Factor and solve each quadratic equation.

Show your work

-t^2 + 12t = 32

Answer:

path =2m

Step-by-step explanation:

Answer:

I believe the answer should be 2m

Answer:

Using spread sheet software to complete business taxes

Enter check and amend data in accordance with organizational and task requirement

Import and export data b/n compatible spread sheet based on software & system procedures

Use manual user documentation and online help to overcome spread sheet design problems

Preview adjust and print spread sheet in accordance with organizational and production

Step-by-step explanation:

1. Using spread sheet software to complete business taxes

A. Enter check and amend data in accordance with organizational and task requirement

B. Import and export data b/n compatible spread sheet based on software & system procedures

C. Use manual user documentation and online help to overcome spread sheet design problems

D. Preview adjust and print spread sheet in accordance with organizational and production

Given:

Sample size = 75 students

Students who spend less than 10 minutes on homework each night = 21

Total students in the school = 1500

To find:

Estimated number of students who would say they spend less than 10 minutes in homework each night.

Solution:

Let A be the event that the student spends less than 10 minutes in homework each night.

Then, the probability that the student spends less than 10 minutes in homework each night is

\(P(A)=\dfrac{\text{Students who spend less than 10 minutes on homework}}{\text{Sample size}}\)

\(P(A)=\dfrac{21}{75}\)

\(P(A)=\dfrac{7}{25}\)

Now, total students in the school is 1500. So, multiply 1500 with P(A) to get the umber of students who would say they spend less than 10 minutes in homework each night.

\(1500\cdot P(A)=1500\times \dfrac{7}{25}\)

\(1500\cdot P(A)=420\)

Therefore, estimated number of students who would say they spend less than 10 minutes in homework each night is 420.

The size of the tank would be suggested to hold 60 small fish is 75 gallon-tank option (C) is 75 gallon-tank.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

It is given that:

A pet store clerk suggested 4 small fish for a 5-gallon fish tank.

4 small fish = 5-gallon

60 small fish = x gallon

x = (5)(60)/4

x = 75 gallon-tank

Thus, the size of the tank would be suggested to hold 60 small fish is 75 gallon-tank option (C) is 75 gallon-tank.

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Answer:

Step-by-step explanation:

The loop will run an infinite number of times

The proportional relationships that are true is  768 mi/320 mi = 5hr/12hr

Given,

In the question:

Ryan drove 320 miles in 5 hours to complete the first part of his trip.

and, It took him 12 hours to drive 768 miles.

In the option, To check which proportional relationships that are true.

What is a proportional ?

Two ratios are said to be in proportion when the two ratios are equal.

Now, According to the question;

For according to the definition:

The appropriate proportional relationship is that the:

=>  768 mi/320 mi = 5hr/12hr

Hence,  the proportional relationships that are true is  768 mi/320 mi = 5hr/12hr

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B) y = 53.8x + 1149.8

C) Total Sales increase from one week to the next by $53.8.

Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.

D) The restaurant's sales for the Monday of the 15th week is expected to be $1956.8

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.

B) As by scatter plot,

The total sales for week 4 is given as 1,365 while that of week 9 is 1,634.

Therefore, we shall determine the equation for the line of best fit using the points;

( 4, 1365) and ( 9, 1634)

The first step would be to determine the slope of this line;

slope = (1634 - 1365)/ (9 - 4)

       = 53.8

The equation of the line in slope-intercept form is thus;

Sales = 53.8(Week) + c

We need to determine c, the y-intercept. We can use the point ( 4, 1365);

1365= 53.8(4) + c

c = 1365-215.2

c = 1149.8

The equation of the line of best fit is thus;

y = 53.8x + 1149.8

C) The slope of the equation for the lines of best fit was found to be 53.8.  

    This value is positive which implies

    Total Sales increase from one week to the next by $53.8.

    The slope in regression is defined as the change in y for every unit change in x.

Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.

D) The equation  for the line of best fit was found to be;

  y = 53.8x+ 1149.8

where y denotes the total sales and x the corresponding week. We are required to determine y when x is 15;

y = 53.8(15) + 1149.8

y = 1956.8

Therefore, the restaurant's sales for the Monday of the 15th week is expected to be $1956.8.

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⇒Let the two unknowns be x and y

It is said that their sum is -7 mathematically it can be written as

\(x+y=-7\)

Their product can be written mathematically as

⇒ x×y=6

\(xy=-6\)

As a results you can see that we have a system of equation that we have to solve and we can solve it by substitution

let us derive the third equation from the first equation by making x the subject of the equation

As a results we have x=-7-y

Now let us substitute the equation to the second equation .

\((-7-y)(y)=6\\-7y-y^{2} =6\\-y^{2} -7y-6=0\\-(y^{2} +7y+6)=0\\y^{2} +7y+6=0\\(y+6)(y+1)=0\\y+6=0\\\\or\\y+1=0\\y=-6\\\\or \\y=-1\)

when y =-1

x=-7-(-1)

x=-7+1

⇒x=-6

When y=-6

x=-7-(-6)

x=-7+6

⇒x=-1

Note there was no need of finding the values of x

the two numbers are

Function:

To know which graph represents our function, we can see that all the graphs have different y and x-intercepts. Meaning that we can calculate these parameters and see which graph is.

• Calculating y-intercept: x = 0

The y-intercept happens at (0, -3).

Based on this, we can see that Graph B is not an option. However, Graph A and C are still options. To evaluate which is the correct one we have to calculate the x-intercept.

2. Calculating the x-intercept: y = 0

Then, the x-intercept is (4, 0).

Answer: Graph A

Answer:

2nd option

I think thats most correct

Answer:

255 miles

Step-by-step explanation:

if 1 inch is 60 miles then you need to times 60 miles by 4.25 which is the same thing as 4 1/4. you then get 255 miles.

Answer:

Step-by-step explanation:

Pictograph

Pictograms are a powerful tool for visualizing data and are widely used in a variety of different fields, from marketing and advertising to science and education.

A pictogram is a type of chart that uses symbols instead of words or numbers to portray data. Pictograms are often used in data visualization and are particularly useful for presenting complex information in a simple and easily understandable way. Pictograms can be used to represent a wide range of data, including statistical information, demographic data, and geographical information. They are also commonly used in advertising and marketing, as they are a powerful tool for communicating ideas and concepts quickly and effectively. Pictograms can be created using a variety of different techniques, including hand-drawn illustrations, computer-generated graphics, and photographs. They are typically presented in a grid format, with each symbol representing a single data point. Pictograms can be used to show trends, compare data sets, and highlight key points. They are also a great way to make data more engaging and interactive, as users can explore the data by clicking on individual symbols or groups of symbols.

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Therefore, the equivalent metric length of a 3-inch scar would be 7.62 centimeters.

Explanation: Metric length is a measurement system that uses the metric unit. The metric unit is more common than the customary unit system in the United States. To convert customary unit lengths to metric lengths, a conversion factor is used.3 inches is the measurement of the scar in customary units. To convert 3 inches to metric units, multiply it by the conversion factor. There are 2.54 centimeters in one inch, which is the conversion factor. To find the equivalent metric length of a 3-inch scar, multiply 3 by 2.54. Therefore, the equivalent metric length of a 3-inch scar would be 7.62 centimeters.  The equivalent metric length of a 3-inch scar would be 7.62 centimeters. Metric length is a measurement system that uses the metric unit. The metric unit is more common than the customary unit system in the United States. To convert customary unit lengths to metric lengths, a conversion factor is used. There are 2.54 centimeters in one inch, which is the conversion factor.

Therefore, the equivalent metric length of a 3-inch scar would be 7.62 centimeters.

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The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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a. The complex number \( \frac{3+4i}{5-2i+3i} \) in Cartesian form is \( \frac{19}{26} + \frac{17}{26}i \).

b.  We can express the solutions in Euler form with principal arguments:

1. Solution 1: \( z_1 = \sqrt[3]{\sqrt{2}}e^{i\frac{\pi}{6}} \)

2. Solution 2: \( z_2 = \sqrt[3]{\sqrt{2}}e^{i\frac{5\pi}{6}} \)

(a) To express the complex number \( \frac{3+4i}{5-2i+3i} \) into Cartesian form, we simplify the expression as follows:

First, let's simplify the denominator: \( 5-2i+3i = 5+i \).

Now, we can rewrite the expression as \( \frac{3+4i}{5+i} \).

To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is \( 5-i \):

\[ \frac{(3+4i)(5-i)}{(5+i)(5-i)} \]

Expanding the numerator and denominator, we have:

\[ \frac{15-3i+20i-4i^2}{25-i^2} \]

Simplifying further, we have:

\[ \frac{15+17i+4}{25+1} \]

\[ \frac{19+17i}{26} \]

Therefore, the complex number \( \frac{3+4i}{5-2i+3i} \) in Cartesian form is \( \frac{19}{26} + \frac{17}{26}i \).

(b) To solve the equation \( (1+i)z^3 = -1+3i \) and list all possible solutions in Euler form with principal arguments, we can follow these steps:

First, let's rewrite the equation in exponential form by converting the complex numbers to their polar forms:

\[ (1+i)z^3 = \sqrt{2}e^{i\frac{\pi}{4}} z^3 = 2\sqrt{2}e^{i\frac{\pi}{2}} \]

Next, we can rewrite the equation in terms of the magnitude and argument of \( z \):

\[ |z^3| e^{i3\theta} = 2\sqrt{2}e^{i\frac{\pi}{2}} \]

From this equation, we can deduce that the magnitude of \( z^3 \) is \( 2\sqrt{2} \), and the argument of \( z^3 \) differs from \( \frac{\pi}{2} \) by a multiple of \( \frac{2\pi}{3} \) (since we have a cubic equation).

So we have two possible solutions for the argument of \( z \):

1. \( \theta = \frac{\frac{\pi}{2}}{3} = \frac{\pi}{6} \)

2. \( \theta = \frac{\frac{\pi}{2}}{3} + \frac{2\pi}{3} = \frac{5\pi}{6} \)

Now, let's find the magnitude of \( z^3 \) using the given magnitude:

\[ |z^3| = \sqrt{2} \]

Finally, we can express the solutions in Euler form with principal arguments:

1. Solution 1: \( z_1 = \sqrt[3]{\sqrt{2}}e^{i\frac{\pi}{6}} \)

2. Solution 2: \( z_2 = \sqrt[3]{\sqrt{2}}e^{i\frac{5\pi}{6}} \)

These are the possible solutions to the equation in Euler form with principal arguments.

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\(\( z_1 = \sqrt[3]{\sqrt{2}}e^{i\frac{\pi}{6}} \)\)

\(\( z_2 = \sqrt[3]{\sqrt{2}}e^{i\frac{5\pi}{6}} \)\)

The supremum of the set A does not exist (it is negative infinity), and the infimum of the set A is 1.

To define the supremum and infimum of the set A, we first need to determine the properties of the set.

The set A is defined as A = {(x-3)/(x-2) ∈ R : x < 0}.

To find the supremum (also known as the least upper bound) of A, we need to find the smallest value that is greater than or equal to all the elements of A. In other words, we are looking for the least upper bound of the set A.

Let's analyze the elements of A:

For x < 0, the expression (x-3)/(x-2) can take on different values depending on the value of x. We need to find the maximum value that this expression can reach for all x < 0.

As x approaches 0 from the left side, (x-3)/(x-2) approaches negative infinity. Therefore, there is no finite supremum for the set A.

Next, let's find the infimum (also known as the greatest lower bound) of A. We need to find the largest value that is less than or equal to all the elements of A. In other words, we are looking for the greatest lower bound of the set A.

Again, analyzing the elements of A:

As x approaches negative infinity, (x-3)/(x-2) approaches 1. Therefore, the infimum of the set A is 1.

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

Work Shown:

A = area of black square

A = 2*2

A = 4

B = area of white symbol

B = (1/3)*A

B = (1/3)*4

B = 4/3

C = total area

C = 4*2

C = 8

Divide the values of B and C to find the fraction of the total area the white symbol covers up.

B/C = (4/3)/8

B/C = (4/3) / (8/1)

B/C = (4/3) divided by (8/1)

B/C = (4/3) times (1/8)

B/C = (4*1)/(3*8)

B/C = 4/24

B/C = 1/6

Answer:

5

Step-by-step explanation:

y= 4x+17

73=4x+17 (subtract 17 by both sides)

20=4x (divide by both sides)

5= x, 5 days

The answer is 966 codes.

It would probably be simplest to simply state the prohibited codes.

023 - narrators code

02x

0x3

x23

Here x is a number between 0 and 9, there are 10 of each, making a total of 30.

203

302

032

Consequently, there are 34 banned codes in all.

There are 103 = 1000 codes in all.

1000 - 34 = 966 codes are available.

What is narrators code?

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The population as an exponential function of time t is given by \(n(t) = 2,000,000 * e^(0.022t)\) when the initial value is 2 million.

The population has a yearly per capita growth rate of 2.2% and the initial value is 2 million, we can express the population as an exponential function using the formula:

\(n(t) = a * e^(rt)\)

In this formula, n(t) represents the population as a function of time t, a is the initial value, e is Euler's number (approximately 2.71828), and r is the annual growth rate expressed as a decimal.

The exponential function for the population with an initial value of 2 million and an annual growth rate of 2.2%, we substitute the given values into the formula:

\(n(t) = 2 * e^(0.022t)\)

To simplify the equation, we can multiply both sides by 1,000,000:

\(n(t) = 2,000,000 * e^(0.022t)\)

Therefore, the population as an exponential function of time t is given by \(n(t) = 2,000,000 * e^(0.022t)\) when the initial value is 2 million.

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Answer:

12 months

Explanation:

Given the function that models the total chacrge of a company as T = 35.00 + 18.75m where;

T is the total charges,

m is the number of months of storage

Given

T = $260.00

we are to find the value of m

Substitute

260 = 35 + 18.75m

18.75m = 260 - 35

18.75m = 225

m = 225/18.75

m = 12

Hence it will take 12 months to cost a new custimer $260.00

Among the given options, the "Success/Failure Condition" is not a requirement for testing means. The other three options—Randomization, Nearly Normal Condition, and 10% Condition—are necessary conditions to be considered when conducting hypothesis tests on means.

Randomization: Randomization is essential to ensure that the samples being compared are representative of the population and to minimize bias. Random assignment of individuals to treatment groups helps control for confounding variables and increases the validity of the statistical analysis.

Nearly Normal Condition: The Nearly Normal Condition assumes that the data follows a roughly normal distribution within each group being compared. This condition is important because many statistical tests, such as t-tests, rely on the assumption of normality to provide accurate results.

10% Condition: The 10% Condition is relevant when sampling from a finite population. It states that the sample size should be no more than 10% of the population size to ensure that the sampling process does not significantly affect the population distribution.

Success/Failure Condition: The Success/Failure Condition is not directly related to testing means. It is typically associated with tests involving proportions, where the condition specifies that both the number of successes and the number of failures should be at least 10 in each sample or category being compared.

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Answer:for .4 it is c=6

Step-by-step explanation:

first you do 6+3=9 then 3+5=8 then add 9+8=17

Answer:

y = 3

Step-by-step explanation:

-7 = -4y + 5

Subtract 5 from both sides to isolate variable y:

-7 - 5 = -4y + 5 - 5

-12 = -4y + 0

-12 = -4y

Divide both sides by -4 to isolate variable y:

-12 ÷ -4 = -4y ÷ -4

(Negative ÷ Negative = Positive)

3 = 1y

3 = y

Check your work:

-7 = -4(3) + 5

Use PEMDAS:

-7 = -12 + 5

-7 = -7

Correct!

In this case, Asset A has a return of 16% and represents 60% of the portfolio, while Asset B has a return of 22% and represents 40% of the portfolio. The correlation between Asset A and B is given as 0.93.

To calculate the expected return of the portfolio, we use the following formula:

Expected Return = (Weight of Asset A * Return of Asset A) + (Weight of Asset B * Return of Asset B) + (2 * Weight of Asset A * Weight of Asset B * Correlation between A and B * Standard Deviation of Asset A * Standard Deviation of Asset B)The expected return for a portfolio composed of two assets, A and B, can be calculated using the weighted average of the individual asset returns, considering their respective weights in the portfolio.

By plug in the given values and performing the calculations, we can determine the expected return for the portfolio comprised of 60% Asset A and 40% Asset B.

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Answer:

7

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

3x + 20 + 2x = 180 (angles lying on the same side of the transversal are supplementary)

=> 5x + 20 = 180

=> 5x = 180 - 20

=> 5x = 160

=> x =160/5 (by transposing)

=> x = 32

Hope you understood!!

The value of x in the given figure is 32 .

Here,

Both 2x and 3x + 20 degrees are on same side of transversal (l) .

So the both are supplementary angles.

So,

3x + 20 + 2x = 180 (angles lying on the same side of the transversal are supplementary)

So,

=> 5x + 20 = 180

=> 5x = 180 - 20

=> 5x = 160

=> x =160/5 (by transposing)

=> x = 32

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After 1st Translation  (x,y) → (x-6.y) = X(-4,4), Y(0,0), Z(1,2)

After 2nd Translation (x, y) → (x+2y+7) = X(4,11), Y(8,7), Z(9,9)

What is translation?

And image After Composition means resultant image after you plot the translated points.

So, Given Vertices are X(2,4), Y(6,0), Z(7,2)

Then after 1st Translation = X(-4,4), Y(0,0), Z(1,2)

After 2nd Translation = X(4,11), Y(8,7), Z(9,9)

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