ABSTRACT REASONING In △EFG, the bisector of
∠F intersects the bisector of ∠G at point H. Explain
why FG — must be longer than FH — or HG . —

Answer:

(7,7.5)

Step-by-step explanation:

midpoint formula:

(10+4)/2=7

(6+9)/2=7.5

(7,7.5)

The number of employees that must be included in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean is 107 employees.

To estimate the mean number of hours worked by all grocery store employees in the county with 95% confidence and a margin of error of 1.5 hours, we can use the sample size formula:

n = (Z * σ / E)²

where:
- n is the required sample size
- Z is the critical value (1.96 for a 95% level of confidence)
- σ is the population standard deviation (7.9 from the previous study)
- E is the margin of error (1.5 hours)

Plugging in the given values:

n = (1.96 * 7.9 / 1.5)²

n ≈ 106.56

Since you cannot have a fraction of an employee, you need to round up to the nearest whole number. Therefore, the researcher must include 107 employees in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean.

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Answer:

\(y = mx + c \\ - 3 = 2m + c \\ - 2 = 4m + c \\ subtract \: (2) - (1) \\ 1 = 2m \\ m = \frac{1}{2} \\ - 3 = 2( \frac{1}{2} ) + c \\ c = - 4 \\ y = \frac{1}{2}x - 4 \)

alternative method

\(\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\)

Answer:

1.5

Step-by-step explanation:

to find x-intercept, sub y = 0

6x - 0 = 9

6x = 9

x = 3/2 = 1.5

this is a question of set of equations and solution is as follows,

Williamston Daily newspaper started printing newspaper.

Three years ago they had 5900 subscribers.

every month there is an increase of 66 new subscribers.

n is the number of months the paper has been printed.

so, the linear model will be  

B= early subscriber + number of month × increments

B= 5900 + n × 66

B= 66 n + 5900

Example - subscribers after 3 months,

n = 3

= 66 x 3 +5900

= 198 + 5900

= 6000

set of equations

A system of equations is a set or collection of equations that you deal with all together at once. Linear equations are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.

Linear equations

Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.

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Answer: 70/13

Step-by-step explanation:

Slope = rise/run

(r-5)/(6-r) = 5/8

30-5r = 8r-40

70 = 13r

70/13 = r

Answer:

The opposite sides of a rectangle are equal in length ⇒ perimeter = 2(3x +1) +2(x + 1) Also the perimeter = 28.

Answer:

P=2(L+W)

Step-by-step explanation:

p=2(L+W)

    2(2x+1)+2(3x-2)

    4x+2+6x-4

    10x-2

As per the remainder that the greatest possible value of 17

The term remainder in math defined as if a number is not completely divisible by another number  then we are left with a value once the division is done

Here we have if x is a positive integer, then r is the remainder when x is divided by 4 and r is the remainder when x is divided by 9.

As we all know that the remainder is always smaller than the divisor.

Here we have also know that it will be 0 if the dividend is evenly divisible or a positive integer less than the divisor.

So, when we divided by 4 then the largest remainder will be 3 and then here we have to  divided by 9, then the largest remainder will be written as

=> r² + R = 32 + 8

=> 9 + 8 = 17

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The probability of obtaining tails and the number 5 is 1/12

the probability of obtaining an even number is 1/2

P(heads and prime number)  1/4

Since the events are independent, the probability of obtaining tails and the number 5 is:

P(tails and 5) = P(tails) * P(5) = (1/2) * (1/6) = 1/12

The coin toss outcome is irrelevant, so the probability of obtaining an even number is:

P(even number) = 1/2

The probability of obtaining heads and a prime number is:

P(heads and prime number) = P(heads) * P(prime number) = (1/2) * (1/2) = 1/4

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The domain and the range of the graphare

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

The graph

The above graph is a quadratic function

The rule of an quadratic function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

In this case, it is -2

So, the range is y > -2

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a. The degree of the function is 2. b. The values of aN, a0 and a3 are 3N, 0, 9. c. Real depths the function are 2. d. Maximum 1 turning point. e. Y- intercept is equal to-3. f. end behaviour x → ∞, y → ∞ and as x→-∞,  y→∞.

An expression, rule or law that defines the relationship between one variable( the independent variable) and another variable( the dependent variable).

depths of a polynomial can be defined as the points where the polynomial becomes zero as a whole. A polynomial having value zero( 0) is called zero of a polynomial.

a. The degree of a polynomial is the highest power of the variable x. So the degree will be 2.

y = -2x²+5x²-x-3

y = 3x²-x-3

b. On comparing the above quadratic equation by its general form:

Y =ax²+bx+c we get a=3

Therefore aN= 3N, a0 =0, a3= 9

c. The largest number of real zeroes = 2 as maximum power of x is 2.

d. The maximum 1 turning point.

e. Y= 3x²-x-3 on putting x=0 we will get y- intercept.

Y= 0-0-3

Y= -3

f. Analysis shows that as

x → ∞, y → ∞ and as x→-∞,  y→∞

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A. 3/16-in.-thick aluminum,  B. 1/4-in.-thick lead. C. 1/2-in.-thick copper. D. 1/8-in.-thick nickel alloy.  Root faces are suitable for the 3/16-in. aluminum thickness, promoting effective weld penetration and strength.

A butt joint design with a 90° V groove angle and 1/16-in. root faces is commonly used for welding thicker materials. Aluminum, being 3/16-in. thick, falls within this range. The V groove angle helps create a strong weld joint, and the 1/16-in. root faces allow for tight butt joints, ensuring good fusion between the materials. The V groove angle determines the shape and depth of the weld, while the root face refers to the gap between the materials to be welded. In this case, the 90° V groove angle and 1/16-in.

Option A, 3/16-in.-thick aluminum, is the most appropriate choice for a butt joint design requiring a 90° V groove angle and 1/16-in. root faces tightly butted against each other. It's important to consult welding codes, specifications.

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The meaning of the phrase is  , that there is a 20% probability that snowfall will occur in that particular region on the following day, according to the weather reporter's forecast.

The phrase "the weather reporter predicts that there is a 20% chance of snow tomorrow for a certain region" means that there is a 20% probability that snowfall will occur in that particular region on the following day, according to the weather reporter's forecast. A 20% chance of snow means that in 100 days, it is expected to snow in that particular area for 20 days. It's worth noting that a 20% probability does not imply that it will not snow at all; instead, it signifies that there is a higher probability of it not snowing than of it snowing. The odds of snow are relatively low, therefore it is always a good idea to check the weather forecast frequently to stay up to date with any changes.

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Answer:

  2153 meters

Step-by-step explanation:

You want to know the distance to a source of sound if it is heard through a medium with a speed of sound of 5030 m/s 6 seconds before it is heard through a medium with a speed of sound of 335 m/s.

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

  time = distance/speed

For some distance d in meters, the two times are d/335 seconds and d/5030 seconds. The time difference is 6 seconds, so we have ...

  d/335 -d/5030 = 6

Multiplying by 337010, we have ...

  1006d -67d = 2022060

  939d = 2022060 . . . . . simplify

  d ≈ 2153.42 . . . . . meters

The source of sound is about 2153 meters away.

__

Additional comment

The distance might rightly be rounded to 2150 meters, since the given numbers are 3 significant figures each.

The solution to all parts is shown below:

(a) The level of significance is 0.01.

(b) Chi-square ≈ 3.916

(c) The P-value is approximately 0.416.

(a) The level of significance is 0.01.

(b) To find the value of the chi-square statistic for the sample, we need to calculate the expected frequencies and then perform the chi-square test. The expected frequencies can be calculated using the formula:

Expected frequency = (row total x column total) / grand total

The table below shows the expected frequencies:

Pottery Type

Site Type Mesa Verde

Black-on-White McElmo

Black-on-White Mancos

Black-on-White Row Total

Mesa Top (189 x247)/628  (189 x 195)/628         (189 x 186)/628

                        ≈ 74.67            ≈ 58.72                  ≈ 56.61 189

Cliff-Talus (213x247)/628     (213x195)/628            (213x186)/628

                    ≈ 83.74                     ≈ 66.48                  ≈ 63.78 213

Canyon Bench (226x247)/628   (226x195)/628        (226x186)/628

                                 ≈ 89.02                 ≈ 71.05           ≈ 67.93 226

Column Total           247                         195                              186         628

Now, we can calculate the chi-square statistic:

Chi-square = Σ [(Observed frequency - Expected frequency)² / Expected frequency]

Chi-square = [(79 - 74.67)² / 74.67] + [(65 - 58.72)² / 58.72] + [(45 - 56.61)² / 56.61] + [(76 - 83.74)² / 83.74] + [(67 - 66.48)² / 66.48] + [(70 - 63.78)² / 63.78] + [(92 - 89.02)² / 89.02] + [(63 - 71.05)² / 71.05] + [(71 - 67.93)² / 67.93]

Chi-square ≈ 3.916

(c) To find or estimate the P-value of the sample test statistic, we need to compare the chi-square statistic to the chi-square distribution.

so, degrees of freedom= (number of rows - 1) x (number of columns - 1)

= (3-1) x (3-1)

= 4.

So, the P-value is approximately 0.416.

(d) Based on the answers in parts (a) to (c), we will fail to reject the null hypothesis. Since the P-value (0.416) is greater than the level of significance (0.01), we do not have sufficient evidence to reject the null hypothesis that site type and pottery type are independent.

(e) In the context of the application, at the 1% level of significance, we do not have enough evidence to conclude that site and pottery type are not independent.

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Answer:

D.6 calls

Step-by-step explanation:

To find the average first we need to add up all the numbers

7+1+4+10+7+4+9=42

Next we would divide 42 by the number of days which is 7 days

42÷7 and 6

Answer:

5624 divided by 5 is 1124.8

7792 divided by 4 is 1948

9015 divided by 8 is 1138.125

8064 divided by 6 is 1344

Hope this helps :D

The relative error of the first-order forward finite difference approximation to I = 0.3 with step size 0.05 is 0, indicating that the approximation is exact.

To calculate the first-order forward finite difference approximation of the integral I at x = 0.3 with a step size of h = 0.05, we can use the formula:

f'(x) ≈ [f(x+h) - f(x)]/h

where f(x) = e^(x^2), x = 0.3 and h = 0.05.

Therefore,

f'(0.3) ≈ [f(0.3 + 0.05) - f(0.3)]/0.05

    = [e^((0.3+0.05)^2) - e^(0.3^2)]/0.05

    = [e^(0.325^2) - e^(0.3^2)]/0.05

    ≈ 0.912

The actual value of f'(0.3) can be found by taking the derivative of f(x) at x = 0.3:

f'(x) = 2xe^(x^2)

f'(0.3) = 2(0.3)e^(0.3^2) ≈ 0.912

The relative error of the approximation is given by:

|f'(0.3) - f'(0.3)_approx| / |f'(0.3)|

= |0.912 - 0.912| / |0.912|

= 0

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Answer:

.37

Step-by-step explanation:

2.99 divided by 8 = .37375 rounded up to your hundredths is .37

Answer:the cone is 9 cm

Step-by-step explanation:

Let h be the height of the cone.

Diameter = 8 cm

Radius = 4 cm

Volume = 48π cm3

31​π×(4)2×h=48π

Answer:

9cm

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

I'm not 100% sure, but i think it's C. :)

Step-by-step explanation:

i think

Answer:

y<-1

Step-by-step explanation:

2(3y-5)<-16

3y-5<-8

3y<-8+5

3y<-3

y<-1

The rate of change of the acute angle made by the ladder with the ground is -.021

According to the question,

Given: length of ladder(L)=30ft

Sliding down the wall at the rate of \($=\frac{d y}{d t}=\frac{-1}{2} \mathrm{ft} / \mathrm{sec}$$\)

To find: Rate of change of the acute angle made by the ladder when upper end is 18 ft above the ground.

Acute angle measure less than 90 degrees. right angle measures 90 degrees. obtuse angle measures more than 90 degrees

Now, we know that

\($$\sin \theta=\frac{y}{30}$$\)

let the time be (t) at general height (h) and at angle(θ)

\($$\begin{aligned}& \Rightarrow \quad \frac{d y}{d t}=-\frac{1}{2} \mathrm{ft} / \mathrm{sec} \\& \Rightarrow \quad \sin \theta=\frac{y}{30}\end{aligned}$$\)

Differentiate above equation

\($$\begin{aligned}\Rightarrow & (\cos \theta)\left(\frac{d \theta}{d t}\right)=\left(\frac{1}{30}\right)\left(\frac{d y}{d t}\right) \\& \text { Substitute } \frac{d y}{d t}=-\frac{1}{2} \mathrm{ft} / \mathrm{sec} . \\\Rightarrow & \frac{d \theta}{d t}=\left(\frac{1}{30}\right)\left(-\frac{1}{2}\right)\left(\frac{1}{\cos \theta}\right)\end{aligned}$$\)

\($$\Rightarrow \frac{d \theta}{d t}=\left(\frac{-1}{60}\right)\left(\frac{1}{\cos \theta}\right)$$\\\)

So, when h=18, from (1)

\($$\begin{aligned}& \Rightarrow \quad \sin \theta=\frac{18}{30} \\& \Rightarrow \sin \theta=\frac{3}{5}\end{aligned}$$\)

As we know that,

\($$\begin{aligned}& \sin ^2 \theta+\cos ^2 \theta=1 \\& =\cos \theta=\sqrt{1-\sin ^2 \theta} \\& =\cos \theta=\sqrt{1-\left(\frac{3}{5}\right)^2} \\& \Rightarrow \cos \theta=\frac{\sqrt{25-9}}{5} \\& \Rightarrow \cos \theta=\frac{4}{5}\end{aligned}$$\)

let the time be (t) at general height (h) and at angle(θ)

2) Substitute \($\left(\cos \theta=\frac{4}{5}\right)$\) from (4) eqn in.

(3) equ,

Then, \($\quad \frac{d \theta}{d t}=\left(-\frac{1}{60}\right)\left(\frac{5}{4}\right) \mathrm{rad} / \mathrm{sec}$\)

\($\frac{d \theta}{d t}=\frac{-1}{48} \mathrm{rad} / \mathrm{sec}$\)

Therefore, the rate of change of the acute angle made by the ladder with the ground is \($\frac{d \theta}{d t}=\frac{-1}{48} \mathrm{rad} / \mathrm{sec}$\).

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Anything that strengthens a response or increases the probability that it will occur is called a "reinforcer". A reinforcer can be anything that the individual finds rewarding or motivating, such as praise, a high five, a tangible reward, or a positive experience.

The use of reinforcers is a common technique in behavior modification and is often used in educational and therapeutic settings. By identifying and providing reinforcers for desired behaviors, individuals can be motivated to continue those behaviors, which in turn increases the probability of success. Reinforcement can also be used to shape new behaviors, by gradually reinforcing steps towards the desired behavior until the full behavior is achieved. In summary, reinforcement is a powerful tool for increasing the probability of desired behaviors and can be used in a variety of settings to improve outcomes.

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The amount of time it would will it take him to achieve his goal is B. $5,136; approximately 24 months.

This refers to the emergency funds that are set aside for situations that were not initially budgeted for.

Hence, because Sammy makes about $2,362/month

Rent, car insurance $1,292

Basic groceries, telephone $420

Snack items $260

Annual Savings $130

Annual emergency savings $210

5 years of vacation savings $50

Total= $2,362

Using Sammy's method of putting these budgets into separate checking accounts, the amount which Sammy needs to save to have x3 of his living expenses and the length of time it would take is $5,136; approximately 24 months.

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Answer/Step-by-step explanation:

(5 x 10) + ( 5 x -15) or 5 x (10 + -15)

5 x 10 = 50

5 x -15 = -75

50 + -75 = -25

Answer:

-25

Step-by-step explanation:

The cost of the bike is $40 and that accessories is $6.65

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Let the cost of the accessories be x, therefore, the cost of the bike is 6x,

According to the equation,

6x × x = 266

6x² = 266

x² = 44.33

x = 6.65

Therefore, the cost of the bike is = 6 × 6.65 = 39.94 ≈ 40

Hence, the cost of the bike is $40 and that accessories is $6.65

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