At a football game, a vender sold a combined total of 191 sodas and hot dogs. The number of sodas sold was 43 more
than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Number of sodas sold:

The altitude of an isosceles triangle is sqrt (a^2 - b^2 / 4).

In the triangle ABC, sides AB and AC are equal (say a) and side BC = b. Let  us consider the triangle ADC which is the right triangle in the isosceles triangle ABC, and by Pythagoras' theorem,

we get that the altitude AD of the isosceles triangle can be obtained:

AD ^ 2 = AC ^ 2 - (BC / 2) ^2

AD ^ 2 =  (a ^ 2 - b ^ 2 / 4)

AD = sqrt (a ^ 2 - b ^ 2 / 4).

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The volumes of the cone and cylinder are 1256m³ and 5652m³

For a cylinder, the formula is πr²h. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h.

Given here dimensions as the height of the cone = 12m and radius of its circular base = 10m and the height of the cylinder = 18m

thus  Volume of the cone = 1⁄3πr²h

                                      = 1/3×3.14×100×12

                                      = 1256m³

And the volume of the cylinder = πr²h

                                                    = 3.14×100×18

                                                     = 5652m³

Therefore the volumes of the cone and cylinder are 1256m³ and 5652m³

Hence,  the volume of the solid is 1256+5652 =6908m³

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Answer:

24 Square Units (B)

Step-by-step explanation:

⭐ The formula for the area of any triangle is: 1/2(bh), where b = base, and h = height.

⭐ The height of a triangle is the triangle's altitude, which can be denoted by a straight line with a right angle. In this problem, the height is given to you.

Let's substitute what we are given to find the area.

Answer:

8(11x-13)

Step-by-step explanation:

[tex]13(5x-8)+23x\\65x-104+23x\\88x-104\\8(11x-13)[/tex]

0.03, 0.04, 0.38, and 1 are the figures that could represent an event's likelihood .Probability is calculated by dividing the total possible outcomes by the number of outcomes that are theoretically possible

Probability is calculated by dividing the total possible outcomes by the number of outcomes that are theoretically possible. Probability differs from odds in this regard. Calculating odds involves dividing the likelihood of a particular event by the likelihood that it won't occur.

The likelihood of success is a measure of probability. the number of potential outcomes. For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We specify P(heads) = 12.

6. P(7) = 1/10

7. P(less than 5) = 4/10 = 2/5

8. P(greater than 10) = 5/10 = 1/2

11. P(divisible by 2 or 3) = 6/10 = 3/5

12. P(moon) = 8/36 = 2/9

13. P(star) = 12/36 = 1/3

14. P(blue moon or planet) = (6+9)/36= 15/36= 5/9

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Answer:

Step-by-step explanation:

6. P(7) = 1/10

7. P(less than 5) = 4/10 = 2/5

8. P(greater than 10) = 5/10 = 1/2

11. P(divisible by 2 or 3) = 6/10 = 3/5

12. P(moon) = 8/36 = 2/9

13. P(star) = 12/36 = 1/3

14. P(blue moon or planet) = (6+9)/36= 15/36= 5/9

Answer:

A. 4,500 + 50g = 6,000

Step-by-step explanation:

25(18) + 50(g) = 6000

4500 + 50g = 6000

The correct option is A.

Answer:

The interest is $36 or $3600 cent

Step-by-step explanation:

6% = 0.06

Take 600 times 0.06 = $36

$1 = 100 cent

$36 = $3600 cent

So, the interest is $36 or $3600 cent

Answer:

Let A = total amount principal + interest

P = principal amount , $600

R = interest rate, 0.06

T = time , 1

A = P(1 + r)^t

A = 600(1 + 0.06)               we dont have to put 1 as exponent

A = 600(1.06)

A = 636

Interest = A - P

Interest = 636 - 600

Interest = 36

Step-by-step explanation:

43 in arithmetic stands for multiplying 4 by three. Suppose x =43; then, x+4*4*4.

If the power is positive, multiply the integer by itself that many times. If the power is negative, multiply the reciprocal of the integer by itself that many times. If the power is 0, the result is always 1.

No, 3:9 and 9:3 are not equivalent. 3^9=19683 and 9^3=729.

4^3=4*4*4\s =16*4\s =64

In the US and Canada, math is the word of choice. In the United Kingdom, Ireland, Australia, and other English-speaking countries, math is the preferred term. There isn't really a rational reason why math grew more popular in certain locations while maths was elsewhere.

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Answer:

9% decrease

Step-by-step explanation:

Hope this helps!

Therefore , the distance travelled by the 2kg block is 281.25m  and the energy of the block earth is  14.0625 J

It can push or pull. Acceleration is caused by unbalanced forces.

The Newton is the symbol for a force (abbreviation is N).The force required to cause a mass of one kilogramme to alter its velocity by one metre per second (m/s) per second is one Newton. The formula is: 1 N = 1 kg m/s2 (kilogram metre per second squared)

Here,

Let s represent the block's total distance travelled.

As a result, the block's work will be equal to the potential energy contained in the spring.

It is given as,

(mgsinθ)×s= 1/2 k[tex]x^{2}[/tex]

( √2​ ×10×sin45 ∘ )×s= 1/2​ ×100 x (0.75*0.75)

s=281 . 25m

Thus, the distance travelled by the block is 281 . 25m.

For energy :

=> 1/2 m v^2

=>  1/2 * 2* (3.75)^2

=> 14.0625  J

Therefore , the distance travelled by the 2kg block is 281.25m  and the energy of the block earth is  14.0625 J

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The distance travelled by the 2kg block is 281.25m  and the energy of the block earth is  14.0625 J

When an object is moved over a distance by an external force, at least a portion of that force must be applied in the direction of the displacement. This is known as work in physics.

The ability to exert a force that causes an item to move is what is meant by the definition of energy as the "power to accomplish work."

Let s= total distance travelled by block.

Therefore, the block's work will be equal to the spring's potential energy.

According to given information,

(mgsinθ)×s= 1/2 k

( √2​ ×10×sin45  )×s= 1/2​ ×100 x (0.75*0.75)

s=281 .25m

Therefore, the distance travelled by the block is 281 . 25m.

For energy we have:

=> E= 1/2 m v^2

=>  E= 1/2 * 2* (3.75)^2

=>E= 14.0625  J

So , the distance travelled by the 2kg block is 281.25m  and the energy of the block earth is  14.0625 J.

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The AAA (angle-angle-angle) similarity theorem states that two triangles' corresponding angles are identical if and only if their corresponding sides are proportionate.

Knowing two angles, such as 32° and 64°, we may calculate the following angle, which is 84°, since 180-(32+64)=84. (This is commonly referred to as the AAA Postulate—which is valid in every way, although two angles are more than enough.) Working backwards will help you understand the proposition better.

The sides and angles of a set of triangles must be equal for them to be congruent. The sides of a triangle with all respective angles equal, i.e. AAA condition, may or may not be equal.

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On solving the provided question, we can say that the value of x = 5√3

and value of y = 10.

How to find the value of x and y?

To find the values of x and y, you will need to use

According to the given question:

Using the table of trig values, we find that

sin30°=1/2

So, this gives us:

1/2 = sin 30° = 5/y

1/2 = 5/y

(1xy)/2 = 5

y= 2×5 =10

Next, using the Pythagorean Theorem, we find that

5²+x²=10²

x²=100−25=75

Solve for x:

x=√75=√3×25=5√3

Complete question:

How do you find the value of X and Y. Y is the hypotenuse, 5 is the adjacent side and X is the opposite side from Y, and in the triangle there is 30 degrees where X and Y lines meet?

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Answer: 4.5 minutes

Step-by-step explanation:

Take 126 divided by 28 = 4.5 minutes

Answer:

x = 30.6 ft

A = 58.1°

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

As the triangle is a right triangle, use Pythagoras Theorem to find length x.

[tex]\implies x^2+19^2=36^2[/tex]

[tex]\implies x^2+361=1296[/tex]

[tex]\implies x^2=935[/tex]

[tex]\implies x=\sqrt{935}[/tex]

[tex]\implies x=30.6\; \sf ft \;\; (3\;s.f.)[/tex]

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute the values into the formula and solve for A:

[tex]\implies \sf \cos A=\dfrac{19.0}{36.0}[/tex]

[tex]\implies \sf A= \cos^{-1}\left(\dfrac{19}{36}\right)[/tex]

[tex]\implies \sf A=58.1^{\circ}\;\;(3\;s.f.)[/tex]

Answer: 520 miles per hour

Step-by-step explanation:

65 times 8 = 520 miles per hour

Therefore , the factors of the given equation are (x + 4), (x - 5) and (x + 1)

The equal sign is used between numerical or changeable expressions to create an equation, such as 3x+5=11.

A number that can be entered as the variable's replacement in an equation serves as the solution.

Here,

The first term, x2, has a coefficient of 1 and is the starting term.

The coefficient of the middle word, +5x, is 5, thus

"The constant," the final word, is +4.

Step 1: Multiply the first term's coefficient by the formula 1 + 4 = 4.

Step 2 is to identify two factors of 4 whose sum equals the middle term's coefficient, which is 5.

     -4    +    -1    =    -5

     -2    +    -2    =    -4

     -1    +    -4    =    -5

        4          +            1      =    5    

Step 3: Rewrite the polynomial by separating the middle term into the two parts 1 and 4 x2 + 1x + 4x + 4 discovered in Step 2 above.

Step-4 : adding the first two terms while excluding similar elements

                   x • (x+1)

             Adding the last two terms together and finding commonalities:

                   4 • (x+1)

Step-5 : In step 4, add up the four terms:

                   (x+4)  •  (x+1)

            Which is the desired factorization

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An example expression is the following:

$100 + $50n

An algebraic expression is a set of letters and numbers, in which the letters are called variables and take on an unknown value, the numbers are coefficients or independent terms while the variables are dependent terms.

We will write an algebraic expression to exemplify what has just been defined, with a verbal example.

A person has a business, and he adds $100 to the box (and his sales are on average $50 per hour, with this we build the expression of total income:

$100 + $50n

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If Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. The amount that is closest to how much she will earn in hourly wages and commission for those two weeks is A $592.

Earnings can be defined as the money a person earn as wages or as salary.

First step is to find the amount that Sandy earns per hours

Earnings per hour = 9+ (0.15×9)

Earnings  = $10.35 per hour

Second step is to find her earnings

Earnings =73 × $10.35

Earnings = $755.55

Closest amount is $592.

Therefore  the correct option is A.

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The complete question is:

Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 73 hours over the last two weeks and had a total of $2,830 in sales before taxes.

Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?

A $592

B $890

C $386

D $298

Answer:

75%

Step-by-step explanation:

[tex]\frac{15}{20} \times 100=75\%[/tex]

Answer:

Step-by-step explanation:

138 cm² = (x + 2) × ( 2x + 3) x 1/2​

138 cm² = x + 2 ×  2x + ) x 1/2​

138 cm² = x + 4x + x * 0.5

0.5/138 cm² = 6x * 0.5 /0.5

6/69cm²  = 6x/6

x = 11.5

This might be wrong so just take the square root of 138.

The arithmetic mean of the set of numbers 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20 is 15.5. This is the average value of the set, and it is affected by all the values in the set.

The arithmetic mean, also known as the average, of a set of numbers is found by adding up all the numbers in the set and dividing by the total number of numbers in the set. In this case, the set of numbers is 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20. When we add up all the numbers in the set, we get a total of 155. There are 10 numbers in the set, so the average is 155 / 10 = 15.5.

To find the arithmetic mean, we first need to add up all the numbers in the set. Then, we divide that sum by the total number of numbers in the set. This gives us the average value of the set.

In summary, the arithmetic mean of the set of numbers 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20 is 15.5. This is the average value of the set, and it is affected by all the values in the set.

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Thousands, hundreds and tens are three examples of values and there are many more.

Value in mathematics is a number that represents the outcome of a computation or function. In the aforementioned example, you may inform your teacher that 5 + 6 Equals 30 or that x + y = 9 if x = 6 and y = 3. A variable or constant can also be referred to as a value.

The number 4 is in this case in the tens column. As a result, the place value of the number four is tens or tens.

Thousands, hundreds and tens are three examples of values and there are many more like ones etc. Moreover after solving any problem for unknown variable the resulting numerical solution can also be termed as value.

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The system has no solution.

What is linear equations?

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y)

We know that

The solution of the system of two linear equations, is the intersection point both lines.

In this problem

The lines are parallel, the lines don't intersect

therefore

The system has no solution

Remember that, if two lines are parallel then their slope are equal

Verify that the slopes are the same

Blue line

take the points  (0,2) and (-2,0)

[tex]m=(0-2) /(-2-0)=1[/tex]

Red line

take the points  (0,-3) and (3,0)

[tex]m=(0+3) /(3-0)=1[/tex]

The slopes are equal

The lines are parallel

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The parallel equation of y = 3x + 1 is y = 3x

The slope is computed mathematically as "rise over run" (change in y divided by change in x).

In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.

That is to say,

Given equation: y = 3x + 1

A point from which the parallel line will pass through is (0,0)

To find the slope using the slope-intercept form:

The slope-intercept form is: y = mx + b

Where, m = slope

b = y - intercept

Now comparing this equation with given equation, we find, slope (m) = 3

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Use the slope 3 and a given point (0,0) to substitute for x₁ and y₁ in the point slope form: y - y₁ = m (x - x₁), which is derived from the slope-equation,

m = (y₂ - y₁)/ (x₂ - x₁)

so, putting the value we get,

y - 0 = 3 ( x - 0 )

or, y + 0 = 3 ( x +0 )

or, y = 3x + 0

or, y = 3x

The graph is shown below:

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The complete question is as follows:

What is the parallel equation of y = 3x + 1

“3 more than 5” written as an algebraic expression is “3+5” which is equal to 8.

In a formula or equation involving mathematical operations, the representation of numbers by alphabet is referred to as algebra. Similar to how a statement explains the link between certain words, algebraic equations describe the connection between unknown variables.

We are given a mathematical statement and have to convert it into an algebraic expression using the information above.

3 more than 5 is obtained after adding 5 to the given number which is 3.

So 3 more than 5 is equal to 3+5=8.

Hence “3 more than 5” written as an algebraic expression is “3+5” which is equal to 8.

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Answer:

C 0.91 D 0.999 E 1.05 and A 1.11 =1

Answer:

If in triangles ABC and DEF, angle A = angle D = right angle, AB = DE (leg), and BC = EF (hypotenuse), then triangle ABC is congruent to triangle DEF.

This is an arithmetic sequence. In this sequence, the common difference is 6 (12 - 3/6 = 6).

A sequence is an ordered arrangement of objects or events which follow one another in a specific order. This order can be based on a mathematical rule or pattern, such as a sequence of numbers, or it can be based on physical or temporal characteristics of the objects or events, such as the order in which they appear in a movie or story. Sequences are useful for representing and analyzing data, as well as for visualizing relationships between objects. They can also be used to model problems, such as predicting the future or solving a puzzle.

This is an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a constant, called the common difference, to the preceding term. In this sequence, the common difference is 6 (12 - 3/6 = 6).

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The mean of the given data set is 26.

One of the most significant and often employed metrics of central tendency is the mean. In mathematics, there are various different kinds of means. In statistics, the mean is the product of all the values in a set of data divided by the total number of values in the data for a particular set of observations.

To put it another way, calculating the mean of a data set only requires adding up all the values and dividing the result by the total number of values.

The mean formula in statistics for a set is defined as the sum of the observations divided by the total number of observations.

Mean = 25+30+27+23+25/5

Mean = 130/5 = 26

Thus, the mean of the given data set is 26.

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The mean formula in statistics for a set is defined as the sum of the observations divided by the total number of observations.

Mean = 25+30+27+23+25/5

Mean = 130/5 = 26

Thus, the mean of the given data set is 26.