the slopes is accurate: the slope of the line for Car 1 is greater than the slope of the line for Car 2.

What is the area of the following shape?

Answers

Answer:

114 square meters

Step-by-step explanation:

formula:1/2×h(a+b)

1/2×12{(12+5)+12}

1/2×12(17+12)

=6×19

=114m^2

Need help with this

Answers

It’s the second one, b

Determine the simple interest earned on $21,500 after 16 years if the APR is 9 %.

Answers

Final answer:

The student asked about the simple interest earned on an investment. The simple interest can be calculated using the formula I = PRT. For a principal of $21,500 at a 9% APR for 16 years, the interest earned is $30,960.

Explanation:

To calculate simple interest, you can use the formula I = PRT, where I is the interest, P is the principal amount (the initial amount of money), R is the rate of interest per period, and T is the time the money is invested for.

In this case, we have:

P (Principal) = $21,500R (Rate) = 9% or 0.09T (Time) = 16 years

Plugging these values into the formula, we get:

I = PRT

I = $21,500 × 0.09 × 16

I = $30,960

The simple interest earned after 16 years is $30,960.

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Final answer:

The simple interest on $21,500 at 9% APR over 16 years is calculated using the formula I = PRT, which gives us a total interest of $30,960.

Explanation:

To calculate the simple interest earned on a sum of money, we can use the formula I = PRT, where I stands for interest, P for principal amount, R for the annual interest rate (in decimal form), and T for the time in years. In this case, the student wants to determine the interest earned on $21,500 at 9% APR for 16 years.

First, convert the interest rate from a percentage to a decimal by dividing by 100:

R = 9% / 100 = 0.09

Next, apply the values to the simple interest formula:

I = PRT

I = $21,500 × 0.09 × 16

I = $30,960

Therefore, the total simple interest earned after 16 years is $30,960.

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