The number -3 is an integer and a rational number.

The 90% confidence interval for the mean score, μ, of all students taking the test is B. 21.8<u<23.0

Given a=0.1, Z(0.05)=1.645 (from standard normal table)

So 90% confidence interval is

xbar+/-Z*s/vn

= 22.4+/-1.645*2.8/sqrt(66)

= (21.83304, 22.96696)

Therefore, the 90% confidence interval for the mean score, μ, of all students taking the test is 21.8<u<23.0.

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The steps given to find the standard deviation of the data-set are as follows:

For this problem, the are 5 values, hence:

n = 5.

The sum of the values is given by:

6 + 7 + 8 + 9 + 10 = 40.

Hence:

[tex]\sum x = 40[/tex]

The mean is given by:

40/5 = 8.

Hence:

[tex]\bar{x} = \frac{\sum x}{n} = 8[/tex]

The sum of the differences squared between each observation and the mean is:

(6 - 8)² + (7 - 8)² + (8 - 8)² + (9 - 8)² + (10 - 8)² = 10.

Hence:

[tex]\sum (x - \bar{x})^2 = 10[/tex]

Dividing by the number of values, we have that 10/5 = 2, hence:

[tex]\frac{\sum (x - \bar{x})^2}{n} = 2[/tex]

Taking the square root, the standard deviation is:

[tex]\sqrt{\frac{\sum (x - \bar{x})^2}{n}} = 2[/tex]

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Answer:

12 yd

Step-by-step explanation:

Since the questions says "assuming that all intersecting sides meet at right angles" means that this shape is made up of 2 rectangles :

So Opposite 16 yd should be the 4 yd at the bottom + missing side

So the answer is 12 yd

Hope this helped and you understood and have a good day

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{1}x+6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so a perpendicular line to that one will have

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{1\implies \cfrac{1}{\underline{1}}} ~\hfill \stackrel{reciprocal}{\cfrac{\underline{1}}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{\underline{1}}{1}\implies -1}}[/tex]

so we're really looking for the equation of a line whose slope is -1 and that it passes through (3 , 2)

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- 1}(x-\stackrel{x_1}{3}) \\\\\\ y-2=-x+3\implies {\LARGE \begin{array}{llll} y=-x+5 \end{array}}[/tex]

Step-by-step explanation:

2x-10x+6=4x-6

2x-10x-4x=-6-6

-12x=-12

x=1

Answer:

14

Step-by-step explanation:

The property which equality 2 demonstrate is: d. Associative property of multiplication.

The associative property of multiplication states that when three (3) numbers are multiplied, the end result (output) would always be the same regardless of the way the numbers are arranged (grouped).

This ultimately implies that, the associative property of multiplication suggest that the way in which factors are arranged (grouped) when multiplying three (3) numbers does not change the product.

Mathematically, the associative property of multiplication can be represented by this expression:

(a × b) × c = a × (b × c)  ≡ (8 × 5) × 6.75 = 8 × (5 × 6.75)

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The volume of the figure in the nearest hundredth is 67 mi³

The formula for determining the volume of a sphere is expressed as;

Volume = 4/ 3 πr³

Where;

To determine the volume, we have to substitute the values of the parameters into the formula

Volume = 4/ 3 × 3. 14 × (4)²

Find the value of the square

Volume = 4/ 3 × 3. 14 × 16

Multiply through

Volume = 200. 96/ 3

Find the quotient

Volume = 66. 98

Volume = 67 mi³

Thus, the volume of the figure in the nearest hundredth is 67 mi³

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Answer:

1x - 19683

Step-by-step explanation:

(I have to assume you meant to simplify the equation)

27 to the third power can also be written as: 27 * 27 * 27

That equals 19683

So the equation would be: 1x - 19683

Answer:

n = -4

Step-by-step explanation:

let the number = n

eight less than = .... minus 8

five times a number =n * 5

eight less than five times n = n * 5 minus 8 = n*5 -8

is means equal to

four more than = .... plus 4

eight times the number = n* 8

four more than eight times the number = n*8+4

n*5-8 is n*8 +4

n*5-8=8n+4

subtract 5n from both sides to put all variables and coefficients on one side

-8 = 3n + 4

subtract 4 from both sides to isolate the variable and coefficient

-12 = 3n

divide both sides by 3 to get n

n = -4

If 80 % (percentage) of marbles are blue then there are 36 blue marbles.

Percentage is the process of representing parts of a number by dividing the number into equal hundreds.

If the total amount is equivalent to 100 then the percentage denotes the number which is identical to the part of the number. In other words percentage denoted as % is part of 100.

The process of converting a part into percentage is by dividing the part by the total amount and multiplying the result by 100.

Now the total number of marbles in the jar is 45 and 80% of them are blue.

Now let us consider this :

so 80% of 45 = 80/100 × 45

or, blue marbles = 36

Hence the number of blue marbles is 36.

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For the given maximization problem there is  no the point in the feasible region which maximizes objective function C = 7x -3y.

A feasible region in any optimization problem is the collection of all the points where all the given constraints are satisfied.

For maximization problem, we will use the corner points of the feasible region and then we will check that on which corner point the objective function is maximum.

Given problem is:

Maximize Objective function C = 7x-3y

When the constraints are  (i) x≥0 , (ii) y≥0 , (iii) -x+5 ≤y

(iv) y ≤ (1/3)x +1

We will graph these constraints and  find the common shaded area.

x≥0,y≥0 represents that the point is in 1st quadrant

For -x+5 ≤y, we will use -x +5 =y

When x= 0 then y=5  and when y=0 then x=5 , then -x +5 =y is a line passing through (0,5) and (5,0)

and on putting (0,0) in -x+5 ≤y we get 5≤0 which is a false statement .

Therefore -x+5 ≤y is region starting with line -x +5 =y and going in direction to opposite to that of (0,0)

For y ≤ (1/3)x +1, we will use y = (1/3)x +1

When x= 0 then y=1  and when y=0 then x=-3 , then y= (1/3)x +1 is a line passing through (0,1) and (-3,0)

and on putting (0,0) in y ≤ (1/3)x +1 we get 0≤1 which is a true statement .

Therefore, y ≤ (1/3)x +1 is region starting with line y = (1/3)x +1 and going in direction of (0,0).

Thus we got the feasible region as shaded in the below attached figure.

The shaded area is unbounded , therefore no point of maximum exist on the feasible region.

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i can't graph it for you but

x is greater than or equal to 7

Price of each ticket without service charge is : 43.569                                                                                                              Service charge : A service charge is an amount that is added to your bill in a restaurant to pay for the work of the person who comes and serves you.

So we have to find out price of each ticket without service charge

Total service charge added on both the tickets : 3%

Step by step solution :

$92.70 (both tickets with service charge)

92.70*3/100

2.781 (service charge for one ticket)

2.781*2= 5.562

92.70-2.781=89.919

89.919/2 = 43.569                                                                                    To learn more about service charge visit brainly.com/question/13840144

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Answer:

Leading coefficient: 2

Exponential term: 2x⁵

Hope this helps.

Answer:

2 and ^5

Step-by-step explanation:

cause the coefficients are the bigger numbers in the beginning

Answer:

y = x - 2

Step-by-step explanation:

5x - 2 = 8 + 5y ( subtract 8 from both sides )

5x - 10 = 5y ( isolate y by dividing both sides by 5 )

[tex]\frac{5}{5}[/tex] x - [tex]\frac{10}{5}[/tex] = y , that is

y = x - 2

Answer: The midpoint is 1/2

Step-by-step explanation: The formula we are using for this problem is (x1+x2/2, y1+y2/2) I substitute the points for the equation and it looked likes this (-1-6/2)(5-8/2) and got 5/2-3/2 and the final answer is 1/2!

Hope this helped C:

Answer:

( -3 1/2, -1 1/2)   or as a desimal (-3.5, -1.5)

Step-by-step explanation:

Brainliest please

Answer:
The two shapes are similar, therefore, [tex]\frac{\text{KJ}}{\text{WZ}} = \frac{\text{JM}}{\text{YZ}}[/tex]

[tex]\frac{12}4 = \frac6n\\\to 3n = 6\\\to n =2[/tex]

The side length YZof a trapezoid WXYZ will be 2 cm.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.

The side lengths are given as:

JK = 12 cm

MJ = 6 cm

WX = 4 cm

WZ = n cm

From the diagram, the trapezoid JKLM is similar to the trapezoid WXYZ.

If the two polygons are similar then the ratio of the corresponding sides of the polygon is constant. The ratios are written as,

JK/WX = KL/XY = LM/YZ = MJ/ZW

JK/WX = MJ/ZW

12/4 = 6/n

3 = 6/n

n = 6/3

n = 2

The side length YZof a trapezoid WXYZ will be 2 cm.

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The equations which is equivalent to 1 whole 1/2 x 3 whole 1/5 = 4 whole 1/2 is 3/2 x 16/5 = 9/2.

Fractions represent the parts of a whole or collection of objects.

A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.

Now given equation is,

1 whole 1/2 x 3 whole 1/5 = 4 whole 1/2

Converting them into simple fraction we get,

1 whole 1/2 = 3/2

3 whole 1/5 = 16/5

4 whole 1/2 = 9/2

Thus, the equation becomes,

3/2 x 16/5 = 9/2

this is the required equivalent equation for the given equation.

Thus, the equations which is equivalent to 1 whole 1/2 x 3 whole 1/5 = 4 whole 1/2 is 3/2 x 16/5 = 9/2.

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Answer:

4:25 I think

Step-by-step explanation:

just added them all up I don't know if that's what you needed yho

Answer:

15:85 or 4:25

Step-by-step explanation:

jfhfjfjfjfjfndndndndndjdjfjfnnfjfjdjfjfjf

If f (0) = 1, then the point is ( 0 , 1 ) on the graph of f (x).

A point on a graph is represented by the form:

( x , y ) where x is the abscissa and y is the ordinate of the function.

We are given a point on the graph of f ( x ) = y as:

f ( 0 ) = 1

Comparing it with f (x) = y, we get that:

x = 0

y = 1

so, the point will become:

( 0 , 1 )

Therefore, we get that, If f (0) = 1, then the point is ( 0 , 1 ) on the graph of f (x).

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Answer:

Step-by-step explanation:

C(3) means the cost of transporting 3 crates of sugar.

It is calculated by substituting the value of n into equation:

The cost of transporting 3 crates of sugar is 460 dollars

Check the picture below.

The solution is, the combined volume of the boxes is 180 unit cube.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

from the given diagram, we get,

there is two boxes in the diagram.

now, we have to find the combined volume.

here, we get,

the boxes are cuboids.

we know that,

Volume of  cuboid = length * width * height

V = l*w*h

here, we get, from the figure,

for 1st box, l = 3, w = 5 , h = 8

so, V  = 3 * 5 * 8 = 120

and, for 2nd box, l = 4, w = 5, h = 3

so, V = 4*5*3 = 60

we get, the combined volume 120 + 60 = 180

Hence, The solution is, the combined volume of the boxes is 180 unit cube.

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Answer:

the first one

Step-by-step explanation: