The digit 3 in 5,630, is 10 times the value of the digit 3 in 342.

For part a, you can use a chi-squared test to determine whether the variance in the sample exceeds the maximum acceptable variance in the population.

The null hypothesis for this test is that the variance in the sample is equal to or less than the maximum acceptable variance, and the alternative hypothesis is that the variance in the sample is greater than the maximum acceptable variance.

To perform the test, you need to first calculate the chi-squared statistic, which is given by:

X² = (n-1) * s² / σ²

where n is the sample size (in this case, 15), s is the sample standard deviation (in this case, 0.014 inches), and σ is the maximum acceptable variance (in this case, 0.0001 inches).

Plugging in the values, you get:

X² = (15-1) * .014² / .0001² = 27.44

Next, you need to determine the degrees of freedom for the test. In this case, the degrees of freedom is equal to the sample size minus 1, so the degrees of freedom is 14.

With the chi-squared statistic and the degrees of freedom, you can look up the p-value in a chi-squared table or use a chi-squared calculator to determine the p-value. The p-value is the probability of observing a chi-squared statistic as large or larger than the one you calculated, assuming the null hypothesis is true.

If the p-value is less than the significance level (in this case, .10), then you can reject the null hypothesis and conclude that the variance in the sample exceeds the maximum acceptable variance. In this case, the p-value is between 0.01 and 0.025, so you can reject the null hypothesis and conclude that the variance in the sample exceeds the maximum acceptable variance.

For part b, you can use a t-test to construct a 90% confidence interval estimate of the variance in the population. The confidence interval is an interval estimate of the true variance in the population, and the 90% confidence level means that there is a 90% probability that the true variance in the population falls within the confidence interval.

To construct the confidence interval, you first need to calculate the standard error of the variance, which is given by:

SE = s / √(n-1)

where s is the sample standard deviation and n is the sample size. Plugging in the values, you get:

SE = 0.014 / √(15-1) = 0.0041

Next, you need to determine the t-value for the confidence interval. The t-value is based on the degrees of freedom and the confidence level. With 14 degrees of freedom and a 90% confidence level, the t-value is 1.76.

With the standard error and the t-value, you can construct the confidence interval as follows:

Lower bound = s² - t * SE = .014² - 1.76 * 0.0041 = 0.00012 inches

Upper bound = s² + t * SE = .014² + 1.76 * 0.0041 = 0.00042 inches

Therefore, the 90% confidence interval estimate of the variance of the ball bearings in the population is .00012 to .00042 inches.

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Answer:

Final mixture is 120 gm

x = 10%      then   (120-x) = 25%

.25(120-x)    + .1 (x)    =  .15 (120)       solve for x= 10% amount

                                                                 then  25% amount = 120-x

Step-by-step explanation:

\(1.4 < \sqrt{2} < 1.5\hspace{5em}1.7 < \sqrt{3} < 1.8 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllll} 1.7& < &\sqrt{3}& < &1.8\\\\ 1.7-\sqrt{2}& < &\sqrt{3}-\sqrt{2}& < &1.8-\sqrt{2}\\\\ 1.7-1.5& < &\sqrt{3}-\sqrt{2}& < &1.8-1.4\\\\ 0.2& < &\sqrt{3}-\sqrt{2}& < &0.4 \end{array}\)

we're subtracting the upper-bound of √2, so is the most we can subtract from 1.7, and we're subtracting the lower-bound of √2 from 1.8, that way the resultant is within range.

The mean is  2,071,798.33

The Median is 1,485,552

The range is 7,425,310

The standard deviation is given as 1961105.68

Mean = (Sum of all populations) / (Number of cities)

= (8,336,817 + 979,576 + 2,693,976 + 2,320,268 + 1,680,992 + 1,584,064 + 1,547,253 + 1,423,851 + 1,343,573 + 1,021,795 + 978,908 + 911,507) / 12

= 24,861,580 / 12

= 2,071,798.33

To find the median, we need to arrange the populations in increasing order and find the middle value. If we arrange these values, we get:

911,507, 978,908, 979,576, 1,021,795, 1,343,573, 1,423,851, 1,547,253, 1,584,064, 1,680,992, 2,320,268, 2,693,976, 8,336,817

Since there are 12 cities (an even number), the median would be the average of the 6th and 7th values:

Median = (1,423,851 + 1,547,253) / 2

= 1,485,552

The mode isn't applicable here as no city population repeats.

The range is the highest population minus the lowest population:

Range = 8,336,817 - 911,507

= 7,425,310

Standard deviation  =  (911507- 2068548.3333333)² +  (978908 - 2068548.3333333)² + (979576  - 2068548.3333333)²  + ( 1021795 -  2068548.3333333)² +  (1343573- 2068548.3333333)²  +( 1423851- 2068548.3333333)² + (1547253- 2068548.3333333)² +( 1584064- 2068548.3333333)² + (1680992- 2068548.3333333)² + ( 2320268- 2068548.3333333)²  +(2693976- 2068548.3333333)² +( 8336817 - 2068548.3333333)² / 12

= 46151226311869 / 12

=  3845935525989.1

\(standard deviation = \sqrt{ 3845935525989.1}\)

=  1961105.6896529

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Answer:

S₂₇ = 1188

Step-by-step explanation:

using the given formula for \(S_{n}\) , that is

\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )

with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then

S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188

Answer:

38.9

Step-by-step explanation:

Answer:

y= 2x + 4

x = 4 + 2

x = 6

Step-by-step explanation:

is it helpful please tell in comments

The probability that she catches 2 gold neon tetras is 10/500 or 2%.

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2 pounds 6 ounces in ounces is equivalent to 38 ounces.

The given measurement is -

2 pounds 6 ounces

In 1 pound, there are 16 ounces.

So, we can write that -

2 pounds 6 ounces = 2 x 16 + 6

2 pounds 6 ounces = 38 ounces

So, 2 pounds 6 ounces in ounces is equivalent to 38 ounces.

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Answer:

Step-by-step explanation:

y

=

1

3

x

−

3

Use the slope-intercept form to find the slope and y-intercept

Slope:

1

3

y-intercept:

(

0

,

−

3

)

Any line can be graphed using two points. Select two

x

values, and plug them into the equation to find the corresponding

y

values.

x

y

0

−

3

3

−

2

Graph the line using the slope and the y-intercept, or the points.

Slope:

1

3

y-intercept:

(

0

,

−

3

)

x

y

0

−

3

3

−

2

image of graph

A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

Answer:

x-3+(8+3*(x+5))

Step-by-step explanation:

This might be incorrect!

I still hope this helps!

The algebraic expression of the given statement could be x-3+(8+3*(x+5)).

WE can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4.

If something is for example, doubled, then you can multiply that thing by 2 and so on  methods can be used to convert description to mathematical expressions.

WE have been given The sum of a number decreased by three, and eight more than the quotient of triple the number and five.

Then an algebraic expression could be;

x-3+(8+3*(x+5))

Therefore, the algebraic expression of the given statement could be x-3+(8+3*(x+5)).

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Step-by-step explanation:

Given :-

And we need to find the slope intercept form of the line . The slope intercept form of a line is y = mx + c , where m is the slope and c is the y intercept. Substitute respective values ,

Solution 1 :-

\(:\implies\) y = mx + c

\(:\implies\) y = 1/4 x + 4

\(:\implies\) 4y = x + 16

\(:\implies\) x - 4y + 16 = 0

Solution 2 :-

\(:\implies\) y - 5 = -4( x +1)

\(:\implies\) y -5 = -4x -4

\(:\implies\) y = -4x +1

Answer:

∠ x = 58°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠  BAD is an exterior angle of the triangle , then

x + 56° = 114° ( subtract 56° from both sides )

x = 58°

Answer:

x/3 + 6 = 14

Step-by-step explanation:

Answer:

88

Step-by-step explanation:

the values of a, m, and x will be √5, 3√5, and 2 respectively.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, A big right triangle has three other right triangles in it.

Since, In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem

For the smallest right triangle,

Hypotenuse = 3

thus,

3² = 2² + a²

a² = 9 - 4

a² = 5

a = √5

For the medium size triangle,

Hypotenuse = 3 + 6 = 9

Other side = 2 + 4 = 6

Base = m

Thus,

9² = 6² + m²

m² = 81 - 36

m² = 45

m = 3√5

For the biggest triangle,

hypotenuse = 3 + 6 + 3 = 12

Height = 2 + 4 + x = 6 + x

base = 5

Since the given triangle is congruent to the smallest triangle,

(6 + x)/ 12 = 2/3

6 +x = 8

x = 2

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Answer:

A.P. : 10, 20, 30, 40, 50

G.P. : 5, 10, 20, 40, 80 .

Step-by-step explanation:

It is given that fourth term of a sequence is 40.

It is not given that whether the sequence is A.P. or G.P.

We need to write two different sequences that satisfy the given condition.

For A.P.,

Required sequence : 10, 20, 30, 40, 50

Here, first term is 10, common difference is 10.

For G.P.,

Required sequence : 5, 10, 20, 40, 80

Here, first term is 5, common ratio is 2.

Therefore, the two sequences are 10, 20, 30, 40, 50  and 5, 10, 20, 40, 80 .

Answer:

Is this a question or free kaching  if it is a question what are we trying to answer. We need details

Step-by-step explanation:

The number of loaf of bread she can make is 13 loaves.

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Here, we have

Given: A baker has 85 cups of flour to make bread. She uses 6 1/4 cups of flour for each loaf of bread.

A = 85 cups

r =  6 1/4 cups

The number of loaf of bread she can make can be calculated by dividing the total amount of flour by the amount of flour per bread;

n = A/r

n = 85/6.25

n = 13.6

Hence, the number of loaf of bread she can make is 13 loaves.

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A point on the scatter plot is defined as (19, 3), which means that an input of 19 is mapped to an output of 3.

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(Input, Output).

One point on the scatter plot for this problem has the coordinates given as follows:

(19, 3).

Hence the meaning is that an input of 19 is mapped to an output of 3.

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Answer:

C. The students would prefer to play sports over going to school

Step-by-step explanation:

Hope this helps :)

can u brainlist

The maximum value of the function f (x) = -1.8x² + 7x - 11 to the nearest hundredth is,  - 4.19.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The function is,

⇒ f (x) = -1.8x² + 7x - 11

Now, We can differentiate with respect to x as;

⇒ f ' (x) = - 1.8 × 2x + 7 × 1 - 0

⇒ f ' (x) = - 3.6x + 7

Put f ' (x) = 0

⇒ - 3.6x + 7 = 0

⇒ 3.6x = 7

⇒ x = 1.94

Now, Again differentiate with respect to x as;

⇒ f ' (x) = - 3.6x + 7

⇒ f '' (x) = - 3.6 × 1 + 0

⇒ f '' (x) = - 3.6 < 0

Hence, Substitute x = 1.94 in function to get maximum value,

⇒ f (x) = -1.8x² + 7x - 11

⇒ f (x) = -1.8 (1.94)² + 7 × 1.94 - 11

⇒f (x) = - 6.77 + 13.58 - 11

⇒ f (x) = - 4.19

Thus, The maximum value = - 4.19

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Answer:

\(17.20 \div 21.5 = \)

The required unit of the price of the wire is given as $ 0.8 per centimeter.

Given that,
Leila purchased 21.5 centimeters of wire for $17.20. To find the unit price in dollars per centimeter.

Rate of change is defined as the change in value with respect to another entity is called rate of change.

Here,
The total length of the wire = 21.5 centimeters.
The total cost of the wire = $17.20
Unit price = 17.20 / 21.5 = $0.80 per centimeter.

Thus, the required unit of the price of the wire is given as $ 0.8 per centimeter.

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Answer: 68y+106=36-y

The derivative of cosec²3x is \(-2 \ cosec^2{3x} \ cot3x\).

In mathematics, a derivative of any function can be defined as the rate of change of any function with respect to a given variable. or we can say that a derivate defines the measure of change with respect to the change in the input or any argument of that function.

If f of x is the function then the derivative of that function is denoted as :

\(\frac{d}{d(x)} f(x)\)

Important Formulas of derivative :

\(\frac{d}{dx} (constant) = 0\\ \\\frac{d}{dx} (x^n) = nx^{n-1}\\\\\frac{d}{dx} (sinx) = cosx\\\\\frac{d}{dx} (cosx) = -sinx\\\\\frac{d}{dx} (tanx) = sec^2x\\\\\frac{d}{dx} (cosecx) = -cosecx.cotx\\\\\frac{d}{dx} (logx) = \frac{1}{x}\)

In the given question

function is , cosec²3x

use the formula \(\frac{d}{dx} (x^n) = nx^{n-1}\)

\(\frac{d}{dx} (cosec^2{3x}) = 2 cosec 3x . \ \frac{d}{dx} (cosec{3x})\)

now, use \(\frac{d}{dx} (cosec{x}) =- cosecx . cotx\)

\(\frac{d}{dx} (cosec^2{3x}) = 2 cosec{ 3x} . (-cosec 3x.cot3x) \\\)

                    =  \(-2 \ cosec^2{3x} \ cot3x\).

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1. There are two performance obligations in a contract to buy a pair of SunBoots from Clarks Inc: Delivery of Sunboots and Discount Coupon.

2. The journal entry to record the revenue for the sale of 1,000 pairs of SunBoots when Clarks cannot estimate the standalone selling price of a pair of SunBoots sold without a coupon is as follows:

Debit Cash $70,000

Credit Sales Revenue $65,800

Credit Deferred Revenue from Discount Coupon $4,200

(To record the sale of 1,000 pairs of SunBoots, including the discount coupon.)

Performance obligations refer to distinct goods and services agreed to be provided in a contract between the two parties.

Performance obligations arise because each separate goods or services benefit the customer distinctly from others.

In accounting for the revenue or costs, efforts should be geared toward recognizing the activity as soon as they bestow or transfer economic benefits to the buyer.

Selling price per pair = $70

Discount coupon = 30%

Estimated percentage of customers who will utilize the coupon = 20%

The number of SunBoots sold = 1,000

Cash $70,000 Sales Revenue $65,800 Deferred Revenue from Discount Coupon $4,200 ($70,000 x 30% x 20%)

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