The equation of the linear function represented by the table in slope intercept form is f(x) = 2x + 2.
What is Linear Function?
A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.
Equation of the linear function in slope intercept form can be represented as y = mx + d, where m is the slope and d is the y intercept.
Slope is the change in y coordinates divided by the change in x coordinates.
y intercept is the point on the line where the line touches the Y axis.
Given points are (-2, -2), (2, 6), (6, 14) and (10, 22).
Consider the points (-2, -2) and (2, 6).
Slope, m = (6 - -2) / (2 - -2) = 8 / 4 = 2
So the equation becomes y = 2x + d
Substituting one of the points (2, 6) in the above equation,
6 = (2 × 2) + d
d = 2
So the equation is y = 2x + 2.
Hence the given linear function can be represented as f(x) = 2x + 2.
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The quotient of -20 and the sum of u and v
Answer:
-20 ÷ (u +v) or -20/(u +v)
Step-by-step explanation:
You want an expression that represents the quotient of -20 and the sum of u and v.
SumThe sum of two quantities is indicated with a plus (+) sign.
"The sum of u and v" is written in symbols as ...
u + v
QuotientThe wording "the quotient of a and b" means "a divided by b". It is written in symbols using a division sign or fraction bar:
a ÷ b or a/b
The desired quotient can be written as ...
-20 ÷ (u +v) or -20/(u +v)
__
Additional comment
The parentheses are needed so that the sum is computed before the quotient is computed. If the expression is typeset, the division bar does the grouping:
[tex]\dfrac{-20}{u+v}[/tex]
simplyfy
(2/x)/(1-4/x)
The result = 2/ (x-4) is obtained by simplifying the provided equation (2/x)/(1-4/x)
What is meant by fraction?A fraction represents a component of a whole or, more generally, any number of equal parts. As in one-half, eight-fifths, and three-quarters, a fraction in conversational English denotes the number of components of a specific size.A portion of something is called a fraction. When the numerator and denominator are split, a number is represented mathematically as a quotient. In a simple fraction, both are integers.A complicated fraction contains a fraction in either the numerator or denominator. Any fraction that is right has a numerator that is less than its denominator. In mathematics, there are three primary fraction types.There are three types of them: mixed fractions, improper fractions, and proper fractions. Fractions are terms with a numerator and a denominator.Given,
[tex]$\frac{\frac{2}{x}}{1-\frac{4}{x}}[/tex]
Use the fractional rule : [tex]$\frac{\frac{a}{b}}{c}=\frac{a}{b \cdot c}$[/tex]
[tex]$=\frac{2}{x\left(1-\frac{4}{x}\right)}[/tex]
Simplify [tex]$x\left(1-\frac{4}{x}\right): \quad x-4$[/tex]
Then we get,
[tex]$=\frac{2}{x-4}[/tex]
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Please help if you can, this is due in two days.
Answer:
8.8
Step-by-step explanation:
Property of similar triangles
Please help me with this question.
The value of x is in the quadrilateral PQRS is 1.6
What are similar quadrilateral?Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.
The ratio of the corresponding angle of a similar quadrilateral are equal.
This means that all quadrilateral are not similar if the ratio of their corresponding sides are not equal
Therefore AD/PS = DC/ SR
= 4/3.2 = 2/x
4x = 2× 3.2
4x = 6.4
divide both sides by 4
x = 6.4/4
x = 1.6
Therefore the value of x or line RS in the quadrilateral PQRS = 1.6
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According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately
two per 1,000 babies in a healthy baby nursery. The number climbs to an average of 30 per 1,000 babies in an intensive care
nursery.
Suppose that 1,000 babies from healthy baby nurseries were randomly surveyed. Find the probability that exactly two babies
were born deaf. Round answer to four decimal places
Answer:
Step-by-step explanation:
According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately two per 1,000 babies in a healthy baby nursery. The number climbs to an average of 30 per 1,000 babies in an intensive care nursery.
15. ______________________ a scientific procedure undertaken to make a discovery, test, a hypothesis or demonstrate a known or unknown fact
Experimentation is a scientific procedure undertaken to make a discovery, test, a hypothesis or demonstrate a known or unknown fact.
What is experimentation in scientific method?Experimentation in the scientific method is the process of testing a hypothesis or theory through the process of collecting data and making observations.
This involves designing and performing experiments to test the hypothesis or theory, and then analyzing the results to determine whether the hypothesis or theory is supported by the data or not.
Experimentation allows for the collection of direct evidence about the hypothesis or theory being tested, which can then be used to make informed decisions about the hypothesis or theory.
Experimentation is the ultimate test of a hypothesis or theory and is fundamental to the scientific method.
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a grocery store sells bananas for 0.70 per pound if the store sells 1/2 ton of bananas how much money will the store receive
Answer:
A ton is equal to 2000 pounds. So half a ton is equal to 2000/2 = 1000 pounds.
If the store sells 1000 pounds of bananas at a price of $0.70 per pound, the total revenue the store will receive is 1000 * $0.70 = $700.
Step-by-step explanation:
Table bellow shows the number of cups of coffee people drink completely the table and work out the mean number of cups of coffee
The mean number of cups of coffee will be 4.
How to calculate the meanThe sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. It is known as the "average" and is the most widely used central tendency measure.
A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
The mean number of cups of coffee will be:
= 140 / 35
= 4.
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esc Calculate the wavelength in meters of electromagnetic radiation that has a frequency of 1.82 x 10^8 s-1¹. (c = 3.00 X 10^8 m/s) k C #C [] CA 9 %
The wavelength in meters of electromagnetic radiation that has a frequency [tex]2.5[/tex] × [tex]10^{5}[/tex] .
How can you determine the electromagnetic radiation's wavelength at different frequencies?The wavelength in meters of electromagnetic radiation that has a frequency of [tex]1.82[/tex] ×[tex]10^{8}[/tex] s-1¹. (c = 3.00 X [tex]10^{8}[/tex] m/s) k C #C [] CA 9 %
The frequency f of electromagnetic waves, or, equivalently, the wavelength c/f, is used to classify them.
The characteristics of electromagnetic radiation include amplitude (brightness), wavelength, frequency, and period. We have shown that the frequency of a light wave is related to its energy by the equation E = h v E=hnu E=h.
v=1.210 3 Hz and
e=310 8 m/s equal v and e, respectively.
3×[tex]10^{8}[/tex]
λ = 2.5 ×[tex]10^{5}[/tex].
The wavelength in meters of electromagnetic radiation that has a frequency 2.5 × [tex]10^{5}[/tex].
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A water tank is being filled with water. Before water is pumped in, the water level in the tank is 14 inches high. After 20 minutes, the water level is 52 inches high.If t represents the time in minutes and h represents the water level, which of the following equations can be used to model this situation?A. h= 39+13tB. h=1.95t-13C. h=1.95t+13
The equation which can be used to model this situation is equals to the h = 1.9t + 14 , where h represents the water level , t represents the time in minutes.
We have, A water tank which is filled with water. Before pumping the water,
The level i.e., high of water in water tank
= 14 inches
After 20 minutes, the level of water in tank = 52 inches
We have to determine the equation to model this situation in form of time "t" in minutes. Let "h" be level of water increases from initial point/ level in t minutes. As the change in water level from initial to after 20 minutes = 52 inches - 14 inches = 38 inches
That is, water level increased 38 inches in 20 minutes. Then rate of increase in level = 38/20 = 1.9 inches per minutes
Now, the for time 't' the equation is formed by multiplying the rate of chenge of water level with 't' and adding initial water level.
=> h = 1.9t + 14
which is linear equation in two variables,i.e., h and t . Hence,the required equation model is h = 1.9t + 14 .
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the difference of two times a number and five is eight
Finney & Associates is an interior decorating firm in Tucson. The following costs were incurred in a project to redecorate the mayor's offices. • Direct material: $29,000 • Direct professional labor: $42,000 The firm's budget for the year included the following estimates: • Budgeted overhead: $800,000 • Budgeted direct professional labor: $640,000 Overhead is applied to contracts by using a predetermined overhead rate that is based on direct professional labor cost. Actual professional labor during the year was $655,000 and actual overhead was $793,000. Question What is the total cost to redecorate the mayor's offices?
The total cost to redecorate the mayor's office by Finney & Associates is $123,500.
How to compute the total production cost:The total production cost consists of direct materials, direct labor, and overhead costs.
The overhead cost can be computed using a predetermined overhead rate or activity-based costing rates.
In this situation, the predetermined overhead rate is the quotient of the budgeted overhead cost and the budgeted direct professional labor cost.
Direct material: $29,000
Direct professional labor: $42,000
Allocated overhead cost: $52,500
Total cost = $123,500
Budgeted overhead: $800,000
Budgeted direct professional labor: $640,000
Predetermined overhead rate = Budgeted overhead/Budgeted direct professional labor cost
= $1.25 ($800,000/$640,000)
Allocated overhead cost = $52,500 ($1.25 x $42,000)
Thus, Finney & Associates can reliably claim that they incurred a total cost of $123,500 in redecorating the mayor's offices.
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Question in picture, pls help
No, there do not exist nonzero constants a and b such that a p(x)+b.
What is nonzero constants?Nonzero constants are numerical values used in mathematical equations which cannot be reduced to zero. They are also referred to as non-zero numbers or constants. Non-zero constants can take on any real or complex number value that is not equal to zero. Non-zero constants are used in various areas of mathematics including linear algebra, calculus, statistics, geometry and trigonometry.
No, there do not exist nonzero constants a and b such that a p(x)+b. q(x) is a polynomial with degree 1. This is because the degree of the polynomial P(x) is 1 and the degree of the polynomial Q(x) is 2, so the degree of the sum of the two polynomials (a p(x)+b. q(x)) must be 2 or greater.
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In a year when the maximum income for Social Security was $118,500, Bart worked at two jobs. In one job he earned $99,112. In his second job, he earned $56,222.
Both of his employers took out Social Security tax. As a result, Bart had paid excess Social Security tax, and the government must return some of it to him. How
much does the government owe him for excess Social Security paid?
Answer:
The government owes Bart the excess Social Security tax that he paid, which is the amount of tax he paid on his income above the maximum income for Social Security. In this case, that would be $118,500 (the maximum income for Social Security) minus $99,112 (what he earned at his first job) minus $56,222 (what he earned at his second job) = $13,166. So the government owes Bart $13,166 for the excess Social Security tax he paid.
Answer:
Step-by-step explanation:
He earned a total of 155,334.
99112 plus 56222.
subtract the max income from the income total
155,334 - 118500 = 36834
He is owed the social security tax he paid on 36834.
The problem does not give the social security rate.
Please any assistance
Answer: y=-4x+4
Step-by-step explanation: the "+4" represents the y intercept, so (0,4)
Answer:
Step-by-step explanation:
3) The following are the trial balance and other information related to Soft Tech, a
consulting engineer.
Soft Tech, Consulting Engineer
Trial Balance
December 31, 2022
Debit Credit
Cash Br. 59,000
Accounts Receivable 99,200
Allowance for Doubtful Accounts Br. 1,500
Supplies 3,920
Prepaid Insurance 2,200
Equipment 50,000
Accumulated Depreciation—Equipment 12,500
Notes Payable 14,400
Share, Capital 104,020
Dividend 34,000
Service Revenue 200,000
Rent Expense 19,500
Salaries and Wages Expense 61,000
Utilities Expense 2,160
Office Expense 1,440
Br. 332,420 Br. 332,420
Other data:
1. Fees received in advance from clients Br.12,000.
2. Services performed for clients that were not recorded by December 31,
Br.9,800.
3. Bad debt expense for the year is Br.2,860.
4. Insurance expired during the year Br.960.
5. Equipment is being depreciated at 10% per year.
6. Fine Tech gave the bank a 90-day, 10% note for Br.14,400 on December 1,
2022.
7. Rent of the building is Br.1,500 per month. The rent for 2022 has been
paid, as has that for January 2023.
8. Salaries and wages earned but unpaid December 31, 2022, Br.5,020.
Instructions
a. From the trial balance and other information given, prepare annual
adjusting entries as of December 31, 2022.
b. Prepare the worksheet
c. Prepare an income statement for 2022, a statement of owner’s equity,
and a classified statement of financial position.
d. Maintain the necessary closing entry.
Briefly describe each of the six guidelines for establishing causality. Give an example of the application of each guideline. Select the correct answer below
Six guidelines for determining causality:
The first guideline is to look for situations where results correlate with suspected causes, even if other factors differ.The second guideline states that groups that differ only in the presence or absence of the suspected cause should be similarly tested for the presence or absence of the effect.A third guideline states that evidence should be sought that the more suspected causes, the more consequences.The fourth guideline states that if an effect could be produced by other possible causes, it should be confirmed that the effect is still present after considering those other potential causes. I'm here.The fifth guideline states that suspected causes should be tested experimentally. The sixth rule is physical Suspected underlying mechanism The effect must be determined to generate.About causalityCausality is a term that refers to the principle of cause and effect, in which knowledge and information can be known automatically without the need for knowledge and mediation from other sciences. that every action derives its certainty and necessity, and the peculiarity of its existence, from some of the former, are things which are accepted without doubt and require no refutation. The necessity and originality of causal systems are parts of humanity, known collectively and beyond doubt.
Cause and effect are defined by the relationship between one event (cause) and another event (effect), where the second event is understood as the result of the first.
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indicate which of the following sentences are statements. (select all that apply.) A. 1,024 is the smallest four-digit number that is a perfect square. B.he is a mathematics major. C.128=26 D.X=26
D. X=26 is a mathematical statements, since it can be either correct or incorrect.
To comprehend any mathematical statement, we must first understand what mathematics is all about. When we answer a math problem, the solution is either correct or incorrect. There is no midway to the problems! Any mathematical statement is in the same scenario. A mathematical statement is either correct or incorrect.
In this scenario, the statement, 'A. 1,024 is the smallest four-digit number that is a perfect square.', and 'B. He is a mathematics major.' are correct statements. And 'C. 128=26' is a incorrect statement. Therefore, these options are not the mathematical statements because A and B is correct statement and C is a false statement. Meanwhile, D. X=26 is a mathematical statement because it is either correct or incorrect, depending on the given problem. Therefore D. X=26 is the correct answer for a mathematical statement.
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solve each of the given inequalities for z. Which of the inequalities has 5 as a solution
The inequality 4(2.8z + 1.75) > -26.6 has 5 as a solution and its solution is, z > - 3.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequalities are,
⇒ 4(2.8z + 1.75) > -26.6
⇒ 2(1.9z + 1.5) ≤ 18.2
Now, We can solve the inequalities as;
1) ⇒ 4(2.8z + 1.75) > -26.6
Divide by 4;
⇒ 2.8z + 1.75 > - 6.65
Subtract 1.75 both side,
⇒ 2.8z > - 6.65 - 1.75
⇒ 2.8z > - 8.4
Divide by 2.8;
⇒ z > - 8.4/2.8
⇒ z > - 3
Clearly, z = 5 is the solution of the above inequality.
2) 2(1.9z + 1.5) ≤ 18.2
Divide by 2;
⇒ 1.9z + 1.5 ≤ 9.1
Subtract 1.5 both side,
⇒ 1.9z ≤ 9.1 - 1.5
⇒ 1.9z ≤ 7.6
Divide by 1.9;
⇒ z ≤ 7.6/1.9
⇒ z ≤ 4
Clearly, z = 5 is not the solution of the above inequality.
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The complete question is this,
Solve each of the given inequalities for z. Which of the inequalities has 5 as a solution?
Inequality 1 Inequality 2
4(2.8z + 1.75) > -26.6 2(1.9z + 1.5) ≤ 18.2
HELPP PLSS What is the measurement of ∠Z
Answer:
Z = 155
Step-by-step explanation:
You know all the angles inside the triangle.
180 - 65 - 90 = X
X = 25
Thus using the supplementary rule (All straight lines have degree of 180), then you can get Z
180 - X = Z
180 -25 = Z
Z = 155
Please I need help , thanks
Answer:
y = -3/4 x + 3
Step-by-step explanation:
y = mx + b You need the m value (slope) and the b (y-intercept value) to the write the equations.
Slope:
Look that the two intercepts of x (4,0) and the y intercept of (0,3). If you start and (4,0) and go up 3 and left 4, you will land back on the line at the point (0,3). Slope is the rise over the run. The rise is up and positive 3. The run is left and negative -4
3/-4 is the same as -3/4
-3/4 is the slope.
y-intercept:
The y intercept is at the point (0,b) In this case, the point is (0,3).
3 is the y-intercept.
y = mx + b Substitute -3/4 for m and 3 for b
y = -3/4 x + 3
The table represents a linear relationship.
x −1 0 1 2
y 2 0 −2 −4
Which of the following graphs shows this relationship?
W
Answer:
Where is the graph
Step-by-step explanation:
I need it
i don’t understand and cant find the formulas to find these things
Answer:
7.30%; $1452.024.45%; 15.56 yearsStep-by-step explanation:
You want the interest rate and account balance after 10 years if the investment of $700 doubles in 9 1/2 years with interest compounded continuously. And, you want the interest rate and doubling time if a $900 investment has a value of $1405 after 10 years with continuous compounding.
Compound interestThese problems are solved by making use of the compound interest formula for continuously compounded interest. In each case, you fill in the values you know, and solve for the one you don't know.
A = Pe^(rt)
$700The investment doubles after 9.5 years, so we have ...
2·700 = 700e^(9.5r)
Dividing by 700 and taking natural logs, we find the rate to be ...
ln(2) = 9.5r
r = ln(2)/9.5 ≈ 0.072963 ≈ 7.30%
Using the exact value in the computation of the balance, we get ...
A = 700e^(10·(ln(2)/9.5)) = 700·2^(10/9.5) = 700·2^(20/19)
A = 1452.02
The annual rate is 7.30%; the balance in 10 years is $1452.02.
$900The balance after 10 years is ...
1405 = 900e^(r·10)
ln(1405/900) = 10r
r = ln(1405/900)/10 ≈ 0.0445398 ≈ 4.45%
As we found above, the relation between r and doubling time is ...
r = ln(2)/t ⇒ t = ln(2)/r
t = ln(2)/0.0445398 ≈ 15.56 . . . . years
The annual rate is about 4.45%; the doubling time is about 15.56 years.
__
Additional comment
In the first problem, we could find the account balance after 10 years using the found interest rate. In that case, it would be $1452.56. Instead, we chose the doubling time to be the exact value in the problem.
There is a "rule of 70" or sometimes the "rule of 72" that tells you the approximate doubling time in years (y) for an interest rate of r%. It is ...
y = 70/r
The amount of error depends on the interest rate and the way interest is compounded.
When the interest is compounded continuously, a slightly different rule gives the exact doubling time:
y = 100·ln(2)/r ≈ 69.31472/r
This is effectively the rule we used above.
What is the Area of this Shape?
Answer:
38.5
Step-by-step explanation:
rectangle = (2.5x2)+1.5=6.5
6.5x5=32.5
both triangle = 4/2 = 2
(1.5x2)x2=6
total area = 32.5 + 6 = 38.5
four more than h is no less than 27.
Answer:
Below
Step-by-step explanation:
four more than h is h+4
no less than 27 means it is greater than or equal to 27
h+4 >= 27
Height in P
0
-1
0.5
1
Time in Seconds (t)
function:
2
h(t) = -16t² + 12t
Move the blue lines to indicate where the basketball
player is going UP in the air.
Complete these sentences (reminder: you can click on
the graph to locate certain values).
The player starts going up at
2.25
The player stops going up at
1.76
NC
seconds.
In mathematical terms, when would the player be
rising?
(0,0.375)
seconds.
WELL
TITT
US
Jan 29s
The quadratic function for the height of the player, h(t) = -16·t² + 12·t indicates the following
The player starts going up at 0 seconds
The player stops going up at 0.375 seconds
The player would be rising in the interval [0, 0.375)
What is a quadratic function?A quadratic function is a function that can be expressed as; f(x) = a·x² + b·x + c, with the values of a, (a ≠ 0) b, and c representing numbers.
The function for the height is; h(t) = -16·t² + 12·t
The time the player starts going up can be found as follows;
The minimum height = -1
When h(t) = -1, we get; -1 = -16·t² + 12·t
-16·t² + 12·t + 1 = 0
Therefore, t = (3 ± √13)/8
t ≈ 0.826 and t ≈ -0.076
However, the value of the time is a natural number, therefore;
The player starts going up at t = 0 seconds.The player stops going up at the maximum height, which can be obtained from the value of the maximum point of a quadratic function, which is; t = -12/(2 × (-16)) = 3/8 = 0.375
The player stops going up at 0.375 secondsIn mathematical terms the player will be rising between the interval, 0 ≤ t < 0.375, which can be expressed as; [0, 0.375)
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The first 4 terms in a sequence are 8,5,2,-1 What is the recursive equation?
Answer: The recursive equation for this sequence is t(n+1)=t(n) - 3.
Step-by-step explanation:
The recursive equation for the given sequence is t(n+1) = t(n) - 3. This means that to find the next term in the sequence, we take the previous term and subtract 3 from it.
For example:
t(1) = 8 (first term in the sequence)
t(2) = t(1) - 3 = 8 - 3 = 5 (second term in the sequence)
t(3) = t(2) - 3 = 5 - 3 = 2 (third term in the sequence)
t(4) = t(3) - 3 = 2 - 3 = -1 (fourth term in the sequence)
In general, the recursive equation t(n+1) = t(n) - 3 will give the nth term of the sequence.
It should be noted that the initial condition provided in the question t(0)=-3, t(n+1)=t(n) +11 is incorrect and will not give the same sequence.
A and B are points on a polygon. A’ and B are the points under a translation. Find B’
By translation the point B' on the polygon is (0, -8).
What is translation?If the point (x, y) is translated h unit to the right and k unit to the up, its image is (x + h, y + k) and the translation is (h, k)If the point (x, y) is translated h unit to the left and k unit to the right, its image is (x - h, y + k) and the translation is (-h, k)If the point (x, y) is translated h unit to the right and k unit to the bottom, its image is (x + h, y - k) and the translation is (h, -k)If the point (x, y) is translated h unit to the left and k unit to the right, its image is (x - h, y - k), and the translation is (-h, -k)Let us try to answer the question.
The coordinates of point A are as follows: (4, 5)
x = 4 and y
The coordinates of point A' are as follows: (9, -1)
x' = 9 and y' = -1
That is, in the third case above, x increased and y decreased.
The point A has been moved to the right and down.
Using the third rule above (x + h, y - k),
x + h = 9
x = 4
Multiply x by 4.
4 + h = 9
Subtraction of 4 from both sides
4 - 4 + h
= 9 - 4
h = 5
y - k = -1
y = 5
Substitute 5 for y
5 - k = -1
Subtraction of 5 from both sides
5 - 5 - k = -1 - 5
-k = -6
Divide each side by -1.
k = 6
In the third case, the translation is (h, -k).
h = 5 and k = 6
The literal translation is (5, -6)
To find B' the image of the point B
B = (-5, -2)
B' = (x + h, y - k)
B' = (-5 + 5, -2 - 6)
B' = (0, -8)
The complete question is :
" A and B are points on a polygon. A' B' are points of the polygon under a translation. Find B'.
A(4,5) A' (9,-1)
B (-5,-2) B' (0,-8)."
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NO LINKS!!
Shown in the figure is a cross-section of a design for a two-story home. The center height h of the second story has not yet been determined. Find h such that the second story will have the same cross-sectional area as the first story.
h = __________ ft
Answer:
h = 13 ft
Step-by-step explanation:
The cross-sectional area of the first story is the area of a rectangle with width 30 ft and height 8 ft. The area of a rectangle is the product of its width and height.
[tex]\begin{aligned}\implies \textsf{Cross-sectional area of first story}&=30 \times 8\\&=240\; \sf ft^2\end{aligned}[/tex]
The cross-sectional area of the second story is made up of a rectangle with width 30 ft and height 3 ft, and a triangle with base 30 ft and height (h - 3). The area of a triangle is half the product of its base and height.
[tex]\begin{aligned}\implies \textsf{Cross-sectional area of second story}&=(30 \times 3)+\dfrac{1}{2} \times 30 \times (h-3)\\&=90+15(h-3)\\&=90+15h-45\\&=(15h+45)\; \sf ft^2\end{aligned}[/tex]
If the second story has the same cross-sectional area as the first story, then:
[tex]\implies 15h+45=240[/tex]
To find h, solve the equation:
[tex]\begin{aligned}\implies 15h+45&=240\\15h&=195\\h&=13\; \sf ft\end{aligned}[/tex]
Therefore, the value of h such that the second story will have the same cross-sectional area as the first story is 13 ft.
A monument is constructed by first laying a row of 60 bricks at ground level. A second row, with two fewer bricks, is centered on that; a third row, with two fewer bricks, is centered on the second; and so on. The top row contains 10 bricks. How many bricks are there in the monument?
Let's call the number of bricks in the ith row as B_i. Then, B_i = 60 - 2 * (i - 1) for i = 1, 2, ..., n, where n is the number of rows.
The number of bricks in the monument can be found by summing up the bricks in each row. So, the total number of bricks is:
T = B_1 + B_2 + … + B_n
= 60 + (60 - 2) + (60 - 4) + … + (60 - 2 * (n - 1))
= 60 * n + (-2) * (1 + 2 + … + (n - 1))
To find the sum of 1 to (n-1), we can use the formula for the sum of an arithmetic series: S_n = n * (a_1 + a_n) / 2, where a_1 = 1 and a_n = n - 1.
Substituting these values into the formula, we get: S_n = (n - 1) * (1 + (n - 1)) / 2 = (n - 1) * n / 2.
Therefore, T = 60 * n + (-2) * (n - 1) * n / 2 = 30 * n^2 + 30 * n.
Finally, to find the number of bricks for n = 10 rows, we substitute n = 10 into the equation:
T = 30 * 10^2 + 30 * 10 = 300 + 300 = 600
So, there are 600 bricks in the monument.
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The weight of a sphere is proportional to its radius cubed. If a sphere of diameter 1 cm has a mass of 10 grams, what diameter sphere has a mass of 640grams?
Answer:
if 1cm-10grams
what Abt 640 grams=64cm
