the american management association is studying the income of store managers in the retail industry. a random sample of 49 managers reveals a sample mean of $45,420. the standard deviation of the population is $2,050. using a 95% level of confidence, what is the confidence interval for the population mean?

The measure of < BAP in the figure of the circle is 30 degrees

< ACB covers same angle as < APB

therefore

< ACB = < BAP = 120

complete the line PB to form another radius. since radius of a circle are equal, an isosceles triangle is created

Isosceles triangle has a unique  property of 2 equal equal sides and equal base angles. one of the angles of the isosceles triangle is < BAP

solving with the new triangle APB

< BAP = < PBA (base angles of isosceles triangle)

< BAP + < PBA + 120 = 180

2 < BAP = 180 - 120

2 < BAP = 60

< BAP = 30 degrees

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Answer:

What you need to do is match with one is a regular, irregular, and or not a polygon.


Each shape has a label like A is a triangle and so on

Put the Label of the shape where it belongs inside the chart

Answer:

If all the sides and interior angles of the polygons are equal, they are known as regular polygons.

C and E are regular polygons.

Irregular polygons are those types of polygons that do not have equal sides and equal angles.

A, B and F are irregular polygons.

3D shapes are irregular polygons.

D is an irregular polygon.

Step-by-step explanation:

In two - factor ANOVA , if there is significant interaction effect then Not necessary that main effects of both factors a and b is significant.

A two- way ANOVA (analysis of variance) is a statistical test used to analyze the difference in means of three or more groups.

Two-Way ANOVA is used to estimate how the mean of a quantitative variable varies according to the levels of two categorical variables. Use two-way ANOVA when you want to know how the combination of two independent variables affects the dependent variable.

Interaction effects occur when the effect of one variable depends on the value of another variable. Interaction effects are common in ANOVA and designed experiments.

We see that interaction effect in ANOVA test is significant . but interaction effect significant is not implies the significance of main effects of factors a and b. So, we conclude that main effects of factor a and b need not be significant.

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Answer:

y = [tex]\frac{1}{3}[/tex] x + 8

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 )

y = - 3x + 2 ← is in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]

the line crosses the y- axis at (0, 8 ) ⇒ c = 8

y = [tex]\frac{1}{3}[/tex] x + 8 ← equation of perpendicular line

The addition of the decimals given as 3.8 and 2.7 will be 6.5.

Decimals simply means the numbers that are not whole numbers. They consist of whole numbers and fractions. Examples include 3.6, 2.1 eyc.

In this case, we want to find the value of 3.8 and the addition to 2.7. This will be:

= 3.8 + 2.7

= 6.5

Therefore, the value is 6.5.

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Sylvia needs tο cοmplete the remaining 7.5 laps in an average time οf 68 secοnds οr less tο break the natiοnal recοrd.

Time is the duratiοn between twο events, speed is the rate at which distance is cοvered per unit time, and distance is the amοunt οf space between twο οbjects οr pοints.

Sylvia has cοmpleted the first 5 laps in a tοtal time οf 5 x 73 secοnds = 365 secοnds.

Tο break the natiοnal recοrd οf 14 minutes 35 secοnds (οr 875 secοnds) fοr running 5000m, Sylvia has 5000m - 5 laps (οf 400m each) = 3000m remaining tο run, which is equivalent tο 7.5 laps (since each lap is 400m).

Let's say Sylvia needs tο cοmplete the remaining 7.5 laps in x secοnds.

Tο break the natiοnal recοrd, the tοtal time fοr running 12.5 laps (οr 5000m) shοuld be 875 secοnds οr less. Sο, we can set up the fοllοwing equatiοn tο find the required average lap time fοr the remaining 7.5 laps:

365 secοnds + 7.5x secοnds ≤ 875 secοnds

Subtracting 365 secοnds frοm bοth sides gives:

7.5x secοnds ≤ 510 secοnds

Dividing bοth sides by 7.5 gives:

x secοnds ≤ 68 secοnds

Sο, Sylvia needs tο cοmplete the remaining 7.5 laps in an average time οf 68 secοnds οr less tο break the natiοnal recοrd.

Therefοre, the answer is 68 secοnds.

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The equivalents of the functions are f(x)+g(x) = -2x²-x+6, g(x) - f(x) =   -2x²-5x+2, f(x).g(x) = -6x³-10x²+8x+8, h(x)-f(x) = 3x²-7x-2, f(x).h(x) = 9x³-6x²-8x and f(x)+g(x)+h(x) = x²-3x+6

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

Given: f(x)  = 3x + 2, g(x) = -2x²-2x+4 and h(x) = 3x²-4x

To solve this problem, just substitute the value of the function and perform the necessary operations on them.

f(x)+g(x)  = (3x+2) + (-2x²-2x+4)

            =  3x+2-2x²-2x+4

           =  -2x²-x+6

g(x) - f(x) = (-2x²-2x+4) - (3x+2)

              =  -2x²-2x+4-3x-2

             =   -2x²-5x+2

f(x).g(x)  = (3x+2)(-2x²-2x+4)

             = -6x³-6x²+12x -4x²-4x+8

            =  -6x³-10x²+8x+8            

h(x) - f(x) = (3x²-4x) - (3x + 2)

             = 3x²-4x-3x-2

             = 3x²-7x-2

f( x) . h(x) = (3x + 2)(3x²-4x)

              = 9x³-12x²+6x²-8x

              = 9x³-6x²-8x

f(x)+g(x)+h(x) = (3x + 2) + (-2x²-2x+4) + (3x²-4x)

                    = 3x+2-2x²-2x+4+3x²-4x

                    = x²-3x+6

Therefore, the equivalents are f(x)+g(x) = -2x²-x+6, g(x) - f(x) =   -2x²-5x+2, f(x).g(x) = -6x³-10x²+8x+8, h(x)-f(x) = 3x²-7x-2, f(x).h(x) = 9x³-6x²-8x and f(x)+g(x)+h(x) = x²-3x+6. You should match them accordingly

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Answer:

b.  12, 17, 23

Step-by-step explanation:

Look at the differences between the numbers.

Number   Difference

2                  

3                      1

5                      2

8                      3    The difference increase by 1 at each step.  The next 3 increase would be:

                        4

                        5

                        6

The next three numbers are:

12                       4

17                        5

23                       6

Answer:

b.

12, 17, 23

Step-by-step explanation:

The diagonals of a square are equal to each other

Let ABCD be a square.

We need to prove that the diagonals are equal to each other

AC=BD and AC and BD bisect each other at right angles

(i) Considering the ΔABC and ΔBAD,

AB=AB ( common line)

BC=AD ( opppsite sides of a square)

∠ABC=∠BAD ( = 90° )

ΔABC≅ΔBAD( By SideAngleSide property)

AC=BD ( by CPCT).

(ii) Now in triangles ΔOAD and ΔOCB,

AD=CB ( opposite sides of a square)

∠OAD=∠OCB ( transversal AC )

∠ODA=∠OBC ( transversal BD )

ΔOAD≅ΔOCB (ASA property)

OA=OC ---------(i)

Similarly OB=OD ----------(ii)

From (i) and (ii)  we can conclude that AC and BD bisect each other.

Now in a ΔOBA and ΔODA,

OB=OD ( from (ii) )

BA=DA

OA=OA  ( common line )

ΔAOB=ΔAOD----(iii) ( by CPCT

∠AOB+∠AOD=180°  (linear pair)

2∠AOB=180°

∠AOB=∠AOD=90°

Therefore, it is proved that AC and BD bisect each other at right angles.

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Answer: $2738.02

Step-by-step explanation:

1) (3000x0.97) = 2910  } Year 1

2) (2910x0.97) = 2822.7  } Year 2

3) (2822.7x0.97) = 2738.019  } Year 3

The property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.

In this question we have been given an expression.

We need to identify the property that is used to multiply two binomials.

(3x+5)(2x+7)=2x(3x+5)+7(3x+5)

Consider two binomials,

(3x+5)(2x+7)

= (2x+7)(3x+5)                     ...............(commutative property)

= 2x(3x+5)+7(3x+5)            ................(distributive property)

Therefore, the property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.

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Answer:

-3,-2,-1,0,1

Step-by-step explanation:

Just replace x with the x value to find the y value

y=x-1

y=-2-1

y=-3

Y=-1-1

y=-2

y=0-1

y=-1

y=1-1

y=0

y=2-1

y=1

hopes this helps please mark brainliest

The mean will be the middle number or 12.1.

According to our question-

The median is the middle number  in the data set when the data set is written from least to greatest.

least to greatest 4.8, 6.9, 12.1, 14.8, 16.2

Hence, The mean will be the middle number or 12.1.

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Answer:

Step-by-step explanation: add 4 to cancel out, dive both sides by 3, y=1.3 repeating

The value of the test statistic is 2.59.

A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data fit the distribution predicted by the statistical test's null hypothesis.

Here, the percentage of residents favored construction is 34%.

[tex]p\leq 0.31\\p > 0.31[/tex]

The test statistics is given by,

[tex]Z=P-\frac{p}{\sqrt{p(1-p)n} }[/tex]

Here n=1600, P=0.34 and p=0.31,

Putting the values,

[tex]Z=0.34-\frac{0.31}{\sqrt{0.31(1-0.31)1600} }\\=2.59[/tex]

Test Statistics = 2.59

Therefore, the value of test statistics is 2.59.

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The number of bicycles that must be manufactured to minimize the cost of 250 and the minimum cost is $11,500.

In the given question,

The cost C in dollars of manufacturing x bicyles at a production plant is given by the function shown below;

C(x) = 3x^2-1500x+199,000

(a) In the given question we have to find the number of bicyles that must be  manufactured to minimize the cost.

The given function is

C(x) = 3x^2-1500x+199,000

To find the maximum or minimum value we firstly find the value of f'(x).

C'(x) = 6x-1500

Now put f'(x)=0

6x-1500=0

Add 1500 on both side, we get

6x=1500

Divide by 6 on both side we get

x=250

Hence, the number of bicycles that must be manufactured to minimize the cost of 250.

(b) Now finding the value of function at x=250

C(250) = 3(250)^2-1500*250+199,000

C(250) = 3*62,500-375,000+199,000

C(250) = 187,500-375,000+199,000

C(250) = 11,500

The minimum cost is $11,500.

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Answer:

-3.5

Step-by-step explanation:

-4x-1+1≤ 13+1

-4x/-4 ≤ 14/-4

x≤ -3.5

The different ways of solving percent increase or percent decrease problems has been described below

What is percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

One way to solve the percentage increase or decrease problem is by multiplying the original number by the percentage given and then adding the result with the original number.

Another method is by multiplier method

Here, the original number is taken as 1 and the given percentage has to be converted to decimal and then  1 and the percentage obtained as decimal is added or subtracted. The result obtained has to be multiplied by the original number to get the required number after increase or decrease

For the first method

Suppose the number is n and it is increased by p%

Required result is

[tex]n + \frac{p}{100}\times n\\n( 1 + \frac{p}{100})[/tex]

For the second method

Suppose the number is n and it is increased by p%

Here n is taken as 1 and p% is converted to decimal

then 1 and p% in decimal form is added

we get (1 + 0._p)

Now the result is obtained is multiplied by n

Required result is

n(1 + 0._p)

[tex]n(1 + \frac{p}{100})[/tex]

In this way the two methods are related

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The size if the angle NOM is 54.

What is angle?

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

What is tangent of circle?

A Tangent of a Circle is a line that touches the circle’s boundary at exactly one point. The tangential point is the place where the line and the circle meet.

Given,

M and N are points on a circle.

QMT is the tangent

O is the center.

angle NOM = 2 angle NLM

NOM = 2(27)

= 54.

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1) Radius of the standard tank = 3 feet

2) Existing volume for the tank is 126[tex]\pi[/tex] cubic feet.

3) Sphere volume for the tank is 36[tex]\pi[/tex] cubic feet.

4)Total volume of the tank is  36[tex]\pi[/tex] + 126[tex]\pi[/tex] = 162[tex]\pi[/tex] cubic feet

5) New volume for the tank is 252[tex]\pi[/tex] cubic feet.

6)Trails of values for r is 4 feet.

What do you mean by Volume?

A three-dimensional object's volume, expressed in cubic units (such as inches, quarts, or centimeters): cubic volume. the volume that a material takes up in a given space.

What is radius?

A line segment connecting the circumference or boundary surface of a circle or sphere to its center.

Given that;

Volume of the standard tank [tex]= \pi r^2h + \frac{4}{3} \pir^3[/tex]

                                                [tex]= \pi 3^2h + \frac{4}{3} \pi3^3\\= 90\pi +36\pi\\= 126\pi \ cubic \ feet[/tex]

Volume of new tank = 2 x Volume of standard tank

                                  =  2 x 126π

                                  = 252π

But according to formula, volume of new tank will be;

[tex]V = \pi r^2h + \frac{4}{3}\pir^3[/tex]

where r = radius of new tank

[tex]\pi r^2 \times 10 + \frac{4}{3} \pi r^3 = 252 \pi\\30r^2 +4 r^3 = 756\\2r^3 + 15r^2-378 = 0\\r = 4.04591\\r \approx 4 feet[/tex]

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The speed of the wind is 50 mile per hour  .

In the question ,

it is given that

the speed of the plane is [tex]=[/tex] 200 miles per hour .

let the speed of the wind is = "w"

So ,the speed of the plane with wind is [tex]=[/tex] 200 + w

and the speed of the plane against  wind is [tex]=[/tex] 200 - w

we know that , distance [tex]=[/tex] speed × time

the plane flew "500 miles" with wind ,

which means ,

500 [tex]=[/tex] (200 + w) × t      .....(1)

and the plane flew 300 miles against the wind ,

which means ,

300 [tex]=[/tex] (200 - w) × t       ......(2)

adding both the equations ,

we get

800 [tex]=[/tex] t ( 200 [tex]+[/tex] w [tex]+[/tex] 200 - w)

800 = t × 400

t = 2

Substituting  , t = 2 in 500 [tex]=[/tex] (200 + w) × t      

we get

500 = (200 + w) × 2

500/2 = 200 + w

250 = 200 + w

w = 250 - 200

w = 50

Therefore , The speed of the wind is 50 mile per hour  .

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Answer:36.1

Step-by-step explanation:

ixl

As per the given equation in form of inequality 4x - 2y > 12 gives  the solution in intercept form as y < 2x -6, and for the given inequality x-intercept is x > 3 and y-intercept is y <-6 with slope equal to 2.

As given in the question,

Given equation in inequality form is :

4x - 2y > 12

Simplify the given equation in intercept form we get,

2y < 4x -12

⇒ y < 2x -6

If we write this inequality in equation form we have,

y = 2x -6

slope of the line is 2

x -intercept is x = 3

y - intercept is y = -6

And in inequality form x > 3 and y < -6.

Therefore, for the given equation in form of inequality 4x - 2y > 12 gives  the solution in intercept form as y < 2x -6, and for the given inequality x-intercept is x > 3 and y-intercept is y <-6 with slope equal to 2.

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The expression is x - a = 8.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Difference between two numbers is 8.

The lesser number is a.

let the another number be 'x'.

So, Difference between two numbers

x - a = 8

Hence, the expression is x - a = 8.

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The simplified form of the given expression; negative 1 and 2 over 3 minus 9 and 2 over 5 as required is; -166/15 (negative 166 over 15).

It follows from the task content that the simplified form of the given expression is to be determined.

Since the given expression is; -1 ⅔ - 9 ⅖.

First, the mixed numbers as in the task content must be converted to fractions so that we have;

- 1 ⅔ = -5/3 and

9 ⅖ = 47/5

Therefore, the required evaluation is; -5/3 - 47/5

= -25/15 - 141/15

= (-25 - 141) / 15

= -166/15

Therefore, the required simplified form of the expression is; negative 166 over 15.

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The students and courses have one to many relationship.

A one to many relationship is such kind of relation which exist when a particular function is linked to many other functions. It means that many elements of the set A is related to a single element of the set B.

In this case, the course is only one but the students studying the course are more in number. The same course is studied by many student but in different manner but the course is same. This is why we conclude that the relationship between the students and the course is one to many.

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Answer:

Line 1 is considered perpendicular

Line 2 is considered parallel

Line 3 is also parallel

Step-by-step explanation:

This should be right if this is the rest to your problem:

1. Line AB formed by A(-1,3) and B(1,5); Line CD formed by C(2,3) and D(-2,7)

2. Line AB formed by A(3,8) and B(-6,5); Line CD formed by C(-6,7) and D(-3,8)

3. Line AB formed by A(2,-7) and B(2,3); Line CD formed by C(-4,0) and D(-4,-5)

The triangle with vertices (−2, 1), (1, 1), and (1, 0) is similar to

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions.

Examining the vertices shows that; Triangle W with vertices (−4, 2), (2, 2), and (2, 0) is in proportion to the given vertices (−2, 1), (1, 1), and (1, 0)

The difference is a scale factor of 2

(−2, 1) * 2 =  (−4, 2)

(1, 1) * 2 = (2, 2)

(1, 0) * 2 = (2, 0)

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From the information, observe that the food and drug Administration is a US government agency that regulates food and drugs for customer safety.

One thing the FDA regulates is the allowable insect parts in various foods.

When wheat is ground into the flour, insects that were in the wheat are ground up as well.

The mean number of insect parts allowed in 100 grams of wheat flour is 75

The FDA takes a random sample of 35 bags of floor for evaluation and finds that their average of 80 insect parts per 100 grams with a standard deviation of 6.3

In this situation use t test for population mean because the population standard deviation is not known.

Hence, the correct option is (2).

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