Evaluate each algebraic expression when a = 4 and b = -2

ab = ________



2( a - b) = _________


2a + 4b = __________

Answer:

Option C 5a+(2b + 3c)

Answer:

what are the options?

Step-by-step explanation:

Answer:

18 inches

Step-by-step explanation:

\(a=\pi r^2\)

This is the formula for finding the area of a circle. We already know the area, so we'll move the terms in the equation to better fit our purposes.

\(r=\sqrt(\frac{a}{\pi} )\)

Now let's substitute.

\(r=\sqrt(\frac{324\pi}{\pi} )\)

We'll cancel out unnessicary terms:

\(r=\sqrt(324)\)

This gives us the following:

\(r = 18\)

In other words, the radius of the circle is 18 inches (NOT square) :D hope this helps :D

The spring will stretch 1.5 times further when the 0.60 kg block is added to the 1.2 kg block.

To determine how much further the spring will stretch when a 0.60 kg block is added to the 1.2 kg block, we need to consider Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

Let's assume that the spring is initially stretched by a certain amount x when only the 1.2 kg block is attached. The force exerted by the spring is given by F = kx, where k is the spring constant.

When the 0.60 kg block is added, the total mass becomes 1.2 kg + 0.60 kg = 1.8 kg. The force exerted by the spring remains the same, but the total mass affects the acceleration of the system according to Newton's second law, F = ma.

Using F = ma, we can find the acceleration of the system: F = (1.8 kg)(9.8 m/s^2) = 17.64 N.

Since F = kx, we can rearrange the equation to find x: x = F/k.

Now, if we assume the spring constant k remains constant, the displacement x will increase by a factor of 1.8 kg/1.2 kg = 1.5.

Therefore, the spring will stretch 1.5 times further when the 0.60 kg block is added to the 1.2 kg block.

To know more about displacement , refer here :

https://brainly.com/question/11934397#

#SPJ11

Answer:

A

Step-by-step explanation:

Since you are multiplying -2 and 12, you can put them in any order as long as you get - 24/5

each number and variable inside the parentheses has an exponent, in this case all of them are 1.

3^2 * x^2 + 4^2

9*x^2+16

final answer:

Statement iii is correct.

The test statistic is significant at the 0.03 level of significance, which is equivalent to a 97% confidence level.

Therefore, we can conclude that a 90% confidence interval for the difference in means will not contain the value 0 (Option I is false). Similarly, a 95% confidence interval for the difference in means will also not contain the value 0 (Option II is false). However, we cannot make any conclusion about a 99% confidence interval for the difference in means.

In general, as the level of confidence increases, the width of the confidence interval also increases. Therefore, it is possible that a 99% confidence interval for the difference in means may include the value 0 even though the 97% level of significance rejects the null hypothesis.

So, the only statement that must be true is III. A 99% confidence interval for the difference in means may or may not contain the value 0.

Learn more about p-value here

https://brainly.com/question/27198724

#SPJ4

The optimal solution is \(m = 10\) at \(x_1 = 2\), \(x_2 = 2\), and \(x_3 = 0\).

To solve the given linear programming model using the 2 Phase Method, we follow a two-step process: Phase 1 and Phase 2.

In this phase, the objective is to obtain an initial feasible solution. We introduce artificial variables, \(x_4\) and \(x_5\), to the system. The initial tableau is set up with these variables and the original constraints. The objective function for this phase is to minimize the sum of the artificial variables, representing the extent to which the constraints are violated.

Using the simplex method, we perform iterations to optimize the artificial variables until their values reach zero. This ensures feasibility in the solution space. Once the artificial variables are eliminated, we proceed to Phase 2.

In this phase, we modify the objective function to match the original objective function, which is to maximize the given expression \(m = -3x_1 - x_2 + x_3\). The initial tableau from Phase 1 serves as the starting point for Phase 2.

We apply the simplex method once again, this time optimizing the original objective function. The iterations continue until an optimal solution is reached. At this point, the values for the decision variables \(x_1\), \(x_2\), and \(x_3\) are obtained from the optimal tableau. In this case, we have \(x_1 = 2\), \(x_2 = 2\), and \(x_3 = 0\), with an objective value of \(m = 10\).

The optimal solution satisfies all the constraints of the linear programming model and maximizes the objective function. It represents the most favorable values for the decision variables that fulfill the given conditions.

Learn more about optimal solution

brainly.com/question/32390549

#SPJ11

In this case, we are given only a partial list of observations. To determine if the process is in control, we would need the complete set of observations to evaluate their values in relation to the control limits.

To construct a control chart and determine if the process is in control, we need to calculate the control limits using the given observations.

Let's start by calculating the average (x(bar)) and standard deviation (σ) of the observations:

Observations: 10, 3, 9, 9, 8, 4

Step 1: Calculate the average (x(bar)):

x(bar) = (10 + 3 + 9 + 9 + 8 + 4) / 6 = 43 / 6 ≈ 7.17

Step 2: Calculate the standard deviation (σ):

1. Calculate the squared deviation for each observation:

\((10 - 7.17)^2, (3 - 7.17)^2, (9 - 7.17)^2, (9 - 7.17)^2, (8 - 7.17)^2, (4 - 7.17)^2\)

= 6.9129, 18.9129, 2.5929, 2.5929, 0.6889, 10.5889

2. Calculate the average of the squared deviations:

(6.9129 + 18.9129 + 2.5929 + 2.5929 + 0.6889 + 10.5889) / 6 ≈ 7.9198

3. Calculate the square root of the average squared deviation:

σ = √(7.9198)

≈ 2.81

Now that we have the average (x(bar)) and standard deviation (σ), we can construct the control chart using two sigma limits. The control limits are calculated as follows:

Upper Control Limit (UCL) = x(bar) + (2 * σ)

Lower Control Limit (LCL) = x(bar) - (2 * σ)

UCL = 7.17 + (2 * 2.81)

≈ 12.79

LCL = 7.17 - (2 * 2.81)

≈ 1.55

Based on the control chart, if any of the observations fall above the UCL or below the LCL, it would indicate an out-of-control process.

To know  more about set visit:

brainly.com/question/30705181

#SPJ11

Answer:

10, 9, 8, -3, -8

Step-by-step explanation:

from top to bottom highest lowest

10

9

8

-3

-8

Answer:

x=−2  - Mark brainiest if this helped!

Step-by-step explanation:

I typed this on another doc and here is the step by step explanation:

Alan can sew 60 feet of fabric in 1.5 minutes.

In mathematics, slope is a measure of the steepness of a line. It is defined as the ratio of the change in the vertical (y) coordinate to the change in the horizontal (x) coordinate between two points on the line. In other words, slope represents the rate at which the line is rising or falling. The slope of a line can be positive, negative, zero or undefined, depending on the direction and steepness of the line. The slope formula is given by:

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

where (x1, y1) and (x2, y2) are two points on the line. The slope is often denoted by the letter m.

We can see that the relationship between time and length of fabric is a linear one. Using the two given points (1, 40) and (2, 80), we can find the slope of the line:

slope = (change in y) / (change in x) = (80 - 40) / (2 - 1) = 40

This means that for every 1 minute, Alan can sew 40 feet of fabric. To find how much fabric he can sew in 1.5 minutes, we can use the equation for a line:

y = mx + b

where y is the length of fabric, x is the time in minutes, m is the slope we just found, and b is the y-intercept (which we can find by plugging in one of the points).

Using the point (1, 40), we get:

40 = 40(1) + b

b = 0

So the equation for the line is:

y = 40x

To find the length of fabric Alan can sew in 1.5 minutes, we plug in x = 1.5:

y = 40(1.5) = 60

Therefore, Alan can sew 60 feet of fabric in 1.5 minutes.

To know more about equation visit:

https://brainly.com/question/29134661

#SPJ1

The complete question is:

Answer:

c=8p

Step-by-step explanation:

Since it is 8 dollars per pound, his total cost c is 6 times p

Therefore,  c = 8p

Answer:

96

Step-by-step explanation:

Answer: 1) Error response times

2) Memory Scanning, visual search

3) Stimulus identification

Step-by-step explanation:1) response times reflext the time it takes to interpret a stimulus,get info from memory, initiate a muscle response

2) The hippocampus retrieves info from the working memory and begins to change the brains physical neural wiring

3) A decisive role in our perception and cognition

In general, there are two areas of psychology where mathematics is heavily utilized: mathematical modeling of psychological theories and experimental phenomena, which gives rise to mathematical psychology, and statistical approaches to quantitative measurement practices in psychology, which give rise to psychometrics.

Answer:

$1.48

Step-by-step explanation:

Meal cost: $7.24

Coffee cost: $2.65

Total cost: $9.89

Now we need to find 15% of 9.89.

This is a percentage question, we need to first multiply 9.89 with 15% then divide it by 100%:

9.89 × 15 ÷ 100 = 1.48 approximately.

Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

A triangle is a three-sided polygon with three vertices and three edges. The number of triangles in the given figure are 1, 3, 9, and 27.

A triangle is a three-sided polygon with three vertices and three edges. It is one of the most fundamental geometric forms.

The number of shaded triangles in each of the triangles is shown below, therefore, the number of triangles in each triangle can are:

1st triangle = 1

2nd triange= 3

3rd triangle = 9

4th triangle = 27

Hence, the number of triangles in the given figure are 1, 3, 9, and 27.

Learn more about Triangles:

https://brainly.com/question/25813512

Answer:

first part is 1, 3, 9, 27

second part is A

third part is 29,524

Step-by-step explanation:

edg 23'

Answer: \(48.5\ ft\)

Step-by-step explanation:

Given

Area of the regular hexagon is \(169.74\ ft^2\)

Length of the apothem is \(l=7\ ft\)

Suppose the side of the hexagon is a

Hexagon can be divided into six equal triangles with same area

Area of a single triangle is

\(\Rightarrow A_1=\dfrac{1}{2}\times 7\times a\\\\\Rightarrow A_1=3.5a\ ft^2\)

Area of hexagon will be equal to area of 6 equal area triangles

\(\Rightarrow 6A_1=169.74\\\Rightarrow 6\times 3.5a=169.74\\\Rightarrow a=8.08\ ft\)

Perimeter of the hexagon is

\(\Rightarrow P=6a\\\Rightarrow P=6\times 8.08\\\Rightarrow P=48.49\approx 48.5\ ft\)

Thus, the perimeter of the hexagon is \(48.5\ ft\)

Answer:

C

Step-by-step explanation:

edge 2021

Answer:

5.6s

Step-by-step explanation:

Given the height reached by the stone modeled by the equation

h(t)=−4.9t2+155 where t is time in seconds.

The stone hits the ground at h(t) = 0

Substitute

0 = -4.9t²+155

4.9t² = 155

t² = 155/4.9

t² = 31.63

t = ±√31.63

t = 5.62seconds

Hence it will take 5.6s to reach the ground(to the nearest tenth)

The investment will double in nine years at an interest rate of approximately 8.09% compounded annually.

To find the value of the (P/A,8%,145) factor, we can use the general formula for the present worth of an annuity:

(P/A, i%, n) = (1 - (1 + i)^(-n)) / i

Substituting the values given:

i = 8%

n = 145

(P/A,8%,145) = (1 - (1 + 0.08)^(-145)) / 0.08

Using a financial calculator or spreadsheet software, we can calculate the value of (P/A,8%,145) as follows:

(P/A,8%,145) ≈ 43.7276 (rounded to four decimal places)

Therefore, the correct choice for the value of (P/A,8%,145) is:

C. (P/A,8%,145) = (P/A,8%,100)(P/A,8%,45) ≈ 43.7276 (rounded to four decimal places)

Regarding the second question, to find the interest rate at which an investment will double in nine years, we can use the future worth factor formula:

(F/P, i%, n) = (1 + i)^n

We want the investment to double, so we have:

(1 + i)^9 = 2

Taking the ninth root of both sides:

1 + i = 2^(1/9)

Solving for i:

i ≈ 0.0809 or 8.09% (rounded to two decimal places)

Therefore, the investment will double in nine years at an interest rate of approximately 8.09% compounded annually.

learn more about investment on

https://brainly.com/question/15105766

#SPJ11

There is a 2.97% probability that more than 2 parts in the sample of 10 will require rework.

The number of parts requiring rework in a sample of 10 follows a binomial distribution with n=10 and p=0.03. We want to find the probability that X exceeds 2, or P(X > 2).

Using the binomial probability formula, we can calculate the probability of X taking any value from 0 to 2 as follows:

P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)

=\((10 choose 0)(0.03)^0(0.97)^10 + (10 choose 1)(0.03)^1(0.97)^9 + (10 choose 2)(0.03)^2(0.97)^8\)

≈ 0.9703

Therefore, the probability that X exceeds 2 can be found as:

P(X > 2) = 1 - P(X ≤ 2)

≈ 1 - 0.9703

≈ 0.0297

So, there is a 2.97% probability that more than 2 parts in the sample of 10 will require rework.

Learn more about probability

https://brainly.com/question/30764478

#SPJ4

It should take approximately 1.98 hours, or around 1 hour and 59 minutes, to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

To calculate the cooking time for a 5.17 pound roast, we can use the recommended guideline of 23 minutes per pound. First, we need to convert the weight from pounds to minutes, and then convert minutes to hours.

Cooking time in minutes = 5.17 pounds * 23 minutes/pound

Cooking time in minutes = 118.91 minutes

To convert minutes to hours, we divide the total minutes by 60:

Cooking time in hours = 118.91 minutes / 60

Cooking time in hours ≈ 1.98 hours

Therefore, it should take approximately 1.98 hours to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

To know more about recommended guideline refer here:

https://brainly.com/question/28617982#

#SPJ11

Answer:

y=2x-2

Step-by-step explanation:

The slope is 2 and your y intercept is already given as -2.

Slope intercept is basically y=mx+b

plug it in so you get y=2x-2

Answer:

Step-by-step explanation:

5*12=60

60*22=1320

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &500000\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=\textit{elapsed time}\dotfill &25\\ \end{cases} \\\\\\ A = 500000(1 + 0.02)^{25} \implies A=500000(1.02)^{25}\implies A \approx 820303\)