A unit fraction is any fraction with 1 as its numerator (top number), and a whole number in the denominator (bottom number).
The table shows the distance Penelope is from the park as she walks to soccer practice. Assume the relationship between the two quantities is linear. Find and interpret the rate of change and initial value. Then write the equation of the function in the form y=mx+b
-- help me
The equation of the function in the form y=mx+b is y = 110x-2020
Rate of a change of functionThe standard equation of a line is expressed as:
y = mx + b
where:
m is the rate of change or slope
b is the intecept
Using the coordinate points
Determine the slope
m = 550/5
m = 110
For the intercept
280 + 110(20) + b
280 = 2200 + b
b = 180 - 2200
b = -2020
Hence the equation of the function in the form y=mx+b is y = 110x-2020
Learn more on rate of change here: https://brainly.com/question/8728504
!!!!!!!!!!!!!!!!!!!!
There are 20 students on a bus. This is 50% of the total number of students. How many total students are there?
50 % =20 Learners
100%= x
x=100/50
=2
=2×20
=40 learners
was this helpful?
en 56 años , daniel tendra 5 veces la edad que tiene ahora
the answer is 15!
Hope this helps!
Which of the following functions has an initial value of -1/2 and a rate of change of 0?
Answer:
a starting value of -1/2 so its starts at -1/2 so lets see which ones start at that
not a
not b
yes c
this isn't a function
and no change so
not a
not b
yes c
yes d(not a function)
c
Hope This Helps!!!
Solve for m
M/8 plus 2/3 equals 7/3
what is -3x + 7 = -1 nice if step by step explanation what is x
Answer:
x = 8/3
Step-by-step explanation:
1. Subtract 7 from both sides.
-3x + 7 = -1
-7 -7
-------------------
-3x = -8
2. Divide both sides by -3
-3x = -8
---- ----
-3 -3
x = 8/3
Solve equation by using the quadratic formula.
15x² + 22x = -8
Answer:
[tex]x[/tex] =[tex]\frac{-2}{3}[/tex] or [tex]x[/tex] = -1
Step-by-step explanation:
quadratic formula⇒ -b ±[tex]\sqrt{b^{2} -4ac}[/tex] / 2a
15[tex]x[/tex]² + 22[tex]x[/tex] = -8
15[tex]x[/tex]² + 22[tex]x[/tex] +8 = 0
taking a=15, b=22 & c=8;
[tex]x[/tex] = (-22 ± [tex]\sqrt{ - 22^{2} 4 × 15 × 8}[/tex])/ 2 x 15 ⇒ (Pls note that the A~s are multiplications.. unable to insert symbols in equations)
= (-22 ± [tex]\sqrt{484 - 480}[/tex]) / 30
= (-22 ± [tex]\sqrt{4}[/tex]) / 30
= (-22 ± 2) / 30
[tex]x[/tex] = [tex]\frac{-22 + 2}{30}[/tex] or [tex]x[/tex] =[tex]\frac{-22 - 2}{30}[/tex]
[tex]x[/tex] = -[tex]\frac{-20}{30}[/tex] or [tex]x[/tex] = [tex]\frac{-30}{30}[/tex]
[tex]x[/tex] =[tex]\frac{-2}{3}[/tex] or [tex]x[/tex] = -1
Students were asked to choose the city they would most like to visit and 5/10 chose either New York or Los Angeles. If 2/10 of the students chose Los Angeles, what fraction chose New York?
Answer:
3/10
Step-by-step explanation:
There are 10 students
5 of them voted either Los Angeles or New York
That means ignore (screw) the other 5 people
If 2/10 students chose Los Angeles,
that is 2/5 because the others didn't choose those cities that are part of the equation (nobody asked about the other people)
So if 5 people chose two groups of cities, and two people chose one city, that meant 3 chose the other
3/10 (remember its out of all of them) Students Voted for New York
Hope this helps :)
-jp524
The following is a table of probabilties calculated from a survey of Bc students with the question asked "How many classes are you taking this semester?"
x: # of classes 1 2 3 4 5
P(x) 0.14 0.29 0.12 0.31 0.14
Using the table, find the following probabilities for a student selected at random:
a.) What is the probability that a student is taking 2 or more classes?
Incorrect
b.) What is the probability that a student is taking at least 3 classes?
c.) What is the probability that a student is taking more than 3 classes?
d.) What is the probability that a student is taking less than 2 classes?
e.) What is the probability that a student is taking no more than 2 classes?
f.) What is the average (mean) amount of classes a student takes at bC?
g.) What is the standard deviation for the amount of classes a student takes at BC? (round to two decimal places)
Considering the discrete distribution, it is found that the desired measures are given as follows:
a) 0.86.
b) 0.57.
c) 0.45.
d) 0.14.
e) 0.43.
f) 3.02.
g) 1.31.
What is the probability distribution?
According to the table, it is given by:
P(X = 1) = 0.14.
P(X = 2) = 0.29.
P(X = 3) = 0.12.
P(X = 4) = 0.31.
P(X = 5) = 0.14.
Item a:
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - P(X = 1) = 1 - 0.14 = 0.86[/tex]
Item b:
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - P(X = 1) - P(X = 2) = 1 - 0.14 - 0.29 = 0.57[/tex]
Item c:
P(X > 3) = P(X = 4) + P(X = 5) = 0.31 + 0.14 = 0.45.
Item d:
P(X < 2) = P(X = 1) = 0.14.
Item e:
[tex]P(X \leq 2) = P(X = 1) + P(X = 2) = 0.14 + 0.29 = 0.43[/tex].
Item f:
The mean is given by the sum of each outcome multiplied by it's respective probability, hence:
E(X) = 0.14(1) + 0.29(2) + 0.12(3) + 0.31(4) + 0.14(5) = 3.02.
Item g:
The standard deviation is given by the square root of the sum of the difference squared of each observation and the mean, multiplied by it's respective probabilities, hence:
[tex]\sqrt{V(X)} = \sqrt{0.14(1-3.02)^2 + 0.29(2-3.02)^2 + 0.12(3-3.02)^2 + ... + 0.14(5-3.02)^2} = 1.31[/tex]
More can be learned about discrete probability distributions at https://brainly.com/question/24855677
3. Which of these numbers, when rounded off to the nearest 1000, gives 99 000? 98 833; 99 583; 99 374; 98 476; 98 783; 99 574; 98 587 (1) (1) (1)
Answer:
Step-by-step explanation:
sorry I tried but it is hard
[tex] \rm \orange{ \mathbb Challenge}[/tex] Solve the given question to be a genius. [tex]\blue{ \rule{18mm}{3.5pt}} \red{ \rule18mm3.5pt} \gray{ \rule18mm3.5pt} [/tex] Answer only if u know the answer [tex]\blue{ \rule{18mm}{3.5pt}} \red{ \rule18mm3.5pt} \gray{ \rule18mm3.5pt}[/tex] [tex]\large{\frak{ \pink{Que}{sti} \purple{on - 1 }}}[/tex] [tex] \rm \large \pink{\textit{ \sf{Find \: the \: sum - } }} \\ \large \red{\sf{ \mapsto100 + 200 + 300.... + 10000 }}[/tex] [tex]\blue{ \rule{18mm}{3.5pt}} \red{ \rule18mm3.5pt} \gray{ \rule18mm3.5pt}[/tex] [tex]\large{\frak{ \pink{Que}{sti} \purple{on - 2}}}[/tex] [tex]\rm\pink{\large{\sf{ \mapsto Sum \: of \: 2 \: consecutive }}} \\ {\large{\sf{square \: numbers \: is \: 21.}} }\\ \large \red{\sf{Find \: the \: smallest \: number.}}[/tex] [tex]\blue{ \rule{18mm}{3.5pt}} \red{ \rule18mm3.5pt} \gray{ \rule18mm3.5pt}[/tex] [tex]\large \orange{\bf{No \: Spam }}[/tex] [tex]\blue{ \rule{18mm}{3.5pt}} \red{ \rule18mm3.5pt} \gray{ \rule18mm3.5pt}[/tex] [tex]\large \fcolorbox{green}{gray}{\tt{ s}}[/tex] [tex]\blue{ \rule{18mm}{3.5pt}} \red{ \rule18mm3.5pt} \gray{ \rule18mm3.5pt} [/tex]
#1
100+200+300..10000
a=100l=10000n=10000/100=100Now
[tex]\\ \rm\Rrightarrow S_{100}=\dfrac{100}{2}(100+10000)=50(10100)=505000[/tex]
#2
Numbers be x and x+1[tex]\\ \rm\Rrightarrow x^2+(x+1)^2=21[/tex]
[tex]\\ \rm\Rrightarrow x^2+x^2+2x+1=21[/tex]
[tex]\\ \rm\Rrightarrow 2x^2+2x=20[/tex]
[tex]\\ \rm\Rrightarrow x^2+x-10=0[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{-1\pm\sqrt{1-40}}{2}[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{-1\pm\sqrt{-39}}{2}[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{-1\pm \sqrt{39}i}{2}[/tex]
No real solutionsDetermine the area enclosed by y=2x+3, the x-axis and the ordinates x=3 and x=4
Answer:
[tex]\displaystyle \int\limits^4_3 {2x + 3} \, dx = 10[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
y = 2x + 3
x-interval [3, 4]
x-axis
See attachment for graph.
Step 2: Find Area
Substitute in variables [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^4_3 {2x + 3} \, dx[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle A = \int\limits^4_3 {2x} \, dx + \int\limits^4_3 {3} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle A = 2 \int\limits^4_3 {x} \, dx + 3 \int\limits^4_3 {} \, dx[/tex][Integrals] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = 2 \bigg( \frac{x^2}{2} \bigg) \bigg| \limits^4_3 + 3(x) \bigg| \limits^4_3[/tex][Integrals] Integrate [Integration Rule - FTC 1]: [tex]\displaystyle A = 2 \bigg( \frac{7}{2} \bigg) + 3(1)[/tex]Simplify: [tex]\displaystyle A = 10[/tex]∴ the area bounded by the region y = 2x + 3, x-axis, and the coordinates x = 3 and x = 4 is equal to 10.
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Learn more about integration: https://brainly.com/question/26401241
Learn more about calculus: https://brainly.com/question/20197752
---
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Solve all 3 Questions. 50 Points + Brainelist
Answer:
i) Using log law: [tex]\log_aa=1[/tex]
[tex]\implies \log_55+1=1+1=2[/tex]
ii) [tex]\log \left(\dfrac{15}{8}\right)+4 \log 2-\log 3[/tex]
Using log law [tex]a \log b=\log b^a[/tex]:
[tex]\implies \log \left(\dfrac{15}{8}\right)+\log 2^4-\log 3[/tex]
[tex]\implies \log \left(\dfrac{15}{8}\right)+\log 16-\log 3[/tex]
Using log law [tex]\log a-\log b=\log (\frac{a}{b})[/tex]:
[tex]\implies \log \left(\dfrac{15}{8}\right)+\log\left(\dfrac{16}{3}\right)[/tex]
Using log law [tex]\log a+\log b=\log(ab)[/tex]:
[tex]\implies \log \left(\dfrac{15}{8}\cdot \dfrac{16}{3}\right)[/tex]
[tex]\implies \log 10[/tex]
Using log law: [tex]\log_aa=1[/tex]
[tex]\implies \log_{10} 10=1[/tex]
iii) Take log of base 10:
[tex]\log_{10}(\sqrt{8.357}\times0.895^2)[/tex]
[tex]\implies \dfrac12\log_{10}(8.357)+2\log_{10}(0.895)[/tex]
Log tables
The characteristic of the logarithm of a number is the exponent of 10 in its scientific notation.
The mantissa is found using the log tables and is always prefixed by a decimal point.
The row is the first two non-zero digits of the number, and the column is the 3rd digit of the number
Use the log tables to find [tex]\log_{10}(8.357)[/tex]:
8.357 = 8.357 × 10⁰
⇒ characteristic = 0
log table: row 83, column 5 ⇒ mantissa 9217
(as there is a 4th digit) Mean difference 7 = 4
mantissa + mean difference = 9217 + 4 = 9221 ⇒ 0.9221
characteristic + mantissa = 0 + 0.9221 = 0.9221
Therefore, [tex]\log_{10}(8.357)=0.9221[/tex]
Use the log tables to find [tex]\log_{10}(0.895)[/tex]:
[tex]0.895 = 8.95\times 10^{-1}[/tex]
⇒ characteristic = -1
log table: row 89, column 5 ⇒ mantissa 9518⇒ 0.9518
characteristic + mantissa = -1 + 0.9518= -0.0482
Therefore, [tex]\log_{10}(0.895)=-0.0482[/tex]
Therefore,
[tex]\implies \dfrac12\log_{10}(8.357)+2\log_{10}(0.895)[/tex]
[tex]\implies \dfrac12 \cdot 0.9221+2\cdot-0.0482[/tex]
[tex]\implies 0.36465[/tex]
Therefore,
[tex]\log_{10}(\sqrt{8.357}\times0.895^2)=0.36465[/tex]
Using [tex]\log_ab=c \implies a^c=b[/tex]
[tex]\implies \sqrt{8.357}\times0.895^2=10^{0.36465}[/tex]
[tex]\implies \sqrt{8.357}\times0.895^2=2.3155[/tex]
Simplify:- ~~~~~~~
[tex] \displaystyle{ \rm{ - \frac{ 2}{5} - ( - \frac{ 3}{10}) - ( - \frac{4}{7}) }}[/tex]
[tex] \sf \dashrightarrow \: - \frac{2}{5} - ( - \frac{3}{10} ) - ( - \frac{4}{7} )[/tex]
When there is a - in front of an expression in parentheses, change the sign of each term in the expression to +
[tex] \sf \dashrightarrow \: - \frac{2}{5} + \frac{3}{10} + \frac{4}{7} [/tex]
Calculate the LCM of denominators
[tex] \sf\frac{ - 28 + 21 + 40}{70} [/tex]
Calculate the difference
[tex] \bf \underline{ \underline \frac{33}{70} }[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{-2}{5}-\left(-\dfrac{3}{10}\right)-\left(-\dfrac{4}{7}\right)[/tex]
(-)(-)=(+)[tex]\\ \rm\rightarrowtail \dfrac{-2}{5}+\dfrac{3}{10}+\dfrac{4}{7}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{-28+21+40}{70}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{-7+40}{70}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{33}{70}[/tex]
Given that, for all values of x,
2x^2 – 3x + 21 = a(x - b)^2 + c
find the value of a, the value of b and the value of c.
Step-by-step explanation:
To find a, the leading coeffiecent of the quadratic is a.
So a is 2.
To find b, we must use the formula
[tex] - \frac{b}{2a} [/tex]
[tex] \frac{ - ( - 3)}{2(2)} = \frac{3}{4} [/tex]
So b=3/4.
To find c, plug in 3/4 into the function,
which we get
[tex]2( \frac{9}{16} ) - 3( \frac{3}{4} ) + 21[/tex]
[tex] \frac{9}{8} - \frac{9}{4} + 21 = \frac{9}{8} - \frac{18}{8} + 21 = - \frac{9}{8} + 21 = 19.875[/tex]
So c=19.875
Please look at the picture and answer it thank you.
¤ Angle sum property of triangle states that the sum of interior angles of a triangle is 180°
8x + 14 + 42 = 180 8x + 56 = 180 8x = 180 - 56 8x = 124 x = 124 / 8 x = 15Have a great day !!
The length of a new rectangular playing field is 3 yards longer than double the width. If the perimeter of the rectangular playing field is 252 yards, what are its dimensions?
Answer:
Given:
Length of a rectangular field is 3 yards longer than double the breadth. Perimeter is 252 yards.[tex] \: [/tex]
To Find:
It's dimensions?[tex] \: [/tex]
Solution:
Let,
Breadth be 'b'So,
length will be 2b + 3
[tex] \: [/tex]
As, we know:
[tex] \bigstar \quad {\underline{ \boxed{ \green{Perimeter = 2 ( length + breadth ) }}}} \quad \bigstar[/tex]
➝ 2[(2b + 3) + b)] = 252
➝ 2( 3b + 3 ) = 252
➝ 6b + 6 = 252
➝ b + 1 = 42
➝ b = 41
[tex] \: [/tex]
Now putting the value of b in second equation:
➝ l = 2(41) + 3 = 85
[tex] \: [/tex]
Hence,
Width is 41 yards length is 85 yards[tex] \: [/tex]
Check:
2( l+b ) = 252
➝ 2( 85 + 41 )
➝ 2( 126 )
➝ 252
_____________________Additional Information:[tex] \: \: \: \: \: \: { \sf{ \mathbb{ \pink{Formula's \: for \: Perimeter}}}}[/tex]
★ Triangle = Sum of all sides
★ Square = 4 × Side
★ Rectangle = 2( l + b )
★ Circle = 2πr
1. We want to know how much money Houston people would like to spend on
restaurants every month. So we randomly find 500 volunteers to do a survey
questionnaire. Identify the population.
A. 500 volunteers
B. Houston people
The table below shows the number of ounces in price for each of the four different bottles of orange juice. Which bottle has a price of $.10 per ounce
Answer:
12 oz bottle
Step-by-step explanation:
See attached image.
¿Qué lugar decimal ocupa el dígito "2" en el número 432,079?
Answer:
Ocupa los miles.
Step-by-step explanation:
400,000
30,000
2,000
70
9
Add the two expression’s
(7w-5) and (-3w+3)
Answer:
d) 4w - 2
Step-by-step explanation:
(7w-5) and (-3w+3)
(7w-5) + (-3w+3)
1(7w-5) + 1(-3w+3)
7w - 5 - 3w + 3
Combine like terms:
7w - 5 - 3w + 3
7w - 3w - 5 + 3
4w - 2
Hope this helps!
Answer all 4 please, rounded to the nearest 10th
The points (-1, -8) and (r, 4) lie on a line with slope 3. Find the missing coordinate
Answer:
r = 3
Step-by-step explanation:
Given: ALMN ~ AQPR, find RQ.
5 8 2r +2 N R 2r +5 A. 11 B. 24 C. 27 D. 32 12 O
How would I solve this problem?
The area of the garden enclosed by the fencing is
A(x, y) = xy
and is constrained by its perimeter,
P = x + 2y = 200
Solve for x in the constraint equation:
x = 200 - 2y
Substitute this into the area function to get a function of one variable:
A(200 - 2y, y) = A(y) = 200y - 2y²
Differentiate A with respect to y :
dA/dy = 200 - 4y
Find the critical points of A :
200 - 4y = 0 ⇒ 4y = 200 ⇒ y = 50
Compute the second derivative of A:
d²A/dy² = -4 < 0
Since the second derivative is always negative, the critical point is a local maximum.
If y = 50, then x = 200 - 2•50 = 100. So the farmer can maximize the garden area by building a (100 ft) × (50 ft) fence.
Gcf of 12 30 and 75 list them
Hey there!
12: 1, 2, 3, 4, 6, & 12
30: 1, 2, 3, 5, 6, 10, 15, & 30
75: 1, 3, 5, 15, 25, & 75
LIKE TERMS: 1 and 3
GCF: 3
Therefore, your answer is: 3
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Whats the pattern for this numbers 5, 3, 9, 2, 13
Step-by-step explanation:
Go and learn numbers , it will be 1 2 3 4 5
On a Math test, Johnny correctly answered 17 questions out of 20. What percent did
he answer correctly?
Answer:
85%
Step-by-step explanation:
Johny answered [tex]\frac{17}{20}[/tex] questions correctly. To change this into percent, just multiply both the numerator and denominator by the number that makes the denominator equal 100. In this case, 5 would make 20 equal 100, so we multiply both the top and bottom by 5.
[tex]\frac{17}{20} *\frac{5}{5}=\frac{85}{100}[/tex]
Your numerator will be your percentage if the denominator is 100.
what is the common greatest factor of 18 and 3
Answer:
It is 3
•°•°•°
Math is poop