Suki is making lemonade to bring to the beach. She has two containers. One holſis one gallon and the other
holds 6 quarts. If she fills both containers, how many cups of lemonađe will she have?
She will have
cups of lemonade.

Answer:

Step-by-step explanation:

4/mx

Answer:

D

Step-by-step explanation:

Answer:

D. \(8a^{9} -4a^{3} +1\)

Step-by-step explanation:

Given \(r(x)=x^{3} -2x+1\) and find \(r(2a^{3} )\) :

Solve for \(r(2a^{3} )\) :

1. \(r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1\)

2. \(r(2a^{3} )=8a^{9} -2(2a^{3})+1\)

3. \(r(2a^{3} )=8a^{9} -4a^{3}+1\)

Answer:

So, if \(r(x)=x^{3} -2x+1\), then \(r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1=8a^{9} -4a^{3}+1\).

Then the answer is D. \(r(2a^{3} )=8a^{9} -4a^{3}+1\)

The logarithm expression can be simplified to:

In(6x^9)-In(x^2) =7·ln(6x)

There are some logarithm properties we can use here.

log(a) - log(b) = log(a/b)

log(a^n) = n*log(a)

(these obviously also apply to the natural logarithm)

Now let's look at our expression, it says that:

In(6x^9)-In(x^2)

Using the first rule, we can rewrite this as.

In(6x^9)-In(x^2) = ln(6x^9/x^2)

Now solving the quotient in the argument:

ln(6x^9/x^2) = ln(6x^7) = 7·ln(6x)

That is the expresison simplified.

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The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

t = 7.46, 0.42

Explanation:

h = 126t - 16t²    [ "h" is height, "t" is time ]

when height is 50 feet

==================

\(\sf use \ quadratic \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0\)

==================

\(\Longrightarrow \sf t = \dfrac{-126\pm \sqrt{126^2-4\left(-16\right)\left(-50\right)}}{2\left(-16\right)}\)

\(\Longrightarrow \sf t = \dfrac{63\pm\sqrt{3169}}{16}\)

\(\Longrightarrow \sf t = 7.46, \ 0.42\)

Let's find

Put h=50

Use quadratic formula

\(\\ \rm\Rrightarrow t=\dfrac{-126\pm\sqrt{126²-4(-16)(-50)}}{-32}\)

\(\\ \rm\Rrightarrow t=7.5s,0.4s\)

Answer:

A

Step-by-step explanation:

Answer:

33.9

Step-by-step explanation:

cos rule:

a²=b²+c²-2xaxbxcosA

rearrange:

cosA=(b²+c²-a²)÷(2xaxb)

solve:

cosx=(8²+22²-16²)÷(2x8x22)

cosx=(64+484-256)÷352

cosx=292÷352

cosx=0.830

cos^-1(shift cos)=33.9

The value of the missing segment n using the product of intersecting chord theorem is 14cm

The product of the segments of two intersecting chords are equal.

The segments of the chords ;

Chord 1 = 4 and n

Chord 2 = 7 and 8

The principle can be related Mathematically thus ;

4 × n = 7 × 8

4n = 56

Divide both sides by 4

4n/4 = 56/4

n = 14

Therefore, the value of n in the question is 14cm

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Answer:

5

Step-by-step explanation:

y=3x-5 if you graph it it will go through -5 and end up at 5,10

The value of \(x\) would be as follows:

\(x = 2\)

Given that,

\(m = -5\)

As we know,

Slope \(= \frac{y_{2} - y_{1} }{{x_{2} - x_{1}} }\)

Here,

\({y_{2} = 10,\)

\(y_{1} = 5\),

\({{x_{2} = x\)

and \(x_{1}} = 3\)

by putting these values,

\(-5/1 = (10 - 5)/(x - 3)\)

⇒ \(-5(x - 3) = 10 - 5\)

⇒ \(-5x = -10\)

⇒ \(5x = 10\)

⇒ \(x = 10/5\)

∵ \(x = 2\)

Thus, "\(x = 2\)" is the correct answer.

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If the angles are complementary, the value of d is C. d = 25.

Complementary angles are two angles whose measures add up to 90° . In the figure below, ∠1 and ∠2 are complementary. Two angles need not be adjacent to be complementary. When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles

In this case, it will be:

25 + 3d - 10 = 90

3d + 15 = 90

Collect like terms

3d = 90 - 15.

3d = 75.

Divide

d = 75/3

d = 25

The correct option is C.

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Answer:

the question is not complete

Answer:

2562.50

Step-by-step explanation:

2.5=0.025

0.025*2500=62.50

2500+62.50=2562.50

Answer:

x=(-2/3)

Step-by-step explanation:

Looked it up on google and got that answer, also used an online linear equation calclator

If z = (6x + 2y)⁹, then the partial derivatives of z are

• with respect to x :

∂z/∂x = 9 (6x + 2y)⁹⁻¹ • ∂(6x + 2y)/∂x

∂z/∂x = 9 (6x + 2y)⁸ • 6

∂z/∂x = 54 (6x + 2y)⁸

• with respect to y :

∂z/∂y = 9 (6x + 2y)⁹⁻¹ • ∂(6x + 2y)/∂y

∂z/∂y = 9 (6x + 2y)⁸ • 2

∂z/∂y = 18 (6x + 2y)⁸

Answer:

x = 5

Step-by-step explanation:

-2 -1(coeffcient of -x) = -3

-3x +3 =-12

subtract 3 (the constant) from both sides

cancelling it on the left and leaving -3x = -15

divide each side by -3 leaving x and 5

x = 5

Answer:

x = mp - n

Step-by-step explanation:

ANSWER

The total monthly expenses fixed is $1,316.05/month

EXPLANATION

Given that ;

The rent payment is $953.20/month

The auto payment is $165.87/month

The telephone payment is $56.98/month

The auto insurance payment is $714.36/six months

Once -a - week outing is $35.00/week

In the given data, the rent, auto, telephone are monthly expenses

since once-a-week outing is $35/week, then, we can calculate the amount spend in a month

There are 4 weeks in a month

Hence, the amount spend in a month is calculated below as

Once-a-week outing = 4 x 35

Once-a-week outing = $140/month

The next step is to find the fixed expenses per month

Fixed expenses per month = rent + auto + telephone + once-a-week outing

Fixed expenses per month = $953.20 + $165.87 + $56.98 + $140

Fixed expenses per month = $1,316.05

Hence, the total monthly expenses fixed is $1,316.05/month

Hello!

The distance, d, is less than 200 miles.

B. d > 200

Answer:

6.438 [litres].

Step-by-step explanation:

1) the condition '5.50 liters are removed' means the coolant 12.5-5.5=7 [litres] with 13.4% solution;

2) the condition 'coolant containing 13.4% antifreeze' means 7*0.134=0.938 [litres] of pure antifreeze in the 7 litres coolant;

3) the condition '5.50 liters of pure antifreeze is then added' means 0.938+5.5 [litres];

4) finally, it is contained 0.938+5.5=6.438 [litres] of antifreeze will be contained in the final mixture.

Answer:

multiply length x width x height.

l x w x h

The proof that line n is perpendicular to both a and b is proved below using definition of right angle and perpendicular transversal theorem.

We are given that;

Line a is parallel to line b

Line m is parallel to line n.

A) We want to prove that line a is perpendicular to n.

From the image, we see that there is a right angle sign on the opposite side of ∠1 facing m.

Now, we know that by definition of a right angle that ∠1 will also be a right angle.

Since angle 1 is a right angle, then we can say the line transversal a is perpendicular to line m.

B) We want to prove that line b is perpendicular to n.

The definition of the perpendicular transversal theorem, states that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Thus, b will be perpendicular to n.

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Answer:

A

Step-by-step explanation:

The volume of prism is b*h, base area is (2.5)*(3.24*(1.1)=8.91. Hence volume is 8.91*6.17=54.97

Answer:

The manager should use a sample size of 12 to determine the average travel expenditure

Step-by-step explanation:

Spent about 20 cents per mile. Distance of 15 miles

We have the mean per a distance, so we use the Poisson distribution. In this distribution, the standard deviation is the square root of the mean. So

\(\mu = 20*15 = 300, \sigma = \sqrt{300} = 17.32\)

Confidence interval:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.95}{2} = 0.025\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

What sample size should the manger use to determine the average travel expenditure?

This is n for which M = 10. So

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(10 = 1.96\frac{17.32}{\sqrt{n}}\)

\(10\sqrt{n} = 1.96*17.32\)

\(\sqrt{n} = \frac{1.96*17.32}{10}\)

\((\sqrt{n})^2 = (\frac{1.96*17.32}{10})^2\)

\(n = 11.52\)

Rounding up

The manager should use a sample size of 12 to determine the average travel expenditure

Answer:

Your answer is correct

Step-by-step explanation:

Use the rules of exponents to simplify the expression.

To raise a power to another power, multiply the exponents.

Multiply 6 by 2.

The correct option is the third.

Answer:

5 and 3/32 of an inch.

Answer:

x= 14.0 (nearest tenth)

Step-by-step explanation:

Please see the attached picture for the full solution.

The round trip distance in miles from city 1 to city 3 is given as follows:

30 miles.

The matrix corresponding to the distances between each of the cities is given by the image presented at the end of the answer.

Looking at row 1, column 3, we have that the distance from city 1 to city 3 is of 15 miles.

For the round trip distance, we have to go back from city 3 to city 1, more 15 miles, hence the distance is given as follows:

2 x 15 = 30 miles.

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Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:

14

Step-by-step explanation:

(3)^2 + 4(3) - 7

9 + 12 - 7

21 - 7

14

Answer:

B. 1.5 inches

Step-by-step explanation:

600/400=3/2=1.5