the lunch cost, including tax and tip 67.31$.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, the Patterson family went to eat lunch at a new restaurant. They spent $52.30 on their meal. The restaurant will add a 7 1/4% tax to the cost of the meal.
total cost after the tax = 52.30*(1 + 7 1/4)%
total cost after the tax = 52.30* 7.25/100 + 52.30
total cost after the tax = 3.79 + 52.30
total cost after the tax = 56.09
Since,
Mr Patterson was very happy with the food and service so he gave a 20% tip to the waitress.
Thus,
Total cost after the tip = 56.09(1 +20/100)
Total cost after the tip = 56.09 * 1.2
Total cost after the tip = 67.308
Therefore, the lunch cost, including tax and tip 67.31$.
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Sin Cos Tan
i need help
Answer:
Step-by-step explanation:
4) SinC = 30/34
C = sin^-1(30/34)
C = 61.93 degrees
A = 90-61.93
A = 28.07 degrees
5) SinA = 24/26
A = sin^-1(24/26)
A = 67.38
one circle c1 of radius 2 is centered at the origin. on top of the circle a second circle, c2, is placed, with radius 1 and center (0, 4). find the center of gravity, ( x, y ) , of the combination of the two circles.
The center of gravity of the combination of the two circles is at (x, y) = (0, 4/5).
The center of gravity, or the center of mass, of a two-dimensional object can be found by taking the weighted average of the x-coordinates and y-coordinates of the individual masses making up the object.
In this case, the two circles can be treated as point masses, with the mass of each circle being proportional to its area. The area of a circle with radius r is given by pi * r^2.
So, for circle c1 with radius 2, its mass is given by:
m1 = pi * 2^2 = 4 * pi
And for circle c2 with radius 1, its mass is given by:
m2 = pi * 1^2 = pi
The x-coordinate of the center of gravity is given by the weighted average of the x-coordinates of the two masses:
x = (m1 * 0 + m2 * 0) / (m1 + m2) = 0
Similarly, the y-coordinate of the center of gravity is given by the weighted average of the y-coordinates of the two masses:
y = (m1 * 0 + m2 * 4) / (m1 + m2) = 4 * (m2 / (m1 + m2)) = 4 * (pi / (4 * pi + pi)) = 4 * (pi / 5 * pi) = 4/5
So, the center of gravity of the combination of the two circles is at (x, y) = (0, 4/5).
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what happens to the expected value of M a, sample size increases? a. It decreases 10, b. t also increases. e. It stays constant. d· The expected value does not change in a predictable manner when sample size increases.
The expected value of M does not change in a predictable manner when sample size increases; it can increase, decrease, or stay the same.
The expected value of M, or the mean of a sample, is determined by the values of the individual elements that comprise it. As such, when the sample size increases, the expected value of M could increase, decrease, or remain constant, depending on the particular values of the individual elements in the sample. This is because the expected value of M is the average of the individual elements and the contribution of each element to the average depends on its value and the number of elements in the sample. Therefore, the expected value of M does not change in a predictable manner when sample size increases. Depending on the individual elements in the sample, the expected value of M could be higher, lower, or constant.
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Cold weather can be especially hard on Kurt's grandfather, so Kurt is knitting him a striped scarf for his birthday. The scarf is almost finished when Kurt discovers a mistake! He has to unravel 0.5 feet of the scarf, and now the remaining part is only 3.75 feet long
Answer:
Kurt originally knitted the scarf to be 3.75 feet + 0.5 feet = 4.25 feet long.
I found the answer by using basic addition. I added the length that Kurt had to unravel (0.5 feet) to the remaining length of the scarf (3.75 feet) to find the original length of the scarf (4.25 feet).
Step-by-step explanation:
Take a factor out of each square root.
√17x² where x > 0
The factor of quadratic equation is x√17
What is quadratic equation?A quadratic equation is one that contains a second-degree polynomial. They are extensively utilized in a wide range of disciplines, including engineering, architecture, finance, biology, and, of course, mathematics.
Factoring is frequently the simplest way to solve a quadratic equation. Finding expressions that can be multiplied together to get the expression on one side of the problem is the process of factoring. A quadratic equation is represented as a product of linear terms if it can be factored.
First you need to find perfect square factors of 17
17 = 1*17
√17 = √1*√17 = 1√17 = √17
we had also √x² = x
So the answer is x√17
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Find the volume of the resulting solid if the region under the curve y = 9/(x ^ 2 + 3x + 2) from x = 0 to x = 1 is rotated about the x-axis and the y-axis.
When a region is rotated about the x-axis, a cylinder is formed. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height of the cylinder.
What is volume of a cylinde ?The volume of a cylinder is the amount of space the cylinder takes up. It is found by multiplying the area of the cylinder's base by its height. The formula for finding the volume of a cylinder is V = πr²h, where r is the radius of the cylinder's base, and h is its height.
The radius of the cylinder is equal to the distance from the x-axis to the highest point on the graph of y = 9/(x² + 3x + 2).
To find the highest point on the graph, we differentiate the function and find the critical points.
Differentiating y = 9/(x² + 3x + 2):
dy/dx = -18x / (x² + 3x + 2)²
Setting dy/dx = 0 and solving for x:
-18x / (x² + 3x + 2)² = 0
x = -3, 2
For x = -3, y = 9/(-3² + 3(-3) + 2) = 9/1 = 9
For x = 2, y = 9/(2² + 3(2) + 2) = 9/8 = 1.125
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1. Find the value of x. Round to the tenths. (Hint: The sum of the angle measures of a
quadrilateral is 360°).
2x+6
15x-8
Answer:
10.7 °
Step-by-step explanation:
In this problem, there are two angles with degrees of 2x + 6 and two angles of degrees of 15x - 8. We know the sum of the four angles is 360, as stated in the problem. Thus we can set up the following equation:
2(2x + 6) + 2(15x - 8) = 360
4x + 12 + 30x -16 = 360
34x - 4 = 360
34x = 364
x ≈ 10.7 °
which of the following equations have no solutions?
choose all answers that apply:
a: −60x+32=32x+60
b: −60x+32=−60x+60
c: −60x+32=32x−60
d: −60x+32=−60x−32
The equations with no solutions are −60x+32=−60x+60 and −60x+32=−60x−32. Options B and D
What are algebraic expressions?Algebraic expressions are described as expressions that are made up of terms, variables, coefficients, constants and factors.
They are also composed of arithmetic operations, such as;
AdditionBracketParenthesesSubtractionMultiplication, etcFrom the information given, we have that the expression or equation without solutions are those with the value of x as 0.
−60x+32=−60x+60
collect like terms
-60x + 60x = 28
Hence, the equations are −60x+32=−60x+60 and −60x+32=−60x−32
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What percent of the
square is shaded in?
When you type your answer
do not include a % sign.
Answer:
1 1/3 or just 1/3
Step-by-step explanation:
What percent of the shape is shaded in?
Alright to start, let's look at the shape, it is divided into 4 equal parts, one part is shaded, which gives us 1/4, or 25% or 0.25. Then there's another part, which is half shaded, that'll be half of 1/4 or 25% or 0.25, which is 1/8 or 12.5% or 0.125. Now all you have to do is add them together.
1/4 + 1/8 = 3/8
25% + 12.5% = 37.5%
0.25 + 0.125 = 0.3725
These are your three answers you can choose from, I guess the second one won't work because the problem states not to include a % sign.
Hope this helped!
PLEASE HELP 15 POINTS
The area of the given given shape which consists of a triangle and a quarter circle to 1 decimal place would be =161.04m².
How to calculate the area of a triangle?The formula used to calculate the are of triangle= ½base×height.
where; Base= 12m
height= 20-12 = 8 m
area = 1/2×12×8 = 48m²
The formula for the area of a quarter circle = πr²/4
where r = 12m
Area = 3.14 × 12²/4
= 3.14×144/4
= 452.16/4
= 113.04m²
Therefore, the area of the figure = 48+ 113.04 = 161.04m²
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Patrick is a great babysitter. He makes $9 an hour. Lila is an even better babysitter. She makes $12 an hour. Lila works 6 hours each week. How many hours does Patrick need to work in order to earn as much money as Lila earns in a week?
Answer:
8 hours
Step-by-step explanation:
We know that since Lila earns $12/hr and works 6 hr/week, she earned 72 since 12 * 6 = 72.
We can let the amount Patrick earns each week represent 9h, where h is the amount of hours he works.
We can solve for h by setting Patrick's equation equal to 72, which is Lila's earnings:
[tex]9h=72\\h=8\\\\9(8)=72\\12(6)=72[/tex]
please just give me an answer to this true or false intro to inequalities:-3a <15,if a=2
Answer: true
Step-by-step explanation:
Two trees are planted next to each other. One tree is 4 meters tall and casts a 16-meter shadow. Determine the height of the other tree if it casts a 29-meter shadow.
1.81 m
3.25 m
7.25 m
12.25 m
The height of the other tree is 7.25 meters
How to determine the height of the other treeFrom the question, we have the following parameters that can be used in our computation:
One tree is 4 meters tall casts a 16-meter shadowUsing the above as a guide, we have the following:
Ratio = Height : Shadow
So, we have
Height : Shadow = 4 : 16
Simplify
Height : Shadow = 1 : 4
So, we have
Height : 29 = 1 : 4
This means that
Height = 29 * 1/4
Evaluate
Height = 7.25
Hence the height is 7.25 meters
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Answer:
The height of the other tree is 7.25 meters
Step-by-step explanation:
LN is tangent to circle O at point M and QM is a diameter. Determine the measure of the following angles. The measure of ∠QML is degrees. The measure of ∠PMN is degrees
LN is tangent to circle O at point M and QM is a diameter. The measure of ∠QML and ∠PMN are 90° and 63° respectively.
1) To Determine the degree measurement of ∠QML
Based on the Perpendicular Tangent Theorem, tangent lines are always perpendicular to a circle's radius at the point of intersection
So, the radius OM is perpendicular to line LN at point M.
Hence,
The value of ∠QML = 90°
2) To determine the degree measurement of angle PMN
∠QMN = ∠QMP + ∠PMN
By the angle addition postulate, we can calculate this measurement as follows:
∠QMN = 90°
∠QMP = 27°
Replace with and substitute the value of angle QML into the equation.
90° = 27° + ∠PMN
∠PMN = 90° - 27° = 63°
Therefore, the value of ∠PMN is 63°
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Albert invests money in an account that earns a yearly dividend. The amount, A, in his account at the end of t years is given by the equation Which statement is correct?
The amount in the account after t years is given as follows:
A(t) = A(0)(1 + r)^t.
In which:
A(0) is the initial amount.r is the growth rate, as a decimal.How to model the situation?The standard definition of an exponential function is given as follows:
y = a(b)^x.
In which:
a is the initial value.b is the rate of change, as a decimal.For an increasing exponential function, the rate of change is given as follows:
b = 1 + r.
In which r is the growth rate, as a decimal.
Considering that the balance increases according to the yearly dividend, the equation is given as follows:
A(t) = A(0)(1 + r)^t.
Missing InformationThe problem is incomplete, hence the general procedure in obtaining the equation was presented, which can be used to analyze the statements.
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The circle has a diameter of 0.2 m.
The height of the square is a fifth of the diameter
of the circle.
Calculate the shaded area in cm.
Give your answer to 2 decimal places.
Rounding to 2 decimal places, the shaded area is 234 cm².
What is the radius of circle?
The radius of a circle is the distance from the center of the circle to any point on the circumference of the circle. It is half of the diameter of the circle.
The diameter of the circle is 0.2 meters, which means the radius of the circle is 0.2 / 2 = 0.1 meters.
The height of the square is a fifth of the diameter of the circle, so the height of the square is 0.2 / 5 = 0.04 meters.
To find the shaded area in cm, we need to find the area of the circle and subtract the area of the square. The area of the circle is given by the formula πr², where r is the radius of the circle. The area of the square is simply the height multiplied by the width, which is equal to the diameter of the circle.
So, the area of the circle is π * 0.1² = 0.0314 square meters. The area of the square is 0.2 * 0.04 = 0.008 square meters. The shaded area is the difference between these two, or 0.0314 - 0.008 = 0.0234 square meters.
To convert the area to cm², we need to multiply by 10⁴. The shaded area in cm² is 0.0234 * 10⁴ = 234 cm².
Rounding to 2 decimal places, the shaded area is 234 cm^2.
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A cable is used to support a 245-m television tower. If the angle the cable makes with the ground is 78°, how long is the cable? _______ m
The length of the cable is, 252.57 m.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A cable is used to support a 245-m television tower.
And, the angle the cable makes with the ground is 78°.
Let the length of the cable = x
Hence, We can formulate;
⇒ sin 78° = 245 / x
⇒ 0.97 = 245 / x
⇒ x = 245/0.97
⇒ x = 252.57 m
Thus, The length of the cable is, 252.57 m.
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suppose you make hot chocolate. it's too hot to drink, so you put it in the freezer to cool it off. if the original temperature is 190 degrees fahrenheit and the freezer is 0 degrees fahrenheit, what will the temperature of the hot chocolate be after 4 minutes? (k
The temperature of the hot chocolate will decrease over time and after 4 minutes, it will be around 56 degrees Fahrenheit.
When you put something hot into a freezer, the temperature of the item will decrease over time until it reaches the temperature of the freezer. The rate of temperature decrease depends on the difference between the original temperature and the temperature of the freezer. In this case, the difference is 190 degrees Fahrenheit. The rate of temperature decrease should be roughly 1 degree Fahrenheit per second. After 4 minutes, the temperature of the hot chocolate should be around 56 degrees Fahrenheit. This is because, after 4 minutes, the hot chocolate would have lost around 190-56 = 134 degrees Fahrenheit of temperature. To be more precise, you would have to factor in how quickly the freezer can cool the hot chocolate, which is usually related to the size of the freezer, the size of the container the hot chocolate is in, and the amount of hot chocolate.
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Type in ALL CAPS 4-digit code
The price paid for the chair will be $90.18
The price for the pen will be $4.23.
How to calculate the new priceA percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
The price paid for the chair will be:
= $83.50 + (8% × $83.50)
= $90.18
The price for the pen will be:
= $4.50 - (60% × 4.50)
= $4.23
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What is the most precise term for quadrilateral ABCD with vertices A(4, 7),
B(6, 5), C(4, 1), and D(2, 5)?
Answer:
Step-by-step explanation:
The most precise term for the quadrilateral ABCD with vertices A(4, 7), B(6, 5), C(4, 1), and D(2, 5) is a trapezoid. A trapezoid is a quadrilateral with exactly one pair of parallel sides.
PLS HELP! I need help with Non-Linear Data on a graph with scatterplot.
The function increased to a maximum value and then decreased.
How do you identify trends in a data plot?We know that a graph can be obtained when we plot the points of the data on a graph. In this case we can see that the data have been graphed accurately as we can see here.
If we look at the graph, we can see that the graph went up and then it started coming down. The implication of that is that the function has attained a maximum point and then began to decrease.
This is clear from the graph that has been shown.
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Dominique is selling merchandise for a school fundraiser. She is selling calendars for $8 each and coffee mugs for $10 each. She must sell at least $600 of merchandise, including at least 40 calendars, to meet her goals. If x represents the number of calendars and y represents the number of mugs, which system of inequalities represents this scenario? 8x + 10y > 600 and y > 40 8x + 10y > 600 and x > 40 8x + 10y ≥ 600 and y ≥ 40 8x + 10y ≥ 600 and x ≥ 40
The inequality that represents the given situation is 8x + 10y ≥ 600
and, x ≥ 40.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
The cost for one calendar = $8
The cost for one coffee mug = $10
Dominique must sell at least $600 of merchandise and it should include at least 40 calendars.
let x be the number of calendars and y be the number of coffee mugs;
then, the inequality is
8x + 10y ≥ 600
and, x ≥ 40
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Answer:
the last one, option D, 8x + 10y ≥ 600 and x ≥ 40
Step-by-step explanation:
took the test xx
what is the volume of the square pyrimd
Answer:
108 cm³
Step-by-step explanation:
V = a²(h/3) = 6²(9/3) = 36·3 = 108 cm³
Find the sum of − x 2 + 2 −x 2 +2 and 3 x 2 − 7 x + 8 3x 2 −7x+8.
The sum of the expressions -x² + 2 and 3x² - 7x + 8 is 2x² - 7x + 10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
Find the sum of -x² + 2 and 3x² - 7x + 8. The sum of the expression is:
= (-x² + 2) + (3x² - 7x + 8)
Collecting like terms:
= -x² + 3x² - 7x + 2 + 8
Simplifying:
= 2x² - 7x + 10
The sum is 2x² - 7x + 10
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In ΔCDE, \text{m}\angle C = (x-4)^{\circ}m∠C=(x−4) ∘ , \text{m}\angle D = (9x+4)^{\circ}m∠D=(9x+4) ∘ , and \text{m}\angle E = (2x+12)^{\circ}m∠E=(2x+12) ∘ . Find \text{m}\angle D.m∠D.
The measure of <D is 130 degree.
What is Angle sum Property?
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Given:
<C= (x-4)
and, <D = 9x+ 4
and, <E = 2x+ 12
Now, In triangle CDE using Angle Sum Property
<D+ <E+ <F= 180
x - 4+ (9x+ 4) + 2x+ 12 = 180
12x + 12 = 180
12x = 168
x= 168/12
x = 14
So, the measure of <D = 9x+ 4 = 9(14) + 4 = 130 degree.
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What is the solution to the equation?
a + 5 and two-thirds = 9
a + 5 and two-thirds = 9. a + 5 and two-thirds + 5 and two-thirds = 9 minus 5 and two-thirds. A = 3 and one-third.
a + 5 and two-thirds = 9. a + 5 and two-thirds + 5 and two-thirds = 9 + 5 and two-thirds. A = 14 and two-thirds.
The solution to the equation is a = 3 1/3
What is the solution to the equation?From the question, we have the following parameters that can be used in our computation:
a + 5 and two-thirds = 9
Express properly
So, we have
a + 5 2/3 = 9
Subtract 5 2/3 from both sides of the equation
This gives
a = 9 - 5 2/3
Evaluate the difference
a = 3 1/3
Hence, the solution is a = 3 1/3
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i need help can someone please teach me thee ways of math :/
the bus value is depreciating, thus is Decay
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &250000\\ r=rate\to 20\%\to \frac{20}{100}\dotfill &0.2\\ t=years \end{cases} \\\\\\ A = 250000(1 - 0.2)^{t} \implies \boxed{A = 250000(0.8)^t} \\\\\\ \stackrel{\textit{after 6 years, t=6}}{A=250000(0.8)^6}\implies \boxed{65536}[/tex]
Graph f(x) = 3x and find the y-intercept and horizontal asymptote.
Part A
Which is the graph of f(x) = 3x?
Part B
Determine the y-intercept and horizontal asymptote.
y-intercept:
horizontal asymptote: y =
The First graph represents the equation y = 3x
The y intercept = 1.5
The horizontal asymptote = infinity
What are intercept and horizontal asymptote?The y -intercept is a point at which the graph of the function touches the y -axis. It is only possible for a function to have zero or one y -intercept.
A horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.
Therefore the y intercept is 1.5 from the graph. and the horizontal asymptote is infinity
The power of the numerator is great than that of denominator.
3x²/1x^0
= 2/0
= infinity.
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express the ratio 1 hr to 15 min in its lowest term
Answer:
4min:1min
Step-by-step explanation:
60:15
divide by 5
12:3
divide by 3
4:1
{c} Factorise: c² - 8c
Answer:
c (c - 8)
Step-by-step explanation:
c² - 8c
First, you have to find the GCF
The Greatest Common Factor is the factor that all have in common. Here the GCF is c
So, we factor c out and has left (c - 8)
So, our equation is
c (c - 8)