the management at new century bank claims that the mean waiting time for all customers at its branches is less than that at the public bank, which is its main competitor. a business consulting firm took a sample of 200 customers from the new century bank and found that they waited an average of 4.5 minutes before being served. another sample of 300 customers taken from the public bank showed that these customers waited an average of 4.75 minutes before being served. assume that the standard deviations for the two populations are 1.2 and 1.5 minutes, respectively. test at a 2.5% significance level whether the claim of the management of the new century bank is true.

Answer: (0, 48)

Step-by-step explanation:

To find the y-intercept, plug the x and y values in the equation y = -3x + b, and leave the b the same.

I will use (11, 15)

15 = -3(11) + b

15 = -33 + b

48 = b

The y-intercept is (0, 48)

Equation is y = -3x + 48

Hope this helps!

So the minimum score required to be eligible to enroll in calculus is 67.

To find the minimum score required to be in the top 20%, we need to find the score that corresponds to the 80th percentile of the distribution.

The standard normal distribution is a normal distribution with mean 0 and standard deviation 1. We can use the standard normal distribution to find percentiles of any normal distribution by using the fact that any normal distribution can be converted to a standard normal distribution through the following formula:

z = (x - mean) / standard deviation

where x is the raw score, mean is the mean of the distribution, standard deviation is the standard deviation of the distribution, and z is the standardized score (also called the z-score).

We can use this formula to convert the scores on the math placement exam to the standard normal distribution. Let x be the minimum score required to be eligible. Then the corresponding z-score would be:

z = (x - 42) / 19

We want to find the value of x that corresponds to the z-score for the 80th percentile, which we can find using a z-table or by using a calculator or computer to find the inverse of the standard normal cumulative distribution function (CDF). The z-score for the 80th percentile is approximately 0.84. Plugging this value into the equation above, we get:

0.84 = (x - 42) / 19

Solving for x, we find that the minimum score required to be eligible is approximately 66. Rounding to the nearest integer, the minimum score required is 67.

So the minimum score required to be eligible to enroll in calculus is 67.

To learn more about standard normal distribution,

visit; brainly.com/question/13781953

#SPJ4

Answer:

About 150,000,000,000 meters

The scientific notation would be  1.5 × 10^11 (just in case you need it)

\(1.5*10^1^1\)

Step-by-step explanation:

Hope this helps:)

The Weighted Average Cost of Capital (WACC) for Snuggly Baby Corp. is calculated based on the company's capital structure, including common equity, preferred equity, and bonds. The WACC is influenced by the expected returns and prices of these securities.

To calculate the WACC, we need to determine the proportion of each component in the capital structure and multiply it by its respective cost of capital.

For Snuggly Baby Corp., the capital structure consists of 6,130,000 shares of common equity, 1,006,000 shares of preferred equity, and 81,400 bonds.

The cost of common equity is calculated using the expected return and the price of the shares. Similarly, the cost of preferred equity is calculated using the expected return and the price of the preferred shares. The cost of debt, represented by the bonds, is calculated using the yield-to-maturity.

Once we have the costs of each component, we multiply them by their respective proportions in the capital structure and sum them up to determine the overall WACC. Please note that to provide an accurate calculation of the WACC, additional information is required, such as the market value of each component and the weights assigned to them in the capital structure. Without this information, it is not possible to provide an exact WACC calculation.

learn more about Weighted Average Cost of Capital (WACC) here:

https://brainly.com/question/30746642

#SPJ11

Students should be able to apply these concepts and tools in real-world situations, such as calculating the probability of winning a game or analyzing data from a scientific Experiment.

The probability is a measure of the possibility of an event happening. It is expressed as a fraction or decimal between 0 and 1, or as a percentage between 0% and 100%. Probability can be used to determine the likelihood of an event happening or not happening.

Data analysis is the process of analyzing data to extract valuable insights from it. It involves examining data sets to uncover trends, patterns, and relationships that can be used to make informed decisions. Data analysis is an important tool in many fields, including business, finance, and science.

The data analysis and probability unit test assesses students' understanding of these concepts and their ability to apply them in real-world situations.

The test typically includes questions that require students to use probability to determine the likelihood of an event happening or not happening, as well as questions that ask students to analyze data sets to extract valuable insights.In order to prepare for the data analysis and probability unit test, students should review the key concepts and formulas related to probability, such as the addition rule, the multiplication rule, and the complementary rule.

They should also practice analyzing data sets using tools like histograms, scatter plots, and box plots, and should be familiar with key concepts like mean, median, and mode.

Finally, students should be able to apply these concepts and tools in real-world situations, such as calculating the probability of winning a game or analyzing data from a scientific experiment.

For more questions on Experiment.

https://brainly.com/question/28214089

#SPJ8

Answer:

y < 3x + \(\frac{5}{2}\)

Step-by-step explanation:

6x > 2y - 5

Adding 5 to both sides

=> 6x + 5 > 2y

=> 2y < 6x+5

Dividing both sides by 2

=> y < \(\frac{6x+5}{2}\)

=> y < \(\frac{6x}{2} + \frac{5}{2}\)

=> y < 3x + \(\frac{5}{2}\)

This is the required slope intercept form in the form \(y = mx+b\)

The lengths of the diagonals of rectangle is 66 units

The properties of a rectangle is given as;

From the information given, we have that;

$WY=14x+10

$XZ=11x+22

Since the diagonals are of the same length, we have;

WY = XZ

14x + 10 = 11x + 22

collect like terms

14x - 11x = 22 - 10

subtract the like terms

3x = 12

Make 'x' the subject of the formula

x = 4

WY = 54 + 10 = 66

XZ = 66

Hence, the values are 66

Learn about diagonals on:

https://brainly.com/question/26154016

#SPJ1

To find the equation that relates the value, V, of Sadie's laptop to the number of months, t, since she purchased it, we can use the concept of linear depreciation.

We know that the laptop's value six months ago was $2,025 and five months from now it will be $1,629. We can use these two points to determine the equation of the line.

Let's denote the value of the laptop as V and the number of months since the purchase as t. We can set up the equation in the slope-intercept form, y = mx + b, where y is the value of the laptop and x is the number of months.

Using the two given points:

Point 1: (6, 2025)

Point 2: (11, 1629)

We can calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

m = (1629 - 2025) / (11 - 6)

m = -396 / 5

m = -79.2

Now, we can substitute one of the points into the slope-intercept form to find the y-intercept (b). Let's use Point 1:

2025 = -79.2 * 6 + b

2025 = -475.2 + b

b = 2025 + 475.2

b = 2500.2

Therefore, the equation that relates the value (V) of the laptop to the number of months (t) since Sadie purchased the laptop is:

V = -79.2t + 2500.2

This equation represents the linear depreciation model, where the laptop's value decreases by $79.2 per month.

Learn more about geometry here:

https://brainly.com/question/19241268

#SPJ11

Answer:

bnnnm

bStep-by-step explanation:

The missing side of the triangle, B, is approximately 13.86 units long.

Let's denote the missing side as B. According to the Pythagorean Theorem, the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side, which is the hypotenuse. Mathematically, this can be represented as:

A² + B² = C²

In our case, we are given the lengths of sides A and C, which are 8 and 16 respectively. Substituting these values into the equation, we get:

8² + B² = 16²

Simplifying this equation gives:

64 + B² = 256

To isolate B², we subtract 64 from both sides of the equation:

B² = 256 - 64

B² = 192

Now, to find the value of B, we take the square root of both sides of the equation:

√(B²) = √192

B = √192

B ≈ 13.86 (rounded to two decimal places)

To know more about Pythagorean theorem here

https://brainly.com/question/343682

#SPJ4

Complete Question:

How do you use the Pythagorean Theorem to find the missing side of the right triangle with the given measures: A= 8, C= 16?

The Expression that have a product greater than 4 is one hundred  and one hundredths times four , the correct option is (d).

In the question ,

four expressions are given as

(a) four times ninety-nine hundredths

= 4 × 99/100

= 4 × 0.99

= 3.96

(b) four times eight-eighths

= 4 × 8/8

= 4 × 1

= 4

(c) three-fourths times four

= 3/4 × 4

= 3

(d) one hundred  and one hundredths times four

= 1.01 × 4

= 4.04

Therefore , The Expression that have a product greater than 4 is one hundred and one hundredths times four .

The given question is incomplete , the complete question is

Which of the following expressions will have a product greater than 4?

(a) four times ninety-nine hundredths

(b) four times eight-eighths

(c) three-fourths times four

(d) one hundred and one hundredths times four

Learn more about Multiplication here

https://brainly.com/question/19130641

#SPJ1

Answer:

term

Step-by-step explanation:

Answer:

\( - 2x + 5y = 10 \\ 5y = 2x + 10 \\ \frac{5}{5} y = \frac{2}{5} x + \frac{10}{5} \\ \bf \: y = \frac{2}{5} x + 2\)

m(gradient)=2/5

Isolate y

\(\\ \sf\longmapsto 5y=2x+10\)

\(\\ \sf\longmapsto y=\dfrac{2}{5}x+2\)

Now

\(\\ \sf\longmapsto m=-5/2\)

Answer:

an increase of 12%

Step-by-step explanation:

68 divided by 77 is 0.88 approximately

100-88 is 12

Tip:

do this for increase and decrease in percentage question

divide small number by big number, and subtract the quotient from 100

Answer:

13%

Step-by-step explanation:

Percent increase is solved as such:

Percent Increase =  %∧ = \((\frac{New~Amount~-~Original~Amount}{Original~Amount}) ~*~10\)

%∧ = \((\frac{77~-~68}{68}) ~*~100 = (\frac{9}{68}) ~*~100 = 0.13 * 100 = 13\%\)

Remember you want to know what percentage the difference is compared to how much your original amount is.

Hope this helps :)

Answer:

62.84 m

Step-by-step explanation:

6*3.14 = 18.84

12*2 = 24

10*2 = 20

total: 62.84

The solution is 62.84 m

The perimeter of the figure is P = 62.84 m

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the perimeter of the figure be represented as P

Now , the figure has a semi circle , a square and a triangle

The side of the square = 12m

So , the number of sides of square in the perimeter of the figure = 2 sides

So , perimeter of 2 sides = 2 x 12 = 24 m

Now , the 2 sides of the hypotenuse of the right triangle is also part of the figure , so

perimeter of 2 sides of the triangle = 2 x 10 = 20 m

Now , the total perimeter of figure = perimeter of the semi circle + 24 + 20

Perimeter of semi circle = 2πr / 2

The radius of the circle = 6 m

Substituting the value of r in the equation , we get

Perimeter of the semi circle = ( 2 x 3.14 x 6 ) / 2

Perimeter of the semi circle = 18.84 m

So , the perimeter of the figure P = 18.84 m + 24 m + 20 m

The perimeter of the figure P = 62.84 m

Therefore , the value of P is 62.84 m

Hence , The perimeter of the figure is P = 62.84 m

To learn more about circle click :

https://brainly.com/question/28391204

#SPJ2

Answer:

\(33.8^{\circ}\)

Step-by-step explanation:

\(\sin x=\frac{10}{18} \implies x=\arcsin(10/18) \approx 33.8^{\circ}\)

The smallest sample observation can be increased by any value up to 0.1 without affecting the value of the sample median.

To find the maximum amount by which the smallest sample observation can be increased without affecting the sample median, we need to consider the definition of the median.

The median is the middle value in a sorted dataset. If the dataset has an odd number of observations, the median is the middle value. If the dataset has an even number of observations, the median is the average of the two middle values.

Since the current smallest sample observation is 8.5, increasing it by any value up to 0.1 would still keep it smaller than any other value in the dataset. This means the position of the smallest observation would not change in the sorted dataset, and therefore, it would not affect the value of the sample median.

The smallest sample observation can be increased by any value up to 0.1 without affecting the value of the sample median.

To know more about median visit

https://brainly.com/question/26177250

#SPJ11

Area = Length X width

Let the width (breadth) = X

The length is double so it is 2x

Area = X * 2x = 2x^2

128 = 2x^2

Divide both sides by 2:

64 = x^2

take the square root of both sides:

x = 8

The breadth = 8 meters

The length = 16 meters

750 sq. Ft / 2 gallons = 375 sq ft per gallon

Divide total square feet by square feet per gallons:

3375 / 375 = 9 gallons total paint required.

Now multiply total gallons needed by price per gallon:

9 gallons x 7.50 per gallon = 67.50

Total cost = $67.50

The height is 67.3 inches.

The standard deviation is a statistic that calculates as the square root of the variance and quantifies the dispersion of a dataset compared to its mean. The standard deviation is determined as the square root of the variance by calculating the departure of each data point from the mean.

Let our height be x inches.

Given,

Mean= μ =64 inches

Standard Deviation=σ=3 inches

Z=1.10

We know,

Z =(x-μ)/σ

⇒x= Zσ + μ

By putting the values of Z,μ and σ we get,

x= 1.10×3 + 64 inches

⇒x= 67.3 inches

The height is 67.3 inches.

To know more about Standard deviation refer to:

brainly.com/question/12402189

#SPJ4

The approximate value of log b to the nearest hundredth is 1.23

Given the following logarithmic expressions

log(5)b and log(9)48

Determine the value of log(9) 48

log(9)48 = 1.762

Equate log(5) b to 1.762 to log(5)b to determine the value of b

log(5)b = 1.762

b = \(5^1.762\)

b = 17.044

log b = log 17.044 = 1.232

Hence the approximate value of log b to the nearest hundredth is 1.23

Read more aobut logarithm here:

https://brainly.com/question/25993029

#SPJ1

The two expressions below have the same value when rounded to the nearest hundredth. log subscript 5 baseline b. log subscript 9 baseline 48 what is the approximate value of log b to the nearest hundredth

The Niagara Falls incline railway rises vertically by approximately 98 feet.

The angle of elevation of 30° indicates the angle between the incline railway and the horizontal ground. The total length of the incline railway is given as 196 feet.

To find the vertical rise, we can use trigonometry. The vertical rise can be determined by calculating the sine of the angle of elevation and multiplying it by the total length of the incline railway:

Vertical rise = Total length × sine(angle of elevation)

Vertical rise = 196 ft × sin(30°)

Vertical rise ≈ 196 ft × 0.5

Vertical rise ≈ 98 ft

Therefore, the Niagara Falls incline railway rises vertically by approximately 98 feet.

You can learn more about Niagara Falls at

https://brainly.com/question/12736955

#SPJ11

Answer:

y = -7x + 3

Step-by-step explanation:

To find the slope intercept equation, isolate y, to put the equation in y = mx + b form

7x = -y + 3

7x - 3 = -y

Rearrange the equation:

-y = 7x - 3

Divide each side by -1:

y = -7x + 3

So, the slope intercept equation is y = -7x + 3

Answer:

y = -7x + 3

I think that's how that goes. I don't remember this stuff too well.

Answer:

7) 889/1000

8) 3/5

9) 3/8

10) 1/4

11) 667/1000

12) 3/4

Answer:

fgffdssSsdddsdddddffffffffggfffg

#a

\(\\ \rm\longmapsto f(x)=x^3-8x^2-x+8\)

#b

\(\\ \rm\longmapsto h(x)=2x^4+x^3-3x^2-x+1\)

#c

\(\\ \rm\longmapsto g(x)=13.2x^3+3x^4-x-4.4\)

All the theorems are proved as follows.

A triangle is a polygon with three sides , three vertices and three angles.

1. The Triangle sum Theorem

According to the Triangle Sum Theorem, the sum of a triangle's angles equals 180 degrees.

To create a triangle ABC, starting at point A, move 180 degrees away from A to arrive at point B.

We turn 180 degrees from B to C and 180 degrees from C to return to A, giving a total turn of 360 degrees to arrive to A.

180° - ∠A + 180° - ∠B + 180° - ∠C = 360°

- ∠A - ∠B  - ∠C = 360° - (180°+ 180°+ 180°) = -180°

∠A + ∠B  + ∠C = 180°

(Hence Proved)

2. Isosceles Triangle Theorem

Considering an isosceles triangle ΔABC

with AB = AC, we have by sine rule;

\(\rm \dfrac{sinA}{BC} = \dfrac{sinB}{AC} = \dfrac{sinC}{AB}\\\)

as AB = AC

sin B = sin C

angle B = angle C

3.Converse of the Isosceles theorem

Consider an isosceles triangle ΔABC with ∠B= ∠C, we have by sine rule;

\(\rm \dfrac{sinA}{BC} = \dfrac{sinB}{AC} = \dfrac{sinC}{AB}\\\)

as  ∠B= ∠C ,

AB = AC

4. Midsegment of a triangle theorem

It states that the midsegment of two sides of a triangle is equal to (1/2)of the third side parallel to it.

Given triangle ABC with midsegment at D and F of AB and AC respectively, DF is parallel to BC

In ΔABC and ΔADF

∠A ≅ ∠A

BA = 2 × DA, BC = 2 × FA

Hence;

ΔABC ~ ΔADF (SAS similarity)

BA/DA = BC/FA = DF/AC = 2

Hence AC = 2×DF

5.Concurrency of Medians Theorem

A median of a triangle is a segment whose end points are on vertex of the triangle and the middle point of the side ,the medians of a triangle are concurrent and  the point of intersection is inside the triangle known as Centroid .

Consider a triangle ABC , X,Y and Z are the midpoints of the sides

Since the medians bisect the segment AB into AZ + ZB

BC into BX + XB

AC into AY + YC

Where:

AZ = ZB

BX = XB

AY = YC

AZ/ZB = BX/XB = AY/YC = 1

AZ/ZB × BX/XB × AY/YC = 1 and

the median segments AX, BY, and CZ are concurrent (meet at point within the triangle).

To know more about Triangle

https://brainly.com/question/2773823

#SPJ1

Answer:

i have that too bro but i need help with it

Step-by-step explanation:

Answer:

Step-by-step explanation:

all values are true

Answer:

Step-by-step explanation:

Formula

The sin(A) =  opposite / hypotenuse

Givens

Opposite = CB = 11

Hypotenuse = AB = 61

Solution

Sin(A) = 11/61

Sin(A) = 0.1803

Answer

Sin(A) = 11/61

Sin(A) = 0.1803