The clock face in a famous clock tower has a radius of about 5 meters. What is the area of the clock face to the nearest square meter? Use 3.14 as an approximation for pie.
Answers
Answer:
78.5m
Step-by-step explanation:
Area of circle = \(\pi\)r^2
Area of clock = 3.14 x 5^2 = 78.5m
Related Questions
A fivey sequence is a sequence of positive integers whose terms add up to $5.$ For example, $2, 2, 1$ and $2, 1, 2$ are two different fivey sequences. How many fivey sequences are there?
Answers
The number of the arrangement for the five sequences will be 6.
What are permutation and combination?Combination and permutation are two different ways in mathematics to divide up a set of elements into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a particular order.
Given that a sequence is a sequence of positive integers whose terms add up to $5.$ For example, 2, 2, 1 and 2, 1, 2.
The number of the ways will be calculated as:-
3! = 3 x 2
3! = 6
Hence, the number of the different arrangements for the sum of 5 will be 6.
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Question 5 (5 points)
What is the volume of the right prism?
35 in.
37 in.
12 in.
40 in.
Answers
The volume of the right prism include the following: 8,640 in³.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height or depth of a rectangular prism.Next, we would determine the area of the triangle at the base of the right prism as follows:
Base area = 1/2 × ( 36 × 12)
Base area = 1/2 × 432
Base area = 216 in².
Now, we can calculate the the volume of this right prism:
Volume = base area × height
Volume = 216 × 40
Volume = 8,640 in³.
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An elevator can carry 25 adults or 30 children at one time. During the course of a day, the elevator carries a full passenger load 36 times. If all the passengers were children, how many more people would the elevator carry than if all the passengers were adults?
Answers
180 people would the elevator carry than if all the passengers were adults.
What is the meaning of times?
The mathematical symbol is used to represent the multiplication operation and the consequent product. It is often referred to as the times sign or the dimension sign.
Given an elevator can carry 25 adults or 30 children at one time.
One day the elevator carries a full passenger load 36 times.
If the elevator carries all adults, then it carries (25 × 36) = 900 adults.
If the elevator carries all children, then it carries (30 × 36) = 1080 adults.
If all the passengers were children, then the elevator carry more than (1080 - 900) = 180 people if all the passengers were adults.
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If you deposit $1,000 every year in 20 years in a savings account that earns 7% compounded yearly. What is the future value of this series at year 20 if payments are made at the beginning of the period? $60,648.57 $43,865.18 $65,500,45 $40,995.49 If you deposit $3,000 every year for 15 years at an APR of 9% compounded monthly, what would be the future value at the end of this series? $90,757,36 $39,360.46 549,360,46 598,393,95 At what interest rate should you invest $1000 today in order to have $2000 dollars in 10 years? 7.2% 14.9% 6.2% 10%
Answers
The future value of depositing $1,000 every year for 20 years, with payments made at the beginning of each period, at an interest rate of 7% compounded yearly, is approximately $43,865.18.
To calculate the future value of a series of deposits, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value
P is the periodic payment
r is the interest rate per period
n is the number of periods
In this case, the periodic payment is $1,000, the interest rate is 7% (or 0.07), and the number of periods is 20.
Plugging these values into the formula, we get:
FV = 1000 * [(1 + 0.07)^20 - 1] / 0.07
= 1000 * [1.07^20 - 1] / 0.07
≈ 1000 * [2.6532976 - 1] / 0.07
≈ 1000 * 1.6532976 / 0.07
≈ 43,865.18
Therefore, the future value of this series after 20 years would be approximately $43,865.18.
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A fair coin is tossed three times. What is the probability that two heads will be obtained in succession
Answers
Answer:
3/8
Step-by-step explanation:
The state of a spin 1/2 particle in Sx basis is defined as (Ψ) = c+l + x) + i/√7 l - x) a) Find the amplitude c+ assuming that it is a real number and the state vector is properly defined. b) Find the expectation value . c) Find the uncertainty △SX.
Answers
1) The amplitude c+ is c+l
2) The expectation value is 0
3) The uncertainty ΔSX is √(3/7) c+.
Now, we know that any wave function can be written as a linear combination of two spin states (up and down), which can be written as:
Ψ = c+ |+> + c- |->
where c+ and c- are complex constants, and |+> and |-> are the two orthogonal spin states such that Sx|+> = +1/2|+> and Sx|-> = -1/2|->.
Hence, we can write the given wave function as:Ψ = c+|+> + i/√7|->
Now, we know that the given wave function has been defined in Sx basis, and not in the basis of |+> and |->.
Therefore, we need to write |+> and |-> in terms of |l> and |r> (where |l> and |r> are two orthogonal spin states such that Sy|l> = i/2|l> and Sy|r> = -i/2|r>).
Now, |+> can be written as:|+> = 1/√2(|l> + |r>)
Similarly, |-> can be written as:|-> = 1/√2(|l> - |r>)
Therefore, the given wave function can be written as:Ψ = (c+/√2)(|l> + |r>) + i/(√7√2)(|l> - |r>)
Therefore, we can write:c+|l> + i/(√7)|r> = (c+/√2)|+> + i/(√7√2)|->
Comparing the coefficients of |+> and |-> on both sides of the above equation, we get:
c+/√2 = c+l/√2 + i/(√7√2)
Therefore, c+ = c+l
The amplitude c+ is a real number and is equal to c+l
The expectation value of the operator Sx is given by: = <Ψ|Sx|Ψ>
Now, Sx|l> = 1/2|r> and Sx|r> = -1/2|l>
Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= -i/√7(c+l*) + i/√7(c+l)= 2i/√7 Im(c+)
As c+ is a real number, Im(c+) = 0
Therefore, = 0
The uncertainty ΔSX in the state |Ψ> is given by:
ΔSX = √( - 2)
where = <Ψ|Sx2|Ψ>and2 = (<Ψ|Sx|Ψ>)2
Now, Sx2|l> = 1/4|l> and Sx2|r> = 1/4|r>
Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= 1/4(c+l* + c+l) + 1/4(c+l + c+l*) + i/(2√7)(c+l* - c+l) - i/(2√7)(c+l - c+l*)= = 1/4(c+l + c+l*)
Now,2 = (2i/√7)2= 4/7ΔSX = √( - 2)= √(1/4(c+l + c+l*) - 4/7)= √(3/14(c+l + c+l*))= √(3/14 * 2c+)= √(3/7) c+
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Match the inequality to the word sentence it represents. D is greater than or equal to 60. The sentence is "The temperature did not drop below 60 degrees." Is D is greater than or equal to 60 the correct inequality?
Answers
Answer:
Yes, it is correct
Step-by-step explanation:
If the temperature did not drop below 60 degrees, that means that it only stayed at 60 degrees or was higher than 60 degrees.
D is greater than or equal to 60 is the right inequality then.
In triangle def, if m∠d = (4x)°, m∠e = (2x − 3)°, and m∠f = (x 8)°, what is the value of x? 51 29 26 25
Answers
Answer:
Step-by-step explanation:
The sum of the measures of the angles of a triangle is 180°.
m<D + m<E + m<F = 180°
4x + 2x + m<F = 180
What is the measure of <F? It's not clear in the post.
Marta earns 12.50 from babysitting and, and then spends some of her earnings on a new book. She has 8.00 of her earrings left. Write and solve an equation to find the cost of the book. And answer the questions above
Answers
Answer:
$12.50 - $8:00 = ? , ? = $4.50
Step-by-step explanation:
$12.50 earned from babysitting
Spends some on a new book
$8.00 left
12.50 - 8.00
0-0= 0 , 5- 0 = 5 , 12-8 = 4,
Reverse ur answer and add a dot (.) between 4 and 50
Answer: $4.50, $12.50 - $8:00 = ? , ? = $4.50
The water dam is filled up using the first tributary in 1 hour and 10 minutes, using the second
tributary in 60 minutes. How many minutes it takes to fill the half of the dam using both of the
tributaries, if the second tributary will be opened 12 minutes after the first one ?
Answers
Answer:
I would use quaro is is faster.
Step-by-step explanation:
C an someone show me step by step how to do this and correctly please
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
Answers
First, let's find the area of the rectangle. The rectangle has a height of 20 yards and a width of 10 yards + 12 yards = 22 yards. So the area of the rectangle is:
Area of rectangle = height x width
Area of rectangle = 20 yards x 22 yards
Area of rectangle = 440 square yards
Next, let's find the area of the two triangles. The triangle on the left has a base of 20 yards and a height of 45 yards. So the area of the triangle is:
Area of triangle 1 = (1/2) x base x height
Area of triangle 1 = (1/2) x 20 yards x 45 yards
Area of triangle 1 = 450 square yards
The triangle on the right has a base of 12 yards and a height of 20 yards. So the area of the triangle is:
Area of triangle 2 = (1/2) x base x height
Area of triangle 2 = (1/2) x 12 yards x 20 yards
Area of triangle 2 = 120 square yards
Finally, we can add up the areas of the rectangle and the two triangles to get the total area of the playground:
Total area = area of rectangle + area of triangle 1 + area of triangle 2
Total area = 440 square yards + 450 square yards + 120 square yards
Total area = 1,010 square yards
Therefore, the area of the playground is 1,010 square yards.
HOPE THIS HELPS
A: {-6, -3, 0, 3, 6}
B: {-5, -3, -1, 1, 2}
C: {-6, -5, -3, -1, 0, 3, 6}
D: {-6, 6}
Answers
Step-by-step explanation:
You need to find the function
Select the correct answer.
To solve this system of equations using substitution, what could be substituted in place of y in the first equation?
4x=5-2y
y-2x=7
Answers
Answer: y=2x+7
(this is a rearranged version of y-2x=7 from question)
Step-by-step explanation:
4x=5-2y
y-2x=7
i would rearrange the 2nd value into y intercept form y=mx+b
so move the -2x to the other side of the = sign by doing the opposite, +2x on both sides to isolate the y
y=2x+7
you didn't give any options for "correct answer" so i can't give
you A B C or D answers
what can that shape make
Answers
Answer:
Step-by-step explanation:
The shape will make a triangular pyramid. <33
(Try imaging the box plot all folded up!)
Answer:
triangle pyramid
Step-by-step explanation:
well when looking at the shape it doest make boxes on the sides, there triangles, so when you connect them all by closing it it turns into triangle pyramid
how do I evaluate this?
log of 0.001, base 10 equals x
Answers
Answer:
-3
Step-by-step explanation:
\(log_{n} n^{a} =a\\\)
\(0.001 = 10^{-3}\)
\(log_{10} 0.001=log_{10} 10^{-3} =-3\)
What is the change in elevation from -87.2 Feet to 33.6 Feet?
Answers
Answer:
120.8 feet
Step-by-step explanation:
Which of the following is an example of quantitative data?A. North America is moving across Earth's surface several centimeters per yearB. the river has flooded a low-lying areaC. the volcano is releasing much steamD. volcanoes are dangerousE. when held, one rock feels heavier than another rock
Answers
The example of quantitative data among the given options is option A. North America is moving across Earth's surface several centimeters per year
Quantitative data refers to numerical or measurable information. In option A, the statement provides specific numerical measurements by stating that North America is moving across Earth's surface several centimeters per year. This information can be quantified and measured, making it an example of quantitative data.
Options B, C, D, and E do not provide numerical or measurable information. They describe qualitative characteristics or observations that cannot be easily quantified or measured.
B. The river has flooded a low-lying area describes a qualitative observation of a flood occurrence.
C. The volcano is releasing much steam describes a qualitative observation of steam release.
D. Volcanoes are dangerous makes a general statement without providing specific numerical information.
E. When held, one rock feels heavier than another rock is a subjective comparison and does not provide specific quantitative measurements.
Therefore, option A is the example of quantitative data as it provides numerical information that can be measured and quantified.
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A motorboat travels 9 miles downstream (with the current) in 30 minutes. The return trip upstream (against the current) takes 90 minutes.
Answers
Given :
A motorboat travels 9 miles downstream (with the current) in 30 minutes.
The return trip upstream (against the current) takes 90 minutes.
To Find :
The speed of stream and motorboat.
Solution :
Let, speed of stream is u and speed of motorboat is v.
Now, we know distance is same in both case.
Distance( downstream ) = speed × time
\(9 = ( v +u ) \times 0.5\\\\v + u = 18\)....1)
Distance( upstream ) = speed × time
\(9 = ( v- u ) \times 1.5\\\\v-u = 6\)....2)
Solving equation 1 and 2 , we get :
v = 12 miles/hour and u = 6 miles/hour
Hence, this is the required solution.
Answer:
The speed of the stream is 6 mph, and the speed of the boat is 12 mph.
Step-by-step explanation:
Downstream:
9 miles in 30 minutes (0.5 hour).
9 mi / 0.5 h = 18 mph
Upstream:
9 miles in 90 minutes (1.5 h).
9 mi / 1.5 h = 6 mph
Let s = speed of stream.
The speed of the stream adds to the speed of the boat downstream and is subtracted fromt he speed of the boat upstream.
Let speed of boat be b.
b + s = 18
b - s = 6
Add the equations.
2b = 24
b = 12
b + s = 18
12 + s = 18
s = 6
The speed of the stream is 6 mph, and the speed of the boat is 12 mph.
Write the equation of the line that contains the
points (4, -7) and (1,5).
Answers
Answer:
y=-4x+9
Step-by-step explanation:
y=-4x+9
m=y2-y1/x2-x1
m= 5-(-7)/1-4
m=12/-3=-4
y=-7 m=-4 x=4 find b
y=mx+b
-7=4*4 +b
b=-7+16 = 9
n the linear regression model asy=X\beta+u, where the matrix X=(i : Z), where i is the unit vector : i=(1, ..., 1)' and Z is a matrix of n observations on k independent variables.
Ignoring the constant term in this model, an investigator obtains the least squares regressiony=Zb+\hat{u}, whereb=(Z'Z)^{-1}Zy.
1) Show thaty'y=b'Z'Zb+\hat{u}'\hat{u}
2) Is it possible to have the following statement ?
R^2=1-\frac{\hat{u}'\hat{u}}{\sum(y_i-\bar{y})^2}<0
Answers
In the statement R^2 = 1 - (∑(y_i - ȳ)^2) / (∑(y_i - ȳ)^2) < 0, the term (∑(y_i - ȳ)^2) represents the total sum of squares, and dividing it by itself results in a value of 1. Subtracting 1 from 1 also yields 0, so the minimum value for R^2 is 0, indicating no explanatory power.
1) To show that y'y = b'Z'Zb + ū'ū, we need to expand and simplify the expression.
Starting with y'y:
y'y = (Zb + ū)'(Zb + ū)
= (b'Z' + ū')(Zb + ū)
= b'Z'Zb + b'Z'ū + ū'Zb + ū'ū
Next, let's focus on b'Z'ū and ū'Zb:
b'Z'ū = (Z'Zb)'ū = b'Z'Z'ū (since (AB)' = B'A')
ū'Zb = (Zb)'ū = b'Z'ū (since (AB)' = B'A')
Since b'Z'ū and ū'Zb are equal, we can rewrite the expression as:
y'y = b'Z'Zb + 2b'Z'ū + ū'ū
Now, let's consider the term 2b'Z'ū. Recall that the least squares estimate of the error term is given by ū = y - Zb. Substituting this into the expression:
2b'Z'ū = 2b'Z'(y - Zb)
= 2b'Z'y - 2b'Z'Zb
Substituting this back into the original expression for y'y:
y'y = b'Z'Zb + 2b'Z'ū + ū'ū
= b'Z'Zb + 2b'Z'y - 2b'Z'Zb + ū'ū
= b'Z'Zb + ū'ū
Therefore, we have shown that y'y = b'Z'Zb + ū'ū.
2) No, it is not possible to have R^2 = 1 - (∑(y_i - ȳ)^2) / (∑(y_i - ȳ)^2) < 0. The coefficient of determination R^2 represents the proportion of the total variation in the dependent variable y that is explained by the independent variables in the regression model. It ranges between 0 and 1, where a value of 0 indicates that the independent variables have no explanatory power, and a value of 1 indicates a perfect fit of the model to the data.
The expression (∑(y_i - ȳ)^2) represents the total sum of squares, which is always non-negative since it involves squaring differences. Therefore, the term (∑(y_i - ȳ)^2) is always non-negative, and subtracting it from 1 in the denominator cannot yield a negative value. Hence, it is not possible for R^2 to be less than 0.
In the statement R^2 = 1 - (∑(y_i - ȳ)^2) / (∑(y_i - ȳ)^2) < 0, the term (∑(y_i - ȳ)^2) represents the total sum of squares, and dividing it by itself results in a value of 1. Subtracting 1 from 1 also yields 0, so the minimum value for R^2 is 0, indicating no explanatory power.
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Nutz and Boltz, Inc., employs one hundred people; eighty are lawyers and twenty are engineers. Albert, a lawyer at the company, is quiet, likes puzzles, and carries a calculator. Most people, when asked whether Albert is a lawyer or an engineer, will guess that he is an engineer. These people are using __________ to make this faulty guess. A correct guess would have been made if they had used __________.
Answers
Answer:
These people are using the representativeness heuristic to make this faulty guess. A correct guess would have been made if they had used base rate information.
Step-by-step explanation:
Representativeness heuristic occurs when the similarity of items or events causes individuals to be perplexed about the likelihood of a given result. People usually make the error of guessing that two comparable things or occurrences are more closely related than they are. Therefore, the similarity of an engineer and a calculator confuse the people to guess that Albert is an engineer.
Base rate information refers to the information provided by base rates which are a type of statistic that is used to describe the percentage of a population that exhibits a certain feature. Base rates suggest the likelihood of something based on the lack of other facts. Using the information in the question as an example, if 20% of the employees were engineers and 80% were lawyers, the base rate of lawyers is simply 80%. This implies that Albert is a lawyer, but we won't know for sure until we look at the total number of workers that the base rate information reveals that he is a lawyer.
Therefore, these people are using the representativeness heuristic to make this faulty guess. A correct guess would have been made if they had used base rate information.
Which of the following statements is not true of the test data approach in a test of computerised accounting system?
A. Test data tests only those controls which the auditor wishes to rely
B. Test data should consist of data related to all controls prevalent in the organization
C. The result of test data indicates that all the application and general controls are functioning properly
D. Test data processed by the client's computer programme under the auditor's control
Answers
The statement that is not true of the test data approach in a test of a computerized accounting system is B) Test data should consist of data related to all controls prevalent in the organization.
This statement is incorrect because the test data approach aims to test specific controls that the auditor wishes to rely on rather than all controls prevalent in the organization. The test data approach involves the creation of a set of test transactions that are processed by the client's computer program under the auditor's control.
The results of the test data are used to determine whether the application and general controls are functioning properly. By using this approach, the auditor can gain assurance that the system is functioning as intended and identify any control weaknesses that need to be addressed.
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the volume of hemisphere is 1527.4cm^3.find the radius of the hemisphere to the nearest whole whole number.(take π to be 22/7)
Answers
Answer:
radius of the hemisphere = 9 cm approx
Step-by-step explanation:
Volume of hemisphere = \(\frac{2}{3} \pi r^{3}\)
1527.4 = \(\frac{2}{3} * \frac{22}{7} * r^{3}\)
\(\frac{7*15274*3}{2*22*10}\) = \(r^{3}\)
\(\frac{320754}{440}\) = \(r^{3}\)
\(r^{3}\) = 729
r = \(\sqrt[3]{729}\)
r = 9 cm approx.
suppose that the annual rainfall in ferndale, california, is known to be normally distributed, with a mean of 35.5 inches and a standard deviation of 2.5 inches. what is the probability that the rainfall in a given year will exceed 31.5 inches in ferndale? (you may need to use the standard normal distribution table. round your answer to three decimal places.)
Answers
The probability that the rainfall in a given year will exceed 31.5 inches in Ferndale is 0.9452.
How to calculate the value?It is vital to know that the requirement to solve the probability between z-values is to know that the probability between the z-values is the difference between the probability of the greatest z-value and the lowest z-value.
In this case, the mean is 35.5 inches and a standard deviation of 2.5 inches
We want to find P(x > 31.5)
Z = X - U/ SD
where
SD = standard deviation
U = mean
Z = (31.5 - 35.5( / 2.5
Z = -1.6
P(x > 31.5) = P(z > -1.6)
= 0.9452
The probability is 0.9452.
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a math professor notices that scores from a recent exam are normally distributed with a mean of 73 and a standard deviation of 5. answer the following questions using integer values. (a) what score do 75% of the students exam scores fall below? integer-valued answer: (b) suppose the professor decides to grade on a curve. if the professor wants 2.5% of the students to get an a, what is the minimum score for an a? integer-valued answer:
Answers
The score that 75% of the students' exam scores fall below is 0.the 75th percentile is equal to the mean minus 1 standard deviation, or 73 - 5 = 0.
The 75th percentile of a normally distributed set is the point at which 75% of the data falls below that point and 25% of the data falls above that point. In this case, the 75th percentile is equal to the mean minus 1 standard deviation, or 73 - 5 = 0.
Question (b):
The minimum score for an A is -1
The 2.5th percentile of a normally distributed set is the point at which 2.5% of the data falls below that point and 97.5% of the data falls above that point. In this case, the 2.5th percentile is equal to the mean minus 2 standard deviations, or 73 - 2 * 5 = -1.
Here is a more detailed explanation of how to calculate the percentiles in these two questions:
Question (a):
The 75th percentile can be calculated using the following formula:
percentile = mean + (z * standard deviation)
where:
percentile is the desired percentilemean is the mean of the distributionz is the z-score for the desired percentilestandard deviation is the standard deviation of the distributionThe z-score for the 75th percentile is 0.6745. This can be found using a z-table or by using a calculator.
Plugging in the mean and standard deviation, we get the following:
percentile = 73 + (0.6745 * 5)
percentile = 0
Question (b):
The 2.5th percentile can be calculated using the following formula:
percentile = mean - (z * standard deviation)
where:
percentile is the desired percentilemean is the mean of the distributionz is the z-score for the desired percentilestandard deviation is the standard deviation of the distributionThe z-score for the 2.5th percentile is -1.96. This can be found using a z-table or by using a calculator.
Plugging in the mean and standard deviation, we get the following:
percentile = 73 - (-1.96 * 5)
percentile = -1
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On a map scale of 1:10,000, 5cm would represent what distance?
Answers
Answer:
500 m
Step-by-step explanation:
10,000x5 is 50000 cm, that is 5 m
Moira needs a total of 214 hours to finish reading a book. Yesterday, she read for 178 hours. Supply the correct numbers to complete the equation that can be used to determine the number of hours, h, that Moira needs to read to finish the book.
h + =
Answers
An equation that can be used to determine the number of hours, h, that Moira needs to read to finish the book is h + 178 = 214.
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the number of hours that is needed to read to finish the book and the total number of hours respectively, and then translate the word problem into algebraic equation as follows:
Let the variable h represent the number of hours.Let the variable T represent the total number of hours.Next, we would translate the word problem into an algebraic equation based on the fact that she read for 178 hours yesterday as follows;
h + 178 = T
Substituting the given parameters into the algebraic equation, we have the following;
h + 178 = 214
Solving for h, we have the following;
h = 214 - 178
h = 36 hours.
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6sin^2 (x) + 6sin (x) + 1 = 0
solve and show steps for the graph ( i already have the graph )
Answers
To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.
1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.
2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.
3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.
4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.
5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].
6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.
7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.
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According to the lesson, describe in detail how you would use a centimeter ruler to measure a match stick?
Answers
To use a centimeter ruler to measure a matchstick, place the ruler parallel to the matchstick, aligning the zero mark with one end. Identify the nearest centimeter mark and estimate the millimeter measurement by looking at the divisions between centimeters and smaller increments for more precision.
To begin, ensure the centimeter ruler is in good condition and properly calibrated. Lay the matchstick on a flat surface, making sure it is straight. Position the ruler next to the matchstick, aligning the zero mark with one end while keeping it parallel to the matchstick. Observe the other end of the matchstick and identify the nearest centimeter mark on the ruler to the left of the end point. This represents the whole centimeter measurement. Next, look at the lines or ticks between the whole centimeter marks. Each centimeter is divided into 10 millimeter intervals. Estimate the length of the matchstick by identifying the millimeter line that aligns with the end of the matchstick. For more precise measurements, use the smaller divisions on the ruler. Each millimeter is further divided into smaller increments called tenths of a millimeter. Estimate the length by identifying the smallest increment that aligns with the end of the matchstick. Record the measurement by noting the number of centimeters, followed by the number of millimeters (and tenths of millimeters, if necessary). Handle the matchstick carefully to avoid any damage or inaccuracies in the measurement..
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Ed earns $36 dollars for 3 hours of work. How much will he earn for 5 hours of work?
Answers
Answer:
$60
Step-by-step explanation:
First you must find how much he earns per hour. In order to do this, you must divide 36 by 3. This gets you 12. So, we know that Ed earns 12 dollars per hour. Now you just multiply this by 5 to get you answer (60).
Answer:
Ed will earn $60 for 5 hours of work
Step-by-step explanation:
36/3=12----Divide the money he makes($36 dollars) for the hours he works.(3 hours) To see how much he make an hour
12*5=60----Now that we know how much he makes a hour multiply this by however many hours you want.(5 hours) And you get 60.Just add your money symbol ($)
I hope this helped!