For Zoey's lemonade recipe, 7 lemons are required to make 14 cups of lemonade. At what rate are lemons being used in lemons per cup of lemonade

Answer: The correct answer is option A. a reference point.

Step-by-step explanation:

An reference point is required to determine whether or not an object moves.

Answer:its d

Step-by-step explanation:

Answer:

C.  \(x=-9 \textsf{ and }x=1\)

Step-by-step explanation:

\((x+4)^2=25\)

\((x+4)(x+4)=25\)

expand the brackets:

\(x^2+8x+16=25\)

subtract 25 from both sides:

\(x^2+8x-9=0\)

factor:

\(x^2+9x-x-9=0\)

\(x(x+9)-1(x+9)=0\)

\((x-1)(x+9)=0\)

solve for x:

\(x-1=0 \implies x=1\)

\(x+9=0 \implies x=-9\)

Answer:

0.2 because Density = Mass / Volume

Density = 25 / 50

Density= 0.2 g/cubic cm

The author of the review is disappointed with the meatball sub casserole recipe posted on Recipe Masters, which did not turn out well despite following the recipe.

The author recommends that others should not attempt to make the recipe and believes that Recipe Masters should ensure that their posted recipes are reliable and thoroughly tested. The author also implies that the quality of the recipes on Recipe Masters is not as advertised, which could potentially lead subscribers to lose faith in the service and seek out free recipe sites instead.

Therefore, a suitable summary of the author's point of view would be: The author is dissatisfied with the meatball sub casserole recipe on Recipe Masters, which did not work out well and believes that Recipe Masters should provide reliable, thoroughly tested recipes as advertised.

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sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)

The sine expression is given as

sin^4x

The above means

sin x raised to the power of 4

This in other words, the expression is represented as

(sin(x))^4

Express 4 as 2 + 2

(sin(x))^(2 + 2)

Apply the law of indices

(sin(x))^2 * (sin(x))^2

This gives

sin^2(x) * sin^2(x)

Hence, sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)

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Answer:

84%

Step-by-step explanation:

84%

63 divided by 75 is 0.84. 0.84 is also 84% so the answer is 84%.

Answer:

84%

Step-by-step explanation:

63: 75*100=

(63*100):75=

6300:75=84

The area of the shaded region in the specified figure of the square containing a circle is 21.5 m², which is the first option

A square is a quadrilateral with all sides of the same length and four interior angles which are right angles.

The figure is a composite figure comprising of a square and a circle

The radius of the circle, r = 5 meters

The side length of the square = 10 meters

The value of π = 3.14

The area of the square = 10 m × 10 m = 100 m²

The area of the circle = π × (5 m)² = 25·π m²

The area of the shaded region is the difference between the area of the square and the area of the circle, therefore;

The area of the shaded region = (100 - 25·π) m²

The area of the shaded region is therefore; (100 - 25 × 3.14) m² = 21.5 m²

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\(f(x) = 2x is linear.f(x) = 4^x is exponential.\) This is where at each level, each branch extends into 4 branches.

In the first prompt, the number of boxes in each row is increasing by a constant amount, so the function is linear. In the second prompt, the number of branches is increasing by a factor of 4 with each level, so the function is exponential.

A linear function is defined as one where the output increases by a constant amount for each increase in the input. An exponential function is defined as one where the output increases by a constant factor for each increase in the input. The first prompt corresponds to a linear function, while the second prompt corresponds to an exponential function.

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The complete question is-

Is the function f(x) = 4^x, where x is the number of branches at level x in a tree diagram, linear or exponential? Explain your answer.

The equation for the circle is

(x - 1)² + (y + 2)² = 9

Then the radius is 3 units and the center is (1, -2), the graph is on the image at the end.

Remember that for an equation for a circle of radius R and center (a, b), the equation is:

(x - a)² + (y - b)² = R²

Here we have the equation of the circle:

x² + y² - 2x + 4y - 4 = 0

We need to complete squares, we will get:

(x² - 2x) + (y² + 2*2y)  = 4

Now we can add in both sides (-1)² and (2)², then we will get:

(x² - 2x + (-1)²) + (y² + 2*2y +  (2)²)  = 4 +  (2)² + (-1)²

(x - 1)² + (y + 2)² = 4 + 4 + 1

(x - 1)² + (y + 2)² = 9 = 3²

Then we can see that the center is (1, -2), and the radius is 3.

The graph of this circle is on the image at the end.

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Answer:

i think 216

Step-by-step explanation:

Answer:

736 ft²

Step-by-step explanation:

The angle measure of LJK is 27 degrees

Following the triangle sum theorem, we have that the sum of the interior angles of a triangle is 180 degrees

Also, we need to know that the sum of angles on a straight line is 180, then, we have;

<JLK = 180 - <LKM = 180 - (8x - 19)

Then, substitute the value, we have that;

<JKL + < JLK + < KJL = 180

Then,

3x - 16 + (180 - (8x - 19)) + 2x + 15 = 180

expand the bracket, we have;

3x - 16 - 8x - 19 + 2x + 15 = 0

add the like terms

-3x + 18 = 0

collect the terms

-3x = -18

x = 6

Then, the angle LJK = 2x + 15 = 2(6) + 15 = 27 degrees

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Answer:

its equal to 150

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

Answer:

Angle A measures 80º.

Step-by-step explanation:

Supplementary angles:

Two angles are called supplementary when their measures add to 180º.

In this question:

Angle A measures 7x + 3

Angle B measures 7x + 23

Since they are supplementary:

\(A + B = 180\)

\(7x + 3 + 7x + 23 = 180\)

\(14x + 26 = 180\)

\(14x = 154\)

\(x = \frac{154}{14}\)

\(x = 11\)

Measure of Angle A:

Since x = 11

7*11 + 3 = 77 + 3 = 80º

Angle A measures 80º.

Answer:

Step-by-step explanation:

a+√b

a-√b

Answer:

81^84375

Step-by-step explanation:

Answer:

\( - \frac{3}{4} \)

Step-by-step explanation:

\( = - 1 \frac{1}{4} + \frac{1}{2} \)

\( = - \frac{5}{4} + \frac{1}{2} \)

\( = \frac{ - 5 + 2}{4} \)

\( = - \frac{3}{4} \)

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

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The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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The detailed answer of this question is:

P(X > 100 | X > 50)=0.455

Given that X follows an exponential distribution, we know that the probability density function (PDF) of X is given by:

f(x) = λe^(-λx) for x ≥ 0

where λ is the rate parameter of the distribution.

We are given that P(X < 50) = 0.25. Using the cumulative distribution function (CDF) of X, we can write:

P(X < 50) = 1 - e^(-λ*50) = 0.25

Solving this equation for λ, we get:

λ = -ln(0.75)/50 ≈ 0.0278

Now, we are asked to find P(X > 100 | X > 50). Using the definition of conditional probability, we can write:

P(X > 100 | X > 50) = P(X > 100 and X > 50) / P(X > 50)

= P(X > 100) / P(X > 50)

= e^(-λ100) / e^(-λ50)

= e^(-λ*50)

Substituting the value of λ, we get:

P(X > 100 | X > 50) = e^(-0.0278*50) ≈ 0.455

Therefore, the probability that a high-risk driver will have an accident after 100 days given that they have not had an accident for the first 50 days is approximately 0.455.

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The height of the building, h, found using ratios between similar figures and within similar figures is as follows;

1. The scale factor, r = 17/6

The height of the building is 99 1/6 meters

2. The within figure ratio is 35/60 = h/170

Heiught of the building is 99 1/6 meters

3. The between figure ratio is 35/h = 60/170

Height of the building is 99 1/6 meters

4. The measure of the angle at the top of the building is 60°

Similar triangles are triangles that have corresponding sides that are proportional, such that the sides of each triangle are a constant multiple of the sides of the other.

The distance from the flagpole = 60 meters

Height of the flagpole = 35 meters

The distance from the building = 170 meters

1. The height of the building found using a scale factor is as follows;

The scale factor, s.f. is the know ratio of the distance from the building to the distance from the flagpole

Therefore; s.f. 170/60 = 17/6

The height of the flagpole is 35 meters

Height of the building = Height of the flagpole × Scale factor

Height of the building = 35 m × 17/6 = 99 1/6

The height of the building found using scale factors is 99 1/6 meters

3. The height of the building found using ratios within the two triangles is found as follows;

The triangles are similar, therefore, their interior angles are congruent, and the trigonometric ratios of the angles are the same.

Within the two triangles, we get;

\(\frac{Height \ of \ flagpole}{Distance \ from \ flagpole} = \frac{Height \ of \ building}{Disrtance \ from \ building}\)

35/60 = h/170

h = 170 × (35/60) = 99 1/6

Height of the building = 99 1/6 meters

3. The triangles formed with the flagpole and the triangle formed with the building are similar triangles, therefore;

Between the two triangles, we get

\(\frac{Height \ of \ the \ flag[pole}{Height \ of \ the \ building } =\frac{Distance \ from \ the \ flagpole}{Distance \ from \ the \ building}\)

Plugging in the known values, we get;

\(\frac{35}{Height \ of \ the \ building} = \frac{60}{170}\)

Height of the building = 35 × 170/60 = 99 1/6

The height of the building is about 99 1/6 meters

4, The triangle formed by the flagpole and the building are similar, therefore, the corresponding angles in the triangles are congruent

The angle at the top of the flagpole corresponds with the angle at the top of the building, therefore;

The angle formed at the top of the flagpole is congruent to the angle formed at the top of the building

The measure of corresponding angles are the same, therefore, the anglle at the top of the building is equal to the angle at the flagpole, which is 60°

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Answer:

The common denominator will be 70

Step-by-step explanation:

To set the fractions to a common denominator, we need to know what number they both share. In this case, both 7 and 10 share the number 70, since 7 * 10 is 70.

Therefore, we can multiply 2/7 by 10/10 and 3/10 by 7/7:

\(\frac{2}{7}\) * \(\frac{10}{10}\) = \(\frac{20}{70}\)

\(\frac{3}{10}\) * \(\frac{7}{7}\) = \(\frac{21}{70}\)

Answer: Common denominator = 70

Step-by-step explanation: In order to find a common denominator, we need to find what number they have in common. That'd be 70. So, now rewrite the fractions like this:

\(\frac{2}{7} = \frac{?}{70}\)

\(\frac{3}{10} = \frac{?}{70}\)

Now, we need to find the equivalent fractions on the right. To do that, use this formula for part 1:

Right denominator / left denominator

Then, what you get after dividing those 2, you multiply by the left numerator.

So, let's plug the numbers in:

70 / 7 = 10

10 * 2 = 20

Therefore, \(\frac{2}{7} = \frac{20}{70}\)

70 / 10 = 7

3 * 7 = 21

Therefore, \(\frac{3}{10} = \frac{21}{70}\)

I hope this helped!

The area of a rectangle does double when dilated by a scale factor of 2, the Perimeter does not double. It increases by a factor of 2.

Brendan's statement that when a rectangle with a length of 6 cm and a width of 4 cm is dilated by a scale factor of 2, the perimeter and area of the rectangle are doubled is incorrect. While the area of the rectangle does indeed increase by a factor of 2 when dilated, the perimeter does not necessarily double.

Brendan's statement and understand the concept of dilation:

1. Perimeter: The perimeter of a rectangle is the sum of all its sides. In this case, the original rectangle has a length of 6 cm and a width of 4 cm, resulting in a perimeter of 2*(6 cm + 4 cm) = 20 cm. If we dilate this rectangle by a scale factor of 2, the new rectangle will have a length of 2 * 6 cm = 12 cm and a width of 2 * 4 cm = 8 cm. The perimeter of the new rectangle is 2*(12 cm + 8 cm) = 40 cm. As we can see, the perimeter has not doubled; it has increased by a factor of 2.

2. Area: The area of a rectangle is calculated by multiplying its length by its width. For the original rectangle with a length of 6 cm and a width of 4 cm, the area is 6 cm * 4 cm = 24 cm². When we dilate the rectangle by a scale factor of 2, the new rectangle will have a length of 2 * 6 cm = 12 cm and a width of 2 * 4 cm = 8 cm. The area of the new rectangle is 12 cm * 8 cm = 96 cm². The area has indeed doubled, as Brendan mentioned.

Therefore, while the area of a rectangle does double when dilated by a scale factor of 2, the perimeter does not double. It increases by a factor of 2. It is crucial to differentiate between the effects of dilation on the area and the perimeter of a shape to have a clear understanding of geometric transformations.

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We were given that:

Answer:

  4.5 kWh

Step-by-step explanation:

You want an estimate of the mean of the solar panel output represented by the given histogram.

The mean of the output values can be estimated as the weighted average of the middle of each interval, weighted by the area of the histogram in that interval.

The computation looks like ...

  \(\dfrac{.5\times1+1.5\times1+2.5\times1+3.5\times4+4.5\times4+5.5\times3+6.5\times 2+7.5\times2}{1+1+1+4+4+3+2+2}\\\\\\=\dfrac{81}{18}=4.5\)

The mean daily energy output of the solar panel is about 4.5 kWh.

<95141404393>

Answer:

19.6

Step-by-step explanation:

According to the

Cosine Theorem

e² = d² + f² - 2dfcos /_E

°Cos 13° = 0.974

e² = (7.1) 2 + (26.5) 2-2 × 26 = 5 × 7.1 × 0.974

=752.66 - 366.516

= 386.14

e = 386.14 = 19.6

When the expression given as 6 + √27/4 - √3 is simplified, the value is 6 - 1/4√3

The expression is given as

6 + root 27over 4 - root 3

Mathematically, the expression can be represented as

6 + √27/4 - √3

Expand 27 as the product of 9 and 3

So, we have the following equation

6 + √27/4 - √3 = 6 + √(9 * 3)/4 - √3

Expand the products in the above equation

So, we have the following equation

6 + √27/4 - √3 = 6 + √9 * √3/4 - √3

Evaluate the square root of 9 in the above equation

So, we have

6 + √27/4 - √3 = 6 + 3/4√3 - √3

Evaluate the like terms in the above equation

So, we have the following equation

6 + √27/4 - √3 = 6 - 1/4√3

Hence, the value of the expression given as 6 + √27/4 - √3 is 6 - 1/4√3

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The probability of getting exactly 9 of them major in STEM is 0.139 or 13.9%.

The probability of getting at most 11 of them major in STEM is approximately 0.898 or 89.8%.

The probability of getting at least 11 of them major in STEM is approximately 0.318 or 31.8%.

a. Exactly 9 of them major in STEM.

In this case, the probability of success (a student majoring in STEM) is 0.27, and the number of trials is 35. The probability of exactly 9 students majoring in STEM is then given by the formula:

P(X = 9) = (35 choose 9) x (0.27)⁹ x (0.73)²⁶

where (35 choose 9) is the number of ways to choose 9 students out of 35, and (0.27)⁹ x (0.73)²⁶ is the probability of 9 successes and 26 failures. Evaluating this expression gives a probability of approximately 0.139 or 13.9%.

b. At most 11 of them major in STEM.

To calculate the probability that at most 11 students out of 35 major in STEM, we can use the cumulative binomial probability distribution. This distribution calculates the probability of at most X successes, where X is any number from 0 to the total number of trials.

The probability of at most 11 students majoring in STEM can be calculated as follows:

P(X <= 11) = P(X = 0) + P(X = 1) + ... + P(X = 11) = 0.898 or 89.8%.

c. At least 11 of them major in STEM.

The probability of less than 11 students majoring in STEM can be calculated using the cumulative binomial probability distribution, as in part (b). Specifically:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)

Subtracting this probability from 1 gives the probability of at least 11 students majoring in STEM:

P(X >= 11) = 1 - P(X < 11) = 31.8%

Again, we can use the binomial distribution formula from part (a), or a binomial probability calculator or statistical software package to calculate this probability.

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Answer:

\(\frac{1}{32} yards^{3}\)

Step-by-step explanation:

\(V=w*h*l\)

↓

\(V= \frac{1}{4} *\frac{1}{4} *\frac{1}{2}\)

=

\(\frac{1}{32} yards^{3}\\\)

Hope this helps!