Sarah was mixing up some lemonade to sell for her lemonade stand. The recipe calls for 3 scoops of lemonade mix to make 2 gallons of lemonade.

If she has 21 scoops of lemonade mix in the container, how many gallons of lemonade can she make?
*

Answer:

Factors of 105 are the list of integers that can be evenly divided into 105. There are overall 8 factors of 105 among which 105 is the biggest factor and 1, 3, 5, 7, 15, 21, 35, and 105 are positive factors. The sum of all factors of 105 is 192 and its factors in Pairs are (1, 105), (3, 35), (5, 21), and (7, 15).

Factors of 105: 1, 3, 5, 7, 15, 21, 35 and 105

Negative Factors of 105: -1, -3, -5, -7, -15, -21, -35 and -105

Prime Factors of 105: 3, 5, 7

Prime Factorization of 105: 3 × 5 × 7 = 3 × 5 × 7

Sum of Factors of 105: 192

Step-by-step explanation:

To calculate the factors of 105, we can use the division method. Let's start with 1.

105 ÷ 1 leaves remainder 0.

Since 105 is not an even number, 2 does not divide 105 completely. Thus, it leaves a remainder.

105 ÷ 3 leaves remainder 0.

105 ÷ 5 leaves remainder 0.

105 ÷ 7 leaves remainder 0.

105 ÷ 15 leaves remainder 0.

105 ÷ 21 leaves remainder 0.

105÷ 35 leaves remainder 0.

105 ÷ 105 leaves remainder 0.

Thus, the factors of 105 that we have obtained are 1, 3, 5, 7, 15, 21, 35, and 105.

Explore factors using illustrations and interactive examples

Factors of 75: The factors of 75 are 1, 3, 5, 15, 25 and 75

Factors of 175: The factors of 15 are 1, 3, 5, and 15.

Factors of 35:  The factors of 35 are 1, 5, 7, and 35.

Factors of 70: The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

Factors of 42: The factors of 1, 2, 3, 6, 7, 14, 21, and 42.

Answer:

y=3x-12

Step-by-step explanation:

to find slope we use y2-y1/x2-x1 by using any 2 points on the graph

(0,-12) (4,0)

0-(-12)/4-0)

12/4

3

The slope is 3

The y intercept is -12 since it crosses the y axis when y=-12

So we write those is y=Mx+b format where m is the slope and b is the y intercept

y=3x-12

Hopes this helps please mark brainliest

Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.

The mathematics curriculum involves examining numbers, the equation the environment we live in, structures, and both actual and hypothetical locations. A function is a variable representation of the relationship between the quantities of intake and the corresponding outputs for each. Simply explained, a function is a collection of inputs that, when combined, provide unique outputs for each input.

Here,

Given :

mass of a population of duckweed is 500g

=>  function m(t)= 500x³^t/45

So,

=> t = 45 hours

Since it is given that the mass of the population of the duckweed triples every 45 hours

it is clear that the time taken for the duckweed to grow a mass triple the original size will be 45 hours .

Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.

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The equation that can be formed with the unit and total costs of filling up the Sedan with 12 gallons of gas is 12p = 50.04, where p = 4.17.

An equation is a mathematical statement that expresses two equal variables.

Equations use the equation sign (=).

The quantity of gas per the Sedan's tank = 12 gallons

The unit cost of a gallon of gas = $4.17

The total cost of filling 12 gallons with gas = $50.04

In equation form, the expression can be written as:

12p = 50.04

Where p = 4.17

Thus, the equation of the total cost is 12p = 50.04, where p = 4.17.

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Step-by-step explanation:

2x + 6=2(x+3)

2x+6=2x+6

4x=0

x=0/4

No answer/no solution

2x + 6 = 2(x+3)

2x + 6 =2x+6

2x-2x=6-6

x=0

I guess I was help full for u

The working of T critical value calculator is explained

What is t test?

t test is the test used  if the sample standard deviation is known and population standard deviation is unknown.

t test is used if the sample standard deviation is known and population standard deviation is unknown.

Here, t value is calculated by the formula

\(t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(\bar{x}\) = mean of the sample

\(\mu\) = mean of the population

s = standard deviation of sample

n = Number of samples

Now, with the help of degree of freedom (n - 1) and the level of significance, the critical value of t is to be noted from the t table. Let it be \(t_{critical}\)

if the value of t lies between \(-t_{critical}\) and \(+t_{critical}\) then the null hypothesis is accepted, otherwise the null hypothesis is rejected.

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The expected gain or loss of an experiment over the long run is called the expected value.

The expected value is the weighted average of all possible outcomes, where the weights are the probabilities of those outcomes occurring. It is calculated by multiplying each possible outcome by its probability of occurring and then adding up these products. The expected value can be used to make decisions and assess risk in various fields, including finance, economics, and gambling. If the expected value is positive, it means that, on average, the experiment will result in a gain, while a negative expected value indicates a loss.

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Answer:

Step-by-step explanation: 44/59 = 0.74576271186 so that means the answer is around 74.5% or 74.6%

Answer:

62 is your answer

Step-by-step explanation:

6 × (36 ÷ 12)² + 8, you can also write 36 ÷ 12 as a fraction, which would look like this: 36/12

Step 1: 6 × 36/12² + 8 = 6 × 3² + 8

Step 2: Multiply 6 and 9

(6)(9)+8 = 54+8

Step 3: Then you add 54 and 9 and you get 62

Answer: 62

The use of the death penalty should not be determined by the opinions of other nations; its popularity among all groups in Texas proves that it is an effective form of punishment.

The issue of the death penalty is one that is hotly debated and controversial. Many nations have abolished it, citing human rights concerns and the possibility of executing innocent people. However, in the state of Texas, the death penalty is still widely used and supported. Despite criticism from other nations, Texans believe that it is an appropriate form of punishment for heinous crimes. In fact, the popularity of the death penalty in Texas is evident in the fact that it is supported by wide margins across all groups. This indicates that Texans believe the death penalty is a just and effective way to deal with violent criminals. While other nations may have their own opinions on the issue, the use of the death penalty in Texas should be based on the beliefs and values of Texans.

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The cost of the treat would be 40 pennies.

In mathematics, an expression is a combination of symbols (such as numbers, variables, and operations) that represents a value.

Expressions can be as simple as a single number or variable, or they can be more complex, involving multiple operations and variables. They can also include functions, exponents, and other mathematical concepts.

Chloe started with 74 pennies and lost 10, so she has 74 - 10 = 64 pennies left. The treat costs 5/8 of her remaining pennies,

Calculate the cost by multiplying 5/8 by 64:

(5/8) x 64 = 40

Therefore, the treat costs 40 pennies.

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Answer:

y=0

Step-by-step explanation:

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.

To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.

Setting the equation of the curve equal to itself, we have:

2 + 4cos(3θ) = 2 + 4cos(3(θ + π))

Simplifying and solving for θ, we get:

cos(3θ) = -cos(3θ + 3π)

cos(3θ) + cos(3θ + 3π) = 0

Using the sum to product formula, we get:

2cos(3θ + 3π/2)cos(3π/2) = 0

cos(3θ + 3π/2) = 0

3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...

Solving for θ, we get:

θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6

We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.

To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.

Using the formula for the area enclosed by a polar curve, we have:

A = 1/2 ∫[a,b] (r(θ))^2 dθ

where a and b are the angles of intersection.

For the small loops, we have:

A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ

Using trigonometric identities, we can simplify this to:

A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ

Evaluating the integral, we get:

A1 = 10π/3

For the large loops, we have:

A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)

Using the same trigonometric identities, we can simplify this to:

A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)

Evaluating the integrals, we get:

A2 = 80π/3

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:

A = A2 - A1 = (80π/3) - (10π/3) = 70π/3

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Answer:

Use slope formula

Angles 2 and 6 are on the corresponding sides of the parallel lines, hence are corresponding angle

Correct option is

Congruent triangles have congruent corresponding parts

Correct choice is

Option b is correct for any line and doesn't make the lines parallel. The rest of the options are correct for parallel lines.

Correct option is the last one:

By percentage, a passive home construction is typically around 50% more expensive compared to a conventional home construction.

A passive home construction is generally more expensive compared to a conventional home construction due to several factors. Passive homes are designed to meet stringent energy efficiency standards, requiring specialized materials, insulation, ventilation systems, and high-performance windows and doors. These energy-saving features contribute to the increased cost of construction. Additionally, passive homes often incorporate advanced technologies like heat recovery systems and solar panels, further adding to the expenses.

However, it's important to note that while the initial construction costs of a passive home may be higher, the long-term energy savings and reduced operating costs can offset the higher upfront investment. Passive homes offer improved energy efficiency, better indoor comfort, and reduced environmental impact, making them a viable choice for those seeking sustainable and energy-efficient housing solutions.

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The constant of variation based on the information is one half.

From the information given, when x is 2, y is 1, when x is 4, y is 2, etc. It should be noted that this is a direct variation.

This will be illustrated as:

y = kx

when y = 1, x = 2.

1 = 2k

Divide both side by 2.

k = 1/2

Therefore, the constant of variation is 1/2.

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LM=XY, then LM-GH= XY - GH and this illustrates the subtraction property of equality.

It should be noted that the subtraction property of equality simply implies that when the same number is subtracted form both sides, then the two sides will still remain equal.

In this case, when LM=XY, then LM-GH= XY - GH. This illustrates the subtraction property.

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a. The person who has the same preferences as Bob is Oral.

b. The person who has the same indifference curves as Bob is Jerry.

c. Bob and Oral have the same preferences (utility function), Bob and Jerry have the same indifference curves because their utility functions are equivalent at different values of y.

a. The person who has the same preferences as Bob is Oral. Oral's utility function U(x,y) = -1/(10+2xy) is equivalent to Bob's utility function U(x,y) = xy when y = -1,000.

b. The person who has the same indifference curves as Bob is Jerry. Jerry's utility function U(x,y) = 1,000xy + 2,000 is equivalent to Bob's utility function U(x,y) = xy when y = 2.

c. The answers to (a) and (b) differ because preferences and indifference curves are two different concepts. Preferences are determined by the utility function, which represents the satisfaction or desirability a person derives from different combinations of goods. Indifference curves, on the other hand, represent combinations of goods that provide the same level of satisfaction or utility. While Bob and Oral have the same preferences (utility function), Bob and Jerry have the same indifference curves because their utility functions are equivalent at different values of y.

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The labor share can be defined as the share of total income or output that goes to labor. The correct answer is: b. B ˉ / (A ˉ k + B ˉ).

To determine the labor share in this production function, we need to find the proportion of total output (Y) that is attributed to labor (L).

Given the production function Y = A ˉ × K + B ˉ × L, we can rewrite it as Y = A ˉ × K + B ˉ × (L/L) = A ˉ × K + B ˉ × (L × (1/L)) = A ˉ × K + (B ˉ / L) × L.

Now, let's express the production function in terms of k = K/L:

Y = A ˉ × (k × L) + (B ˉ / L) × L = A ˉ k × L + B ˉ.

The labor share (L_share) can be calculated as the proportion of output attributed to labor, which is L_share = (A ˉ k × L) / Y.

Dividing both the numerator and denominator by L, we have:

L_share = (A ˉ k × L) / (A ˉ k × L + B ˉ).

Comparing this expression with the provided options, we can see that the correct answer is:

b. B ˉ / (A ˉ k + B ˉ).

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Answer:

60 points

Step-by-step explanation:

Every time he earns points we add.

Every time he loses points we subtract.

We can write an equation to resemble the problem and simplify.

45 - 40 + 80 - 25

5 + 80 - 25

85 - 25

60

Best of Luck!

The evaluated integral using substitution is (1/2.7)(1 + x^3)^2.7 + C.

We will use a substitution method to evaluate the integral of x^2 (1 + x^3)^1.7 dx.

Step 1: Choose a substitution. In this case, we'll let u = 1 + x^3. This substitution simplifies the integrand, as it directly involves a term inside the integral.

Step 2: Compute the differential du. Differentiating u with respect to x, we get du/dx = 3x^2. Rearranging, we have du = 3x^2 dx.

Step 3: Modify the integral using the substitution. The given integral becomes ∫(1/3)u^1.7 du, where we have divided by 3 to account for the 3x^2 dx term in our substitution.

Step 4: Evaluate the modified integral. To do this, we will use the power rule for integration:

∫u^n du = (1/(n+1))u^(n+1) + C, where n ≠ -1

In our case, n = 1.7, so the integral becomes:

(1/(1.7+1))u^(1.7+1) + C = (1/2.7)u^2.7 + C

Step 5: Replace u with the original expression in terms of x:

(1/2.7)(1 + x^3)^2.7 + C

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The cosine of angle J is given as follows:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

For the angle J in this problem, we have that:

Hence the cosine of angle J is given as follows:

\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)

\(\cos{J} = \frac{4\sqrt{98}}{98}\)

\(\cos{J} = \frac{2\sqrt{98}}{49}\)

As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

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Answer:

6

Step-by-step explanation:

Trust

Answer:

M=-73/8

Step-by-step explanation:

4. (2, 16)

The vertex of a quadratic is where the function changes directions.

Finding the Vertex

As stated the vertex is where the function changed from increasing to decreasing or vice versa. Since this graph opens downward, the vertex will be where the maximum is. The maximum occurs that (2, 16). Therefore, the vertex is also at (2, 16).

Had the quadratic opened upwards, the vertex would occur at the minimum value.

Writing the Equation

Since we know the vertex, we can find the equation for the quadratic. Quadratic formulas can be written as y = a(x - h)² + k. In this formula, a is a constant that tells us whether the graph opens up or down, h is the x-value of the vertex, and k is the y-value of the vertex. So, to find the equation, we can plug in the values we know for the vertex. Then make the a-value negative because we know the graph opens down.

Step-by-step explanation:

can you please send of this pic of this question in brainly ...

so that I can answer

Answer:

310000000

That’s the answer

Answer:

12

Step-by-step explanation:

\(6y \geqslant 72 \\ divide \: both \: side \: by \: 6 \\ y \geqslant \frac{72}{6} \\ y \geqslant 12\)

Answer:

6y > 72

Inequality Form: y > 12

Interval Notation: (12,infinite loop)

I have answered have a good day.

Answer:

g(10) = 31

f(-3) = -2

h(2) = -7

j(7) = 333

j(3) = 17

I hope the last 2 were for the same function lol