Three cups of solution A are added to 6 cups of solution B, forming a new solution. Solution A contains 10% chlorine. Solution B contains an unknown percentage of chlorine. The mixture of the two solutions contains 20% chlorine. What percentage of chlorine is in solution B?

Step-by-step explanation:

The first step is to add 6 to both sides

3x =15+6

3x=21

Divide both sides by 3

X = 7

The solution set of the equation is {0}

A. The values of the variable that make a denominator zero are [tex]x = 3[/tex] and [tex]x = -3[/tex]. This is because when [tex]x = 3[/tex] or [tex]x = -3[/tex], the denominator of the fraction [tex]x^2 - 9[/tex] becomes zero, causing the entire equation to become undefined.

B. To find the solution of the equation, we can first multiply both sides by the common denominator, [tex]x^2 - 9[/tex]:

[tex](5/x+3-3/x-3)(x^2-9) = (5x/x^2-9)(x^2-9)[/tex]

Simplifying and combining like terms, we get:

[tex]5x - 9 - 3x + 9 = 5x[/tex]

[tex]2x = 5x[/tex]

Subtracting [tex]5x[/tex] from both sides, we get:

[tex]-3x = 0[/tex]

Dividing by -3, we find that the solution of the equation is x = 0.

Therefore, the solution set of the equation is {0}.

See more about solution of equations at: https://brainly.com/question/28586904

#SPJ11

Answer:

1st one: (x-7)

2nd: (-x+7)

3rd: (5x+3)

Step-by-step explanation:

1: you subtract like terms so first you do 3x-2x which is x and do -2-5 and get -7 so its (x-7)

2: do 2x-3x and get (-x) and then do 5-(-2) and get 7 so the answer is (-x+7)

3: first do 2x+3x and get 5x and then do 5+(-2) and get 3 so the answer is (5x+3)

Answer:

Step-by-step explanation:

( 3x - 2 ) - ( 2x + 5 ) = 3x - 2 - 2x - 5  = x - 7

( 2x + 5 ) - ( 3x - 2 ) = 2x + 5 - 3x + 2 = - x + 7

( 2x + 5 ) + ( 3x - 2 ) = 2x + 5 + 3x - 2 = 5x + 3

The expression when evaluated is 256

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

8 power of 8/3

Mathematically, this can be expressed as

8^(8/3)

When evaluated using a calculator, we have

8^(8/3) = 256

Hence, the solution is 256

Read more about expression at

https://brainly.com/question/4541471

#SPJ1

a)1.746

b)0.119

To compare the null hypothesis that the population mean of the increase in sales is at least 50 units against the observed mean of 41.3 units, we will use both the critical value approach and the p-value approach.

For the critical value approach, we need to use the standard deviation of 12.2 units as well as the sample size of 20 supermarkets. This gives us a critical value of 1.746. As the observed mean (41.3 units) is less than 1.746 standard deviations away from the mean of 50 units, we can conclude that the null hypothesis cannot be rejected at the 5% level of significance.

For the p-value approach, we will use the same sample size and standard deviation. This gives us a p-value of 0.119, which is greater than the 5% level of significance. Thus, we can also conclude that the null hypothesis cannot be rejected at the 5% level of significance.

It is important to note that we are assuming that the data is normally distributed, and that there is no bias in the sample.

Learn more about critical value approach and p-value approach

brainly.com/question/14284760

#SPJ11

Answer:

1/9

Step-by-step explanation:

I plugged it into a calculator.

Answer:

x = 50

Step-by-step explanation:

sin 40º = 32 / x

0.64 = 32 / x

x = 32 / 0.64

x =~ 50

It will take about 5.18 years for the car to be worth 8,200.

We can use the given formula to find the value of the car after x years:

[tex]V = 20,000(0.8)^x[/tex]

We want to know how long it will take for the car to be worth 8,200. So we can set V equal to 8,200 and solve for x:

[tex]8,200 = 20,000(0.8)^x[/tex]

Dividing both sides by 20,000 gives:

[tex]0.41 = (0.8)^x[/tex]

Taking the logarithm of both sides with base 0.8, we get:

[tex]log0.8(0.41) = x[/tex]

Using a calculator, we can find:

x ≈ 5.18

Therefore, it will take about 5.18 years for the car to be worth 8,200.

for such more question on years

https://brainly.com/question/25537936

#SPJ4

Answer:

11.97 lb

Step-by-step explanation:

To find the force that the rope must exert on the cart to keep it from rolling down the ramp, we need to resolve the forces acting on the cart along the direction of the ramp and perpendicular to the ramp.

First, we resolve the weight of the cart into its components. The weight of the cart acting vertically downwards can be resolved into a component perpendicular to the ramp and a component parallel to the ramp.

The component perpendicular to the ramp is given by:

W_perp = W * cos(theta) = 40lb * cos(15°) = 38.6lb

The component parallel to the ramp is given by:

W_parallel = W * sin(theta) = 40lb * sin(15°) = 10.4lb

where W is the weight of the cart, and theta is the angle of inclination of the ramp.

Next, we resolve the force exerted by the rope into its components. The force exerted by the rope can be resolved into a component perpendicular to the ramp and a component parallel to the ramp.

The component perpendicular to the ramp is given by:

F_perp = F * cos(phi) = F * cos(60°) = 0.5F

The component parallel to the ramp is given by:

F_parallel = F * sin(phi) = F * sin(60°) = 0.87F

where F is the force exerted by the rope, and phi is the angle of inclination of the rope.

To keep the cart from rolling down the ramp, the force exerted by the rope must balance the weight of the cart along the direction of the ramp. That is,

F_parallel = W_parallel

0.87F = 10.4lb

Solving for F, we get:

F = 11.97lb

Therefore, the force that the rope must exert on the cart to keep it from rolling down the ramp is approximately 11.97lb.

The area οf the shaded regiοn will be (area οf bigger rectangle - area οf white rectangle) 5x²+7x-26.

A rectangle is a type οf quadrilateral, which is a fοur-sided pοlygοn. A rectangle has the fοllοwing prοperties:

It has fοur straight sides, which are perpendicular tο each οther (at right angles).

It has fοur right angles (90-degree angles).

Its οppοsite sides are equal in length and parallel tο each οther.

Its diagοnals are equal in length and bisect each οther.

Nοw,

Area οf shaded regiοn= area οf bigger rectangle - area οf white rectangle.

As Area οf rectangle= length × Breadth

then

Area of shaded region [tex]= (3x-4)(2x+2)-(x-3)(x-6)[/tex]

[tex]=6x^2+6x-8x-8 -x^2+6x+3x-18\\=5x^2+7x-26[/tex]

hence,

         The area οf the shaded regiοn will be 5x²+7x-26.

To know more abοut rectangles visit the link

https://brainly.com/question/29123947

#SPJ1

Substituting in the given values for a and b, we can solve for d and find that it is approximately 9.48 inches.

Pythagorean Theorem is a mathematical formula that states that the square of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the other two sides. It is expressed as a2 + b2 = c2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

The given diagram is a right triangle with two of its sides labeled in inches. To find the length of the third side (d), one must use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, d is the hypotenuse, so d2 = a2 + b2. Therefore, substituting in the given values for a and b, we can solve for d and find that it is approximately 9.48 inches.

For more questions related to right triangle,

https://brainly.com/question/6322314

#SPJ1

The greatest common factor of 8m2 and 7b3 is the largest monomial that can divide both 8m2 and 7b3. So, the greatest common factor of 8m^(2) and 7b^(3) is 1.


The greatest common factor (GCF) of two monomials is the product of the greatest common factor of their coefficients and the greatest common factor of their variables. In this case, the greatest common factor of the coefficients is 1, since 8 and 7 have no common factors other than 1. The GCF of the variables is 1, since m and b have no common factors. Therefore, the GCF of 8m^(2) and 7b^(3) is 1*1 = 1.

Here is a step-by-step explanation:
1. Find the GCF of the coefficients: GCF(8,7) = 1
2. Find the GCF of the variables: GCF(m^(2),b^(3)) = 1
3. Multiply the GCF of the coefficients and the GCF of the variables: 1*1 = 1
4. The GCF of 8m^(2) and 7b^(3) is 1.

Know more about monomial here:

https://brainly.com/question/2279092

#SPJ11

According to the solving  the value of given function h’(5) h’(5) = [2f’(5)g(5)] / g(5)² + f(5) / g(5)²

A function is described as a relationship between a group of inputs with one output each. A function is, to put it simply, a relationship between inputs in which each input is connected to exactly one output. Every function has a domain and a codomain, or range. A function is typically represented by the notation f(x), where x represents the input.

To find the value of h’(5), we need to find the derivative of h(x) first. We can use the product rule and the quotient rule to do that:

h(x) = f(x)g(x) + f(x)/g(x)

h’(x) = f’(x)g(x) + f(x)g’(x) + [g(x)f’(x) – f(x)g’(x)] / g(x)² (by the quotient rule)

h’(x) = [f’(x)g(x) + g(x)f’(x)] / g(x)² + [f(x)g’(x) – f(x)g’(x)] / g(x)² + f(x) / g(x)²

h’(x) = [2f’(x)g(x)] / g(x)² + f(x) / g(x)²

Now we can find h’(5) by plugging in x = 5:

h’(5) = [2f’(5)g(5)] / g(5)² + f(5) / g(5)²

To know more about functions visit:

brainly.com/question/22340031

#SPJ1

The graph is shown in the image attached.

To solve an equation by graphing, you need to graph the equation on a coordinate plane and find the points where the graph intersects the x-axis. These points correspond to the solutions of the equation, which are the values of x that make the equation true here.

Therefore, to solve the equation by graphing, we plot the graph, locate the points where the graph intersects the x-axis, and read the solutions from the graph.

Learn more about graphing:https://brainly.com/question/17267403

#SPJ1

Answer: If you did 100 Joules of work to lift your backpack, then the work you did is equal to the force applied multiplied by the distance lifted. Let's say you lifted the backpack a distance of d meters with a force of F Newtons. Then:

100 J = F x d

Now, if half of everything falls out of your backpack, the force required to lift the backpack will be reduced by half, so the new force required will be F/2. The distance lifted remains the same. So the work done to lift the backpack using half the force is:

Work = (Force x Distance) / 2

= (F x d) / 2

But we know that F x d = 100 J, so we can substitute this in the equation above:

Work = (F x d) / 2

= 100 J / 2

= 50 J

Therefore, the work you will do to lift your backpack the same distance with half the force is 50 Joules.

Step-by-step explanation:

Answer:

isosceles triangle.

Step-by-step explanation:

To classify triangle WXY by its sides, we need to determine whether all three sides are equal, two sides are equal, or all three sides are different. We can do this by calculating the lengths of the sides using the distance formula:

Side WX:

sqrt[(x2 - x1)^2 + (y2 - y1)^2] = sqrt[(-1 - 4)^2 + (-3 - (-10))^2] = sqrt[5^2 + 7^2] = sqrt(74)

Side WY:

sqrt[(x2 - x1)^2 + (y2 - y1)^2] = sqrt[(11 - 4)^2 + (-5 - (-10))^2] = sqrt[7^2 + 5^2] = sqrt(74)

Side XY:

sqrt[(x2 - x1)^2 + (y2 - y1)^2] = sqrt[(11 - (-1))^2 + (-5 - (-3))^2] = sqrt[12^2 + 2^2] = sqrt(148)

Since the lengths of sides WX and WY are equal, but the length of side XY is different, we can classify triangle WXY as an isosceles triangle. Specifically, it is an isosceles triangle with sides WX and WY equal.

The number line is plotted on the graph below

A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.

If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions

It displays information as a series of data points called 'markers' connected by straight line segments

Given data ,

Let the number line be represented by graph A

Now , the points on the graph are

A = { 4 , -3 , 1 }

The opposites of the number points A is given by

A' = { -4 , 3 , -1 }

The values of the sets A and A' are plotted on the line plot graph

Hence , the line plot is solved

To learn more about line plot click :

https://brainly.com/question/10666342

#SPJ1

Therefore , the solution of the given problem of triangle comes out to be  the shape is 55 square miles.

Because a triangular has two or more extra sections, it is a polygon. It's shape is a simple rectangle. A triangular shape can only be distinguished from a parallelogram by its sides A, B, and C. A singular plane rather than a cube is produced by Euclidean geometry when the edges are not perfectly collinear. A shape is referred to as triangular if it has three sides and three angles. An angle is the point where a quadrilateral's three sides meet. A triangle's sides add up to 180 degrees.

Here.

Two triangles with a base of 10 miles and heights of 7 miles and 4 miles can be formed from the composite design.

The following method can be used to determine a triangle's area:

A = (1/2)bh

where A represents area, B represents foundation, and H represents height.

We can calculate each triangle's area using the following formula:

=> Area of 1st triangle

=>  (1/2)(10)(7) = 35 square miles

=> Area of 2nd triangle

=>  (1/2)(10)(4) = 20 square miles

The two triangles' combined regions make up the composite shape's surface area.

55 square miles is the combined shape's area

=>  (35 + 20).

Consequently, the combined size of the two triangles in the shape is 55 square miles.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

1/4

The nth term of a geometric sequence can be found using the formula:

a_(n) = a_(1) * r^(n-1)

where a_(1) is the first term of the sequence and r is the common ratio.

Given a_(1) = 4, r = 1/2, and n = 5, we can substitute these values into the formula to get:

a_(5) = 4 * (1/2)^(5-1)

= 4 * (1/2)^4

= 4 * (1/16)

= 1/4

Therefore, the 5th term of the geometric sequence is a_(5) = 1/4.

Learn more about Geometric

brainly.com/question/13008517

#SPJ11

Answer:

16 percent decrease

Step-by-step explanation:

What is rhombus ?

A rhombus is a special type of parallelogram in which two pairs of opposite sides are congruent. That means all the sides of a rhombus are equal.

What is the Area of a Rhombus?

The area of a rhombus can be defined as the amount of space enclosed by a rhombus in a two-dimensional space. To recall, a rhombus is a type of quadrilateral projected on a two dimensional (2D) plane, having four sides that are equal in length and are congruent.

Using Diagonals                A = ½ × d1 × d2

Using Base and Height        A = b × h

Using Trigonometry        A = b2 × Sin(a)

the correct answer is the option (C) 340 cm^2

To know more about rhombus click:

https://byjus.com/maths/area-of-rhombus/

#SPJ1

An equation which Lupe should use include the following: k = 2p/x².

In this exercise, you are required to make "k" the subject of formula in the given mathematical expression by using the following steps.

p = 1/2kx²

By multiplying both sides of the mathematical expression by 2, we have the following:

2p = kx²

By dividing both sides of the mathematical expression by x², we have the following:

k = 2p/x²

In conclusion, we can reasonably infer and logically deduce that the spring constant can be calculated by using k = 2p/x².

Read more on expression here: brainly.com/question/25767785

#SPJ1

The Euclidean algorithm can be applied to Gaussian integers in the same way it is applied to ordinary integers. In this case, we are given x = 3+2i and y = 2-5i and we need to find q and r such that x = qy + r and d(r) < d(y).

First, we divide x by y to get a quotient and remainder:
x/y = (3+2i)/(2-5i) = (3+2i)(2+5i)/(2-5i)(2+5i) = (16+7i)/29 = 0.551724 + 0.241379i

Since q and r must be Gaussian integers, we round the real and imaginary parts of the quotient to the nearest integer to get q = 1 + 0i = 1.

Next, we multiply q by y and subtract from x to get the remainder:
r = x - qy = (3+2i) - (1)(2-5i) = 1+7i

Finally, we check that d(r) < d(y):
d(r) = 1^2 + 7^2 = 50
d(y) = 2^2 + (-5)^2 = 29

Since d(r) > d(y), we need to adjust our quotient and remainder. We can do this by subtracting 1 from the real part of q and adding y to the remainder:
q = 0 + 0i = 0
r = (1+7i) + (2-5i) = 3+2i

Now, d(r) = 3^2 + 2^2 = 13 < 29 = d(y), so our final answer is q = 0 and r = 3+2i.

For more such questions on Euclidean algorithm.

https://brainly.com/question/12930118#

#SPJ11

Answer:

Both of the shapes correspond with one another.

(For explanation, look to the second image. Brainly would not let me submit that for an unknown reason)

(It is my explanation)

Good luck!

angle = tan⁻¹(2,500 / 31,680)

angle ≈ 4.51 degrees

Therefore, the angle of descent is approximately 4.51 degrees.

When two rays collide at a given point, an angle is created. Indicated by the symbol is the "angle," also known as the "opening" between these two beams. Many angles, such as 60°, 90°, etc., are usually stated as numbers in degrees.

To find the angle of descent, we can use the tangent function, which relates the opposite and adjacent sides of a right triangle:

tan(angle) = opposite / adjacent

In this case, the opposite side is the change in elevation, which is 2,500 feet, and the adjacent side is the distance traveled, which is 6 miles or 31,680 feet (since 1 mile = 5,280 feet).

So we have:

tan(angle) = 2,500 / 31,680

To solve for the angle, we can take the inverse tangent (or arctangent) of both sides:

angle = tan⁻¹(2,500 / 31,680)

Using a calculator, we get:

angle ≈ 4.51 degrees

Therefore, the angle of descent is approximately 4.51 degrees.

To know more about angle visit:

https://brainly.com/question/28451077

#SPJ1

The expression is not a polynomial, as it's exponent is not an integer number.

An expression represents a polynomial when these following conditions are satisfied:

The exponent for this problem is of [tex]5\sqrt{7}[/tex], which is a non-integer exponent, hence the expression is not a polynomial. Any integer exponent would make the expression in fact represent a polyonomial.

More can be learned about expressions and polynomials at brainly.com/question/14810078

#SPJ1

Answer:

A. The number of actual outcomes is 6 (since there are 6 sides to the block).

B. The number of all possible outcomes would be the number of ways the block could land on the table, which is also 6 (since each of the 6 sides is equally likely to face up).

C. The probability that the block will land with either the T, C or R facing up is the probability of landing on any one of those 3 sides. Since there are 3 such sides, and each side is equally likely to face up, the probability is 3/6 or 1/2.

Answer: Less than three would be like 2 or 1 or any negative number.

Step-by-step explanation: Three munis anything is less than the 3 you had to start with.

The distance between the x and y intercepts of that line is √13/2. The correct answer is (B).

To find the distance between the x and y intercepts of a line, we can use the distance formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)

First, we need to find the x and y intercepts of the line. The x intercept is where the line crosses the x-axis, so we can set y to 0 and solve for x. Similarly, the y intercept is where the line crosses the y-axis, so we can set x to 0 and solve for y.

Using the point-slope form of a line, we can find the equation of the line passing through the points (1,2) and (−0.5,1):
y - 1 = (1 - 2)/(−0.5 - 1)(x - (-0.5))
y - 1 = -2(x + 0.5)
y = -2x - 1

Now we can find the x and y intercepts:
For the x intercept, set y to 0:
0 = -2x - 1
2x = -1
x = -1/2

For the y intercept, set x to 0:
y = -2(0) - 1
y = -1

So the x intercept is (-1/2, 0) and the y intercept is (0, -1). Now we can use the distance formula to find the distance between these two points:
d = √((-1/2 - 0)² + (0 - (-1))²)
d = √((-1/2)² + (1)²)
d = √(1/4 + 1)
d = √(5/4)
d = √13/2

Therefore, the distance between the x and y intercepts of the line is √13/2.

Learn more about x and y-intercept here: https://brainly.com/question/24363347.

#SPJ11