These tables represent a quadratic function with a vertex at (0, -1). What is
the average rate of change for the interval from x= 7 to x = 8?
X
0
1
23
4
5
6
y
-1
-2
-5
-10
-17
-26
-37
Interval
0 to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
Average rate
of change
-1
-3
679
-11
3-2
0-2
0-2
0-2
3-2
d

Answer:

1.5 or 3/2

Step-by-step explanation:

The division results the quotient is 1.5

The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication. In simple words, division can be defined as the splitting of a large group into smaller groups such that every group will have an equal number of items.

Given:

We have to divide 12.645 by 8.43

So,   12.645/8.43

= 12645/ 8430

=           8430 | 12645   | 1 . 5

                         8430

                      -______

                          42150

                          42150

                         _______

                               0  

Hence, the quotient is 1.5.

Learn more about division here:

https://brainly.com/question/21416852

#SPJ5                        

Answer:

The median is 5, mode is 5, and range is 12

Step-by-step explanation:

Answer:

MEDIAN - 5

MODE - 2 (4times)

RANGE - 13-1=12 (12 is the range)

Step-by-step explanation:

MEDIAN - Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.

MODE - The mode is the element that occurs most in the data set. In this case, 2 occurs 4 times.

RANGE - Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is 13-1=12

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

A. To represent the number of grams present after n hours, we can use the equation:

N(n) = 15 × (1 - 0.2)^n

Where:

N(n) is the number of grams present after n hours,

15 is the initial amount of the substance in grams,

0.2 represents the decay rate of 20% per hour, and

^n represents the exponentiation operation.

B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:

N(24) = 15 × (1 - 0.2)^24

Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.

C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:

1 = 15 × (1 - 0.2)^n

To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:

log(0.8)(1/15) = n

Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.

Therefore, the answers are:

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

for such more question on grams

https://brainly.com/question/13439286

#SPJ8

Answer:

(A)

Step-by-step explanation:

The survey follows of women's height a normal distribution.

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

The new height requirements would be 57.7 to 68.6 inches

The given parameters are:

\mathbf{\mu = 63.5}μ=63.5 --- mean

\mathbf{\sigma = 2.5}σ=2.5 --- standard deviation

(a) Percentage of women between 58 and 80 inches

This means that: x = 58 and x = 80

When x = 58, the z-score is:

\mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

This gives

\mathbf{z_1= \frac{58 - 63.5}{2.5}}z

1

=

2.5

58−63.5

\mathbf{z_1= \frac{-5.5}{2.5}}z

1

=

2.5

−5.5

\mathbf{z_1= -2.2}z

1

=−2.2

When x = 80, the z-score is:

\mathbf{z_2= \frac{80 - 63.5}{2.5}}z

2

=

2.5

80−63.5

\mathbf{z_2= \frac{16.5}{2.5}}z

2

=

2.5

16.5

\mathbf{z_2= 6.6}z

2

=6.6

So, the percentage of women is:

\mathbf{p = P(z < z_2) - P(z < z_1)}p=P(z<z

2

)−P(z<z

1

)

Substitute known values

\mathbf{p = P(z < 6.6) - P(z < -2.2)}p=P(z<6.6)−P(z<−2.2)

Using the p-value table, we have:

\mathbf{p = 0.9999982 - 0.0139034}p=0.9999982−0.0139034

\mathbf{p = 0.9860948}p=0.9860948

Express as percentage

\mathbf{p = 0.9860948 \times 100\%}p=0.9860948×100%

\mathbf{p = 98.60948\%}p=98.60948%

Approximate

\mathbf{p = 98.61\%}p=98.61%

This means that:

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

So, many women (outside this range) would be denied the opportunity, because they are either too short or too tall.

(b) Change of requirement

Shortest = 1%

Tallest = 2%

If the tallest is 2%, then the upper end of the shortest range is 98% (i.e. 100% - 2%).

So, we have:

Shortest = 1% to 98%

This means that:

The p values are: 1% to 98%

Using the z-score table

When p = 1%, z = -2.32635

When p = 98%, z = 2.05375

Next, we calculate the x values from \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

Substitute \mathbf{z = -2.32635}z=−2.32635

\mathbf{-2.32635 = \frac{x - 63.5}{2.5}}−2.32635=

2.5

x−63.5

Multiply through by 2.5

\mathbf{-2.32635 \times 2.5= x - 63.5}−2.32635×2.5=x−63.5

Make x the subject

\mathbf{x = -2.32635 \times 2.5 + 63.5}x=−2.32635×2.5+63.5

\mathbf{x = 57.684125}x=57.684125

Approximate

\mathbf{x = 57.7}x=57.7

Similarly, substitute \mathbf{z = 2.05375}z=2.05375 in \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

\mathbf{2.05375= \frac{x - 63.5}{2.5}}2.05375=

2.5

x−63.5

Multiply through by 2.5

\mathbf{2.05375\times 2.5= x - 63.5}2.05375×2.5=x−63.5

Make x the subject

\mathbf{x= 2.05375\times 2.5 + 63.5}x=2.05375×2.5+63.5

\mathbf{x= 68.634375}x=68.634375

Approximate

\mathbf{x= 68.6}x=68.6

Hence, the new height requirements would be 57.7 to 68.6 inches

Answer:

456

Step-by-step explanation:

Product means an answer derived from multiplication.  Therefore, if the product is 155952, and one value is 342, then the following equation is true:

342x = 155952, or 342 * x = 155952

Divide 155952 by 342 to get: 456.

Check the work in the equation:

342(456) = 155952

155952 = 155952, which is true, so the answer is 456.

If I helped, please make this answer brainliest! ;)

Answer:

4 1/2 meters is equal to 4.5

Step-by-step explanation:

This is the correct answer to 4 1/2 meters. :)

Answer: The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers: List the prime factors of each number. Multiply those factors both numbers have in common.

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

4(3m-2)+2(2m-1)

4(3×5-2)+2(2×5-1)

4×13+2×9

52+2×9

52+18

5(2)^2-2(7) = 6

6(7+2)/2 = 27

Therefor the correct answer is the < symbol.

I hope this helps! :)

A la sala de cine ingresaron 180 niños y 165 adultos.

De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:

3 · x + 5 · (345 - x) = 1365

Donde x es el número de niños que asistieron a la sala de cine.

Ahora despejamos la variable correspondiente mediante propiedades algebraicas:

3 · x + 1725 - 5 · x = 1365

1725 - 2 · x = 1365

2 · x = 1725 - 1365

2 · x = 360

x = 180

Ahora, el número de adultos es:

y = 345 - 180

y = 165

Para aprender más sobre ecuaciones algebraicas: https://brainly.com/question/20307002

#SPJ1

Answer:

796871

Step-by-step explanation:

Based on the given conditions, formulate:

5000 x (1 - (1 + 10%) 10)

-------------------------------                                                                  

           1 - (1 + 10%)                                                                          

Evaluate the equation/expression:

796871.23005

Find the closest integer to

798871.23005

=  796871

Yes, It can be written with commas

It will be,

\(378 , 972\)

The correct expanded form using Laws of exponents is:

Two-thirds times two-thirds times two-thirds times two-thirds

Some of the laws of exponents are:

1) When multiplying like bases, keep the base the same and add the exponents.

2) When raising a base with a power to another power, keep the base the same and multiply the exponents.

3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

Now, we want to solve the expression given as: (²/₃)⁴

When we expend this, we arrive at:

²/₃ × ²/₃ × ²/₃ × ²/₃

This among the options is Option A which is:

Two-thirds times two-thirds times two-thirds times two-thirds

Read more about Laws of exponents at: https://brainly.com/question/11761858

#SPJ1

According to the information we can infer that the parallel line would be AD or CF. Additionally, the perpendicular lines would be CB or FE.

To identify the parallel lines we must look at the figure and find the lines that have the same direction as the line BE and that would never intersect with the segment BE, according to the above, we can infer that the parallel lines would be:

On the other hand, the lines perpendicular to CF would be CB or FE because they make 90° angles with segment CF. Additionally, the face that would be parallel to ABC is DEF.

Learn more about lines at: https://brainly.com/question/30003330

#SPJ1

The equation for the total value is 0.01p + 0.25q = 3.90

The equation for the total number of coins is p + q = 54

Let p represent the number of pennies and q represent the number of quarters in the jar.

The total value of the coins can be expressed as the sum of the values of the pennies and quarters.

Since each penny is worth $0.01 and each quarter is worth $0.25, the equation for the total value can be written as:

0.01p + 0.25q = 3.90

Additionally, we know that there are a total of 54 coins in the jar, so the equation for the total number of coins can be written as:

p + q = 54

These two equations form a system that can be solved simultaneously to find the values of p and q.

Read more about equations

brainly.com/question/22688504

#SPJ1

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

Explanation:

We have these two events

The experimental (aka empirical) probabilities of each are

Note how P(A) is not 1/2 like we expect; however it's fairly close because 9/20 = 0.45 while 1/2 = 0.5 in slight contrast. The experimental probability never 100% lines up with the theoretical probability, but will get closer as you do more trials (due to the law of large numbers). A similar situation happens with P(B). The theoretical probability would be P(B) = 1/6 = 0.1667

Events A and B are independent, which allows us to multiply the probabilities:

P(A and B) = probability of getting tails and rolling a '2'

P(A and B) = P(A)*P(B)

P(A and B) = (9/20)*(1/5)

P(A and B) = (9*1)/(20*5)

P(A and B) = 9/100 which points the answer to choice C

--------------

Slight alternative method:

P(A and B) = P(A)*P(B) = (36/80)*(16/80) = 0.09 = 9/100

this method involves typing (36/80)*(16/80) into your calculator.

The DJ will charge them $575.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given that,

Booking fee for DJ = $350

Rate for an hour = $45

Let x be the number of hours DJ is lasting.

Expression to find the total charge for x hours is 350 + 45x.

The Martins want to book the DJ for a party that will last 5 hours.

Cost for the DJ party for Martins = 350 + (45 × 5) = $575

Hence the cost for the DJ party booked by Martins is $575.

Learn more about Expressions here :

https://brainly.com/question/29696241

#SPJ9

Answer:

a) r(t) = (10, 5, -5) + (5, 5, 0)*t

b) (0, -5, -5)

Step-by-step explanation:

a) 2x + 4 -2y -5 = -3z -6

2x - 2y +3z +5 =0

(10, 5, -5)

(15, 10, -5)

(5, 5, 0)

r = (10, 5, -5) + (5, 5, 0)*t

b) The yz plane is given by the equation x = 0.

x = 0  in the vector equation of a straight line if and only if  t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.

Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

the answers is a. bones to bones

Answer:

ANSWER

Step-by-step explanation:

Without knowing the specific function w(x), it is impossible to determine the domain of the inverse function w^-1(x). However, in general, the domain of an inverse function is the range of the original function, and vice versa.

If we assume that w(x) is a one-to-one function (which is necessary for it to have an inverse function), we can determine the range of w(x) and use it to find the domain of w^-1(x).

For example, if we know that w(x) is a function that takes all real numbers except x=2, then the range of w(x) is (-∞,2) U (2,∞). The domain of w^-1(x) is then the same as the range of w(x), which is (-∞,2) U (2,∞). Therefore, the domain of w^-1(x) is x ≠ 2.

Without more information about w(x), we cannot determine the domain of w^-1(x) more precisely.

the sum of the values of a and b such that f(x) = \(2ax^2 + bx + 3\) has a relative extremum at the point (-1,2) is 2.5.

If the function f(x) = \(2ax^2 + bx + 3\) has a relative extremum at the point (-1,2), then the derivative of the function must be zero at x = -1. This is because at a relative extremum, the slope of the tangent line is zero.

So, we need to find the derivative of f(x) and set it equal to zero at x = -1:

f'(x) = 4ax + b

f'(-1) = 4a(-1) + b = -4a + b = 0

Solving for b, we get:

b = 4a

Now, to find the sum of a and b, we just need to substitute b = 4a into the expression for f(x) and use the fact that f(-1) = 2:

f(x) = \(2ax^2 + bx + 3\)

f(-1) = \(2a(-1)^2 + b(-1) + 3 = 2\)

Substituting b = 4a, we get:

2a(1) - 4a + 3 = 2

2a - 4a + 3 = 2

-2a = -1

a = 1/2

Then, using b = 4a, we get:

b = 4(1/2) = 2

So, the sum of a and b is:

a + b = 1/2 + 2 = 2.5

Therefore, the sum of the values of a and b such that f(x) = \(2ax^2 + bx + 3\)has a relative extremum at the point (-1,2) is 2.5.

Learn more about sum here

https://brainly.com/question/641910

#SPJ1

Answer:

I'm not sure

Step-by-step explanation:

sorry need point

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

For more such question on monopolist. visit :

https://brainly.com/question/28336090

#SPJ8

Answer:

Step-by-step explanation:

the answer is 0.01

The base of the exponential form  is 10 and the power is -2 therefore the answer is 0.01 if the power was 2 the answer would have been 100

to learn more visit the link below

https://brainly.com/question/27804970?referrer=searchResults

Answer:

29π/12.

Step-by-step explanation:

Multiply by π/180

= 435π/180

= 29π/12 radians.