What is the area of the triangle with vertices (1, 4), (3, 1) and (11, 1)?

Both the given expression are equivalent expression as 5m + 4.

Given that,
to determine whether the two given expressions are equivalent ot each other,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
5(m + 1 ) - 1 = 2(2m + 2) + m
5m + 5 - 1 = 4m + 4 + m
5m + 4 = 5m + 4

Thus, Both the given expression are equivalent expression as 5m + 4.

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Answer:

I hope this helps for you

The number of ways that the teacher can arrange the row is  185328000

Given,

Number of male students = 12

Number of female students = 13

Number of students teacher needs to select = 8

The row arrangement is like; 4 men in the middle and  2 women on each end;

Here,

Order of the arrangement is considered.

So, permutation can be used.

Female students selected = ¹³P₂

Male students selected = ¹²P₄

Then,

Number of ways for the arrangement =  ¹³P₂ × ¹²P₄

= 15600 × 11880

= 185328000

That is,

The teacher can arrange a row with 4 men in the middle and 2 women on each end in 185328000 ways.

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99.7% of the Manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.

On Subtracting 1 from your sample size, we get

100 – 1 = 99.

On Subtracting confidence level from 1, and then divide by two.

(1 – .997) / 2 = 0.0015

Now, df = 99 and α = 0.0015

from the table at df = 99 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

28 / √(100) = 2.8

Now, 2.262 × 2.8 = 6.33

So, the confidence interval be,

(100 - 6.33 , 100 + 6.33) = (44.67 , 56.33)

Hence, 99.7% of the Manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.

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Answer:

x=2

Step-by-step explanation:

x/2 = 1 (multiply by 2 both sides)

x= 2

The answer is 10,000

The inequality and the maximum possible width are 12w  ≥ 132 and 11 feet respectively

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

If the room is 12 feet long and  Tom had enough paint to cover an area of 132 square feet. This implies Tom had paint that can cover greater or equal to 132 square feet of area. Thus:

L x w ≥ A

where l = 12 feet, A = 132 square feet

12w  ≥ 132    (This is the inequality)

To solve for width:

12w  ≥ 132

w ≥ 132 /12

w ≥ 11 feet

Therefore, the inequality is 12w  ≥ 132 and the maximum possible width is  11 feet

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Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).

The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.

The fundamental presumptions of the binomial distribution are that each trial has only one possible outcome, that each trial has the same success probability, and that each trial is independent of the others or mutually exclusive.

The likelihood of success is constant from trial to trial, and subsequent trials are independent. A binomial distribution, which derives from counting successes across a series of trials, has just two possible outcomes on each trial.

Hence, Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).

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Answer:

i suggest using -2 to multiply the figures in the bracket as a first step

Step-by-step explanation:

then you'll have something like this

-2x - 10 - 4 = 5x

-2x - 14 = 5x

-14 = 5x + 2x

-14 = 7x

x = -14/7

x = -2. hope this helps

We REJECT the null hypothesis that these rats came from a population with a mean of 32 in favour of the alternative that they were selected in a way that the mean was different from 32 because our test statistic is bigger than this (in absolute value).

In the given question,

The population mean is 32g with a st. dev. of 4g.

We collect a sample of n=25 mice with a sample average of 30.4g.

We wish to test the hypothesis that these were drawn randomly from the population.

So our null hypothesis is

H0: mean = 32

Our alternative hypothesis is

HA: mean ≠ 32.

This is a two-sided test.

A sample mean should have the same mean as the population mean, and the sample st. dev. should be (pop st. dev./√n).

In this case, under the null hypothesis, the sample mean should be distributed with an average of 32 and a st. dev. of 4/√25 = 4/5 = 0.8.

To test this hypothesis, we need to calculate a test statistic and compare it to a critical value of the standard normal distribution.

Our test statistic is:

z = (Observed value - hypothesized value) / (st. dev. in sample mean)

z = (30.4-32)/0.8

z = -1.6/0.8

z = -2.

The critical value of the z-distribution with α/2 = 0.05/2 = 0.025 is 1.96.

We REJECT the null hypothesis that these rats came from a population with a mean of 32 in favour of the alternative that they were selected in a way that the mean was different from 32 because our test statistic is bigger than this (in absolute value).

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The right answer is:

A colony of laboratory mice consists of several thousand mice. The average weight of all the mice is 32 grams with a standard deviation of 4 grams. A laboratory assistant was asked by a scientist to select 25 mice for an experiment. However, before performing the experiment the scientist decided to weigh the mice as an indicator of whether the assistant’s selection constituted a random sample or whether it was made with some unconscious bias (perhaps themice selected were the ones that were slowest in avoiding the assistant, which might indicate some inferiority about this group). If the sample mean of the 25 mice was 30.4, would this be significant evidence, at the 5 percent level of significance, against the hypothesis that the selection constituted a random sample?

If 5 out of 200 things were flawed, the population's estimated defect percent would be 2.5%.

Percent, which is a relative figure used to denote hundredths of any amount. Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified. The word "percent" simply refers to "per hundred," and the sign for percentage is %. By multiplying the total or whole number by 100, one percent (or 1%) is equal to one hundredth of the whole or whole.

Here,

Total number of items=200

number of defective items=5

Percentage of defective items,

=5/200*100

=2.5%

Therefore, if 5 out of 200 things were defective, the population's estimated percentage of defective items is 2.5%.

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Answer:

yes y/x = 5/2

Step-by-step explanation:

y/x = 5/2, 10/4=5/2, 15/6=5/2, 20/8=5/2

Step-by-step explanation:

0.5×3×4= 6cm^2

6×8

=48cm^3

Adjacent angles of a parallelogram are supplementary.

[tex]3x+10+8x+5=180 \\ \\ 11x+15=180 \\ \\ 11x=165 \\ \\ \boxed{x=15} \\ \\ \\ \\ 5y+3(15)+10=180 \\ \\ 5y+55=180 \\ \\ 5y=125 \\ \\ \boxed{y=21}[/tex]

Answer:

The solution to the given expression would be 23.

Step-by-step explanation:

1. Remove the parentheses:

[tex]2.3*6+2.3*4[/tex]

2. Multiply the numbers 2.3 by 6: 13.8

[tex]13.8+4*2.3[/tex]

3. Multiply the numbers 2.3 by 4: 9.2

4. Add the numbers 13.8 by 9.2: 23

= [tex]23[/tex] ←Our Final Solution

____________________________________________

Hope this helps!

When evaluating an exercise, evaluators record their observations in the exercise evaluation guide (eeg). observations that should be recorded include d.) a and b

When analyzing an activity, evaluators record their observations in the Exercise Evaluation Guide (EEG) (EEG). Actual time needed by exercise participants to perform the necessary tasks and resources used are among the observations that should be recorded.

EEGs (Exercise Evaluation Guides) offer a reliable instrument to direct exercise monitoring and data gathering. EEGs list capability aims and crucial tasks that are in line with exercise objectives and core capabilities.

EEGs achieve a number of objectives:

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Answer:

A ; D ; F

Step-by-step explanation:

32 - 4(5) = 12

32 - 20 = 12 (ok)

11 + 6(5) = 22

11 + 30 = 22

41 = 22 (false)

18-2(5) = 9

18 - 10 = 9

8 = 9 (false)

5/5 + 5 = 6

1 + 5 = 6

6 = 6 (ok)

3(5)+ 1 = 9

15 + 1 = 9

16 = 9 (false)

25/5 + 4 = 9

5 + 4 = 9

9 = 9 (ok)

The least amount of extra cash Lilianna requires is $126 and the inequality is [tex]x+$68\geq 194[/tex]

What justifies an inequality?

The relationship between two values in an imbalanced algebraic statement is represented by an inequality in mathematics. One of the two variables can be larger than, more than or equal to, smaller than, or equal to another value by using a sign of inequality.

Let

The least amount of extra money is x.

The fact that

[tex]x+$68\geq 194[/tex]

The problem is represented by inequality.

Solve for x.

[tex]x+$68\geq 194\\x\geq $126[/tex]

The least amount of money Lilianna requires is $126

and inequality is [tex]x+$68\geq 194[/tex]

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The  proportion of the total variation in the sample y-values that can be explained by the estimated linear relationship between x and y is 0.48

Given:

SSR = 1.9350

SST = 4.012

we are asked to find the proportion of the total variation in the sample y-values that can be explained by the estimated linear relationship between x and y.

To find the sample proportion we need to divide.

SSR/SST

= 1.9350/4.012

= 0.48

Hence we get the required answer as 0.48

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Answer:

33.45 is the price of 11 dog food cans

well, let's noticed, the original amount is $271 and 12 years later it turned to $417, so

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$417\\ P=\textit{initial amount}\dotfill &271\\ r=rate\to r\%\to \frac{r}{100}\dotfill &0\\ t=years\dotfill &12\\ \end{cases}[/tex]

[tex]417=271(1 + \frac{r}{100})^{12}\implies \cfrac{417}{271}=\left( \cfrac{100+r}{100} \right)^{12} \implies \sqrt[12]{\cfrac{417}{271}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[12]{\cfrac{417}{271}}=100+r\implies 100\sqrt[12]{\cfrac{417}{271}}-100=r\implies {\Large \begin{array}{llll} \stackrel{\%}{3.657\approx r} \end{array}}[/tex]

The greatest volume of the cone made be 4372.7 m³.

Given, a right triangle whose hypotenuse is 22 m long is revolved about one of its legs to generate a right circular cone.

Let the base of the right triangle be, b

and the height of the right triangle be, h

Using Pythagoras Theorem, we get

22² = b² + h²

484 = b² + h²

Now, the height of the cone be, h and the radius of the cone be, b

Volume of the cone =  1/3πb²h

as, b² = 484 - h²

Volume = 1/3π(484 - h²)h

Volume = 1/3π(484h - h³)

On differentiating, we get

V' = 1/3π(484 - 3h²)

h² = 484/3

h = 22/√3

h = 22√3/3

b = 22√2/√3

Volume = 1/3π(22√2/√3)(22√2/√3)(22√3/3)

Volume = 1/9√3π(22³)(2)

Volume = 4372.7 m³

Hence, the greatest volume of the cone made be 4372.7 m³.

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Answer:

there's no picture

Q=1,Q'=0 as an active-high input s-r latch has a 1 on the s input and a 0 on the r input.

An SR latch (Set/Reset) is an asynchronous device that solely depends on the state of the S and R inputs and does not require any input from the control signals. The illustration demonstrates how two NOR gates with a cross-feedback loop may be used to build an SR latch. Set-reset, or S-R, latches are therefore the most basic type of bistable device. We can connect two NOR gates so that the output of one feeds back into the input of the other, and vice versa, to create an S-R latch, as shown below: The Q and not-Q outputs are supposed to be in opposing states.

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1) $9.27  (far store), $9.87 (near store)

2) $0.169 per mile

3) 4.6 miles , 16.8 miles

4) $0.78, $2.84

5) $10.05 to the far store, $12.71 to the near store

What is Cost?

A mathematical formula known as the cost function is used to graph how production costs will change depending on the output level. To put it another way, it calculates the overall cost of production based on the quantity that is produced.

1) Let's compare chicken costs:

$3.09 * 3 = $9.27  (far store)

$3.29 * 3 = $9.87 (near store)

2) Now let's look at how much it costs to travel in your car:

    [tex]\frac{3.87}{23} = 0.169\ per \ mile[/tex]

           = $0.169 per mile.

3) Next, let's look how much it costs to travel to each store from the gas used. Multiply by 2 because you not only have to drive there, but also back home for the round trip:

2.3 miles * 2 = 4.6 miles

8.4 miles * 2 = 16.8 miles

4) Now to find the cost of gas for the respective trips:

$0.169 * 4.6 = $0.78

$0.169 * 16.8 = $2.84

5) We can just eyeball it from here that it's not worth it to travel, but for completion's sake, let's add the gas and chicken costs together:

$9.27 + $0.78 = $10.05 to the far store

$9.87 + $2.84 = $12.71 to the near store

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After evaluation, the resultant value of the function f(2009) is 1.9021.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Any input for x results in a single output for y.

Considering that x is the input value, we would state that y is a function of x.

So, evaluate f(2009) as follows:

Given that f(x) is a function with all positive real numbers satisfying the requirement that f(x) > 0 and for all x > 0 and also:

[tex]\begin{aligned}&f(x-y)=\sqrt{f(x y)+1} \\&x > 0, y > 0 \\&\text { for, } x=1, \text { and } y=\frac{1}{2} \\&f\left(1-\frac{1}{2}\right)=\sqrt{f\left(1 \times \frac{1}{2}\right)+1} \\&f\left(\frac{1}{2}\right)^2=f\left(\frac{1}{2}\right)+1 \\&f\left(\frac{1}{2}\right)=\frac{1+\sqrt{5}}{2}\end{aligned}[/tex]

Now, consider: x = 2009 and y = 0

[tex]\begin{aligned}&f(2009-0)=\sqrt{f(2009 * 0)+1} \\&f(2009)=\sqrt{f(0)+1} \\&f(2009)=\sqrt{f\left(\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}\right)+1} \\&f(2009)=\sqrt{\sqrt{f\left(\frac{1}{\sqrt{2}} * \frac{1}{\sqrt{2}}\right)+1}+1} \\&f(2009)=\sqrt{\sqrt{f\left(\frac{1}{2}\right)+1}+1} \\&f(2009)=\sqrt{\sqrt{\frac{1+\sqrt{5}}{2}+1}+1} \\&f(2009)=\sqrt{\sqrt{\frac{3+\sqrt{5}}{2}}+1} \\&f(2009)=\sqrt{\sqrt{5.2362}+1} \\&=\sqrt{3.6180} \\&=1.9021\end{aligned}[/tex]

Therefore, after evaluation, the resultant value of the function f(2009) is 1.9021.

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The point of the coordinate plane is ( 0.5 , 1 )

what is coordinate plane ?

The definition of a coordinate plane is as follows: A coordinate plane, often referred to as a rectangular coordinate plane grid, is a two-dimensional plane made up of the Y-axis, a vertical line, and the X-axis, a horizontal line.

solution:

A( -3, -5) and B( 2, 7 ), m:n = 1:1

using section formula

P = [ { (mx2+nx1)/ (m+n) , { (my2+ny1)/ (m+n) }]

  = [ 1(2) + 1(-3) / 2 , 1( 7 ) + 1(-5) / 2 ]

  = ( 0.5 , 1 )

Hence the coordinate plane point is ( 0.5 , 1 )

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The scale factor from the scale drawing to the actual triangle is; 1/3

The area of a triangle is calculated using the formula;

A = ¹/₂bh

Where;

A is area.

b is base.

h is height.

The two sides of the rectangle are 6 units and 3 units. Use the measurements in the formula. "u" is for units.

Thus;

A = ¹/₂(6)(3)  

A = 9 square units

The scale factor, represented by the variable "k", tells you how much a shape enlarged or reduced. If "k" is greater than 1, the shape enlarged. If "k" is greater than 0 and less than 1, the shape reduced

In this case, since the drawing is smaller than the actual triangle, the scale factor will be a fraction less than 1 and greater than 0.

The scale factor is used for side length. When it's used to find a side length, we use "k" multiplied by a side. Since the information we know is area, we find k² first, then isolate "k".

Divide the depicted triangle area by the actual area.

k² = 9 ÷ 81

k² = 1/9

√k² = √(1/9)

k = 1/3

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