Answer:
Rate of change is 3 miles every 1 minute
equation: f(x)=x(3)
Step-by-step explanation:
according to the table, every minute eddy runs is another 3 miles he has traveled. therefor the equation would be f(x)=x(3) with x being the time in minutes. For example, if f(x) or the time in minutes was 4 then f(4)=4(3) which equals 12 miles as the table shows.
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An urn contains 19 red marbles, 29 blue marbles, and 43 yellow marbles. one marble is to be chosen from the urn without looking. what is the probability of choosing a red marble?
The probability of choosing a red marble is 1/6.
What is probability ?Probability is the chance of occurring a certain event out of total possible events that can order in a given situation.
According to the given question an urn contains 19 red marbles, 29 blue marbles, and 43 yellow marbles.
So there are total of ( 19 + 29 + 43 ) = 85 marbles.
∴ No. of sample space N(s) = 85.
No. of red marble N(red) = 19.
One marble is to be chosen from the urn without looking the probability of choosing a red marble P(red) is N(red)/N(s) which is
P(red) = 19/85
P(red) = 1/5.
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solve by completing the square t² - 6t = 7
Answer:
t = 7 or t = -1
Step-by-step explanation:
You can use a calculator or:
t² - 6t = 7
-> t² - 6t -7 = 0
-> t² - 7t + t - 7 = 0
-> t(t-7) + (t-7) = 0
-> (t-7) . (t+1) = 0
-> t = 7 or t = -1
Answer:
T = 7
Step-by-step explanation:
How you find T is by multiplying different numbers and squaring them by subtracting until you get to the number that equals to 7
please help! i can never understand these problems
Answer:
1234567891011121314151617181920
The answer please for my online class
Answer:
B. -500
Step-by-step explanation:
\( \dfrac{(2a^4)^2}{a^0a^5} = \)
\( = \dfrac{2^2a^8}{a^5} \)
\( = 4a^3 \)
\( = 4(-5)^3 \)
\( = 4(-125) \)
\( = -500 \)
Can you show the working out as well please?
Answer:
BC = 60
Step-by-step explanation:
3X + X = 80 <---- X = BC
3X + X = 4X
4X = 80 <---- DIVIDE BOTH SIDES BY 4
4X ÷ 4 = X
80 ÷ 4 = 20
20 × 3 = 60
Answer:
AB = 20 m
BC = 60 m
Step-by-step explanation:
Let AB be x
So BC becomes 3x
AC is 80 metres
So,
x+3x = 80
4x = 80
Dividing both sides by 4
x = 20
So,
AB = 20 metres
While
BC = 3(20) = 60 metres
what is the midpoint of segment AB if A and B are located a (2,-1) and (8,3)?
Answer:
(5,1)
Step-by-step explanation:
to fins the midpoint add both x points and divide by 2. then, both y points and divide by 2.
8+2/2 , 3-1/2
10/2 , 2/2
5 , 1
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use the method of lagrange multipliers to find the maximum volume of a rectangular box with its diagonal to be l
Consider a rectangular box with dimensions length (L), width (W), and height (H).The method of Lagrange multipliers can be used to find the maximum volume of a rectangular box with its diagonal length fixed at l.
Consider a rectangular box with dimensions length (L), width (W), and height (H). We want to maximize the volume of the box, V = LWH, subject to the constraint that the diagonal length is fixed at l.
To apply the method of Lagrange multipliers, we introduce a Lagrange multiplier λ and form the following function:
F(L, W, H, λ) = LWH + λ(D² - L² - W² - H²),
where D is the fixed diagonal length, and the term λ(D² - L² - W² - H²) is the constraint equation.
We then take partial derivatives of F with respect to L, W, H, and λ, and set them equal to zero to find critical points. Solving these equations, we obtain:
∂F/∂L = WH - 2λL = 0,
∂F/∂W = LH - 2λW = 0,
∂F/∂H = LW - 2λH = 0,
∂F/∂λ = D² - L² - W² - H² = 0.From equations (1)-(3), we find that WH = 2λL, LH = 2λW, and LW = 2λH. Dividing these equations, we get (WH)/(LW) = L/H, (LH)/(LW) = W/H, and (LW)/(LH) = W/L. Simplifying, we have L = W = H, which means the dimensions of the box are all equal.
Substituting L = W = H into equation (4), we have 3L² = D², or L = W = H = D/√3.
Therefore, the maximum volume of the rectangular box is (D/√3)³ = D³/√27.
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On june 1, 2021, portugal inc. reported a cash balance of $12,000. during june, portugal made deposits of $5,000 and made disbursements totalling $14,000. what is the cash balance at the end of june?
The cash balance at the end of June is $3000.
What are disbursements in accounting?The amounts transferring from one account to another are said to be disbursements in accounting.
So, there are subtracted from the initial balance to get the current balance.
Calculation:It is given that,
On June 1, 2021, Portugal inc. reported a cash balance of $12,000.
During June, Portugal made deposits of $5000 and made disbursements totaling $14,000.
The initial cash balance = $12,000
Made a deposit of $5000 = $12,000 + $50000
⇒ $17, 000
Also made disbursements of $14,0000
⇒ Cash balance at the end = $17,000 - $14,000 = $3000
Therefore, in the end, the cash balance is $3000.
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Convert 5 3/5 to a mixed number
It is a mixed number,
an improper would look like this,
\( \frac{20}{4} \)
and a mixed would look like this
\(2 \times \frac{6}{7} \)
What is the area of this figure? Use 3.14 for pi.
A. 4.5 mm2
B. 9 mm2
C. 11.56 mm2
D. 18.61 mm2
Answer:
Step-by-step explanation:
area of triangle = 1/2 * base * height = 1/2 * 9 = 9/2
area of semicircle = 22/7 * {3 root 2 / 2}^2 = 22/7 *18 / 4 = 22/7 *9/2 = 198/14=99/7
area of figure = 99/7 + 9 /2 =18.6mm2
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Answer:
area of figure= area of semi circle + area of triangle
area of semi circle= 1/2πr²
1/2×3.14×2.12×2.12
1/2×14.11
= 7.06
area of triangle = 1/2×base×height
but I am going to use the Pythagoras theorem to find the its height
= hypotenus² = base²+height²
3²=2.12²+h²
9=4.5+h²
9-4.5=h²
√4.5=√h²
h= 2.12
so area of triangle= 1/2×4.24×2.12
=4.5
area of figure = 70.6+4.5
= 75.1mm²
hope it helps even if its not correct just wanted to try
3
Natalie bought 3/4 pound flour for baking. She used 2/3 of the flour to make cookies. How many pounds of flour did she use?
Answer:
it blurry
Step-by-step explanation:
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
208, 204,200,...
Find the 45th term.
Step-by-step explanation:
please mark me as brainlest
Answer: 32
Step-by-step explanation:
This is an example of an arithmetic sequence as the difference between the first 3 terms is constant. We can see that 4 is constantly being subtracted.
\(a_{n}=a+(n-1)d\) is the formula for an arithmetic sequence.
\(a_{n}\) = nth term
a = the first term in the sequence
n = term you are looking for (in this case 45)
d = common difference between the terms (in this case -4)
∴
\(a_{n}=a+(n-1)d\)
\(a_{45} =208+(45-1)(-4)\\a_{45}=32\)
the early income of a girl is rupees 150000 the tax free allowance is rupees 100000 if the text for the first rupees 20000 is 12% and for the remaining is 15% how much tax should she pay in a year ?
Answer:
Rs 6900
Step-by-step explanation:
To calculate the tax amount the girl should pay in a year, we need to determine the taxable income and then apply the corresponding tax rates.
The taxable income is calculated by subtracting the tax-free allowance from the girl's early income:
Taxable Income = Early Income - Tax-Free Allowance
Taxable Income = 150,000 - 100,000
Taxable Income = 50,000
Now, we can calculate the tax amount based on the given tax rates:
For the first 20,000 rupees, the tax rate is 12%:
Tax on First 20,000 = 20,000 * 0.12
Tax on First 20,000 = 2,400
For the remaining taxable income (30,000 rupees), the tax rate is 15%:
Tax on Remaining 30,000 = 30,000 * 0.15
Tax on Remaining 30,000 = 4,500
Finally, we add the two tax amounts to get the total tax she should pay in a year:
Total Tax = Tax on First 20,000 + Tax on Remaining 30,000
Total Tax = 2,400 + 4,500
Total Tax = 6,900
Therefore, the girl should pay 6,900 rupees in tax in a year.
help plssss lolllllll
Answer:
12 in
Step-by-step explanation:
12 divided by 3 = 4
So every number is just divided by 4
12 divided by 4 = 3
20 divided by 4 = 5
16 divided by 4 = 4
Add them all together
3 + 5 + 4 = 12
12 is your answer
If QR = 5x, RS = x + 3, and QS = 9, what is QR?
The value of QR is 5
What is a line segment?A line segment can be defined as the part of a straight line bounded by two different end points, and also contains every point on the line between its endpoints.
From the information given, the line QS has segments, line QR , RS and QS with R and the midpoint between Q and S
Given the points;
QR = 5xRS = x + 3 QS = 9We have that;
QR + RS = QS
substitute the values
5x + x + 3 = 9
collect like terms
6x = 9 - 3
6x = 6
Make 'x' the subject
x = 6/ 6
x = 1
But QR = 5x = 5(1) = 5
Thus, the value of QR is 5
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The complete question;
If R is the midpoint of QS and QR = 5x, RS = x + 3, and QS = 9, what is QR?
What is the slope of the line that passes through the point (-4,-4)and (6,4)?
Answer:
slope = 0.8
Step-by-step explanation:
HOPE THIS HELPS :)
I need to know how to do this step by step. I'm having trouble with figuring out what comes first and What do I have to do next when solving the problem
The given inequality is
\(3y\leq2y+3\)First, we need to isolate y
To do that we want to move 2y from the right side to the left side, then
To do that subtract 2y from 3y and subtract 2y from (2y + 3)
\(3y-2y\leq2y-2y+3\)Since 3y - 2y = 1y
Since 2y - 2y = 0
\(\begin{gathered} 3y-2y\leq(2y-2y)+3 \\ 1y\leq0+3 \end{gathered}\)Since 0 + 3 = 3
Then the answer is
\(\begin{gathered} 1y\leq3 \\ y\leq3 \end{gathered}\)The answer is B
Find the values of x and y
The ratio of men to women working for a company is 5 to 6. If there are 102 women working for the company, what is the total number of employees?
Answer:
187 people
Step-by-step explanation:
5 to 6 is the same as 5/6. 5 is the men and 6 is the women. We know that there are 102 women so we can arrange this equation.
\(\frac{5}{6}\) = \(\frac{x}{102}\)
Re-arrange the equation to find x, or the number of men in the company.
\(\frac{(102*5)}{6}\) = x
x = 82
We have found the number of men in the company. Now add the number of men and women.
102 + 82 = 187
187 total people!
Answer: 187 employees
Step-by-step explanation:
ratio of men to women: 5:6
number women working for company: 102
to work out the number of men working for the company, you must first find out what you have to multiply 6 by to get to 102
therefore you do 102/6 which is 17
now you do 17x5 to work out how many men are working for the company which is 85
total number of employees: 102+85=187
A textbook is opened at random. What page numbers is the book opened to if the product of the opened page numbers is 132?
The book is opened to pages 11 and 12.
How to get the product of the page
So, we can write the equation:x * (x + 1) = 132
Expanding the equation, we get:
x² + x = 132
To solve for x, we need to rewrite the equation as a quadratic equation:
x²+ x - 132 = 0
Now, we can factor the quadratic equation:
(x - 11)(x + 12) = 0
This equation has two solutions for x:
x = 11
x = -12
Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.
So, the book is opened to pages 11 and 12.
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The numbers in this sequence increase by 30 each time. 20 50 80 110 The sequence continues in the same way. Which number in the sequence will be closest to 300?
The number in the sequence closest to 300 is 320.
What is sequence?
In mathematics, a sequence is an ordered list of numbers or other objects that follow a specific pattern or rule. Each element in the sequence is called a term, and the position of a term in the sequence is called its index.
To find the number in the sequence closest to 300, we can subtract 110 from 300 to get 190, and then divide by 30 to find how many additional terms we need to add to the sequence after 110:
(300 - 110) / 30 = 6
So we need to add 6 more terms to the sequence after 110.
The next term in the sequence after 110 is:
110 + 30 = 140
And the 6th term after that is:
140 + 30(6) = 320
So the number in the sequence closest to 300 is 320.
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What is the sum of 4 squared, 3 cubed and 2 to the fourth power?
Answer:
59
Step-by-step explanation:
4²+3³+2⁴
= (4×4) + (3×3×3) + (2×2×2×2).
= 16+27+16
= 59
Given: f(x) = 11(0.92)X
Is this exponential growth or decay?
What is the rate of growth or decay?
What was the initial amount?
A curve y=f(x) defined for values of x>0 goes through the point (1,0) and is such that the slope of its tangent line at (x,f(x)) is 4/x^2?7/x^6, for x>0.
The slope of the tangent line at (x,f(x)) is given by the derivative f'(x). Thus, we have: The function f(x) is:
f(x) = -4/x - (7/5)/x^5 + 27/5
f'(x) = 4/x^2 - 7/x^6
To find the function f(x), we need to integrate f'(x) with respect to x. We have:
∫ f'(x) dx = ∫ (4/x^2 - 7/x^6) dx
Integrating each term separately, we get:
f(x) = -4/x - 7/(5x^5) + C
where C is the constant of integration. We can find the value of C by using the fact that the curve passes through the point (1,0):
0 = -4/1 - 7/(5*1^5) + C
C = 4/5
Therefore, the function f(x) is:
f(x) = -4/x - 7/(5x^5) + 4/5
Note that this function is defined for x > 0, as specified in the problem statement.
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Evaluate the expression and write your answer in the form a+bi.
√−25
The express in the form of a + bi would be 0 + 5i.
What is meant by Complex numbers?Complex numbers are those expressed as a + ib, where a, b are real numbers and 'i' is a fictitious number called a "iota." i is equal to (√-1). A pair of real and imaginary numbers combined in the form a + bi.
When a and b are real numbers, a complex number is one with the formula a + bi. The complex number has two parts: real component (a) and imaginary part (b). If both the real and imaginary components of two complex numbers are identical, only then are the two complex numbers equal.
Let the given expression be \($\sqrt{-25}$$\).
We have to evaluate the expression.
\($$\begin{aligned}\sqrt{-25} & =\sqrt{-1 \cdot 25} \\& =\sqrt{-1} \sqrt{25} \\& =i(5) \\& =5 i\end{aligned}$$\)
The express in the form of a + bi = 0 + 5i.
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You roll a 6-sided die. What is P(1)? Write your answer as a fraction or whole number.
Answer:
1/6
Step-by-step explanation:
A die has equal sides of frequency, so, that means, P(1-6) would have an equal chance of on each side. The rate would be 1/6.
The solution is : Probability of getting 1 is, P(1) = 1/6.
What is probability?
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
given that,
You roll a 6-sided die.
now, we have to find the Probability of getting 1
we know that,
A die has equal sides of frequency, so, that means, P(1-6) would have an equal chance of on each side.
The rate would be 1/6.
i.e. total number of outcomes = 6
no. of favorable outcome for the event of getting 1 = 1
so, P(1) = 1/6.
Hence, Probability of 1 is 1 out of 6:
i.e. 1/6
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2) A contractor is installing some special light bulbs for two floors in a building. For the first floor, she purchased 5 natural-light bulbs and 2 ceiling bulbs at a cost of $23. For the second floor, she purchased 3 natural-light bulbs and 4 ceiling bulbs at a cost of $25. How much does each type of bulb cost?
By forming and solving the equations we know that the ceiling bulbs and natural bulbs cost $12.30 and $4.46 respectively.
What are equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.
An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others. Let's learn more about math equations in this tutorial.
So, we can form 2 equations as follows:
5n + 2c = 23 ⇒ n = (23 - 2c)5 ...(1)
3n + 4c = 25 ...(2)
Now, insert n = (23 - 2c)5 in equation (2).
3n + 4c = 25
3(115 - 10c) + 4c = 25
345 - 30c + 4c = 25
-26c = - 320
c = 12.30
Now, insert c = 12.30 in equation (1):
5n + 2c = 23
5n + 2(12.30) = 23
5n + 24.6 = 2.3
5n = -22.3
n = 4.46
Therefore, by forming and solving the equations we know that the ceiling bulbs and natural bulbs cost $12.30 and $4.46 respectively.
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A candy dish is filled with a mix of yellow and pink jelly beans Brian and Ali take turns picking a jelly bean without looking are these 2 events dependent or independent
Given:
Brian and Ali take turns picking a jelly bean without looking
Required: Dependent or independent event
Explanation:
Brian picked a jelly bean first and after Ali picked second. The probability of Ali picking up depends on the jelly bean.
Hence the events are depndent.
Final Answer: Dependent events
A cab company charges $2 per cab ride, plus an additional $3 per mile driven. How long is a cab ride that costs $47? Write and solve an equation to find the answer.
Answer:15 miles
Step-by-step explanation:
Subtract 2 from 47 because each ride is $2 then divide 3 from 45 to get 15 miles $3 per mile to check you could multiply to 15 to get 45.
please help me with this question
The correct simplified form of the expression is x + 5.
a) The mistake that Hannah has made is incorrectly combining the terms 3x and -2x. Instead of subtracting the coefficients of x, she subtracted the entire expression 2x from 3x.
b) To simplify the expression correctly, we need to combine like terms. In this case, the like terms are the ones with the variable x.
The expression 3x + 5 - 2x can be rewritten as (-2x + 3x) + 5.
Now, let's combine the like terms:
(-2x + 3x) + 5 = x + 5
Therefore, the correct simplified form of the expression is x + 5.
To further clarify, Hannah mistakenly thought that subtracting 2x from 3x would result in 1x (or just x). However, when subtracting or adding terms with the same variable, we need to consider the coefficients. In this case, 3x - 2x simplifies to x, not 1x.
It's important to pay attention to the signs and operations when combining terms. In this scenario, Hannah overlooked the need to subtract the coefficients of x and ended up with an incorrect result.
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