A round shaped wall clock frame is made of a steel rod with length of 1.57m. calculate the radius,in m, of the frame.​

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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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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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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Answer:

I hope this helps for you

Answer:

17.85

Step-by-step explanation:

You first divide 12.75 by 5, to see the price for one pound of pretzels. Then, you times that by 7, because you want to know how much it would cost for Lupita to but 7 pounds of pretzels. That would equal 47.85, which is your answer.

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?

The answer is 10,000

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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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]

The player who has the better record between Jamal and Brian as required in the task content is; Jamal.

It follows from the task content that the player who has the better record between Jamal and Brian is to be determined.

Since it is given that Jamal and Brian 7/9 and 5/8 of their free throws respectively;

It follows that when expressed as a percentage; we have;

For Jamal;

7 / 9 × 100% = 77.78%

For Brian;

5 / 8 × 100% = 62.5%.

Ultimately, the player who has the better record for free throws is; Jamal since he has a greater percentage success rate for free throws.

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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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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!

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)

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 18}}{\left( \cfrac{30}{100} \right)18}\implies 5.4[/tex]

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]

Slope of y = 2x +80 is 2, y-intercept is 80, x-intercept is -40.

Slope is defined as how much the y-coordinate changes with respect to the x-coordinate. Slope remains constant anywhere on the line.

Given equation is y = 2x + 80, where y is total amount of spending by tourist in Florida, in billions of dollars and x represents the number of years since 2013.

Equation of a line in slope-intercept form is,

y = mx + c, where m is the slope of the line and c is the y-intercept.

Comparing the given equation with slope-intercept form, we get,

m = 2 and c = 80

Domain of the equation includes number of years from 2013 - 2017 and the range of the equation is the corresponding y values.

Since slope is positive, as x value increases, y value also increases.

x- intercept is the point where the line touches the x-axis. y-coordinate will be zero at that point.

0 = 2x + 80 ⇒ x = -40

For the equation y = 2x +80, slope = 2, y-intercept = 80, x-intercept = -40.

Domain is the set of all number of years from 2013 - 2017 and range is the corresponding amount spend by tourist in the years from 2013-2017. As x value increases, y value also increases.

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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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Answer:

12.78

Step-by-step explanation:

He has 25.65, sold 3.87. 25.65-3.87=21.78

The total number of games would be 15 games.

What are the Permutation and Combination?

Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.

Consider each team playing with the other team once

Total number of games scheduled = Number of ways of selecting 2 from 6 teams

               [tex]=^nC_r\\\\=^6C_2\\\\=\frac{6!}{2!*4!}\\\\=15[/tex]

Hence the total number of games would be 15 games.

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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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The function in the graph is y = x² - 1 and the inverse of the function is y = √(x + 1) and the graph is attached

Examining the graph the vertex is v(h, k) = (0, -1)

Quadratic equation is of the form

y = a(x + h)² + k

using the vertex we write the equation as

y = a(x + 0)² - 1

using point (1, 0) a is calculated

0 = a(1 + 0)² - 1

a = 1

The equation of the graph is

y = a(x + 0)² - 1

y = x² - 1

The domain of the equation is all real numbers and the range is calculated from the inverse

x = √(y + 1)

y + 1 ≥ 0

y ≥ -1

Inverse function

y = x² - 1

x² = y + 1

x = ±√(y + 1)

exchanging the variables

y = ±√(x + 1)

taking the positive function

y = √(x + 1)

here the domain and range is exchanged

range: all real numbers

domain: x  ≥ -1

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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

Answer:

CPCTC

Step-by-step explanation:

BD is perpendicular to AC, forming two right triangles. The hypotenuses are congruent, as is our leg that we will call b. If we use Law of Sines to find our angles a and c (no matter the values), we would find that because b is the same leg in both triangles and the hypotenuses are congruent, angles a and c are congruent, so therefore your missing angle in both triangles is congruent, and using a trig function will find that AD and CD are congruent, making all of both triangles congruent.

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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Answer:

x=2

Step-by-step explanation:

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

x= 2

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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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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Answer:

there's no picture

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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