In four middle schools, the teacher to student ratio is equivalent. How many teachers and students are at each school? Enter the correct answers in the boxes in the table. ​

Step-by-step explanation:

Probabibility = 1/6 * 1/6 = 1/36 = 2.77%.

Answer:

\(f(x) = 2x^3 -5x^2+2x+1\\\\by \ trail \ and \ error, \\\\f(1) = 2(1^3) -5(1^2) +2(1) +1 = 2 - 5 + 2 + 1 = 0\\\\Therefore, 1 \ is \ a \ root \ of \ f(x).\\\\=> (x -1) \ is \ a \ factor \ of \ f(x).\)

Now using long division,

\(\mathrm{Factor}\:2x^3-5x^2+2x+1:\quad \left(x-1\right)\left(2x^2-3x-1\right)\)

\(\quad \left(x-1\right)\left(2x^2-3x-1\right)\\\\(x-1)(x-\frac{3+\sqrt{17} }{4})(x+\frac{3-\sqrt{17} }{4} )\)

Therefore , the roots are

                         \(1 , \frac{3+\sqrt{17} }{4} , \frac{3-\sqrt{17} }{4}\)

(-2,3) is the point of intersection of AB and CD is denoted by M.

When two lines or more than two lines cross each other in a plane, this is called the intersection of lines, and the lines are called intersecting lines. They have a common point called the point of intersection.

Given that, the points A (-4,4), B (6,-1), C(0,5) and D (-5,0) on a Cartesian plane. Join A and B. Join C and D. And then we have to write down the co-ordinates of the point of intersection of AB and CD.

The graph of the following information is shown as below.

And the coordinates of point of intersection of AB and CD is denoted by M.

From the graph the coordinates of point of point of intersection of AB and CD is (-2,3) respectively.

Hence, (-2,3) is the required answer.

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The measure of each exterior angle of a regular hexagon ( six sided regular polygon is 60°.

Option C)60° is the correct answer.

A polygon is simply a two-dimensional a plane shape enclosed by line segments called sides.

The formula for calculating the exterior angles of a polygon is;

E = 360° ÷ number of sides

Given the data in the question;

So we substitute the value for number of sides into the expression above.

E = 360° ÷ number of sides

E = 360° ÷ 6

E = 60°

The measure of each exterior angle of a regular hexagon ( six sided regular polygon is 60°.

Option C)60° is the correct answer.

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Answer: (C) 60°

Just took it on edge

Answer:

x=31

Step-by-step explanation:

x=180-149

x=31

Answer:

36pi meters squared

Step-by-step explanation:

The area of a square is calculated using the formula "pi(r)^2" To find the radius (r), we divide the diameter by 2 (12/2=6). We know that the radius is six and 6^2 = 36. The last step is to multiply by pi.

Answer:

9

Step-by-step explanation:

-5t=-45

divide both sides by -5

-5t/5 would leave just t

-45/-5 would be 9

so t=9

lmk if you need more help i would be happy to help more

The sailcloth having vertices of 0, 0), (4, 0), and (3, 6), with a sailcloth cost  of $11.75 per square yard is $141

The given parameters;

Cost of the sailcloth per square yard = $11.75

Vertices of the sailcloth are; (0, 0), (4, 0), and (3, 6)

The cost of purchasing the sailcloth = The area of the sailcloth × Cost per square yard

Taking the base length as; 4 - 0 = 4

The height = The distance from the x-axis to the highest point on the sailcloth = The highest y-value = 6

Which gives;

The area of the sailcloth = Area of a triangle = \(\dfrac{1}{2} \times 4 \times 6 = 12\)

The area of the sailcloth = 12 yard²

The cost of purchasing the sailcloth = 12 yard² × $11.75/yard² = $141

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Answer:

line mo

Step-by-step explanation:

Because the triangle are congrument

RST and MNO are the triangle

RT is a line in the RST triqangle

it is equal to the MO line in MNO

The simplest radical form of √5/12 is 1/2√5/3

Radical form:

Radical means the opposite of an exponent that is represented with a symbol '√' also known as root.

Given,

Here we have the number √5/12.

Now, we have to convert this into simplest radical form.

To convert this into radical form, first we have to expand the given terms,

Then we get,

=> √5 x √1/12

We know that, 4 x 3 is 12, So, we have to replace 12 with the expression 4 x 3, then we get,

=> √5 x √1/4 x 3

We know that the value of √4 is 2,

Then the expression is rewritten as,

=> 1/2√5/3

Therefore, the simplest radical form is 1/2√5/3.

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Area of the figure is 150 units²

A semicircle is a half of a circle or the locus of all points that are equidistant from two endpoints on a diameter of a circle. It can be thought of as a curved shape that looks like half of a circle, with a flat side on one end.

The area of a semicircle can be found using the formula:

Area = (πr²)/2

where r is the radius of the circle.

Area of given figure= Area of rectangular part + Area of semicircle-Area of semicircle

=10×15

=150units².

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The complete question is;

Find the Area of the figure below, composed of a rectangle and one semicircle,

with another semicircle removed. Round to the nearest tenths place.

Image is attached below.

The total number of squares that can be formed with 4 of the 200 points as vertices is 39,600.

The equation for calculating the total number of squares that can be formed with 4 of the 200 points as vertices are:

Number of squares = (200 Choose 4) x (4!/2) = (200!/196! x 4!) x (4!/2)

Using the factorial notation, this simplifies to:

Number of squares = (200 x 199 x 198 x 197) x (2) / (4 x 3 x 2 x 1)

The number of squares = 39,600.

Solving the equation, the total number of squares that can be formed is 39,600.

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Answer:

5

Step-by-step explanation:

The Fundamental theorem of Algebra states that a polynomial of degree n has n roots, some may be complex.

11\(x^{5}\) + 5x - 3 = 0 ← is a polynomial of degree 5

Thus the equation will have 5 roots

Answer:

c = 0.50(0.48)(1525)

Step-by-step explanation:

If 52% of the students are female, then

100% - 52% = 48% of the students are male

48% = 48/100 = 0.48

To find the number of students who are male:

⇒ total number of students x 0.48 = 0.48 x 1525

Half = 50% = 50/100 = 0.50

⇒ half of the male students = 0.50 x 0.48 x 1525

Solution:  c = 0.50(0.48)(1525)

Answer:

5 to 3

Step-by-step explanation:

15/3=5

6/3=3

Answer:

5:2

Step-by-step explanation:

15:6 can both be divided by 3, 15/3 = 5, 6/3 = 2, making the ratio,

5:2 hope i helped you (and could i have brainliest it would help me!)

Answer: x=20

Step-by-step explanation:

If im wrong, sorry

The angles of a triangle add up to 180 degrees.

(3x+5)+(2x+17)+(2x+18)=180

add the ones alike

3x + 2x + 2x=7x

5+17+18=40

so, 7x+40=180

we need to get the variable by itself so we take away 40 first by subtracting it from both sides of the equal sign

7x=140

we take away 7 from x by dividing it- opposite of multiplication is division

x=20

Answer:

x = 20

Step-by-step explanation:

3x+5° + 2x+18° + 2x+17° = 180° (sum of interior angles in a triangle is 180°)

collect like terms

3x + 2x + 2x + 5° + 18° + 17° = 180°

7x + 40° = 180°

solving for x

x = (180 - 40)/7

x = 140/7

x = 20

There are number of 42 different types of shirts are available from this company.

We have to given that,

A shirt company had 3 designs each of which can be made with short or long sleeves.

And, There are 7 patterns available.

Hence, Total number of different types of shirts are available from this company are,

⇒ 3 × 2 × 7

⇒ 42

Thus, There are 42 different types of shirts are available from this company.

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Answer:

c. triangle ghj

d. triangle nop (i could be wrong for both though)

Step-by-step explanation:

Two shapes that are the same size and the same shape are congruent. They are identical in size and shape

Answer:

Write your question.

Step-by-step explanation:

We're waiting...

Answer:

whats the question?

Step-by-step explanation:

Answer:

Step-by-step explanation:

As per picture we have:

This gives us:

Two sides and included angle congruent - ASA postulate

As per above congruency we have:

Finding CD:

Answer:

\(6.8\ cm\)

Step-by-step explanation:

\(We\ are\ given:\\OM\ is\ altitude\ of\ \triangle AOB\\ON\ is\ altitude\ of\ \triangle DOC\\Now,\\Lets\ only\ focus\ on\ the\ interior\ triangles\ inside\ the\ two\ above\ triangles.\\They\ are:\\\triangle OMA\ and\ \triangle ONC.\\\\We\ observe\ that:\\\angle AMO=90[As\ it\ is\ the\ altitude\ of\ \triangle AMO]\\\angle ONC=90[As\ it\ is\ the\ altitude\ of\ \triangle ONC]\\Hence,\\\angle AMO= \angle ONC=90\\\\\)

\(We\ also\ observe\ that,\\\angle MOA\ and\ \angle CON\ are\ vertically\ opposite\ as\ they\ are\ one\ pair\\ of\ opposite\ angles\ formed\ by\ the\ intersection\ of\ Lines\ AC\ and\ MN.\\We\ know\ that,\\"When\ two\ straight\ lines\ intersect,\ the\ pairs\ of\ vertically\ opposite\\ angles\ formed\ are\ equal".\\Hence,\\\angle MOA= \angle CON\)

\(Lastly,\\We\ are\ given\ that,\\MO=ON\)

\(Now,\\The\ ASA\ Congruence\ Criterion\ states\ that' If\ two\ angles\ and\ the\ includ\\ side\ of\ one\ triangle\ is\ equal\ to\ the\ corresponding\ angles\ and\ the\ includ\\ side\ of\ the\ second\ triangle,\ both\ triangles\ are\ congruent'.\\Hence,\\\triangle AMO \cong \triangle CNO.\)

\(Hence,\\AM=NC [Corresponding\ Parts\ of\ Congruent\ Triangles]\\We\ can\ observe\ that,\\CD=DN+NC\\Hence,\\DN=2.6\ cm [Given]\\NC=AM=4.2\ cm [Proven]\\Hence,\\DC=2.6+4.2=6.8\ cm\)

The amount of money that is currently in the RRSP fund is approximately $117,303.70.

To know the amount of money in RRSP

Use the formula for the future value of an annuity:

\(FV = PMT * ((1 + r/n)^(n*t) - 1) / (r/n)\)

where:

FV = future value

PMT = regular payment

r = interest rate

n = number of compounding periods per year

t = number of years

For the first 5 years, we have:

PMT = $2,487.00

r = 6% per year, compounded quarterly, so r/n = 0.06/4 = 0.015

n = 4 quarters per year

t = 5 years

Plug the values into the formula

FV1 = $2,487.00 * (\((1 + 0.015)^(4*5)\) - 1) / (0.015)

= $39,947.05

For the last 9 years, we have:

PMT = $2,487.00

r = 8% per year, compounded quarterly, so r/n = 0.08/4 = 0.02

n = 4 quarters per year

t = 9 years

FV2 = $2,487.00 * (\((1 + 0.02)^(4*9)\) - 1) / (0.02) = $77,356.65

Sum up the two amounts to know the total future value in RRSP

FV_total = FV1 + FV2

= $39,947.05 + $77,356.65

= $117,303.70

Hence, the current balance in the RRSP is approximately $117,303.70.

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The question is incomplete, kindly find the complete question below

Sue has contributed $2,487.00 every three months for the last 14 years into an RRSP fund. The interest earned by these deposits was 6% compounded quarterly for the first 5 years and 8% compounded quarterly for the last 9 years. How much money is currently in the RRSP? The balance is $. (Round the final answer to the nearest cent as needed. Round intermediate values to four decimal places as needed

5x+30=45

tkae the 30 to the other side and it becomes

5x=45-30

that gives you 15. then you want to divide 5 by 15

and then that gives you 3

x=3

Hope this helps you!

Answer:

-49

Step-by-step explanation:

Answer:

12$

Step-by-step explanation:

It says she paid a fee of 15, since total for six months is 87 it means the fee is included. So basically taking out the fee she paid a total of 72.

NOW you can divide by 6. which will give you 12 dollars per month.

This can trick people because they dont subtract the fee and think they can just divide by 6.

The correct trigonometric, notation for z = 1+2i is √5 (cos 63.4° + i sin 63.4°).

The complex number z can be written in trigonometric form as z = r(cos θ + i sin θ), where r represents the magnitude of z and θ represents the argument (or phase) of z.

In this case, the magnitude of z is √(1² + 2²) = √5.

To find the argument θ, we can use the inverse tangent function:

θ = arctan(2/1) = 63.4°.

Therefore, the trigonometric notation for z is √5 (cos 63.4° + i sin 63.4°).

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The best response for a person handling biohazards with an open wound on their hands is to not  work with biohazards until the cut is healed or cleared by a healthcare professional to work with the use of waterproof bandages and double gloves.

Biohazards are extremely dangerous because they can get into the human body and cause a lot of damage.

This is why a person with an open would or existing cut should not handle a biohazard until they are cleared to to so by a trained healthcare professional.

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Based on the distance that Beryl is standing from the finish line, and the distance till Jeremy finishes the race, the minimum possible distance between Beryl and Jeremy is 29 feet.

Beryl has finished the race and is the first person to do so. She has then gone further such that Beryl is now about 15 feet beyond the finish line.

Jeremy on the other hand, still has to cover 14 feet before he can reach the finish line.

The minimum possible distance between them is therefore:

= Distance past the finish line for Beryl + Distance to the finish line for Jeremy

= 15 + 14

= 29 feet

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Answer:

76 unit

Step-by-step explanation:

because added the rectangle size and added the 60 with 16