Your parents have given you some money to spend with your friends at Water World. You already have purchased a banana split for $7, and you end the day with $17. WRITE AND SOLVE an equation to find how much money you started the day at Water World with.

Answer:

x=−3±i√72x=-3±i72

Step-by-step explanation:

Write the problem as a mathematical expression.

x2+3x+4=0x2+3x+4=0

Use the quadratic formula to find the solutions.

−b±√b2−4(ac)2a-b±b2-4(ac)2a

Substitute the values a=1a=1, b=3b=3, and c=4c=4 into the quadratic formula and solve for xx.

−3±√32−4⋅(1⋅4)2⋅1-3±32-4⋅(1⋅4)2⋅1

Simplify.

Tap for fewer steps...

Simplify the numerator.

Tap for more steps...

x=−3±i√72⋅1x=-3±i72⋅1

Multiply 22 by 11.

x=−3±i√72

The solution of the quadratic equation is x = (-3 / 2) ± √(7/4)i.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the quadratic equation is x² + 3x + 4 = 0. The quadratic equation will be solved as,

x² + 3x + 4 = 0

( x + 3/2 )² + 4 - 9 / 4 = 0

( x + 3/2 )² = -4 + 9/4

( x + 3/2) = ±(√7/4)i

x = (-3/ 2) ± (√7/4)i

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Answer: 106,000 dollars

Step-by-step explanation:

She paid 36,000 dollars as income tax and 60,000 on the rent property tax and 96,000 dollars + 10,000 dollars is 106,000 dollars.

Answer:

3

Step-by-step explanation:

Answer:

-17

Step-by-step explanation:

Ans. - 17

We just substitute the values of a, b and c and find the answer

The equation of the ellipse whose center is (0, 0), vertex is at (6, 0) and co-vertex is at (0, 5) is given by \\([\frac{x^2}{36}+\frac{y^2}{25}=1\]\).

According to the standard form, the equation of an ellipse with its center at (0, 0) is given by:

\(\[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]\)

Where the ellipse has a horizontal major axis if `a > b` and a vertical major axis if `b > a`.Here, the center of the ellipse is at (0, 0), the vertex is at (6, 0) and the co-vertex is at (0, 5).

It follows that the major axis is the x-axis and the minor axis is the y-axis.

Hence, the major axis has a length of 2a = 2(6)

= 12 units and the minor axis has a length of

2b = 2(5)

= 10 units.

Thus, `a = 6` and

`b = 5`.

Substituting these values in the standard equation of the ellipse, we get:

\(\[\frac{x^2}{6^2}+\frac{y^2}{5^2}=1\]\[\Rightarrow \frac{x^2}{36}+\frac{y^2}{25}=1\]\)

Therefore, the equation of the ellipse whose center is (0, 0), vertex is at (6, 0) and co-vertex is at (0, 5) is given by \\([\frac{x^2}{36}+\frac{y^2}{25}=1\]\).

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The probability that Victor selects a code that has four even digits is approximately 0.0238 or 1/42.

To solve this problem, we can use the permutation formula to determine the total number of possible codes that Victor can choose. Since he can only use each digit once, the number of permutations of 10 digits taken 4 at a time is:

P(10,4) = 10! / (10-4)! = 10 x 9 x 8 x 7 = 5,040

Next, we need to determine how many codes have four even digits. There are five even digits (0, 2, 4, 6, and 8), so we need to choose four of them and arrange them in all possible ways. The number of permutations of 5 even digits taken 4 at a time is:

P(5,4) = 5! / (5-4)! = 5 x 4 x 3 x 2 = 120

Therefore, the probability that Victor selects a code with four even digits is:

P = (number of codes with four even digits) / (total number of possible codes)

= P(5,4) / P(10,4)

= 120 / 5,040

= 1 / 42

≈ 0.0238

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(a) The total distance traveled over the entire trip is approximately 94.9998 km.

(b) The average speed for the entire trip is approximately 38.51 km/h.

(a) To calculate the total distance traveled over the entire trip, we need to add up the distances covered during each leg of the trip.

Distance = Speed * Time

For the first leg:

Speed = 60.0 km/h

Time = 50.0 min = 50.0/60 = 0.8333 hours (converted to hours)

Distance1 = 60.0 km/h * 0.8333 hours = 49.9998 km

For the second leg:

Speed = 0.0 km/h (car is not moving)

Time = 13.0 min = 13.0/60 = 0.2167 hours (converted to hours)

Distance2 = 0.0 km/h * 0.2167 hours = 0 km

For the third leg:

Speed = 45.0 km/h

Time = 60.0 min = 60.0/60 = 1 hour

Distance3 = 45.0 km/h * 1 hour = 45.0 km

Total Distance = Distance1 + Distance2 + Distance3

Total Distance = 49.9998 km + 0 km + 45.0 km

Total Distance ≈ 94.9998 km

Therefore, the total distance traveled over the entire trip is approximately 94.9998 km.

(b) To calculate the average speed for the entire trip, we can use the formula:

Average Speed = Total Distance / Total Time

Total Time = (Time spent driving leg 1) + (Time spent driving leg 2) + (Time spent driving leg 3) + (Time spent eating lunch and buying gas)

Time spent driving leg 1 = 50.0 min = 50.0/60 = 0.8333 hours (converted to hours)

Time spent driving leg 2 = 13.0 min = 13.0/60 = 0.2167 hours (converted to hours)

Time spent driving leg 3 = 60.0 min = 60.0/60 = 1 hour

Time spent eating lunch and buying gas = 25.0 min = 25.0/60 = 0.4167 hours (converted to hours)

Total Time = 0.8333 hours + 0.2167 hours + 1 hour + 0.4167 hours

Total Time ≈ 2.4667 hours

Average Speed = 94.9998 km / 2.4667 hours

Average Speed ≈ 38.51 km/h

Therefore, the average speed for the entire trip is approximately 38.51 km/h.

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Answer

well no

Step-by-step explanation:

Answer:

99 and 33

Step-by-step explanation:

let x and y be the 2 numbers, with x being the larger of the 2, then

x + y = 132 → (1)

x - y = 66 → (2)

add (1) and (2) term by term to eliminate y

(x + x) + (y - y) = 132 + 66

2x + 0 = 198

2x = 198 ( divide both sides by 2 )

x = 99

substitute x = 99 into (1) and solve for y

99 + y = 132 ( subtract 99 from both sides )

y = 33

the 2 numbers are 99 and 33

An elevator stop for 23 floor.

it went up so +18

it came down so -11

again it went upward +16

so... 18-11+16

=18+16-11

=34-11

=23

An elevator or lift is a cable-assisted, hydraulic cylinder-assisted, or roller-track assisted machine that vertically transports people or freight between floors, levels, or decks of a building, vessel, or other structure. They are typically powered by electric motors that drive traction cables and counterweight systems such as a hoist, although some pump hydraulic fluid to raise a cylindrical piston like a jack.

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Answer:

  24th floor

Step-by-step explanation:

You want to know where an elevator stopped if it started at the first floor, went up 18, down 11, and back up 16.

If it started at the first floor and went up 1, it would be at the 2nd floor. Starting from the first floor and going up 18, it would be at the 19th floor.

Down 11 floors from there is the 8th floor. Back up 16 floors from the 8th floor puts the elevator at the 24th floor.

The elevator stopped at the 24th floor.

__

Additional comment

If there is no 13th floor, then it may have stopped at the 25th floor.

The solution which we get for the given question is , x = 5/2 and y = 5/4 answer.

Isolating x,

2x = 9x - 14y

2x-9x = 9x-9x -14y

-7x = -14y

-7x/-7 = -14y/-7

x = 2y

Therefore substituting value of x on equation 2,

9(2y) = 40 - 14y

18y = 40 - 14y

18y+14y = 40 -14y+14y

32y = 40

32y/32 = 40/32

y = 5/4

Therefore , x = 10/4 = 5/2

as because x =2y.

An equation is a mathematical statement which equated two value using the equal sign. Eg.) 2x = y

These expressions on either side of the equals sign are referred to as the equation's "left" and "right" sides. The right-hand side of an equation is usually assumed to be zero. The generality will still be there as  because we can balance it by subtracting the right-hand side expression from the expressions on both sides.

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The type of average that can be found is the median. The median is the middle value of the data set when the values are arranged in order. In this case, the median is 11, as shown by the line inside the box.

Value is the relative worth, merit, or importance of something. It is subjective and can be determined by a variety of factors, including personal preferences, beliefs, and economic forces. Value is a concept that can be applied to many different aspects of life, including economic goods, personal relationships, and objects. Value is determined by how much someone is willing to pay for something or how much someone needs something. In economics, value is determined by the market, which is based on supply and demand. In personal relationships, value is determined by the mutual respect, trust, and understanding between two people. In objects, value is determined by the sentiment and meaning it holds for the owner. Ultimately, value is a perception of worth, and its true value is subjective.

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The value of the rectangular cuboid will be 6,355.725 mm³.

Given that:

Length, L = 7.50 x 10² mm

Width, W = 102.1 mm

Height, H = 0.083 mm

A cuboid's volume is determined by multiplying its length, breadth, and height. A cuboid is a six-sided, three-dimensional geometry where the length, breadth, and height correspond to the three perpendicular sides. Add the length, breadth, and height together to obtain the volume.

The volume of the cuboid is calculated as:

V = 7.50 x 10² mm x 102.1 mm x 0.083 mm

V = 6,355.725 mm³

Thus, the value of the rectangular cuboid will be 6,355.725 mm³.

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The complete question is given below.

Determine the volume of the cuboid.
V = 7.50 x 10² mm x 102.1 mm x 0.083 mm

The system of equations that can be used to determine the amount of rice and beans to consume in order to meet the desired calorie and protein intake is ii. 220r + 16b = 18.25.

To solve this problem, we need to consider the given information about the calories and protein content of rice and beans. Let's analyze the equations provided:

i. 216r + 5b = 435

In this equation, 216 represents the number of calories in one cup of rice, 'r' represents the number of cups of rice consumed, 5 represents the number of grams of protein in one cup of beans, and 'b' represents the number of cups of beans consumed. The equation equates the total calories from rice and beans (216r + 5b) to the desired calorie intake of 435. However, this equation does not account for the protein content.

ii. 220r + 16b = 18.25

In this equation, 220 represents the number of calories in one cup of beans, 'r' represents the number of cups of rice consumed, 16 represents the number of grams of protein in one cup of beans, and 'b' represents the number of cups of beans consumed. The equation equates the total calories from rice and beans (220r + 16b) to the desired calorie intake of 18.25. This equation also considers the protein content.

Therefore, the system of equations that can be used to determine the amount of rice and beans to consume in order to meet the desired calorie and protein intake is ii. 220r + 16b = 18.25.

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Answer:

It would be 7.81 miles.

Step-by-step explanation:

I hope this helps you out

Answer:

Distance between Gas Station and House = 7.81 miles.

Given: House location ( 4, 3 ) and Gas station location ( 10, 8)

        On graph 1 unit = 1 mile.

To find: Distance between Gas Station and House

We use the Distance formula to find the distance between two points

From given points and formula,Since, 1 unit = 1 mile

Therefore, Distance between Gas Station and House = 7.81 miles.

Step-by-step explanation:

done the test

If you drew a line through the points, three other points  would be

(5,-2)  , (9,-5)  and (-7,7)

Given :

The points (-3, 4) and (1, 1)

Find the equation of the line that connect two given points to find three other points on the line

Equation of the line is y=mx+b

where m is the slope and b is the y intercept

slope formula is

\(m= \frac{y_2-y_1}{x_2-x_1} =\frac{1-4}{1+3} =\frac{-3}{4}\)

Now find out b using point (1,1)

\(x=1, y=1\\y=mx+b\\1=\frac{-3}{4} (1)+b\\1=\frac{-3}{4}+b\\\\1+\frac{3}{4} =b\\\\b=\frac{7}{4}\)

The equation of the line that connects two points

\(y=\frac{-3}{4}x+\frac{7}{4}\)

To find other 3 points , we plug in some random number for x and find out y

\(y=\frac{-3}{4}x+\frac{7}{4}\\x=5\\y=\frac{-3}{4}(5)+\frac{7}{4}=-2\\\\x=9\\y=\frac{-3}{4}(9)+\frac{7}{4}=-5\\\\x=-7\\y=\frac{-3}{4}(-7)+\frac{7}{4}=7\\\)

Three other points are

(5,-2)  , (9,-5)  and (-7,7)

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Answer:

To construct a triangle with angles 67° and 54° and a side length of 6 cm, follow these steps:

Using a ruler, draw a horizontal line segment of length 6 cm. This will be the base of the triangle.

Using a pair of compasses, set the distance to 3 cm (half the length of the base). Place the point of the compasses on one end of the base line, and draw an arc above the line.

Repeat step 2 on the other end of the base line. The two arcs should intersect at a point above the base line.

Using a protractor, measure the angle between the base line and one of the arcs. It should be 67°.

Using a pencil, draw a line segment connecting the intersection of the arcs to one end of the base line. This line segment will be one of the sides of the triangle.

Measure the length of this line segment using a ruler. This will be the length of the side adjacent to the 67° angle.

The resulting triangle should have angles of 67°, 54°, and 109° (the sum of the angles in any triangle is 180°). The length of the side adjacent to the 67° angle can be measured using a ruler.

Answer:

Yes. if you're talking about factions then yes. If it wasn't, it would've had something like 90.7. So yes it is a whole number.

Step-by-step explanation:

In the given situation the given values can be correctly modeled by a (B) linear function.

What is a linear function?
A linear function has a straight line as its graph. A linear function has the form shown below. a + bx = y = f (x).

A linear function consists of one independent variable and one dependent variable.

The independent and dependent variables are X and Y, respectively.

In mathematics, the terms "linear function" refers to two distinct but connected concepts: In calculus and related subjects, a polynomial function of degree zero or one with a graph that is a straight line is referred to as a linear function.

Therefore, in the given situation the given values can be correctly modeled by a (B) linear function.

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Answer:

Step-by-step explanation:

i just put the numbers in X

for example

g(x) = 5 - 2(0)

g(x)= 5- 2(2)

g(x)= 5-2 (8)

Hope this helps!! :)

good luck you got this

A random variable is a quantitative outcome of a chance experiment.

A probability distribution includes the likelihood of each possible outcome.

A random variable is a variable whose value is determined by chance or randomness. It is often used to represent a numerical outcome of a chance experiment, such as the result of a coin toss, the roll of a die, or the outcome of a survey. Random variables can take on any numerical value, but it is often useful to assign probabilities to each possible value. This probability, known as a probability distribution or probability density function, describes the likelihood that a given value of the random variable will occur.

A normal distribution is a type of probability distribution that is symmetrical and bell-shaped, with the mean, median, and mode all equal. The values of the distribution are spread out around the mean, with the majority of the values within one standard deviation of the mean. A normal distribution is also known as a Gaussian distribution, as it was discovered by Carl Friedrich Gauss in the early 19th century.

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To maximize the number of interviews, 12 undergraduate students, 4 graduate students, and 4 faculty members should be hired. The maximum number of interviews that can be conducted is 684.

Let x, y, and z be the number of undergraduate students, graduate students, and faculty members hired, respectively. The objective is to maximize the number of interviews, which is given by the function

N = 18x + 25y + 30z.

The total cost of hiring interviewers is given by the function

C = 100x + 150y + 200z.

The constraints are x + y + z ≤ 20 (due to transportation limitations), and C ≤ 3200 (the budget constraint). Using linear programming techniques, we can solve for the optimal values of x, y, and z, which are 12, 4, and 4, respectively.

The maximum number of interviews is 18(12) + 25(4) + 30(4) = 684.

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Answer:

192 is the answer

Step-by-step explanation:

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The combined area is 0.9545.

Given:

The area under the normal curve to the left of z=-2 plus the area

under the normal curve to the right of z = 2.

Area under the normal curve to the left of z = -2 is:

= 0.0228

Area under the normal curve to the right of z = 2

= 0.9772

Combined area is = 0.9545

Therefore The combined area is 0.9545.

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An x-bar and R-chart were constructed using the given data. The x-bar chart displays the sample averages, while the R-chart shows the sample ranges. By analyzing these charts, we can determine if the process is in control.

To construct the x-bar and R-charts, we use the sample averages and sample ranges provided in the table. The x-bar chart helps us monitor the central tendency of the process, while the R-chart monitors the variability or dispersion within the samples.

Plotting the x-bar chart:

   Calculate the overall mean (x-double bar) by averaging all the sample averages.

   Calculate the average range (R-bar) by averaging all the sample ranges.

   Calculate the control limits for the x-bar chart using the formulas: Upper control limit (UCL) = x-double bar + A2 * R-bar, Lower control limit (LCL) = x-double bar - A2 * R-bar, where A2 is a constant factor depending on the sample size.

   Plot the sample averages on the x-bar chart along with the control limits.

Plotting the R-chart:

   Calculate the control limits for the R-chart using the formulas: UCL = D4 * R-bar, LCL = D3 * R-bar, where D3 and D4 are constant factors depending on the sample size.

   Plot the sample ranges on the R-chart along with the control limits.

By examining the x-bar and R-charts, we can assess whether the process is in control. If the data points fall within the control limits, with no specific patterns or trends, the process is considered in control. If any data points fall outside the control limits or show non-random patterns, it suggests the process is out of control and further investigation is required.

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THIS QUESTION IS INCOMPLETE HERE IS THE GENERAL SOLUTION.

9514 1404 393

Answer:

  (x, y) = (7, 2)

Step-by-step explanation:

We assume you want the solution to this system of equations.

Since you're seeking help from "technology", it is appropriate to use the technology of a graphing calculator to find the solution. The attachment shows it to be (x, y) = (7, 2).

__

The coefficient of x in the first equation is 1, so it is convenient to use that equation to write an expression for x:

  x = 4y -1 . . . . . add 4y to the equation

  3(4y -1) +5y = 31 . . . . substitute for x in the second equation.

  17y = 34 . . . . . . . . . . . simplify, add 3

  y = 2 . . . . . . . . divide by 17

  x = 4(2) -1 = 7 . . . . use the equation above to find x

The solution is (x, y) = (7, 2).

The probability of completing the final examination in one hour or less, given a normal distribution with a mean of 79 minutes and a standard deviation of 8 minutes, is approximately 0.8413.

To find the probability of completing the exam in one hour or less, we need to convert one hour (60 minutes) into z-scores. The formula for calculating the z-score is (x - μ) / σ, where x is the value we want to convert, μ is the mean, and σ is the standard deviation.

In this case, we want to find the z-score for 60 minutes. Substituting the values into the formula, we have (60 - 79) / 8 = -2.375.

Next, we need to find the probability associated with this z-score. We can look up the corresponding probability from a standard normal distribution table or use a calculator. The probability corresponding to a z-score of -2.375 is approximately 0.0087.

However, we are interested in the probability of completing the exam in one hour or less, which includes all values less than or equal to 60 minutes. Since we are dealing with a continuous distribution, we need to consider the area under the curve up to the z-score of -2.375. This area represents the probability of completing the exam in one hour or less.

Looking up the z-score of -2.375 in the standard normal distribution table, we find that the corresponding probability is approximately 0.0087. Therefore, the probability of completing the exam in one hour or less is approximately 0.0087 or 0.8413 (rounded to four decimal places).

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Answer:

A: 236 sqaure ft.

B: 4 cans

Step-by-step explanation:

Sure, I can help you with that.

Part A:

The total surface area of a rectangular prism is calculated using the following formula:

Total surface area = 2(lw + wh + lh)

where:

In this case, we have:

Plugging these values into the formula, we get:

Total surface area = 2(8*6+6*5+8*5) = 236 square feet

Therefore, the total surface area of the doghouse is 236 square feet.

Part B:

Since the bottom of the doghouse will not be painted, we only need to paint the top, front, back, and two sides.

The total surface area of these sides is 236-6*8 = 188 square feet.

Therefore,

we need 188 ÷ 50 = 3.76 cans of paint to paint the doghouse.

Since we cannot buy 0.76 of a can of paint, we need to buy 4 cans of paint.

Answer:

A)  236 ft²

B)  4 cans of paint

Step-by-step explanation:

The given diagram (attached) shows the doghouse modelled as a rectangular prism with the following dimensions:

The formula for the total surface area of a rectangular prism is:

\(S.A.=2(wl+hl+hw)\)

where w is the width, l is the length, and h is the height.

To find the total surface area of the doghouse, substitute the given values of w, l and h into the formula:

\(\begin{aligned}\textsf{Total\;surface\;area}&=2(6 \cdot 8+5 \cdot 8+5 \cdot 6)\\&=2(48+40+30)\\&=2(118)\\&=236\; \sf ft^2\end{aligned}\)

Therefore, the total surface area of the doghouse is 236 ft².

\(\hrulefill\)

As the bottom of the doghouse will not be painted, to find the total surface area to be painted, subtract the area of the base from the total surface area:

\(\begin{aligned}\textsf{Area\;to\;be\;painted}&=\sf Total\;surface\;area-Area\;of\;base\\&=236-(8 \cdot 6)\\&=236-48\\&=188\; \sf ft^2\end{aligned}\)

Therefore, the total surface area to be painted is 188 ft².

If one can of paint will cover 50 ft², to calculate how many cans of paint are needed to paint the doghouse, divide the total surface area to be painted by 50 ft², and round up to the nearest whole number:

\(\begin{aligned}\textsf{Cans\;of\;paint\;needed}&=\sf \dfrac{188\;ft^2}{50\;ft^2}\\\\ &= \sf 3.76\\\\&=\sf 4\;(nearest\;whole\;number)\end{aligned}\)

Therefore, 4 cans of paint are needed to paint the doghouse.

Note: Rounding 3.76 to the nearest whole number means rounding up to 4. However, even if the number of paint cans needed was nearer to 3, e.g. 3.2, we would still need to round up to 4 cans, else we would not have enough paint.