The sales receipt for the purchase includes the sales tax
The sales tax is 6%The price at the top is $7.50The original price at the top is $12.50How to determine the percent of sales tax?The sales tax is calculated as:
Percentage sales tax * (Sum of Items subjected to tax) = Sales tax.
So, we have:
T * (3 + 0.5) = 0.21
Evaluate the sum
T * (3.5) = 0.21
Divide both sides by 3.5
T = 6%
Hence, the sales tax is 6%
The price at the topThe price (p) at the top is calculated using:
p = 13 - 3 - 2 - 0.5
Evaluate the difference
p = 7.5
Hence, the price at the top is $7.50
The original price at the top60% of the original price (P) is p.
So, we have:
60% * P = p
Substitute 7.5 for p
60% * P = 7.5
Divide both sides by 60%
P = 12.5
Hence, the original price at the top is $12.50
Read more about sales tax and discounts at:
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when each edge of a cube is decreased by 1 cm, its volume is decreased by 91 cm^3 .Find the length of the a side of the original cube.
Step-by-step explanation:
the original side length is x.
the volume of a block is length × width × height.
so, for a cube with all sides being equal, the volume in our case is x³ (x × x × x).
now, with the same formula but with every side shortened by 1 cm we get
(x-1)(x-1)(x-1) = x³ - 91 (the original volume minus 91)
now, we have to do the multiplications.
(x-1)(x-1) = x² - 2x + 1
(x²-2x+1)(x-1) = x³ - x² - 2x² + 2x + x - 1 = x³ -3x² + 3x -1
x³ - 3x² + 3x - 1 = x³ - 91
-3x² + 3x = -90
-x² + x = -30
x² - x = 30
x² - x - 30 = 0
the general solution to such a squared equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = -1
c = -30
x = (1 ± sqrt((-1)² - 4×1×-30))/(2×1) =
= (1 ± sqrt(1 + 120))/2 = (1 ± sqrt(121))/2 =
= (1 ± 11)/2
x1 = (1 + 11)/2 = 12/2 = 6
x2 = (1 - 11)/2 = -10/2 = -5
a negative number does not make any sense for a side length, so our solution is x = 6 cm.
the original side length of the cube is 6 cm.
to check :
6³ = 216
(6-1)³ = 5³ = 125
216 - 125 = 91
perfect.
help i’ll mark brainlist
A kite string is 100 feet long from the kite to the ground. The string makes a 45° angle with the ground
About how high off the ground is the kite? Leave your answer as a simplified radical
Answer:
It's not very high
Step-by-step explanation:
The angle that the string and the ground maje, is acute, because it's smaller than a right angle. So, since it is an acute angle, it's not very high. It is about 30cm high.
HELP ME PLEASE
Solve for x: -6 – 5x = 29
Answer:
x = -7
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (&Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, add 6 to both sides of the equation:
-5x - 6 = 29
-5x - 6 (+6) = 29 (+6)
-5x = 29 + 6
-5x = 35
Next, divide -5 from both sides of the equation:
(-5x)/-5 = (35)/-5
x = 35/-5
x = -7
-7 is your answer for x.
~
The accompanying table shows the number of bacteria present in a certain culture
over a 5 hour period, where x is the time, in hours, and y is the number of
bacteria. Write an exponential regression equation for this set of data, rounding all
coefficients to the nearest hundredth. Using this equation, determine the number o
bacteria present after 13 hours, to the nearest whole number.
Hours (x) Bacteria (y)
0 1892
1
2106
2
2
2342
3
2525
4
2819
4
5
5
3042
The general form of the exponential regression equation that models the number of bacteria is y = ab^x
The exponential regression equation is y = 1910.38 * 1.1^x
How to determine the exponential regression equation?The dataset is given as:
x y
0 1892
1 2106
2 2342
3 2525
4 2819
5 3042
To determine the exponential regression equation, we make use of a graphing calculator.
From the graphing calculator, we have the following calculation summary
a = 1910.38
b = 1.10
An exponential regression equation is represented as:
y = ab^x
So, we have:
y = 1910.38 * 1.1^x
Hence, the exponential regression equation is y = 1910.38 * 1.1^x
Read more about regression equations at:
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Approximately how many grams of radium will remain after 4 grams have decayed for 2400 years
Answer:
1.4
Step-by-step explanation:
Find the volume of the cone. Round your answer to the nearest tenth.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
Radius (r) = 2 cmheight (h) = 8 cmNow, let's apply the formula :
[tex]\qquad \sf \dashrightarrow \:v = \frac{1}{3} \pi {r}^{2} h[/tex]
[tex]\qquad \sf \dashrightarrow \:v = \frac{1}{3} \times 3.14 \times {(2)}^{2} \times 8[/tex]
[tex]\qquad \sf \dashrightarrow \:v = \frac{100.48}{ 3} [/tex]
[tex]\qquad \sf \dashrightarrow \:v = 33.49333333.....[/tex]
[tex]\qquad \sf \dashrightarrow \:v \approx33.5 \: \: cm {}^{3} [/tex]
X2-7x+6; x2-5x-6 please help
Answer: (x−6)(x−1)(x+1)
if 2.5kg of potatoes cost £1.40
work out the cost of 4.25kg of potatoes
Answer:2.5 kg of potatoes cost £1.40 Work out the cost of 4.25 kg of potatoes. 1.25kg=70p 2.5 kg=1.40 3.75 kg=2.10 Done.
Step-by-step explanation: hope this helps love!!
divide y⁴-2y³-7y²+8y+12 by (y-3) using long division method
please give answer
PLEASE LOOK AT PICTURE AND HELP!!!
Answer:
answer A
Step-by-step explanation:
nnnnmmmkkkkkkookl
Find the next three terms in the sequence. 24,20,16,12…. (If you could explain it that would be great too. It’s a bit confusing)
Answer:
the next three numbers should be 8, 4, 0
Step-by-step explanation:
it reduces by 4 each time
24 - 4 = 20
20 - 4 = 16
16 - 4 = 12
12 - 4 = 8
8 - 4 = 4
4 - 4 = 0
First term =a=24
common difference=d=20-24=-4
Formula
a_n=24-4(n-1)a_5
24-4(4)8a_6
24-5(4)4a_7
24-6(4)0Factor completely 2x2 − 2x − 40. 2(x − 5)(x 4) (2x − 10)(x 4) (x − 5)(2x 8) 2(x − 4)(x 5).
The factor the given polynomial are 2,(x+4),(x-5).
We have given that the equation,
[tex]2x^2 -2x -40[/tex]
What is the meaning factor?Factoring a polynomial is expressing the polynomial as a product of two or more factors.
We can factor out a 2.
[tex]2(x^2 - x - 20)[/tex]
Now, we can write down the 2 and factor the [tex](x^2 - x - 20)[/tex].
[tex](x^2-x - 20)=x^2-5x+4x-20\\ =x(x-5)+4(x-5)\\ =(x+4)(x-5)[/tex]
[tex]f(x)=2x^2 -2x -40=2(x^2 - x - 20)=2(x+4)(x-5)[/tex]
Therefore, the factor the given polynomial are 2,(x+4),(x-5).
To learn more about the factor visit:
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what is the least common denominator of 1/3 and 1/6
Answer: 6. this is like 3rd grade math just multiply 1/3 and 1/6 to see
Answer:
1/2
Step-by-step explanation:
1/6/1/3=1/2or2
I the not understand the question properly
What is the measure of
Answer:
25
if j 25 L is going to be 25
PLS HELP I'LL MARK BRAINLIEST
Answer:
Domain: (-∞, -5) ∪ (-1, ∞)
Step-by-step explanation:
Note:
For f(x) > 0: See the points of x for which the graph of f(x) lies above the x-axis.
For f(x) < 0: See the points of x for which the graph of f(x) lies below the x-axis.
We need to find the domain of f(x) for which f(x) < 0
From the graph, we can tell:
f(x) < 0 on (-∞, -5) ∪ (-1, ∞)
Therefore: The domain on which the given graph f(x) is negative, is (-∞, -5) ∪ (-1, ∞)
The owners of cami's carnival kept track of how many visitors they had each day last summer. this box plot shows the results. carnival visitors 50 70 90 110 130 150 what fraction of the days did the carnival have 70 or fewer visitors?
Answer: 1/3
Step-by-step explanation: 50, and 90, 2/6 reduces to 1/3.................2 pp ignore the 2 and p I'm in mobile
Please help me with this problem
Evaluate (-½·3)³
Answer: -27/8
Step-by-step explanation:
[tex]\left(-\frac{1}{2}\cdot \:3\right)^3[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=-a^n,\:\quad \mathrm{if\:}n\mathrm{\:is\:odd}[/tex]
[tex]\left(-\frac{1}{2}\cdot \:3\right)^3=-\left(\frac{1}{2}\cdot \:3\right)^3[/tex]
[tex]=-\left(\frac{1}{2}\cdot \:3\right)^3[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n[/tex]
[tex]\left(\frac{1}{2}\cdot \:3\right)^3=\left(\frac{1}{2}\right)^3\cdot \:3^3[/tex]
[tex]=-\left(\frac{1}{2}\right)^3\cdot \:3^3[/tex]
[tex]=-\frac{1}{8}\cdot \:3^3[/tex]
[tex]=-\frac{1}{8}\cdot \:27[/tex]
[tex]=-\frac{27}{8}[/tex]
Please help! will give brainlest! locks in 30 min!
Answer:
LAST CHOICE IS THE ANSWER.Step-by-step explanation:
#BRAINLIESTBUNCHAnswer:
[tex]-\sqrt{3}[/tex]
Step-by-step explanation:
tan (θ) = [tex]-\frac{\sqrt{3} }{2}[/tex] ÷ [tex]\frac{1}{2}[/tex]
tan (θ) = [tex]-\sqrt{3}[/tex]
hope this helps and is right!! p.s. i really need brainliest :)
Does the budgeted amount cover the actual amount for expenses, savings, and emergencies?
A)
No, it's short $207.00,
No, it's short $227,00,
o
Yes, there's a surplus of $207.000
D)
Yes, there's a surplus of $227.00,
Answer:
No its short 207
Step-by-step explanation:
Took the test on UsaTestPrep got it right :)
Bye loves <3
Answer:
the one b4 is wrong its a surplus of 207 .-.
Step-by-step explanation:
this is correct usatestprep also lol
pls help!! and thank you
find the area of the circles
Answer:
10) 25π OR 78.5398...yd 11) 1/4π OR 0.785398...ft 12) 100π OR 314.159265....in
Step-by-step explanation:
area of a circle = πr^2 (π x radius squared)
the radius is just half the diameter
so for eg:
number 10)
diameter = 10 yd so radius = 5 yd
5 squared = 25
π x 25 yd = 25π OR 78.5398...yd
i hope this helped :)
Stretch
2. A gym runs two fitness classes, spinning and circuits.
On Saturday 100 people visited the gym.
18 people attended the spinning class.
10 people attended both classes.
56 people did not attend either class.
a) Represent this information on a Venn diagram
६
S
Ic с
10
(3)
56
A person who attended the gym is selected at random. .
Find the probability that this person:
b) attended only circuits
(2)
c) attended exactly one class
(2)
d) attended spinning, given that they attended circuits
. (2)
The probability that a person chosen at random attended only circuits is 0.16.
The probability that a person chosen at random attended exactly one class is 0.0288.
The probability that a person chosen at random attended spinning, given that they attended circuits is 0.10
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability a person chosen at random attended only circuits = number of people who atended circuits / total number of the people at the gym
16/100 = 0.16
Probability a person chosen at random attended exactly one class = (number of people who atended circuits only / total number of the people at the gym) x (number of people who atended spinning class only / total number of the people at the gym)
16/100 x 18/100 = 0.0288
Probability a person chosen at random attended spinning, given that they attended circuits= 10/100 = 0.10
Please find attached the required diagram. To learn more about probability, please check: https://brainly.com/question/13234031
The Furnace Creek Airport in Death Valley, California, has an elevation of 64 meters below sea level. The lowest point in New Orleans, Louisiana, has an elevation of -2 meters. What is the difference between the elevation in New Orleans and the elevation at the Furnace Creek Airport?
Answer:66 meters
Step-by-step explanation:
just change the negative to a positive and add them together. It would be 66.
The space shuttle carries c pounds of cargo, and each piece of cargo weighs 212.66 pounds. Which of the following expressions represents the number of pieces of cargo?
Answer:
The answer would be B. c ÷ 158.14
Step-by-step explanation:
i just took this test :) the question was:
The space shuttle carries c pounds of cargo, and each piece of cargo weighs 158.14 pounds. Which of the following expressions represents the number of pieces of cargo The space shuttle carries c pounds of cargo, and each piece of cargo weighs 158.14 pounds? Which of the following expressions represents the number of pieces of cargo?
A. c × 158.14
B. c ÷ 158.14
C. c - 158.14
D. c + 158.14
Question 2 (Multiple Choice Worth 1 points)
(04.02 MC)
3
What is the y-intercept of the line perpendicular to the line y = - x + 5 that includes the point (-3,-3)?
4
O
Aiw
4
01
07
O
21
4
Answer:
y- intercept = 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{3}{4}[/tex] x + 5 ← is in slope- intercept form
with slope m = - [tex]\frac{3}{4}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{3}{4} }[/tex] = [tex]\frac{4}{3}[/tex] , then equation of perpendicular line is
y = [tex]\frac{4}{3}[/tex] x + c
to find c substitute (- 3, - 3 ) into the equation
- 3 = - 4 + c ⇒ c = - 3 + 4 = 1
that is the y- intercept of the perpendicular line is c = 1
How many cards are in each pack? There are __ cards in each pack
Answer:
there are 52 cards in each pack
Answer:
52.
Step-by-step explanation:
A deck of cards have 52 cards.
·[tex]3\sqrt{10}\ times -6\sqrt{30}[/tex]
Due by 12:23
Answer:
-180√3
Step-by-step explanation:
3√10 x - 6√30
= 3x-6 x -√10 x √30
= -18 x√300
= -18 x 10√3
= -180√3
Which equation represents a graph with a vertex of (−3,2)?
Answer:
y = 4x² + 24x + 38
Step-by-step explanation:
X + Y-2 (3X-4Y+3) please simplify this
thanks
Answer:
-5x+9y-6
Step-by-step explanation:
Step 1:
Remove bracket,
x+y-6x+8y-6
collect like terms and simplify,
x-6x+y+8y-6= -5x+9y-6
i need help cause is due at 11:59 est
Answer:
Matt used diameter of the ball instead of Radius
Step-by-step explanation:
The volume of a sphere is given as:
4/3πr³⇒ Matt made an error in his calculation by failing to covert the value of the diameter given to Radius.
⇒ By dividing the diameter by 2 = 15 / 2 = 7.5, we obtain the Radius, which is what Billy did in her own calculation.