Ryan is making a fruit drink. The directions say to mix 3 cups of water with 1 1/2 scoops of powdered fruit mix.
1. how many cups of water should he use with 6 scoops of fruit mix?
2. Rate needed
3. What is the unit rate?
4. Interpretation of unit rate?

To make x the subject of the expression, we have; x = 16y^2 - 5.

Subject of formula is a topic in mathematics which involves expressing an alphabet in terms of other alphabets in the given expression. From the given question, to make x the subject implies expressing x in terms of other variables in the given expression.

So that, [tex]\frac{\sqrt{x + 5} }{4}[/tex] = y

square both sides of the expression to have;

(x + 5)/ 16 = y^2x + 5

= 16y^2x = 16y^2 - 5

Therefore to express x as a subject of formula for the given expression, we have;

x = 16y^2 - 5

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Answer:

208 mm

Step-by-step explanation:

A = Area. P = Perimeter. B = base.

Let's say H = Height

P = 2B + 2H

Now we already know the perimeter is 68 mm, so P = 68:

68 = 2B + 2H

In addition, we know that the base is 26 mm, so B = 26:

68 = 2(26) + 2H

68 = 52 + 2H

16 = 2H ==> subtract 52 on both sides

H = 8  ==> the height of the rectangle is 8 mm

A = B * H  

A = 26 * 8  ==> plugin B=26 and H=8 into the Area formula

A = 208  ==> simplified

Hence, the area is 208 mm.

No, this does not approximate a normal distribution.

This does not confirm the first part of the Central Limit Theorem, which states that the sum of a large number of independent random variables will approximate a normal distribution. To calculate the probability of a normal distribution, we need to calculate the mean and standard deviation of the sample. We can then use this information to calculate the z-score of a given value in the sample. The z-score will tell us how many standard deviations away from the mean a certain value is. If the z-score follows a normal distribution then the sample approximates a normal distribution. However, if the z-score does not follow a normal distribution then the sample does not approximate a normal distribution.

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Answer:

[tex]m = \frac{y2 - y1}{x2 - x1} where \: m \: is \: slope[/tex]

(8,3)=(x1,y1)

(10,3)=(x2, y2)

Now,

[tex]m = \frac{3 - 3}{10 - 8} \\ = 0[/tex]

For class 10, the midpoint formula in the coordinate geometry for the endpoints ( x₁ , y₁ ) and ( x₂ , y₂ )  is given by:

( x , y ) = [( x₁ + x₂)/2 , (y₁ + y₂)/2].

As given in the question,

In the coordinate geometry of class 10,

To get the x and y coordinate of the midpoint following points need to follow:

Therefore, in the coordinate geometry of class 10 the midpoint formula is given by ( x , y ) = [( x₁ + x₂)/2 , (y₁ + y₂)/2].

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Answer:

1st one: y=x+2

2nd one: y=x/4

3rd one: y=3x

4th one: y=x-5

The spread of the sampling distribution is equal to the standard deviation divided by the square root of the sample size.

What is sample size?

The sample size is defined as the number of observations used to estimate a given population. The population was used to determine the size of the sample. The process of selecting a subset of individuals from a population to estimate the characteristics of the entire population is known as sampling. For analysis, the number of entities in a subset of a population is chosen.

The spread of the sampling distribution is proportional to the spread of the sample and its size. We calculate the spread of the sampling distribution as the population standard deviation divided by the square root of the sample size.

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Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

y=3x+13; y=7x+17

Step: Solve y = 3x + 13 for y:

y=3x+13

Step: Substitute 3x + 13 for y in y = 7x + 17 :

y=7x+17

3x+13= 7x+17

3x+13+-7x=7x+17+-7x (Add -7x to both sides)

-4x+13=17

-4x+13+-13=17+-13 (Add -13 to both sides)

-4x=4

-4x/-4 = 4/-4 (Divide both sides by -4)

x=-1

Step: Substitute -1 for x in y=3x+13:

y=3x+13

y=(3)(-1)+13

y=10(simplify both sides of the equation)

Answer:

x= -1 and y= 10

(Hope this helped!)

Area of concave hexagon = 24

To find the area of the concave hexagon, we can divide it into two triangles and a rectangle. The side lengths of the rectangle are the difference of the radii of the two circles (4-2=2) and the distance between the centers of the circles, which can be found using the Pythagorean theorem. Using that we can find the area of the rectangle and the two triangles. The area of the hexagon is the sum of the areas of these three shapes.

In the given case, let the distance between the centers of the circles be 'd'.

d^2 = (4+2)^2

d = √((4+2)^2) = √(36) = 6

Area of rectangle = 26 = 12

Area of each triangle = (1/2)(2d) = (1/2)(2*6) = 6

Area of hexagon = 12 + 2*6 = 24

Area of concave hexagon = 24

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The ratio of bottles of orange juice to bottles of apple juice in the cafeteria's refrigerator is 2 : 1.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

Given, In the cafeteria's refrigerator, there are 11 bottles of orange juice and 22 bottles of apple juice.

Therefore, The ratio of bottles of orange juice to bottles of apple juice is,

orange juice : apple juice = 22 : 11.

orange juice : apple juice = 2 : 1.

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Answer:

Step-by-step explanation:

Uh sorry but there is no picture here

Answer:

no graph is attached

Step-by-step explanation:

Answer:We know that the area of a rectangle is represented by the product of its length and width, so the equation for the area of the rectangle is:

A = l * w

We also know that the area of the rectangle is given as 32X^3 and the length of the rectangle is 4X. Therefore, we can substitute these values into the equation:

32X^3 = (4X) * w

To find the width of the rectangle, we can divide both sides of the equation by 4X:

w = 32X^3 / 4X

Simplifying the equation, we can get the value of w:

w = 8X^2

So the width of the rectangle is 8X^2

Step-by-step explanation:

0.80 is the expected value of wei's ticket. This can be solved by using the concept of probability.

The word "probability" derives from the Latin word "probitatem," which means "credibility, likelihood," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

As, we know

E(x) = x₁. p(x₁) + x₂ . p(x₂) + ....... + x(n). p(x(n))

From the table it is shown that,

E(x) = (68% × 0) + (24% × 0) + (6% × 5) + (2% × 25)

or, E(x) = 0.80

then the expected value of Wei's ticket is: 0.80

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The probability of a senior student taking statistics or calculus is 0.82. This is calculated by adding the probability of a senior student taking statistics (0.15) and a senior student taking calculus (0.35).

p(a or b) = p(a) + p(b) - p(a and b)

p(a) = 15/100 = 0.15

p(b) = 35/100 = 0.35

p(a and b) = 15/100 = 0.15

p(a or b) = 0.15 + 0.35 - 0.15 = 0.82

The probability of a senior student taking either statistics or calculus is 0.82. This is calculated by adding the probability of a senior student taking statistics (0.15) and a senior student taking calculus (0.35) and subtracting the probability of a senior student taking both statistics and calculus (0.15). The probability of a senior student taking statistics is calculated by dividing the number of seniors taking statistics by the total number of students surveyed (15/100 = 0.15). The probability of a senior student taking calculus is calculated by dividing the number of seniors taking calculus by the total number of students surveyed (35/100 = 0.35). The probability of a senior student taking both statistics and calculus is calculated by dividing the number of seniors taking both statistics and calculus by the total number of students surveyed (15/100 = 0.15). Therefore, the probability of a senior student taking either statistics or calculus is 0.82.

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Answer:

yes, because there aren't other even prime numbers.

Step-by-step explanation:

2 Is the only even prime number

3 is odd

5 is odd

7 is odd

11 is odd

13 is odd

And so on

The zeros of the polynomial y = 3p³ - 8p² + 4p are calculated to be 0, 2/3, and 2.

The zeros of a function, sometimes referred to as the roots or solutions, are the values of the independent variable (x) for which the function equals zero. In other words, these are the x-coordinates of the points where the graph of the function crosses the x-axis. You can get the zeros of a function by setting its value to zero and then figuring out what value(s) of x the equation needs.

For example, if the function is f(x), you would set f(x) to 0 and then find x:

For example, if the function is f(x), you would set f(x) to 0 and then find x:

f(x) = x² + 2x - 3 = 0

This equation can be written as (x-3)(x+1) = 0.

Inferring from the x-values that x - 3 = 3 or x + 1 = -1, x² + 2x - 3 = -1, 3

As a result, the zeros of the function f(x) = x² + 2x - 3 are -1 and 3.

In the issue at hand, y = 3p³ - 8p² + 4p

y = p(3p - 2)(p - 2) (p - 2)

Taking the zeros,

0 = p(3p - 2)(p - 2)

p = 0,

3p - 2 = 0,

p = 2 / 3,

p - 2 = 0, p = 2

The zeros of the polynomial or roots are (0, 2/3, and 2).

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The equation of the line that passes through (3, 19) and (9, 25) will be y = x + 16.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The points are given below.

(3, 19) and (9, 25)

The equation of the line that passes through (3, 19) and (9, 25) will be given as,

(y - 25) = [(25 - 19) / (9 - 3)](x - 9)

y - 25 = (6/6)(x - 9)

y - 25 = x - 9

y = x - 9 + 25

y = x + 16

The equation of the line that passes through (3, 19) and (9, 25) will be y = x + 16.

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Answer:

1/3

Step-by-step explanation:

f(gx)-2

formula use the solve this problem

The information provided indicates that it will take 78 minutes to load.

Time may be described in mathematics as a continuing and continuous series of events that take place one after another, from the past through the present, and into the future. The length of events or the gaps between them may be measured, compared, or even ordered using time.

If loading three and a half trucks takes 42 minutes, loading one truck will take 42 / 3.5 minutes, or 12 minutes. The time needed to load is calculated by multiplying the minutes per vehicle by 6.5. In this scenario, it would take 78 minutes to load 6 1/2 trucks (12 x 6.5). The time taken is calculated using the formula t = 12n, where n indicates the number of trucks and t is the time in minutes.

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Angle m∠3 is 79degree

What is linear pair?

Linear pair of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.

Given;

m∠1= (x+70)

m∠2= (5x+54)

Here, m1=m2

substituting the values of m1 and m2

x+70=5x+54

70+54=5x-x

124=4x

x=31 substituting in m2

m2=101

Now, m2+m3=180 (linear pair of angles)

101+m3=180

m3=79degree

So, the measure of angle m3 will be 79degree.

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Assuming that the y-axis tick marks will be separated by 50 (50, 100, 150, and so on). The largest value that should appear on the y-axis is 400.

Largest value:

The maximum value of a dataset is often called the maximum value (max for short), and the minimum value is often called the minimum value (or min). The difference between the maximum and minimum values, sometimes called the range, is calculated by subtracting the minimum value from the maximum value.

Researchers varied the time of the experiment to measure the activity of the enzyme on glucose-6-phosphate (substrate). This happened because the enzyme acted on glucose-6-phosphate to produce glucose and a phosphate ion (Pi).

The concentration of phosphate ions was measured in the experiment. Therefore, time is the independent variable plotted on the x-axis and phosphate ion concentration is the dependent variable plotted on the y-axis.

The measured phosphate ion concentration ranges from 0 to 355. The maximum possible value is 355, so the y-axis range must be between 0 and 400. So the maximum value on the y-axis is 400.

50 units should separate the y-axis ticks. All tick marks are evenly spaced.

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The point on the number line is between 6 and 7

From the question, we have the following parameters that can be used in our computation:

Number = square root 38

The square root of 38 is approximately 6.16441400296898.

This number is between 6 and 7 on the number line, closer to 6.

Also, it should be noted that

It's not a rational number so it's not on the number line with integers, but it can be represented as a decimal or as an irrational number.

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Answer:

Step-by-step explanation:

Yes, by side 6cm, 8cm, 10cm be a right angle triangle.

explain, by pythagoras theorem,

                 (hypotenuse)^2 = (perpendicular)^2 + (base)^2

             =>    (10)^2 = (6)^2 + (8)^2

            =>      100 = 36 + 64

            =>      100 = 100

so, it is verifying the phythagoras theorem, hence it will form a right angle triangle with side 6cm, 8cm, and 10cm.

The amount it would cost to paint the outside of the box is £208

From the question, we are to determine calculate how much it would cost to paint the outside of the box

To do this, we will calculate the surface area of the box

The surface area of a box is given by

S.A = 2(lw + lh + wh)

Where S.A is the surface area

l is the length

w is the width

and h is the height  

From the given information,

l = 10 cm

w = 80 cm

h = 20 cm

Thus,

S.A = 2(10×80 + 10×20 + 80×20)

S.A = 2(800 + 200 + 1600)

S.A = 2(2600)

S.A = 5200 cm²

Also, from the given information

The paint costs £0.04 per cm2

Thus,

The cost is £0.04 × 5200

= £208

Hence, the cost is £208

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The measure of the angle x in the isosceles triangles are;

x = 44°

1) x = 80°

An isosceles triangle is a triangle that has a pair of congruent sides and a pair of congruent angles.

The measure of the specified angle are found as follows;

The isosceles triangle that has 92° as the exterior angle, indicates that we get;

Base angles of the isosceles triangle = (180° - 92°)/2 = 44°

Vertical angles theorem, indicates that the vertical angle and the base angles of the second isosceles triangle are congruent.

Base angles of the second isosceles triangle = 44°

1) The angle adjacent to the angle x is a base angle of the isosceles triangle that has a base angle of 70°

The vertex angle of the isosceles triangle = 180° - 2 × 70° = 40°

The measure of the section of the indicated 90° angle that is a part of the isosceles triangle that has angle x as the vertex angle = 90° - 40° = 50°

The measure of angle x found using the relationship between the angles in an isosceles is; x = 180° - 2 × 50° = 80°

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Answer:

3600 square units

Step-by-step explanation:

From inspection of the given diagram, the area of the rectangle is:

[tex]\implies \sf Area=9 \cdot 4 = 36\; units \; squared[/tex]

Given matrix:

[tex]\left[\begin{array}{rr}5&10\\-8&4\end{array}\right][/tex]

To find the area scale factor, find the absolute value of the matrix determinant:

[tex]\implies \left| \:5 \cdot 4 - 10 \cdot (-8) \right|=\left|20+80\right|=100[/tex]

Therefore, the area of the image of the rectangle under the given matrix transformation is:

[tex]\implies \sf Area=36 \cdot 100=3600\;square\;units[/tex]

Answer:

A) ( -10, -7)

Step-by-step explanation:

x = -10 is a vertical line going through x = -10

No matter what y is, x will be -10

Plug -10 into the first equation to find the y value

y = 2/5(-10) - 3

y = -4 - 3

y = -7

Answer:

(12m + 5 ) - (3m - 2)

12m + 5 - 3m + 2

12m - 3m + 5 +2

9m + 7

Answer:

[tex] \sf \: 9m + 7 [/tex]

Step-by-step explanation:

Given expression,

→ (12m + 5) - (3m - 2)

Let's simplify the expression,

→ (12m + 5) - (3m - 2)

→ 12m + 5 - 3m + 2

→ (12m - 3m) + (5 + 2)

→ (9m) + (7)

→ 9m + 7

Hence, the answer is 9m + 7.

The correct answer would be an option (B) which graph represents a linear function.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

A linear function is defined as a function in the form of f(x) = mx + c where 'm' and 'c' are real numbers.

It represents the line's slope-intercept form, which is written as y = mx+ c.

As per graph (B),

This is a linear function that represents a line, i.e., its graph is a line. Here,

'm' is the slope of the line

'c' is the y-intercept of the line

'x' is the independent variable

'y' (or f(x)) is the dependent variable

Hence, the correct answer would be an option (B).

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