What is the radius of the circle?

1) The original price of the t-shirt is $20.6.

2) Price of the t-shirt before the discount is $20.6.

What is discount?

Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.

Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.

1) Here the Cost price of the t-shirt = $15.45

She bought t-shirt which is cost of 75% of the original price. Then

=> 75% =15.45

Original  price = 15.45×\(\frac{100}{75}\)

=> original price = $20.6

Hence the original price of the t-shirt is $20.6.

2) The cost price of the t-shirt = $15.45

Then cost price = (100%-25%) of original price

=> 15.45 = 75% of original price

=> original price = \(\frac{15.45*100}{75}\) = $20.6.

Hence price of the t-shirt before the discount is $20.6.

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Answer:

I'm pretty sure its choice c and d i'm sorry if its not i did all the math, although i might have gotten it wrong, just double check.

Step-by-step explanation:

Answer:

1)

b) Profit divided by number of writers

c) Profit divided by expenses

2)

b) Yes. According to both definitions, website B generates more profit per resource invested.

Answer:

False

Step-by-step explanation:

According to an act of Congress a firm cannot have more than 100 partners

The regression equation for predicting the height of girls at age 18 based on their height at age 2 is:

y ≈ 68.953 + 1.210x

The correlation coefficient illustrates how closely two variables are related to one another. This coefficient's range is from -1 to +1. This coefficient demonstrates the degree to which the observed data for two variables are significantly associated.

Based on the given information, we can use the linear regression model to predict the height of girls at age 18 based on their height at age 2. Here are the summary statistics:

n = 70 (sample size)

x = 87.25 (mean height at age 2 in cm)

y = 166.54 (mean height at age 18 in cm)

R = 0.664 (correlation coefficient)

S = 3.33 (standard deviation of height at age 2 in cm)

\(S_y\) = 6.07 (standard deviation of height at age 18 in cm)

To predict the height of girls at age 18 (y) based on their height at age 2 (x), we can use the regression equation:

y = a + bx

where a is the y-intercept (predicted height at age 18 when x = 0) and b is the slope of the regression line.

From the given information, we have the following values:

x = 87.25

y = 166.54

R = 0.664

Using these values, we can calculate the slope (b) of the regression line:

b = R * (\(S_y\) / S)

 = 0.664 * (6.07 / 3.33)

 ≈ 1.210

Next, we can calculate the y-intercept (a) using the formula:

a = y - b * x

 = 166.54 - 1.210 * 87.25

 ≈ 68.953

Therefore, the regression equation for predicting the height of girls at age 18 based on their height at age 2 is:

y ≈ 68.953 + 1.210x

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Answer:

d. 89°

Step-by-step explanation:

The given measure of the angles formed are;

m∠AED = 48°, m\(\widehat{AG}\) = 175°

According to circle theorem, the angle formed by a chord and a tangent of a circle is given by half of the measure of the arc intercepted by the chord in the direction of the angle;

Therefore;

m∠AED = (1/2) × m\(\widehat{ABE}\)  = 48°

∴ m\(\widehat{ABE}\) = 2 × 48° = 96°

m∠AEF = (1/2) × m\(\widehat{AGE}\)

m\(\widehat{ABE}\) + m\(\widehat{AGE}\) = 360° (angle round a circle)

∴ m\(\widehat{AGE}\) = 360° - m\(\widehat{ABE}\) = 360° - 96° = 264°

m\(\widehat{AGE}\) = m\(\widehat{AG}\) + m\(\widehat{EG}\)

∴ m\(\widehat{EG}\) = m\(\widehat{AGE}\) - m\(\widehat{AG}\) = 264° - 175° = 89°

m\(\widehat{EG}\) = 89°.

Answer:

$305.9022863 or $305.90 (rounded to 2 decimal places)

Step-by-step explanation:

It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula  

A= P(1+R)^n

A= the total amount P=Initial amount       R= rate  n=time period

P=$100 R=15% or 0.15(decimal)  n=8 (years)  

A= 100 (1.15)^8

A= 100(3.059022863)

A=305.9022863

The amount you will have after 8 years is $220

The formula for calculating simple interest is expressed as:

SI =PRT

P is the principal = $100

T is the time = 8 years

R is the rate. = 15%

SI = 100 * 8 * 0.15
SI = $120

Amount after 8years = $100 + $120
Amount after 8years = $220

Hence the amount you will have after 8 years is $220

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On solving the provided question, we can say that by using N= 2X + 1 or  N = 2X-1  will do the job for composite numbers.

By multiplying two small positive integers, you can create a composite number, which is a positive integer. Likewise, any positive integer that has at least one divisor besides itself and 1. Positive whole numbers make up composite numbers. It lacks prime (that is, it has divisors other than 1 and itself). The first several composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, and are frequently referred to simply as "composites." In other words, composite odd numbers encompass all non-prime odd numbers. for illustration: 9, 15, 21, etc. No. As a result, 2 only possesses the divisors 1 and 2. To put it another way, since 2 only has two divisors, it is not a composite number.

by using N= 2X + 1

or

N = 2X-1

will do the job for composite numbers.

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To find an exponential regression equation for the given set of data, we need to express it in the form of y = ab^x, where a represents the initial value of the car and b represents the growth or decay factor.

Using the provided data, we can form the following table:

Years (x) Value in dollars (y)

0 15600

1 14254

2 12189

3 10822

4 9618

5 7994

6 6686

To find the exponential regression equation, we can use statistical software or calculators that provide regression analysis. Using these tools, we can obtain an equation in the form of y = ab^x. Let's assume the equation is:  y = 15600 * (0.91)^x

Rounding the coefficient to the nearest hundredth, we get: y = 15600 * (0.91)^x

To determine the value of the car after 15 years, we substitute x = 15 into the equation: y = 15600 * (0.91)^15

Evaluating the expression gives us the value of the car after 15 years.

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Answer:

cosR = \(\frac{5}{13}\)

Step-by-step explanation:

assuming the right triangle has ∠ Q = 90° with legs 5 and 12

then this is a 5- 12- 13 right triangle with hypotenuse PR = 13 cm

then

cosR = \(\frac{adjacent}{hypotenuse}\) = \(\frac{QR}{PR}\) = \(\frac{5}{13}\)

The area of the rectangular animal pen with fencing of 200 m with a length of 60 m is 2400 sq m

Perimeter refers to the length of the boundary of a given shape.

Perimeter = 2(l + b)

where l is the length

b is the breadth

Given,

Perimeter = 200 m

l = 60 m

200 = 2(60 + b)

100 = 60 + b

b = 100 - 60

b = 40 m

The other side of the rectangle is 40 m.

The area is the expanse covered by a shape

Area = l * b

= 60 * 40

= 2400 sq m

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Based on the given sample data, we cannot say for sure whether males and females spend a different amount of time studying in a week.

To determine whether males and females spend a different amount of time studying in a week, we can perform a hypothesis test.

Let's assume the null hypothesis H₀ is that the mean study time for males and females is the same, a

nd the alternative hypothesis $H₁ is that the mean study time is different. Mathematically, we can write this as:

H: μ₁ = μ₂

H₁; μ₁ - μ₂

where μ₁ is the population mean study time for females and μ₂ is the population mean study time for males.

To perform the hypothesis test, we can use a two-sample t-test. The test statistic is given by:

t = x₁ - x₂ /√{s₁²}{n₁} + {s₂²}{n₂}

where {x}₁ and s₁ are the sample mean and standard deviation of study time for females, n₁ is the sample size for females, x₂ and s₂ are the sample mean and standard deviation of study time for males, and n₂ is the sample size for males.

Plugging in the given values, we get:

t = {12.3 - 14.1}/ {√{{11.2²}/ {103} + {16.8²}/{92}}}

t = -1.194

Using a significance level of alpha = 0.05, and degrees of freedom equal to (103-1)+(92-1) = 193, we can find the critical t-values from a t-distribution table as -1.972 and 1.972

Since our calculated test statistic t=-1.194$ falls outside the critical region (-1.972, 1.972), we cannot reject the null hypothesis.

Therefore, we do not have enough evidence to conclude that the mean study time for males and females is different.

In conclusion, To determine whether males and females spend a different amount of time studying in a week, we can perform a hypothesis test. Let's assume the null hypothesis H₀ is that the mean study time for males and females is the same, and the alternative hypothesisH₁ is that the mean study time is different. Mathematically, we can write this as:

H₀ : μ₁ = μ₂

H₁; μ₁ - μ₂

where μ₁ is the population mean study time for females and μ₂ is the population mean study time for males.

To perform the hypothesis test, we can use a two-sample t-test. The test statistic is given by:

t = x₁ - x₂ /√{s₁²}{n₁} + {s₂²}{n₂}

Plugging in the given values, we get:

t = {12.3 - 14.1}/ {√{{11.2²}/ {103} + {16.8²}/{92}}}

Using a significance level of alpha = 0.05, and degrees of freedom equal to (103-1)+(92-1) = 193, we can find the critical t-values from a t-distribution table as -1.972 and 1.972

Since Our calculated test statistic t=-1.194 falls outside the critical region (-1.972, 1.972), we cannot reject the null hypothesis.

Therefore, we do not have enough evidence to conclude that the mean study time for males and females is different.

In conclusion, based on the given sample data, we cannot say for sure whether males and females spend a different amount of time studying in a week.

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We used the formula for the volume of a rectangular prism. We denoted the width of the aquarium as x and plugged in the given values for length and height, as well as the given volume of 595 cubic inches, the width of the aquarium is 7 inches.

Using the formula for the volume of a rectangular prism, we can solve for the width of the aquarium. Let's denote the width as x.

length × width × height.

We are given that the length is 17 in, the height is 5 in, and the volume is 595 cubic inches. We can set up the equation:

(17 × 5)x = 595

Simplifying the equation gives us:

85x = 595

Dividing both sides by 85:

x = 7

Therefore, the width of the aquarium is 7 inches.

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Answer:

domain and the range

Step-by-step explanation:

The intrinsic rate of increase depends on the initial population size, but for any given population size, it is 11.5 times the population size

The intrinsic rate of increase (r) is given by the difference between the birth rate (b) and the death rate (d), divided by the average population size (N) over the same period of time:

r = (b - d) / N

In this case, the birth rate is 6 beetles per year, and the death rate is 0.5 beetles per year. We can assume that the population is growing exponentially, which means that the average population size over the year is half the initial population size. Therefore:

N = N0 / 2

where N0 is the initial population size.

Putting it all together, we get:

r = (6 - 0.5) / (N0 / 2)

r = 11.5 / N0

The intrinsic rate of increase depends on the initial population size, but for any given population size, it is 11.5 times the population size. For example, if the initial population size is 100 beetles, the intrinsic rate of increase is: r = 11.5 / 100 = 0.115 per year

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Mrs. Rosenblatt's class has an average grade of 87. After realizing she left out Joe's score of 65, the new mean will be lower than 87.

Explanation:

To find the new mean, we need to calculate the sum of all the grades in the class, including Joe's score of 65, and divide it by the total number of students in the class. Let's assume there are n students in the class.

The sum of all the grades in the class, including Joe's score, will be (87 * n) + 65, since the average grade before Joe's score was added was 87. Therefore, the new mean will be:

[(87 * n) + 65] / (n + 1)

Expanding this expression, we get:

(87n + 65) / (n + 1)

Simplifying this expression, we get:

(87n / (n + 1)) + (65 / (n + 1))

Since n is a positive integer, the value of (87n / (n + 1)) will be slightly less than 87. Therefore, the new mean will be slightly less than 87, reflecting the lower score added to the class average.

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Given the provided coordinates of the points, The shape that is formed is a parallelogram because the slopes of the opposite sides are same.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

slope between (1,1) and (4,4),

m1 = 4-1/4-1 =3/3 =1

slope between (4,-2) and (7,1),

m2= 1+2/7-4 = 3/3 =1

m1=m2

similarly, slope between (1,1) and (4,-2),

m3= -2-1/4-1 = -3/3 =-1

slope between (7,1) and (4,4)

m4= 1-4/7-4 = -3/3 =-1

m3=m4

So, slopes of opposite sides are same that means they are parallel, The shape is parallelogram.

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the smallest sample size n that provides the desired accuracy is a) 97 that is Sample size should be atleast 97

given that a 95% confidence interval for the mean of a population is to be constructed and must be accurate to within 0.3 unit.

i.e. margin of error <0.3

Std devition sample = 1.5

For 95% assuming sample size large we can use z critical value

Z critical = 1.96

we have

1.96*1.5/\(\sqrt{n}\)< 0.3

9.8 < \(\sqrt{n}\)

n> 96.04

approximate 97

Sample size should be atleast 97 to get an accurate margin of error 0.3

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The percent sign is already taken care of, so you'll just input the numeric part only to fill in the green box.

========================================================

Explanation:

Focus on the first row only. This is because we are 100% certain that the person ordered a hot beverage based on the keyword "given".

There are A = 22 who ordered a large hot drink out of B = 5+48+22 = 75 who ordered a hot beverage.

The probability we're after is therefore A/B = 22/75 = 0.29 = 29% approximately.

a. Null hypothesis: Proportion of patients cured by the drug is less than or equal to 50%

Alternative hypothesis: Proportion of patients cured by the drug is greater than 50%

b. Test statistic = 1.4

c. At the 5% significance level, we fail to reject the null hypothesis. We cannot conclude that the proportion of patients cured by the drug is greater than 50%.

a. The null hypothesis would be that the proportion of patients cured by the drug is equal to or less than 50%, while the alternative hypothesis would be that the proportion of patients cured by the drug is greater than 50%.

b. To calculate the test statistic, we can use the formula:

z = (P - p) / sqrt(p × (1 - p) / n)

Where P is the sample proportion of patients cured, p is the hypothesized proportion of patients cured (in this case, 0.5), n is the sample size, and sqrt refers to the square root function.

Plugging in the values, we get

z = (0.52 - 0.5) / sqrt(0.5 × 0.5 / 400) = 1.4

c. To determine if we can reject the null hypothesis at the 5% significance level, we need to compare the test statistic (1.4) to the critical value of the standard normal distribution at a 5% level of significance, which is 1.645.

Since the test statistic (1.4) is less than the critical value (1.645), we fail to reject the null hypothesis. Therefore, we cannot conclude that the proportion of patients cured by the drug is greater than 50% at the 5% significance level.

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Answer:

9 in. i think

Step-by-step explanation:

(c) The student misses the bus by the difference between the total distances covered by the bus and the student.

(a) To determine the distance covered by the bus from the moment the student starts chasing it until the moment the bus passes by the stop, we need to consider the relative motion between the bus and the student. Let's break down the problem into two parts:

1. Acceleration phase of the student:

During this phase, the student accelerates until reaching the bus's velocity. The initial velocity of the student is zero, and the final velocity is the velocity of the bus. The time taken by the student to accelerate is given as 1.70 s.

Using the equation of motion:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can calculate the acceleration of the student:

a = (v - u) / t

  = (0 -\(v_{bus}\)) / 1.70

Since the student starts 200 m ahead of the bus, we can use the following kinematic equation to find the distance covered during the acceleration phase:

s = ut + (1/2)at^2

Substituting the values:

\(s_{acceleration}\) = (0)(1.70) + (1/2)(-\(v_{bu}\)s/1.70)(1.70)^2

              = (-\(v_{bus}\)/1.70)(1.70^2)/2

              = -\(v_{bus}\)(1.70)/2

2. Constant velocity phase of the student:

Once the student reaches the velocity of the bus, both the bus and the student will cover the remaining distance together. The time taken by the bus to cover the remaining distance of 200 m is given as 36 s - 1.70 s = 34.30 s.

The distance covered by the bus during this time is simply:

\(s_{constant}_{velocity} = v_{bus}\) * (34.30)

Therefore, the total distance covered by the bus is:

Total distance = s_acceleration + s_constant_velocity

              = -v_bus(1.70)/2 + v_bus(34.30)

Since the distance covered cannot be negative, we take the magnitude of the total distance covered by the bus.

(b) To determine the distance covered by the student during the 36 s, we consider the acceleration phase and the constant velocity phase.

1. Acceleration phase of the student:

Using the equation of motion:

s = ut + (1/2)at^2

Substituting the values:

\(s_{acceleration}\) = (0)(1.70) + (1/2\(){(a_student)}(1.70)^2\)

2. Constant velocity phase of the student:

During this phase, the student maintains a constant velocity equal to that of the bus. The time taken for this phase is 34.30 s.

The distance covered by the student during this time is:

\(s_{constant}_{velocity} = v_{bus}\) * (34.30)

Therefore, the total distance covered by the student is:

Total distance =\(s_{acceleration} + s_{constant}_{velocity}\)

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Answer: 33.6% of X = 26800

X = 26800 / 33.6%

   = 26800 / 0.336

  = 33.6%

HOPE THIS HELPS HAVE A AWESOME NIGHT/DAY✨

Step-by-step explanation:

Answer:

2997.2

Step-by-step explanation:

Answer:

none of the above

Step-by-step explanation:

the all diferent in there own ways

Answer:

Which triangle(s) are congruent to triangle ABC? The triangle JGH

Step-by-step explanation:

Triangle ABC is congruent to triangle JGH

Answer:

-5

Step-by-step explanation:

Answer:

The answer to the question provided is -27.

Answer:

-27

Step-by-step explanation:

Answer

Step-by-step explanation:

DE: 3x + 20

EF: 2x + 40

DE+ EF= DF

3x+20 +2x + 40 = 170

5x + 60 =170

5x= 110

x= 22

Answer:

x = 22

DE = 86

EF = 84

Step-by-step explanation:

DF=DE+EF

170= (3x +20) + ( 2x+40)

170 = 5x + 60

5x = 170 - 60

5x = 110

x = 110 / 5

x = 22

DE =3x + 20 = 3(22) + 20 = 66 + 20 = 86

EF= 2x + 40 = 2(22) + 40 = 44 + 40 = 84

I hope I helped you^_^

Answer:

\(33.72 \: square \: yards \)

Step-by-step explanation:

\(4 \times 10 = 40 \\ {2}^{2} \pi \div 2 = 6.28 \\ 40 - 6.28 = 33.72\)

The value of z that divides the standard normal distribution so that half the area is on one side and half is on the other is 0.00.

To understand this better, let's visualize the standard normal distribution. The graph of the standard normal distribution is a bell-shaped curve that is symmetrical around the mean of 0.

When we say that half the area is on one side and half is on the other, we mean that the area under the curve to the left of the z-score is equal to the area under the curve to the right of the z-score.

Since the standard normal distribution is symmetric, this occurs when the z-score is equal to 0.00. At this point, the area to the left of 0.00 is 0.50 (or 50%), and the area to the right of 0.00 is also 0.50 (or 50%).

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The area of the teacher workroom is 64 feet squared