natalie has $330mto send at the amusment park of this total amount 5% is soent on games, 5/11 is for food and drinks, and she spends $13 on parking. the rest of her budget is spent on buying a ticket for herself and a friend. what is the price of one ticket

Answers

Answer 1

Answer:

Step-by-step explanation:

This is a word problem involving percentages. To solve it, we need to follow these steps:

Identify the given information and the unknown quantity. In this problem, we are given that Natalie has $330 to spend at the amusement park, 5% is spent on games, 5/11 is for food and drinks, and she spends $13 on parking. The unknown quantity is the price of one ticket.

Write an equation that relates the given information and the unknown quantity. We can use the fact that the sum of all parts of the whole is 100%1. Let x be the price of one ticket. Then we have:

games+food and drinks+parking+tickets0.05×330+115​×330+13+2x​=total amount=330​

Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:

16.5+150+13+2x2x2xxx​=330=330−16.5−150−13=150.5=2150.5​=75.25​

Therefore, the price of one ticket is $75.25.


Related Questions

1/2x^2+3x-5 min or max

Answers

The function f(x) = (1/2)x^2 + 3x - 5 has a minimum value

Classifying the function as min or max

To determine whether the function f(x) = (1/2)x^2 + 3x - 5 has a minimum or maximum value, we can use the fact that the vertex of a quadratic function represents the minimum or maximum point of the function.

To find the x-coordinate of the vertex, we can use the formula x = -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively.

In this case, a = 1/2 and b = 3, so we have:

x = -b/2a = -(3)/(2(1/2)) = -3

To find the corresponding y-coordinate, we can substitute x = -3 into the function:

f(-3) = (1/2)(-3)^2 + 3(-3) - 5 = -9.5

Since the coefficient of the quadratic term is positive, we know that the parabola opens upward and the vertex represents a minimum value.

Therefore, the minimum value of the function is -9.5, which occurs at x = -3.

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Simplify. Simplify. Express your answer as a single term, without a denominator.
pls helpppppp

Answers

Simplifying further, you can move any negative exponents to the denominator by changing their sign:

t⁻² u⁻⁶ v⁴ = v⁴ / (t² u⁶)

what is denominator  ?

In a fraction, the denominator is the bottom number that represents the total number of equal parts into which the whole is divided. For example, in the fraction 3/4, the denominator is 4, which indicates that the whole has been divided into four equal parts.

In the given question,

When multiplying two terms with the same base, you can add their exponents, so:

t⁻¹ u v⁴* t⁻¹ u⁻⁷ v⁰ = t⁻² u⁻⁶ v⁴

Simplifying further, you can move any negative exponents to the denominator by changing their sign:

t⁻² u⁻⁶ v⁴ = v⁴ / (t² u⁶)

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For each graph below, state whether it represents a function. I don’t know if I got them right

Answers

Answer:

Step-by-step explanation:

Use the vertical line test. If you can draw a vertical line that cuts more than one point then the graph is not a function.

The only one that is incorrect is graph 4. It is a function (no vertical line will cut the graph more than once).

The value of a certain collectible card in dollars from January 2020 to May 2021 can be modeled by the function V(m)=250m2 – 3,500m + 18,000, where m is the approximate number of months since the start of 2020.

Over what period was the value of the card declining?

< m

Answers

If the value of a certain collectible card in dollars from January 2020 to May 2021 can be modeled by the function V(m)=250m² – 3,500m + 18,000, the value of the card was declining over the period 0 < m < 7.

To determine when the value of the collectible card was declining, we need to look for when the first derivative of the function is negative. If the first derivative of the function is negative over a certain period, then the function is decreasing over that period. The first derivative of the function V(m) is:

V'(m) = 500m - 3,500

To find when the value of the card was declining, we need to solve the inequality V'(m) < 0. Solving for m, we get:

500m - 3,500 < 0

500m < 3,500

m < 7

Therefore, the value of the card was declining over the period 0 < m < 7. This corresponds to the months from January 2020 to July 2020. During this period, the first derivative of the function V(m) is negative, which means the value of the card was decreasing.

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From the observation deck of a skyscraper, Brandon

Answers

The horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.

How to solve

Given that:-

The angle is = 45

The height of the skyscraper is 1140 feet.

The horizontal distance will be calculated by applying the angle property in the right angle triangle.

tan45  =  (  P  /  B  )

B  =  P  /  tan45

B  =  P                                 Since ( tan45 =1 )

B  =  1140 feet.

Therefore the horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.

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From the observation deck of a skyscraper, Brandon measures a 45^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 1140 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.

PLS HELP THIS IS DUE TOMORROW

Answers

Answer: y = -|x + 1| + 1

Step-by-step explanation:

Since this is a "V" shaped graph, we know it uses the absolute value function. This is the parent function:

    y = |x|

This represents the transformations:

➜ a is amplitude

➜ h is horizontal shift

➜ k is vertical shift

    f(x) = a | x - h | + k

Next, we see it is shifted one unit upwards.

    y = |x| + 1

Then, we see it is also shifted one unit left.

➜ Note that this shift is -h units, so we will use positive for moving left.

    y = |x + 1| + 1

Lastly, we see this graph is flipped and has a negative slope, or amplitude.

    y = -|x + 1| + 1

Hawk thinks his heartrate will increase as he increases his skateboarding speed. To see if this relationship exists, he records six different speeds and models it with a scatterplot and regression output.

A scatterplot is shown with the x axis labeled Speed, miles per hour, and the y axis labeled Pulse, beats per minute. The points on the graph increase from 9.5 and 68 to 15.8 and 116.


Regression Statistics
Multiple R 97.28153%
R Square 94.63696%
Adjusted R Square 93.29620%
Standard Error 4.806846736
Observations 6


df SS MS F
Regression 1 1,630.910231 1,630.910231 70.58453
Residual 4 92.42310217 23.10577554
Total 5 1,723.333333


Coefficients Standard Error t Stat p-Value
Intercept 1.301246992 10.66036651 0.122064001 0.908735
Speed 7.315685846 0.870763656 8.401459797 0.001098


Part A: Write the equation of the regression line using the regression output. (2 points)

Part B: What do the slope and intercept parameters mean using the context of the problem? (4 points)

Part C: Compute the margin of error that Hawk should use if he wants to provide a 99% confidence interval for the slope. Assume that conditions for inference are satisfied. (4 points)

Answers

Part A:
The equation of the regression line can be written as:
Pulse = 1.301 + 7.316 × Speed

Part B:
The slope of the regression line (7.316) represents the change in pulse (in beats per minute) that is associated with a one-unit increase in speed (in miles per hour). In other words, for every 1 mile per hour increase in speed, Hawk's pulse is expected to increase by approximately 7.316 beats per minute, on average.

The intercept of the regression line (1.301) represents the estimated pulse rate (in beats per minute) when the speed is zero. However, in the context of the problem, it does not have a meaningful interpretation because it is not possible to achieve zero speed in skateboarding.

Part C:
The margin of error for a 99% confidence interval for the slope can be calculated using the formula:

Margin of Error = t-value × Standard Error

where the t-value is the critical value from the t-distribution with n-2 degrees of freedom and α/2 = 0.005 (since we want a 99% confidence interval).

From the regression output, we have:

n = 6 (number of observations)
Standard Error = 4.806846736

The degrees of freedom for the t-distribution is n-2 = 4. Using a t-table or calculator, the critical value for a 99% confidence interval with 4 degrees of freedom is approximately 4.604.

Therefore, the margin of error is:

Margin of Error = 4.604 × 4.806846736 = 22.102

The 99% confidence interval for the slope is:

7.316 ± 22.102

or

(-14.786, 29.418)

Therefore, with 99% confidence, we can say that the true slope of the relationship between pulse and speed is within the interval (-14.786, 29.418).
Final answer:

The equation of the regression line is Pulse = 1.301 + 7.316 * Speed. The slope parameter represents how pulse rate changes with skateboarding speed. The margin of error for a 99% confidence interval for the slope is 2.517.

Explanation:

Part A: The equation of the regression line can be written as: Pulse = 1.301 + 7.316 * Speed

Part B: The slope parameter of 7.316 means that for every 1 unit increase in skateboarding speed, the pulse rate increases by an average of 7.316 beats per minute. The intercept parameter of 1.301 represents the pulse rate at a speed of 0 miles per hour (which doesn't have a specific meaning in this context).

Part C: To compute the margin of error for a 99% confidence interval for the slope, we use the formula: margin of error = critical value * standard error. The critical value for a 99% confidence interval is approximately 2.896. Plugging in the values, we get margin of error = 2.896 * 0.870 = 2.517 (rounded to three decimal places).

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Consider the function.

f(x)=2log5(x−2)+1

On what interval is the function positive?

Enter your answer in the box. Round to the nearest hundredth.

Answers

The function is positive when its output, f(x), is greater than zero.

2log5(x−2)+1 > 0

2log5(x−2) > -1

log5(x−2) > -1/2

x - 2 > 5^(-1/2)

x - 2 > 0.4472

x > 2.4472

Therefore, the function is positive when x is greater than 2.4472.

The interval on which the function is positive is (2.45, infinity).

A scientist has two solutions, which she has labeled solution a and solution
b. each contains salt. she knows that solution a is 65% salt and solution b is 80% salt. she wants to obtain 150 ounces of a mixture that is 70% salt. how many ounces of each solution should she use?

Answers

Let x be the number of ounces of solution a and y be the number of ounces of solution b.

We know that the total amount of mixture needed is 150 ounces, so we can write:
x + y = 150

To achieve a 70% salt mixture, we can write the equation:
0.65x + 0.8y = 0.7(150)

To solve for x and y, we can use substitution or elimination. Let's use substitution to solve for x.

From the first equation, we have:
x = 150 - y

Substituting this into the second equation:
0.65(150 - y) + 0.8y = 105

Simplifying:
97.5 - 0.65y + 0.8y = 105
0.15y = 7.5
y = 50

Now that we know y, we can find x using either of the original equations:
x + y = 150
x + 50 = 150
x = 100

Therefore, the scientist should use 100 ounces of solution a and 50 ounces of solution b to obtain 150 ounces of a mixture that is 70% salt.

A specific radioactive substance follows a continuous exponential decay model. It has a half-life of 16 days. At the start of the experiment, 65.7 g is present.
(a) Lett be the time (in days) since the start of the experiment, and let
y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
y = ei
(b) How much will be present in 13 days?
Do not round any intermediate computations, and round your
answer to the nearest tenth.
08
X
Oina
3

Answers

Answer:

Step-by-step explanation:

(a) Lett be the time (in days) since the start of the experiment, and let

y be the amount of the substance at time t.

Write a formula relating y to t.

Use exact expressions to fill in the missing parts of the formula.

Do not use approximations.

y = ei

Answer: (a) The formula relating the amount of substance, y, to time, t, is given by:

y = y₀ * e^(-λ*t)

where y₀ is the initial amount of the substance, λ is the decay constant, and e is the mathematical constant approximately equal to 2.71828.

The half-life, T½, is related to the decay constant as:

T½ = ln(2)/λ

We are given that the half-life of the substance is 16 days, so we can solve for λ:

λ = ln(2)/T½ = ln(2)/16

Substituting this value of λ in the formula for y, we get:

y = 65.7 * e^(-ln(2)*t/16)

(b) To find the amount of substance present after 13 days, we substitute t = 13 in the formula for y:

y = 65.7 * e^(-ln(2)*13/16) ≈ 42.1

Rounding to the nearest tenth, we get y ≈ 42.1 g. Therefore, approximately 42.1 g of the substance will be present after 13 days.

Step-by-step explanation:

According to a recent poll, 22% of US adults get an average of 7 or more hours of sleep per night. Assume this is the parameter value for the population. Suppose you select a simple random sample of 50 US adults and find that 10 of them get an average of 7 or more hours of sleep per night. Let p(hat) = the proportion in the sample who get an average of 7 or more hours of sleep per night.

Assuming the polling information is true, the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night is ?
answer is .3664

If needed, use the z-table to answer the question.

Answers

assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

The mean of the sample proportion distribution is given by:

μp(hat) = p = 0.22

The standard deviation of the sample proportion distribution is given by:

σp(hat) = sqrt((p*(1-p))/n) = sqrt((0.22*0.78)/50) = 0.0802

To find the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night, we need to find the z-score corresponding to this value:

z = (0.20 - 0.22) / 0.0802 = -0.2494

Using a standard normal table or calculator, we find that the probability of obtaining a z-score of -0.2494 or less is 0.4019. Therefore, the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night,

Hence assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.

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An employee at a department store is stocking cell phone cases. He has a box of 80 cases. Among the 80 cases, 40 are black, 10 are white, and 30 are pink. If he reaches into the bag randomly and removes one at a time, what is the probability that the first three cases are all pink? Please help I have no clue how to do this at all. I listen in math class but this is hard!

Answers

The probability of drawing a pink case on the first draw is 30/80.

What is probability?

Probability is a branch of mathematics that deals with the measurement and analysis of random phenomena. It is the study of the likelihood or chance of an event occurring. It involves analyzing and predicting the likelihood of certain outcomes based on the available information and the rules of probability theory. Probability is used extensively in various fields, including statistics, physics, finance, engineering, and computer science, among others.

In the given question,

The probability of drawing a pink case on the first draw is 30/80. Since the cases are not replaced, the probability of drawing a pink case on the second draw is 29/79 (there are now 29 pink cases left out of 79 total cases). Similarly, the probability of drawing a pink case on the third draw is 28/78. Therefore, the probability of drawing three pink cases in a row is:

(30/80) * (29/79) * (28/78) = 0.0412 or about 4.12%.

So, the probability that the first three cases are all pink is 0.0412 or about 4.12%.

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Confusing Calculus Parametric Equations Question

Answers

Rounding to the nearest meter, we get that the bullet will hit the ground 18603 meters away from the gun.

what is acceleration?

The rate at which an object's velocity varies with respect to time is known as its acceleration. It is a vector quantity whose definition is the product of the velocity change and the time period during which the change takes place. Depending on the direction and size of the velocity change, acceleration may be positive, negative, or zero. Acceleration in physics is frequently represented by the letter "a," and its SI unit is metres per second squared (m/s2).

To find when the bullet will hit the ground, we need to find the time at which y = 0.

y = vo sin(a) t - (1/2)g[tex]t^2[/tex], where g is the acceleration due to gravity (9.8 m/s^2).

Setting y = 0, we get:

0 = vo sin(a) t - (1/2)g[tex]t^2[/tex]

Solving for t using the quadratic formula, we get:

Since we want the time when the bullet hits the ground, we take the positive root:

t = (vo sin(a) + √((vo sin(a))^2 + 2gy)) / g

Plugging in the values given, we get:

t = (550 m/s * sin(a) + √((550 m/s * sin(a))^2 + 2 * 9.8 m/s^2 * 0)) / 9.8 m/s^2

Simplifying, we get:

t = (550 m/s * sin(a)) / 9.8 m/s^2

t = 35.27 seconds (rounded to two decimal places)

To find how far from the gun the bullet will hit the ground, we need to find the value of x at this time:

x = vo cos(a) t

Plugging in the values given, we get:

x = 550 m/s * cos(a) * 35.27 s

x = 18602.57 meters

Rounding to the nearest meter, we get that the bullet will hit the ground 18603 meters away from the gun.

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on any day ,the probability that marcus will get a seat on the schoo bus is 0.93 . what is the probability that he does not get a seat on the school bus?

Answers

Marcus not getting a seat on the school bus is therefore 0.07 or 7% likely as 0.07 percent of people will not receive a seat .

what is probability ?

The prospect of an event happening is assessed by probability. It is a number between zero and 1, where 0 denotes an improbable occurrence and 1 denotes a certain occurrence. For instance, if we flip a fair coin, the odds of obtaining heads are 0.5, or 50%, and the odds of receiving tails are also 0.5, or 50%. In each case, there are various ways to compute probability. In general, if an event has n equally possible results and k of them are favourable, the likelihood that the event will occur is: Event P = k/n . All possible outcomes are thought to be equally likely under what is referred to as the classical probability.

given

Simply put, the likelihood that Marcus won't obtain a seat on the school bus is the complement of the likelihood that he will.

By deducting the probability from 1, one can determine the complement of a probability. So:

Chance of not being seated equals one less than the likelihood of being seated.

The likelihood of not getting a seat is equal to 1 - 0.93.

0.07 percent of people will not receive a seat.

Marcus not getting a seat on the school bus is therefore 0.07 or 7% likely as 0.07 percent of people will not receive a seat .

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I need help with this econ question. Thank you.

Answers

Answer:

c + 3.6 + 3.4 + 4.1 + 2.3 = 18.6

c + 13.4 = 18.6

c = 5.2

$5.2 trillion was spent on consumption.

the following figure, assume that a and b = 3, c = 5, e = 12, and d = 13​

Answers

Looking at the information provided, we can guess the triangle is similar to the one attached.

Therefore the area of the joint triangle is 40.825 unit²

How did we find the area of the joint triangle?

a = b = 3 is the side lengths of the equilateral triangle c = 5 is the side length shared by both triangles = 12 which is the base of the right triangled = 13 which is the hypotenuse of the right triangle

The height of the equilateral triangle is 4.33 units.

Looking at this information, we solve for the area of the  equilateral triangle;

Area = (base × height) / 2 (5 × 4.33) / 2= 10.825

Area = (base × height) / 2

Area of the right angle triangle = (12 × 5) / 2 = 30

The total area 10.825 + 30 = 40.825

The above answer is partly based on the figure provided in the image. The numbers used were the ones provided by you, except for the height of the equilateral triangle.

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Looking at the information provided, we can guess the triangle is similar to the one attached. Therefore the area of the joint triangle is 40.825 unit²

How did we find the area of the joint triangle?

a = b = 3 is the side lengths of the equilateral triangle

c = 5 shared by both triangles

12 = the base of the right triangle

13 = the hypotenuse of the right triangle

4.33 = height of the equilateral triangle

To solve the total area, we say

Triangle 1

Area = (base × height) / 2

(5 × 4.33) / 2= 10.825

Triangle 2

Area = (base × height) / 2

Area of the right angle triangle = (12 × 5) / 2 = 30

The total area ∴ 10.825 + 30 = 40.825

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CAN SOMEONE PLEASE HELP me with the correct answer!!!!! I need this done please help like please

Answers

answer: 164 degrees

reasoning: circle = 360 degrees
360-115= 245
245-81= (164 degrees)

Jermaine invested $3,200 in a defined-contribution account. Assuming he is in a 20% marginal tax bracket, how much did he lower his income taxes with the investment

Answers

Jermaine's income tax was lowered by $640 as a result of the investment.

Investment calculation

Assuming that the defined contribution account is a tax-deferred retirement account, Jermaine can lower his income taxes by the amount of his contribution multiplied by his marginal tax rate. The formula for this tax savings is:

Tax savings = Contribution × Marginal tax rate

Using the given values, Jermaine's contribution to the account is $3,200 and his marginal tax rate is 20%. Substituting these values into the formula, we get:

Tax savings = $3,200 × 0.20 = $640

Therefore, Jermaine can lower his income taxes by $640 by contributing $3,200 to the defined contribution account.

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please help
What is the distance to the earth’s horizon from point P?

Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

x =
mi

Answers

The measure of distance x, that is, the distance between a point P and the point of horizon, is equal to 284.372 miles.

How to find the distance to the earth horizon from a given point

In this problem we must determine the distance between a point P located about earth's circumference and the point of horizon, located on earth's circumference. Since the line between these two points is tangent to earth, then, distance x can be found by Pythagorean theorem:

x = √[(3959 mi + 10.2 mi)² - (3959 mi)²]

x = 284.372 mi

The distance x is equal to 284.372 miles.

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Suppose that the function f is defined as follows.

Answers

Answer:

Step-by-step explanation:

If the function y=e−2x is vertically compressed by a factor of 3, reflected across the y-axis, and then shifted down 2 units, what is the resulting function? Write your answer in the form y=ceax+b

Answers

The resulting function is given as follows:

[tex]y = \frac{e^{2x}}{3} - 2[/tex]

How to obtain the resulting function?

The parent function in the context of this problem is given as follows:

[tex]y = e^{-2x}[/tex]

When the function is vertically compressed by a factor of 3, we have that it is divided by three on the range, hence:

[tex]y = \frac{e^{-2x}}{3}[/tex]

When the function is reflected across the x-axis, we multiply by -1 on the domain, hence:

[tex]y = \frac{e^{2x}}{3}[/tex], as -2x x -1 = 2x.

When it is shifted down two units, we subtract by two on the range, hence:

[tex]y = \frac{e^{2x}}{3} - 2[/tex]

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HOW TO SOLVE LINEAR REGRESSIONS

Answers

The equation has the form Y= a + bX, where Y is the dependent variable (that's the variable that goes on the Y axis), X is the independent variable (i.e. it is plotted on the X axis), b is the slope of the line and a is the y-intercept.

Read the piccture and thank you

Answers

Minimum because it has that u shape but if was an n shape then it is a maximum

find the measure of angle PRT

Answers

It is 45 because a circle is 360 degrees and 90 x 4 is so it can’t be 90, 180 would be half of the circle also.
Answer:

measure of Angle PRT = 90 degrees

Step-by-step explanation:

A circle with center T exists -- Given

Point R is on the the circle. -- THIS IS AN ASSUMPTION BASED ON THE PICTURE (if you have more information that makes this not true, the rest of this logic fails).

Line segment TR is the radius of the circle. -- Definition of radius

Line PR is tangent to the circle. -- PR touches at exactly one point: R

Angle PRT has a vertex as point R. -- definition of angle PRT

Since PR is tangent to the circle, TR is perpendicular to PR -- consequence of lines perpendicular to circles

Perpendicular lines form right angles. -- Consequence of two congruent angles that form a straight angle pair.

The measure of a right angle is 90 degrees. -- definition of right angle

Therefore, the measure of angle PRT is 90 degrees.

Please help me!
Which of these graphs represent a function?

Answers

Answer:

  X

Step-by-step explanation:

You want to identify the graph that represents a function.

Vertical line test

A graph represents a function if no vertical line intersects the graph in more than one place.

W – the line x=0 intersects the graph at y = -4 and at y = 4. This graph is not the graph of a function.

X – At points where the graph might overlap, one point is identified as not include, (1, -1) for example, while the other point is identified as included (1, 1) for example. This means there is only one function value at that point, so this is the graph of a function.

Y – The vertical line x=-2 intersects the graph in an infinite number of points. This graph is not the graph of a function.

Z – The vertical line x=0 intersects the graph at y = -2, y = 0, and y = 2. This graph is not the graph of a function.

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Need help. What is the x value pic attached below​

Answers

The value of x in the function f(x) = (1/3)^x - 2 such that f(x) = 7 is -2

Calculating the value of x

From the question, we have the following equation that can be used in our computation:

f(x) = (1/3)^x - 2

When the value of f(x) is 7, we have

(1/3)^x - 2 = 7

So, we have

(1/3)^x = 9

Take the log of both sides

x = log(9)/log(1/3)

Evaluate

x = -2

Hence, the value of x is -2

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Please help me understand this

Answers

Answer:

To find the value of y, we can use the slope formula:

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

We know that the slope is 5, and the two points on the line are (5,y) and (4,1). We can substitute these values into the slope formula to get:

5 = (y - 1) / (5 - 4)

Simplifying this equation gives:

5 = y - 1

Adding 1 to both sides gives:

y = 6

Therefore, the value of y is 6.

Step-by-step explanation:

Factor the expression. x^2-14x-32

Answers

Answer:

[tex](x-2)(x+16)[/tex]

Step-by-step explanation:

Use graphing calculator and find the x-intercepts.

what is the x-intercepts of y=-3x(4-x)

Answers

The x-intercepts of the given function y = -3x(4-x) are x = 0 and x = 4.

As we know that the x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses

To determine the x-intercepts of a function, we need to set y=0 and solve for x.

In this case, we have:

y = -3x(4-x)

0 = -3x(4-x)

0 = 3x(x-4)

Therefore, the x-intercepts occur when either 3x=0 or x-4=0.

Solving for x, we get:

3x = 0, x = 0

x - 4 = 0, x = 4

Therefore, the x-intercepts of y=-3x(4-x) are x=0 and x=4.

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B as a % of A is equal to A as a % of (A+B). Find B as a % of A.

Answers

Option (b), 62% is correct.

How to solve

By the given condition,

B/A = A/(A + B) ..... (1)

Now to find the percentage of A = B, we consider B = Ax. From (1), we get

Ax/A = A/(A + Ax)

or, x = 1/(1 + x)

or, x² + x - 1 = 0

Using the quadratic formula, we get

x = {- 1 ± √(1 + 4)}/2

= (- 1 ± √5)/2

Since x cannot be negative, we take

x = (- 1 + √5)/2

≈ 0.62

Therefore the required percentage is

= 0.62 × 100%

= 62%


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B as a percentage ofAis equal to Aas a

percentage of(A+B). How much percent

of A is B?

(a) 60%

(b) 62%

(C) 64%

(d) 66%

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