label the following number on the line in the appropriate location
3/5
120%
0.07
83%
1 2/3
35%
______0__________1__________2__​

Answer:

See below

Step-by-step explanation:

\(( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) = 1 - 2 { \cos}^{2} \theta \\ \\ LHS = ( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) \\ \\ = \sin^{2} \theta - \cos^{2} \theta \\ \\ =1 - \cos^{2} \theta - \cos^{2} \theta \\( \because \sin^{2} \theta =1 - \cos^{2} \theta) \\ \\ = 1 - 2 { \cos}^{2} \theta \\ = RHS\)

Thus proved

Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.

What are basic arithmetic operations?

Basic arithmetic operations are fundamental mathematical calculations that involve manipulating numerical values using a set of basic operations.

To find out how many points Antonio needs to score in his next game to reach an average of at least 100 points per game, we can use the following formula:

Total points needed = (number of games + 1) × average score goal - total points scored so far

In this case, Antonio has played 5 games, so the number of games he will have played after his next game is 6. His goal is an average of 100 points per game, so his average score goal is 100. The total points he has scored so far is:

105 + 95 + 97 + 82 + 110 = 489

Substituting these values into the formula, we get:

Total points needed = (6) × (100) - 489

Total points needed = 600 - 489

Total points needed = 111

Hence, Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.

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Answer:

the action of inflating something or the condition of being inflated.

"the inflation of a balloon"

ASTRONOMY

(in some theories of cosmology) a very brief exponential expansion of the universe postulated to have interrupted the standard linear expansion shortly after the Big Bang.

2.

ECONOMICS

a general increase in prices and fall in the purchasing value of money.

"policies aimed at controlling inflation"

Answer:

0

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

a2+b2+c2

4^2+6^2= c2

16+36=52

C=52

√52=7

C=7

Answer:

7

Step-by-step explanation:

This is a right triangle so we can find the value of c using the pythagoras' teorem

c^2 = a^2 + b^2

c^2 = 4^2 + 6^2

c^2 = 52

c = 7 approximately

Answer:

230cm²

Step-by-step explanation:

We can split the shape into 2 parts - the triangle and the rectangle.

The area of the retangle is 10*17cm = 170cm²

The area of the triangle  = 1/2 * (22-10) * (17-7)

                                         =  1/2 * 12 * 10 = 60

Therefore the total area is equal to 170+60 = 230cm²

Answer:

\(BC=5.1\)

\(B=23^{\circ}\)

\(C=116^{\circ}\)

Step-by-step explanation:

The diagram shows triangle ABC, with two side measures and the included angle.

To find the measure of the third side, we can use the Law of Cosines.

\(\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}\)

In this case, A is the angle, and BC is the side opposite angle A, so:

\(BC^2=AB^2+AC^2-2(AB)(AC) \cos A\)

Substitute the given side lengths and angle in the formula, and solve for BC:

\(BC^2=7^2+3^2-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-42\cos 41^{\circ}\)

\(BC^2=58-42\cos 41^{\circ}\)

\(BC=\sqrt{58-42\cos 41^{\circ}}\)

\(BC=5.12856682...\)

\(BC=5.1\; \sf (nearest\;tenth)\)

Now we have the length of all three sides of the triangle and one of the interior angles, we can use the Law of Sines to find the measures of angles B and C.

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

In this case, side BC is opposite angle A, side AC is opposite angle B, and side AB is opposite angle C. Therefore:

\(\dfrac{\sin A}{BC}=\dfrac{\sin B}{AC}=\dfrac{\sin C}{AB}\)

Substitute the values of the sides and angle A into the formula and solve for the remaining angles.

\(\dfrac{\sin 41^{\circ}}{5.12856682...}=\dfrac{\sin B}{3}=\dfrac{\sin C}{7}\)

Therefore:

\(\dfrac{\sin B}{3}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin B=\dfrac{3\sin 41^{\circ}}{5.12856682...}\)

\(B=\sin^{-1}\left(\dfrac{3\sin 41^{\circ}}{5.12856682...}\right)\)

\(B=22.5672442...^{\circ}\)

\(B=23^{\circ}\)

From the diagram, we can see that angle C is obtuse (it measures more than 90° but less than 180°). Therefore, we need to use sin(180° - C):

\(\dfrac{\sin (180^{\circ}-C)}{7}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin (180^{\circ}-C)=\dfrac{7\sin 41^{\circ}}{5.12856682...}\)

\(180^{\circ}-C=\sin^{-1}\left(\dfrac{7\sin 41^{\circ}}{5.12856682...}\right)\)

\(180^{\circ}-C=63.5672442...^{\circ}\)

\(C=180^{\circ}-63.5672442...^{\circ}\)

\(C=116.432755...^{\circ}\)

\(C=116^{\circ}\)

\(\hrulefill\)

Additional notes:

I have used the exact measure of side BC in my calculations for angles B and C. However, the results will be the same (when rounded to the nearest degree), if you use the rounded measure of BC in your angle calculations.

answer is 261

Step-by-step explanation:

add both numbers together

The measure of side length x in the right triangle is approximately 6.03 cm.

The figure in the image is a right triangle having one of its interior angle at 90 degrees.

From the figure:

Angle θ = 37 degrees

Adjacent to angle θ = 8 cm

Opposite to angle θ = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( θ ) = opposite / adjacent

Plug in the given values and solve for x:

tan( 37 ) = x / 8

x = tan( 37 ) × 8

x = 6.03 cm

Therefore, the value of x is 6.03 cm.

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Answer:

The answer is 3 or x<3.

Answer:

m<FCE = 45°

Step-by-step explanation:

Given that ∆ABD ≅ ∆FEC, therefore,

<A ≅ <F

<B ≅ <E

<ADB ≅ <FCE

m<ADB = 45°

Therefore,

m<ADB = m<FCE = 45°

m<FCE = 45°

There are two degrees, one variable and one number.

Answer:

2

Step-by-step explanation:

Zack purchased approximately 269.608 shares of the mutual fund.

To determine the number of shares Zack purchased, we need to divide the total amount he invested by the offer price of the mutual fund.

Given:

Investment amount: $5,500

Offer price: $20.40

To calculate the number of shares, we divide the investment amount by the offer price:

Number of shares = Investment amount / Offer price

Number of shares = $5,500 / $20.40

To simplify the calculation, we can divide both the numerator and denominator by 10. This does not change the result, but it makes the division easier:

Number of shares = $550 / $2.04

Now, we can perform the division:

Number of shares ≈ 269.6078

Since we are asked to round to thousandths, we can round the result to three decimal places:

Number of shares ≈ 269.608

Therefore, Zack purchased approximately 269.608 shares of the mutual fund.

It's important to note that in financial calculations, it is common to round the number of shares to the nearest whole number since partial shares are not typically traded. In that case, Zack would have purchased 270 shares. However, since the question asks for the answer rounded to thousandths, we have provided the answer as 269.608 shares.

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Answer:

4% used pastels.

Step-by-step explanation:,,

green is the most

5 isnt blue.green,yello or red

The percentage of the class-preferred pastels will be 25%. The color there has most pastels will be Green. And the number of pastels that are colors other than blue, green, red, or yellow will be 7.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

Out of 24 students, 6 preferred to use pastels for their portraits while 4 preferred to use watercolors. Then the percentage of the class preferred pastels will be

P = 6 / 24 x 100

P = 0.25 x 100

P = 25%

Jasmin bought a box of 40 assorted colored pastels, 1/5 are blue, 3/10 are green, 20% are red and 5 are yellow. Then the number of pastels of each color will be

Blue = 1/5 = 8 / 40 = 8

Green = 3/10 = 12 / 40 = 12

Red = 0.2 = 1/5 = 8 / 40 = 8

Yellow = 5

The number of pastels are colors will be

⇒ 40 - 8 - 12 - 8 - 5

⇒ 40 - 33

⇒ 7

The color there has most pastels will be Green. And the number of pastels that are colors other than blue, green, red, or yellow will be 7.

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Answer:

We have to write the equation in standard form of a vertical line that pass through point (3,0).

Vertical lines are expressed as x = constant.

In this case, as it has to pass through (3,0), the line is x = 3.

Answer: x = 3

We need to find the probability that two people are selected from the accounting department and one will be from the sales department. To do that, we need first to determine the total amount of people. We have that for each department the number of people is:

Therefore, the total number of people is:

Now, for this problem, we need to use combinatoric of a selection without replacement. The number of possible combinations of possible "r" combinations of a population of "n" individuals is given by the formula:

In our case we have to determine first the total number of combinations from selecting 3 people of the total population, that is:

replacing in the formula we get:

Solving the operations we get:

Now we find the possible combination of getting 2 people from a total of 5 people from the accounting department, that is:

replacing in the formula we get:

Solving the operations we get:

Now we find the total combinations of getting 1 person from a total of 3 people in the sales department, that is:

Replacing in the formula:

Solving the operations we get:

The total number of possible outcomes is then the product of both combinations, that is:

The probability is then given by the formula:

Replacing we get:

Solving we get:

Answer: the answer is 3

Step-by-step explanation:

because the leaf is the ones place so all you need to do is count the amount of 5's in each stem

Answer: h = 22.5

Step-by-step explanation:

Total angle area of a 12 sided polygon is 1800

1. One angle would be 1800/12= 150

2. Add 30 one each side to cancel out and only leave 8h.

3. To get rid of the 8 we divide the the other side by 8.

The answer is 22.5

Answer: D 22.5 i got it right on the exam

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

the two numbers' primary factors are as follows:

-25\(b^{2}\) + 15b

Common prime factors can be multiplied to determine the GCF:

=> -25\(b^{2}\)  = -(5)(5) * \(b^{2}\)

=> 15b = (5)(3)b

The expression can be factored in the following fashion because the GCF is 5b:

=> -(5)(5) * \(b^{2}\) +  (5)(3)b

=> (5b)(-5b+3)

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

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Answer:

0.7727 = 77.27% probability that it is small or green

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

11 large + 11 small = 22 total marbles = 22 total outcomes

11 small marbles  + 6 green large marbles = 17 desired outcomes.

What is the probability that it is small or green?

\(p = \frac{17}{22} = 0.7727\)

0.7727 = 77.27% probability that it is small or green

The anwer is YES, let's see why:

If we solve for y, as in the second equation, we can see that "y" will have a value depending on which value "x" will take.

Actually, this is the meaning of function involving independent and dependent variables ( x and y, respectively)

Answer:

Step-by-step explanation:

the consecutive are 39,40,41 and the smallest here is 39

Hope this helped

The mean absolute deviation is 2.5.

The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.

How to calculate the mean deviation from the mean:

Given data:1, 1, 3, 5, 5, 6, 8, 11

So, mean of the data is

= 1+ 1 +3 +5 +5+ 6+ 8 +11 / 8

= 40 /8=

5

Now, Mean absolute deviation is

= | 1-5| + |1-5| + |3-5 | + |5-5| + |5-5| + |6-5| + |8-5| + |11-5|/ 8

= 4 + 4 + 2+ 0 + 0+ 1 + 3 +6 /8

= 20/8

=2.5

Hence, the mean absolute deviation is is 2.5.

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Answer:

The magnitude of the vector is 9.165 and it's direction is 40.6°

Step-by-step explanation:

A vector quantity is a quantity that has both size (magnitude) and direction. Examples of vector quantities are force, velocity and impulse.

Magnitude of vector v is given by

|v| = √6²+7²

= √36+49

= √84

= 9.165

Direction of vector v is obtained by:

\( \tan( \theta) = \frac{x}{y} \)

\(\theta = {tan}^{ - 1} ( \frac{6}{7}) \)

\(\theta = {40.6°}\)

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Answer:

17.5

Step-by-step explanation:

35÷y = 140 ÷ 70

or, 35 = 2y

or, y= 17.5

Answer:

h = 13.5 cm

Step-by-step explanation:

When:

V = 64 cm³

B = 24 cm²

Then:

h = 8 cm

Ratio stuff:

\(h=(\frac{72}{64})( \frac{36}{24} )(8)\\h=1.6875(8)\\h= 13.5\)

Answer:

The correct answer is Option c (120).

Step-by-step explanation:

The given value is:

\(a_1=1\)

\(a_n=n(a_{n-1})\)....(equation)

On putting the value of \(a_1\) in the above equation, we get

⇒ \(a_2=2(a_{2-1})\)

        \(=2(a_1)\)

        \(=2\times 1\)

        \(=2\)

⇒ \(a_3=3(a_{3-1})\)

        \(=3(a_2)\)

        \(=3\times 2\)

        \(=6\)

⇒ \(a_4=4(a_{4-1})\)

        \(=4(a_3)\)

        \(=4\times 6\)

        \(=24\)

hence,

⇒ \(a_5=5(a_{5-1})\)

        \(=5(a_4)\)

        \(=5\times 24\)

        \(=120\)

Thus the above is the correct solution.

According to the information, this number on an abacus would look like this: tens of a thousand = 10,000, units of a thousand = 6,000, hundreds = 500, tens = 10, and units = 6.

To illustrate this value on an abacus we must find the number of this operation as shown below:

Now we must express it in an abacus, then we must separate each number by classifying it in the type of units to which it corresponds as shown below:

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