You purchased 7 3/4 lb of candy for your party. You're expecting to have 10 guests attend your party. How much candy will each guests get?

Answer:

£60

Step-by-step explanation:

Let the original price of the shirt be £x.

Reduction in price = 20% of x = 0.2x

Selling price of the shirt = x - 0.2x = 0.8 x

Since, the shirt was sold for £48

Therefore, 0.8x = 48

x = 48/0.8

x = £60

Our solution set will be {x | x R, x ≤ 7 5/6}.

What is the solution set?

The solution set for an equation is the collection of all possible solutions to that equation. If an equation has no solutions, the solution set is denoted by the ∅ symbol. ∅ refers to the null set (or empty set).

In our problem it is given:

x - 6 \(\frac{1}{3}\) \(\leq\)  1\(\frac{1}{2}\)

To each side, add 6 1/3.

x \(\leq\)  1 \(\frac{1}{2}\) + 6 \(\frac{1}{3}\)

Change the 1/2 and the 1/3 to a common denominator to add them together.

x \(\leq\) 1 \(\frac{3}{6}\) +6 \(\frac{2}{6}\)

x \(\leq\) 7 \(\frac{5}{6}\)

Therefore our final solution set will be {x | x ∈ R, x ≤ 7 \(\frac{5}{6}\)}.

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Hi there!

\(\large\boxed{5(5c - 1y)}\)

25c - 5y

Factor out 5 from each term:

5(5c - 1y)

Answer: plz mark as brainliest

Step-by-step explanation:The table below shows the net effect of a person’s mental state and occupation on his or her truth telling.

Suppose that Dorothy is telling the truth. Then she is sane (and hence a pure mathematician) and Charlie is sane. Bob says that Charlie is insane, so Bob is not telling the truth. Since he says he’s pure, he’s actually applied and hence Charlie is telling the truth. But then he’s applied and sane applied mathematicians do not tell the truth. This is a contradiction.

Therefore, Dorothy is not telling the truth. Thus, both Charlie and Dorothy are insane (hence Dorothy is pure). Consequently, Bob is telling the truth. Therefore Bob is pure (and sane, since he is a truth teller). Since Charlie says that Bob is applied, he is not telling the truth. Since we know that he is insane, he must be pure.

Since Alice says that Charlie is pure, she is telling the truth. Therefore she is insane and consequently applied.

In summary:

Alice is an insane applied mathematician.

Bob is a sane pure mathematician.

Charlie is an insane pure mathematician.

Dorothy is an insane pure mathematician.

Alice: Alice claims to be insane. If she is telling the truth, then her belief is incorrect, and she is, in fact, sane.

Mathematicians and statisticians solve problems in industry, academia, and government by using formulas and data.

Alice: Alice claims that she is insane. If she's telling the truth, her belief is incorrect, and she's perfectly normal. Alice is thus either pure or applied.

Bob: Bob declares himself to be pure. Bob's belief is correct, and he is indeed pure, because pure mathematicians tell the truth.

Charlie claims to be applied, but Alice claims Charlie is pure. Alice's claim about Charlie is true because applied mathematicians lie, and Charlie is actually pure.

Dorothy: Dorothy asserts that she is sane. Dorothy's belief is correct, and she is indeed sane, because the beliefs of sane mathematicians are correct.

Therefore, the four mathematicians are Alice (either pure or applied), Bob (pure), Charlie (pure), and Dorothy (sane).

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Answer:

135 In the 3rd year

Step-by-step explanation:

240-35= 205

205-35=170

170-35=135        (Or just use a calculator)

Answer:

35

Step-by-step explanation:

4 times 8 +3=35

Answer:

Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer

★» -30, 10

★» Yes, I use ★» at the beginning of each sentence, it's my style.

Answer:Its c

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

divide 780 and 20

P = a = 3, since a, b, and c must add up to 6, and since a is the only positive number, it must be 3.

A positive number is any real number greater than zero. Examples of positive numbers include 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and so forth. Positive numbers can be expressed in scientific notation, as fractions, as decimals and as whole numbers. Positive numbers have a variety of applications in mathematics, science, economics and engineering.

P = a = 3, since a, b, and c must add up to 6, and since a is the only positive number, it must be 3.

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Answer:

1. 48a/24a³b²; domain {a ≠ 0 and b ≠ 0}  2. 15b³/24a³b² ; domain {a ≠ 0 and b ≠ 0}

Step-by-step explanation:

1. To have a denominator 24a³b², we multiply 2/a²b² by 24a/24a.

So, 2/a²b² × 24a/24a = 48a/24a³b². For this expression to the valid, the domain is a ≠ 0 and b ≠ 0

2. To have a denominator 24a³b², we multiply 5b/8a³ by 3b²/3b².

So, 5b/8a³ × 3b²/3b². = 15b³/24a³b². For this expression to the valid, the domain is a ≠ 0 and b ≠ 0

If we sample the function x(t) = cos(75t) at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is equal to half of the highest frequency component in the continuous signal.

In this case, the highest frequency component in x(t) is 75 Hz, as determined by the coefficient of t in the cosine function. According to the Nyquist-Shannon sampling theorem, to accurately represent a signal, the sampling frequency must be at least twice the highest frequency component. Therefore, the Nyquist frequency in this scenario would be 2 * 75 Hz = 150 Hz.

Since we are sampling at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is 150 Hz / 2 = 75 Hz. Hence, when sampling x(t) at the Nyquist frequency, the resulting discrete frequency would be 75 Hz.

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Answer:

2x-2+2x-2+x+x=50

6x-4=50

6x=54

x=9

hope this helps

have a good day :)

Step-by-step explanation:

The decomposition of Ni3 produces nitrogen gas and iodine. How many grams of the reactant would be required to react completely to give 1.18 g of iodine?To begin with, write the balanced equation for the decomposition of Ni3:2Ni3(s) → 3I2(s) + N2(g)

From the balanced equation above, the stoichiometric ratio between Ni3 and I2 is 2:3 that is, for every 2 moles of Ni3 decomposed, 3 moles of I2 is produced.To find the mass of Ni3 that would produce 1.18 g of I2, we need to find the number of moles of I2 produced first.The molar mass of I2 = 253.8 g/molNumber of moles of I2 produced = Mass / Molar mass = 1.18 / 253.8 = 0.004645 molFrom the stoichiometry, 2 moles of Ni3 produce 3 moles of I2, which can be written as:2 mol Ni3 → 3 mol I2

The number of moles of Ni3 that would produce 0.004645 mol of I2 can be obtained using the ratio:2 mol Ni3 / 3 mol I2 = 0.6666667 mol Ni3The mass of Ni3 required to produce 1.18 g of I2 can be obtained by multiplying the number of moles of Ni3 obtained above by the molar mass of Ni3:Mass = moles x molar mass = 0.6666667 x 100.7= 67.11 gTherefore, 67.11 g of Ni3 would be required to react completely to give 1.18 g of iodine.

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Answer:

304.5 cm2

Step-by-step explanation:

Think imaginatively, we got two congruent triangles and two rectangles with different dimensions.

S.A. of 2 triangles = 2*( 1/2 x B x H)

= 2*( 1/2 x 10.5 x 14) = 147 cm2

Rectangle 1 = 5*17.5 = 87.5 cm2

Rectangle 2 = 5*14 = 70 cm2

Total = 147 + 87.5 + 70 = 304.5 cm2

Answer:

-63

Step-by-step explanation:

\[x²-3x+18\]

discriminant=b²-4ac=(-3)²-4*1*18=9-72=-63

Answer:

\(\boxed {\boxed {\sf -63}}\)

Step-by-step explanation:

The discriminant is the portion of the Quadratic Formula that is under a square root. It helps us identify if a function has 2,1, or 0 solutions.

The quadratic formula is:

\({x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}\)

where the quadratic is: ax²+bx+c

The part under the square root is just:

\(b^2-4ac}\)

We are given the quadratic:

x² -3x+18

Therefore,

Substitute the values into the formula for the discriminant.

\((-3)^2-4(1)(18)}\)

Solve the exponent.

\(9-4(1)(18)}\)

Multiply.

\(9-72\)

Subtract

\(-63\)

Since the discriminant is negative, there are no real solutions. There are imaginary solutions though.

Answer: 12.6 would be the answer

Step-by-step explanation:

Answer:

B) 6.3 m

Step-by-step explanation:

Answer:

5,022 Students

Step-by-step explanation:

All you have to do it multiply!

Like so:

81*62= 5,022

The shaded area is 7.33 square centimeters.

Remember that for an arc defined by an angle θ on a circle of radius R, the area is:

A = (θ/360°)*3.14*R²

In this case the angle is 120°.

Here we just need to take the difference between the area of the arc in the larger circle and the area of the smaller one, then we will get:

Area = (120°/360°)*3.14*( (4cm)² - (3cm)²)

Area = 7.33 cm²

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The product of the HCF and LCM of 12 ,18,30 can be written as 1080.

The H.C.F.  can be described as the greatest factor  that can be found when expressing given two or more numbers, on the other hand the LCM can be described as the least factor that exist between a two given number.

factors of 12 are: 3, 4, 2, 6, 12.

factors of 18 are: 2, 3 , 6 9 , 18

factors of 30 are ; 2, 3, 6, 5, 10

HCF; The factor that is greatest among the factors of the numbers = 6

To calculate the LCM, we need to find to find the prime factor of the three numbers as:

Prime factor of 12 are ;  2*2*3

Prime factor of 18 are ; 2*3*3

Prime factor of 12 are ; 2*3*5

LCM is now the multiplication of the prime factors which is the highest occurrence of them in either numbers as ; 2*2*3*3*5 =180

From the given numbers we can see that the HCF = 6 and LCM = 180, then if we find the product as (6*180)=1080 which is the number of the product of the lowest common factor as well as the highest common factor.

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He made the mistake on line 1.

2x^2 - 8x + 5....move the 5 to the other side

2x^2 - 8x = -5....now divide by 2

x^2 - 4x = -5/2

x^2 - 4x + 4 = -5/2 + 4

(x - 2)^2 = -5/2 + 8/2

(x - 2)^2 = 3/2

x - 2 = (+-)sqrt 3/2

x = 2 + sqrt 3/2 or x = 2 - sqrt 3/2

He made mistake on line 1.

Marvin was completing the square, and his work is shown below. Identify the line where he made his mistake. f(x) = 2x2 − 8x + 5. Line 1: f(x) = 2(x^2 − 8x) + 5 Line 2: f(x) = 2(x^2 − 8x + 16) + 5 − 32 Line 3: f(x) = 2(x − 4)^2 − 27

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The expression 5m + 5c represents the total amount earned by Bryan, where "m" is the number of lawns mowed and "c" is the number of cars washed.

To calculate the total amount earned by Bryan, we need to consider the earnings from both mowing lawns and washing cars.

The expression that represents the total earned by Bryan is given by:

E = (earnings from mowing lawns) + (earnings from washing cars)

Since Bryan earns $5.00 per lawn mowed and $5.00 per car wash, the expression can be written as:

E = 5m + 5c

Here, "m" represents the number of lawns mowed and "c" represents the number of cars washed.

To find the total earned, simply substitute the values of "m" and "c" into the expression and calculate the result. For example, if Bryan mows 3 lawns and washes 2 cars, the total earned would be:

E = 5(3) + 5(2)

= 15 + 10

= $25.00

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Sophia should budget the total cost calculated in step 3 to fill up her tank when she gets home.

To determine the amount Sophia should budget for refueling when she gets home, we need to consider the following terms:
Fuel efficiency:

Determine the miles per gallon (mpg) that Sophia's car gets. we can find this information in the car's manual or online.

Gas price: Find the current price per gallon of gasoline in Sophia's area. You can check local gas stations or websites that track gas prices.

Determine the fuel efficiency of Sophia's car (miles per gallon or mpg).
Calculate the total number of gallons needed to drive 291 miles by dividing 291 miles by the car's mpg.
Example:  

If Sophia's car has a fuel efficiency of 29 mpg, the calculation would be 291 miles / 29 mpg = 10 gallons.
Multiply the total number of gallons needed by the current gas price per gallon to find the total cost.

Example:  If the gas price is $3 per gallon, the calculation would be 10 gallons * $3 = $30.

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Answer:

A strong linear relationship between two or more independent variables

Step-by-step explanation:

Multicolinearity underestimates the statistical significance of the independent variables. It exists when an independent variable is highly correlated with one or many other independent variables giving rise to a large standard error.

The required, a. percent change each year is 32%. and after approximately 5.76 years, Mountain Creek will have over 2,000 snowboarders with season passes.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,
a. The percent change each year can be calculated as,
percent change = ((y times 1.32)/y - 1) x 100
percent change = (1.32 - 1) x 100
percent change = 32%

So the percent change each year is 32%.

b. We can solve for x when y = 2,000 by substituting these values into the given equation and solving for x,
2,000 = 205(1.32)ˣ

(1.32)ˣ = 2,000/205

x = log base 1.32 (2,000/205)

x = 5.76 (rounded to two decimal places)

Therefore, after approximately 5.76 years, Mountain Creek will have over 2,000 snowboarders with season passes.

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Therefore, the average value of f(x) on the closed interval [2, 6] is:-1.848

To find the average value of f(x) on the interval [2, 6], you need to use the formula for the average value of a function. That formula is given as:

average value of f(x) = (1/(b-a)) * ∫[a,b] f(x)dx

Here, a = 2 and b = 6. So, we have:

average value of f(x) = (1/(6-2)) * ∫[2,6] f(x)dx

Now, f(x) = (x² + x)cos(5x).

Therefore,∫[2,6] f(x)dx = ∫[2,6] (x² + x)cos(5x) dx

This integral can be evaluated using integration by parts.

Let u = (x² + x) and dv = cos(5x)dx.

Then, du/dx = 2x + 1 and v = (1/5)sin(5x).

Using the integration by parts formula, we have:

∫(x² + x)cos(5x)dx = uv - ∫vdu= (x² + x)(1/5)sin(5x) - ∫[(1/5)sin(5x)][(2x + 1)dx]= (x² + x)(1/5)sin(5x) - (2/25)cos(5x) - (2/25)xsin(5x) + C

Putting the limits of integration, we get:

∫[2,6] f(x)dx = [(6² + 6)(1/5)sin(5(6)) - (2/25)cos(5(6)) - (2/25)6sin(5(6))] - [(2² + 2)(1/5)sin(5(2)) - (2/25)cos(5(2)) - (2/25)2sin(5(2))]≈ -1.848

Therefore, the average value of f(x) on the closed interval [2, 6] is:-1.848

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Answer: x = 25 mi

Step-by-step explanation:

Sides QO and TR are corresponding.

Sides QP and TS are corresponding.

Sides OP and RS are corresponding.

Create the proportion to solve for x:

5/x = 6/30

Cross multiply:

6x = 150

Divide both sides by 6:

x = 25 mi

Hope this helps!

The solution to the system of equation y = -3x + 1 and 10x + 2y = -6 is x = -2 and y = 7.

Given the equation in the question

To solve for the values of x and y.

First, plug the first equation into the second equation and solve for x.

10x + 2y = -6

Plug in y = -3x + 1

10x + 2( -3x + 1 ) = -6

Solve for x

10x - 6x + 2 = -6

4x + 2 = -6

4x = -6 - 2

4x = -8

x = -8/4

x = -2

Now, plug x = -2 into the first equation and solve for y.

y = -3x + 1

Plug in x = -2

y = -3( -2 ) + 1

y = 6 + 1

y = 7

Therefore, the solution is (-2,7).

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Answer:

7%

Step-by-step explanation:

\(\frac{2.45}{35} = \frac{x}{100}\)

\(2.45*100\) and \(35x\)

\(\frac{245}{35} = \frac{35x}{35}\)

\(245/35=7\)