Answer:
To simplify the given expression, let's combine like terms and simplify each term:
2b² - 4b + 1 - b² - b - 4b² - 2b + 6
Combine like terms:
(2b² - b² - 4b²) + (-4b - b - 2b) + (1 + 6)
Simplify each term:
(-3b²) + (-7b) + (7)
The simplified expression is:
-3b² - 7b + 7
1=10km
. A photocopier makes 8 copies in 20 seconds. At that same rate, how many whole
copies can the photocopier make in 48 seconds?
Answer:
Step-by-step explanation:
20 seconds = 8 copies
so every 2.5 seconds, 1 page is made( 20sec/8 page = 2.5 page per second)
2.5 sec = 1 page
48 sec = x page
now you cross multiply, and that goes to: 2.5x = 48
isolate for x
x= 48/2.5
x= 19.2 but it says whole pages so you round down
x = 19 pages in 49 seconds
A shop employs eight men and two women. The mean weekly wage of the ten employees is £396.
The mean weakly wage of the 8 men is £400.
Calculate the mean weekly wage of the 2 women.
Answer:
The mean weekly wage for the two women is £380.
Step-by-step explanation:
We can use the weighted mean formula to solve this problem.
Firstly, we calculate the total weekly wage for the ten employees by multiplying the mean weekly wage by the total number of employees:
Total weekly wage = Mean weekly wage x Number of employees
Total weekly wage = £396 x 10
Total weekly wage = £3,960
We can then subtract the total weekly wage for the eight men to find the total weekly wage for the two women:
Total weekly wage for 2 women = Total weekly wage - Total weekly wage for 8 men
Total weekly wage for 2 women = £3,960 - (£400 x 8)
Total weekly wage for 2 women = £3,960 - £3,200
Total weekly wage for 2 women = £760
Now, we can calculate the mean weekly wage for the two women by dividing their total weekly wage by the number of women:
Mean weekly wage for 2 women = Total weekly wage for 2 women / Number of women
Mean weekly wage for 2 women = £760 / 2
Mean weekly wage for 2 women = £380
Therefore, the mean weekly wage for the two women is £380.
Halp me this the question
Answer:
26 + 22 + ? = 52
Step-by-step explanation:
52 horses in total.
26 brown and 22 black. 26 + 22 = 48.
52 - 48 = 4 (number white horses)
What is the formula for the test statistic, and the distribution for the test statistic? be sure to include the degrees of freedom.
The formula for the test statistic depends on the type of hypothesis test being conducted. However, in general, the test statistic is calculated by taking the difference between the sample statistic (such as the sample mean or proportion) and the hypothesized population parameter, and dividing by the standard error of the statistic.
The distribution of the test statistic also depends on the type of test being conducted. For example, if conducting a t-test with a sample size less than 30, the test statistic follows a t-distribution with degrees of freedom equal to the sample size minus 1. If conducting a z-test or a large sample t-test with a sample size greater than or equal to 30, the test statistic follows a standard normal distribution (i.e., a z-distribution).
It is important to consult the appropriate distribution table and degrees of freedom when interpreting the test statistic to determine the p-value and make a decision about the hypothesis.
The formula for the test statistic and its distribution depend on the specific hypothesis test being conducted. I'll provide the information for two common tests: the t-test and the chi-square test.
1. T-test:
The formula for the test statistic in a t-test is:
t = (sample mean - population mean) / (sample standard deviation / √n)
where n is the sample size. The distribution for the test statistic is the t-distribution with (n-1) degrees of freedom.
2. Chi-square test:
The formula for the test statistic in a chi-square test is:
χ² = Σ [(observed frequency - expected frequency)² / expected frequency]
The distribution for the test statistic is the chi-square distribution with (k - 1) degrees of freedom, where k is the number of categories in the contingency table.
Remember to use the appropriate test and formula based on your specific research question and data.
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The theoretical probability that you will try out for the school play is 1/10. There at e22 students in your grade that try out for the school play. How many students are in your grade?
Use Theoretical probability there are 220 students in the grade.
We can use the formula for theoretical probability to find the number of students in the grade:
P(event) = number of favorable outcomes / number of total outcomes
In this case, the probability of a student trying out for the school play is 1/10, so we have:
1/10 = number of students who try out / total number of students in the grade
We can simplify this equation by multiplying both sides by the total number of students in the grade:
total number of students in the grade * 1/10 = number of students who try out
Multiplying both sides by 10, we get:
total number of students in the grade = 10 * number of students who try out
Substituting the given value of 22 for the number of students who try out, we get:
total number of students in the grade = 10 * 22
total number of students in the grade = 220
Therefore, there are 220 students in the grade.
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1. Explain how a logarithmic function relates to an exponential function.
2. Explain the format of the logarithmic function log3 (x + 5) = 4 and then
solve.
Logarithmic functions and exponential functions are inverse functions of each other
The value of x in the equation log₃ (x + 5 ) = 4 is 76
How to solve the functionThe format of the logarithmic function log₃ (x + 5 ) = 4 is
log of (x + 5) in base 3 equals 4solving the equation
3⁴ = x + 5
81 = x + 5
x = 76
the solution to the equation log3 (x + 5) = 4 is x = 76.
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What it would -3x+5<-16 look on a number line
The solution to the inequality is x > 7
Given data ,
To represent the inequality -3x + 5 < -16 on a number line, follow these steps:
Step 1:
Solve the inequality for x
-3x + 5 < -16
Step 2:
Subtract 5 from both sides of the inequality
-3x < -16 - 5
-3x < -21
Step 3:
Divide both sides of the inequality by -3. Note that when dividing by a negative number, the direction of the inequality sign should be reversed:
x > (-21)/(-3)
x > 7
Step 4:
Plot a closed circle on 7 (since the inequality is strictly greater than) and shade the region to the right of 7 on the number line
Hence , the inequality is x > 7
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Please please please please please I am in sixth grade so it should be easy and please help me
Answer:6
Step-by-step explanation:
dependent is the varible
The small submarine is at –1,320 feet in relation to sea level. The submarine needs to be at 180 feet below sea level in 60 minutes.
What does the average rate of ascent need to be?
19 feet per minute
18 feet per minute
17 feet per minute
16 feet per minute
To calculate the average rate of ascent we need to use the following formula:
rate = (final depth - initial depth) / time
Plugging in the given values:
rate = (180 ft - (-1,320 ft)) / 60 min = 1,500 ft / 60 min = 25 ft/min
However, since the submarine is currently below the desired depth, the rate needs to be negative (i.e. descending). So, we need to subtract the ascent rate from the descent rate:
ascent rate = (-1,320 ft - (-180 ft)) / 60 min = -1,140 ft / 60 min = -19 ft/min
total rate = 25 ft/min - 19 ft/min = 6 ft/min
Therefore, the average rate of ascent needed would be 17 feet per minute (rounding to the nearest whole number).
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A recipe for mac and cheese calls for 8 cups of pasta for every 6 cups of cheese. Suppose a restaurant is making a large batch of mac and cheese using 15 cups of cheese. How much pasta would they need?
To find out how much pasta the restaurant needs, we can use the ratio of pasta to cheese given in the recipe: 8 cups of pasta for every 6 cups of cheese.
First, we need to determine the ratio of cheese to pasta. We can do this by taking the reciprocal of the original ratio, which gives us 6 cups of cheese for every 8 cups of pasta.
Next, we can set up a proportion with the known amount of cheese (15 cups) and the unknown amount of pasta (let's call it x cups):
6 cups of cheese / 8 cups of pasta = 15 cups of cheese / x cups of pasta
We can cross-multiply to solve for x:
6 cups of cheese * x cups of pasta = 8 cups of pasta * 15 cups of cheese
Simplifying this equation gives:
x = (8 cups of pasta * 15 cups of cheese) / 6 cups of cheese
x = 20 cups of pasta
Therefore, the restaurant would need 20 cups of pasta to make the large batch of mac and cheese using 15 cups of cheese, according to the recipe.
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Please helppp me find bd
The length of segment BD, which represents the altitude of the triangle, is given as follows:
BD = 6.
What is the geometric mean theorem?The geometric mean theorem states that the length of the altitude of a triangle is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.
The altitude segment for this problem is given as follows:
BD.
The bases for this problem are given as follows:
3 and 12.
Hence the length of segment BD is obtained as follows:
(BD)² = 3 x 12 -> geometric mean formula
(BD)² = 36
(BD)² = 6².
BD = 6.
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Erica works in a soda-bottling factory. As bottles pass her on a conveyer belt, she puts caps on them. Unfortunately, Erica sometimes breaks a bottle before she can cap it. She gets paid
4
6¢ for each bottle she successfully caps, but her boss deducts
2¢ from her pay for each bottle she breaks. Erica is having a bad morning. Fifteen bottles have come her way, but she has been breaking some and has only earned 6¢ so far today. How many bottles has Erica capped and how many has she broken?
Write a system of equations representing this situation. Solve the system of equations using two different methods: substitution and elimination. Demonstrate that each method results in the same solution
Erica works in a soda-bottling factory and earns 46¢ for each successfully capped bottle but loses 2¢ for each bottle she breaks. After capping some bottles, she has earned only 6¢ and has broken some bottles. To determine how many bottles Erica capped and how many she broke, a system of equations can be used.
Let x be the number of bottles Erica capped and y be the number of bottles she broke. Then the following system of equations can be written:
46x - 2y = 6 (Equation 1)
x + y = 15 (Equation 2)
To solve the system of equations using substitution, we can isolate one of the variables in terms of the other from Equation 2, and substitute it in Equation 1. From Equation 2, y = 15 - x. Substituting this in Equation 1, we get 46x - 2(15 - x) = 6. Simplifying the equation, we get 48x - 30 = 6, which gives x = 9. Therefore, Erica has capped 9 bottles and broken 6 bottles.
To solve the system of equations using elimination, we can multiply Equation 2 by 46 to eliminate y. This gives us 46x + 46y = 690. Subtracting Equation 1 from this equation, we get 48y = 684, which gives y = 14.25. However, y cannot be a fractional value, so we can round it to the nearest whole number, which gives y = 14. Substituting y = 14 in Equation 2, we get x = 1. Therefore, Erica has capped 1 bottle and broken 14 bottles.
Both methods lead to different solutions, but this is because one of the solutions obtained is not feasible. Erica cannot cap a fraction of a bottle or break a fraction of a bottle. Therefore, the solution obtained using the elimination method needs to be rounded to the nearest whole number, which then gives the same solution as the substitution method, that Erica capped 9 bottles and broke 6 bottles.
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Erica works in a soda-bottling factory and earns 46¢ for each successfully capped bottle but loses 2¢ for each bottle she breaks. After capping some bottles, she has earned only 6¢ and has broken some bottles. To determine how many bottles Erica capped and how many she broke, a system of equations can be used.
Let x be the number of bottles Erica capped and y be the number of bottles she broke. Then the following system of equations can be written:
46x - 2y = 6 (Equation 1)
x + y = 15 (Equation 2)
To solve the system of equations using substitution, we can isolate one of the variables in terms of the other from Equation 2, and substitute it in Equation 1. From Equation 2, y = 15 - x. Substituting this in Equation 1, we get 46x - 2(15 - x) = 6. Simplifying the equation, we get 48x - 30 = 6, which gives x = 9. Therefore, Erica has capped 9 bottles and broken 6 bottles.
To solve the system of equations using elimination, we can multiply Equation 2 by 46 to eliminate y. This gives us 46x + 46y = 690. Subtracting Equation 1 from this equation, we get 48y = 684, which gives y = 14.25. However, y cannot be a fractional value, so we can round it to the nearest whole number, which gives y = 14. Substituting y = 14 in Equation 2, we get x = 1. Therefore, Erica has capped 1 bottle and broken 14 bottles.
Both methods lead to different solutions, but this is because one of the solutions obtained is not feasible. Erica cannot cap a fraction of a bottle or break a fraction of a bottle. Therefore, the solution obtained using the elimination method needs to be rounded to the nearest whole number, which then gives the same solution as the substitution method, that Erica capped 9 bottles and broke 6 bottles.
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Find the measure of Arc BED
180 degrees
142 degrees
218 degrees
72 degrees
The measure of arc BED in the circle is calculated as:
m(BED) = 218 degrees.
How to Find the Measure of an Arc?For us to be able to find the measure of the arc, we need to recall that the measure of the intercepted arc is the same as the central angle measure opposite it.
Arc BED will therefore have the same measure as that of the central angle, therefore:
measure of arc BED = 360 - 52 - 90 [note that arc DC is equal to 90 degrees while arc BC is equal to 52 degrees]
Measure of arc BED = 218 degrees.
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Shadrach rents out 30 offices for $1,600 per month for each office and 10 offices for $2,000 per month for
each office. What is the total rent per month that Shadrach collects for these 40 offices?
Answer:
$68000
Step-by-step explanation:
Answer:
$6800
Step-by-step explanation:
30x1600+10x2000
=48000+2000
=68000
A container has 56 gallons of water and is being filled at a rate of gallon per second. Another container has 64 gallons of water is
draining at a rate of gallon per second. After how many seconds will the two containers will have the same amount of water?
Round your answer to the nearest tenth.
After 4 seconds, both containers will have the same amount of water.
Let's assume that after "t" seconds, both containers will have the same amount of water.
In "t" seconds, the first container will have 56 + t gallons of water.
In "t" seconds, the second container will have 64 - t gallons of water.
To find out when both containers will have the same amount of water, we need to solve the equation:
56 + t = 64 - t
By solving for "t", we get:
2t = 8
t = 4
Therefore, after 4 seconds, both containers will have the same amount of water.
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During a blizzard, the town of Somerville got 60 centimeters of snow in one day! The next few days were sunny, so 55 millimeters of snow melted. But then, Somerville got another 120 millimeters of snow. How many centimeters of snow does Somerville have now?
Somerville now has 66.5 centimeters of snow.
In the initial blizzard, the town of Somerville got 60 centimeters of snow in one day. After a few sunny days, 55 millimeters of snow melted. To convert millimeters to centimeters, we divide by 10. Therefore, 55 millimeters of snow is equal to 5.5 centimeters of snow that melted.
So, the total amount of snow that was left after the sunny days was 60 - 5.5 = 54.5 centimeters of snow.
But then, Somerville got another 120 millimeters of snow. Converting millimeters to centimeters by dividing by 10, we get that 120 millimeters of snow is equal to 12 centimeters of snow.
To find out how many centimeters of snow Somerville has now, we add the remaining snow from the initial blizzard (54.5 centimeters) to the new snowfall (12 centimeters).
Therefore, Somerville now has 66.5 centimeters of snow.
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the daily revenue at a university snack bar has been recorded for the past five years. records indicate that the mean daily revenue is $2500 and the standard deviation is $300. suppose that 100 days are randomly selected. what is the probability that the average daily revenue of the sample is between $2450 and $2460?
Therefore, the probability that the average daily revenue of the sample is between $2450 and $2460 is approximately 0.0443 or 4.43%.
The distribution of the sample means of size n = 100 from a population with mean μ = $2500 and standard deviation σ = $300 can be approximated by a normal distribution with mean = μ = $2500 and standard deviation = σ/√n = $300/√100 = $30.
Thus, we need to find the probability that the sample mean falls between $2450 and $2460.
Z-score for $2450:
z = (2450 - 2500) / 30 = -1.67
Z-score for $2460:
z = (2460 - 2500) / 30 = -1.33
Using a standard normal distribution table or calculator, we can find the probabilities associated with these z-scores:
P(z < -1.67) = 0.0475
P(z < -1.33) = 0.0918
Therefore, the probability that the average daily revenue of the sample is between $2450 and $2460 is:
P(-1.67 < z < -1.33) = P(z < -1.33) - P(z < -1.67)
= 0.0918 - 0.0475
= 0.0443
So, the probability is approximately 0.0443 or 4.43%.
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Find the product of 2.1n(6n + 3.4).
12.6n + 3.4.
8.1n + 3.4.
8.1n2 + 7.14n.
12.6n2 + 7.14n.
Answer:
The correct answer is 12.6n2 + 7.14n.
Step-by-step explanation:
To find the product of 2.1n(6n + 3.4), we can use the distributive property of multiplication:
2.1n(6n + 3.4) = 2.1n(6n) + 2.1n(3.4)
Simplifying this expression gives:
12.6n^2 + 7.14n
Therefore, the product of 2.1n(6n + 3.4) is 12.6n^2 + 7.14n.
Answer:
12.6n2 + 7.14n.
Step-by-step explanation:
2.1×n×(6n+3.4)
Rewrite the expression
2.1×n(6n+3.4)
Calculate the product
2.1n(6n+3.4)
Apply the distributive property
2.1n×6n+2.1n×3.4
Multiply the terms
12.6n
2
+2.1n×3.4
Solution
12.6n
2
+7.14n
Nayeli fue a la tienda de comestibles y compró botellas de gaseosas y botellas de jugo. Cada botella de refresco tiene 25 gramos de azúcar y cada botella de jugo tiene 15 gramos de azúcar. Nayeli compró 5 botellas de refresco más que botellas de jugo y todas juntas contienen 205 gramos de azúcar. Escribe un sistema de ecuaciones que podría usarse para determinar la cantidad de botellas de refresco compradas y la cantidad de botellas de jugo compradas. Defina las variables que utiliza para escribir el sistema.
These equations can be used to determine the number of bottles of soda (R) and the number of bottles of juice (J) purchased by Nayeli. The resulting system of equations is:
25R + 15J = 205
R = J + 5.
To solve this problem, we can set the following variables:
R = Number of bottles of soda purchased.
J = Number of bottles of juice purchased.
We can establish the following equations based on the information provided:
"Each bottle of soda has 25 grams of sugar": So the total amount of sugar in the bottles of soda is 25R.
"Each bottle of juice has 15 grams of sugar": Therefore, the total amount of sugar in the bottles of juice is 15J.
"Nayeli bought 5 more bottles of soda than bottles of juice": Therefore, the number of soda bottles is equal to the number of juice bottles plus 5, which can be expressed as R = J + 5.
"All together contain 205 grams of sugar": So the sum total of sugar is 25R + 15J, which equals 205.
The resulting system of equations is:
25R + 15J = 205
R = J + 5.
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a company orders 29 boxed lunches from a deli for $339.30. assume each boxed lunch is the same price. if c represents the total cost in dollars and cents of the lunch order for any number, b, of boxed lunches ordered, write a proportional equation for c in terms of b that matches the context.
Answer:
11.7b
Step-by-step explanation:
If you do 339.30 divided by 29 it equals 11.7 but the full equation would be c=11.7b
The proportional equation for the total cost 'c' in terms of the number of boxed lunches 'b' is:
c = (339.30 / 29) * b
What is proportion?
The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.
Let's assume that each boxed lunch costs the same amount, denoted by the variable 'x'.
We are given that the company ordered 29 boxed lunches for a total cost of $339.30. Therefore, we can write the equation:
29x = 339.30
To find the cost 'c' for any number 'b' of boxed lunches, we can set up a proportion:
29x / 29 = 339.30 / b
Simplifying this equation, we get:
x = 339.30 / 29
Now, we can substitute this value of 'x' back into the equation:
c = bx = b * (339.30 / 29)
Therefore, the proportional equation for the total cost 'c' in terms of the number of boxed lunches 'b' is:
c = (339.30 / 29) * b
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Haley is shipping these cubes in a wooden box. The inside measurements of the box are shown. Haley will put as many cubes in the box as possible. She wants to be able to close the box using a lid. What is the greatest number of cubes that Haley can fit in the box and still be able to close the lid? Show or explain how you got your answer.
The greatest number of 4 cm cubes that Haley can fit in the box and still be able to close the lid is 6.
First, we need to determine the dimensions of the box in terms of the length of a side of a cube. We can do this by finding the smallest dimension of the box and dividing it by the length of the side of a cube.
The smallest dimension of the box is the height, which is 6 cm. Therefore, the length of the side of a cube must be a factor of 6.
The length and width of the box are both 8 cm, so the length of the side of a cube must be less than or equal to 8 cm.
We can check the factors of 6 to find the largest possible size of the cube that can fit in the box:
A cube with side length 6 cm would fit in the box, but the lid would not be able to close.
A cube with side length 4 cm would fit in the box, and the lid would be able to close, so this is the largest size cube that can fit in the box.
To determine how many 4 cm cubes can fit in the box, we need to find the volume of the box and divide by the volume of a single cube. The volume of the box is:
V_box = length x width x height
V_box = 8 cm x 8 cm x 6 cm
V_box = 384 cm³
The volume of a single 4 cm cube is:
V_cube = side length³
V_cube = 4 cm x 4 cm x 4 cm
V_cube = 64 cm³
Dividing the volume of the box by the volume of a single cube gives us the maximum number of cubes that can fit in the box:
384 / 64 = 6
Therefore, the greatest number of 4 cm cubes that Haley can fit in the box and still be able to close the lid is 6.
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I'm having a really hard time on this question and it's really late I just want to get this done
Answer:
48cm³
Step-by-step explanation:
volume = (7 X 6 X 1) + (3 X 2 X 1)
= (42 + 6)
= 48cm³
solve the given system of inequalities in two variables.
please help .
The equations (x,y) | x + y > 1 and y (1/2)x + 2 have these solutions as their solutions.
To solve the system of inequalities without using graphs, we can use algebraic methods. First, we can rearrange the second inequality to slope-intercept form y < (1/2)x + 2.
This inequality represents a line with slope 1/2 and y-intercept 2. Next, we can identify the region of the coordinate plane that satisfies the first inequality, x + y > 1. This region is above the line x + y = 1. To check which side of the line satisfies the inequality, we can test a point, such as (0,1),
0 + 1 > 1
This is true, so the region above the line x + y = 1 satisfies the inequality.
Finally, we can combine the regions from the two inequalities to find the solution set. The solution set is the region above the line x + y = 1 and below the line y = (1/2)x + 2.
Therefore, the solution set can be expressed as,
{(x,y) | x + y > 1 and y < (1/2)x + 2}.
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Complete question - solve the given system of inequalities in two variables.
x + y > 1
y < 1/2x + 2
26. In sentence 8 (reproduced below), the writer wants to provide evidence to clarify the previous sentence's point about what advocates fail to consider.
In many areas, purchasing or renting land for a tiny home requires compliance with local building codes.
Which of the following versions of the underlined text would best accomplish this goal?
(A) (as it is now)
(B) costs more than the home itself
(C) is an inconvenient and time-consuming process
(D) can be avoided if a friend is willing to share land
(E) may be unnecessary if the homeowner claims to be camping
The following versions of the underlined text would best accomplish this goal is an inconvenient and time-consuming process
This version of the underlined text best accomplishes the writer's goal of providing evidence to clarify the previous sentence's point about what advocates fail to consider. By mentioning that compliance with local building codes is an inconvenient and time-consuming process, it highlights a significant factor that advocates may overlook when promoting the idea of purchasing or renting land for a tiny home. This evidence emphasizes the challenges and potential barriers involved in the process, which helps to clarify the previous point and provide a more comprehensive understanding of the situation.
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A flower bed has the shape of a rectangle 21 feet long and 12 feet wide. What is its area in square yards?
The area of the flower bed in square yards is 28 Square yards.
The area of the rectangular flower bed in square yards, we need to convert the measurements from feet to yards. There are 3 feet in 1 yard, so:
Length in yards = 21 feet / 3 = 7 yards
Width in yards = 12 feet / 3 = 4 yards
Now we can calculate the area in square yards:
Area = Length × Width
Area = 7 yards × 4 yards
Area = 28 square yards
Therefore, the area of the flower bed in square yards is 28 square yards.
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Pls help due today xx
Answer:
21x+6
Here is the answer
Its a pleasire
Answer:
21x+6
Step-by-step explanation:
first distrbute the 3 on the brackets
and note that in mathematics when there is no sign just like after the 3 it means it's multiplication
3(2x+5)+3(5x-3)
=6x+15+15x-9
now add or subtract
=21x+6
that is the simplest we can get and we can't find the value of x cuz this is not an equation
(there is no equal sign and numbers on both sides )
Please draw a stem and leaf diagram for this…
The stem and leaf for the data values is
60 | 0.8 3.5
70 | 2.8 3.8 5.5 7.8 8.3 9.7
80 | 0.6, 2.1, 4.5
How to draw a stem and leaf for the data valuesFrom the question, we have the following parameters that can be used in our computation:
Data values:
82.1 72.8 78.3 77.8 60.8 79.7 73.8 75.5 80.6 84.5 63.5
Sort in order of tens
So, we have
60.8 63.5
72.8 73.8 75.5 77.8 78.3 79.7
80.6, 82.1, 84.5
Next, we draw the stem and leaf as follows:
a | b
Where
a = stem
b = leaf
Using the above as a guide, we have the following:
60 | 0.8 3.5
70 | 2.8 3.8 5.5 7.8 8.3 9.7
80 | 0.6, 2.1, 4.5
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A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 85m long and 57m wide. What is the length of a training track running around the field? Do not round any intermediate computations. Round your final answer to the nearest hundredth and be sure to include the correct unit. If necessary, refer to the list of geometry formulas.
Answer:
463.52 meters
Step-by-step explanation:
To find the length of the training track running around the field, we need to calculate the perimeter of the entire field.
The field is made up of a rectangle with dimensions 85m by 57m, and two semicircles with a radius of 57/2 = 28.5m.
The perimeter of the rectangle is 2(85m) + 2(57m) = 284m.
The perimeter of each semicircle is half the circumference of a full circle with radius 28.5m, which is π(28.5m) = 89.76m. So the total perimeter of both semicircles is 2(89.76m) = 179.52m.
Therefore, the total perimeter of the field is 284m + 179.52m = 463.52m.
Rounding to the nearest hundredth, the length of the training track running around the field is 463.52 meters.
In △RST, what is the length of segment RT? Right triangle RST with RS measuring 36 and angles R and T measure 45 degrees. 18 72 36radical 3 36radical 2
The length of segment RT is given as follows:
[tex]RT = 36\sqrt{2}[/tex]
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The right angle in this problem is given as follows:
S, as R = T = 45º.
As the other two angles have the same measure, we have that the two sides are RS = ST = 36, hence the hypotenuse RT is given as follows:
h² = 36² + 26²
[tex]h = \sqrt{2 \times 36^2}[/tex]
[tex]RT = 36\sqrt{2}[/tex]
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Find the volume of the figure. Use 3.14 for .
◄20 cm→
24 cm
The volume of the cone is 251.20 cubic centimeters if the diameter of the cone is 20 cm and the height of the cone is 24 cm.
The diameter of the cone = 20 cm
The radius of the cone = diameter /2 = 20/2 = 10cm
The height of the cone = 24 cm
The volume of the cone is calculated by using the formula is:
V = (1/3)*π* [tex]r^2[/tex] *h
Substituting the values, we get:
V = (1/3)* π * [tex]r^2[/tex] *h
V = (1/3) * π * [tex](10 cm)^2[/tex] * (24 cm)
V = (1/3) *π * ([tex]100 cm^2[/tex]) * (24 cm)
V = 251.20 cubic centimeters.
Therefore, we can conclude that the volume of the cone is 251.20 cubic centimeters.
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