this is a question on a review assignment that i’m stuck on , my summer school teacher said i could get help if i needed. any help would be greatly appreciated

If the mean is 382 and standard deviation is 97 then according to empirical rule 50% students scored  between 285 and 479 on the exam.

Given mean of 382 and standard deviation of 97.

We have to calculate the percentage of students scored between 285 and 479 on the exam.

Percentage is a number or ratio that is expressed in terms of 100.

We have to use z statistic in this question.

z=X-μ/σ

where μ is mean and

σ is standard deviation

from 285 to 382

z=285-383/97

=-1

p value =0.1587.

From 382 to 479

z=479-382/97

=97/97

=1

p value =0.3413

Total probability from 285  to 382 is 0.3413+0.1587=0.5

Percentage=5/10*100

=50%

Hence the percentage of students scored between 285 and 479 is 50%.

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Answer:

See below

Step-by-step explanation:

Looks like positive linear to me....slope is up and to the right (positive) and the line drawn shows it ot be approx linear

The rational function represented in the given graph is; f(x) = 1/(x - 4)

From the given graph , the vertical asymptote is at x = 4

Let's find out the vertical asymptote of each function

To find out vertical asymptote we set the denominator = 0

A) x + 4 = 0

x = -4

This is not correct

B) 4x = 0

x = 0

Not correct

C) Denominator does not have a variable and so is also incorrect

D) x - 4 = 0

x = 4

Thus, this is correct

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[tex]x = y + 5 \\ y = x - 5[/tex]

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

[tex]x = - y - 2 \\ y = - 2 - x[/tex]

[tex]x = 6y + 1 \\ 6y = x - 1 \\ y = \frac{x - 1}{6} [/tex]

[tex]x = y - 11 \\ y = x + 11[/tex]

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

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

[tex]basically \: flip \: x \: and \: y \: then \: solve \: for \: y[/tex]

The equation which represents the number sentence given in the task content is; n/3 + 9 = 21.

According to the task content, it follows that the sentence given is; Nine more than the quotient of a number and 3 is 21.

Since, the quotient of a number and 3 can be written as; n/3.

Consequently, the correct equation is; n/3 +9 = 21.

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Answer:

Yes,

Common ratio = 5.

Step-by-step explanation:

If its geometric it will have a common ratio.

5/1 = 5

25/5 = 5

125/25 = 5

So its geometric with commo ratio 5.

Answer:

[tex]y \geq - 6[/tex]

Step-by-step explanation:

the range is all the y values shown in the graph, so as you can see, the y values are all those greater than or equal to -6

Answer:

Step-by-step explanation:

We are given two sides and one angle opposite to one of the known sides.

In order to find the missing side we need to use the law of sines.

Find the angle opposite to the second known side, let it be x.

Find the missing third angle y, using angle sum theorem:

Find the required side length z, the distance from the plane to the observer tower, using the law of sines again.

Note. At this point you can use the law of cosines as we have found the angle between the known sides.

So the required distance is 7.7 km

Answer:

These lines are perpendicular.

Step-by-step explanation:

Put both equations in the slope intercept form of a line.

y = -6x - 8  This is already in the slope intercept form for a line

-x + 6y = 12  Add x to both sides of the equation

6y = x + 12  Divide through the whole equation by 6

y = 1/6x +2  

Now we compare the two slopes of -6 and 1/6.  They are negative reciprocals of each other.  That means that the line are perpendicular.

The correct option is option () Connect the point with a line through the center of the circle.

According to the problem,

So, the correct option is option ()Connect the point with a line through the center of the circle.

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Answer:

Exact Form: x = -5/2

Decimal Form: x = -2.5

Mixed Form: x = 2 1/2

Answer:

Step-by-step explanation:

5(x+2)=3x+5

5x+10=3x+5

5x=3x-5

2x=-5

x=-0.4

The isosceles triangle is proved below.

The complete information wasn't found. The proofing of the triangle will be illustrated. It should be noted that the angles opposite to the equal sides of an isosceles triangle are also equal.

Proof: Consider an isosceles triangle ABC where AC = BC.

We need to prove that the angles opposite to the sides AC and BC are equal, that is, ∠CAB = ∠CBA.

We first draw a bisector of ∠ACB and name it as CD.

Now in ∆ACD and ∆BCD we have,

AC = BC                                                                (Given)

∠ACD = ∠BCD                                                    (By construction)

CD = CD                                                               (Common to both)

Thus,  ∆ACD ≅∆BCD                                        (By SAS congruence criterion)

So, ∠CAB = ∠CBA                                              (By CPCT)

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The table that represents a function is:

A function is an expression that represents the relationship between two variables. The variables in this case are the dependent and independent variables.

To identify a function, you need to note that no variable of x should be equal to y.

The formular is represented this way: y = f(x). The table that satisfies this condition is the Y table.

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The expression that shows the amount of money in dollars that Maggie has d - 3

An equation is an expression that shows the relationship between two or more numbers and variables.

Let d represent the amount of money Ron has on Tuesday. Hence:

Money Maggie has = d - 9 + 6 = d - 3

The expression that shows the amount of money in dollars that Maggie has d - 3

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The total surface area of the composite figure is calculated as 444 m².

Total surface area = surface area of the bottom rectangular prism + surface area of the top triangular prism - area of the shared surface.

Surface area of the triangular prism = (S1 + S2+ S3)L + bh = (16 + 10 + 10)5 + (6)(16) = 276 m²

Rectangular prism surface area = 2(wl + hl + hw) = 2(5×16 + 4×16 + 4×5) = 328 m²

Area of shared surface = 2(16)(5) = 160 m²

Total surface area = 328 + 276 - 160 = 444 m².

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The expression that help Anna and Damien count the rabbits at their store is (3 * 3) + (4 * 2)

An equation is an expression that shows the relationship between two or more numbers and variables.

Anna has counted 3 cages with 3 rabbits in each. Damien counted 4 cages with 2 rabbits in each. Hence:

Total rabbits = (3 * 3) + (4 * 2)

The expression that help Anna and Damien count the rabbits at their store is (3 * 3) + (4 * 2)

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Answer:

B

Step-by-step explanation:

Drop an altitude. Either of the two resulting right triangles with legs of length 5 and x and a hypotenuse of 10.

By the Pythagorean theorem, it follows that the answer is B.

Answer:

just divide 3125 by 5 and your answer is 625

Step-by-step explanation:

Using division, 3125 by 5 and get answer 625.

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

If 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.

Division can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

Thus,  a / b = a divided in b equal parts.

We have been given 5x = 3125

Divide by 5 each sides;

x = 3125/5

x = 645

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Finding the roots of an equation is done using the equation systems  [tex]y=2x^{3}+4x^{2} -x+5[/tex] & [tex]y= -3x^{2} +4x+9[/tex] .

This equation seems to have the following form:[tex]2x^{3}+4x^{2} -x+5= -3x^{2} +4x+9[/tex]

We must assess the appropriate set of equations that may be utilized to identify the equation's roots.

By drawing the equations' graph, we may determine the equation's root. We can suppose that the left and right sides of the following equations are two independent equations for the sake of graphing.

Therefore,

[tex]y=2x^{3}+4x^{2} -x+5[/tex]

[tex]y= -3x^{2} +4x+9[/tex]

The graphs of these two equations are now shown in the identical coordinate plane. The roots of the equation given will be the crossing point(s).

The equation system that we may utilize to get the root of the formula given is thus,

[tex]y=2x^{3}+4x^{2} -x+5[/tex]

[tex]y= -3x^{2} +4x+9[/tex]

So, the correct answer is option C.

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Answer:

[tex]\sf t_{20}= 0[/tex]

Step-by-step explanation:

      [tex]\sf \boxed{\bf n^{th} \ term = a + (n-1)d}\\\\\text{Here, a is the first term ; d is the common difference }[/tex]

6th term is 14 ⇒ [tex]\sf t_6 = 14[/tex]

                a + (6 - 1)d = 14

                    a  +  5d = 14  --------------(I)

14th term is 6 ⇒[tex]\sf t_{14} = 6[/tex]

             a + (14-1)d = 6

                  a + 13d = 6 ----------------(II)

Subtract equation (II) from equation(I)

        (I)          a + 5d = 14

        (II)         a + 13d = 6

                    -    -          -

                            -8d = 8

                               d  = 8 ÷(-8)      

                              [tex]\sf \boxed{\bf d= (-1)}[/tex]

Plugin d = -1 in equation (I)

a + 5(-1) = 14

      a -5  = 14

             a = 14 + 5

             [tex]\sf \boxed{\bf a = 19}[/tex]  

20th term:

 [tex]\sf t_{20}= 19 + 19*(-1)[/tex]

       = 19 - 19

   [tex]\sf \boxed{\bf t_{20} = 0}[/tex]

Answer:

0

Step-by-step explanation:

The number of terms of an Arithmetic progressions has the formular.

Tn = a + ( n - 1 ) d

From the question,

6th term = 14

14th term = 6

Therefore,

a + 5d = 14 -----------(1)

a + 13d = 6 ----------(2)

subtracting

-8d = 8

dividing bothsides by -8

[tex] \frac{ - 8d}{ - 8} = \frac{8}{ - 8} \\ d = - 1[/tex]

Therefore,

common difference= -1

substituting the value of d into equation (1)

a + 5 ( -1) = 14

a - 5 = 14

a = 14 + 5 = 19

First term = 19

For the 20th term

T 20 = a + 19d

19 + 19 ( -1 )

19-19 = 0

Therefore,

20th term = 0

The quadrants of the points that needs to be graphed  are:

Since the points that was given are:

A(2, 4)        B(0, -3)  

C(1, -1)       E(-4,1)    

G(-3,-2)      I(0, 2)

D(3, 3)        F(2,0)  

H(-2, 3)     J(-1,-4)

Then, we plot all the coordinate above on a graph (see image attached)

Hence, from the image attached graph, the categories that can be seen are:

Quadrant 1 is  Points A and D

Quadrant 2 is  Points E and H

Quadrant 3 is Points G and J

Quadrant 4 is Points C

x-axis-  Point F

y-axis- Point B and I

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Answer:

(2, 60°)

Step-by-step explanation:

A point in polar form (a,b) is represented by a radius and an angle (r, ϴ). To convert, use the formula r² = a² + b² to get r, and  [tex]tan^{-1}[/tex](b/a) = ϴ

[tex]r = \sqrt{1^{2} + \sqrt{3} ^{2} }[/tex]

[tex]r = \sqrt{1+3}[/tex]

[tex]r = \sqrt{4}[/tex]

= 2

[tex]tan^{-1}[/tex]([tex]\sqrt{3}[/tex]/1) = ϴ

= 60°

Answer:

False

Step-by-step explanation:

Prisms can have more than one base.

The expression that represents well the geometric sequence is [tex]f(n) = 8 \cdot 2^{n-1}[/tex] and the value of the fourth term is 64. (Correct choice: B)

Geometric sequences are exponential expressions with discrete domain, whose form is presented and explained below:

[tex]f(n) = a \cdot r^{n-1}[/tex], where a, r are real numbers and n is a natural number.     (1)

Where:

According to the statement, we know that the first term of the geometric sequence is 8 and between any two consecutive terms there is a common ratio of 2. If we know that a = 8, r = 2 and n = 4, then the fourth term of the series by means of (1) is:

[tex]f(4) = 8 \cdot 2^{4-1}[/tex]

f(4) = 8 · 8

f(4) = 64

The expression that represents the geometric sequence is [tex]f(n) = 8 \cdot 2^{n-1}[/tex] and the value of the fourth term is 64.

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Answer:

The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north.

Step-by-step explanation:

• To find the magnitude of the resultant vector, we have to use Pythagoras's theorem:

[tex]\boxed{a^2 = b^2 + c^2}[/tex]

where:

a ⇒ hypotenuse (= resultant vector = ? mi)

b, c ⇒ the two other sides of the right-angled triangle (= 452 mil North, 767 mi West).

Using the formula:

resultant² = [tex]452^2 + 767^2[/tex]

⇒ resultant =  [tex]\sqrt{452^2 + 767^2}[/tex]

⇒ resultant = 890.3 mi

• To find the direction, we can find the angle (labeled x in diagram) that the resultant makes with the north direction:

[tex]tan (x) =\frac{767}{452}[/tex]

⇒ [tex]x = tan^{-1} (\frac{767}{452} )[/tex]

⇒ [tex]x = \bf{59.5 \textdegree}[/tex]

∴ The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north .

Answer:

[tex]\displaystyle Approximately\:59°\:at\:a\:magnitude\:of\:approximately\:890\:miles[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:\theta \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:\theta \\ \frac{OPPOCITE}{ADJACENT} = tan\:\theta \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:\theta \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:\theta \\ \frac{ADJACENT}{OPPOCITE} = cot\:\theta[/tex]

We must use trigonometry to help us find the direction of the aeroplane's resultant vector. Do as I do:

[tex]\displaystyle \frac{452}{767} = cot\:x \hookrightarrow cot^{-1}\:\frac{452}{767} = x; 59,488772482...° = x \\ \\ \boxed{59° \approx x}[/tex]

Now, we will use the Pythagorean Theorem to find the magnitude of the aeroplane's resultant vector. Do as I do:

[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 767^2 + 452^2 = c^2 \\ \sqrt{792593} = \sqrt{c^2}; 890,27692321... = c \\ \\ \boxed{890 \approx c}[/tex]

Therefore, the direction and magnitude of the aeroplane's resultant vector are approximately eight hundred ninety miles at an angle of elevation of fifty-nine degrees.

I am joyous to assist you at any time.

The inflation rate between 2017 and 2018 is 2.86%.

Inflation rate is used to determine the rate at which the general price levels in an economy is increasing with the passage of time.

The inflation rate = (2018 CPI / 2017 CPI) - 1

(180 / 175) - 1 = 0.0286 = 2.86%

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tan45° = cot45° = 1

---> If tanA + cotA = 2, then A is 45°.

---> tan²A + cot²A = 1² + 1² = 2

The correct answer is 2

Answer:

Step-by-step explanation:

All pyramids have a volume as one-third of a prism with the same base area and the same height.

This will make the formula for the volume [tex]\frac{1}{3}(base*height)[/tex]. We already know the height of the pyramid is 10, but the area of the base for this rectangle would be its length and its width. Let's calculate this:

[tex]7*2.3=16.1\hspace{0.1cm}in^2[/tex]

Let's put these values back into the formula:

[tex]V=\frac{1}{3}(16.1*10)\\ V=\frac{1}{3}(161)\\ V= 53.7\hspace{0.1cm}in^3[/tex]

Shipping points are independent organizational entities within which processing and monitoring of the deliveries, as well as goods issue, is carried out. A delivery is processed by one shipping point only.

"FOB shipping point" or "FOB origin" means the buyer is at risk once the seller ships the product. The purchaser pays the shipping cost from the factory and is responsible if the goods are damaged while in transit. "FOB destination" means the seller retains the risk of loss until the goods reach the buyer.

Please check the attached file for a complete answer.

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