Answer:
The number is 5
Step-by-step explanation:
Let the number be x,
13 - x = 2x - 2
or, 13 + 2 = 2x + x
or, 3x = 15
so, x = 5
Solve the following variation problem
The interest on an investment varies directly as the rate of interest.
If the interest is $49 when the interest rate is
4%, find the interest when the rate is
7.7%
Answer:
$94.325
Step-by-step explanation:
Given interest (I) varies directly as rate of interest (R) then the equation relating them is
I = kR ← k is the constant of variation
To find k use the condition I = 49 when R = 4 , then
49 = 4k ( divide both sides by 4 )
12.25 = k
I = 12.25R ← equation of variation
When R = 7.7 , then
I = 12.25 × 7.7 = $94.325
An acre of land has an area of exactly 43,560 square feet. Which of the following is a reasonable estimate for the area of an acre of land?
A.
4 × 10-4 sq ft
B.
4 × 103 sq ft
C.
4 × 10-3 sq ft
D.
4 × 104 sq ft
Because an acre is 10 times the size of a football pitch and is often used area as a unit of measurement for broad regions, answer option (D) is a plausible estimate.
What is area?The size of a surface area can be expressed as an area. The surface area is the area of an open surface or the boundary of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a shape or flat layer. The area of an object is the entire amount of space occupied by a planar (2-D) surface or shape. Make a square with a pencil on a piece of paper. A two-dimensional character. On paper, the area of a shape is the amount of space it takes up. Assume the square is made up of smaller unit squares.
(D) 4 104 sq ft is the right answer.
Considering that an acre of land has an area of exactly 43,560 square feet, answer selections (A) and (C) are both too tiny, as they are both less than 1% of the size of an acre. Answer option (B) is 100 times the size of an acre and hence far too huge.
Because an acre is 10 times the size of a football pitch and is often used as a unit of measurement for broad regions, answer option (D) is a plausible estimate.
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1) In a standard deck of 52 cards, you draw 2
cards without replacement. Find:
P(Jack and then Queen):
(hint: a deck of cards has 4 Jacks and 4 Queens)
Probabilities are used to determine the chances of an event
The value of P(Jack and then Queen) is 4/663
How to determine the probabilityThe given parameters are:
n = 52
Jack = 4
Queen = 4
The probability P(Jack and then Queen) is calculated as:
P(Jack and then Queen) = P(Jack) * P(Queen)
So, we have:
[tex]P = \frac{4}{52} * \frac{4}{51}[/tex]
Simplify
[tex]P = \frac{1}{13} * \frac{4}{51}[/tex]
Evaluate the product
[tex]P = \frac{4}{663}[/tex]
Hence, the value of P(Jack and then Queen) is 4/663
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Solve each absolute value equation
2=|x|-1
Answer:
x = ±3
Step-by-step explanation:
2 = |x| - 1
Add 1 to both sides: |x| = 3
⇒ x = ±3
Solution:
2 = |x| - 1Remember, the number inside the absolute value bars will always be positive. This means that if -5 is between two bars, it will become 5.
=> 2 + 1 = |x|=> 3 = |x|Let's review 2 ways that this equation can go through:
(3 = |3|) = (3 = 3) True(3 = |-3|) = (3 = 3) TrueHence, the measure of x is ±3.
Help with #1 so I can get the gist of it please?
Answer:
so you graph at (0,2), and go up one, over two for every other point you graph.
Step-by-step explanation:
rise over run.
basically, the m is the slope, and b is the y intercept (where it intersects the y axis).
so when looking at how to graph the line based on 1/2 or any other number, I use rise/run, which is basically telling us tha we need to go up one and over 2 (1/2)
if that makes any sense, let me know if you have any further questions. you got this, youre doing your best!!
slope is the start of your endless pain.
ced tea. How do you make a larger batch of this mixture? Describe your procedure and use the table below to organize your results. Add more columns to the table if needed
Answer:
whats the question ?
Step-by-step explanation:
explain pls
Please help me I’ll give 20 points :)
Answer:
B
Step-by-step explanation:
because when simplified we get b
Answer:
1. AStep-by-step explanation:
1.[tex] {x}^{2} - 4x - 12 \\ {x}^{2} + 2x - 6x - 12 \\ x(x + 2) - 6(x + 2) \\ (x - 6)(x + 2) \\ [/tex]
Suppose that your data shows that Saturn orbits every 29.5 years. To the nearest hundredth of an au, how far is Saturn from the Sun?
Answer:
Step-by-step explanation:
it’s 9.55 au
Saturn is 9.57 au far from the sun
What is third law of Kepler ?
Kepler's third law, also called the law of periods, states that the square of the orbital period is proportional to the cube of its mean distance R.
Let time period of earth = T (e)
Time period of Saturn will be = T(s) = 29.5 T(e)
(since , it is given that Saturn orbits every 29.5 years )
distance of earth from sun = r(e) = 1.5 * [tex]10^{11}[/tex] m
distance of Saturn from the sun = r(s) = ?
using Kepler's third law
[tex]T^{2}[/tex] is directly proportional to [tex]r^{3}[/tex]
[tex]T(s)^{2}[/tex]/[tex]T(e)^{2}[/tex] = [tex]r(s)^{3}[/tex] / [tex]r(e)^{3}[/tex]
r(s) = r(e) [tex](T(s) / T(e))^{2/3}[/tex]
r(s) = 14.32 * [tex]10^{11}[/tex] m = 9.57 au
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I need help with this question, how do I find the value of x??
Answer:
Im sure that you need to subtract so 140 minus 15 is 130
Answer: x is 20 degrees
Step-by-step explanation:
145 + 15 = 160
180 - 160 = 20
( straight line: 180 degrees )
How much cubic centimeters of dirt must be removed when digging for a foundation of a building if the excavation is 32m long, 12m wide, and 8m deep
Answer:
3,072m
Step-by-step explanation:
32 × 12× 8= 3,072 (This is only you are multiplying them all)
If you are trying to find the area then its: 384m
$9,800.00 is invested at an annual rate of 11.6%, compounded continuously. How long will it take for that investment to grow to a value of 149,000.00? Round your answer (in years) to two decimal places at the END of your calculations.
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.875/100
r = 0.03875 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 10,000.00(1 + 0.03875/12)(12)(7.5)
A = 10,000.00(1 + 0.003229167)(90)
A = $13,366.37
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $10,000.00 at a rate of 3.875% per year compounded 12 times per year over 7.5 years is $13,366.37.
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$149000\\ P=\textit{original amount deposited}\dotfill & \$9800\\ r=rate\to 11.6\%\to \frac{11.6}{100}\dotfill &0.116\\ t=years \end{cases} \\\\\\ 149000=9800e^{0.116\cdot t}\implies \cfrac{149000}{9800}=e^{0.116\cdot t}\implies \cfrac{745}{49}=e^{0.116t}[/tex]
[tex]\log_e\left( \cfrac{745}{49} \right)=\log_e\left( e^{0.116t} \right)\implies \log_e\left( \cfrac{745}{49} \right)=0.116t \\\\\\ \cfrac{\ln\left( \frac{745}{49} \right)}{0.116}=t\implies 23.46\approx t[/tex]
help me help me help me
Answer:
should be 67 Step-by-step explanation:
Answer:
They are Vertical angles, and it is 67 degrees
Step-by-step explanation:
please help i need answer asap
Answer:
1: x=-3
2: x=1 is the answer
The scale for the drawing of a rectangular playing field is 2 inches=7 feet.
Find an equation you can use to find the dimensions of the actual field. What
are the actual dimensions? PLS HELP
Answers YAVE NO IDEA
Step-by-step explanation:
I DONT KNOWWWW
Which statement best describes a command economy?
Government intervention in economic choices is strictly forbidden.
The government determines economic choices and makes most decisions.
The decisions made by producers and consumers drive all economic choices.
Producers and consumers make some economic choices while the government makes others.
Help me with this question please:)!!
p = x² coefficient * x⁰ coefficient
= 6 * -3 = -18
R = x coefficient = 7
now you have to find 2 numbers that multiply to give -18 and add to give 7
the numbers are 9 and -2
so
S = 9
P = -18
q = -2
r = 7
Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is exponential, and use the table to justify your answer.
A. g(x) is exponential; an exponential function increases faster than a linear function.
B. g(x) is exponential; g(x) has a lower starting value and higher ending value.
C. f(x) is exponential; an exponential function increases more slowly than a linear function.
D. f(x) is exponential; f(x) increased less overall than g(x).
Answer:
the correct answer should be c
A boat heading out to sea starts out at Point AA, at a horizontal distance of 1347 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 9^{\circ}
∘
. At some later time, the crew measures the angle of elevation from point BB to be 3^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
The distance from point A to B is 2723.8 feet.
Trigonometric ratioTrigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let h represent the height of the light house, hence:
tan(9) = h/1347
h = 213.3 feet
Let d represent the distance from point B to the lighthouse base, hence:
tan(3) = 213.3/d
d = 4070.8 feet
Distance from point A to B = 4070.8 feet - 1347= 2723.8 feet.
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Answer:
2744.1
Step-by-step explanation:
I got the question right
which represents a function HURRY PLSSS (90 POINTS)
Answer:
neither a or b
Step-by-step explanation:
a function has to have each X have a Y
a domain is paired with exactly one range value.
it has to pass the vertical line test
independent variable is X
dependant variable is Y
student name = x
colors/teachers is Y
so since there is the chance the students can have the same teacher and/or favorite color. then it is not a function
If 1/3 gallon of paint covers 1/6 of a wall, then how many quarts of paint are needed for the entire wall?
Answer:
8 quarts
Step-by-step explanation:
There are 4 quarts in a gallon. If 1/3 of a gallon cover 1/6 of a wall, then an entire gallon will cover 1/2 of the wall. This means that 2 gallons will completely cover the wall. 2 gallons equals 8 quarts.
Answer:
8 quarts
Step-by-step explanation:
1/3 of a gallon = 1/6 of the wall
x of gallon = 1 of the wall
so x = 1/3 * 6 = 2 gallons
and 1 gallon = 4 quarts
then 2 gallon = 4*2 = 8 quarts
Solve for a.
5a−12=3
Enter your answer in the box.
a =
[tex]5a - 12 = 3 \\ 5a = 3 + 12 \\ 5a = 15 \\ a = \frac{15}{5} \\ a = 3[/tex]
Answer:
[tex]a=3[/tex]
Step-by-step explanation:
Given the following question:
[tex]5a-12=3[/tex]
To solve this equation, we need to add 12 on both sides and then isolate the variable for a.
[tex]5a-12=3[/tex]
[tex]-12+12=0[/tex]
[tex]12+3=15[/tex]
[tex]5a=15[/tex]
[tex]\frac{5a}{5} =\div5[/tex]
[tex]15\div5=3[/tex]
[tex]a=3[/tex]
Hope this helps.
Kyle types college reports for $1.70 per page. He also charges $6 to cover the cost of supplies. How many pages did he write if he charged $40.00? Write and solve an equation.
Answer:
$1.70p + $6 = $40.00
Step-by-step explanation:
$1.70p + $6 - $6 = $40.00 - $6
$1.70p = $34.00
$1.70p ÷ 1.70 = $34.00 ÷ 1.70
p = 20
He wrote 20 pages.
Jack read 9 books in 15 months. What was his rate of reading in months per book? Include units.
Your answer should be written in fraction form (mixed number)
Answer:
3/5 books
Step-by-step explanation:
Divide 9 by 15 to get 0.6
0.6=3/5
Find the domain for the expression:
y/y-5 + 1/y+8
Answer:
1/y+4
Step-by-step explanation:
1-5+1/y+8
1/y+(1-5+8)
1/y+4
[tex] \frac{y}{y} - 5 + \frac{1}{y} + 8 [/tex]
→[tex](1 - 5) + \frac{1}{y} + 8[/tex]
→[tex]-4 = \frac{ - 4}{1} = \frac{ - 4 \: • \: y}{y} [/tex]
→[tex] \frac{ - 4 \: • \: y + 1}{y} = \frac{1 - 4y}{y} [/tex]
→[tex] \frac{(1 - 4y)}{y} + 8[/tex]
→[tex]8 = \frac{8}{1} = \frac{8 \: • \: y}{y} [/tex]
→[tex] \frac{(1 - 4y) + 8 \: • \: y}{y} = \frac{4y + 1}{y} [/tex]
→[tex] \frac{4y + 1}{y} [/tex]
Find the value of x.
(4x + 10°
17
122°
A. 33
B. 28
C. 12
a
D. 20
Answer:
28°
Step-by-step explanation:
vertically opp angles will be equal
4x+10=122
4x = 112
x=28
When 0 is in the numerator in the answer of an equation; 2x = 0; x = 0/2 , the answer is WHAT?
NOT POSIBLE
0
2
Answer:
undefined
Step-by-step explanation:
this is explained in graphing lines because if the slope is 0/2 the the line is a undefined line
What is the value of the rational expression 2x2+ 5x +9/x2+2x -1?
A.)-7
B.)-9
C.)9
D.)7
(Help Please.)
Answer:
hai
Step-by-step explanation:
Which equation has the solution x = 5? Select each correct answer. 18−2x=9 32−4x=12 11 + 6x = 22 25x+4=9 x5+5=6 3x + 1 = 9
PLS HELP ME
Answer:
32 - 4x = 12
Step-by-step explanation:
Substitute x = 5 into the equations and compare:
18 - 2x = 18 - (2 x 5) = 18 - 10 = 8 incorrect
32 - 4x = 32 - (4 x 5) = 32 - 20 = 12 correct
11 + 6x = 11 + (6 x 5) = 11 + 30 = 41 incorrect
25x + 4 = (25 x 5) + 4 = 125 + 4 = 129 incorrect
[tex]x^5+5=(5^5)+5=25+5=30[/tex] incorrect
3x + 1 = (3 x 5) + 1 = 15 + 1 = 16 incorrect
solve by factorising x2 + 8x + 15 = 0
Answer:
x = - 3/2 thats the answer
Show working pls
Find the area of the following composite shapes
Answer:
112 sq cm
Step-by-step explanation:
Area of the square:
A = s^2
= 8^2
=64 sq cm
Area of a triangle:
A = 1/2•b•h
= 1/2•8•12
= 48 sq cm
Area of total shape:
A_square + A_triangle
= 64 + 48
= 112 sq cm