how many ounces of a 30% alcohol solution must be added to a 70% alcohol solution to make 50 ounces of a 40% alcohol solution?

Answer:

0.609

Step-by-step explanation:

convert to a fraction then convert to a decimal by dividing the numerator and denominator :)

Answer:

CD = 36°

Step-by-step explanation:

the measure of secant angle BFE is half the difference of the measures of the intercepted arcs , that is

[tex]\frac{1}{2}[/tex] (BE - CD) = ∠ BFE

[tex]\frac{1}{2}[/tex] (128 - x) = 46 ( multiply both sides by 2 to clear the fraction )

128 - x = 92 ( subtract 128 from both sides )

- x = - 36 ( multiply both sides by - 1 )

x = CD = 36°

Considering AB=BC, the matrices A, B, and C are square matrices such that matrix B is invertible.

Now, post-multiply both sides of 

[tex]AB=BC by  {B}^{−1} [/tex]

[tex] {ABB}^{−1} = {BCB}^{−1} [/tex]

Solving the obtained equation for A by using the properties

[tex]AI= {BCB}^{−1} \\ A= {BCB}^{−1} [/tex]

Therefore, the required matrix A is BCB−1

A matrix, also known as matrices, is a rectangular array or table of letters, numbers, or other symbols arranged in rows and columns that is used to represent a mathematical object or a characteristic of one.

In linear algebra, matrices represent linear maps and enable explicit computations. Since most properties and operations of abstract linear algebra can be expressed in terms of matrices, the study of matrices constitutes a significant portion of linear algebra.

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With given features we can definably say that Both triangles are congruent under ASA Criteria.

A triangle is a closed polygon made up of three line segments that intersect at three different angles.

If the sides and angles of two triangles are the same length, the triangles are said to be congruent. As a result, two triangles can be superimposed side by side and angle by angle. Congruence is the term used to describe the relationship between an object and its mirror image. When two objects or shapes superimpose on one another, they are said to be congruent. They are identical in terms of shape and size. Line segments of the same length and angles of the same measure are congruent in the context of geometric figures.

Given far opposites angle are same = 25°

Given intersected line makes equal line

Intersecting angles are equal due to vertically opposite angle theorem.

Then we have,

Angle = Angle

Side = Side

Angle = Angle

With this features we can definably say that Both triangles are congruent under ASA Criteria.

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Answer: Solutions for x - 4,4,-5 and for y - 3,-3, 0

Step-by-step explanation: I wrote the solutions in order. To solve this question I combined both equations to eliminate the y variable to solve for x. It looked like this :  [tex]x^2+x=20[/tex]. I brought the 20 to the other side and got [tex]x^2+x-20=0[/tex]. Then I factored and got [tex](x+5)(x-4)[/tex] which means x = -5 and x = 4. Finally I plugged in these values into the equation to find the possible y values.

Based on the traffic flow model, the city should close the road with the least amount of traffic. From the diagram, we see that the road with the least amount of traffic is Salisbury St.

(a) Constraints:

The flow into and out of Jones St. is equal to the total flow into and out of Salisbury St. and Edenton St.

The flow into and out of McDowell St. is equal to the total flow into and out of Salisbury St. and Edenton St.

The flow into and out of Salisbury St. is equal to the sum of the flow into and out of Jones St. and McDowell St.

The total flow into and out of each street must be greater than or equal to 0.

Let x, y, z, and w be the traffic flow in cars per hour along Jones St., Salisbury St., Edenton St., and McDowell St., respectively. Then the system of linear equations that models this scenario is:

x - y - z = 0

w - y - z = 0

y + z - x - w = 0

x, y, z, w ≥ 0

(b) Augmented matrix representation:

[1 -1 -1 0 | 0]

[0 -1 -1 1 | 0]

[1 -1 1 -1 | 0]

[1 0 0 0 | 0]

Gauss-Jordan reduction:

[1 0 0 0 | 0]

[0 1 0 0 | 0]

[0 0 1 0 | 0]

[0 0 0 0 | 0]

The final augmented matrix is shown above. The solution to the system is x = 0, y = 0, z = 0, and w = 0.

(c) If the city were to close one of these 4 roads, then the traffic would have to be rerouted. Based on the traffic flow model, the city should close the road with the least amount of traffic. From the diagram, we see that the road with the least amount of traffic is Salisbury St. Therefore, the city should close Salisbury St.

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Answer:

$51

Step-by-step explanation:

At each age his grandmother gives him three times his age in money.

3 x 5

3 x 8 ...

The amount of time it require to water all the parts of her lawn is, 63 minutes

Division is a mathematical operation, in which we distribute the number in equal parts, the number on the upper side is the total quantity and the number on the bottom side is equal parts of numbers which have to be distributed.

We denote division by '÷' this symbol.

Given that,

Ms. Reynold's sprinkler system has 9 stations that water all parts of her front and back lawn.

Each station runs for an equal amount of time

it takes 49 minutes for the first 7 stations to water

The amount of time it require to water stations = ?

First, we need to calculate time required to water 1 station,

t =  Total time taken / Total station watered

  =   49 / 7

  =   7  minutes/station

So

Time for water all parts = 7 x 9

                                       = 63 minutes

Hence, the required time is 63 minutes

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The equation x-3/ 2y=-12 when solved for the variable y is y = x-3/-24

We have to make 'y' the subject from the equation, we have;

x-3/2y=-12

By solving for the variable, we need to work it out.

Also, we have to make it stand alone on one end of the equality sign.

cross multiply the values

x - 3(1) = -12(2y)

multiply the values

x-3 = -24y

Make 'y' the subject by dividing both sides by the coefficient of y

y = x-3/-24

Hence, the equation is y = x-3/-24

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The dilated points are:

W': (-1, 2)

X': (2.5, 0)

Y': (-0.5, -2).

Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.

Given:

Triangle WXY with vertices W(-4, 8), X (10, 0), and Y(-2, -8).

And the scale factor is 1/4.

So, the image points are,

W': (-4/4, 8/4) = (-1, 2)

X': (10/4, 0/4)  = (2.5, 0)

Y': (-2/4, -8/4) = (-0.5, -2)

Hence, the image points are given above.

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Step-by-step explanation:

[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } [/tex]

So let find cos

We know that

[tex] \tan {}^{2} (x) + 1 = \sec {}^{2} (x) [/tex]

We know the value of tan

[tex]( \frac{8}{5} ) {}^{2} + 1 = \sec {}^{2} (x) [/tex]

[tex] \frac{64}{25} + 1 = \sec {}^{2} (x) [/tex]

[tex] \frac{89}{25} = \sec {}^{2} (x) [/tex]

[tex] \frac{ \sqrt{89} }{5} = \sec(x) [/tex]

Sec is the reciprocal of cosine so cosine is

[tex] \cos( \alpha ) = \frac{5}{ \sqrt{89} } [/tex]

Which becomes

[tex] \cos( \alpha ) = \frac{5 \sqrt{89} }{89} [/tex]

So since we know cos a, let's find sin

[tex] \sqrt{ \frac{1 - \frac{5 \sqrt{89} }{89} }{2} } [/tex]

[tex] \sqrt{ \frac{89 - 5 \sqrt{89} }{2} } [/tex]

Answer: 5x^-10 * -2x^4

To simplify this expression, we will multiply the coefficients (the numbers in front of the variables) and add the exponents of x.

5 * -2 = -10

-10x^(-10 + 4) = -10x^-6

So, the simplified expression is:

-10x^-6

2.-4x^2 * 3y^-5 * 2y^7 * x^-6

To simplify this expression, we will multiply the coefficients and add the exponents of x and y.

-4 * 3 * 2 = -24

-24x^2 * y^(-5 + 7) * x^(-6)

-24x^2 * y^2 * x^-6

-24x^(2 - 6) * y^2

-24x^-4 * y^2

So, the simplified expression is:

-24x^-4 * y^2

Step-by-step explanation:

(a). Name of internet service provider is categorical variable because it cannot be quantified or measured. It can be divided into different categories according to the service they provide.

A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Measurement scale used for determination is nominal scale, also called the categorical variable scale.

(b). Time in hours, spent surfing the internet per week is continuous numerical variable because time can be measured over an infinite number of real values within a given interval.

A variable is said to be continuous if it can assume an infinite number of real values within a given interval.

Measurement scale used for determination is ratio scale.

(c). Whether the individual uses a mobile phone to connect to the internet is categorical variable because the answer can only be yes or no and it cannot be measured numerically.

A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Measurement scale used for determination is nominal scale, also called the categorical variable scale.

(d). Number of online purchases made in a month is discrete numerical variable because it is a value that arises through a counting process.

A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval), but those numeric values have a clear quantitative interpretation.

Measurement scale used for determination is interval scale.

(e). Where the individual uses social networks to find sought -after information is categorical variable because the answer can only be yes or no and it cannot be measured numerically. It can be either he/she uses or he/she do not.

A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Measurement scale used for determination is nominal scale, also called the categorical variable scale.

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Probability that a randomly chosen part (a) has a P(flaw) = 0.2 and

has no major flaws b) P(No major flaws) = 0.95

The probability that an event will occur is determined by probability: P(A) = f / N. Probability and odds are related, but probability determines what the odds are. Probability is required before calculating the likelihood that an event will occur.

To find the probability of flaws, we can find the probability of no flaws first by dividing by 100:

P(no flaw) = 80/100 = 0.8

So then:

P(flaw) = 1 - P(no flaw) = 1 - 0.8 = 0.2

P(flaw) = 0.2

B) First, we need to find the probability of major flaws:

P(major flaws) =

P(Major flaws) = 0.05

So to find the probability of no major flaws:

P(No major flaws) = 1 - P(major flaws) = 1 - 0.05 = 0.95

P(No major flaws) = 0.95

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Answer:

I think it’s 730 days

Step-by-step explanation:

Answer:

A = 648π cm²

Step-by-step explanation:

the area (A) of a semicircle is half the area of a circle , then

A = [tex]\frac{1}{2}[/tex] πr² ( r is the radius ) , then

A = [tex]\frac{1}{2}[/tex] × π × 36² = [tex]\frac{1}{2}[/tex] × π × 1296 = 648π cm²

The required value of x for the diagonals of parallelogram is 8.

Let ABCD be the parallelogram, and let the diagonals AC and BD intersect at point E.

We know that in a parallelogram, the diagonals bisect each other. So, we have:

AC = 2AE and BD = 2BE

We are given that AC = 4x + 2 and BD = 5x - 6. Substituting in the above equations, we get:

2AE = 4x + 2 and 2BE = 5x - 6

Dividing both sides by 2, we get:

AE = 2x + 1 and BE = (5x - 6)/2

Since AE and BE are the same length (they are both half the length of the diagonals), we have:

2x + 1 = (5x - 6)/2

Multiplying both sides by 2, we get:

4x + 2 = 5x - 6

Subtracting 4x from both sides, we get:

8 = x

Therefore, the value of x is 8.

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A hypothesis that there is some sort of relationship between the variables is where scientists start their inquiry. The alternative, or null hypothesis, asserts that there is no such relationship. Although the null hypothesis may not appear fascinating, it is a crucial component of research.

The claim can be supported by either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is the same as the value specified in the claim. If the null hypothesis is the assertion, then the alternative hypothesis statement is the antithesis of the null hypothesis. A hypothesis is a well-informed, logically-supported guess about the answer to a scientific question. Although it is the experiment's anticipated outcome, it does not constitute experimental proof. The information obtained may or may not be supported, depending on the information received. Simple hypotheses simply state the relationship between two independent and dependent variables. Examples: If you stay up late, you will feel fatigued the next day.

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Answer:

f(-2) = 2

Step-by-step explanation:

Using the graph, we can determine the y value when x = -2.

When x = -2, the y value is 2.

f(-2) = 2

Answer:

The first/top option

Step-by-step explanation:

First, we can find the inequality that the line is representing. X is the number of hours she has already done, and she has five hours more to do to fulfill the 12 or more hours of required service. The inequality would be x+5≥12.

The minimum that X has to be is 7 because any value lower than 7 would make the inequality false[ ex. 6 + 5 ≠ 12 ]. The arrow would be pointing to the right, because 7 is the minimum value, not the max, so any value higher than 7 would still make the inequality true. Lastly, the circle would be filled, because 7 is included in the set of values that make the inequality true[ 7 + 5 = 12 ].

So, the answer would be the first option.

The algebraic expression is,

⇒ 5 (6 - n)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ five times the difference between six less than a number.

Now, Let a number = n

Hence, We can formulate;

⇒ 5 (6 - n)

Thus, The value of expression is,

⇒ 5 (6 - n)

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Answer: To find out how much you would pay for 2.5 kg of tomatoes at $1.50 per kg, we need to multiply the weight of the tomatoes by the price per kg:

Cost = 2.5 kg x $1.50/kg

   = $3.75/kg x 2.5 kg

   = $9.38

So, you would pay $9.38 for 2.5 kg of tomatoes at $1.50 per kg.

Step-by-step explanation:

The y-intercept of the graph of a function is the point at which the graph intersects the y-axis. In other words, it's the value of the function when x=0.

So to find the y-intercept of f(x) = 57(3.2)x, we can substitute x=0 into the function:

f(0) = 57(3.2)(0)

f(0) = 0

So the y-intercept of this function is (0,0).

Using the concept of proportion, Gianna will have enough yards to make 18 bows

To solve this problem, we need to apply the concept of proportions.

In order to make 1 bow, she needs 1/5 yard of ribbon

Representing this in an equation form will be;

1 bow = 1/5 yard

18 bow = x yard

cross multiply both sides and solve for x

x * 1 = 18 * (1/5)

x = 3.6 yards

From the above, there will be enough yards to make 18 bows.

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Answer:

Step-by-step explanation:

no idea sorry :/

The length of the altitude CH is 17.234.

Altitude of a triangle is defined as the perpendicular line segment joining the vertex to the opposite side.

The figure for the triangle is given below.

Here the area of a triangle can be found in two ways.

Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height

Consider the triangle ABC given below.

Area of the triangle when considered base as BC and altitude as AC is,

Area, A = [tex]\frac{1}{2}[/tex] × BC × AC

BC = AB Sin (50) = 35 sin(50)

AC = AB Sin (40) = 35 sin(40)

A = [tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40))

Area of the triangle when considered base as AB and altitude as CH is,

Area, A = [tex]\frac{1}{2}[/tex] × AB × CH

A = [tex]\frac{1}{2}[/tex] × 35 × CH  

Area of the same triangle will be equal when find in different ways.

[tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40)) = [tex]\frac{1}{2}[/tex] × 35 × CH  

Cancelling the terms which are on both sides,

CH = 35 sin(50) sin(40)

CH = 35 × 0.766 × 0.643

CH = 17.234

Hence the length of the altitude is 17.234.

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Answer: 3.6

Step-by-step explanation:

3/5 is equal to 20% (3 divided by 5 times 100)

1.2 is 20% of 6

So, 3.6 is 3/5 of 6

Answer:Rewrite the equation in vertex form.

Tap for more steps...

y

=

4

(

x

−

1

)

2

−

9

Use the vertex form,

y

=

a

(

x

−

h

)

2

+

k

, to determine the values of

a

,

h

, and

k

.

a

=

4

h

=

1

k

=

−

9

Since the value of

a

is positive, the parabola opens up.

Opens Up

Find the vertex

(

h

,

k

)

.

(

1

,

−

9

)

Find

p

, the distance from the vertex to the focus.

Tap for more steps...

1

16

Find the focus.

Tap for more steps...

(

1

,

−

143

16

)

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

x

=

1

Step-by-step explanation:

Answer: 90 miles in 180 minutes

Step-by-step explanation: Since 90 minutes is two times 45, there would be 2 miles in one minute. Then, you multiply 2 times 45 so therefore you get 90 miles in 180 minutes.

Lauren was 13 miles away from the restaurant when Aidan reached it.

Travel refers to the act of moving from one place to another, often over a distance or by means of transportation.

Lauren and Aidan both left their offices at 6:15 P.M. and traveled for 20 minutes (from 6:15 P.M. to 6:35 P.M.) before Aidan arrived at the restaurant. During this time, Lauren traveled at a speed of 39 miles per hour, so she covered a distance of:

distance = speed x time

distance = 39 miles/hour x (20 minutes / 60 minutes/hour) = 13 miles

After 20 minutes, Aidan arrived at the restaurant, having traveled for 20 minutes at a speed of 42 miles per hour. The distance he covered during this time is:

distance = speed x time

distance = 42 miles/hour x (20 minutes / 60 minutes/hour) = 14 miles

Since they both traveled the same distance to the restaurant, but Aidan arrived there first, Lauren must have been 1 mile behind him when he arrived at the restaurant.

Therefore, Lauren was 14 - 1 = 13 miles away from the restaurant when Aidan reached it.

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The Original Price of helmet is $20.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The helmet Clare plans to buy is on sale for 20% less than the original price.

let the sale price be x.

So, the Original price is (x+5).

Also, Sales price = Original price - 20% of Original price

x= x+ 5 - 0.20(x+5)

x = x+ 5 - 0.20x - 1

0.20x = 4

x= 4/ 0.20

x= $20

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