The Smiths spend 10% of their budget on entertainment. Their total budget this year is $2,000 more than last year, and this year they plan to spend $2,450 on entertainment. What was their total budget last year?

Answer:

70

Step-by-step explanation:

mark = 1    1 times 14 = 14

Brian = 5   5 times 14 = 70

Brian receives 70 sweets, as Mark's 14 sweets represent 1 part of the ratio 1:3:5, indicating that 1 part equals 14 sweets and Brian's 5 parts equal 70 sweets.

Mark, Paul, and Brian share sweets in a ratio of 1:3:5, which means that for every sweet Mark gets, Paul gets 3, and Brian gets 5. Since Mark gets 14 sweets, we can use this information to calculate how many sweets Brian gets. First, let's find out what one 'part' of the ratio is worth by dividing the number of sweets Mark gets by his ratio number:

Mark's sweets (14) / Mark's ratio (1) = 14 sweets per ratio part.

Next, determine Brian's share by multiplying the sweets per ratio part by Brian's ratio number:

Brian's share = sweets per ratio part (14) * Brian's ratio (5) = 70 sweets.

Therefore, Brian gets 70 sweets.

Answer:

You can use the Subtraction property of equality

You have to subtract 3 on both sides to have x alone, which will give you x=4

Answer:

SUbtraction

7-3=4 so X is 4

Step-by-step explanation:

Answer:

You're Correct

Step-by-step explanation:

Keep up your good work

Answer:

F(2)=-7

Step-by-step explanation:

f(-2)=2x-3

you substitute the x on the positive 2

2(-2)=-4

-4-3-=7

-7

Hence the result of the function is x is -2 is -7

Given the function f(x) = 2x-3,

Domain of a function is the input value for which the function exists.

The range of the function is the output value for which the function exists

From the question, we can see that we are to find the resulting range if the domain of the function is -2.

To get f(-2), we will need to substitute x as 2 into the function as shown

f(-2) = 2(-2) - 3

f(-2) = -4 - 3

f(-2) = -7

Hence the result of the range with the domain of -2 is -7

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Answer:

The answer is 0.2. It is an irrational number with a repeating 2. It should have a line over the two to represent it repeating.

Step-by-step explanation:

First divide 2 by 9.

Use a calculator or do it by hand.

You get your answer.

Option D is correct, the decimal which is equivalent to the fraction 2/9 is 0.2

The given fraction is two divided by nine, 2/9

Two is the numerator and nine is the denominator

We have to find the equivalent decimal number of fraction 2/9

To do this we have to divide 2 by number nine

When two is divided by nine we get 0.222

2/9 =0.22

=0.2

Hence, the decimal which is equivalent to the fraction 2/9 is 0.2, option D is correct.

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Answer:

I think the plastic cup are 24

Answer:

[tex]30x^{7} y^{4}[/tex]

Step-by-step explanation:

simplify

Final answer:

The equivalent expression for (3x^2y)(10x^5y^3) is 30x^7y^4, obtained by multiplying the coefficients and adding the exponents of like bases.

Explanation:

The question asks for the equivalent expression of the product (3x^2y)(10x^5y^3).

To find the equivalent expression, we need to apply the properties of exponents, which state that when multiplying two powers with the same base, we add the exponents. We can also multiply the coefficients in a usual way. Let's break it down into steps:

Multiply the coefficients (numbers outside the exponents): 3 × 10 = 30.

Add the exponents of x: x^2 × x^5 = x^(2+5) = x^7.

Add the exponents of y: y^1 × y^3 = y^(1+3) = y^4.

Combine the results: 30x^7y^4.

Therefore, the equivalent expression for (3x^2y)(10x^5y^3) is 30x^7y^4.

For step one, they want you to factor 5,000 into a 5 and ?. To find the missing value, we can divide:

5,000 / 5 = 1,000

So, 1000 goes in the first blank.

For step two, 1,000 also goes in the second blank since the first 2 numbers are being multiplied.

For step three, multiply the last two numbers.

30 * 1000 = 30,000

So, 30000 goes in the last blank.

Best of Luck!

Answer: 30000 goes in the last one

Step-by-step explanation:

Answer:

The base is natural number e = 2.71828...

Step-by-step explanation:

By definition of natural log, the base is e = 2.71828...

The base of the function y = ln(x) is the irrational number e (approximately 2.71828).

The base of the function y = ln(x) is the base of the natural logarithm, which is the irrational number e (approximately 2.71828). The natural logarithm function ln(x) is the inverse function of the exponential function e^x. So, if y = ln(x), then x = e^y.

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Answer:

I wish i could help but im dumb :(

Step-by-step explanation:

Answer:

Option 2

Step-by-step explanation:

V= Base x Height

If the Height = 15in and the V = 90in^3 then 90 ÷ 15 = 6

Please mark brainliest ;)

I like to work backwards to see if the common difference is the same.

So I take 16 and work to the left.

So I say 16 - 21  which is -5.

Then I do 21 - 26 which is -5.

Finally, 26 - 31 which is -5.

So what I am doing here is just taking the number that is on the right and subtracting it by the number that appears to the left of it.

Notice that I always get -5 and that has to be because in order for this to have a common difference, the result must always be the same if you are working with the method I used above.

So, our common difference is -5.

Answer:

x = 16

Step-by-step explanation:

4x - 7 = 3x + 9

4x = 3x + 16

1x = 16

x = 16

Answer:

[tex]\frac{\sqrt{6}+\sqrt{2} }{4}[/tex]

Step-by-step explanation:

Using the difference formula for cosine and the exact values

cos45° = sin45° = [tex]\frac{\sqrt{2} }{2}[/tex], cos30° = [tex]\frac{\sqrt{3} }{2}[/tex], sin30° = [tex]\frac{1}{2}[/tex]

cos(a - b) = cosacosb + sinasinb

Note 15° = 45° - 30°, thus

cos15°

= cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= ([tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] ) + ([tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{1}{2}[/tex] )

= [tex]\frac{\sqrt{6} }{4}[/tex] + [tex]\frac{\sqrt{2} }{4}[/tex]

= [tex]\frac{\sqrt{6}+\sqrt{2} }{4}[/tex]

Answer:

[tex]\frac{\sqrt{6} +\sqrt{2} }{4}[/tex]

Step-by-step explanation:

Answer:

  2,042,975

Step-by-step explanation:

Josh can choose 9 of his 25 classmates using the function C(n,k), which tells the number of combinations of n objects taken k at a time.

__

Here, Josh wants to choose 9 from 25 classmates. The number of possible choices is ...

  C(n, k) = n!/(k!(n-k)!)

  C(25, 9) = 25!/(9!(25 -9)!) = 25·24·23·22·21·20·19·18·17÷(9·8·7·6·5·4·3·2·1)

  = 2,042,975

__

Additional comment

In effect, the first ticket can go to any of 25 classmates, the second to any of 24, and so on. The last ticket can go to any of 17 classmates. This product 25·24·...·17 counts each group of classmates 9! times. Since the order in which they are chosen does not matter, the final number is then ...

  25!/(16!·9!) = 2042975

Answer:

The restrictions partly depend on the type of function.

You can’t divide by  0

You can’t take the square (or other even) root of a negative number, as the result will not be a real number.

In what kind of functions would these two issues occur?

the function is a rational function and the denominator is  

0

for some value or values of x,  

f ( x ) = x + 1 2− x

is a rational function

the function is a radical function with an even index (such as a square root), and the radic and can be negative for some value or values of x.  

f ( x ) = √ 7 − x

is a radical function

The following table gives examples of domain restrictions for several different rational functions.

Hope this helped

Answer:

The answer is 6.

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

A can is a cylinder

V = pi r^2 h

The diameter is 6.4  we want the radius

r = d/2 = 6.4/2 = 3.2

V = 3.14 * (3.2)^ * 12.3

V =395.48928 cm^3

1 cm^3 = 1ml

V = 395.48928 mL

A can of soda has 355 mL

We are over estimating because the can narrows on the ends and the height is actually shorter because the ends do not have volume but are metal to contain the soda.  We also did not take into account the curve in the bottom of a can of soda.

Answer:

395.48928 cm³

40.48928 cm³ greater than an actual can

Step-by-step explanation:

Volume of can:

pi × r² × h

3.14 × (6.4/2)² × 12.3

395.48928 cm³

Actual can: 355 cm³

395.48928 - 355 = 40.48928 cm³

Answer:

t = 5.46 secs and t = 2.42 secs

Step-by-step explanation:

The distance of the ball from the ground is given by:

[tex]s(t) = -16t^2 + 126t[/tex]

When the ball is at a distance 211 ft from the ground, that means s(t) = 211 ft. we need to find t:

[tex]211 = -16t^2 + 126t[/tex]

[tex]=> 16t^2 -126t + 211 = 0[/tex]

Using the quadratic formula:

[tex]t = \frac{-b + \sqrt{b^2 - 4ac} }{2a}[/tex] and [tex]t = \frac{-b - \sqrt{b^2 - 4ac} }{2a}[/tex]

where a = 16, b = 126 and c = 211

Hence:

[tex]t = \frac{-(-126) + \sqrt{(-126)^2 - 4(16)(211)} }{2(16)}[/tex]     and          [tex]t = \frac{-(-126) - \sqrt{(-126)^2 - 4(16)(211)} }{2(16)}[/tex]

[tex]t = \frac{126 + \sqrt{15876 - 13504} }{32}[/tex]                     and           [tex]t = \frac{126 - \sqrt{15876 - 13504} }{32}[/tex]

[tex]t = \frac{126 + \sqrt{2372} }{32}[/tex]                                and           [tex]t = \frac{126 - \sqrt{2372} }{32}[/tex]

[tex]t = \frac{126 + 48.703 }{32}[/tex]                                and           [tex]t = \frac{126 - 48.703 }{32}[/tex]

[tex]t = \frac{174.703}{32}[/tex]                                     and           [tex]t = \frac{77.297}{32}[/tex]

=> t = 5.46 secs and t = 2.42 secs

This means that the ball will be at 211 feet at two different times, first, after 2.42 seconds and then after 5.46 seconds.

This makes sense because the ball is projected upwards, which means that when going up, it attains 211 feet and also, when coming back down, it also attains 211 feet.

To determine the time when the ball is 211 feet off the ground, set s(t) equal to 211 and solve the resulting quadratic equation (-16t^2 + 126t - 211 = 0) using the quadratic formula. Discard the negative solution as it represents a time before launch.

In response to the given question, we need to determine the time when the ball is 211 feet from the ground given the formula s(t)=-16t^2 + 126t. This is a quadratic equation which can be solved for t using the quadratic formula.

First, we need to set the equation equal to 211 to solve for when the ball is this distance off the ground. So, -16t^2 + 126t = 211. Rearrange the equation: -16t^2 + 126t - 211 = 0.

Now, apply the quadratic formula t = [-b ± sqrt(b^2 - 4ac)] / 2a, where a = -16, b = 126, and c = -211. This yields two solutions corresponding to the times at which the ball is 211 feet from the ground. The negative solution represents a moment before the ball is launched, hence we discard it. The positive value is the time at which the ball attains a height of 211 feet.

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2/3Answer:

Step-by-step explanation:

Answer:

96.12

Step-by-step explanation:

89x.0.08 is 7.12 add that to 89 gives you 96.12

The answer is 2 and 1. Hope this help btw

Answer:

In geometry, the pentagonal prism is a prism with a pentagonal base. It has with 7 faces, 15 edges, and 10 vertices

Step-by-step explanation:

Answer:

From the Law of cosines we see that Line AB^2 (or side c^2) equals

AB^2 = a^2 + b^2 -2ab *cos (C)

AB^2 = 6*6 + 7*7 -2*6 * 7 * cos(59)

AB^2 = 85 -84 * 0.51504

AB^2 = 85 - 43.26336

AB^2 = 41.73664

AB = 6.4603900811

AB = 6.5 (rounded)

Step-by-step explanation:

Answer:

height = 142.00 ft

height ≈ 200. 82 ft

height ≈ 245.95 ft

Step-by-step explanation:

The picture below represent the image of the draw bridge. The illustration will form a right angle triangle. The hypotenuse is each half of the drawbridge which is 284 ft long. The opposite side  of the triangle is facing the drawbridge half leg and the adjacent side is horizontal length. This is the side that made the angle with the drawbridge half leg(hypotenuse).

The question ask us to find the height of the drawbridge when it rise which is the opposite sides of the triangle when the angle is 30° , 45° and  60°.

Using SOHCAHTOA principle,

Angle 30°

sin 30° = opposite/hypotenuse

sin 30°  = height/284

cross multiply

height = 0.5 × 284

height = 142.00 ft

Angle 45°

sin 45° = height/284

height = 284 × 0.70710678118

height = 200.818325857

height ≈ 200. 82 ft

Angle 60°

sin 60 = height/284

cross multiply

height = 0.86602540378  × 284

height = 245.951214675

height ≈ 245.95 ft

The question asks about the height a drawbridge rises at different angles. This is a trigonometry problem that can be solved by using the sine of the angle to calculate the height of the bridge when raised. The height corresponds to the 'opposite' side in a right triangle formed by the raised drawbridge.

This question appears to be asking about how high a drawbridge rises based on an angle, x, which is a trigonometry problem. Assuming that the drawbridge forms a right triangle when it rises, the height can be calculated using the sine of the angle, x. Sine of x is equal to the opposite side (height of the bridge when it is raised) over the hypotenuse (half of the drawbridge's length).

Applying these trigonometric principles, calculations for each scenario would look like the following:

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Answer:

A:

p = 65s, 0《s《20

p = 1300, s > 20

B:

p = 300 + 40s, s》0

C:

p = 900

Step-by-step explanation:

Salmesman A:

p = 65s

65s = 1300

s = 20

Salesman B:

p = 300 + 40s

Salesman C:

p = 900

Answer:

A:

p = 65s, 0《s《20

p = 1300, s > 20

B:

p = 300 + 40s, s》0

C:

p = 900

Step-by-step explanation:

Salmesman A:

p = 65s

65s = 1300

s = 20

Salesman B:

p = 300 + 40s

Salesman C:

p = 900

Step-by-step explanation:

Answer:

(2,0)

Step-by-step explanation:

Solve by graphing:

Use a graphing tool to graph the lines y=2x -4 and y = -x+2.

The lines intercept at point (2,0).

Therefore, the solution to the set of equations is (2,0).

[tex]x=2\\y=0[/tex]

Brainilest Appreciated!

Answer:

(0, -4) and (2,0)

Step-by-step explanation:

Answer:

196 cent^3

Step-by-step explanation:

mark brainliest please :)

Answer:

190 cents skimpy simple

190 cent