A mixture of purple paint contains 6 teaspoons of red paint and 15 teaspoons of blue paint. To make the same shade of purple paint using 1 teaspoon of red paint, how much blue paint would you need?

Answer:

89,892

Step-by-step explanation:

\(x+y\)

\((38,221)+(51,671)\)

\(89,892\)

The solution is the point (0, 1/6) y = 1/6

Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.

In this case, the equation is in slope-intercept form (y = mx + b),

where m represents the slope (-3/4) and b represents the y-intercept (1/6).

The slope-intercept form allows us to determine various properties of the equation.

Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.

Each pair of x and y values that satisfy the equation represents a solution.

For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:

y = (-3/4)(0) + 1/6

y = 1/6

Therefore, the solution is the point (0, 1/6).

In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.

Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.

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The length of 2 sides and an angle between them is given A = ½ × b × c × sin(α) If two angles and the length between them is given A = For an isosceles right triangle A = ½ × a.

If the height (i.e. the altitude) and base of an isosceles triangle are known, the area can be easily calculated. The area of the isosceles triangle is calculated by multiplying the height by the base and dividing by two. As a result, an isosceles triangle has two equal sides and two equal angles. The name is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.

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Answer:

\(\boxed {\boxed {\sf x \approx 105.3}}\)

Step-by-step explanation:

To solve for x, remember the right triangle trigonometry ratios (soh-cah-toa).

If we look at the angle given (θ), then we see that 36 is adjacent or next to the 70° angle. x is the hypotenuse because it is opposite the right angle. So, we have to use cosine (adjacent and hypotenuse).

\(cos (\theta)=\frac {adjacent}{hypotenuse}\)

\(cos(70)=\frac{36}{x}\)

Cross multiply. (Multiply the first numerator by the second denominator. Then, multiply the first denominator by the second numerator).

\(\frac{cos(70)}{1}=\frac{36}{x}\)

\(cos(70)*x= 36\)

Since we want to solve for x, we must isolate the variable. Divide both sides by the cosine of 70.

\(\frac{cos(70)*x}{cos(70)}=\frac{ 36}{cos(70)}\\x= 105.2569584\)

Round to the nearest tenth. The 5 in the hundredth place tells us to round the 2 to a 3.

\(x \approx 105.3\)

x is about 105.3

Answer:

~

Step-by-step explanation:

To make it easier to graph using a translation, we can rewrite the given equation as:

y - 5 = √√4x + 16

This is obtained by subtracting 5 from both sides of the equation.

The graph of the original equation y = √√4x+16 +5 can be obtained by taking the graph of y = √√4x + 16 and shifting it upwards by 5 units. The graph of y = √√4x + 16 is a square root function that has a vertical stretch of 2, a horizontal compression of 4, and a vertical translation of 16 units upwards. So the graph of the given equation y = √√4x+16 +5 will be the same as the graph of y = √√4x + 16, but shifted upwards by 5 units.

the one that has 65 and 54, 3rd one

Answer:

Triangle three(bottom left corner)

Step-by-step explanation:

We know one angle must be 61, as it is given. The other angle can be found by subtracting 126 from 180.

So 180-126 = 54

So the two angles we are looking for are 61 and 54.

However none of the triangles have that those numbers, so we must find the third side. Using that the sum of the angles must be 180,

180-61-54 = 65

So the third angles must be 65

So now we look for the triangle that has 2 of the following: 65, 54, 61

Triangle 3 fits this.

When Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include

A. 27, 22, 17, 12, 7

D. 100, 95, 90, 85, 80

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, when Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include 27, 22, 17, 12, 7 and 100, 95, 90, 85, 80. In this cases, there are difference of 5.

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Complete question

Jackson wrote different patterns for the rule "subtract 5". Select all of the patterns that he could have written.

27, 22, 17, 12, 7

5, 10, 15, 20, 25

55, 50, 35, 30, 25

100, 95, 90, 85, 80

75, 65, 55, 45, 35

The unknown values in the triangle is calculated to be

PL = 14.3 cm

CY = 7.74

NY = 9.9 mm

LJ = 8.3

The unknown values in the triangle is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

1. using Sin = opposite / hypotenuse - SOH

sin x = PL / PX

sin 54.25 = PL / 17.62

PL = sin 54.25 * 17.62

PL = 14.3 cm

2. using Tan = opposite / adjacent - TOA

tan 52.67 = CY / 5.9

tan 52.67 * 5.9 = CY

CY = 7.74

3. using Sin = opposite / hypotenuse - SOH

sin 33.06 = YC / NY

NY = 5.4 /  sin 33.06

NY = 9.9 mm

4. using Tan = opposite / adjacent - TOA

tan 55.05 = LJ / VJ

tan 55.05 * 5.8 = LJ

LJ = 8.3

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The function f(d) that models this discount on an item that costs d dollars is f(d) = d - 15

The given parameters are

Discount = $15

Value = d

The function f(d) that models this discount on an item that costs d dollars is

f(d) = Value - Discount

This gives

f(d) = d - 15

Hence, the function f(d) that models this discount on an item that costs d dollars is f(d) = d - 15

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Answer:

10 cm³

Step-by-step explanation:

According to Archimedes, if we place an object in water, the rise of the water in mL will be the volume of the object in cm³.

Without the rock, the water measures 20 mL.

With the rock, the water measures 30 mL.

The change here is \(30-20=10\), so 10 cm³ is the volume of the rock.

Hope this helped!

the correct option is:

"The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."

A circle is defined as the set of equidistant points to a given point which is the center of the circle.

That distance to the center is called the radius.

Here, the center is at the point (0, 0), also called the origin, so if the distance between the point A and the origin, then point A lies on top of the circle P.

From that, we conclude that the correct option is:

"The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."

That is the only proof that we can (and should) use to prove that a point lies on a circle.

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Answer:

The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."

Step-by-step explanation:

I did the test

The joint relative Frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.

The joint relative frequency of students who do not like to run and enjoy swimming, we need to find the intersection of the row and column corresponding to those categories in the two-way frequency table.

Given the following information from the table:

Likes running: 28

Does not like running: 46

Column totals: 74

Enjoys swimming: 62

Enjoys cycling: 90

Row totals: 110

The joint relative frequency, we divide the number of students who do not like running and enjoy swimming by the total number of students:

Joint relative frequency = (Number of students who do not like running and enjoy swimming) / (Total number of students)

From the table, the number of students who do not like running and enjoy swimming is given as 46.

Total number of students is given as 74.

Joint relative frequency = 46 / 74

Calculating this value, we find that the joint relative frequency is approximately 0.6216, which is equivalent to 62.16%.

Therefore, the joint relative frequency of students who do not like to run and enjoy swimming is approximately 62.16%.

In conclusion, the joint relative frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.

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Answer:

Step-by-step explanation:

1 )

\(\frac{2}{5}( \frac{5x}{4} - \frac{10}{3})-\frac{4x}{3} \\\frac{x}{2} - \frac{4}{3} - \frac{4x}{3}\\ \frac{-5x}{6}-\frac{4}{3}\)

2 )

\(\frac{17x}{8}+\frac{3x}{4}+\frac{1}{6}-\frac{7x}{12}+\frac{17}{3}\\ \frac{51x}{24}+\frac{18x}{24}-\frac{14x}{24}+\frac{35}{6}\\\frac{55x}{24}+\frac{35}{6}\)

Answer:

1. 2.5 miles

2. 21.33 km

Step-by-step explanation:

15miles/6hours=2.5 miles

80km/3.75min=21.33km

Hope this helped!!!

We have

In order to simplify this expression, we will use the next rule

We use the rule and we simplify

Answer:

A (192)

A^2(H/3)=8^2(9/2)=192

Answer:

192

Step-by-step explanation:

the volume of the square pyramid is 192

Answer:

1175 gallons (rounded)

Step-by-step explanation:

The volume of a cylinder is given by the formula \(V=\pi r^2h\) .

r is the radius, h is the height.

\(V=\pi (5)^2 (2)=\pi(25)(2)=50\pi\approx 157.08\) cubic feet

Each cubic foot contains 7.48 gallons, so \(V=157.08\times 7.48=1175\) gallons (rounded).

Just for fun, each cubic foot weighs 62.4 pounds, so the water in the pool weighs about 9801 pounds -- more than 4 tons!

Answer:

1,175,108gallons of water

Step-by-step explanation:

do the volume of the cylindrical pool that is base area multiply by height to get 157.1 feet then you do 1cubic feet is 7.48 gallons what about 157.1 feet cubic

Data partitioning is dividing the sample data into three sets for training, validation, and testing of the data mining algorithm performance..

What is Data Partitioning?

To improve query processing performance or make databases easier to administer, data partitioning is a technique that involves distributing data across multiple tables, disks, or sites.

How are data partitions created?

The partitioning process can be carried out by either creating multiple smaller databases, each with their own tables, indices, and transaction logs, or by dividing only a few items, such as a single table. As part of horizontal partitioning, various rows are placed in various tables.

What does ETL's data splitting mean?

Datasets must be partitioned in order to be efficiently accessed by queries, which is a key approach. Based on the unique values of one or more columns, it arranges the data in a hierarchical directory structure.

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Answer:

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.

Here, the triangle ABC is an obtuse triangle, as ∠A measures more than 90 degrees.

Answer:

Step-by-step explanation:

Answer:

c. The period is 2π

Step-by-step explanation:

The period of a function is the smallest value of $p$ for which\( f(x+p) = f(x)\) for all x.

For the function f(x) = 2cos(x^2), we can see that f(x+2π) = f(x) for all x.

This is because the cosine function has a period of 2π. Therefore, the period of f(x) = 2cos(x^2) is \(\boxed{2\pi}\)

Answer:

X: amount of a spare part of price $74 per unit.

Y: cost of purchasing X spare parts.

Step-by-step explanation:

We can imagine that X represents the amount of an object, for example a car spare part,  which price is $74 per unit.

Then, Y would represent the cost of purchasing X units of that spare part.

Answer:

£26.77

Step-by-step explanation:

450(100% + 2%)^6

= 450 (1.02)^6

= 506.77.

506.77 - 480 - 26.77.

Riley had £26.77 left.

Answer:

9

Step-by-step explanation:

The opposite sides of a parallelogram are congruent.

Answer:

9

Step-by-step explanation:

Parallel sides are always equal. :)

The value of variable x is,

⇒ x = 42

We have to given that;

In a right triangle,

⇒ sin (x + 10)° = cos (4x - 4)°

Now, We can simplify as;

⇒ sin (x + 10)° = cos (4x - 4)°

⇒ cos (90 - (x + 10))° = cos (x - 4)°

⇒ 90 - (x + 10) = x - 4

⇒ 90 - x - 10 = x - 4

⇒ 80 + 4 = 2x

⇒ 2x = 84

⇒ x = 42

Thus, The value of variable x is,

⇒ x = 42

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The measures of the remaining three angles of the decagon are 40, 50 and 130 degrees.

A decagon is a polygon with 10 sides. In a regular decagon, the interior angles add up to 1440 degrees, and the exterior angles add up to 360 degrees.

Therefore, seven of the angles of a decagon have measures whose sum is 1220. Of the remaining 3 angles, exactly two are complementary and exactly two are supplementary.

Complementary angles sum up to 90 degrees while supplementary angles sum up to 180 degrees.

Therefore,

1440 - 1220 = 220

Let the angles be a, b and c.

Therefore,

a + b + c  =220

a + b = 90

b + c = 180

Hence,

a = 220 - 180

a = 40°

b = 90 - 40

b = 50°

c = 180 - 50

c = 130°

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The values of x and y by the Cramer's rule are 3 and 2 respectively.

Cramer's rule only works if the determinant of the coefficient matrix A is not equal to zero, which means that the system has a unique solution. If det(A) = 0.

We know that we have to form a matrix and find the determinant so that we can solve by the Cramer's rule.

1   1  =  5

1  -1       1

D = (1 * -1 ) - (1 * 1)

= - 2

Dx is obtained from;

5   - 1

1      1

Dx = -6

x = Dx/D

x = - 6/-2

x = 3

Again Dy is obtained from;

1    5

1    1

Dy =  -4

y = Dy/D

y = -4/-2

y = 2

Thus;

x = 3 , y = 2

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