Using proportions, it is found that the rate of 31 mills means that their property tax is of 3.1%.
What is a proportion?A proportion is a fraction of a total amount.
The Staff family pays a rate of 31 mills in property tax, which means that for each $1000, $31 is paid in tax. Hence the rate is given by:
r = 31/1000 = 3.1/100 = 3.1%.
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A caterpillar moves at a constant speed of 1/2 inches per second. Let x represent the time travel in seconds and y represent the distant travel in inches. I Really need help with this!
Step-by-step explanation:
Expression = 1/2x = y
Easy algebraic expression
~Done~
Austin finished his English assignment ib 1/3 hours.then he completed his math assignment in 2/5 hours. What wS the total time hw sentence this two assignments
Answer:
11/15
Step-by-step explanation:
sum the two 1/3+2/5=11/15
Use the number line. How many 2-yard
long pieces of pipe can be cut from two
1-yard long pieces of pipe?
Answer:
Answer:
16 inches
Step-by-step explanation:
2 1/4 = 9/4 inches
Number of pieces = 36 / 9/4
= 36 + 4/9
= 16 inches
two coins are flipped then a card is drawn. there are how many total outcomes? deck is 52 and coins are fair.
Answer:
208
Step-by-step explanation:
A coin can have 2 total outcomes
A card deck can have 52 total outcomes
Im flipping 2 coins and then drawing a card
2 x 2 x 52 = 208
1 fith of the sum of the 3 times a number and 9
Answer
3*9=27
27/ 1/5
5.25
Step-by-step explanation:
5.25=5 1/4
What is the total of all 3 tickets below. use the menu to solve
Answer:
$103.14
Step-by-step explanation:
The calculation of slips are amounted to a total of $103.14
Suppose you deposit $2500 in a savings account that pays you 5% interest per year. (Calculator)
(a) How many years will it take for you to double your money?
Answer:
14.20669 years
Roughly 14 years and 2.5 months.
Step-by-step explanation:
Assuming this is compound interest.
The formula is [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]A=[/tex] Final Amount
[tex]P=[/tex] Principal Amount
[tex]r=[/tex] Interest Rate
[tex]n=[/tex] # of times interest is compounded per year
[tex]t=[/tex] Time in years
We are looking for the times in years to double the money so
[tex]2500*2=5000[/tex]
[tex]A=5000[/tex]
[tex]P=2500[/tex]
[tex]r=0.05[/tex]
[tex]n=1[/tex]
[tex]t=?[/tex]
Lets solve for [tex]t[/tex] .
Step 1.
Plug in our numbers into the compound interest formula.
[tex]5000=2500(1+\frac{0.05}{1}) ^{1*t}[/tex]
Step 2.
Simplify the equation.
Evaluate [tex]1+\frac{0.05}{1}=1.05[/tex]
Evaluate [tex]1*t=t[/tex]
[tex]5000=2500(1.05) ^{t}[/tex]
Step 3.
Divide both sides of the equation by [tex]2500[/tex]
[tex]\frac{5000}{2500}=1.05 ^{t}[/tex]
Evaluate [tex]\frac{5000}{2500}=2[/tex]
[tex]2=1.05 ^{t}[/tex]
Step 4.
Take the natural log of both sides of the equation and rewrite the right side of the eqaution using properties of exponents/logarithms.
[tex]ln(2)=t*ln(1.05)[/tex]
Step 5.
Divide both sides of the equation by [tex]ln(1.05)[/tex]
[tex]\frac{ln(2)}{ln(1.05)}=t[/tex]
Step 6.
Evaluate
[tex]t=14.20669[/tex]
Roughly 14 years and 2.5 months.
Which graph represents an exponential function?
Answer:
The first one
Step-by-step explanation:
As x increases, the value of y approaches infinity. As x decreases, the value of y approaches 0.
Hope it helps
A two-variable inequality is shown in the graph.
Which point is not included in the solution set for the inequality?
(–1, 3)
(0, 4)
(1, 5)
(2, 4)
The point which is not included in the solution set for the inequality of the two-variable inequality shown in the graph is (-1,3).
How to graph the inequality?Inequality of a graph is represented with the greater then(<), less then(>) or with the other inequity signs. The inequality line on the graph is represented with the dotted lines.
A two-variable inequality is shown in the graph. It is a parabola. The vertex form of parabola is the equation form of quadratic equation which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.
The standard equation of the vertex form of parabola is given as,
[tex]y=a(x-h)^2+k[/tex]
Here, (h, k) is the vertex point. In the graph, vertex points are (1,2). Thus, the equation become,
[tex]y=a(x-1)^2+2\\[/tex]
By the point of graph (0,3), find the value of a,
[tex]3=a(0-1)^2+2\\3=a+2\\a=3-2\\a=1[/tex]
Thus, the equation become,
[tex]y=1(x-1)^2+2\\y=x^2-2x+1+2\\y=x^2-2x+3\\[/tex]
The graph of this line is attached below. In this graph only point (-1,3), does not fall hence, does not satisfy the equation.
Thus, the point which is not included in the solution set for the inequality of the two-variable inequality shown in the graph is (-1,3).
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Answer:
Its (-1,3)
Step-by-step explanation:
Identify the center and radius of each equation (x-5)² + (y+7)² =64
Answer:
Radius: 8
Center: (5,-7)
Step-by-step explanation:
(x−a)2 + (y−b)2 = r2
To find the radius: find the square root of 64
To find the center, get the opposite of -5 and 7
opposites are: 5, -7
center is (5,-7)
the circumference of a circle is c centimeters. The diameter of thhe circle is 13 centimeters. which expression best represents the value of pi
Answer:
c/d
Step-by-step explanation:
The value of π is the ratio of the circumference of any circle to it's diameter, irrespective of it's size.
write three addition problems that have a sum of -2
Answer:
1. -5+3
2. -6+4
3. -8+6
Step-by-step explanation:
they all will equal -2
Question 2 help meeee pleaseee
Thank you
3 cm/h easy peasy
Step-by-step explanation:
12 cm in 4 hrsFor 1 cm : 12/4 = 3 cmwhat is 34x50^2+89-89 divided by 89
Answer:
(34×(50^2))+89-(89÷89)=8,5088
Step-by-step explanation:
hope this helps if not let me know have a great day
Use the diagram to write an equation that describes the position and the radius of ⊙P.
(x – 4)2 + (y + 2)2 = 16
(x + 4)2 + (y – 2)2 = 16
(x + 4)2 + (y – 2)2 = 4
(x – 4)2 + (y + 2)2 = 4
The equation of circle p with center at (-4, 2) and a radius of 4 units is (x + 4)² + (y - 2)² = 16
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The circle p has center at (-4, 2) with a radius of 4 units, hence, the equation is:
(x - (-4))² + (y - 2)² = 4²
(x + 4)² + (y - 2)² = 16
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2. A more efficient packing of the discs is obtained by dividing the metal sheet into hexagons and cutting the circular lids and bases from the hexagons (see the last figure). Show that if this strategy is adopted, then
[tex] \frac{h}{r}=\frac{4 \sqrt{3}}{\pi} \approx 2.21 [/tex]
This exercise is about optimization and seeks to prove that if the new strategy of packing the discs is adopted, then h/r = [tex]\sqrt[4]{3}[/tex]/n ≈2.21.
What is the proof for the above strategy?We must determine the amount of metal consumed by each end, or the area of each hexagon.
The hexagon is divided into six congruent triangles, each of which has one side (s in the diagram) in common with the hexagon.
Step I
Next, let's derive the length of s = 2r tan π/6 = (2/([tex]\sqrt{3}[/tex])r². From this we can state that the area of each of the triangles are 1/2(sr) = (1/[tex]\sqrt{3}[/tex])r²
while the total area of the hexagon is 6 * (1/[tex]\sqrt{3}[/tex])r² = (2/[tex]\sqrt{3}[/tex])r².
From the above, we can state that the quantity we want to minimize is given as:
A = 2πrh + 2* (2/[tex]\sqrt{3}[/tex])r²
Step 2
Next, we substitute for h and differentiate. This gives us:
da/dr = - (2V/r²) + [tex]\sqrt[8]{3r}[/tex].
Let us equate the above to zero.
[tex]\sqrt[8]{3r} ^{3}[/tex] = 2V = 2πr²h ⇒ h/r =[tex]\sqrt[4]{3}[/tex]/n
The above is approximately 2.21
Because d²A/dr²=[tex]\sqrt[8]{3}[/tex] + 4V/r[tex]^{3}[/tex] > 0 the above minimizes A.
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Which expression is equivalent to (-36) - 128b ? *
Answer:
-36-128b
Step-by-step explanation:
Simply take -36 out of the parentheses to get -36-128b.
dan makes pizza. he puts 6 pepperoni on each pizza. he makes 7 pizzas.
how many pepperonis does he use?
if he has 6 pepperoni and he puts them on 7 pizzas
6x7=42
50 points each question (visit profile for more). Please help. How do I solve?
Answer:
Check the image of solution
A cone has a height of 6 inches and a radius of 7 inches. What is the volume? Keep your answer in terms of pi.
Answer:
V≈307.88in³
Step-by-step explanation:
V=πr2h
3=π·72·6
3≈307.87608in³
Answer:
[tex]98\pi[/tex]
Step-by-step explanation:
The formula of the volume of a cone is given by [tex]V=\frac{\pi r^2h}{3}[/tex], which, applying the values yields [tex]V=\frac{\pi 7^26}{3} = 98\pi[/tex]
Triangle PQR has ZP = 63.5° and ZQ = 51.2° and r = 6.3 cm. Find the other two sides and unknown angle. Options :
A R = 65.3°, p = 6.21 cm and q = 5.40 cm
B R = 65.3°, p = 5.21 cm and q = 5.40 cm
C R = 65.3°, p = 6.21 cm and q =4.40 cm
D R = 65.3°, p = 3.21 cm and q = 4.40 cm and q = 4.40 cm
Answer:
ben told it was 78
Step-by-step explanation:
ben said that
If 1/(a + b + c) = 1/a + 1/b + 1/c, show that 1/(a + b + c)^3 = 1/a^3 + 1/b^3 + 1/c^3
Expanding the cube, we have
[tex]\dfrac1{(a+b+c)^3} = \left(\dfrac1{a+b+c}\right)^3 \\\\ = \dfrac1{a^3} + \dfrac1{b^3} + \dfrac1{c^3} + 3 \left(\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2}\right) + \dfrac6{abc}[/tex]
so it remains to be shown that
[tex]3 \left(\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2}\right) + \dfrac6{abc} = 0[/tex]
Factorize the grouped sum on the left as
[tex]\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2} = \dfrac1{abc} \left(\dfrac ca + \dfrac ba + \dfrac cb + \dfrac ab + \dfrac bc + \dfrac ac\right)[/tex]
so that with simplification, it remains to be shown that
[tex]\dfrac ca + \dfrac ba + \dfrac cb + \dfrac ab + \dfrac bc + \dfrac ac + 2 = 0[/tex]
With a little more manipulation, we have
[tex]\dfrac ba + \dfrac ca = \dfrac{a+b+c}a - 1[/tex]
[tex]\dfrac cb + \dfrac ab = \dfrac{a+b+c}b - 1[/tex]
[tex]\dfrac bc + \dfrac ac = \dfrac{a+b+c}c - 1[/tex]
so that our equation simplifies to
[tex]\dfrac{a+b+c}a + \dfrac{a+b+c}b + \dfrac{a+b+c}c - 1 = 0[/tex]
which we can factorize as
[tex](a+b+c)\left(\dfrac1a+\dfrac1b+\dfrac1c\right) - 1 = 0[/tex]
Finish up by using the hypothesis:
[tex]\left(\dfrac1{\frac1{a+b+c}}\right)\left(\dfrac1a+\dfrac1b+\dfrac1c\right) - 1 = 0[/tex]
[tex]\underbrace{\left(\dfrac1{\frac1a+\frac1b+\frac1c}\right)\left(\dfrac1a+\dfrac1b+\dfrac1c\right)}_{=1} - 1 = 0[/tex]
and the conclusion follows.
If f(x)= x^3 + 6x^2 - 9x + 14 and x-2 is a factor of f(x), then find all of the zeros of f(x) algebraically.
Answer
Write properties of function:
x intercept/zero: [tex]x_1=-7[/tex]; [tex]x_2=-1[/tex]; [tex]x_3=2[/tex]
factorized form: [tex]f(x)=(x+1)(x-2)(x+7)[/tex]
Explanation
Write properties of function: Write properties of function:
x intercept/zero: [tex]x_1=-7[/tex]; [tex]x_2=-1[/tex]; [tex]x_3=2[/tex]
factorized form: [tex]f(x)=(x+1)(x-2)(x+7)[/tex]
Answer: Write properties of function:
x intercept/zero: [tex]x_1=-7[/tex]; [tex]x_2=-1[/tex]; [tex]x_3=2[/tex]
factorized form: [tex]f(x)=(x+1)(x-2)(x+7)[/tex]
Each member of a 5-member cross-country team runs a course. Their individual times are as follows:
2 hours 17 minutes
2 hours 48 minutes
1 hour 53 minutes
2 hours 19 minutes
1 hour 38 minutes
The team’s overall score is the average number of minutes it takes for its members to complete the course. What is this team’s score?
Step-by-step explanation:
the average is the sum of all data points divided by the number of data points (5).
2 hours 17 minutes
2 hours 48 minutes
1 hour 53 minutes
2 hours 19 minutes
1 hour 38 minutes
------------------------------
8 hours 175 minutes
175 minutes = 2 hours 55 minutes
so, we need to add this to the 8 hours and get
10 hours 55 minutes
this we need to divide by 5 for the average time
(10 hours 55 minutes) / 5 = 2 hours 11 minutes =
= 2×60 + 11 = 120 + 11 = 131 minutes.
so, their score is 131.
= $3500
= $4750
What is the value of each?
Answer:
The boat is 2000 and the bird is 750.
Step-by-step explanation:
1. 750+750=1500
1500+2000=3500
2. 2000+2000=4000
4000+750=4750
write equivalent fractions for 3\5 and 1\4 using 20 as the conman denominator
Answer:
12/20=3/5 5/20=1/4 so the answer would be 12/20 + 5/20
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
Answer:
984
Step-by-step explanation:
Solve for the base: 14 x 10
Solve for the sides: 2(1/2(10 x 24))
Solve for the backside: 10 x 24
Solve for the slanted plane or front: 14 x 26
Answer:
the answer is in the picture
The first to answer first will brainliest
Answer:
[tex]\sf \left(-\dfrac{1}{2},-\dfrac{1}{8}\right)[/tex]
See the graph below.
Equation: y = x³
Only (-0.5, -0.125) lies on the graph of the equation y = x³
option D is correct.Answer asap and only if yk 100% its correct
Answer:
1.35 square miles I think
Step-by-step explanation:
Answer:
Julie travels 1.35 miles on the same path every day.
Area = 1.35 miles
Step-by-step explanation:
What we know so far:
- It takes 2.4 miles to walk from house to school.
- The distance from the park to school is 2.1 miles.
- It takes 1.5 miles to walk from your house to the park.
The area of a triangle is 0.5 or 1/2 x base x height.
As a result, 1.5 x 1.8 divided by two equals 1.35.
So, Julie walks 1.35 miles every day on the same route.
Area = 1.35 miles
Hope this helps! :D Brainliest?
Please help me I can’t get it right
=====================================================
Work Shown:
[tex]2\sqrt{b} + 5 = 11 - \sqrt{b}\\\\2x + 5 = 11 - x\\\\2x+x = 11 - 5\\\\3x = 6\\\\x = 6/3\\\\x = 2\\\\\sqrt{b} = 2\\\\b = 2^2\\\\b = 4\\\\[/tex]
What I did for a good portion of the early steps is replace [tex]\sqrt{b}[/tex] with x. Then I solved for x like with any normal equation. Once x is isolated, plug in [tex]x = \sqrt{b}[/tex] and isolate b itself.
------------
Let's check the answer:
[tex]2\sqrt{b} + 5 = 11 - \sqrt{b}\\\\2\sqrt{4} + 5 = 11 - \sqrt{4}\\\\2*2 + 5 = 11 - 2\\\\4 + 5 = 11 - 2\\\\9 = 9 \ \ \ \ \checkmark\\\\[/tex]
The answer of b = 4 is confirmed.
It's always a good idea to check the answer with any equation. This is especially true with square root equations because the solution might be extraneous (meaning that it works in some equations but not in the original starting equation).