1. What must be added to X^2 + 8X to make the expression a perfect square trinomial ?


2. If the discriminant of a quadratic equation is zero, Does it mean that the equations has 1 solution?

No, the first 5 people to arrive at a town meeting is not a random sample of the town's residents.

A random sample is a subset of a population that is selected in a way that gives each member of the population an equal chance of being selected. In this case, the first 5 people to arrive may not be representative of the entire population, as they may not have been selected randomly, and their arrival at the meeting may have been influenced by factors such as their proximity to the meeting place, their level of interest in the topic, or their schedule. A more structured method of selection, such as random digit dialing or door-to-door visits, would be necessary to obtain a random sample of the town's residents.

Learn more about random sampling here:https://brainly.com/question/24466382

#SPJ4

x = 0 and Reduced cost = -4: This combination is not possible for decision variable x and its corresponding reduced cost.

Based on the complementary slackness condition in linear programming, the values of the decision variable x and its corresponding reduced cost can provide insights into the feasibility and optimality of the solution.

In the given scenarios:

x = 20 and Reduced cost = -4:

This combination is possible as a non-zero value of x with a negative reduced cost indicates that x is a non-basic variable and has a potential to increase in order to improve the objective function value.

x = 0 and Reduced cost = -4:

This combination is not possible because if x is a non-basic variable with a reduced cost of -4,

it implies that increasing x from zero would improve the objective function value, violating the complementary slackness condition.

x = 0 and Reduced cost = 0:

This combination is possible as x can be a basic variable with a reduced cost of zero,

indicating that it is at its lower bound and does not need to change.

x = 20 and Reduced cost = 0:

This combination is possible as a non-zero value of x with a reduced cost of zero implies that x is a non-basic variable and has already reached its upper bound,

so it does not need to change to improve

the objective function value.

Learn more about variable here:

https://brainly.com/question/15078630

#SPJ4

(a) 95% confidence interval for the difference between female and male times is (11.954, 255.591).

(b) The assumptions and conditions for the two-sample t-test are met, so we can use the results of the test and confidence interval.

a) To construct a 95% confidence interval for the difference between female and male times, we can use a two-sample t-test. Let's denote the mean time for female swimmers as μf and the mean time for male swimmers as μm. We want to test the null hypothesis that there is no difference between the two means (i.e., μf - μm = 0) against the alternative hypothesis that there is a difference (i.e., μf - μm ≠ 0).

The formula for the two-sample t-test is:

t = (Xf - Xm - 0) / [sqrt((s^2f / nf) + (s^2m / nm))]

where Xf and Xm are the sample means for female and male swimmers, sf and sm are the sample standard deviations for female and male swimmers, and nf and nm are the sample sizes for female and male swimmers, respectively.

Using the data from the plots, we get:

Xf = 917.5, sf = 348.0137, nf = 15

Xm = 783.7273, sm = 276.0625, nm = 28

Plugging in these values, we get:

t = (917.5 - 783.7273 - 0) / [sqrt((348.0137^2 / 15) + (276.0625^2 / 28))] = 2.4895

Using a t-distribution with (15+28-2) = 41 degrees of freedom and a 95% confidence level, we can look up the critical t-value from a t-table or use a calculator. The critical t-value is approximately 2.021.

The confidence interval for the difference between female and male times is:

(917.5 - 783.7273) ± (2.021)(sqrt((348.0137^2 / 15) + (276.0625^2 / 28)))

= 133.7727 ± 121.8187

= (11.954, 255.591)

Therefore, we can be 95% confident that the true difference between female and male times is between 11.954 and 255.591 minutes.

b) Assumptions and conditions for the two-sample t-test:

Independence, We assume that the observations for each group are independent of each other.

Normality, We assume that the populations from which the samples were drawn are approximately normally distributed. Since the sample sizes are relatively large (15 and 28), we can rely on the central limit theorem to assume normality.

Equal variances, We assume that the population variances for the female and male swimmers are equal. We can test this assumption using the F-test for equality of variances. The test statistic is,

F = s^2f / s^2m

where s^2f and s^2m are the sample variances for female and male swimmers, respectively. If the p-value for the F-test is less than 0.05, we reject the null hypothesis of equal variances. If not, we can assume equal variances. In this case, the F-test yields a p-value of 0.402, so we can assume equal variances.

Sample size, The sample sizes are both greater than 30, so we can assume that the t-distribution is approximately normal.

To learn more about confidence interval here:

https://brainly.com/question/24131141

#SPJ4

Answer:

Volume = 12

Step-by-step explanation:

Answer:

12cm³

Step-by-step explanation:

L=3cm

W=2cm

H=2cm

Volume=L*W*H

Volume =3*2*2

=12 cm³

The diagonal of the given brick using the Pythagorean Theorem is 5√2.

So, let the diagonal be 'x'.

Pythagorean formula: x² = b² + h²

Now,

Therefore, the diagonal of the given brick using the Pythagorean Theorem is 5√2.

Know more about the Pythagorean theorem here:

brainly.com/question/654982

#SPJ9

Answer:

B the number that is 6 to the right of 1 on the number line

Step-by-step explanation:

you only have a few months left, keep fighting~

The function f(x) varies directly with x, and when x = 12, f(x) is equal to 4. To determine the value of f(x) when x = 3, we can use the concept of direct variation.

In direct variation, two quantities are proportional to each other. Mathematically, this can be expressed as f(x) = kx, where k is the constant of variation. In this case, we know that f(x) = 4 when x = 12. To find the value of f(x) when x = 3, we can set up a proportion:

f(x)/x = 4/12

Cross-multiplying, we get:

12f(x) = 4x

Now, we substitute x = 3 into the equation:

12f(3) = 4(3)

Simplifying further, we find:

12f(3) = 12

Dividing both sides by 12, we get:

f(3) = 1

Therefore, when x = 3, the value of f(x) is 1.

To learn more about direct variation: -brainly.com/question/29150507#SPJ11

5 dollars equals 500 pennies, once 5 dollars times 100 equals 500. What's 5 dollars in cents? 5 dollars equals 500 cents, once 5 dollars times 100 equals 500.

The answer is C. 1/3, and there is a 1/3 chance that the number chosen by the student will be a prime number.

To find the probability that the number chosen by the student will be a prime number, we first need to determine how many prime numbers are in the range from 4 to 24. The prime numbers in this range are 5, 7, 11, 13, 17, 19, and 23. There are 7 prime numbers in total.

Next, we need to determine the total number of possible outcomes, which is the number of slips of paper in the hat. There are 21 slips of paper in the hat, since there are 21 numbers from 4 to 24 inclusive.

Therefore, the probability of selecting a prime number is the number of favorable outcomes (7) divided by the total number of possible outcomes (21):

P(prime number) = 7/21

Simplifying this fraction, we get:

P(prime number) = 1/3

Therefore, the answer is C. 1/3, and there is a 1/3 chance that the number chosen by the student will be a prime number.

Learn more about prime number.

https://brainly.com/question/30358834

#SPJ4

Yes, the sample size would be large enough if the population is school-aged children and young adults in the United States as this is a simple random sampling.

Simple random sampling is used for randomly selecting the sample size for research. No member in the population has a higher chance in comparison to others for selection in sampling. Every individual has an equal chance to be a part of the sample for the study. This is a type of probability sampling method.

The probability sampling method states that every individual has a fair and equal chance to be selected as a research sample. It includes simple random sampling, stratified sampling, systematic sampling, and cluster sampling. Here the researchers have picked around 150 students and young adults which is an appropriate amount of simple random sample for the study.

Learn more about sampling methods here https://brainly.com/question/17743025

#SPJ4

Answer:

a + 4b - 24

Step-by-step explanation:

simply multiply 4 to the numbers in the brackets. If there is an unknown variable then write it as it is. Don't forget the to multiply the signs as well.

4 x 1/4a = 1a = a

4 × b = 4b

4 × -6 = -24

Answer:

a + 4b - 24

Step-by-step explanation:

Expand brackets. Each term in the brackets is multiplied by 4.

4( 1/4a) + 4(b) + 4(-6)

4/4a + 4b - 24

Answer:

17. first box- 88

second box- 176

18. first box- 9

second box- 5 5/8

Step-by-step explanation:

See photo.

The plan will result in the price of the feed reaching $12.00 fastest is Plan B because it reaches within 5 weeks.

The process of making choice is by identifying the correct decision, gathering information, and assessing alternative solutions.

Felix’s Feed Mill sells chicken feed for $8. 00 per bag.

This price is no longer high enough to create a profit.

Felix decides to raise the price. He is considering four different plans.

The plan will result in the price of the feed reaching $12.00 fastest will be

Plan A: Raise the price by $0. 10 each week until the price reaches $12. 0.

⇒ $0.10 × 20 = $2

This plan will take 20 weeks to reach at a price of $12.

Plan B: Raise the price by 10 percent each week until the price reaches $12.0. The price of this plan will be in t weeks is

\(12 = 8 *1.1^t\\\\t = 4.25 \approx 5\)

This plan will take less than 5 weeks.

Plan C: Raise the price by the same amount each week for 8 weeks, so that in the eighth week the price is $12.0. The amount will be

Amount = 2/8 = $0.25

Plan D: Raise the price by $0.25 each week until the price reaches $12. 0.

⇒ 0.25 × 8 = $2

This will take 8 weeks.

More about the decision-making link is given below.

https://brainly.com/question/3369578

The length of the hypotenuse is 13 cm.

Let's denote the shorter leg of the right triangle as "x" cm.

According to the given information, the longer leg is 7 cm more than the shorter leg, so its length is "x + 7" cm.

The hypotenuse is 3 cm more than twice the length of the shorter leg, so its length is "2x + 3" cm.

Using the Pythagorean theorem, we can set up the equation:

(shorter leg)^2 + (longer leg)^2 = (hypotenuse)^2

Plugging in the values:

x^2 + (x + 7)^2 = (2x + 3)^2

Expanding and simplifying:

x^2 + x^2 + 14x + 49 = 4x^2 + 12x + 9

Rearranging and simplifying further:

0 = 2x^2 - 2x - 40

Dividing both sides by 2:

x^2 - x - 20 = 0

Factoring the quadratic equation:

(x - 5)(x + 4) = 0

Setting each factor equal to zero:

x - 5 = 0 or x + 4 = 0

Solving for x:

x = 5 or x = -4

Since the length of a side cannot be negative, we discard the solution x = -4.

Therefore, the shorter leg of the right triangle is 5 cm.

To find the length of the hypotenuse, we substitute the value of x into the equation for the hypotenuse:

hypotenuse = 2x + 3 = 2(5) + 3 = 10 + 3 = 13 cm

Know more about hypotenuse here:

https://brainly.com/question/29407794

#SPJ11

Answer:

£ 31620

Step-by-step explanation:

Antonio's salary = £ 31000

He gets a 2 % pay rise.

So, first let's find the amount that get raised.

31000 × 2% =  £ 620

So,  it's clear for you that his salary has get rose by £ 620.

There fore, his new salary is,

31000 + 620 = £ 31620

Hope this helps you.

Let me know if you have any other questions :-)

The given statement "you must make sure all entities of a proposed system can fit onto one diagram." is False because it is not necessary to fit all entities.

It is not necessary to fit all entities of a proposed system onto a single diagram, nor is it forbidden to break up a data model into more than one diagram. The size and complexity of a data model will often require it to be spread across multiple diagrams, with each diagram representing a subset of the entities and their relationships.

In fact, breaking up a data model into smaller, more manageable diagrams can be beneficial for understanding and communicating the system's structure and behavior. By grouping related entities and relationships together, each diagram can provide a clear and focused view of a specific aspect of the system.

However, it is important to maintain consistency and clarity across all diagrams, using a standard notation and labeling convention. Each diagram should also clearly indicate its position within the larger data model, to ensure that the relationships and dependencies between entities are properly understood.

Overall, while it is not necessary to fit all entities onto a single diagram, it is important to carefully plan and structure the data model into manageable and meaningful subsets for effective communication and understanding.

To learn more about entities click on,

https://brainly.com/question/29023409

#SPJ4

Hi!

Pi: The number π is a mathematical constant. It is defined as the ratio of a circle's circumference to its diameter, and it also has various equivalent definitions. It appears in many formulas in all areas of mathematics and physics. It is approximately equal to 3.14159.

Hope this Helps!

Yours Truly,

Answer:

59% chance

Step-by-step explanation:

Statistics from the past ten years predict that the chance of rain on any single day in April in Asha’s hometown is 41%. If Asha’s birthday is April 10, what is the chance of it not raining on Asha’s birthday?

Asha's birthday in in April. The chance of rain on any single day in April is 41%. So, there is a 41% chance of rain.

But, that's not what the problem is asking for. The problem is asking for the chance of not raining. To solve for this, we use simple algebra.

100%(all of the time) - 41%(how much it happens) = 59%

The 59% is the chance of it not raining on Asha's birthday.

Hope this helps! Happy birthday, Asha!

Answer:

A'(3, 0)

B'(6, -1)

C'(2, -3)

Answer:

\(c=6\)

Step-by-step explanation:

The absolute maximum of a continuous function \(f(x)\) is where \(f'(x)=0\). Therefore, we must differentiate the function and then set \(x=-5\) and \(f'(x)=0\) to determine the value of \(c\):

\(f(x)=xe^{-x}+ce^{-x}\)

\(f'(x)=-xe^{-x}+e^{-x}-ce^{-x}\)

\(0=-(-5)e^{-(-5)}+e^{-(-5)}-ce^{-(-5)}\)

\(0=5e^{5}+e^{5}-ce^{5}\)

\(0=e^5(5+1-c)\)

\(0=6-c\)

\(c=6\)

Therefore, when \(c=6\), the absolute maximum of the function is \(x=-5\).

I've attached a graph to help you visually see this.

The value for m in the equation 1.7m = 0.85 is B. 0.50.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information given, 1.7m = 0.85

Divide through by 1.7

1.7m / 1.7 = 0.85 / 1.7

m = 0.5

The correct option is C.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Using the principle of proportional relationship, the length of hair grown by the dog in 1 week would be 0.2 inches

Setting up the relationship thus :

12.5 weeks = 2.5 inches

1 week = p inches

Cross multiply

12.5p = 2.5

Divide both sides by 12.5

p = 2.5 / 12.5

p = 0.2 inches

Hence, the length grown in 1 week is 0.2 inches

Learn more : https://brainly.com/question/25625086

Answer:

y=-0.5x+2 (-4,0) (0,2)   y=0.5x+6 (0,6)(12,0)

Step-by-step explanation:

Desmos

Answer:

Yes, I can evaluate the expression 25+2.005-7.253-2.977.

First, we combine like terms in the expression:

25 + 2.005 - 7.253 - 2.977 = (25 - 7.253) + (2.005 - 2.977)

Next, we simplify the expressions inside each set of parentheses:

(25 - 7.253) + (2.005 - 2.977) = 17.747 + (-0.972)

Finally, we add the two terms together to get the final answer:

17.747 + (-0.972) = 16.775

Therefore, the value of the expression 25+2.005-7.253-2.977 is equal to 16.775.

hope it helps...

Mark as brainliest

Answer:

6

Step-by-step explanation:

Step 1: How many males are there?

40% of 60 = 0.4 × 60 = 24

There are 24 males.

Step 2: Of the 24 males, how many wear a hat?

25% of 24 = 0.25 × 24 = 6

Answer: 6

Answer:

the answer is number is the last one

Given:

The graph of a line.

To find:

The slope of the graphed line.

Solution:

From the given graph it is clear that the line passes through the points (-2,2) and (2,5). So, the slope of the line is:

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

\(m=\dfrac{5-2}{2-(-2)}\)

\(m=\dfrac{3}{2+2}\)

\(m=\dfrac{3}{4}\)

Therefore, the slope of the given graphed line is \(m=\dfrac{3}{4}\).