If tan∅ = √15÷10, find cot∅

Answer:

4 people

Step-by-step explanation:

9-2= $7

28/7 = 4

Answer:

$70

Step-by-step explanation:

it is between both. I hope this helps

Answer:

$65 ≤ x ≤ $135

It can also be written as $65 ≤ x AND x ≤ $135

Step-by-step explanation:

Now, one should know the meaning of compound inequality. A compound inequality is the inequality which simply combines the two simple inequalities.

Now, in an inequality, three relations are performed, equal to, less than and greater than. You can combine 'equal to' with 'less than' or 'greater than' according to situation given.

Notice that in given sign

≤

the value at left side or the pointed side will be small or lesser than the value at right side. Also notify that if inverted, like this ≥

Value of left side will be greater. Means the value at pointed side will always be smaller. The lower bar is sign of equal to

if this is written

x ≤ 3

It means that x can be equal to three or any value less than 3 means 2,1,0,-1 etc.

Now in question given, it is stated that money should be not less than $65 means it can either be $65 or more but not less than it. Lets assume 'x' as the amount required,

So one inequality is

$65 ≤ x

For second condition which is amount should be no more than $135, means it can be $135 or less, so inequality is

x ≤ $135

Remember that we use AND in the answer because both statements of inequality are need to be fulfilled or satisfied.

Answer:

m<1: 51

m<2: 61

m<3: 29

Step-by-step explanation:

m<1 = 51, because to find the 3rd angle, you need to add the other two angles and then subtract 180 from that answer.

61 + 68 = 129

180 - 129 = 51

m<2 = 61, because it's a vertical angle, meaning that the angle that's opposite to it exactly, is the same. So since the angle opposite to m<2 is 61, that's what the answer would be.

m<3 = 29, because all you need to do is add 90 and 61, and then subtract 180 by the answer. I got 90 as one of the angle measurements because there's a right triangle, meaning it's 90. Then since we already know what angle 2 is (61) then all you need to do is add:

90 + 61 = 151

Then subtract:

180 - 151 = 29

Step-by-step explanation:

[tex]\text{If is}\ \dfrac{3}{5}^4,\ \text{then}\ \dfrac{3}{5}^4=\dfrac{3\cdot3\cdot3\cdot3}{5}=\dfrac{81}{5}=16\dfrac{1}{5}\\\\\text{If is}\ \left(\dfrac{3}{5}\right)^4=\left(\dfrac{3}{5}\right)\left(\dfrac{3}{5}\right)\left(\dfrac{3}{5}\right)\left(\dfrac{3}{5}\right)=\dfrac{3\cdot3\cdot3\cdot3}{5\cdot5\cdot5\cdot5}=\dfrac{81}{625}[/tex]

Answer:

Option C.

Step-by-step explanation:

Given information: RSTU is a parallelogram, Digonals RT and SU intersect each other at point V, UV=(x-3) and VS=(3x-13).

According to the properties of a parallelogram, the diagonals of a parallelogram bisect each other.

Using the properties of parallelogram we can say that point V divides the diagonal SU in two equal parts, UV and VS.

[tex]VS=UV[/tex]

[tex]3x-13=x-3[/tex]

Subtract x from both sides.

[tex]2x-13=-3[/tex]

Add 13 on both sides.

[tex]2x=10[/tex]

Divide both sides by 2.

[tex]x=5[/tex]

Therefore, the correct option is C.

Answer:

option 3: x=5

Step-by-step explanation:

just took quiz

Answer:

16 pieces.

Step-by-step explanation:

4/1/4=16

The number of pieces of rope he cut is 16 pieces.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

The length of rope= 4foot

Length of each piece=0.25

Now,

To find the number of pieces of rope Kyle cut, we need to divide the length of the rope by the length of each piece:

number of pieces = length of rope / length of each piece

In this case, Kyle cut a 4 foot piece of rope into pieces that are 0.25 feet long, so we can plug these values into the formula:

number of pieces = 4 / 0.25

number of pieces = 16

Therefore, by algebra the answer will be 16 pieces.

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Answer:

there will be enough for each school to get 11 computers

Step-by-step explanation:

use a calculator and put in 992 divided by 11. your answer should appear as 90.1818182

Yes, there are enough computers 992 to be distributed to 90 schools.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a county has 90 schools. The county received 992 new computers.

The required computers for 90 schools will be calculated as,

Computer required = 90 x 11

Computer required = 990

Available compters = 992

Remaining = 992 - 990 = 2 computers

Therefore, there are enough computers 992 to be distributed to 90 schools.

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Answer:

Using [tex]\pi =3.14[/tex] the volume of the cylinder is [tex]1471.875\ m^{3}[/tex]

Step-by-step explanation:

We are using [tex]\pi =3.14[/tex].

We know that volume of a cylinder is [tex]\pi (r)^2h[/tex]

For this we have

Height of the cylinder is given that is [tex]18.75\ m[/tex]

And the radius of the cylinder is unknown,

But there is a hint in which we can see that the diagonal,height and diameter forms a right angled triangle (or a cone).

Where [tex]21.25\ m[/tex] is the hypotenuse.

Using Pythagoras formula.

[tex](Hypotenuse)^2=(base)^2+(perpendicular)^2[/tex]

We can find the value of diameter which is the base over here.

So,

[tex]d=\sqrt{(21.25)^2-(18.75)^2}=\sqrt{(451.56-351.56)}=\sqrt{(100)}=10\ m[/tex]

Then radius [tex]\frac{diameter}{2} =\frac{10}{2}=5\ m[/tex]

Now using the above values and plugging it on to the formula.

Volume [tex]=\pi (r)^2h=(3.14)(5)^2\times 18.75=1471.875\ m^3[/tex]

So the volume of the cylinder is [tex]1471.875\ m^3[/tex]

Answer:

the slope is -3

m=-3

i tried my best :(

Answer:

A) The sum of given digits is 5417.412

B ) The sum of given digits is 401.103  

Step-by-step explanation:

Given sum of numbers as :

A ) 5 × 10³ + 4 × 10² + 1 × [tex]10^{1}[/tex] + 7 × [tex]10^{0}[/tex] + 4 × [tex]\frac{1} {10^{1}}[/tex] + 1 × [tex]\frac{1}{10^{2}}[/tex] + 2 × [tex]\frac{1}{10^{3}}[/tex]

Or , 5000 + 400 + 10 + 7 × 1 + 0.4 + 0.01 + 0.002

or, ( 5400 + 10 + 7 ) + ( 0.4 + 0.01 + 0.002 )

Or, 5417 + 0.412

Or, 5417.412

Hence The sum of given digits is 5417.412

B ) 4 × 10² + 1 × ( 1 [tex]\frac{1} {10^{1}}[/tex] ) + 3 × [tex]\frac{1}{10^{3}}[/tex]

Or, 400 + 1 × ([tex]\frac{10+1}{10}[/tex] ) + 0.003

Or, 400 + [tex]\frac{11}{10}[/tex] + 0.003

Or, 400 + 1.1 + 0.003

Or, 401.103

Hence The sum of given digits is 401.103  

Answer

Answer:

1) 5417.412

2) 401.13

Step-by-step explanation:

1) [tex]$ 5 \times 10^3 + 4 \times 10^2 + 1 \times 10^1 + 7 \times 10^0 + 4 \times \frac{1}{10^1} + 1 \times \frac{1}{10^2} + 2  \times \frac{1}{10^3} $[/tex]

[tex]$ 5 \times 10^3 = 5000 $\\ $  4 \times 10^2 = 400 $ \\ $   1 \times 10^1 = 10 $\\$  7 \times 10^0 = 7 \times 1 = 7 $\\$  4 \times \frac{1}{10^1} = 0.4 $\\$ 1 \times \frac{1}{10^2} = 0.01 $\\ $  2  \times \frac{1}{10^3} = 0.02 $ \\[/tex]

Combining we have: [tex]$ 5000 + 400 + 10 + 7 + 0.4 + 0.01 + 0.002 = $[/tex] 5417.412.

2) [tex]$ 4 \times 10^2 + 1 \times 1\frac{1}{10^1} + 3 \times \frac{1}{10^2} $[/tex]

[tex]$ 4 \times 10^2 = 400 $\\$ 1 \times 1\frac{1}{10^1} = 1 \times \frac{11}{10} = 1 \times 1.1 = 1.1 $\\$ 3 \times \frac{1}{10^2} = 0.03 $[/tex]

Combining we have: 400 + 1.1 + 0.03 = 401.13.

Hence, we have the answers.

Answer:

m∠FAD=48°

Step-by-step explanation:

we know that

The Perpendicular Bisector Theorem states that: A radius that bisect a chord is perpendicular to the chord

we have

FD=DE

The radius AC bisect the chord FE

so

AC is perpendicular to FE

The triangle FAD is a right triangle

m∠FAD+m∠AFD=90° ---> by complementary angles in a right triangle

we have

m∠AFD=42°

substitute

m∠FAD+42°=90°

m∠FAD=90°-42°

m∠FAD=48°

Answer:

10 hours

Step-by-step explanation:

Two boats leave a port at the same​ time, one going north and the other traveling south.

Southbound boat rate = 40 mph

The northbound boat travels 18 mph faster than the southbound boat.

Northbound boat rate = 40 + 18 = 58 mph

Two boats rate = 40 + 58 = 98 mph (this means they are apart 98 km after one hour)

Total distance = 980 miles

Total rate = 98 mph

Time [tex]=980:98=10[/tex] hours

Answer:

$54

Step-by-step explanation:

let the initial amount of money per person be x

let the total cost of the pizza be y

Before one person left:

10x = y ------------> (eq 1)

After one person left, each of the 9 remaining people had to pay $0.60 extra.

9(x+0.6) = y ----------(eq 2)

equating y from both equations

10x = 9(x+0.6)

10x = 9x+(0.6)(9)

10x = 9x + 5.4     (subtract 9x from both sides)

10x - 9x = 5.4

x = 5.4 (substitute this back into equation 1)

10x = y

y = 10(5.4) = $54

Final answer:

The total bill for the pizza was $54.00. Each of the ten people would have contributed $5.40, but after one person left, the remaining nine paid an additional 60 cents each.

Explanation:

When the tenth person left the group, the nine remaining people each had to pay 60 cents extra for the pizza. This means that the contribution of the tenth person would have been 9 times 60 cents, which is $5.40. To find the total bill, we also need to add the amount that the remaining nine people paid before the extra charge. Since each person originally was going to pay the same amount, this amount is also $5.40. Therefore, each of the 10 people would have paid $5.40 making the total bill 10 times $5.40, which equals $54.00.

Answer:

0.02419354838

"The answer to the question 9 divided by 372 is 0.02419.

To calculate [tex]\[ \frac{9}{372}[/tex] , simply divide the numerator (9) by the denominator (372):

[tex]\[ \frac{9}{372} = \frac{9}{372} \][/tex]

[tex]\[ \frac{9}{372}[/tex] = 0.02419

This fraction cannot be simplified any further because 9 and 372 do not have any common factors other than 1. So, [tex]\[ \frac{9}{372}[/tex]  is already in its simplest form and its value in decimal is 0.02419.

Final answer:

The height of the coin when Jake tosses it is 6 feet.

Explanation:

The equation that models the height and time of the parabola is [tex]h(t) = -16t^2 + 24t + 6.[/tex]

To find the height of the coin when Jake tosses it, we need to determine the height at time t = 0.

Plugging in t = 0 into the equation, we have [tex]h(0) = -16(0)^2 + 24(0) + 6[/tex]

= 6 feet.

So the height of the coin when Jake tosses it is 6 feet.

Answer: B

4x^{6} - 2x^{5} + 4x^{3} -x^{2} +4x

Step-by-step explanation:

3x⁵ - 2x³ + 4x  + 4x⁶ - 5x⁵ + 4x³ - x² =

= 4x⁶ + 3x⁵ - 5x⁵ - 2x³ + 4x³ - x² + 4x

= 4x⁶ - 2x⁵ + 2x³ - x² + 4x

Answer:

n+132

Step-by-step explanation:

Final answer:

The theorems about parallelograms are used in mathematics to find unknown sides or angles and to prove properties of figures. When dealing with vectors, the parallelogram rule for vector addition helps find the resultant by constructing a parallelogram with the vectors as sides and the diagonal as the resultant.

Explanation:

To use theorems about parallelograms to solve problems, we often apply these principles to find unknown sides or angles or to prove certain properties about the figures we are dealing with. For example, one theorem states that opposite sides of a parallelogram are congruent, which can be useful when you need to find the length of a missing side.

Regarding vector addition, the parallelogram rule is applied. According to this rule, if we are adding two vectors, say vector A and vector B, we place them tail to tail, draw the vectors such that they form adjacent sides of a parallelogram, and then the resultant vector is represented by the diagonal of the parallelogram that starts from the common tail of the two vectors.

Similarly, if we need to find the resultant of three or more vectors, we use the parallelogram rule iteratively. We first find the resultant of the first two vectors and then add the third vector to this resultant using the same rule. This process is based on the associative and commutative properties of vector addition.

Total distance traveled by Doris during practice is 2875 meters

Step-by-step explanation:

Given

Distance run by Doris = 2.5km

Converting into meters (as the distance has to be added to other distances, all the distances should be in same unit)

2.5*1000= 2500 meters

Distance covered sprinting = 300 meters

distance walked = 1/4 of 300

[tex]=\frac{300}{4} = 75m[/tex]

Hence,

The total distance will be:

[tex]= Distance\ ran+Distance\ sprinted+Distance\ walked\\= 2500+300+75\\=2875\ meters[/tex]

Hence,

Total distance traveled by Doris during practice is 2875 meters

Keywords: Measurement, Distance

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Answer:

The original price of the computer is $ 6,000  .

Step-by-step explanation:

Given as :

The selling price for the computer = $ 1,500.00

The discount coupon = 75 %

Let the original price or market price of computer = $ x

Now,

Discount % = [tex]\dfrac{\textrm market price - \textrm selling price}{\textrm market price}[/tex] × 100

Or, 75 % = [tex]\dfrac{\textrm x - \textrm 1500}{\textrm x}[/tex] × 100

Or, [tex]\frac{75}{100}[/tex] = [tex]\dfrac{\textrm x - \textrm 1500}{\textrm x}[/tex]

Or, [tex]\frac{1500}{x}[/tex] = 1 - [tex]\frac{75}{100}[/tex]

Or, [tex]\frac{1500}{x}[/tex] = [tex]\frac{100 - 75}{100}[/tex]

Or, [tex]\frac{1500}{x}[/tex] = [tex]\frac{25}{100}[/tex]

Or, x = [tex]\frac{150000}{25}[/tex]

∴  x = $ 6,000

Hence The original price of the computer is $ 6,000  .  answer

Answer:

1) Actual Measurements of Gym = 50 m x 40 m

2)The actual measurements of the closet  =20 m x 10 m

3) if 1 cm  = 12 m the actual dimensions of the gym  are : 60 m x  48 m

4) The area of the gym =  2000 sq m

Step-by-step explanation:

Here, the question is INCOMPLETE.

I am attaching the correct figure for the reference.

Here, The dimensions of Closet are   =   2 cm , 1 cm

The dimensions of gym are = 5 cm , 4 cm

Now as the scale represents 1 cm  = 10 m

So, the ACTUAL dimensions of the closet are :

2 cm  = 2 x  1 cm  = 2 x 10 m   = 20 m

1 cm  = 10 m

And, the ACTUAL dimensions of the gym  are :

5 cm  = 5 x  1 cm  = 5 x 10 m   = 50 m

4 cm  = 4 x  1 cm  = 4 x 10 m   = 40 m

Now, solving the giver parts:

1) Actual Measurements of Gym = 50 m x 40 m

2)The actual measurements of the closet  =20 m x 10 m

3) if 1 cm  = 12 m

the ACTUAL dimensions of the gym  are :

5 cm  = 5 x  1 cm  = 5 x 12 m   = 60 m

4 cm  = 4 x  1 cm  = 4 x 12 m   = 48 m

4) The area of the gym = LENGTH x WIDTH

                                        =  50 m x 40 m   = 2000 sq m.

Answer:

4 more gallons of paint

Step-by-step explanation:

Answer:

$132 in ratio of 2:3:6 is $24, $36 and $72.

Step-by-step explanation:

Dividing $132 in ratio of 2:3:6

Let share of first be = [tex]2x[/tex]

Share of second will be = [tex]3x[/tex]

Share of third will be = [tex]6x[/tex]

Adding the shares

⇒ [tex]2x+3x+6x=11x[/tex]

Total value = $132

So we have,

[tex]11x=132[/tex]

Dividing both ides by 11.

[tex]\frac{11x}{11}=\frac{132}{11}[/tex]

[tex]x=12[/tex]

∴ First share = [tex]2\times 12=\$24[/tex]

∴ Second share = [tex]3\times 12=\$36[/tex]

∴ Third share = [tex]6\times 12=\$72[/tex]

Within 1% , 0.00333 % of the job is complete.

Step-by-step explanation:

The question requires you to find 1/3 of 1%

This is equal to 1/3*1% = 1/3 * 0.01 = 0.00333 % of the job is complete.

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Answer:

0.333 %

Step-by-step explanation:

1/3 expressed as a percentage is: 1/3 * 100 = 33.3 %

Given that the maximum possible percentage is 1, then we have to divide this result by 100 (because 100/100 = 1). So, 33.3 % is transformed into 33.3/100 = 0.333 %.

Answer:

[tex]m\angle A=\tan^{-1}(\frac{m}{n})[/tex]

[tex]AB=\sqrt{m^2+n^2}[/tex]

Step-by-step explanation:

Given:

In Δ ABC

m∠C= 90°

[tex]BC=m[/tex]

[tex]AC=n[/tex]

For the triangle ABC we can apply trigonometric ratio to find m∠A.

We have:

[tex]\tan\angle A=\frac{BC}{AC}[/tex]

Substituting values of side BC and AC

[tex]\tan \angle A=\frac{m}{n}[/tex]

Taking inverse tan to get m∠A.

∴ [tex]m\angle A=\tan^{-1}(\frac{m}{n})[/tex]

AB can be found out using Pythagorean theorem:

AB being the hypotenuse can be written as

[tex]AB^2=BC^2+AC^2[/tex]

Substituting values of side BC and AC

[tex]AB^2=m^2+n^2[/tex]

Taking square roots both sides:

[tex]\sqrt{AB^2}=\sqrt{m^2+n^2}[/tex]

∴ [tex]AB=\sqrt{m^2+n^2}[/tex]

Answer:

3x^4-75

Step-by-step explanation:

3(x^2+5)(x^2-5)

3(x^4+5x^2-5x^2-25)

3(x^4-25)

3x^4-75

Just multiply each term out and combine like terms.

Mean = -2

Median = -1

Mode = Nil

Range = 38

Step-by-step explanation:

Given data is:

-18, 10, -20, -11, 9, 18

Arranging the data in ascending order

-20, -18, -11, 9, 10, 18

Mean:

Mean is given by the formula

[tex]Mean=\frac{Sum}{items}[/tex]

Items are: 6

[tex]Mean = \frac{-20-18-11+9+10+18}{6}\\= \frac{-12}{2}\\= -2[/tex]

Mode:

Mode is the most frequent value in the data. So,

As there is no value repeated in the data. There is no mode

Median:

Median is the middle value of the data. As the no. of data value are even,

the average of middle 2 values is mode.

Note that the data has to be arranged in ordered to find median

Here,

[tex]Median = \frac{-11+9}{2}\\=\frac{-2}{2}\\= -1[/tex]

Range:

Range is the difference between the largest and smallest value of the data

Here

Largest value = 18

Smallest value = -20

So,

[tex]Range = Largest\ value-Smallest value\\= 18-(-20)\\= 18+20\\=38[/tex]

Hence,

Mean = -2

Median = -1

Mode = Nil

Range = 38

Keywords: Data, Median

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Answer:

∠ MLN = 21°

Step-by-step explanation:

See the attached diagram.

We are given that ∠ OLN = 31° and ∠ MLO = 52°.

So, the diagram is like that OL is the baseline of both the angles and two different lines one LM and the other LN are drawn from point L such that two angles will form and the measurement of ∠ OLM = 52° and ∠ OLN = 31°.

So, there will another angle form which is ∠ MLN which measures (52 - 31) = 21° (Answer)

Answer:

the rate of change is 0.1

Step-by-step explanation:

the rate of change is the slope

which equals to (y2-y1)/(x2-x1)

(2.7-2.3)/(17-13)=0.1