The rate at which the speed of the wind changes at the 50th mile is 258.114 miles per hour
How to estimate the rate at which the speed of the windFrom the question, we have the following parameters that can be used in our computation:
Function: S(d) = 86log d + 112
Express the above function properly
So, we have the following representation
S(d) = 86log(d) + 112
From the question, we have:
Distance = 50th mile.
This means that
d = 50
Substitute the known values in the above equation, so, we have the following representation
S(50) = 86log(50) + 112
Evaluate the logarithm
So, we have the following representation
S(50) = 86 * 1.699 + 112
Evaluate the products
S(50) = 146.114 + 112
Lastly, we have
S(50) = 258.114
Hence, the speed is 258.114 miles per hour
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What is the Pythagorean theorem? How do you use it to find the length of a missing side in a right triangle? Give an example and show your work.
The sum of squares of two sides of a triangle is equal to another side of a triangle is called the Pythagorean theorem.
It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
c^2=a^2+b^2--------(1)
Where a,b, and c are sides of a triangle.
To measure the length of the missing side in a right triangle using the Pythagorean theorem:
c^2=a^2+b^2
By using this formula we can find the length of a missing side.
To understand more we have to solve an example:
let A, B, and C are points of a triangle AB, BC, and CA are the sides of the triangle.
Consider BC=3cm CA=4cm AB=?
Use equation(1) to find the length of AB
AB^2=BC^2+CA^2
AB^2=3^2+4^2
AB^2=9+16=25
AB=5cm
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green and yellow dye are mixed in a 5:6 ratio to make 44 litres of lime-coloured dye. A further 8 litres of yellow dye are added to the mixture.
What is the new ratio of green to yellow dye in its simplest form?
Answer:
62.5% or in decimal form 0.625
Step-by-step explanation:
Help me? Care to explain also?
*Gives Brainliest for best ans easy to read answer!*
Answer:
B
Step-by-step explanation:
Answer: The answer is B
Step-by-step explanation:
if you divide 7 by 12 you will get a decimal and a non terminating 3
The cash price of a refrigerator is rs 34 500. The hire purchase price is a deposit of Rs 6500 and 10 % simple interest on the outstanding balance,to be paifd in 24 monthly installments.Calculate the amount of each monthly instalment.
Amount of each monthly statement is 1400.
According to question ,
Cash price of refrigerator =34500
Deposit money=6500
Outstanding money=28000
Rate of interest=10%
Time period=24 months or 2 years
∴Simple interest =(principal ×rate of interest×time)÷100
⇒(28000×10×2)÷100
⇒5600
∴The total amount to be paid in 2 years is 28000+5600 =33600
∴Amount to be paid in one month =33600÷24=1400
∴Amount of each monthly statement is 1400.
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What is ALWAYS true about the
coordinates of x-intercepts?
the x-value will be 0
the x-value will be equal to the y-value
the y-value will be 0
Answer:
The y-value will be 0
Step-by-step explanation:
The x-value will be 0 when we find the y-intercept
the x-value will be equal to the y-value is only at origin (0,0)
The answer is the y-value will be 0
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
What is the distance between points F and G?
Help please
A.) (-12,-18)
B.) (18,12)
C.) (-18,-12)
D.) (12,-18)
I think the answer be 12 and -18 D
Find the value of x and the two equations
× is 7
(7×+5) is 54
(5×+19) is 59
At a birthday party, Samuel ate
Complete the statement:
1
10
of the birthday cake.
If the cake can be represented as 1 =
10
10
that means we can find out how much cake is left by taking
and then subtracting the amount Samuel ate.
The expression [DROP DOWN 1] represents this situation.
10
10
If the cake can be represented as 1 = 10/10, that means we can find out how much cake is left by taking and then subtracting the amount Samuel ate. The expression [1 - 1/10] represents this situation.
How to complete the expressionFrom the question, we have the following parameters that can be used in our computation:
Cake = 1 or 10/10
Samuel's bite = 1/10
The amount remaining is calculated as
Amount remaining = Cake - Samuel's bite
Substitute the known values in the above equation, so, we have the following representation
Amount remaining = 1 - 1/10
The above represents the required expression
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b) Without a calculator, evaluate (0.1)² = (0.1)4
Answer:
false
Step-by-step explanation:
The left side equals 0.01
The right side equals 0.4
The two sides are not equal. This is a false equation.
Answer:0.01=0.0001
Step-by-step explanation:
what is the answer to 3^4 + 18 ÷ 3 +2
Answer:
89
Step-by-step explanation:
[tex] {3}^{4} + \frac{18}{3} + 2 \\ = 82[/tex]
o Answer:
It's 89 and I didnt mean to reaspond to this question so report it
Jess has a 4-digit password for her mobile phone.
Each digit can be between 0 and 9 inclusive.
a How many choices are possible for each digit of the code?
b What is the total number of 4-digit passwords that Jess can create?
Jess would like to choose an even number.
The code can start with a zero.
c How many different ways are possible now?
a. The number of choices possible for each digit of the code is of: 10.
b. The total number of 4-digit passwords that Jess can create is of: 10,000.
c. The number of different ways to create even passwords is of: 5,000.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial, according to the rule presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Each digit can be between 0 and 9 inclusive, hence the number of outcomes possible for each digit of the password is given as follows:
10.
The password is composed of four digits, hence the total number of passwords possible is of:
N = 10 x 10 x 10 x 10 = 10,000.
Considering that Jess would like an even number, there are only five outcomes possible for the last digit (0, 2, 4, 6 or 8), hence the number of outcomes is of:
N = 10 x 10 x 10 x 5 = 5,000.
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please help me with this question
many thanks
Answer:
111 girls
Step-by-step explanation:
You have 924 people classified as 383 men, 356 women, and the remainder children. 2/5 of the children are boys, and you want to know the number of girls.
GirlsThe number of children is ...
924 -383 -356 = 185
The 3/5 of children that are not boys are girls, so ...
girls = 3/5(185) = 111
There are 111 girls in the theater.
If 5 log 3 3x=15, what is the value of x?
The value of x for the expression 5log(3x) = 15 is 6.7.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 5log(3x) = 15. The value of x for the expression will be calculated as,
5log(3x) = 15
log(3x) = 15 / 5
log(3x) = 3
3x = e³
x = 20 / 3
x = 6.7
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Polynomial uing Remainder Theorem and Factor Theorem checking uing ynthetic diviion. X^4 - x^3 - 3x^2 4x 2 ÷ (x 2)
The remainder of the polynomial using the remainder theorem and factor theorem is 6.
Apply the remainder theorem,
When we divide a polynomial
f(x) by (x − c)
f(x) = (x − c)q(x) + r
f(c) = 0 + r
Here,
f(x)=(x−c)q(x)+rf(c)=0+r
and (x−c) is (x−(−2))
Therefore,
f(−2) = [tex](-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2[/tex]
= 16 + 8 − 12 − 8 + 2
= 6
Hence, the remainder of the polynomial using the remainder theorem is 6.
Whereas using the factor theorem and doing synthetic division, we get,
x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide
the coefficients of the polynomial as follows -
-2 | 1 -1 -3 4 2
-2 6 -6 4
-----------------------------------------
1 -3 3 -2 6
Hence, we get that 6 is the remainder when ([tex]x^4-x^3-3x^2+4x+2[/tex]) ÷ (x+2), using the factor theorem.
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The complete question is -
Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, [tex]x^4-x^3-3x^2+4x+2[/tex] ÷ (x+2)
15. Robert wants to invest $20,000 in an account
with an annual interest rate of 1.9%. How much
extra will he have after two years if he
compounds continuously, instead of collecting
simple interest monthly? Round answer to the
nearest dollar.
[A] $800
[B] $750
[C] $711
[D] $683
[E] $821
To find the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly, we need to calculate the compound interest on the investment.
The compound interest is calculated by multiplying the principal (the initial amount invested) by the compound interest rate, raised to the power of the number of compounding periods. In this case, the compound interest rate is 1.9%/12 = 0.158% per month, and there are 12*2 = 24 compounding periods (12 months per year for 2 years).
The compound interest is therefore calculated as follows:
Compound interest = $20,000 * e^(0.158%*24) - $20,000
= $20,000 * e^0.3832 - $20,000
= $20,000 * 1.454 - $20,000
= $4,080 - $20,000
= -$15,920
So the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly is -$15,920. Therefore, the correct answer is [A] $800.
x^2-12x+43 i need some help with this maths question
In order to solve a quadratic equation with one unknown, we need to factor it. If at first glance we can't find easy roots, we do a discrimination.
[tex]f(x)=x^2-12x+43[/tex]Δ[tex]f(x)=b^2-4ac=(-12)^2-4(43)[/tex]Δ[tex]=-28[/tex]If this value is less than zero, Δ[tex]< 0,[/tex] we determine that it has no solution belonging to the set of real numbers. We will find a conjugate and two complex roots. ([tex]a+bi[/tex])
Let's use the following formulas to find the roots.
[tex]x_{1}=\frac{-b-\sqrt{D} }{2a}= \frac{12-\sqrt{-28} }{2}=6-\sqrt{7}i[/tex][tex]x_{2}=\frac{-b-\sqrt{D} }{2a}= \frac{12+\sqrt{-28} }{2}=6+\sqrt{7}i[/tex]Complex Solutions:
[tex]6+\sqrt{7}i[/tex][tex]6-\sqrt{7}i[/tex]A pair of positive integers a and b is such that their greatest common divisor is 5 and their least common multiple is 55. Find the smallest possible value of a+b.
Answer:
Step-by-step explanation:
The greatest common divisor of two integers a and b is a divisor common to both integers that is greater than any other common divisor. The least common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b.
To find the smallest possible value of a+b, we can start by trying to find the smallest possible values of a and b that satisfy the given conditions.
Since the greatest common divisor of a and b is 5, we know that both a and b must be divisible by 5. We can write a = 5x and b = 5y, where x and y are positive integers.
The least common multiple of a and b is 55, so we know that both a and b must be factors of 55. We can write 55 as the product of its prime factors: 55 = 5 * 11. Since a is divisible by 5, we know that a must be equal to 5 or 25. Similarly, since b is divisible by 5, we know that b must be equal to 5 or 25.
There are four possible pairs of values for a and b: (5,5), (5,25), (25,5), and (25,25). The smallest of these is (5,5), which gives us a+b = 5+5 = 10. Therefore, the smallest possible value of a+b is 10.
Tamba jut received a bonu which increaed hi dipoable income by $860. If Tamba' marginal propenity to conume (mpc) i 0. 75, hi conumption rie by _______
The formula for calculating the change in consumption is MPC x Change in Disposable Income.Thus, Tamba's change in consumption = 0.75 x $860 = $645
The marginal propensity to consume (MPC) is a measure of the proportion of an increase in disposable income that is spent on consumption. In Tamba's case, his MPC is 0.75, which means that for every $1 increase in his disposable income, he will spend 75 cents on consumption. The formula for calculating the change in consumption is MPC x Change in Disposable Income. Therefore, when Tamba's disposable income increased by $860, his consumption increased by 0.75 x $860 = $645.
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The table shows a school district's enrollment
for two successive years. Write a linear function
using the data (with x representing the year
number), and then use the model to predict the
enrollment in Year 4.
Year 1 - 8295
Year2 -8072
to get the equation of any straight line, we simply need two points off of it, let's use those two in the table
[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{Year}{x}&\stackrel{students}{y}\\ \cline{1-2} 1&8295\\ 2&8072\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{1}~,~\stackrel{y_1}{8295})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8072}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8072}-\stackrel{y1}{8295}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{1}}} \implies \cfrac{ -223 }{ 1 } \implies - 223[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8295}=\stackrel{m}{- 223}(x-\stackrel{x_1}{1}) \\\\\\ y-8295=-223x+223\implies {\Large \begin{array}{llll} y=-223x+8518 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{for year 4, x = 4}}{y=-223(4)+8518} \implies y=7626~students[/tex]
Which of the following is an example of rational function?
1.f(x)=3x²+1 over x-1
2.x over 3 = 8 over 3
3.1 over 3x-1 +3<0
An example of a rational function is the first equation given, f(x)=3x²+1 over x-1.
A rational function is a type of function that can be expressed as the ratio of two polynomials. In this equation, the numerator is a polynomial of degree 2 (3x²+1), and the denominator is a polynomial of degree 1
(x-1).
The second equation given, x over 3 = 8 over 3, is not an example of a rational function. This equation is a rational expression, which is an expression that is the ratio of two polynomials, but it is not a function because it does not map a single input to a single output.
The third equation given, 1 over 3x-1 +3<0, is not an example of a rational function either. This equation is an inequality, not a function, and it does not have a ratio of two polynomials.
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question 1 options: what is the common difference in the sequence 7, 12, 17, 22, 27, ...? put the just the number in the blank.
The common difference in the sequence 7, 12, 17, 22, 27,… is that the difference between two numbers increases by five in the ascending order.
A sequence can be referred to or considered as the set of observations, which usually consists of numbers arranged in such a way that they described a common characteristic between them. A sequence can be exhaustive or inclusive, depending upon the numbers being used in the continuity of the sequence. It can also be said that a sequence is a logical arrangement.
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Complete question
what is the common difference in the sequence 7, 12, 17, 22, 27, ...?
please help with this question
Answer: the answer should be C :)
Step-by-step explanation:
the slope (x) is -3/4 and the y-intercept is -2
list the reasons and statement reasons why line AE ≅ A.F
. Thanks!
Add missing statements and reasons.
Statement Reason
7. FC ≅ EC CPCTC8. AE ≅ A.F. Transitive propertyHELP ME PLEASE ITS DUE AT 8 (50 POINTS)
Jamir bought p pencils that cost $0.10 each and F folders that cost $.35 each. A 8.75% sales tax will be applied to the total cost.
PART ONE:
Which expression repersents the total amount Jamir paid,including tax? Write the letter of the correct answer on the line below.
a) 0.0875 (p + f) + 0.0875 (0.10p+0.35f)
b) (0.10p + 0.35f) + 0.0875 (0.10p+0.35P)
c) 0.35(0.0875f) + 0.10(0.0875p)
d) 0.35(1.0875f) + 0.10(1.0875f)
Answer=
PART B
Explain why each of the other answers are worng.
LAST PART
Jamir purchased a dozen pencils and 8 folders. How much did he spend in all,after all tax was applied? Show your work please
Answer$=
Answer:
b) (0.10p + 0.35f) + 0.0875 (0.10p+0.35P)
first is Jamir total cost + the sales tax of 0.0875 of the total cost
a. this is wrong because both is the sales tax only, theres no total cost include
c. wrong because its just also sales tax only
d. wrong because the total cost must only multiplied by the sales tax
PART B
12(0.10) + 8(0.35)
= 1.2 + 2.8
= $4 as the total cost
4(1.035)
= $4.14 as after tax bill
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Prove that every point on the perpendicular bisestor of a segment is equidistant from the endpoint of segment​.
Every point on the perpendicular bisector of a segment is equidistant from the endpoint is hence proved
The line segment AB and let MN is the perpendicular bisector of AB line segment.
we prove the required result by congruence of triangles.
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure
From the figure,
Let P be any point on the perpendicular bisector MN. Join A to P and B to P.
To show AP=BP
In ΔANP and ΔBNP
PN=PN {common side in both triangles }
∠PNA=PNB=90°{ MN is ⊥ bisector of AB}
AN=NB {N is mid point}
By SAS rule of congruent ΔANP≅BNP
By CPCT (corresponding Parts of congruent triangles)
AP=BP
But P is point on MN
Therefore, every point on the perpendicular bisector of line segment AB is equidistant from the segments endpoints.
Hence Proved.
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A steep line has a bigger ____________ than a flat line
a steep line line has a bigger absolute greater slope than a flat line
a local civic theatre has 22 seats in the first row and 21 rows in all. each successive row contains 3 additional seats. how many seats are in the civic theatre
Using the arithmetic progression, If a theatre has 30 rows of seats there are 22 seats in the first row,21 in the second row, 51 in the third row, then the total number of people that the theatre hold is 2400
The total number of rows = 51
Number of seats in the first row = 22
Number of seats in the second row = 21
Number of seats in the third row = 51
Common difference= Second term - first term
= 26-22
= 4
The given sequence is in arithmetic progression
Substitute the values in the equation
= 15[44+29×4]
= 15[44+116]
= 15×160
= 2400
Hence, using the arithmetic progression, if a theatre has 51 rows of seats and there are 22 seats in the first row,21 in the second row, 51 in the third row, then the total number of people that the theatre hold is 2400
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Use the given information to prove that angle 8 is congruent to angle 1. Use two-column proof.
By using the properties of angle, it can be proved that [tex]\angle 8 \cong \angle 1[/tex]
What is angle?
An angle is a figure formed by two straight lines that intersect each other. It is a measure of the amount of rotation between two lines or planes, typically measured in degrees or radians. Angles are used in mathematics to describe relationships between lines, shapes and objects, and they are also used in everyday life to measure and construct objects. Angles are an important part of geometry and trigonometry, and they are also used in physics, engineering, and other sciences.
[tex]\angle 8 \cong \angle 5[/tex] Vertically Opposite angle
[tex]\angle 5 \cong \angle 1[/tex] Corresponding angle
[tex]\angle 8 \cong \angle 1[/tex] Transitivity property of congruency
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Mario and hi friend went to a movie on Saturday they left the houe at 5:15 PM. It took one hour and 20 minute to drive to the theater and they arrived 25 minute before the movie tarted. What time did the movie tart?
By applying the algebra concept, we can conclude that the movie that Mario and his friend watched starting at 7 PM
The use of algebra in everyday life.
Algebra is a branch of mathematics that uses numbers, symbols, or letters to solve math problems. In everyday life, algebra is often used for financial planning, traveling time calculation, and so on.
In the above problem, we can take some notes as follows:
Departure time (x) = 5:15 PM
Travel time (t) = 1 hour 20 minutes
Arrival time (y) = 25 minutes
If z is the playing time of the movie, then z can be expressed mathematically in the following way:
z = x + t + y
= 5:15 + 1 hour 20 minutes + 25 minutes
= 6:60 PM or generally written 7:00 PM
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