a mixture of 3% disinfectant solution is to be made from 5% and 2% disinfectant solutions. how much of each solution should be used if 21 gallons of 3% solution are needed?

Answer: D

Step-by-step explanation:

x = y = 48 , by using angle sum property of triangle.

What are the properties of triangle?

A triangle's characteristics are:

1. Three sides, three angles, and three vertices make up a triangle.

2. A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property.

3. Any two triangle sides can add up to a length that is longer than the third side.

4. The greatest side of a triangle is the side that faces the largest angle.

5. The sum of the triangle's internal opposite angles is equal to any of its outer angles. This is referred to as the triangle's outside angle property.

In the given triangle , two sides of the triangle are equal and we know angle opposite to equal sides are equal therefore both angle x and y are equal.

Now, Using angle sum property of triangle

x + y + 84 = 180 degree

x + x + 84 = 180

2x + 84 = 180

2x = 180 - 84

2x = 96

x = 96/2  

x = 48

Similary , y = 48 as x and y are equal.

Therefore, x = y = 48

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Ethical research methods include D. doing your best to select an unbiased sample.

In research, ethical considerations are a set of principles that guide your research designs and practices. Active consent, informed consent, anonymity, confidentiality, potential for harm, and results communication are among these principles.

The standards of conduct for scientific researchers are governed by research ethics. To protect the dignity, rights, and welfare of research participants, it is critical to follow ethical principles. Many ethical norms in research, for example, guidelines for authorship, copyright and patenting policies, data sharing policies, and peer review confidentiality rules are intended to protect intellectual property interests while encouraging collaboration.

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The deceleration of the train is -3 ms^-2.

Given:

A train is moving along a Straight track with a speed of 30 ms^-1 when it reaches point A. the driver applies the brakes and the train decelerates at a constant speed until it comes to a stop 150 m from point A

we know that:

v^2 - u^2 = 2as

where

v = 0

u = 30 ms^-1

s = 150 m

0^2 - 30^2 = 2a*150

0 - 900 = 300*a

-900 = 300*a

a = -900/300

a = -3 ms^-2

Negative acceleration is nothing but the deceleration so a = -3 ms^-2.

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Answer:

6 hours.

Step-by-step explanation:

Subtract initial fee from total. (67 - 19 = 48).

Divide by the hourly rate. (48 / 8 = 6).

The bike was rented for 6 hours.

The equation of line passes through the point (1, -5) will be;

⇒ y = - 3x - 14

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (1, -5).

And, The slope of the line is,

⇒ m = - 3

Now,

Since, The equation of line passes through the point (1, -5).

And, Slope of the line is,

⇒ m = - 3

Thus, The equation of line with slope - 3 is,

⇒ y - 1 = - 3 (x - (-5))

⇒ y - 1 = - 3 (x + 5)

⇒ y - 1 = - 3x - 15

⇒ y = - 3x + 1 - 15

⇒ y = - 3x - 14

Therefore, The equation of line passes through the point (1, - 5) will be;

⇒ y = - 3x - 14

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Answer:

[tex]y_{min}=-17[/tex]

[tex]y_{max}=15[/tex]

Step-by-step explanation:

Given function:

[tex]y=2x^2-12x+1[/tex]

The critical points are those values of x which make the derivative of the function zero.  

Differentiate the function:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2 \cdot 2x^{2-1}-12x^{1-0}+0[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=4x-12[/tex]

Set the derivative to zero and solve for x:

[tex]\implies 4x-12=0[/tex]

[tex]\implies 4x=12[/tex]

[tex]\implies x=3[/tex]

To find the y-value of the critical point, substitute the found value of x into the function:

[tex]\implies 2(3)^2-12(3)+1[/tex]

[tex]\implies 2(9)-12(3)+1[/tex]

[tex]\implies 18-36+1[/tex]

[tex]\implies -18+1[/tex]

[tex]\implies -17[/tex]

Therefore, the critical point is (3, -17).

To find the endpoints of the function in the interval [0, 7], substitute x = 0 and x = 7 into the function:

[tex]\begin{aligned} x=0 \implies 2(0)^2-12(0)+1&=0-0+1\\&=1\end{aligned}[/tex]

[tex]\begin{aligned} x=7 \implies 2(7)^2-12(7)+1&=2(49)-12(7)+1\\&=98-84+1\\&=14+1\\&=15\end{aligned}[/tex]

Therefore:

Therefore the minimum y-value is -17 and the maximum y-value is 15 in the given interval [0, 7]

The minimum and maximum y value of the function is -17 and 15 respectively.

This is a basic problem in calculus.

Given function: [tex]y=2x^{2} -12x+1[/tex]

Step 1: First, let's find the derivative of the function

[tex]\frac{dy}{dx} = 2.2x^{2-1} -12x^{1-0} +0\\\frac{dy}{dx} = 4x-12[/tex]

Step 2: Equate the derivative with zero

4x-12=0

x=3

Therefore, x=3 is the critical value for x

Step 3: Find the critical value for y

[tex]y=2x^{2} -12x+1[/tex]

[tex]y=2\times3^{2} -12\times3+1\\y=-17[/tex]

Thus, the critical points for the function [tex]y=2x^{2} -12x+1[/tex] are (3,-17)

Step 4: Find endpoints using the given interval [0,7]

This can be done by substituting x1=0 and x2=7 simultaneously in the given function and finding y1 and y2.

For x1=0,

[tex]y1=2\times0^{2} -12\times0+1\\y1=0+0+1\\y1=1[/tex]

For x2=7,

[tex]y2=2\times7^{2} -12\times7+1\\y2=98-84+1\\y2=15[/tex]

Now, we have both critical points and endpoints.

Therefore, The minimum and maximum y value of the function is -17 and 15 respectively.

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Answer:

Step-by-step explanation:

Yahweh’s

The percentage of women that answered that they don't even like soccer is 85%

From the information, in the a survey of 500 women, 75 answered that they like soccer. Those that don't like soccer will be the difference between the values. This will be:

= 500 - 75

= 425

Therefore, the percentage of women that answered that they don't even like soccer will be:

= Those that don't like soccer / Total number × 100

= 425/500 × 100

= 85%

The percentage is 85%.

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Complete question

In a survey of 500 women, 75 answered that they like soccer. What percentage of women answered that they don't even like soccer?

The type of software should Jace use will be "Entry level accounting system" as his company has 17 employees who work full time. The company has a number of very dedicated clients, and last year they generated $2 million in revenue.

Entry-level accounting includes typical accounting operations such as accounts payables and receivables, as well as basic financial reporting. These are, predictably, among the most affordable items; some sellers even provide an entry-level bundle for free for a brief time as a trial period. Entry-level accounting jobs are the initial level of accounting positions for people who are just starting out in their careers. Accounting Representative, Accounting Executive, Accounting Assistant, Accounting Associate, Entry-Level Accounting Clerk, Staff Accountant, and Bookkeeper are examples of entry-level occupations.

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The ordered pair which is a solution to the system of inequalities is: (-1, 0).

In order to determine which ordered pairs are true solutions based on the given system of inequalities, we would have to test each of the ordered pairs by substituting their values into the system of inequalities as follows;

For ordered pair (4, 3), we have:

-7x + 3y > -1

-7(4) + 3(3) > -1

-28 + 9 > -1

-19 > -1 (False).

For ordered pair (2, 8), we have:

-7x + 3y > -1

-7(2) + 3(8) > -1

-14 + 24 > -1

10 > -1 (True).

5x - 9y > -6

5(2) - 9(8) > -6

10 - 72 > -6

-62 > -6 (False).

For ordered pair (-1, 0), we have:

-7x + 3y > -1

-7(-1) + 3(0) > -1

7 + 0 > -1

7 > -1 (True).

5x - 9y > -6

5(-1) - 9(0) > -6

-5 - 0 > -6

-5 > -6 (True).

For ordered pair (-2, 2), we have:

-7x + 3y > -1

-7(-2) + 3(2) > -1

14 + 6 > -1

20 > -1 (True).

5x - 9y > -6

5(-2) - 9(2) > -6

-10 - 18 > -6

-28 > -6 (False).

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Answer:

15y

Step-by-step explanation:

3 times 5 is 15 with the variable

a) since all the angles on the triangle are next to a given angle we just subtract the given angle from 180 to find the unknown angle

180-150=30=x

180-80=100=y

180-130=50=z

Sum of All triangles angles is always 180 degrees but we can still check

30+100+50

130+50=180

Now for the B triangle every angle is across from it like this means the triangle angle is equal to that

a= 40 degrees

b= 95 degrees

c= 45 degrees

And this also equal 180 degrees

Hopes this helps please mark brainliest

Answer:

1st Question Answer:

X=30

y=100

z=50

2nd Question Answer:

a=40

b=95

C=45

Step-by-step explanation:

1st Question : Since the angles of a straight line add up to 180 , we can subtract the degree of the angle given by 180 which gives us the answer . also we can make certain the angle is right because angles of a traingle add up to 180

2nd Question: Since the angles in the second question are parallel (which means they are the same) . we can easily find the answer . we can make sure the answer is right by using the same way ( angles of a triangle add up to 180)

Answer:

2x^2

__________

x+3 | 3

2x + 2

3

- 2 x - 3

_________

R = - 1

The missing values in the ratio table include the following:

A = 2

B = 6

In Mathematics, a proportional relationship can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order for the ratio of the number of people to liters of ginger ale needed to have a proportional relationship, the variables x and y must have the same constant of proportionality.

Next, we would calculate the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 24/4

Constant of proportionality (k) = 6.

Now, we can determine the value of A and B:

A = x/k

A = 12/6

A = 2

For the value of B, we have:

B = x/k

B = 36/6

B = 6.

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Answer: A=2 and B=6

Step-by-step explanation: I hope this helped you

:D

The true statement about the sentence 'sample of gas is enclosed in a container of fixed volume' are:

When a sample of gas is been enclosed in a container of fixed volume then then if the container temperature is been reduced then the kinetic energy of the gas will reduce.

Therefore the first and the third option are correct.

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The measure of θ from the given trigonometric equation is 31°.

Given that, sin47°=cosθ and sinθ=cos(θ+16).

We know from geometry if the sum of two angles is 90°, then one angle is called the complement of the other.

The complementary angles are:

sinθ=cos(90-θ)

secθ=cosec(90-θ)

tanθ=cot(90-θ)

A) So, sin47°=cos(90°-47°)

⇒ sin47°=cos43°

Thus, θ=43°

B) sinθ=cos(θ+16)

⇒ sinθ=cos(43+16)

⇒ sinθ=cos 59°

⇒ sin(90-31)=cos 59°

Thus, θ=31°

Therefore, the measure of θ from the given trigonometric equation is 31°.

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The GCF of the number given as 45 and 27 is 9 and the factored expression is 9(5 - 3)

From the question, we have the following statement

The greatest common factor of 45 and 27

Rewrite the given expression as follows

This is represented using

45 and 27

Factor out 3 from the expression

So, we have the following representation

15 and 9 => Factored 3

Factor out 3 from the expression

So, we have the following representation

5 and 3 => Factored 3 * 3

So, we have

Factored = 3 * 3 = 9

This represents the GCF

So, the GCF is 9

In (a), we have

5 and 3 => Factored 3 * 3

This means that

45 - 27 = 3 * 3(5 - 3)

Evaluate the product

45 - 27 = 9(5 - 3)

Hence, the factored expression is 9(5 - 3)

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Answer: $2100

Step-by-step explanation:

Since 12.5 percent of 2400 is 300, Just subtract 300 from 2400 to get the selling price with no sales tax. And the final answer is $2100.

If the remainder is paid in equal monthly payments of $250. the number of month that the payments must be made is 24.

First step is to find the remainder after down payment

Remainder  = 6500-500

Remainder  = 6000

Now let find the number of monthly payment

Number of monthly payment = Remainder  / Monthly payment

Number of monthly payment = 6000 / 250

Number of monthly payment = 24

Therefore the monthly payment is 24.

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After solving the equation made for a triangle, the value of angle A will be equal to 21.

Simple polygons with three sides and three internal corners make up triangles. Being one of the fundamental geometric shapes, it is symbolized by the symbol and consists of three connected vertices.

As per the given data in the question,

Angle A is 13 less than angle C.

Let angle C is x then angle A is equal to (x - 13) and,

Angle B is 11 less than 4 times of angle C then,

B = 4x - 11

Add all the angles and equate them with 180.

(x -13) + (4x - 11 ) + x = 180

6x -24 = 180

6x = 180 + 24

x = 204/6

x = 34.

Substitute x = 34 in angle A

A = (x - 13)

A = 21.

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The "Poisson distribution" is the probability distribution that comes the closest to accurately describing that many dog bite patients visit this hospital across any given day.

For the given data of,

An average of two dog bite victims show up at Carver Memorial Hospital each day.

A probability distribution that most accurately predicts the number of dog bite victims who visit this hospital on any given day is characterized as the "Poisson distribution."

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Answer: Answer B: m angle 5 = 152 because m angle 2 = m angle 5

Step-by-step explanation: im in 8th grade math in 7th grade

Taking into account the definition of a system of linear equations, the number of 2-pointers and 3-pointers Sarah made is 2 and 3 respectively.

A system of linear equations is a set of equations relating two or more unknown values, the goal of which is to determine those values so that the equations are true.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

x + y= 10

2x+3y= 24

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "x" from the first equation:

x= 10 - y

Replacing this expression in the second equation:

2×(10-y)+3y= 24

Solving:

2×10 -2y +3y= 24

20 -2y +3y= 24

-2y +3y= 24 - 20

y= 4

Remembering that x= 10 -y, you get:

x= 10 -4

x= 6

Finally, the number of 2-pointers Sarah made is 2 and the number of 3-pointers she made is 3.

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Answer:

(2.5×20)2=100 then square root of 100;

✓100=10

Hence answer is 10

Answer:

  -4.697 in/s

Step-by-step explanation:

You want to know the rate of change of radius of a cone 11 inches high with a radius of 5 inches and a volume that is decreasing at the rate of 541 cubic inches per second.

The volume of a cone is given by ...

  V = π/3r²h

The rate of change is found by implicit differentiation:

  V' = (π/3)((2rr')h +r²h')

Here, the height is constant, so h' = 0. Solving for r', we find ...

  r' = 3V'/(2πrh)

Using the given values of V', r, and h, we find the rate of change of radius to be ...

  r' = 3(-541 in³/s)/(2π(5 in)(11 in)) = -1623/(110π) in/s ≈ -4.69652 in/s

The radius is decreasing at about -4.697 inches per second.

__

Additional comment

The initial radius of the cone is irrelevant to the problem, since we want to know the rate of change at a specific different radius. Whether the cone is inverted or not is also irrelevant to its volume.

The length of each wire is 12.8 feet

The television antenna makes an angle 90 with the ground

The height of the antenna is 10 feet

The wires are anchored to the base which is 8 feet

We need to calculate the length of the wires

The height of the wire can be calculated by using pythagoras theorem

h² = b² + p²

h² = 8² + 10²

h² = 64 + 100

h = √164

h = 12.8

Therefore, the length of each wire is 12.8 feet

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The first five terms of the arithmetic sequence with the formula a(n) = a(n - 1) - 5 is; -5, -10, -15. -20, -25

The general formula for an arithmetic sequence is;

aₙ = a + (n - 1)d

where;

a is first term

d is common difference

aₙ is the nth term of the sequence

Now we are given the formula for the nth term of a sequence as;

a(n) = a(n - 1) - 5

Thus;

1) First term is when n = 1;

a(1) = a(1 - 1) - 5

a(1) = -5

2) Second term is when n = 2;

a(2) = -5(2 - 1) - 5

a(2) = -5 - 5

a(2) = -10

3) Third term is when n = 3;

a(3) = -5(3 - 1) - 5

a(3) = -15

4) Fourth term is when n = 4;

a(4) = -5(4 - 1) - 5

a(4) = -20

5) Fifth term is when n = 5;

a(5) = -5(5 - 1) - 5

a(5) = -25

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Complete question is;

Write the first five terms sequence defined by a(n) = a(n - 1) - 5