Answer:
$65.04
Step-by-step explanation:
Given:
Total amount left by the customer on table = $80
It contains cost of the food + 15% tip + 8% sales tax.
Sales tax and tip are calculated from the cost of food.
To find:
Cost of the food = ?
Solution:
Let the cost of food = $[tex]x[/tex]
As per given question statement:
Tip = 15% of [tex]x[/tex]
Sales Tax = 8% of [tex]x[/tex]
Money left on table = Cost of food + Tip + Sales tax
$80 = [tex]x[/tex] + 15% of [tex]x[/tex] + 8% of [tex]x[/tex]
Now, let us solve the equation:
[tex]\$80 = x + 15\%\ of\ x + 8\%\ of\ x\\\Rightarrow 80 = x + \dfrac{15}{100} \times x + \dfrac{8}{100} \times x\\\Rightarrow 80 = \dfrac{100x + 15\times x + 8\times x}{100}\\\Rightarrow 80 = \dfrac{123x}{100}\\\Rightarrow 80 \times 100= 123x\\\Rightarrow x = \dfrac{8000}{123}\\\Rightarrow \bold{x = \$65.04}[/tex]
Therefore, the cost of food, rounded off to nearest cent is $65.04.
Answer:
Step-by-step explanation:
The cost of the food as x, the tips as 0.15, and the tax as 0.08x. Then setting up and solving the equation x+0.15x+0.08x=80.
Convert 2 centimeters into feet. Round your answer to the nearest hundredth.
.066
1 Centimeter = 0.03280839895 Feet
The conversion of 2 centimeters into feet would be 0.066 feet.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.
We have to determine the conversion of 2 centimeters into feet.
Since one centimeter = 0.03280839895 feet
Therefore two centimeters = 2×0.03280839895 feet
⇒ two centimeters = 0.0656167
Round the answer to the nearest hundredth.
⇒ two centimeters = 0.066
Therefore, the conversion of 2 centimeters into feet would be 0.066 feet.
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Which fraction below is NOT equivalent to 1/3 2/6 3/9 4/12 5/13
Answer:
5/13 (irreducible)
Step-by-step explanation:
1/3=2/6=3/9=4/12 are all thirds of the total.
Use the figure to find the Total Area. 48 sq. units 84 sq. units 96 sq. units
Answer:
84 sq. units
Step-by-step explanation:
Total area is:
6*6 + 4*1/2*6*√(5² - (6/2)²) = 36 + 12*√16= 36 + 48 =84 sq. unitsWhat is the probability of getting a 10 or a jack from a deck of poker cards (52 cards)?
Answer:
15.38%
Step-by-step explanation:
there are four 10 cards and four jack cards.
4+4=8
you want to get one from 52 cards, so it's 8 out of 52. 8/52
to calculate the percentage, you multiply 8 by 100, then divide by 52.
8*100/52=15.38 (rounded answer)
Are the ray AB and BA the same? if yes why and if no why
Answer:
No,the ray AB and BA are not same because the ray AB denotes the ray(light) is coming from the direction through A while the ray BA denotes the ray is coming from the direction through B.
x = 2, w = -1, y = 6, z = 4 x²+4w - 2y
Answer:
-12Step-by-step explanation:
[tex]x = 2\\ w = -1\\ y = 6\\ z = 4\\x^2+4w-2y\\[/tex]
[tex](2)^2 +4(-1) -2(6)\\4 -4 -12\\0-12\\\\=-12[/tex]
Answer:
4x² + 4w - 2y
4(2)² + 4(-1) - 2(6)
4×4 + (-4) - 12
16 - 4 - 12
12 - 12
0 is the answer
Point u is on line segment tv given tv = x + 10, tu =3x-8, and Uv = 10 determine the numerical length of tv
Answer:
[tex]|tv = 14[/tex]
Step-by-step explanation:
Given
[tex]|tv = x + 10[/tex]
[tex]|tu = 3x - 8[/tex]
[tex]|uv = 10[/tex]
Required
Determine length of tv
Length tv is calculated by adding lengths tu and uv.
In other words
[tex]tv = tu + uv[/tex]
Substitute values for tv, tu and uv
[tex]x + 10 = 3x-8+10[/tex]
Collect like terms
[tex]x - 3x = -8+10 -10[/tex]
[tex]-2x = -8[/tex]
Divide both sides by -2
[tex]x = 4[/tex]
Recall that [tex]|tv = x + 10[/tex]
Substitute 4 for x
[tex]|tv = 4 + 10[/tex]
[tex]|tv = 14[/tex]
Hence, the length of line segment tv is 14
Simplify the following expression. (3m/4-2)+8 A. 8m/4 B. 9m/4 C. 3m+24/4 D. 3m+28/4
Answer:
C
Step-by-step explanation:
Given
( [tex]\frac{3m}{4}[/tex] - 2 ) + 8 ( remove parenthesis )
= [tex]\frac{3m}{4}[/tex] - 2 + 8
= [tex]\frac{3m}{4}[/tex] + 6
= [tex]\frac{3m}{4}[/tex] + [tex]\frac{24}{4}[/tex] ← add the numerators leaving the denominator
= [tex]\frac{3m+24}{4}[/tex] → C
A rectangular cake has a length of 25in, a width of 18in, and a height of 4in. Each container of frosting can cover 200 square inches.
Answer:
9 containers of frosting
Step-by-step explanation:
25 x 18 x 4, gives you 1800 square inches, divide 1800 by 200 and you get 9
ustin's hair is 3 1/4 inches long. How long will it be in 2 months if it grows 1/2 inch each month? Which method will NOT give the correct number of inches?
Answer:
3 1/2
Step-by-step explanation:
1/4 + 1/4
(1x4) + (1x4)
=_________
4x4
=8/16
8÷8
=_________
16÷8
=3 1/2
the fourth term of an arithmetic
progression is one less than twice the
second term If the sixth term is 7,
find the first term
Answer:
2
Step-by-step explanation:
Given AP where:
a₄ = 2a₂ - 1a₆ = 7To find
a₁ = ?Since
a₄ = a₁ + 3da₂ = a₁ + da₆ = a₁ + 5dInitial equations will change as:
a₁ + 3d = 2(a₁ + d) - 1 ⇒ a₁ + 3d = 2a₁ + 2d - 1 ⇒ a₁ = d + 1a₁ + 5d = 7 ⇒ a₁ = 7 - 5dComparing the above:
d + 1 = 7 - 5d6d = 6d = 1Then:
a₁ = d + 1 = 1 + 1 = 2a₁ = 2The first term is 2
solve for x 6 (8X minus 1) equals 9 (x + 2)
Answer:
x = [tex]\frac{8}{13}[/tex]
Step-by-step explanation:
Given
6(8x - 1) = 9(x + 2) ← distribute parenthesis on both sides
48x - 6 = 9x + 18 ( subtract 9x from both sides )
39x - 6 = 18 ( add 6 to both sides )
39x = 24 ( divide both sides by 39 )
x = [tex]\frac{24}{39}[/tex] = [tex]\frac{8}{13}[/tex]
last month you had an outstanding check of $87.90 that had not yet been cashed, so it did not show up on your statement. This month, you wrote checks totaling $379.42. You made one deposit of $100, and you withdrew $60 from an ATM. If the check from last month was cashed and recorded on your statement, and if the bank paid $0.23 in interest, then by how much did your account balance change this month?
Answer:
Step-by-step explanation:
Deposit made = + $ 100 . 00
withdrawal made = - $ 60 .00
check of last month encashed = - $ 87 . 90
interest paid by bank = + $ 00 . 23
-----------------------------------------------------------------------
Net effect = - $ 47.67
the account balance reduces by amount = $ 47.67
40% of the cost was tax. if the taxes paid were $15,000, what was the total cost of the car?
Answer:
$37500
Step-by-step explanation:
For this we can simply create a proportion of the percentages.
.4 / 1 == 15000 / x
Now we solve for x:
x = 15000/.4
x = 37500
Thus, the cost of the car was $37,500.
Cheers.
Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).
Answer: [tex]\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV[/tex] = 1087.5
Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.
An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.
Given the points, determine the vectors:
P = (5,0,0); Q = (0,9,0); R = (0,0,4)
vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)
vector QR = (0,9,0) - (0,0,4) = (0,9,-4)
Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:
n = PQ × QR = [tex]\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right][/tex][tex]\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right][/tex]
n = 36i + 0j + 45k - (0k + 0i - 20j)
n = 36i + 20j + 45k
Equation of a plane is generally given by:
[tex]a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0[/tex]
Then, replacing with point P and normal vector n:
[tex]36(x-5) + 20(y-0) + 45(z-0) = 0[/tex]
The equation is: 36x + 20y + 45z - 180 = 0
Second, in evaluating the triple integral, set limits:
In terms of z:
[tex]z = \frac{180-36x-20y}{45}[/tex]
When z = 0:
[tex]y = 9 + \frac{-9x}{5}[/tex]
When z=0 and y=0:
x = 5
Then, triple integral is:
[tex]\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx[/tex]
Calculating:
[tex]\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx[/tex]
[tex]\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx[/tex]
[tex]\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx[/tex]
[tex]\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx[/tex]
[tex]\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx[/tex]
[tex]\frac{1}{45} [30375-60750+118462.5-39150][/tex]
[tex]\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx[/tex] = 1087.5
The volume of the tetrahedon is 1087.5 cubic units.
The tripple integration will be [tex]\int\limits^a_E \int\limits^a_E \int\limits^a_E {xy} \, dV[/tex] = 1087.5
What is triple integration?The triple integration is used to identify the volumes of the objects or for analyzing three dimension of the object.
To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedron is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.
An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.
Given the points, determine the vectors:
P = (5,0,0); Q = (0,9,0); R = (0,0,4)
vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)
vector QR = (0,9,0) - (0,0,4) = (0,9,-4)
Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:
n = PQ × QR = [tex]\left[\begin{array}{ccc}i&j&k\\5&-9&-0\\0&9&-4\end{array}\right] \left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right][/tex]
n = 36i + 0j + 45k - (0k + 0i - 20j)
n = 36i + 20j + 45k
Equation of a plane is generally given by:
[tex]a(x-x_o)+b(y-y_o)+c(z-z_o)=0[/tex]
Then, replacing with point P and normal vector n:
[tex]36(x-5)+20(y-0)+45(z-0)=0[/tex]
The equation is: 36x + 20y + 45z - 180 = 0
Second, in evaluating the triple integral, set limits:
In terms of z:
[tex]z=\dfrac{180-36x-20y}{45}[/tex]
When z = 0:
[tex]y=9+\dfrac{-9x}{5}[/tex]
When z=0 and y=0:
x = 5
Then, triple integral is:
[tex]\int\limits^5_0 \int\int xy\ dzdydx[/tex]
Calculating:
[tex]\int\limits^5_0 \int\int xy\ dzdydx[/tex]
[tex]\int\limits^5_0 \int\int xy\ (\dfrac{180-36x-20y}{45}-0)dydx[/tex]
[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 180xy-36x^2y-20xy^2dydx[/tex]
[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 90xy^2-18x^2y^2-\dfrac{20}{3}xy^3dydx[/tex]
[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 2430x-1458x^2+\dfrac{94770}{125}x^3-\dfrac{23490}{375}x^4dx[/tex]
[tex]\dfrac{1}{45} [30375-60750+118462.5-39150][/tex]
[tex]\int\limits^5_0 \int\int xy\ dzdydx=1087.5[/tex]
The volume of the tetrahedron is 1087.5 cubic units.
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Use the graph of f(x)=x^2 to find a number δ such that ∣x^2−1∣<0.1 whenever 0<|x−1|<δ.
Answer:
[tex]\delta=0.0333[/tex]
Step-by-step explanation:
[tex]|x^2-1}=|x-1||x+1|<0.1[/tex]
[tex]|x|-|1|<|x-1|<1[/tex]
[tex]|x|<2[/tex]
[tex]|x+1|<3[/tex]
Hence
[tex]|x-1|<\frac{0.1}{|x+1|}[/tex]
[tex]|x-1|<\frac{0.1}{3}=0.333 =\delta[/tex]
Hopefully you get what I meant!!
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 210 engines and the mean pressure was 5.0 pounds/square inch (psi). Assume the population standard deviation is 0.9. The engineer designed the valve such that it would produce a mean pressure of 4.9 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic.
Answer:
The test statistics is [tex]t = 1.610[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 210
The sample mean is [tex]\= x = 5.0 \ pounds /square \ inch[/tex]
The standard deviation is [tex]\sigma = 0.9 \[/tex]
The population mean is [tex]\mu = 4.9 \ psi[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu}{ \frac{\sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{5 - 4.9}{ \frac{ 0.9 }{ \sqrt{ 210 } } }[/tex]
=> [tex]t = 1.610[/tex]
if X^8 = (2^2)^4, what is X^2
Answer:
x^2 = 4
Step-by-step explanation:
X^8 = (2^2)^4
Rewriting
x^8 as (x^2) ^4 since we know that a^b^c = a^(b*c) and 2*4 = 8
(x^2) ^4 = (2^2)^4
Since the exponents are the same the bases must be the same
x^2 = 2^2
x^2 = 4
NASA is building a satellite that is roughly the shape of a sphere. If the satellite weighs 14.25 pounds per cubic foot before launch, and has a diameter of 4.7 feet, what is the total weight in pounds of the satellite on Earth? Use π = 3.14.
Answer:
774 lb
Step-by-step explanation:
weight = volume * density
radius = diameter/2
volume = (4/3)πr^3
volume = (4/3)(3.14)(4.7/2 ft)^3
weight = (4/3)(3.14)(4.7/2 ft)^3 * 14.25 lb/ft^3
weight = 774 lb
An electrician disconnected 5 wires of different colors from their respective connections and forgot the order in which they were placed. Assuming you connect them by trying different sorts and that the last one is correct, how many tries must you do before getting it right?
Answer:
120 tries
Step-by-step explanation:
You can try 5 different wires in the first connection.
Then you have 4 wires left, so you try 4 wires in the second connection. Remember, you are now trying 4 wires for each of the first 5, so up to here you already made 4 * 5 tries = 20 tries.
Next you try 3, then 2, then you have 1 left.
Number of tries: 5 * 4 * 3 * 2 * 1 = 120
Answer: 120 tries
If 8 people can pick the apples from trees in 6 days, how long will it take12 people?
The bases of a trapezoid will measure 14.5 ft and 22.5 ft. What is the minimum height of the trapezoid of the patio is to have an area os no less than 259 sq ft?
Answer:
14 ft
Step-by-step explanation:
The area of a trapezoid is given by
A = (1/2)(b1 +b2)h
You want ...
A ≥ 259
(1/2)(14.5 +22.5)h ≥ 259
37/2·h ≥ 259
h ≥ 259(2/37)
h ≥ 14 . . . . . . . feet
The height must be no less than 14 feet.
HELP ASAP
8^2 – 10x - 3
NEED ALL STEPS PLZZZZ
Answer:
hope this attachment will help you
Solve 1 over 36 = 6x−3.
Answer:
x = 109/216
Step-by-step explanation:
Solve for x:
1/36 = 6 x - 3
Hint: | Reverse the equality in 1/36 = 6 x - 3 in order to isolate x to the left hand side.
1/36 = 6 x - 3 is equivalent to 6 x - 3 = 1/36:
6 x - 3 = 1/36
Hint: | Isolate terms with x to the left hand side.
Add 3 to both sides:
6 x + (3 - 3) = 3 + 1/36
Hint: | Look for the difference of two identical terms.
3 - 3 = 0:
6 x = 1/36 + 3
Hint: | Put the fractions in 1/36 + 3 over a common denominator.
Put 1/36 + 3 over the common denominator 36. 1/36 + 3 = 1/36 + (36×3)/36:
6 x = 1/36 + (36×3)/36
Hint: | Multiply 36 and 3 together.
36×3 = 108:
6 x = 1/36 + 108/36
Hint: | Add the fractions over a common denominator to a single fraction.
1/36 + 108/36 = (1 + 108)/36:
6 x = (1 + 108)/36
Hint: | Evaluate 1 + 108.
1 + 108 = 109:
6 x = 109/36
Hint: | Solve for x.
Divide both sides by 6:
x = (109/6)/36
Hint: | Multiply 36 and 6 together.
36×6 = 216:
Answer: x = 109/216
Answer:
x = 109/216
Step-by-step explanation:
Add 3, divide by 6.
[tex]\dfrac{1}{36}=6x-3\\\\3+\dfrac{1}{36}=6x\\\\\dfrac{109}{(36)(6)}=\boxed{x=\dfrac{109}{216}}[/tex]
A researcher examines the records of all registered voters in one city and finds that 43% are registered democrats. Is the evaluated group a population or a sample?
Answer: Population
Step-by-step explanation: Population is refers to the whole or entire members or of a given set. This is different from a sample which is used to refer to members of a subset (a subset is a certain portion or fraction of an entire set). In the scenario above, since the evaluation was based on the entire number of registered voters in the country, this means we are referring to a population. The inference about the percentage of democratic voters was drawn from a pool of all the entire number of registered voters available in the country and not from a certain subset or portion of registered voters. Hence, the evaluated group is a population.
A teacher records the amount of time it took a random sample of students to finish a test and their scores on that test. Let x be the score and y be the amount of time. Conduct a hypothesis test of the claim that there is a linear correlation between the variables, using a 0.10 level of significance. Find the PERCENTAGE OF THE VARIANCE IN THE Y-VALUES THAT CAN BE EXPLAINED BY THEIR LINEAR RELATIONSHIP WITH THE X-VALUES.
Answer:
The question is incomplete. The complete table is:
Score in percent (X): 80, 75, 70, 90, 95, 100, 75, 60, 75, 95
Time in minute (Y) : 45, 48, 40, 50, 40, 30, 30, 39, 38, 55
The answer is 0.55 %
Step-by-step explanation:
ΣX = 815
ΣY = 425
ΣX x Y = 34565
Σ = 67925
Σ[tex]$Y^2$[/tex] = 18699
So, correlation coefficient, b
[tex]$b= \frac{n \Sigma XY- \Sigma X \Sigma Y}{\sqrt{n \Sigma X^2-( \Sigma X)^2} \times \sqrt{(n \Sigma Y^2 -(\Sigma Y)^2}}$[/tex]
[tex]$b = \frac{(10 \times 34565)-(815 \times 425)}{\sqrt{(10 \times 67925)-(815)^2} \times \sqrt{(10 \times 10699)-(425)^2}}$[/tex]
[tex]$b= -\frac{725}{9779 \times 2702}$[/tex]
b = -0.0741
Correlation Determination:
[tex]$B^2 = (-0.0741)^2$[/tex]
= = 0.0055 = 0.55%
Therefore, 0.55 percentage of the variation in y can be explained by x variable.
If 15 oranges cost Rs. 70,how much do 39 oranges cost ?
Answer:
firstly divide 70 by 15 and when the product came multiply it with 39Step-by-step explanation:
70 ÷ 15 = 4.66
4.66 × 39 = 181.974
Consider the system of equations. y = 3x + 2 y = − 2 3 x − 4 Explain why these particular equations can be graphed immediately. Explain why these particular equations can be graphed immediately.
The equations can be graphed immediately because the slopes and the y-intercepts are known
The system of equations is given as:
y = 3x + 2y = -2/3x - 4The equations in the system are linear equations, and they are represented as:
[tex]y = mx + b[/tex]
Where:
m represents the slopeb represents the y-interceptFrom the given system, we can find the slopes and the y-intercepts of both functions easily
Hence, the equations can be graphed immediately because the slopes and the y-intercepts are known
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20+2x=x+56 solve for x
Answer:
Rearrange the numbers to their like terms.
which is 2x-x=56-20.
x=36.
The solution to the equation is x = 36.
To solve the equation 20 + 2x = x + 56 for the variable x, you can follow these steps:
Step 1: Move all terms containing x to one side of the equation by subtracting x from both sides:
20 + 2x - x = x + 56 - x
20 + x = 56
Step 2: Subtract 20 from both sides to isolate the x term:
20 + x - 20 = 56 - 20
x = 36
Therefore, the solution to the equation is x = 36.
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This visual representation shows the sets of real numbers. Which statement is true regarding the number sets? a. All integers are also rational numbers. b. All rational numbers are also integers. c. Some integers are also rational numbers, but not all integers are rational numbers. d. Integers and rational numbers have no numbers in common. explain your answer and say the answer
Answer:
A.
Step-by-step explanation:
The visual representation is All integers are also rational numbers
what are rational number?A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0. The set of rational numbers is denoted by Q.
So, we have sets of real number.
As. we know
All natural numbers, whole numbers, and integers are rationals, but not all rational numbers are natural numbers, whole numbers, or integers.
Hence, integers are also rational numbers
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