The scale factor used to represent the model from the real object size is y = (260/3)x
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the real object size and x represent the size of the model.
Given that:
y = (260/3)x
The scale factor used to represent the model from the real object size is y = (260/3)x
Find out more on equation at: https://brainly.com/question/2972832
en 56 años , daniel tendra 5 veces la edad que tiene ahora
the answer is 15!
Hope this helps!
A container in the shape of a pyramid has a rectangular base with dimensions of 5 inches by 15 inches. The height of the
rectangular pyramid is 12 inches. Marbles fill half the volume of the container.
How many more cubic inches of marbles are needed to finish filling the container?
Enter your answer in the box.
? ins
Answer:
150 in³
Step-by-step explanation:
We want to find half the volume of a rectangular pyramid. The volume of the whole pyramid is given by the formula ...
V = 1//3LWH
V = 1/3(5 in)(15 in)(12 in) = 300 in³
Then the volume of the half that is not filled with marbles is ...
1/2V = 1/2(300 in³) = 150 in³
150 cubic inches of marbles are needed to finish filling the container.
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]
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?
Question 8 of 10
James wants to tile his floor using tiles in the shape of a trapezoid. To make
the pattern a little more interesting he has decided to cut the tiles in half
along the median. The top base of each tile is 13 inches in length and the
bottom base is 19 inches. How long of a cut will John need to make so that
he cuts the tiles along the median?
O A. 16 inches
B. 3 inches
C. 6 inches
D. 32 inches
Answer:
C .6 inches
Step-by-step explanation:
I'm not sure of my answer
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
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!!!
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:
Solve for m
M/8 plus 2/3 equals 7/3
[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 solutionsGcf 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:)
!!!!!!!!!!!!!!!!!!!!
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.
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
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]
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.
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!
Determine 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
Given: ALMN ~ AQPR, find RQ.
5 8 2r +2 N R 2r +5 A. 11 B. 24 C. 27 D. 32 12 O
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 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
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
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
what is the common greatest factor of 18 and 3
Answer:
It is 3
•°•°•°
Math is poop
Alvin had 30 beads more than Bobby Cathy had thrice as many beads as
Alvin. They had a total of 345 beads. How many beads did Bobby have?
Answer:
Bobby has 45 beads
Step-by-step explanation:
Let x be the number of beads Bobby has.
Then, (x + 30) is the number of beads Alvin has.
Then, 3 (x + 30) is the number of beads Cathy has.
3 (x + 30) + (x + 30) + x = 345
3x + 90 + x + 30 + x = 345
5x + 120 = 345
5x = 225
x = 45
Therefore, Bobby has 45 beads.
¿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
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
help me worth 40 points lol :)
Answer:
Not worth 40 points. Poster is a liar.
R=15 --> 30/2 , H=320
Anyways, because you lied, I won't show my work.
Volume= 72,000pi or 226194.6711
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
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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