Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup. How much pure sugar is in x grams of 10% syrup?​

4(-6), 6(-4), and 12(-2). (-2). Each one adds up to -24. I am aware of this because if you multiply the two numbers and one of the numbers is negative, the result will also be negative. The item will be favorable if there are just two drawbacks.

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Answer:

Below

Step-by-step explanation:

sin (90 -0) = sin (90) = 1

Remember   sin^2 + cos^2 =1

  for theta       sin2 + (3/4)^2

                         sin^2 = 1 - 9/16 = 7/16

                            sin (theta) = ± sqrt(7) /4

The speed of the cars are 50mph and 60mph

Let's call the speed of the slower car "x". The faster car is traveling at "x + 10 mph".

The total distance both cars travel is 660 miles, and the time it takes for them to meet is 6 hours.

Using the formula for distance = rate x time, we can set up the equation:

x * 6 + (x + 10) * 6 = 660

Expanding and simplifying, we get:

12x + 60 = 660

Subtracting 60 from both sides:

12x = 600

Dividing both sides by 12:

x = 50 mph

So the slower car is traveling at 50 mph and the faster car is traveling at 60 mph.

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Answer:

Below

Step-by-step explanation:

From 7 to 10 AM is THREE hours (if the times are all on the same day)

Answer:

Step-by-step explanation:

As an example, let's say I have a pond 7 feet long, 6.5 feet wide, and 3 feet deep. That gives me approximately 1,000 gallons of water. The average recommended gallons per inch of fish is 10. To calculate how many inches of fish I can fit in my pond I would divide 1,000 by 10: 1,000/10 = 100.

I know it is not the answer but I hope this helps you.

Answer:

The scarf cost:

$9.91

Step-by-step explanation:

9.92 - 0.01 = 9.91

Answer: 4

Step-by-step explanation:

Alexia has 22$ total:
Therefore, after taking away the 10$ dollar admission fee, she has 12$ left.

12$ dolars divided by 3$ dollars per ride equal 4 rides.

The answer is 4 rides to spend exactly 22$

The probability of success at the second mall is 3/4 which mall should be chosen in order to maximize the expected profit $135,000.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

First mall:

Profit if successful = $300,000

Loss if otherwise = $100,000

Probability of success = 1/2

Second mall:

Profit if successful = $200,000

Loss if otherwise = $60,000

Probability of success = 3/4

If probability of profit 'P(profit)' = 3/4

Then,

Probability of loss P(loss) = 1 - P(profit)

P(loss) = 1 - 3/4 = 1/4

Expected profit:

= [P(profit) x profit] + [P(loss) x loss])

= (0.75 x $200,000) + (0.25 x (-$60,000))

= 150,000 - 15000

= $135,000

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The equation of the line is y = x + 6

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following highlights

The graph intersect the y-axis at y = 6

This means that the intercept c is 6

Also, as x changes by 1, the y values changes by 1

This mean sthat the slope is 1

So, we have

y = mx + c

This gives

y = x + 6

Hence, the equation is y = x + 6

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The linear equation on the graph can be written as:

y = (3/2)*x + 6

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁), then the slope will be:

a = (y₂ - y₁)/(x₂ - x₁)

In this case we can see the points (0, 6)  (so the y-intercept is b = 6)  and (4, 10)

Then the slope will be:

a = (10 - 6)/(4 - 0) = 6/4 = 3/2

Then the linaer equation is:

y = (3/2)*x + 6

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The least common denominator for each pair of fractions is as follows:

33.) = 6

33.) = 634.) = 7

33.) = 634.) = 735.) = 30

The least common denominator is defined as the lowest number that can divide a given set of numbers.

28= 2×2×7

7 = 7

The least common denominator would be 7

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The sum of 5 of the interior angles of a regular octagon is 675°.

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."

A regular octagon has equal interior angles.

And one interior angle is equal to 135°.

The sum of 5 of the interior angles of a regular octagon,

= 135 x 5

= 675°

Therefore, the sum is 675°.

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A catapult launches a pumpkin from the base of a hill. The hill follows an incline with the height in meters, y, in terms of horizontal distance in meters, x, given by the equation y=0.9x. 40m is the height, where the pumpkin lands on the hill.

The term "horizontal distance" refers to the separation between two places measured with a slope of 0%. Vertical distance is the distance following the direction of gravity, while horizontal distance is the distance along the ground surface. The distance between an observer and a building represents as that of an example of horizontal distance, and the structure's height serves as an illustration of vertical distance. A projectile's range is the horizontal distance it covers. Horizontal refers to something that is parallel to it. Anything that forms a 90-degree angle (right angle) with the horizontal or the horizon is referred to as vertical since it is the opposite of the horizontal. The line that spans from left to right is therefore considered to be horizontal.

Given that,

The hill follows an incline with the height in meters y,

in terms of horizontal distance in meters x,

The given equation becomes: y = 0.9x

The height of the pumpkin, as it is launched up hill, is given by the function:

y = -0.1x² + 4.9x

now, finding point of intersection, we get:

0.9x = -0.1x² + 4.9x    [as y = 0.9x]

or, 0.1x² - 4x = 0

or,  x (0.1x - 4) = 0

or, x = 0 (this is not possible)

and 0.1x = 4

or, x = 40

40 is the height, in meters, where the pumpkin lands on the hill.

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Answer: Dude this is pretty easy!

Step-by-step explanation: Use the process of elimination.

Hint: It's just subtraction or addition. Trust me it's easy.

Answer:

Step-by-step explanation:

1/4 min, 15 sec

Answer:

a. Point C is at (8,8)

b. See image/expl

c. AngleABC = 140°

Step-by-step explanation:

You can just count squares to find the slope of AD. To find points along AD, go

UP1 and OVER4

UP1 and OVER4 is the slope 1/4.

Start from B and go

UP1 and OVER4.

Parallel lines have the same slope. Perpendicular lines have slopes with opposite sign and "flipped". To make CD perpendicular to AD the slope should be -4/1 or 4/-1 is the same thing. To find C go from D

UP4 and BACK1

this is the slope 4/-1

1/4 and 4/-1 are negative reciprocals (opposite sign and flipped over) so the lines will be perpendicular.

You cab use this explanation for part b. Or you the slope calculations using the coordinates. See image.

part c, see image.

Solution is in the attachment!!

a) The measure of angle 3 is given as follows: m < 3 = 3x + 105.

b) The value of x is given as follows: x = 10.

c) It is not possible for a triangle to have side lengths 5, 8 and 14, as the sum of the lengths of the two smaller sides would be less than the length of the larger side.

The measure of angle 1 is given as follows:

m<1 = 3x + 15.

As the sum of the measures of the internal angles of a triangle is of 180º, and there is a right triangle, we have that angles 1 and 2 are complementary, hence:

m < 1 + m < 2 = 90

3x + 15 + m < 2 = 90

m < 2 = 75 - 3x.

An angle is always supplementary with it's exterior angle, hence the measure of angle 3 is obtained as follows:

m < 2 + m < 3 = 180

75 - 3x + m < 3 = 180

m < 3 = 180 - 75 + 3x

m < 3 = 3x + 105.

For an isosceles right triangle, the two non-right angles measure 45º, hence the value of x is obtained as follows:

3x + 15 = 45

3x = 30

x = 30/3

x = 10.

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The salary of each of specialist, manager and director are $62,000, $75,000 and $90,000.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Let x, y and z be the salary of specialist, manager and director respectively.

From the given information, we have three linear equations.

5x + 2y + z = 550,000

6x + 3y + 2z = 777,000

8x + 0y + 2z = 676,000

From the third equation,

2z = 676,000 - 8x

z = 338,000 - 4x

Substituting the value of z in the first equation,

5x + 2y + 338,000 - 4x = 550,000

x + 2y = 212,000

2y = 212,000 - x

y = 106,000 - (1/2) x

Substituting z = 338,000 - 4x and y = 106,000 - (1/2) x in the second equation 6x + 3y + 2z = 777,000,

6x + 3(106,000 - (1/2) x) + 2(338,000 - 4x) = 777,000

6x + 318,000 - (3/2)x + 676,000 - 8x = 777,000

(6x - 3/2 x - 8x) + (318,000 + 676,000) = 777,000

-(7/2) x = -217,000

x = 62,000

y = 106,000 - (1/2) x = 75,000

z = 338,000 - 4x = 90,000

Hence the salary of each specialist is $62,000, each manager is  $75,000 and each director is $90,000.

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The cost of each popcorn is $0.75 while the cost of each drink is $1.25

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

Let p represent the number of popcorn and d represent the number of drinks that Liliana bought.

Liliana spends $4.00 on 2 boxes of popcorn and 2 drinks, hence:

2p + 2d = 4       (1)

Nadette spends $5.25 on 2 boxes of popcorn and 3 drinks, hence:

2p + 3d = 5.25    (2)

To solve using elimination method, subtract equation 1 from 2, hence:

d = $1.25

substitute the value of d in equation 1 to get p:

2p + 2(1.25) = 4

p = $0.75

The value of p and d are $0.75 and $1.25 respectively

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The amount of money that Joe needs to pay would be = $15,918.50

In the year 2018, the percentage of social security = 6.2%

Joe's taxable income= $128,400.00

The annual salary of Joe = $256,750.00

The amount of money that joe should not pay is 6.2% of $256,750.00.

That is;

= 6.2/100 × 256,750.00

= 1591850/100

= $15,918.50

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Answer:

(a)

f(x) = 30, for x ≤ 200

f(x) = 0.03(x - 200) + 30, for x > 200

(b) $34.50

(c) 356

Step-by-step explanation:

Let x = number of minutes.

(a)

f(x) = 30, for x ≤ 200

f(x) = 0.03(x - 200) + 30, for x > 200

(b)

Here, x = 350, so x > 200.

f(x) = 0.03(x - 200) + 30

f(350) = 0.03(350 - 200) + 30

f(350) = 0.03(150) + 30

f(350) = 4.5 + 30

f(350) = 34.5

$34.50

(c)

f(x) = 0.03(x - 200) + 30

0.03(x - 200) + 30 = 34.68

0.03(x - 200) = 4.68

x - 200 = 156

x = 356

The value of y when x = 28 is given as follows:

y = 0.5.

A direct proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

An inverse proportional relationship is defined as follows:

y = k/x.

When x = 7, y = 2, hence the constant k is obtained as follows:

2 = k/7

k = 14.

Hence the equation is:

y = 14/x.

When x = 28, the value of y is obtained as follows:

y = 14/28

y = 0.5.

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The measure of the largest exterior angle is 96°.

Heptagon is a two-dimensional shape with seven angles, seven vertices, and seven edges. This seven-sided polygon “heptagon” is made up of two words ‘Hepta’ and ‘Gonia’, which means seven angles. Another name given to it is septagon or 7-gon.

In heptagon, the sum of the interior angles is equal to 900 degrees. The sum of exterior angles of a heptagon is 360 degrees.

Here, x°+2x°+3x°+4x°+5x°+7x°+8x°=360°

30x°=360°

x°=12°

So, 8x°= 96°

Therefore, the measure of the largest exterior angle is 96°.

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Answer:

x = 3  rounded to the nearest whole number (actually 2.735)

Step-by-step explanation:

The triangle formed by the sides of length 7x, 12x and 32 form a right triangle with the side of length 32 as they hypotenuse

By the Pythagorean theorem

c² = a² + b² where c = hypotenuse, a and b being the other two sides

Plugging in values we get

38² = (7x)² + (12x)²

1,444 = 49x² + 144x² = 193x²

Switching sides:

193x² = 1444

x² = 1444/193 = 7.48

x = √7.48= 2.735 = 3  rounded to the nearest whole number

Since the pavement at the new shopping mall is being laid, a transformation that is applied from brick A to brick B include the following: D. translation.

In Mathematics, a transformation can be defined as the movement of a point from its original (actual) position to a final (new) location. This ultimately implies that, when an object (pre-image) is transformed, all of its points would be transformed as well to form a new image such as the following:

In Mathematics, a translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.

In conclusion, a translation was applied to both brick A and brick B.

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We can classify them as -

There are six primary statement forms in Propositional Logic -

Given are the statements as -

We can classify them as -

Therefore, we can classify them as -

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The duration of the task is 2.5 days

The task duration if Mr. Bean gets sick is 1.5 days

An equation is an expression showing two or more numbers and variables linked together by a mathematical operation. Types of equations are linear, quadratic, cubic and so on depending on the degree of the variable.

Mr. Hummer works on the task for 3 hours, Mr. Cold works on the task 9 hours, and Mr. Bean works 8 hours on the task

Total time spent on task = 3 hours + 9 hours + 8 hours = 20 hours

Working day has 8 hours, therefore:

1 working day = 8 hours

20 hours = 20 hours * 1 working day per 8 hour = 2.5 days

If Mr. Bean is sick:

Total time spent on task = 3 hours + 9 hours = 12 hours

12 hours = 12 hours * 1 working day per 8 hour = 1.5 days

The task duration if Mr. Bean gets sick is 1.5 days

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Answer: Not necessarily. Dividing the pie chart into 5 equal sections might be a way to display categorical data if the number of categories is 5. However, dividing it into 5 sections might not be the best way to display the data if the number of categories is different than 5 or if any category has a significantly higher or lower proportion than the others. In this case, it may be more appropriate to use a different scale to display the correct ratio. It is important to consider data distribution and visualization clarity before choosing how to display categorical data.

Answer: 3 1/2

Step-by-step explanation:

Since positive and a negative make a negative the product would be a negative. Now we multiply 2/1 (because is the same as 2) times - 7/4, which gives us - 14/4. -14/4 = 3 1/2. Have a nice day ;)

The simplified form of the exponential expression [tex]b^{n- 2}\times{b^{n-3} = b^{2n - 5}[/tex].

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

Given, An exponential expression [tex]b^{n- 2}\times{b^{n-3}[/tex].

We know, Same base multiplication is exponent addition.

Therefore,

[tex]b^{n- 2}\times{b^{n-3} = b^{n - 2 + n - 3}[/tex].

[tex]b^{n- 2}\times{b^{n-3} = b^{2n - 5}[/tex].

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3 pounds of grapes she buy grapes in the market.

A division is a process of splitting a specific amount into equal parts.

Given that each pound of grapes cost 0.85.

Clarissa buys grapes and pays a total of 2.55.

We have to find the number of pounds of grapes does she buy.

To find this we have to divide 2.55 by 0.85.

Two point five five by zero point eight five.

2.55/0.85

3 pounds of grapes.

Hence, 3 pounds of grapes she buy grapes in the market.

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