Solve the system of equations. State the decimal solution to the nearest hundredth.



2.5x+3.75y=10.5


1.25x−8.5y=−5.25

Answer:

1. 11π/6

2. 43π/18

3. -π/4

4. - 43π/18

5. 23π/6

6. 25π/18

Step-by-step explanation:

A full circle has a measure of 360° in degrees and 2π radians in radians.

Since a full circle has a measure of 2π radians, then half a circle has a measure of π radians, and a quarter circle has a measure of π/2 radians.

1. 2π - π/6 = 11π/6

2. 61π/36 - π/2 = 61π/36 - 18π/36 = 43π/18

3. 5π/4 - π = π/4; -π/4

4. -36π/18 - 7π/18 = -43π/18

5. 2π + π + 5π/6 = 23π/6

6. 36π/18 - 11π/18 = 25π/18

Use identities:

Then apply to the left side of the given equation:

Proved

£40 is shared as £5, £15 and £20. 88p is shared as 16p, 32p and 40p. 180° is shared as 40°, 40° and 100°

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

a) Share £40 in the ratio 1:3:4

For the first ratio = (1/8) * £40 = £5

For the second ratio = (3/8) * £40 = £15

For the third ratio = (4/8) * £40 = £20

b) Share 88p in the ratio 2:4:5

For the first ratio = (2/11) * 88p = 16p

For the second ratio = (4/11) * 88p = £32

For the third ratio = (5/11) * 88p = 40p

c) Share 180° in the ratio 2:2:5

For the first ratio = (2/9) * 180° = 40°

For the second ratio = (2/9) * 180° = 40°

For the third ratio = (5/9) * 180° = 100°

The ratios are shown above

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The value of angle PSQ is  136. 9 degrees

It is important to note the following;

Then, we have that;

30x + 6  + 11x - 5 = 180 degrees

Now, let's collect the like terms

30x + 11x + 6 - 5 = 180

add or subtract the like terms

41x = 180 - 1

41x = 179

Divide the values, we get;

x = 4. 36

Then,

PSQ = 30x + 6

PSQ = 136. 9 degrees

Learn about supplementary angles at: https://brainly.com/question/2046046

#SPJ1

The perimeter of the plate is 60"

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

Length = 18"

Width = 12"

The perimeter of the rectangle piece can be calculated as

Perimeter = 2 * (Length + Width)

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 * (18 + 12)

Evaluate

Perimeter = 60

Hence, the perimeyer is 60"

Read more about perimeter at

https://brainly.com/question/24571594

#SPJ1

Based on the information, it can be inferred that Mr. Incredible did more work than Dash moving the train car.

To calculate the work that Mr. Incredible and Dash did moving the train car, we must apply the following mathematical formula:

According to the above, we only have to replace the values according to each case.

According to the above, it can be inferred that Mr. Incredible made more effort than Dash because they did 500,000 J and 500 J of work respectively.

Learn more about joules in: https://brainly.com/question/25982371

#SPJ1

The toy rocket will hit the ground after approximately 3.86 seconds.

The rocket will hit the ground when its height is equal to zero, so we can use the equation h = -4.97t^2 + 38.5t + 5.6 to find the value of t that satisfies this condition. To do this, we set h equal to zero and solve for t:

0 = -4.97t^2 + 38.5t + 5.6

-5.6 = -4.97t^2 + 38.5t

4.97t^2 - 38.5t - 5.6 = 0

This is a quadratic equation and can be solved using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 4.97, b = -38.5, and c = -5.6.

Plugging in these values, we get:

t = (-(-38.5) ± √((-38.5)^2 - 4 * 4.97 * -5.6)) / (2 * 4.97)

t = (38.5 ± √(1466.25 + 113.92)) / 9.94

t = (38.5 ± √1580.17) / 9.94

The square root of 1580.17 is 39.67, so:

t = (38.5 ± 39.67) / 9.94

t = (38.5 + 39.67) / 9.94 or (38.5 - 39.67) / 9.94

The first solution gives us a time of approximately 3.86 seconds, while the second solution is negative and therefore represents an unrealistic result.

The toy rocket will hit the ground after approximately 3.86 seconds.

Learn more on quadratic equation: https://brainly.com/question/20038608

#SPJ1

Answer:

So Andrea and Casey each make $52 after working for 3 hours.

Step-by-step explanation:

Let's call the number of hours that Andrea and Casey work "x".

The amount of money that Andrea makes in a given hour can be represented as 25 + 9x.

The amount of money that Casey makes in a given hour can be represented as 10 + 14x.

We want to find the number of hours it takes for Andrea and Casey to make the same amount of money, which we can represent as:

25 + 9x = 10 + 14x

To solve for x, we can isolate x by subtracting 10 from both sides of the equation:

15 + 9x = 14x

Next, we can isolate 9x by subtracting 14x from both sides of the equation:

15 = -5x

Finally, we can divide both sides of the equation by -5 to solve for x:

-3 = x

So it takes 3 hours for Andrea and Casey to make the same amount of money. To find the amount of money, we can plug in x = 3 back into either of the equations:

Andrea's equation: 25 + 9x = 25 + 9 * 3 = 25 + 27 = 52

So Andrea and Casey each make $52 after working for 3 hours.

The sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl. The test statistic is 50 and then the p-value is 32.93

Mean is the ratio of the sum of all observations to the number of observations. Standard deviation is the measure in which it shows how much the variation such as spread, dispersion,  from the mean exists and the study of jordanian children in exercise 64, the sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl.

For the study of jordanian children in exercise 64, the sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl.

Given that, exercise n =64

mean  = 11.3 mg/dl

standard deviation = 1.6mg/dl

The test statistic is 50

the p-value is calculated by, (n-mean) / (standard deviation)

(64 - 11.3) / (1.6)

32.93

Therefore, the p-value in which it obtains a more precise value is 32.93

Learn more about mean here:

https://brainly.com/question/30023845

#SPJ4

The polynomial for the shaded area will be 3x² + 15x and x² + 6x + 8.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

19. The area is given as,

A = (x + 5)(3x)

A = 3x² + 15x

19. The area is given as,

A = (x + 4)(x + 2)

A = x² + 6x + 8

The polynomial for the shaded area will be 3x² + 15x and x² + 6x + 8.

More about the area of the rectangle link is given below.

https://brainly.com/question/20693059

#SPJ1

The numbers 2 2 2 2 can be arranged to make the equation true as follows

The numbers arranged by applying the rule which had acronym of PEMDAS

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

applying the sequence the problem is solved as follows

= (2 + 2/2)²

solving the parenthesis first we solve the problem inside the parenthesis. Inside the parenthesis we start with division

= (2 + 2/2)²

= (2 + 1)²

Then addition

= (3)²

having completed the parenthesis, we solve for the exponents

= 9

Learn more about PEMDAS here:

https://brainly.com/question/29393553

#SPJ1

The density of water is 1 g/mL, so for this problem, we would multiply 103.8 mL by 1 g/mL to get our answer of 103.8 grams.

The density of water is 1 gram per milliliter (1 g/mL). This means that for every milliliter of water, there is 1 gram. Therefore, to answer the question of how many grams of C12H24012 is needed to acquire the needed volume of water (103.8 mL), we need to multiply the volume of water by the density of water. To do this, we will use the equation: Mass (g) = Volume (mL) x Density (g/mL). For this problem, the equation would be: Mass (g) = 103.8 mL x 1 g/mL.Therefore, the answer to the question is 103.8 grams of C12H24012 is needed to acquire the needed volume of water.In conclusion, to figure out how many grams of C12H24012 is needed to acquire the needed volume of water, we need to multiply the volume of water (in mL) by the density of water (in g/mL). The density of water is 1 g/mL, so for this problem, we would multiply 103.8 mL by 1 g/mL to get our answer of 103.8 grams.

Learn about density here:

https://brainly.com/question/29463645

#SPJ4

15 ounces of herbs should be mixed to produce a mixture of costing $2.50 per ounce.

What is meant by addition?

In mathematics, addition is the process of fusing two or more integers. The numbers being added are known as addends, while the outcome of the addition process, or the final response, is known as the sum. It is one of the fundamental mathematical operations we employ on a daily basis. We add numbers in many different contexts.

Given that, an herbalist has 15 ounces of herbs costing $3 per ounce.

Let the ounces of herbs costing $2 per ounce that should be added to the above herbs be 'x'

Cost of total mixture is 15*3 + x*2 = (x+15)*2.5

15*(3-2.5) = x*(2.5-2)

15*0.5 = x*0.5

x = 15

Therefore, 15 oz of herbs for $2 should be added.

To learn more about total amount calculation, refer to the link below:

https://brainly.com/question/26959824

#SPJ1

The triangles are congruent by SSS and the transformation rule is (x, y) ⇒ (x - 4, y)

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

Triangles EFD and GH

The triangles are congruent because they have equal corresponding side lengths

The corresponding sides of the triangles are congruent

So, the congruent statement is SSS

From the figure, we can see that:

EFD is shifted left by 4 units

So, the rule is

(x, y) ⇒ (x - 4, y)

Read more about transformation at

https://brainly.com/question/27224272

#SP{J1

WE CAN USE THE GRAPH THAG CA HELP US IN THE PROBLEM

The probability of obtaining a random sample of 75 units from a production process where the true fraction of nonconforming product is 0.01 is extremely high. This is because 0.01 is an extremely low fraction, meaning that out of the 75 units in the sample, only 0.75 would be expected to be nonconforming.

The probability that the fraction of nonconforming product is exactly 0.01 (with 0.75 nonconforming units out of 75) can be calculated using the binomial distribution. This distribution assumes that each unit has an independent probability of being nonconforming, and that this probability is the same for each unit. The probability that the sample will have exactly 0.75 nonconforming units out of 75 is 0.907.

Thus, the probability that the true fraction of nonconforming product is exactly 0.01 is very high, and it is likely that a random sample of 75 units drawn from the production process will have a fraction nonconforming that is close to 0.01.

To learn more about random sample:

https://brainly.com/question/24466382

#SPJ4

Answer:

Jennifer raised $25

Rebecca raised £50

Derek raised $37.50

Matthew raised $75

Step-by-step explanation:

J: 50% = dividing by 2, 50/2= 25

R: 50 is 100%, because that was the total

D: 75% = dividing by 4, timsing by three, so 50/4 is 12.5 x 3 is 37.5, put it into currency $37.50

M: We add another 25% onto 50 so 25+50=75.

(hope this works!!)

The area of this compound figure is 85 cm².

The area of the compound figure given is calculated by subtracting the small area of the  figure from the big figure.

A (total) = 9 cm x 15 cm

A (total) = 135 cm²

The area of the small figure is calculated as follows;

A (small) = ( 9 cm - 4 cm ) x ( 15 cm - 5 cm )

A (small) = ( 5 cm ) x ( 10 cm )

A (small) = 50 cm²

The area of this compound figure = ( 135 cm² - 50 cm² ) = 85 cm²

Learn more about area of compound figure here: https://brainly.com/question/15981553

#SPJ1

Answer: -8 + (-4 )(look at the image for the solution)

Step-by-step explanation:

The predicted femur length for someone with a height of 218 cm is 68 cm.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

From the graph,

Coordinates = (30, 127), (35, 139), (40, 151).

Now,

The equation of the line of best fit.

y = mx + c

Where x is the femur length and y is the height.

Take two coordinates.

m = (139 - 127) / (35 - 30)

m = 12/5

m = 2.4

And,

(30, 127) = (x, y)

127 = 2.4 x 30 + c

127 - 72 = c

c = 55

So,

y = 2.4x + 55

Now,

For y = 218.

Solve for x.

218 = 2.4x + 55

218 - 55 = 2.4x

163 = 2.4x

x =163/2.4

x = 67.9

x = 68 cm

Thus,

The predicted femur length for someone with a height of 218 cm is 68 cm.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ9

A scatter plot would best display the relationship between the number of hours a student spent studying for several tests and the student's grade on each test.

A scatter plot is a graph that displays the relationship between two continuous variables. In this case, the number of hours a student spent studying is the independent variable, which would be plotted on the x-axis. The student's grade on each test is the dependent variable, which would be plotted on the y-axis. Each data point would represent a single test, with the x-coordinate indicating the number of hours studied for that test and the y-coordinate indicating the grade received.

By using a scatter plot, you can easily identify any patterns or relationships between the number of hours studied and the student's grades on each test. It can also help to identify any outliers or anomalies in the data.

To learn more about scatter plot here:

https://brainly.com/question/29231735

#SPJ4

Answer:

c

Step-by-step explanation:

trust me

Answer: [tex]8d^{2} (8d^3 - 3)[/tex]

Step-by-step explanation:

8d^2 is the GCF for this binomial

The probability that a box of 40 light bulbs will last for 5 years is very low, due to the short mean lifetime of 2 months and the relatively high standard deviation of 0.25 months.

The mean lifetime of a particular type of light bulb is given as 2 months, and the standard deviation is given as 0.25 months. The mean lifetime represents the average time that the light bulbs will last, while the standard deviation represents how much the lifetimes of the bulbs vary from the mean.

To determine the probability that a box of 40 light bulbs will last for 5 years, we need to convert the given information into a format that we can work with. 5 years is equal to 60 months, and since we have 40 light bulbs, we can assume that the lifetimes of the bulbs are independent and identically distributed. This means that the probability of one bulb lasting for 60 months is the same as the probability of any other bulb lasting for 60 months.

Next, we need to calculate the standard deviation of the sample mean. The standard deviation of the sample mean represents how much the means of different samples of size 40 would vary from the population mean. The formula for the standard deviation of the sample mean is given by the following equation:

standard deviation of the sample mean = standard deviation of the population / square root of the sample size

In this case, the standard deviation of the population is given as 0.25 months, and the sample size is 40. Therefore, the standard deviation of the sample mean is:

0.25 / sqrt(40) = 0.0395

Now that we have the mean lifetime and the standard deviation of the sample mean, we can use the normal distribution to determine the probability that a box of 40 light bulbs will last for 5 years. We can assume that the lifetimes of the bulbs follow a normal distribution with a mean of 2 months and a standard deviation of 0.0395 months (which is the standard deviation of the sample mean).

To find the probability that a bulb will last for 60 months, we can use the following equation:

z = (x - μ) / σ

where z is the standard score, x is the value we want to find the probability for (60 months in this case), μ is the mean, and σ is the standard deviation.

Plugging in the values, we get:

z = (60 - 2) / 0.0395 = 1509.49

To find the probability corresponding to this standard score, we can use a standard normal distribution table or a calculator. The probability is extremely small (close to zero), which means that it is highly unlikely that all 40 light bulbs will last for 5 years.

To know more about probability here.

https://brainly.com/question/11234923

#SPJ4

Answer: Region Z

Step-by-step explanation: Region X is smaller than Region Y, while Region Y is smaller than Region Z.

Answer:

Step-by-step explanation:

Bottom right is the correct graph.  Plot the line y ≤ 3x-4 and shade the area below the solid line.  Next plot y < -2x +3 and shade the area below the dashed line.  Where the 2 shaded areas intersect is the solution.  Bottom right graph show this.

The IR spectrum described could be an alkyl chloride with a carbonyl group, such as chloroform ([tex]CHCl_{3}[/tex]).

The IR spectrum described suggests the presence of several functional groups in the compound.

The strong, broad band in the 3600 to 3100 inverse centimeter range corresponds to the stretching vibration of the O-H bond in alcohols, while the strong, spiked peak in the 3000 to 2800 inverse centimeter range corresponds to the stretching vibration of the C-H bond in alkanes. The weak peak near 1850 inverse centimeters corresponds to the stretching vibration of the C=O bond in ketones, while the sharp peak near 1640 inverse centimeters corresponds to the stretching vibration of the C=C bond in alkenes.

The series of spiked bands in the 1500 to 1200 inverse centimeter range corresponds to the bending vibrations of the C-H bond in alkanes, while the two strong bands at 990 and 910 inverse centimeters correspond to the stretching vibration of the C-Cl bond in alkyl chlorides.

Based on this information, the compound that matches the IR spectrum described could be an alkyl chloride with a carbonyl group, such as chloroform ([tex]CHCl_{3}[/tex]).

For similar question on ir spectrum,

https://brainly.com/question/9593236

#SPJ4

The inequality representing the situation is w >= 15, where w represents the weight of a can of tomatoes and the inequality states that it must be greater than or equal to 15 ounces.

The inequality that represents the situation is w >= 15, where w represents the weight of a can of tomatoes. This inequality states that the weight of a can of tomatoes is greater than or equal to 15 ounces, meaning that every can of tomatoes weighs at least 15 ounces.

This inequality represents a constraint or a condition on the weight of a can of tomatoes. In mathematical terms, the inequality w >= 15 says that the value of w, which represents the weight of a can of tomatoes, must be greater than or equal to 15 ounces. Any value that satisfies this inequality is considered a valid solution for the weight of a can of tomatoes. For example, 15 ounces, 16 ounces, 17 ounces, and so on are all valid weights for a can of tomatoes that meet the requirement of weighing at least 15 ounces.

Learn more about inequality here:

https://brainly.com/question/28823603

#SPJ4

The complete question is:

At a supermarket, Each tomato can in a store weighs at least 15 ounces.

Let w stand in for the can of tomatoes' weight.

Which inequality best captures the circumstances?

[tex]w < 15 w < 15 W > 15 w > 15[/tex]

Answer: 1) (0, -3) & 2) (0,0)

Step-by-step explanation: