given a pair of similar triangles find the missing length x and the missing angles a,b,c ​

Answers:

90 ounces of solution A.

60 ounces of solution B.

====================================================

Explanation:

x = amount of solution A

150-x = amount of solution B

Each amount is in ounces and they add to 150 ounces.

Solution A is 35% salt, so we get 0.35x ounces of pure salt from solution A.

Solution B is 60% salt, so we get 0.60*(150-x) = 90-0.60x ounces of pure salt from solution B.

We want 150 ounces of 45% salt solution, which means we want 150*0.45 =  67.5 ounces of pure salt when everything is mixed.

Here's a table showing this info

[tex]\begin{array}{|c|c|c|} \cline{1-3}& \text{Mixture} & \text{Pure Salt}\\\cline{1-3}\text{Solution A} & \text{x} & 0.35\text{x}\\\cline{1-3}\text{Solution B} & 150-\text{x} & 0.60(150-\text{x}) = 90-0.60\text{x}\\\cline{1-3}\text{Total} & 150 & 150*0.45 = 67.5 \\\cline{1-3}\end{array}[/tex]

Cleaning up the table a bit shows

[tex]\begin{array}{|c|c|c|} \cline{1-3}& \text{Mixture} & \text{Pure Salt}\\\cline{1-3}\text{Solution A} & \text{x} & 0.35\text{x}\\\cline{1-3}\text{Solution B} & 150-\text{x} & 90-0.60\text{x}\\\cline{1-3}\text{Total} & 150 & 67.5 \\\cline{1-3}\end{array}[/tex]

Focus on the "pure salt" column.

We want the 0.35x and 90-0.60x to add to 67.5

So,

0.35x+(90-0.60x) = 67.5

90-0.25x = 67.5

-0.25x = 67.5-90

-0.25x = -22.5

x = -22.5/(-0.25)

x = 90

She must use 90 ounces of solution A.

150-x = 150-90 = 60 ounces of solution B must be used as well.

-------------------

Check:

35% of 90 = 0.35*90 = 31.5 ounces of pure salt comes from solution A.

60% of 60 = 0.60*60 = 36 ounces of pure salt comes from solution B.

31.5+36 = 67.5 ounces of pure salt in total, which matches with the value mentioned earlier. The answers are confirmed.

The method of midpoint rectangles is a numerical integration technique used to approximate the area under a curve.

It is based on the idea of breaking up the area under the curve into a series of rectangles and approximating the area of each rectangle using the midpoint of the interval.

For example,

Let's say we want to approximate the area under the curve f(x) = x^2 from x = 0 to x = 2 using the method of midpoint rectangles.

We divide the interval into n = 4 subintervals of width 0.5.

We can calculate the midpoints of the intervals as follows:

interval 1: (0,0.5)

interval 2: (0.5,1)

interval 3: (1,1.5)

interval 4: (1.5,2)

We find the height of each rectangle as the value of f(x) at the midpoint of the interval.

interval 1: f(0.25) = 0.25^2 = 0.0625

interval 2: f(0.75) = 0.75^2 = 0.5625

interval 3: f(1.25) = 1.25^2 = 1.5625

interval 4: f(1.75) = 1.75^2 = 3.0625

We multiply the width of each rectangle (0.5) by the height of each rectangle to find the area of each rectangle:

interval 1: 0.5 * 0.0625 = 0.03125

interval 2: 0.5 * 0.5625 = 0.28125

interval 3: 0.5 * 1.5625 = 0.78125

interval 4: 0.5 * 3.0625 = 1.53125

Finally, we add the areas of all the rectangles to find the total approximate area under the curve:

0.03125 + 0.28125 + 0.78125 + 1.53125 = 2.64375

Hence, using this method the area under the curve f(x) = x^2 from x = 0 to x = 2 is approximately 2.64375.

Note: The precision of the result will depend on how many rectangles you use, and how small you make the rectangles.

The more rectangles we use and the smaller width of each rectangle, the more accurate our result will be.

To learn more about midpoint rectangles:

https://brainly.com/question/29838928

#SPJ4

The ordered pair that is included in the solution to this system of inequalities is: B. (−6, −3)

In order to determine the ordered pair is included in the solution to this system of linear inequalities, we would first of all translate the word problem into an algebraic equation as follows;

y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ 2x/3 + 1.

y is less than negative one-fourth times x plus 2 ⇒ y < -x/4 + 2.

Next, we would use an online graphing calculator to graphically solve the system of linear inequalities. Therefore, the required solution for the given system of linear inequalities is the shaded area below the solid line, which is given by the ordered pair (−6, −3).

Read more on inequality here: brainly.com/question/12952773

#SPJ1

The Lakewood Times had a 30.4% increase in the number of subscribers after it was bought out.

What is the percentage increase?

Percent increase is a way of measuring how much something has increased relative to its original value. It is expressed as a percentage, and it is calculated by taking the difference between the new value and the original value, and then dividing that difference by the original value, and then multiplying by 100.

Formula: % increase = (new value - original value) / original value x 100

To find the percent increase, you can use the formula:

% increase = (new value - old value) / old value x 100

In this case, the percent increase would be:

% increase = (6201 - 4770) / 4770 x 100 = 30.4%

Hence, The Lakewood Times had a 30.4% increase in the number of subscribers after it was bought out.

To learn more about the percentage increase, visit:

https://brainly.com/question/28398580

#SPJ1

Answer:C. Approx. Normal

Step-by-step explanation:

Note that these points are not different from each other and are on the same line y = 5/3x - 2.

Any point on this line will have the coordinates (x, y) such that y = 5/3x - 2.

Generally, A point on a line is any place along that line that is represented by a set of coordinates in either two- or three-dimensional space, denoted by the letters x, y, or x, y, z, respectively.

An equation, such as y = mx + b, may be used to define a line in a mathematical context. In this equation, m refers to the slope, while b refers to the y-intercept.

Any point that can be made to fit into this equation is up for grabs.

Read more about points on a line

https://brainly.com/question/7158994

#SPJ1

Answer:

It is not possible for the sum of consecutive integers to be -11. The sum of n consecutive integers is n times the average of the first and last integers. The average of any two integers is a fraction, which when multiplied by n, will always yield a fraction, which cannot equal -11. Therefore it is not possible to have n consecutive integers that sum to -11.

The distribution of the histogram for the large packages colors is given as follows:

Right skewed.

The distribution depends on whichever of the mean or the median is greater, as follows:

Hence the distribution is defined as follows:

The ordered data-set is given as follows:

21, 21, 24, 30, 32, 86.

The median is the mean of the two-middle values, hence:

Median = (24 + 30)/2

Median = 27.

The mean is the sum of all the observations divided by the number of observations, hence:

Mean = (21 + 21 + 24 + 30 + 32 + 86)/6

Mean = 35.67.

Mean > median, hence the distribution is right skewed.

More can be learned about distributions at brainly.com/question/25800303

#SPJ1

This question involves the binomial probability distribution. The probability of exactly 2 successful outcomes (in this case, visitors who are looking for the website) in 5 trials (visitors to the website) can be calculated using the formula:

P(X = 2) = (5C2)(0.12)^2(0.88)^3

Where C represents the binomial coefficient and 0.12 and 0.88 represent the probability of a successful outcome (looking for the website) and unsuccessful outcome (not looking for the website), respectively.

Calculating this gives:

P(X = 2) = (5C2)(0.12)^2(0.88)^3 = 100.01440.4712 = 0.066

So the probability that, in a random sample of 5 visitors to the website, exactly 2 are looking for the website is 0.066 or about 6.6%.

Two straightforward equations are all that are left for us to solve. Therefore, the x and y values determine the coordinates of the orthocenter.

When two rays or straight lines intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points meet. The Latin word "angulus," which means "corner," is where the term "angle" first appeared.

Its coordinates are determined using the orthocenter formula. Let's take a look at the triangle ABC in the illustration above. AD, BE, and CF are the perpendiculars that are drawn from the vertices A(x1,y1), B(x2,y2), and C(x3,y3), respectively. The three elevations come together at point O.

The slope of the triangle's sides must first be determined using the following formula:

m = y2 - y1/x2 - x1

The slope of the triangle ABC's altitudes will now be the line's perpendicular slope.

Line slope perpendicular to the plane is -1/m

Let mAC be the slope of the AC. Hence,

mAC = y3 - y1/x3 - x1

Similarly, mBC = (y3 - y2)/(x3 - x2)

Now, the corresponding altitudes' slopes are as follows:

BE slope: mBE = -1/mAC

AD slope: mAD = -1/mBC

Now, in order to determine the equations of the lines that coincide with BE and AD, we will use the slope point form equation of a straight line.

Hence,

mBE = (y - y2)/(x - x2)

mAD = (y - y1)/(x - x1)

As a result, we are left with two equations that are simple to answer. The orthocenter's coordinates are thus determined by the values of x and y.

The complete question is :

The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other.

Take an example of a triangle ABC.

To learn more about angle, refer to:

https://brainly.com/question/25716982

#SPJ4

If the magnitude of two vectors is 10 and 6 and their dot product is 30, then the angle between the vectors is 60°.

What is a vector?

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

There are two ways to define a dot product: algebraically and geometrically. The sum of the products of the matching entries of the two number sequences is the definition of the dot product in algebra. Geometrically, it is the sum of the cosine of the angle formed by the two vectors and their Euclidean magnitudes.

The magnitude of the vector 1 is, |a| = 10

The magnitude of the vector 2 is, |b| = 6

The dot product of the two vectors is, a·b = 30.

The formula for dot product of vectors is -

a·b = |a| |b| cos θ

Solve the equation to get the angle -

30 = (10 × 6) cos θ

30 = 60 cos θ

cos θ = 30/60

cos θ = 1/2

θ = cos^-1 (1/2)

θ = 60°

Therefore, the angle is obtained as 60°.

To learn more about vector from the given link

https://brainly.com/question/25705666

#SPJ1

The following statements are true: if augmented matrices of two linear systems are row equivalent, the systems have the same solution set; two matrices are called row equivalent if one matrix can be transformed into another by applying a sequence of elementary row operations; in an echelon form of a matrix, all entries in a column below the leading entry are zero; the reduced echelon form of a matrix is not defined uniquely.

The row replacement operation, when performed on a matrix, results in interchanging two rows. This statement is not true. Row replacement operations can also be used to add multiples of one row to another, it doesn't necessarily interchange two rows.

The statement "if augmented matrices of two linear systems are row equivalent, the systems have the same solution set." is true. Row equivalence is a property of matrices that describes how two matrices can be transformed into one another by performing elementary row operations. If two matrices are row equivalent, it means that they can be transformed into the same row echelon form, which implies that they have the same row space, and therefore the same solution set.

The statement "two matrices are called row equivalent if one matrix can be transformed into another by applying a sequence of elementary row operations." is true. Two matrices are row equivalent if one matrix can be transformed into another by applying a sequence of elementary row operations, such as row interchanges, row scaling, and row replacement.

The statement "in an echelon form of a matrix, all entries in a column below the leading entry are zero." is true. An echelon form of a matrix is a matrix that has the following properties: all non-zero rows are above any rows of all zeroes, the leading entry of a non-zero row is to the right of the leading entry of the row above it. In an echelon form of a matrix, all entries in a column below the leading entry are zero.

To know more on augmented matrices

https://brainly.com/question/26320234

#SPJ4

The results of the ANOVA test may not be reliable.

The conditions that must be met for the results of an ANOVA test to be reliable are that the observations must be independent of each other and randomly selected from their populations (A). Additionally, the variances for each population must be approximately equal to each other (B). This can be tested with the F-test, which is calculated by dividing the variance of the sample means by the variance of the individual observations. This test is used to determine if the variability between the groups is greater than the variability within the groups. If the F-test returns a value greater than 1, then the variances are not equal and the results of the ANOVA test may not be reliable. Lastly, the populations from which each group is drawn must be approximately Normal (C). This can be tested with a Shapiro-Wilk test or a visual inspection of a histogram or qqplot. If the populations are not normally distributed, then the results of the ANOVA test may not be reliable. The hypothesized means of the populations from which each group is drawn must be approximately equal (D). This can be tested with a t-test or a confidence interval. If the means are significantly different, then the results of the ANOVA test may not be reliable.

Learn more about ANOVA test here:

https://brainly.com/question/30127764

#SPJ4

The Scale Factor is 0.75, or 3/4

Scale factor is a ratio of two related lengths, areas, volumes, or other quantities. It is used to describe how a figure is enlarged or reduced in size. For example, when a figure is enlarged, the scale factor is greater than one, and when a figure is reduced, the scale factor is less than one. Scale factors can be used to calculate the lengths of sides and areas of figures when one side or area is known.


The Scale Factor is calculated by dividing the coordinates of point A' (9, 3) by the coordinates of point A (12, 4). Therefore, the Scale Factor is 0.75, or 3/4.

To know more about scale factor click-
https://brainly.com/question/2826496
#SPJ1

Patient needs to 500,000 unit of penicillin, then according to capsule availability we shall provide the 2 capsules of 200,000 unit and 1 capsule of 100,000 unit.

The doctor orders 500,000 unit of penicillin for the patient. the capsule available are 200,000 unit and 100,000 units.

we have to find out the number of capsules required for 500,000 unit,

let's see,

we have 200,000 unit of penicillin and 100,000 units of penicillin available,

patient need of 500,000 unit of penicillin,

so we shall provide the 2 capsule of 200,000 units of penicillin and 1 capsule of penicillin 100,000 unit to the patient,

learn more about capsule.

https://brainly.com/question/13020190

#SPJ4

Answer: We can set up a system of equations to represent the given information:

Let x be the number of adult tickets sold

Let y be the number of student tickets sold

x + y = 56 (the total number of tickets sold is 56)

5x + 3y = 232 (the total amount of money made is 232 dollars)

To find the number of adult and student tickets sold, we can use the first equation to solve for one of the variables in terms of the other, and then substitute that into the second equation.

x + y = 56

x = 56 - y

Now we can substitute this value of x into the second equation:

5(56 - y) + 3y = 232

280 - 5y + 3y = 232

280 = 8y

y = 35

So, 35 student tickets were sold, and 56 - 35 = 21 adult tickets were sold.

Step-by-step explanation:

The tall of the building is 175m and the baseball strikes the ground in 4.53 seconds, 195 ft/s.

Assume that the acceleration due to gravity is 10m/s2.  

The equation for the ball’s velocity in the downward direction is

v(t) = at + v₀.

Here

v₀=10m/s a=10m/s² v(t)=60m/s

Solving this for  t we get the:  

[tex]t =\frac{60m/s-10m/s}{10m/s^2}\\ \\t=\frac{50m/s}{10m/s^2}\\[/tex]

t=5s

The total distance traveled will be  

[tex]x(t)=\frac{1}{2} at^2+v_{0} +x_{0}[/tex]

Here x₀ = 0 and we get:

[tex]x(t)=\frac{1}{2} (10m/s^2)(5s)^2+(10m/s)(5s)[/tex]

x=125m+50m

x=175m

The given values are:

u = 50 ft/s

h = 555 ft

g = 32 ft/s²

Let the time taken by the ball to reach the ground be t and the velocity of the ball as it hits the ground be v.

Use the third equation of motion

v²=u²+2as

v²=50²+2*32*555

v = 195 ft /s

Thus, the ball strikes the ground with a velocity of 195 ft/s.

Use the first equation of motion

v = u + at

195 = 50 + 32 t

32 t = 145

t = 4.53 second

Thus, the ball reaches the ground in 4.53 seconds.

To know more about equations of motion:

https://brainly.com/question/13246412

#SPJ4

Exponential growth is a type of growth that occurs when the rate of increase is proportional to the current amount.

To learn more about logarithmic evaluation refer to:

https://brainly.com/question/29168400

#SPJ1

The 4th line plot picture correctly shows the data of the lengths of the sticks that were 3, 3, 4, 3, 3, 5, 4, 6, 5 and 4 inches.

A line plot is a graph that uses symbols to represent data above a frequency number line. It is used to arrange the data simply and is very simple to understand.

A line plot is a graphical representation of data on a number line which uses dots, crosses, or any other symbol. The scale of the graph is represented by each mark, which corresponds to a particular quantity.

The data on a number line can be graphically represented using symbols using a line plot graph. In contrast to a line graph, no cartesian plane or x and y axes are used in this data representation. Simple lines are drawn on a number line to represent a line plot graph.

Learn more about line plot

https://brainly.com/question/29573088

#SPJ1

Full question:

Andre measured the lengths of 10 sticks to the nearest inch. the lenghts of the sticks were 3,3,4,3,3,5,4,6,5 and 4 inches. Click on the line plot that shows these data. Lengths of Sticks (in inches) Lengths of Sticks (in inches) Lengths of Sticks (in inches) Lengths of Sticks.

The percentage increase in snakes from last year to this year at the Cincinnati Zoo is 20%.

The percentage increase refers to the ratio of the increase in the number of snakes in the zoo.

The percentage increase can be computed as the quotient of the amount of increase divided by the previous number of snakes, multiplied by 100.

The number of snakes in the zoo last year = 25

The number of snakes in the zoo currently = 30

The increase in the number of snakes = 5 (30 - 25)

The percentage increase = 20% (5/25 x 100)

Thus, we can conclude that the number of snakes in the Cincinnati Zoo has increased by 20 percent since last year.

Learn more about percentages at https://brainly.com/question/24877689

#SPJ1

Answer: D. The distance from A to C

Step-by-step explanation:

This formula can be used to find the distance between two points on a three-dimensional coordinate system:

D(x, y, z) = [tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2} }[/tex]

If you apply the formula for all options, you will find the distance from A to C is equal to [tex]\sqrt{5}[/tex]. The other distances are:

A. [tex]\sqrt{17}[/tex]

B. [tex]\sqrt{45}[/tex]

C. [tex]\sqrt{44}[/tex]

So, the answer is D.

The probability of getting exactly 1 three, to the nearest thousandth is 0.347.

Binomial distribution is the distribution of a random variable X for which there are only two possibilities. The probability p for the success and the probability of 1-p for the failure, which consist of n trials.

The binomial distribution has the formula,

P(x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ

where x : number of times for a specific outcome within n trials

p : probability of success in each trial

n : number of trials

Given that a fair die is rolled 3 times.

Here, n = 3, x = 1

p = probability of getting three for 1 trial = 1/6

1 - p = 1 - 1/6 = 5/6

P(1) = ³C₁ (1/6)¹ (5/6)³⁻¹

     = 0.347

Hence the probability of getting exactly 1 three is 0.347.

Learn more about Binomial Distribution here :

https://brainly.com/question/14565246

#SPJ1

The probability of one defective compressor among the first 6 examined, the probability of four or more defective compressors among the first 6 examined, and the probability of 1 to 3 defective compressors among the first 6 examined are 0.1136, 0.1212, and 0.7955 respectively.

(a) .1136, .1212 and 0.7955 respectively.

(i) P(X=1) = C(5,1) / C(12,6) = 5/66 = 0.1136

(ii) P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) = C(5,4) / C(12,6) + C(5,5) / C(12,6) + C(5,6) / C(12,6) = .1212

(iii) P(1≤X ≤3) = P(X = 1) + P(X = 2) + P(X = 3) = C(5,1) / C(12,6) + C(5,2) / C(12,6) + C(5,3) / C(12,6) = 0.7955

The probability of one defective compressor among the first 6 examined is P(X = 1) = C(5,1) / C(12,6) = 5/66 = 0.1136. The probability of four or more defective compressors among the first 6 examined is P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) = C(5,4) / C(12,6) + C(5,5) / C(12,6) + C(5,6) / C(12,6) = .1212. The probability of 1 to 3 defective compressors among the first 6 examined is P(1≤X ≤3) = P(X = 1) + P(X = 2) + P(X = 3) = C(5,1) / C(12,6) + C(5,2) / C(12,6) + C(5,3) / C(12,6) = 0.7955.

Therefore, the probability of one defective compressor among the first 6 examined, the probability of four or more defective compressors among the first 6 examined, and the probability of 1 to 3 defective compressors among the first 6 examined are 0.1136, 0.1212, and 0.7955 respectively.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

Step-by-step explanation:

Answer:

36/11 or 3.2727

Step-by-step explanation:

A unit rate is a rate with 1 in the denominator.

Since you didn't specify, I assume 6/11 per 1/6 rate.

Divide 6/11 by 1/6

[tex]\frac{6}{11} /\frac{1}{6}[/tex]

Multiply the reciprocal:

[tex]\frac{6}{11} *\frac{6}{1}=\frac{36}{11}[/tex]

Answer:

  10 yards

Step-by-step explanation:

You want the height of a cylinder of radius 3 yards that has a volume of 282.6 cubic yards, using pi = 3.14.

The volume of a cylinder is given by ...

  V = πr²h

Using the given values, this is ...

  282.6 yd³ = 3.14(3 yd)²·h = 28.26h yd²

Dividing by the coefficient of h, we find it to be ...

  h = (282.6 yd³)/(28.26 yd²) = 10 yd

The height of the cylinder is 10 yards.

There are two vertical angles created by the intersection of two lines.

To learn more about vertical angles, refer to:

https://brainly.com/question/1673457

#SPJ1

To determine the cost of 6 pencils at 60 cents a dozen, we need to convert the price per dozen to the price per pencil. We know that a dozen is equal to 12, so we can use the following formula:

Price per pencil = (Price per dozen) / (Number of items per dozen)

So, in this case:

Price per pencil = (60 cents) / (12 pencils)

To convert cents to dollars, we divide by 100.

Price per pencil = (60/100) $ = 0.6 $

To find the total cost for 6 pencils we multiply the price per pencil by the number of pencils

Cost of 6 pencils = 6 * 0.6 = 3.6 $

So the cost of 6 pencils at 60 cents a dozen is 3.6 $.

Answer:

50

Step-by-step explanation:

140/x = 168/60

x = 60*140/168 = 50

Answer:

50

Step-by-step explanation:

168/60=2.8

140/2.8=50

Answer:

$963.00

Step-by-step explanation:

.9(3x150) + .95(2x200) + 250

.9(450) + .95(400) + 250

405 + 308 + 250 = 963

If we are taking 10% off, that is like leaving 90% (.9) on.

If we are taking 5% off, that is like leaving 95% ( .95) on.

No discount for the watch because she only bought one.