Ramla has two full 1.5 litre bottles of water. She wants to fill as many glasses as possible with water from the bottles. Each glass can hold 180 millilitres of water.
How many glasses can Ramla completely fill?

Exponential expression → exponential function

9ˣ → y = 9ˣ

(3/4)ˣ → y = (3/4)ˣ

6ˣ → y = 6ˣ

bˣ → y = bˣ

An exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Given,

Exponential expressions to exponential function

3⁵ : f(x)= 3⁵

(1/4)ˣ : y = (1/4)ˣ

By the above pattern

Exponential expressions to exponential function

9ˣ : y = 9ˣ

(3/4)ˣ : y = (3/4)ˣ

6ˣ : y = 6ˣ

bˣ : y = bˣ

Hence, y = 9ˣ, y = (3/4)ˣ, y = 6ˣ and y = bˣ are the functions for expression

9ˣ, (3/4)ˣ, 6ˣ and bˣ  respectively.

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Answer:

2.5 pages an hour

Hope this helps! Sorry if I'm wrong!

Answer:

y = 1/8

Step-by-step explanation:

Divide both sides by 4/5, 1/10 divided by 4/5; 4/5y divided by 4/5. In 4/5y divided by 4/5, the two 4/5s cancels out, leaving y alone. 1/10 divided by 4/5 equals to 1/8. Now you have, 1/8 = y, which is the same thing as y = 1/8. Therefore, the value of y is 1/8.

Answer: 1/8

Step-by-step explanation:

4/5y=1/10

*multiply both sides by 5, and you'll get

4y=1/2

*divide both sides by 4

y=1/8

The critical value for an 80% confidence interval is 1.28.

To find the critical value for constructing an 80% confidence interval for the difference in two proportions, we need to use the z-table.

Step 1: Find the critical value.

Since we want an 80% confidence interval, the remaining area (1 - 0.80 = 0.20) is divided equally into the two tails. Each tail has an area of 0.10. To find the critical value, we look for the z-score that corresponds to an area of 0.10 in the standard normal distribution table.

Using the z-table or a calculator, we find that the z-score for an area of 0.10 (one tail) is approximately 1.28.

Therefore, the critical value for an 80% confidence interval is 1.28.

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To determine the maximum number of 2/0 AWG THW aluminum compact conductors permitted in a 2½-inch PVC conduit, Schedule 80, we need to consult the applicable electrical code or standards.

The number of conductors allowed in a conduit is typically governed by factors such as fill capacity and heat dissipation.

The specific requirements may vary depending on the jurisdiction and the electrical code being followed. It is recommended to consult the local electrical code or a qualified electrician to ensure compliance with the regulations in your area.

They will be able to provide the precise guidelines and restrictions for conductor fill capacity based on the conduit size, type, and the specific application.

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The part of the z-score denoting hundredths is found in the interior of the table.

In a standard normal distribution table, also known as a z-table, the z-scores are presented with two parts: the tenths and the hundredths. The tenths are found in the row headings (or sometimes column headings) on the edges of the table, while the hundredths are located in the columns within the interior of the table.

To find a specific z-score in a z-table, first identify the tenths value in the row headings, and then locate the corresponding hundredths value in the columns of the same row. The intersection of the row and column will provide you with the desired probability associated with that particular z-score. The z-table helps in calculating the area under the curve in a standard normal distribution, which is essential for various statistical analyses and probability calculations.

Remember, the z-score is a measure of how far a data point is from the mean in terms of standard deviations. A positive z-score indicates that the data point is above the mean, while a negative z-score indicates that it is below the mean.

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The expression 5⁴/5² will result in 5².

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

In another word, if we divide two numbers by each other then the upper word is called the numerator, and a lower word is called the denominator.

For example a fraction 1/5 here 1 will be the numerator and 5 will be denominated.

Given that, 5⁴/5²

5⁴/5² = 5²×5²/5²

⇒ 5²

Hence "The expression 5⁴/5² will result in 5²".

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Answer:

Step-by-step explanation:

Given line m:

Relationship of line m with following lines:

1. y = 4/5x + 3

2. y = -4/5x + 3

3. y = - 5/4x + 3

Answer:

Volume of cone in term of π = 21π yd³

Step-by-step explanation:

Given:

Height of cone = 7 yd

Base radius of cone = 3 yd

Find:

Volume of cone in term of π

Computation:

Volume of cone = (1/3)(π)(r)²(h)

Volume of cone in term of π = (1/3)(π)(3)²(7)

Volume of cone in term of π = (1/3)(π)(9)(7)

Volume of cone in term of π = (π)(3)(7)

Volume of cone in term of π = 21π yd³

Step-by-step explanation:

Algebra is the branch of mathematics that

Answer:

To make 700 copies the machine requires 5 minutes and 36 seconds.

Step-by-step explanation:

Given, A machine makes 500 copies in 4 minutes.

∴ The time required to make 1 copy is = (4/500) minutes.

= 0.008 minutes.

So, the time required to make 700 copies is,

= 0.008×700 minutes.

= 5.6 minutes or 5 minutes 36 seconds.

The given box has a square base and an open top, which means it has no top cover. Let us assume the side length of the square base to be 'x' and the height of the box to be 'h'. the dimensions of the box that minimize the amount of material used are 15.87cm x 15.87cm x 11.90cm.

Then, the volume of the box can be given as;`

V = x^2h = 3000`cm³

The dimensions of the box must be found to minimize the amount of material used. For that, we need to find the surface area of the box.

Since the box has no top, the surface area is the sum of the areas of its five faces. Therefore, the surface area 'S' can be given by;

`S = x² + 4(xh)

`Now, we can substitute the value of 'h' from the volume equation;

`h = 3000/x²`

So, the surface area equation becomes;`

S = x² + 4(xh)``S = x² + 4x(3000/x²)`

`S = x² + 12000/x`

To minimize the surface area, we need to differentiate the above equation with respect to 'x'.`

dS/dx = 2x - 12000/x²

`Equating the above equation to zero and solving for 'x', we can get the value of 'x' at which the surface area is minimized.

``2x - 12000/x² = 0``

2x³ - 12000 = 0``

x³ = 6000`

`x = 15.87cm

`Now that we have found the value of 'x', we can find the value of 'h' using the volume equation.`

`x²h = 3000``

15.87²h= 3000`

`h = 11.90cm

`Therefore, the dimensions of the box that minimize the amount of material used are 15.87cm x 15.87cm x 11.90cm.

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Answer:

Length = 14cm

Breadth ( AKA Width) = 9cm

Step-by-step explanation:

1) Address the facts

(L)Length = b + 5

(W)Width = b

(P)Perimeter = 46cm

= 2(b + 5 +b)

= 2(2b + 5) 2)Simplify the equation

3) Make b the SOTF (subject of the formula)

46 = 2(2b + 5)

46 = 4b + 10 3a) Simplify further

36 = 4b 3b) Minus 10 on both sides

9 = b

\____ 3c) Divide by 4 on both sides to get JUST b

4) Substitute aka replace the letters with numbers

L = b + 5

= 9 + 5

= 14cm

W = b = 9cm

Therefore the breadth(/width) is 9cm and the length is 14cm :)

Answer:

8 and 1/3

Step-by-step explanation:

Answer:

8 1/3

Step-by-step explanation:

25 ÷ 3 = 8 and remainder = 1 =>

25 = 8 × 3 + 1 =>

25/3 =

(8 × 3 + 1) / 3 =

8 + 1/3 =

8 1/3

The likelihood that a researcher will obtain the same result using the same measures the next time he or she tests a hypothesis is Reliability.

In statistics and psychometrics, reliability is the overall consistency of measurements. Measurements are more reliable when similar results are obtained under the same conditions. Reliable results are accurate, reproducible, and consistent from test event to test event. In other words, if the testing process were repeated on a group of test takers, they would yield essentially the same results. Various types of confidence factors with values ​​ranging from 0.00 (large error) to 1.00 (no error) are commonly used to indicate the amount of error in the assessment.

Examples: include measurements of a person's height and weight. Very reliable in many cases. There are several general classes of reliability estimates: 71.

Retest reliability measures the consistency of test results from one test to the next. Measurements are collected by a single rater using the same method or equipment and the same test conditions. This includes intra-rater reliability.

Inter-method reliability measures how consistent test results are when there is variation in the method or instrumentation used. This means that inter-rater reliability can be ruled out.

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Answer:

8,13,48

Step-by-step explanation:

Third = A(3) = -2 + (3-1)(5) = -2 + 10 = 8

Fourth = A(4) = -2 +(4-1)(5) = -2 + 15 = 13

Eleventh = A(11) = -2 + (11-1)(5) = -2 + 50 = 48

Answer:

C) y= 2/3x -2/3

Step-by-step explanation:

(y-y1)=m(x-x1)

y+2=2/3(x+2)

y+2= 2/3x + 4/3

y= 2/3x -2/3

Answer:

We can write a proportion from this image:

x/2 = (x+2)/3

3x=2(x+2)

3x=2x+4

x=4

Let me know if this helps!

Answer:

n=60

Step-by-step explanation:

The sum of interior angles in a triangle will always be equal to 180. Knowing this, we can set up the following equation:

n+90+30=180

n+120=180

Subtract both sides by 120

n+120-120=180-120

n=60

I hope this helps!

Answer:

60

Step-by-step explanation:

if the bottom corner on the left is a right angle, its 90. because we already have 30. its 90+30+120. Triangles total angles is 180.

The best prediction of the average amount of money spent on groceries for a household that has 7 people can be determined by examining the scatterplot and estimating the corresponding value on the y-axis.

Based on the scatterplot, the best prediction for the average amount of money spent on groceries for a household with 7 people would be around $160.

To arrive at this prediction, we observe the position on the x-axis where the number of people in the household is 7. Then, we look at the corresponding position on the y-axis to determine the average amount of money spent on groceries. In this case, the scatterplot suggests that households with 7 people tend to spend around $160 on groceries.

It's important to note that this prediction is based on the pattern observed in the given scatterplot, and there may be some variability or uncertainty in the actual amount spent on groceries for a specific household with 7 people.

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1. The equation of the tangent plane to the surface z = x^2 + xy + y^2 at point P0(-1, 1, 1) is z = -2x + 3y + 4.

2. The equation of the tangent plane to the surface z = x^2y + e^(xy)sin(y) at point P0(1, 0, 0) is z = x - y.

3. The equation of the tangent plane to the surface z = y/x + xy at point P0(4, 1, 8) is z = 3x - 2y - 7.

1. To find the tangent plane to the surface z = x^2 + xy + y^2 at point P0(-1, 1, 1), we need to compute the partial derivatives of z with respect to x and y. The partial derivatives are:

∂z/∂x = 2x + y

∂z/∂y = x + 2y

Evaluating these derivatives at P0, we have ∂z/∂x = -2 + 1 = -1 and ∂z/∂y = -1 + 2 = 1. Thus, the equation of the tangent plane can be written as:

z = z0 + (∂z/∂x)(x - x0) + (∂z/∂y)(y - y0)

  = 1 + (-1)(x + 1) + (1)(y - 1)

  = -2x + 3y + 4

2. For the surface z = x^2y + e^(xy)sin(y), the partial derivatives are:

∂z/∂x = 2xy + y^2e^(xy)sin(y) + e^(xy)cos(y)

∂z/∂y = x^2 + xy^2e^(xy)sin(y) + e^(xy)sin(y)cos(y)

Evaluating these derivatives at P0, we have ∂z/∂x = 0 and ∂z/∂y = 1. Therefore, the equation of the tangent plane is simply z = x - y.

3. For the surface z = y/x + xy, the partial derivatives are:

∂z/∂x = -y/x^2 + y

∂z/∂y = 1/x + x

Evaluating these derivatives at P0, we have ∂z/∂x = -1/16 + 1 = 15/16 and ∂z/∂y = 1/4 + 4 = 17/4. The equation of the tangent plane can be written as:

z = z0 + (∂z/∂x)(x - x0) + (∂z/∂y)(y - y0)

  = 8 + (15/16)(x - 4) + (17/4)(y - 1)

  = 3x - 2y - 7

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Answer:

(x + 4)

Step-by-step explanation:

x - 2 = 0, so x = 2

x - 4 = 0, so x = 4

x - 6 = 0, so x = 6

The option which is not a factor of the cubic equation is (x+4)

The algebraic equations having variables with power 3 are referred to as cubic equations. A generalized form of a cubic equation is ax³+ bx²+ cx + d = 0.

Given here: The cubic function f(x)=x³-12x²+44x-48

Clearly in the options the list of factors are -4,6,2,4

Checking for all 4 options we get

f(-4)=-4³-12×4²+44×(-4)-48

     =-64-192-176-48≠0

f(6)=6³-12×6²+44×(6)-48

    =216-12×36+264-48

    =0

f(2)=2³-12×4+44×2-48

    =8-48+88-48

    =0

Similarly we can find for x=4 that f(4)=0

Hence, The option which is not a factor of the cubic equation is (x+4)

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Answer: Median is 5

Step-by-step explanation: To find the median, we first need to arrange the numbers in order from least to greatest:

0 0 3 7 10 27

The median is the middle number, or the average of the two middle numbers if there are an even number of values. In this case, there are 6 values, so the median is the average of the two middle numbers:

median = (3 + 7) / 2

median = 5

Therefore, the median of the given numbers is 5.

Answer:

(A). \(y\leq -3x+3\)

Step-by-step explanation:

The equation of any straight line; a linear equation, can be interpreted as \(y=mx+b\), where 'm' is the slope of the line, 'b', is the y-intercept, and the values of 'x' and 'y' are simply coordinates!

Let's find the slope of the straight line, and that can be done in various ways. Since they gave us two points, I would use the following formula to find slope:  \(m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

Let's assign each coordinate(s) to correspond to the formula (It doesn't matter what order, as long as you follow the rule that you've set up).

\((x_{1},y_{1}), (x_{2}, y_{2})\)  So now that know this, we can just plug in the values that we know, which we already know everything.

\((0,3) (2,-3)\)

\(m=\frac{-3-3}{2-0}\) → This then gives us; \(m=-3\), which means the slope is -3! Now we have one part of the equation. This means that we can easily eliminate options B and D since they give a slope of positive three, which is false.

Now, let's move onto the y-intercept. How do we solve that? The y-intercept is generally known as a point that crosses the y-axis. This means that the x value is always going to be zero. This means that we know the point on the graph is: \((0,y)\). So all we have to do is use that information, and look at the graph! It looks like there is a point that does an x-value of zero.

We can see that the point we are looking at is; \((0,3)\), and the y-value is only what we are looking for. So now, we know that several components of the graph. We know so far that the slope is -3 and the line crosses the y-axis at (0,3), now we move on to determine the inequality part of the graph.

There are rules that determine how a graph is shaded—and let's figure that out.

Shading above the line is represented when 'y' is greater than the inequality itself.

Shading below the line is represented when 'y' is less than the inequality.

The shading occurs below the line, right? That means y is less than the inequality, and since the line is solid, the line can also equal the inequality. Now; with all of this to mind, y is less than or equal to -3x +3 is written or known as; \(y\leq -3x+3\), which means the answer is A.

Answer:

A. y<_ - 3x + 3

I just took the quiz

Answer:

5

Step-by-step explanation:

You divide 15 by 3 and get the answer 5

Answer:

5

Step-by-step explanation:

3 divided by 15 = 5 so Dan can buy 5 blackberries in total with his money. Pls brainliest!

Answer: D) -20.99

Step-by-step explanation:

-4.97-2.36+-5.19-8.47 = -20.99

Answer:

1. the plastic will be 0.48 cm thick after 3 folds

Step-by-step explanation:

Answer:

1.5/2 or 75%

Step-by-step explanation:

3/2=1.5

4/2=2