The following data represent the age (in weeks) at which babies first crawl based on a survey of 12 mothers. The data are normally distributed and s=9.904 weeks. Construct and interpret a 90% confidence interval for the population standard deviation of the age (in weeks) at which babies first crawl. 31 39 36 38 51 48 55 Click the icon to view the table of critical values of the chi-square distribution. choice.
Select the correct choice below and fill in the answer boxes to complete your
(Use ascending order. Round to three decimal places as needed.) O
A. If repeated samples are taken, 90% of them will have the sample standard deviation between ___ and___
B. There is a 90% probability that the true population standard deviation is between ___ and ___
C. There is 90% confidence that the population standard deviation is between and___ and ___​

Answer:

b

Step-by-step explanation: got it right on edge

Answer:

B

Step-by-step explanation:

got it right on edge

Step-by-step explanation:

Taking the provided equation ,

\(\implies \dfrac{3x+4}{5}-\dfrac{2}{x+3} =\dfrac{8}{5} \)

1) Here denominator of two fractions are 5 and x +3 . So their LCM will be 5(x+3)

\(\implies \dfrac{(x+3)(3x+4)-(2)(5)}{5(x+3)}=\dfrac{8}{5} \)

2) Transposing 5(x+3) to Right Hand Side . And 5 to Left Hand Side .

\(\implies 5(3x^2+4x+9x+12 -10) = 40(x+3)\)

3) Multiplying the expressions.

\( \implies 5(3x^2+13x+2) = 40x + 120 \)

4) Opening the brackets .

\(\implies 15x^2+ 65x + 10 = 40x + 120 \)

5) Transposing all terms to Left Hand Side .

\(\implies 15x^2 + 65x - 40x + 10 - 120 = 0 \\\\\implies 15x^2 +25x - 110 = 0\)

6) Solving the quadratic equation .

\(\implies 5(3x^2+5x -22) = 0 \\\\\implies 3x^2+13x-22 = 0 \\\\ \implies x = \dfrac{-b\pm \sqrt{b^2-4ac}}{4ac} \\\\\implies x = \dfrac{-5\pm \sqrt{5^2-4(-22)(3)}}{2(3)} \\\\\implies x = \dfrac{-5\pm \sqrt{289}}{6}\\\\\implies x =\dfrac{-5\pm 17}{6} \\\\\implies x = \dfrac{17-5}{6},\dfrac{-17-5}{6}\\\\\implies x = \dfrac{12}{6},\dfrac{-22}{6} \\\\\underline{\boxed{\red{\bf\implies x = 2 , \dfrac{-11}{3}}}}\)

Answer:

\(x=2\\x=-\frac{11}{3}\)

Step-by-step explanation:

Solve the rational equation:

\(\displaystyle \frac{3x+4}{5}-\frac{2}{x+3}=\frac{8}{5}\)

To eliminate denominators, multiply by 5(x+3) (x cannot have a value of 3):

\(\displaystyle 5(x+3)\frac{3x+4}{5}-5(x+3)\frac{2}{x+3}=5(x+3)\frac{8}{5}\)

Operate and simplify:

\(\displaystyle (x+3)(3x+4)-5(2)=(x+3)(8)\)

\(\displaystyle 3x^2+4x+9x+12-10=8x+24\)

Rearranging:

\(\displaystyle 3x^2+4x+9x+12-10-8x-24=0\)

Simplifying:

\(\displaystyle 3x^2+5x-22=0\)

Rewrite:

\(\displaystyle 3x^2-6x+11x-22=0\)

Factoring:

\(\displaystyle 3x(x-2)+11(x-2)=0\)

\(\displaystyle (x-2)(3x+11)=0\)

Solving:

\(x=2\\x=-\frac{11}{3}\)

After answering the presented question, we can conclude that This is equation true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3): a = 30.8/(11n+3)

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

We are given that the factored form of 30.8n+8.4 is a(11n+3).

To find the value of a, we can expand the product a(11n+3) and equate it to the given expression 30.8n+8.4.

Expanding a(11n+3), we get:

a(11n+3) = 11an + 3a

Equating this to 30.8n+8.4, we have:

11an + 3a = 30.8n + 8.4

We can factor out an "a" from the left-hand side:

a(11n + 3) = 30.8n + 8.4

Now we can see that this is the same as the given factored form, so we can equate the two expressions:

a(11n + 3) = a(11n + 3)

This is true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3):

a = 30.8/(11n+3)

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Answer:

five trucks per hour

Step-by-step explanation:

The answer is \(y^{4+6}\) = \(y^{10}\)

CuI's molar solubility is determined to be 1.27 x 10⁻¹².

The quantity of ions dissolved per litre of solution is measured by molar solubility. The quantity of ions that are dissolved in this situation's amount of solvent is represented as solubility.

Think about the equation.

Cu+(aq) CuI.(s) + I- (aq)

Let's assume that CuI (s) has a molar solubility of "S" mol/L.

Thus,

Product of solubility = [Cu+(aq)] + [ I-(aq)] → [Cu+(aq)] Ksp

[ I-(aq)] ———(1)

We are aware of

For CuI, the solubility product Ksp is 1.27 x 10⁻¹².

Consequently, from equation (1)

1.27 × 10⁻¹² = S.S

S² =1.27 × 10⁻¹²

= (1.27 × 10⁻¹² )½ = 1.127 x 10⁻⁶ M

Therefore, CuI has a molar solubility of 1.127 x 10-6 M.

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The number of red balls to the number of green balls is 3 : 2

The distribution of the balls is given as:

6 red, 4 green, 2 yellow and 3 blue balls

The number of red balls to the number of green balls is represented as:

Ratio = Red : Green

So, we have:

Ratio = 6 : 4

Simplify

Ratio = 3 : 2

Hence, the number of red balls to the number of green balls is 3 : 2

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Answer:

see explanation

Step-by-step explanation:

(a)

given y is inversely proportional to x² then the equation relating them is

y = \(\frac{k}{x^2}\)

to find k use any ordered pair from the table

using (1, 4 ) and substituting into equation

4 = \(\frac{k}{1^2}\) = \(\frac{k}{1}\) , thus

k = 4

y = \(\frac{4}{x^2}\) ← equation of proportion

(b)

when y = 25 , then

25 = \(\frac{4}{x^2}\) ( multiply both sides by x² )

25x² = 4 ( divide both sides by 25 )

x² = \(\frac{4}{25}\) ( take square root of both sides )

x = ± \(\sqrt{\frac{4}{25} }\) = ± \(\frac{2}{5}\)

then

positive value of x when y = 25 is x = \(\frac{2}{5}\)

=================================================

Explanation:

Let's consider the expression (x-y)^2. It expands out to x^2-2xy+y^2. The terms are:

Each of those terms either has a single variable with an exponent of 2, or has the exponents add to 2. Think of 2xy as 2x^1y^1.

In short, this means that the degree of each monomial term is 2.

----------

Now consider (x-y)^3. It expands out into x^3-3x^2y+3xy^2+y^3.

We have terms that either have a single variable and the exponent is 3, or the exponents add to 3. The degree of each term is 3.

----------

This pattern continues.

In general, for (x-y)^n, where n is any positive whole number, the degree of each term in the expansion is n. If you picked any term, added the exponents, then the exponents will add to n.

1.The measure of the central angle is 90°.

2.Equation of x=12.

3.The measure of the angle that bisects the minor arc is 45°.

4.The measure of the major arc is 270°.

The circle in the example illustration has a radius of 10 units and a centre of O. AOB is a central angle that the minor arc AB intercepts.

The fact that the measure of a central angle is equal to the measure of its intercepted arc can be used to determine the measure of the central angle. So, we must determine the minor arc's measure, AB. The circle's diameter is 2r = 20 units because its radius is 10 units. The minor arc AB is one-fourth of the circle's circumference, or (1/4) * 20 = 5 units. As a result, the minor arc's measure is 5 radians.

Radians to degrees conversion

5π * (180/π) = 90° degrees

Therefore, the measure of the central angle AOB is 90° degrees.

To find  Equation of x,

8x=96°

x=96°/8

x=12

Hence, Equation of x will be 12.

The angle that bisects the minor arc AB is half the measure of the central angle AOB. So, the measure of the bisecting angle is:

(1/2) * 90° = 45°

The major arc ACB is the difference between the circumference of the circle and the minor arc AB. So, the measure of the major arc ACB is:

2πr - 5π = 15π

for major arc,

We must multiply by (180/) degrees/radian in order to convert the measure from radians to degrees. The main arc ACB's degree measurement is as follows:

15π * (180/π) = 270°

Therefore, the measure of the major arc ACB is 270°.

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All the three locations has been checked below.

Using Pythagoras theorem,

12² = 8² + x²

144 - 64 = x²

x= √80

x=8.9

Now, using Trigonometry

tan F = P/B

tan F= 8/8.9

and, sin F = P/H

      sin F= 8/12 = 2/3

and, cos F = B/H

        cos F= 12/8.9

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Answer:

y = x + 60

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (20, 80) and (x₂, y₂ ) = (40, 100) ← 2 points on the line

m = \(\frac{100-80}{40-20}\) = \(\frac{20}{20}\) = 1

the line crosses the y- axis at (0, 60 ) ⇒ c = 60

y = x + 60 ← equation of line

You have a rectangle around a rectangle.  Since you have

the pool plus deck as having length = (x+25) and width = (x+9)

then x is twice the width of the deck. However, the equation for the total area of pool and deck is still area = length*width

y = (x+25)(x+9)

y = x2 + 9x + 25x + 225

y = x2 + 34x + 225  where x represents twice the width of the deck

9514 1404 393

Answer:

  96 cubic feet

Step-by-step explanation:

A volume that is 16 ft by 18 ft by 1/3 ft will be ...

  V = LWH

  V = (16 ft)(18 ft)(1/3 ft) = 96 ft³

96 cubic feet of concrete are needed.

Answer:

Hi

Please mark brainliest ❣️

Answer:

x^2*x^-12= 1/x^10

D

Step-by-step explanation:

The correct answer is option D, which is 105, 90, 75, 60, 45.

Answer:

-18 is an integer but not a whole number

Step-by-step explanation:

a whole number is only positive numbers and 0 itself while an integer is basically any number that isn't a decimal or a fraction. -18 is an integer, but it can't be a whole number because it is a negative number.

The correct options for folded and assembled into a triangular prism are;

Option A and Option D.

What is Triangle?

A triangle is a three sided polygon, which has three vertices and three angles.

Given that;

The triangular prism figure after fold is given.

Now, The triangular prism figure is contain two triangles and three squares.

So, In option A;

There are two triangles and three squares.

And, In option D;

There are two triangles and three squares.

Thus, The correct options for folded and assembled into a triangular prism are;

Option A and Option D.

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Answer:

  4 and 5

Step-by-step explanation:

For answering questions like this, it can be useful to remember a few of the powers of small integers:

  2^4 = 16

  2^5 = 32

A logarithm can be considered to be an exponent of the base.

  \(\log_b(x) = a \ \Longleftrightarrow\ b^a=x\)

The ordering of powers of 2 relative to the number of interest (17) is ...

  16 < 17 < 32

  2⁴ < 17 < 2⁵ . . . . . . . . . . . . . . . . . . . expressed as powers of 2

  log₂(2⁴) < log₂(17) < log₂(2⁵) . . . . . log₂ of the above inequality

  4 < log₂(17) < 5 . . . . . . . . . . . . . . . . showing the values of the logs

Log₂(17) lies between 4 and 5.

__

Additional comment

Using the "change of base" formula, you can use a calculator to find the value of log₂(17). It shows you the value is between 4 and 5.

  log₂(17) = log(17)/log(2) . . . . . . using logs to the same base

Given dimensions of the room:

Length: \(\displaystyle\sf 12.5 \,m\)

Width: \(\displaystyle\sf 9 \,m\)

Height: \(\displaystyle\sf 7 \,m\)

Area of each wall:

\(\displaystyle\sf Area_1 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_2 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_3 = 9 \times 7 = 63 \,m^2\)

\(\displaystyle\sf Area_4 = 9 \times 7 = 63 \,m^2\)

Area of each door:

\(\displaystyle\sf Area_{\text{door}} = 2.5 \times 1.2 = 3 \,m^2\)

Area of each window:

\(\displaystyle\sf Area_{\text{window}} = 1.5 \times 1 = 1.5 \,m^2\)

Total area occupied by doors:

\(\displaystyle\sf Total_{\text{doors}} = 2 \times Area_{\text{door}} = 2 \times 3 = 6 \,m^2\)

Total area occupied by windows:

\(\displaystyle\sf Total_{\text{windows}} = 4 \times Area_{\text{window}} = 4 \times 1.5 = 6 \,m^2\)

Total wall area excluding doors and windows:

\(\displaystyle\sf Total_{\text{wall\,area}} = (Area_1 + Area_2 + Area_3 + Area_4) - Total_{\text{doors}} - Total_{\text{windows}}\)

\(\displaystyle\sf = (87.5 + 87.5 + 63 + 63) - 6 - 6\)

\(\displaystyle\sf = 275 - 6 - 6\)

\(\displaystyle\sf = 263 \,m^2\)

Cost of painting the walls:

\(\displaystyle\sf Cost_{\text{painting}} = Total_{\text{wall\,area}} \times 3.50\)

\(\displaystyle\sf = 263 \times 3.50\)

\(\displaystyle\sf = 920.50 \,Rs\)

Therefore, the cost of painting the walls of the room at Rs. 3.50 per square meter is Rs. 920.50.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The slope which shows  the cost per guest is $35 per guest

The given cost for 50 guests is $2150.

The cost for 75 guests is $3025.

It can also be represented as:

(Guest, Cost) =(50, $2150) & (75, $3025)

The slope can now be calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (50, $2150) & (75, $3025)

Substituting the given values in the equation as follows:

Slope = (3025 - 2150)/(75 - 50)

Slope = 35

Hence, the slope is $35 per guest.

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Answer:

Option D.   \(g(x)=5(0.8)^{x}+2\)

Step-by-step explanation:

Main concepts

Concept 1: identifying horizontal asymptote

Concept 2: assuring decreasing exponential function

Concept 1. identifying horizontal asymptote

Any exponential function of the form \(y=a*b^x\) has a horizontal asymptote on the x-axis.  A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number.  Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units.  Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.

Concept 2. assuring decreasing exponential function

Exponential functions of the form \(y=a*b^x\) increase or decrease based on the value of "b".

Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.

To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.

Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.

Answer:

9 +10=21

Step-by-step explanation:

Looking at the distribution sets 1-8 the one that seems to be closest to the mean is distribution 1 because all the data of distribution 1 lie on 5.

The distribution closest to the mean is determined by comparing the mean of the dataset, to the given mean.

The mean of the various distributions is determined as;

Distibution 1; mean = (9 x 5) = 45/9 = 5

Distibution 2; mean = (2x3  + 3 +  4x2  +  8 + 9 + 11) /9 = 5

Distibution 3; mean = (2x3  +  4x2  +  5 + 7 + 9 + 10) /9 = 5

Distibution 4; mean = (2x3  +  4x2  +  5 + 7 + 9 + 10) /9 = 5

The mean of the remaining distributions, from 5 to 8 is also 5, as already given in the statement.

If we look at all the distributions, we would see that, all the data of distribution 1 lie on 5, making it the most closest the mean of the distribution.

Thus, looking at the distribution sets 1-8 the one that seems to be closest to the mean is distribution 1 because all the data of distribution 1 lie on 5.

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We were told that he can buy 2 apples for $1.5, it means that the cost per apple is

1.5/2 = $0.75 per apple

For the second option, He can buy 6 apples for $4.50. It means that the cost per apple is

4.5/6 = $0.75

The cost per apple is the same for both options

Answer:

B. 3/5

Step-by-step explanation:

Answer:

hii

Step-by-step explanation:

3(x-2)-2x+3=-12

3 times x = 3x

3 times -2 = -6

3x-6-2x+3=-12

3x + 2x = 5x

-6 + 3 =-3

i don't know the rest I'm sorry