Consider the two functions. Which statement is true? A) Function 1 has a greater rate of change by 2 B) Function 2 has a greater rate of change by 2 C) Function 1 has a greater rate of change by 3 2 D) Function 2 has a greater rate of change by 3 2

Answer:

0.5

Step-by-step explanation:

The slope m of a linear equation y = mx + b that goes through point (-9,6) and point (-3, 9) would have the following formula

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 6}{-3 - (-9)} = \frac{3}{6}= \frac{1}{2}[/tex] or 0.5

Where [tex](x_1,y_1), (x_2, y_2)[/tex] are the coordinates of the 2 points that this line goes through

Answer:

The answer to your question is below

Step-by-step explanation:

See the graph below

Process

1.- Find the distance from A to B, B to C, C to D, A to D

Formula

d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]

d AB = [tex]\sqrt{(1 + 3)^{2} + (6 - 5)^{2}}  = \sqrt{17}[/tex]

dBC = [tex]\sqrt{(-2 -6)^{2} + (3 - 1)^{2}}  = \sqrt{68}[/tex]

dCD = [tex]\sqrt{(-1 - 3)^{2} + (-3 +2)^{2}}  = \sqrt{17}[/tex]

dAD = [tex]\sqrt{(-1 + 3)^{2} + (-3 - 5)^{2}}  = \sqrt{68}[/tex]

2.- Find the perimeter

Perimeter = 2[tex]\sqrt{17} + 2\sqrt{68}[/tex] = [tex]6\sqrt{17}[/tex] u

3.- Find the area

Area = [tex]\sqrt{17} x \sqrt{68}[/tex]

Area = [tex]\sqrt{17x68} = \sqrt{1156} = 34 u^{2}[/tex]

Answer:

See below.

Step-by-step explanation:

x < 2   f(x) = |x|.

x ≥ 2   f(x) =  3.

Answer:

Side of 40 and height of 20

Step-by-step explanation:

Let s be the side of the square base and h be the height of the box. Since the box volume is restricted to 32000 cubic centimeters  we have the following equation:

[tex]V = hs^2 = 32000[/tex]

[tex]h = 32000/ s^2[/tex]

Assume that we cannot change the thickness, we can minimize the weight by minimizing the surface area of the tank

Base area with open top [tex]s^2[/tex]

Side area 4hs

Total surface area [tex]A = s^2 + 4hs[/tex]

We can substitute [tex]h = 32000/ s^2[/tex]

[tex]A = s^2 + 4s\frac{32000}{s^2}[/tex]

[tex]A = s^2 + 128000/s[/tex]

To find the minimum of this function, we can take the first derivative, and set it to 0

[tex]A' = 2s - 128000/s^2 = 0[/tex]

[tex]2s = 128000/s^2[/tex]

[tex]s^3 = 64000[/tex]

[tex]s = \sqrt[3]{64000} = 40[/tex]

[tex]h = 32000/ s^2 = 32000/ 40^2 = 20[/tex]

Answer:

The answer to your question is  x = 0 and x = 1

Step-by-step explanation:

Equation

                       [tex]\frac{x}{x - 2} + \frac{x - 1}{x + 1} = -1[/tex]

1)

                      [tex]\frac{x(x + 1) + (x - 2)(x - 1)}{(x - 2)(x + 1)} = - 1[/tex]

Expand

2)                  x² + x + x² - x - 2x + 2 = -1(x - 2)(x + 1)

Simplify

3)                  2x² -2x + 2 = -1(x² + x - 2x - 2)

4)                  2x² - 2x + 2 = -x² + x + 2

Equal to zero

5)                  2x² - 2x + 2 + x² - x - 2 = 0

6)                  3x² - 3x = 0

Factor

7)                  3x(x - 1) = 0

8)                  3x₁ = 0                   x₂ - 1 = 0

9)                    x₁ = 0/3                x₂ = 1

10)                  x₁ = 0                    x₂ = 1

It is 12 miles from house to school

Solution:

Given that, Jeff wants to know how many miles it is from his house to school

On a map, the scale is 0.5 inches = 2 miles

His house island school are 3 inches apart on the map

So, from the given scale,

0.5 inches = 2 miles

Distance between school and house in map = 3 inches

Therefore,

0.5 inches = 2 miles

Muliply both sides by 6

[tex]0.5 \times 6\ inches = 6 \times 2\ miles\\\\3\ inches = 12\ miles[/tex]

Thus, it is 12 miles from house to school

Step-by-step explanation:

the sum of angles in a triangle is 180°. so if a triangle is equivalent, each degree will be 180/3 = 60°

Answer:The faster person will do the job in 7.53hours

Step-by-step explanation:

Let t=faster person

Let t-1= the other person

The job to be done =1

Each person will do a fraction of the job

4/t+4/t-1=1

Multiply both sides wit t(t-1)

4(t+1)+4t=t(t-1)

4t+4+4t=t^2+t

8t+4=t^2+t

0=t^2+t-8t-4

t^2-7t-4=0

Use Almighty formular to solve d quadratic equation

X=-b+- rootb^2-4ac/2a

X=t,a=1,b=-7 c=4

Substituting the values you get:

t=-7 +- root 49+16/2

t=-7 +- root 65/2

t=7 +8.06/2=15.06/2

t=7.53 hours

Answer:

Step-by-step explanation:

A salesperson at a car dealership has a salary of 900 dollars per week plus 3% commission on sales if a salesperson has sales of $72000 in one week, it means that the amount of commission that was received by the salesperson would be

3/100 × 72000 = 0.03 × 72000 = $2160

Therefore, the total amount of pay that the salesperson would receive for the week would be

900 + 2160 = $3060

Answer:

Voters can select their members in 10possible ways

Step-by-step explanation:

According to the question, the voters are to elect 3members out of 5 candidates, this means they are to select any 3 candidates of their choice from a pool of 5 candidates. Since "combination" has to do with selection, we use the combination formula.

To select 'r' objects from 'n' pool of objects, we have;

nCr = n!/(n-r)!r!

5C3 = 5!/(5-3)!3!

5C3 = 5!/2!3!

5C3 = 5×4×3×2×1/2×3×2

= 120/12

5C3 = 10

Candidates can therefore vote in 10 possible ways

Answer:

See explanation!

Step-by-step explanation:

We know that the maximum miles allowed before oil change is 5,000miles (thus Kaci can drive less or up to 5,000 miles but not more).

Kaci has already driven 3,450miles since last oil change.

Inequalities are typically employed to show a relating or comparative relationship between expressions and can be identified by the sybolism of less, more or/and equal to (i.e. [tex]<[/tex] , [tex]>[/tex] , [tex]\leq[/tex], [tex]\geq[/tex] ).

Let us denote the miles Kaci can drive before oil changing again by [tex]x[/tex], then we can write the following inequality:

[tex]3450+x\leq 5000[/tex]

solving for the remaining miles [tex]x[/tex] allowed

[tex]3450+x\leq 5000\\x\leq 5000-3450\\x\leq 1550[/tex]

Thus Kaci can drive up to and including 1550 miles before chaging car oil again.

Final answer:

Kaci can drive up to 1550 more miles before needing an oil change, based on the advice not to exceed 5000 miles between oil changes and the fact she has already driven 3450 miles.

Explanation:

The question asks us to write and solve an inequality that will help determine how many more miles Kaci can drive before needing an oil change. It is given that her car has already been driven 3450 miles since the last oil change, and she has been advised not to exceed 5000 miles between oil changes.

To solve this, let x represent the number of miles Kaci can still drive before reaching the 5000-mile limit. The inequality that represents this situation would be:

3450 + x ≤ 5000

To find the value of x, we subtract 3450 from both sides of the inequality:

x ≤ 5000 - 3450

x ≤ 1550

Therefore, Kaci can drive up to 1550 more miles before needing her oil changed again.

Answer:The percentage of bottles expected to have a volume less than 32 or is 40.13%

Step-by-step explanation: The volumes of soda in quart soda bottles can be represented by a Nomal model with a= 32.3 oz

b=1.2 oz

Let S be the volume of randomly selected soda bottles

Y-score: S-a/b

For S=32 oz

Substitute the values of S,a and b into the equation

Y=32-32.3/1.2

Y=-0.25

Probability of bottles that have a volume less than 32 oz is

P(S<32)=P(Y<-025)= 0.40129

Percentage of bottles that have volume less than 32 oz will be

0.40127×100%=40.13%

Answer:

3hr 31mins

Step-by-step explanation:

First we convert miles to kilometers

1 miles to km = 1.60934 km

26.2 miles = 26.2 x 1.60934 = 42.164708

A typical marathon approx = 42.165km

If our runner covers 12 km = 1 hr

then he'll cover 42.165km = 42.165/12 = 3.5137 hrs

= 3 hrs + (0.514 * 60 mins) = 3hrs + (30.84mins)

Allan going at that speed would complete the marathon in appox = 3hrs : 31mins.

Answer:

2.34m2

Step-by-step explanation:

boom

Answer:

Option D. -0.80

Step-by-step explanation:

A scatter plot that shows a set of data points having two properties

1). If the points are clustered close to the line that reveals the high correlation.

2). Data points are clustered close to the line having slope down to the right or negative slope.

Therefore, Option D. has the highest correlation with negative slope.

Answer:

x= −5621/201

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3 /7x+5 =  812/7772/7-7

3 /7x+5=  1/67+−7

3 /7x+5=(  1/67+-7)(Combine Like Terms)

3 /7x+5=  −468 /67

3 /7x+5= −468/67

Step 2: Subtract 5 from both sides.

3 /7x+5−5=−468/67−5

3 /7x=−803/67

Step 3: Multiply both sides by 7/3.

(  7/3)*(3/7x)=(7/3)*(−803/67)

x= −5621/201

Answer:

The sale price of the car is $48000.

Step-by-step explanation:

i) let the sale price of the car be = $x

ii) the premium is given as 16%

  therefore the premium of the car will be equal to = 16% of $x

  the premium of the car will be = $0.16x

iii) therefore total price of car in terms of sale price x  = $x + $0.16x

           therefore total price = $1.16x

iv) total price is given as $55,680

Therefore   $55,680 = $1.16x,    therefore $x = [tex]\dfrac{55,680}{1.16} = \$\hspace{0.15cm}48000[/tex].

Therefore the sale price of the car is $48000.

Answer:

[tex]P(16.6 < \bar X < 22.6) = P(\frac{16.6-19}{3} <Z< \frac{22.6-19}{3})= P(-0.8 < Z < 1.2)[/tex]

[tex]P(16.6 < \bar X < 22.6) =P(-0.8<Z<1.2) = P(Z<1.2)-P(Z<-0.8) = 0.88493- 0.211855= 0.673[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(19,6)[/tex]  

Where [tex]\mu=19[/tex] and [tex]\sigma=6[/tex]

And we select n =4 fish. For this case we want to find this probability:

[tex] P(16.6 < \bar x < 22.6) [/tex]

And since the distribution for X is normal then the distribution for the sample mean is also normal and given by:

[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}}=3)[/tex]

And the z score is given by:

[tex]z = \frac{\bar x -\mu}{\sigma_{\bar x}}[/tex]

And if we apply this formula we got:

[tex]P(16.6 < \bar X < 22.6) = P(\frac{16.6-19}{3} <Z< \frac{22.6-19}{3})= P(-0.8 < Z < 1.2)[/tex]

And we can find this probability with this operation using the normal standard table or excel:

[tex] =P(-0.8<Z<1.2) = P(Z<1.2)-P(Z<-0.8) = 0.88493- 0.211855= 0.673[/tex]

To find the probability that the mean weight of four randomly selected fish will be between 16.6 and 22.6 pounds, we can use the Central Limit Theorem. The probability is 0.7556.

To find the probability that the mean weight of four randomly selected fish will be between 16.6 and 22.6 pounds, we can use the Central Limit Theorem. The Central Limit Theorem states that if we take multiple samples from a population with any distribution, the distribution of the sample means will approach a normal distribution. In this case, we have a normally distributed population with a mean of 19 pounds and a standard deviation of 6 pounds.

To calculate the probability, we need to standardize the range of weights using the formula for the standard error of the mean:

Standard error of the mean (SE) = Standard deviation / sqrt(sample size)

We will use the formula:

Z = (X - mean) / SE

Where X is the upper and lower bounds of the range, mean is the population mean, and SE is the standard error of the mean.

First, let's calculate the standard error of the mean:

SE = 6 / sqrt(4) = 3

Then, we can calculate the z-scores for the upper and lower bounds:

Z_upper = (22.6 - 19) / 3 = 1.2

Z_lower = (16.6 - 19) / 3 = -1.1333

Since the z-scores are in standard deviation units, we can look up the corresponding probabilities in the standard normal distribution table:

P(16.6 < X < 22.6) = P(-1.1333 < Z < 1.2)

Using the table, we can find the probabilities:

P(Z < -1.1333) = 0.1293

P(Z < 1.2) = 0.8849

Finally, we can calculate the probability between the two bounds:

P(16.6 < X < 22.6) = P(Z < 1.2) - P(Z < -1.1333) = 0.8849 - 0.1293 = 0.7556

https://brainly.com/question/32117953

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Answer:

Total time spent by Tiwa to set up the computer and install software = 6 hours

Step-by-step explanation:

Given:

Time spent by Tiwa to set up  her computer = [tex]1\frac{1}{2}\ hours[/tex]

Time spent to install the software is 3 times the time she took to set up the computer.

To find the total time Tiwa took to set up her computer and install the software.

Solution:

Time spent by Tiwa to install the software can be given as:

⇒ [tex]3\times 1\frac{1}{2} \ hours[/tex]

In order to multiply mixed numbers we first change them to fractions.

We multiply the denominator to the whole number and add the numerator to it. Then we write the number as numerator of a fraction with the same denominator.

So, [tex]1\frac{1}{2}=\frac{3}{2}[/tex]

So, we have:

⇒ [tex]3\times \frac{3}{2}\ hours[/tex]

⇒ [tex]\frac{9}{2}\ hours[/tex]

Total time spent by Tiwa to set up the computer and install software can be given as:

⇒ [tex]\frac{3}{2}\ hours+\frac{9}{2}\ hours[/tex]

Since denominators are same, so we simply add the numerators.

⇒ [tex]\frac{3+9}{2}\ hours[/tex]

⇒ [tex]\frac{12}{2}\ hours[/tex]

⇒ [tex]6\ hours[/tex]

Answer:

x ≥ 120

Step-by-step explanation:

i) Let x be the number of packages of cards

ii) we know that Pablo currently has 1200 cards.

iii) Therefore the equation required is

15x + 1200 ≥ 3000 because we know that there are 15 cards in a package and the greater than equal to sign is used because Pablo has to collect at least 3000 cards

iv) Solving the equation we get

    15x + 1200 ≥ 3000

⇒  15x ≥ (3000 - 1200)

⇒ 15x ≥ 1800

⇒ x ≥ (1800 ÷ 15)

∴ x ≥ 120

answer

x ≥ 120

Step-by-step explanation:

Step-by-step explanation:

i) Let x be the number of packages of cards

ii) we know that Pablo currently has 1200 cards.

iii) Therefore the equation required is

15x + 1200 ≥ 3000 because we know that there are 15 cards in a package and the greater than equal to sign is used because Pablo has to collect at least 3000 cards

iv) Solving the equation we get

   15x + 1200 ≥ 3000

⇒  15x ≥ (3000 - 1200)

⇒ 15x ≥ 1800

⇒ x ≥ (1800 ÷ 15)

∴ x ≥ 120

Final answer:

A chemist cannot achieve a 34% concentration by mixing 20% and 30% acid solutions, as it is outside the possible range of concentrations achievable by combining these two solutions, option no 4.

Explanation:

When a chemist is mixing two acid solutions, one with a 20% concentration and the other with a 30% concentration, they can obtain a range of concentrations between the two provided percentages by varying the proportions of each solution mixed. The concentrations that could not be obtained would be any value outside of the 20% to 30% range because the resulting mixture cannot exceed the concentration of the higher concentrated solution or be lower than the concentration of the less concentrated solution. Therefore, a 34% concentration could not be obtained by mixing a 20% solution with a 30% concentration.

Answer:

Ms. Thomas was driving at constant rate of 52 miles/hour.

Step-by-step explanation:

Given:

Total time to travel (t) = 45 minutes

Distance drove (d) = 39 miles

we need to find the constant rate in miles per hour at which she was driving.

Solution:

Now we know that;

We need to find constant rate at miles per hour;

But time is given in minutes.

So we will convert minutes into hour by dividing by 60 we get;

time [tex]t =\frac{45}{60}= 0.75\ hrs[/tex]

Now we know that;

Distance is equal to rate times time.

framing in equation form we get;

distance [tex]d =rt[/tex]

Or

rate [tex]r= \frac{d}{t} = \frac{39}{0.75}= 52 \ mi/hr[/tex]

Hence Ms. Thomas was driving at constant rate of 52 miles/hour.

Answer:11.38

Step-by-step explanation:

290-257=33 /290=.11379 x 100=11.37  =11.38

Final answer:

To find the percentage of racers who did not complete the marathon, we add those who gave up and those who were disqualified, a total of 31 racers. The percentage is then calculated using the formula for percentage, resulting in 10.7% of racers not completing the marathon.

Explanation:

To find the percentage of racers who did not complete the marathon, we first need to determine the total number of racers who did not finish. This includes those who gave up and those who were disqualified. In this case, 27 racers gave up, and 4 were disqualified, giving us a total of 31 racers who did not complete the marathon.

To calculate the percentage, we use the formula:

Percentage = (Number of racers who did not complete / Total number of racers) × 100%

Plugging the numbers into the formula gives us:

Percentage = (31 / 290) × 100% = 0.1069 × 100% = 10.69%

Rounding to the nearest tenth of a percent, 10.7% of racers did not complete the marathon.

See the attached picture:

Edited graph 4. I missed the negative sign in front of the one. The new graph is attached.

Answer:

$600

Step-by-step explanation:

Let the random variable [tex]X[/tex] denote the damage in $ incurred in a certain type of accident during a given year. The probability distribution of [tex]X[/tex] is given by

                        [tex]X : \begin{pmatrix}0 & 1000 & 5000 & 10\; 000\\0.81 & 0.09 & 0.08 & 0.02\end{pmatrix}[/tex]

A company offers a $500 deductible policy and it wishes its expected profit to be $100. The premium function is given by

                    [tex]F(x) = \left \{ {{X+100, \quad \quad \quad \quad \quad \text{for} \; X = 0 } \atop {X-500+100} , \quad \text{for} \; X = 500,4500,9500} \right.[/tex]

For [tex]X = 0[/tex],  we have

                              [tex]F(X) = 0+100 = 100[/tex]

For [tex]X = 500[/tex],

                             [tex]F(X) = 500-500+100 = 100[/tex]

For [tex]X = 4500[/tex],

                            [tex]F(X) = 4500-500+100 = 4100[/tex]

For [tex]X = 9500[/tex],

                            [tex]F(X) = 9500-500+100 = 9100[/tex]

Therefore, the probability distribution of [tex]F[/tex] is given by

                           [tex]F : \begin{pmatrix} 100 & 100 & 41000 & 91000\\0.81 & 0.09 & 0.08 & 0.02\end{pmatrix}[/tex]

To determine the premium amount that the company should charge, we need to calculate the expected value of [tex]F.[/tex]

[tex]E(F(X)) = \sum \limits_{i=1}^{4} f(x_i) \cdot p_i = 100 \cdot 0.81 + 100 \cdot 0.09 + 4100 \cdot 0.08 + 9100 \cdot 0.02[/tex]

Therefore,

                             [tex]E(F) = 81+9+328+182 = 600[/tex]

which means the $600 is the amount the should be charged.

Answer:

  16 mph

Step-by-step explanation:

The relationship between distance, speed, and time is ...

  speed = distance/time . . . . . "miles per hour"

Malcom's distance was 32 miles each way, for a total of 64 miles. Then his average speed was ...

  speed = (64 mi)/(4 h) = 16 mi/h

Answer:

yes

Step-by-step explanation:

because it is not a whole number so you cant tell

Answer:

Malcolm is showing evidence of gambler's fallacy.

This is the tendency to think previous results can affect future performance of an event that is fundamentally random.

Step-by-step explanation:

Since each round of the roulette-style game is independent of each other. The probability that 8 will come up at any time remains the same, equal to the probability of each number from 1 to 10 coming up. That it has not come up in the last 15 minutes does not increase or decrease the probability that it would come up afterwards.

Answer:

The answer to your question is below

Step-by-step explanation:

Data

∠1 = 105°

Process

a)

∠2 = 180 - 105 = 75°          supplementary angles

∠3 = ∠2 = 75°                     supplementary angles

∠4 = 105°                            vertical angles

∠5 = 105°                            corresponding angles

∠6 = 180 - 105 = 75°           alternate interior angles

∠7 = ∠6 = 75°                      supplementary angles

∠8 = 105°                             alternate interior angles

b)

∠3 = 80°

∠1 = 180 - 80 = 100°           supplementary angles

∠2 = 80°                              vertical angles

∠4 = 100°                              supplementary angles

∠5 = 100°                             supplementary angles

∠6 = 80°                               alternate interior angles

∠7 = 80°                               corresponding angles

∠8 = 100°                              supplementary angles

Answer:

8.

Step-by-step explanation:

5, 10, 12, 4, 6, 11, 13, 5

Arrange in ascending order:

4, 5, 5, 6, 10, 11, 12, 13.

The median is the mean of the 2 middle numbers:

= (6 + 10) / 2

= 8.

Answer:

  OT, OU, OR

Step-by-step explanation:

Point O is the center of the circle, so will be one end of any radius. Segments are shown from point O to points T, U, and R on the circle. Each of those segments is a radius:

  OT, OU, OR . . . . are radii

_____

OS would also be a radius, but no segment is shown there, and it doesn't show in any answer choice.