2.550 gallons in 30 days?​

Answer:

Nadia can make 10 different juices.

To choose one type of fruit, she has 4 options.

To choose two types of fruit, she needs to use a combination of 2 fruits from 4, which can be calculated using the formula:

n! / (k! * (n - k)!)

where n is the total number of items, k is the number of items to choose, and ! is the factorial function.

So, Nadia can make 6 different juices with two types of fruit:

- Apple and Banana

- Apple and Orange

- Apple and Pear

- Banana and Orange

- Banana and Pear

- Orange and Pear

Therefore, the total number of different juices that Nadia can make is 4 + 6 = 10.

The equation of the line is y = -11x + 232

The given parameters are:

Slope (m)= -11

Point (x1, y1) = (31, -109)

The linear equation is then calculated as:

y = m(x - x1) + y1

This gives

y = -11(x - 31) - 109

Evaluate the product

y = -11x + 341 - 109

Evaluate the like terms

y = -11x + 232

Hence, the equation of the line is y = -11x + 232

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

The height of a triangle with a hypotenuse of 23 and angle between base and hypotenuse of 75° is h= 23sin(75)

An equation is an expression that shows the relationship between two or more variables and numbers.

Trigonometric ratio shows the relationship between the sides and angles of a right angle triangle.

Let us assume that the right triangle has a altitude h, hypotenuse of 23 and angle between base and hypotenuse is 75°, hence:

sin(75) = h/23

h= 23sin(75)

The height of a triangle with a hypotenuse of 23 and angle between base and hypotenuse of 75° is h= 23sin(75)

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

Maximum value: \((-1, \frac{7}{2})\)

Step-by-step explanation:

Given the quadratic function, f(x) = -½x² - x + 3

where a = -½, b = -1, and c = 3

Since the value of a is negative, then it means that the graph of the parabola opens downward. Therefore, its vertex is the maximum point.

The vertex of the parabola occurs at the point (h, k).

Axis of symmetry:  x = h.

The axis of symmetry is the imaginary straight line that passes through the x-intercept which divides a parabola into two symmetrical parts. To find the value of the h coordinate of the vertex (h, k), use the following formula:

\(x = \frac{-b}{2a}\)

\(x = \frac{-(-1)}{2(-1/2)} = -1\)

Now that we have the value for h, substitute its value into the original quadratic function:

h = -½(-1)² - (-1) + 3

h = 7/2 or 3.5

Vertex (h, k) =  \((-1, \frac{7}{2})\)

Therefore, the maximum value of the function is \((-1, \frac{7}{2})\).

Answer:it’s 11.9

Step-by-step explanation:

Answer:

Let's denote:

- The number of orders Diane served as `D`

- The number of orders Sam served as `S`

- The number of orders Boris served as `B`

From the problem, we know:

1. `D + S + B = 54` (the total number of orders they served)

2. `D = S - 6` (Diane served 6 fewer orders than Sam)

3. `B = 2S` (Boris served 2 times as many orders as Sam)

We can substitute equations 2 and 3 into equation 1 to solve for the variables:

Substitute `D` and `B` in equation 1:

`(S - 6) + S + 2S = 54`

Combine like terms:

`4S - 6 = 54`

Add 6 to both sides:

`4S = 60`

Divide by 4:

`S = 15`

Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:

`D = S - 6 = 15 - 6 = 9`

`B = 2S = 2 * 15 = 30`

So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.

Answer:

d = 2 and terms are 6, 8, 10 12 and 14

Step-by-step explanation:

we know

\( a_{n} = a_{1} + (n-1)d \)

here a(n) = nth term

a1 = 1st term

n = no. of term

d = common difference

putting the values we get,

178 = 6 + (87-1)d

⇒ 178 = 6 + 86d

⇒86d = 172

⇒ d = 2

So required common difference is 2.

Now the first term is 2

so second term is a2 = 6 + ((2-1)×2) = 8

third term = 6 + ((3-1)×2) = 10

fourth term = 6 + ((4-1)×2) = 12

fifth term = 6 + ((5-1)×2) = 14

Answer:

The best and most correct answer among the choices provided by the question is

The statement that points out his most serious omission is "What if the electric bill increases?".

Step-by-step explanation:

the upper 40 percent round answers to 1 decimal place is 113.1

mean( \(\mu\\\)) = 117 mg/dL

S.D.(σ) = 15.2 mg/dL

The r code which is used to get 40th percentile in qnorm(0.4,117, 15.2 ) = 113.1

What is mean?

Mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations), the geometric mean, and the harmonic mean.

What do you mean by geometric mean?

Geometric Mean (GM) is the average value or mean which signifies the central tendency of the set of numbers by finding the product of their values.

What do you mean by arithmetic mean?

The quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables.

What do you mean byharmonic mean?

The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals.

What do you mean by Standard Deviation?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Find out more about mean and standard deviation:

https://brainly.com/question/475676

#SPJ1

Answer:to what

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

12 - 10 = 2 - 9 = -7

Answer:

Step-by-step explanation:

Write the equation that describes the line with slope = 2 and y-intercept = in slope-intercept form. 312. Jy = 2x+. D.) x = 2y+ 2/2. 14x ...

Answer:

nine 9 classes in the histogram

A.x+y=4 andy y=-x+4=21

The ratio of the sides EF/LM after the transformation is 1/8

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Dilation is the increase or decrease in size of a figure by a factor while translation is the movement of a point up, down, left or right.

Given the tansformation:

Hence:

LM = 8 * EF

EF/LM = 1/8

The ratio of the sides EF/LM after the transformation is 1/8

Find out more on transformation at: https://brainly.com/question/1548871

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

a. B1 is better than B2.

Step-by-step explanation:

Hyperplane is a geometric shape which has subspace whose dimension is one less than ambient space. Hyperplane that maximizes the margin it will have better generalization. Margin is calculated by \(\frac{2}{||W||}\). The correct option is a.

Answer:

A

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

took the test

The polar expression of a complex number in its rectangular form 4(cos120° + i sin120°) = -2 + 2√3 i.

Let Z = a + ib be a complex number in the cartesian form represented by point P(a, b) in the complex plane then Z = r cos∅ + i r sin∅ =r is called the polar form of a complex number.

We have.

z = 4(cos120° + i sin120°)

z = 4(cos(90 + 30)° + i sin(90 + 30)°)

Using trigonometry

cos (90 + ∅) = -sin ∅ and sin (90 + ∅) = -cos ∅

So, 4( -sin (30)° + i cos (30)°)

= 4 ( -1/2 + i √3/2)

= -4(-1/2) + i 4(√3/2)

= -2 + 2√3 i

Thus, the rectangular form is 4(cos120° + i sin120°) = -2 + 2√3 i.

Learn more about polar form here:

brainly.com/question/16106487

#SPJ5

Answer:

Need Decimal-

Step-by-step explanation:

By reducing it to simplest form :

Thus, the value of 'x' for the centroid of triangle ABC is found as: x = 3.

The intersection of the triangle's three medians is known as the centroid. The segments that join a vertex to the opposing side's midway are known as medians.

The centroid for triangle ABC in this image is located at point D. It is simplest to create all three medians and seek for the point of intersection to determine a triangle's centroid. The centroid is the point at which gravity is greatest for a triangle formed of a uniform material.

From the property of centroid of triangle:

BD = 2*DF

Put the given values:

6x+6 = 2(8x - 12)

6x + 6 = 16x - 24

10x = 30

x = 3

Thus, the value of 'x' for the centroid of triangle ABC is found as: x = 3.

Know more about the  centroid of triangle

https://brainly.com/question/30301613

#SPJ1

Answer:

-5/6

Step-by-step explanation:

By the application of Analytical geometry the rate of change of y with respect to x is -5/6.

what is Analytical geometry?

Analytical geometry is a branch of mathematics that studies geometric shapes and figures using analytical methods. It is a branch of mathematics that uses algebraic techniques to describe geometric shapes and figures. It involves the use of analytical equations and formulas to study geometric concepts. Analytical geometry is used to study the properties of points, lines, angles, circles, and other geometric shapes. It can also be used to solve problems involving angles, distances, and areas of figures. In addition, analytical geometry can be used to find the intersection of two lines, calculate the area of a circle, and calculate the volume of a cylinder. Analytical geometry is a powerful tool used in many scientific and engineering fields.

The rate of change of y with respect to x for this line is -5/6
Therefore -5/6 is rate of change in this graph.

To learn more about Analytical geometry from the given link

https://brainly.com/question/23036034

#SPJ1

Answer:

15x+25 ; 70

Step-by-step explanation:

Given that,

Fernando cleans pools for the summer for $25 an hour plus a supply fee of $15.

Here, $25 is constant and $15 increases as the number of hour increase. For x hours, the cost for Fernando to clean a pool is given by :

y = 15x+25

For 3 hours,

y = 15(3)+25

= 45 + 25

= 70

So, the required option is (c) " 15x+25 ; 70 ".

Answer:

a-1. See part a-1 of the attached excel file for the time series plot.

a-2. The linear trend is not appropriate

b. The quadratic trend equation is y = -0.1618x^2 + 2.889x + 5.7022

c. Revenue in year 11 is 17.90.

Step-by-step explanation:

a-1. Construct a time series plot. Comment on the appropriateness of a linear trend.

Note: See part a-1 of the attached excel file for the time series plot.

a-2. Comment on the appropriateness of a linear trend.

Note: See part a-2 of the attached excel file for the time series plot with a linear trend.

From the time series plot with a linear trend, it can be seen that the movements of the time series plot and the linear trend are not the same. This implies that the linear trend is not appropriate

b. Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast revenue.

Note: See part b of the attached excel file for the quadratic equation trend.

From the quadratic equation trend, we obtained the following quadratic trend equation that can be used to forecast revenue:

y = -0.1618x^2 + 2.889x + 5.7022 ……………. (1)

Where;

y = Revenue

x = Year

c. Using the trend equation developed in part (b), forecast revenue in year 11.

Substituting x = 11 into equation (1), we have:

y = (-0.1618 * 11^2) + (2.889 * 11) + 5.7022 = 17.90

Therefore, revenue in year 11 is 17.90.

The relationship between logarithms and exponential functions is fundamental and provides a powerful tool for finding solutions in various mathematical and scientific contexts.

Logarithms are the inverse functions of exponential functions. They allow us to solve equations and manipulate exponential expressions in a more manageable way. By taking the logarithm of both sides of an exponential equation, we can convert it into a linear equation, which is often easier to solve.

One of the key properties of logarithms is the ability to condense multiplication and division operations into addition and subtraction operations. For example, the logarithm of a product is equal to the sum of the logarithms, and the logarithm of a quotient is equal to the difference of the logarithms.

Logarithms also help us solve equations involving exponential growth or decay. By taking the logarithm of both sides of an exponential growth or decay equation, we can isolate the exponent and solve for the unknown variable.

This is particularly useful in fields such as finance, population modeling, and radioactive decay, where exponential functions are commonly used.

Furthermore, logarithms provide a way to express very large or very small numbers in a more manageable form. The logarithmic scale allows us to compress a wide range of values into a smaller range, making it easier to analyze and compare data.

In summary, the relationship between logarithms and exponential functions enables us to simplify and solve equations involving exponential expressions, model exponential growth or decay, and manipulate large or small numbers more effectively.

For more such question on logarithms visit:

https://brainly.com/question/25993029

#SPJ8

Answer:

-13

Step-by-step explanation:

-4-3(3)

-4-9 = -13

Answer: D

Step-by-step explanation:

This is a translation, so this means side lengths are preserved because a translation is a rigid motion. If all the side lengths are the same, then the perimeters must be the same.

Possible Answers:

y = 1/4x + 17

y = -4x + 17

y = 3x + 5

y = 4x - 17

Correct answer:

y = -4x + 17

Explanation:

Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.