To find the total bill including the service charge, multiply the original meal cost by 15% to calculate the service charge. Then, add this to the original meal cost to get the total of £75.21.
Explanation:The question involves Mathematics as it requires calculating the total bill including the service charge which is essentially calculating a percentage of the original amount. To determine the total amount to be paid, one must first calculate the 15% service charge on the £65.40 meal and add it to the original amount. The service charge is calculated by converting the percentage to a decimal and multiplying it by the meal cost: 0.15 × £65.40.
Let's do the calculation:
Find the service charge: 0.15 × £65.40 = £9.81Add the service charge to the original bill: £65.40 + £9.81 = £75.21The total bill after adding the 15% service charge to the £65.40 meal cost is £75.21.
The equation of the line of best fit of a scatter plot is y = 8x − 1. What is the slope of the equation?
Answer:
8
Step-by-step explanation:
I just took the test.
You earn $56 for washing 8 cars. How much do you earn for washing 5 cars?
what is a verbal expression?
A mathematical verbal expression is a translation into words of an algebraic expression that can consist of different operations, numbers and varibles ur welcome.
For example, the following is a verbal phrase: "John went to the store and bought five apples. Each apple cost $1.25. How much did John spend before tax?" To translate it to a verbal model, the problem solver represents the problem in simplified words that represent the cost of the apple times the number of apples bought. To translate it further to a mathematical phrase, the problem solver puts numbers in the problem: "$1.25 times 5."
Find f. f ''(x) = −2 + 24x − 12x2, f(0) = 4, f '(0) = 18
Answer:
f(x) = -x⁴ + 4x³ - x² + 18x + 4
Step-by-step explanation:
If we take the integral of f''(x) with respect to x, we get that f'(x)= -2x + 12x² - 4x³ + C.
Substituting in f'(0)=18, we get C=18.So, f'(x) = -2x + 12x² - 4x³ + 18.If we take the integral of f'(x) with respect to x, we get that f(x) = -x² + 4x³ - x⁴ + 18x + C.
Substituting in f(0) = 4, we get C=4.So, f(x) = -x⁴ + 4x³ - x² + 18x + 4To find the function f, we need to integrate its second derivative, then use the given initial conditions to solve for the constant of integration and find the exact function f(x).
Explanation:To find the function f, we need to integrate its second derivative. We integrate each term of the second derivative separately, using the power rule for integration. So, f''(x) = -2 + 24x - 12[tex]x^2[/tex] becomes f'(x) = -2x + 12[tex]x^2[/tex] - 4[tex]x^3[/tex] + C, where C is the constant of integration. Then, we integrate f'(x) to find f(x), again using the power rule for integration. Finally, we use the given initial conditions, f(0) = 4 and f'(0) = 18, to solve for the constant of integration and find the exact function f(x).
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) 20% of computer chips from a certain manufacturer are defective. if 100 computer chips are purchased, what is the approximate probability that at least 20 of them are defective
Logarithmic Functions Question, Many Points
I got the first part of this question correct, I believe.
I was supposed to find the graph with a base of 3 (attached), but now I need to justify my answers, which I don't understand. Here are the choices:
The graph of f(x)= log_3 x+c must intersect with the line y= c+1 when x= 3.
The graph of f(x)= log_3 x+c must intersect with the line y= c when x= 3.
The graph of f(x)= log_3 x+c must intersect with the line x= c when y= 3.
The graph of f(x)= log_3 x+c must intersect with the line x= c+1 when y= 3.
A surveyor wants to measure the distance from the north end (point b ) to the south end (point c) of a body of water. He creates a right triangle by using point A which is 17.5 m due west of point c and at a 30 degree angle with point b. Find the distance across the lake
The distance across the body of water from point b (north end) to point c (south end) can be found using trigonometry and the sine ratio. Given that the angle is 30° and the distance from point A to point b is 17.5 m, the distance across the water (from point b to point c) is 8.75m.
Explanation:The problem at hand is a trigonometry problem which can be solved by using the sine ratio. In trigonometry, the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the angle is given as 30°, and we are asked to find the distance from point b (north end) to point c (south end), which is the side opposite to the 30° angle. Therefore, we can set up the following equation using the sine ratio: sin(30°) = opposite/hypotenuse.
In this instance, the hypotenuse is the distance from point A to point b, which is given as 17.5 m. Thus, the equation becomes sin(30°) = distance from point b to point c / 17.5 m. Solving this for the distance from point b to point c would mean multiplying both sides by 17.5 m, giving us: distance from point b to point c = sin(30°) * 17.5 m.
Upon calculation, we find that sin(30°) equals 0.5, so therefore the distance from point b to point c, which is the distance across the body of water is 0.5 * 17.5m = 8.75 m.
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Identify the coefficient of each term of the polynomial.
-2x+9
what is The coefficient of the first term is ....
what isThe coefficient of the second term is
Final answer:
The coefficient of the first term '-2x' in the polynomial is -2, and the coefficient of the second term '9' is 9.
Explanation:
In the polynomial -2x+9, each term has a coefficient. A coefficient is a number that multiplies the variable. The variable in the first term is x, and it is being multiplied by -2. Therefore, the coefficient of the first term is -2. The second term is a constant and does not have a variable associated with it. However, by convention, we can think of this term as 9 times x0, since any number raised to the zero power is 1. The coefficient of this constant term is 9.
At 0°C, the volume of a gas is 22 liters. For each degree the temperature T (in degrees Celsius) increases, the volume V (in liters) of the gas increases by 225. Write an equation that represents the volume of the gas in terms of the temperature.
Answer:
V=2/25T+22
Step-by-step explanation:
PLEASE HELP -Given the graph of rectangle QUAD and its reflection.
Use the coordinates of the images' vertices, Q and Q' to algebraically find the line of reflection. In your final answer, include all of your work.
Answer:
Q = (-5, 2)
Q' = (6, 2)
(-5 + 6/2 , 2 + 2/2) = (1/2, 2)
Vertical line through the mid point would be x = 1/2
In qam with 2 possible amplitudes, how many possible states
8.
Howmet Corporation needs $200,000 in 5 years.
Find the required quarterly payment into a sinking fund if funds are invested in an account earning 10% per year compounded quarterly.
$38,050.00
$6,716.00
$32,760.00
$7,830.00
what is the volume of the cube shown below? 2 1/4
The volume of the given cube is 11.4 cubic units.
What is volume of cube?The volume of a cube is defined as the total number of cubic units occupied by the cube completely. A cube is a three-dimensional solid figure, having 6 square faces. Volume is nothing but the total space occupied by an object.
The edge of the given cube is [tex]2\frac{1}{4}[/tex] =2.25 units.
We know that, the volume of a cube is a³, where a is an edge.
Here, volume = (2.25)³
= 11.390625
≈ 11.4 cubic units
Therefore, the volume of the given cube is 11.4 cubic units.
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3. Jared has two ropes. Each rope is 9 inches long. How many inches of rope does he have in all?
The length of one rope = 9 in
Number of ropes Jared have = 2.
The total inches of rope does Jared have will be calculated as under -
We can add the length of two ropes as = 9 in + 9 in = 18 in
Or we can do it by other method as well.
The other method is by multiplying -
The total inches of rope does Jared have = The length of one rope × Number of ropes Jared have
The total inches of rope does Jared have = 9 in × 2 ropes = 18 in
Which is the equation of an ellipse centered at the origin with foci on x-axis, x-intercepts +7, -7 and y-intercepts +2,
-2?
Answer:
It's B on edge.
Step-by-step explanation:
What form of a quadratic function would be graphed having the vertex at the same point as the y-intercept
9514 1404 393
Answer:
a form with no horizontal translation of the parent function
Step-by-step explanation:
If the vertex is the y-intercept, then it has not moved horizontally from its position in the parent function. The form of the quadratic is one without any horizontal translation.
A quadratic function with its vertex and y-intercept at the same point would be in the form f(x) = ax². The coefficients b and c must be zero for the vertex to be at the origin (0,0), and by varying a, we can achieve a vertical stretch or shrink without altering the y-intercept.
The student's question pertains to the graph of a quadratic function with specific conditions on its vertex. If a quadratic function has its vertex at the same point as its y-intercept, then the vertex is located at the origin (0,0), because the y-intercept is the point where the graph crosses the y-axis, and at the vertex, the value of y is at its maximum or minimum depending on the direction of the parabola.
The standard form of a quadratic function is f(x) = ax² + bx + c. For the function to have its vertex at the origin, both b and c would need to be zero, making the function f(x) = ax². This represents a parabola that opens upwards if a is positive, or downwards if a is negative.
To maintain the y-intercept, we must ensure that the transformation applied to the graph, such as a vertical or horizontal shrink, does not alter the location of the vertex. A horizontal shrink is achieved by making a larger absolute value while ensuring that it remains positive or negative in accordance with the original direction of the parabola.
after lily's graduation party, 1/2 of of the cake was left. she shared the remaining cake equally with her sister Kayla and her brother Logan. what fraction of the original cake did each of them get?
show all your work please
Question 21 [t-interval] a random sample of size 18 is drawn from a population that is normally distributed. the sample mean is 58.5, and the sample standard deviation is found to be 11.5. determine a 95% confidence interval about population mean.
a. [52.78,64.22]
b. [53.78,63.22]
c. [53.18,63.81]
d. [54.04,62.96]
Answer:
Option a. [52.78,64.22]
Step-by-step explanation:
We are given that a random sample of size 18 is drawn from a population that is normally distributed.
Sample mean is 58.5, and the sample standard deviation is found to be 11.5 i.e., X bar = 58.5 and s = 11.5
The pivotal quantity for calculating 95% confidence interval is;
[tex]\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
So, 95% confidence interval about population mean is given by;
P(-2.110 < [tex]t_1_7[/tex] < 2.110) = 0.95
P(-2.110 < [tex]\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.110) = 0.95
P(-2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] < [tex]{Xbar - \mu}[/tex] < 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ) = 0.95
P(X bar - 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] < [tex]\mu[/tex] < X bar + 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ) = 0.95
95% confidence interval about [tex]\mu[/tex] = [ X bar - 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] , X bar + 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ]
= [ 58.5 - 2.110 * [tex]\frac{11.5}{\sqrt{18} }[/tex] , 58.5 + 2.110 * [tex]\frac{11.5}{\sqrt{18} }[/tex] ]
= [ 52.78 , 64.22 ]
Therefore, 95% confidence interval about population mean is [52.78 , 64.22].
Michelle invests $1000 at a bank offering 3% compounded quarterly. Write an equation to model the growth of the investment.
A) A = 1000(1.03)4t
B) A = 1000(1+.03
4
)t
C) A = 1000(1+.03
4
)4t
D) A = 1000((1.03)
4
)4t
Answer:
C. [tex]1000( \frac{1+.03}{4})^{4t}[/tex]
Step-by-step explanation:
What is the area of the rhombus shown below? A. 110.5 square units B. 129.2 square units C. 221 square units D. 15 square units
the answer is A. 110.5
The area of the rhombus is 110.5 square units if the lengths of the diagonal of a rhombus are 13 and 17 units option (A) 110.5 square units is correct.
What is a rhombus?A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.
We have a rhombus shown in the picture with dimensions:
As we know,
The area of the rhombus is given by:
A =pq/2
p and q are the lengths of the diagonal of a rhombus.
p = MK = 13 units
q = JL = 17 units
Plug the values in the formula:
A = (13×17)/2
A = 221/2
A = 110.5 square units
Thus, the area of the rhombus is 110.5 square units if the lengths of the diagonal of a rhombus are 13 and 17 units option (A) 110.5 square units is correct.
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99 POINTS!!!: if i have a circle with a radius of 6 in and it is cut into 8 equal slices (like a pie) and the coordinates are (8, 5) then
what is the central angle,
what is the measure of the arc that 2 pieces together would intercept,
and the equation that represents
and circumference?
PLEASE HURRY!!!
6(z+2)-2(2z+5)=18 show step by step
Based on the family the graph below belongs to, which equation could represent the graph
Answer: Second option y=log(2x)+3
Solution:
Based on the family of graphs shown in the attached file, the equation could represent the graph is y=log(2x)+3
This graph is the graph of the funtion y=log(x) stretched horizontally by a factor of 2 and translated 3 units upward.
hey can you please help me posted picture of question
Which description best describes the three-dimensional object that is formed when the segment is rotated about the axis as shown?
an oblique cylinder
a cone with an open base
a triangular prism
a hollow pyramid
Second option is correct. A cone with open base is formed when the segment is rotated about the axis as shown in figure.
What is solid revolution?A solid revolution is a three dimensional figure obtained by rotating a two-dimensional figure or (curve) around a straight line(called the axis) that lies in the same plane.
According to the question
If we see in the given figure, there is a triangle about a vertical line. As the triangle is revolved about a line, the vertices A and C remain stationary. While the vertex B which follows the path of circle. As the triangle rotates, AB creates the outline of cone.
Hence, Option second is correct i.e. a cone with an open base.
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Answer: A cone with an open base.
Step-by-step explanation:
The correct answer is a cone with an open base. When this segment is rotated around the axis as shown, the three-dimensional object formed will be a cone with no base. If you imagine mirroring the segment shown, you will create a triangle with no base. Next, if you imagine spinning this triangle around, you will be left with a cone. Since the segment does not connect to the axis at the bottom, the resulting cone will have an open base.
A visual example of a cone is attached below.
The fraction 7/8 is a multiple of what unit fraction?
(2x3z2)3
------------------
x3y4z2 * (x-4z3)
Henry cut a piece of yarn that was 11/6 into two pieces. List to different pairs of fractions that could show the lengths , in feet , of the two pieces.
The penguin exhibit at a zoo has a raised circular island that is surrounded by water. The diameter of the island is 20 meters. One penguin swims half way around the island before hopping out.
How far did the penguin swim?
Answer:
10pi
Step-by-step explanation:
The answer is 10pi
A rectangle floor is 24 feet long and 9 feet wide. what is it’s area of the floor in square yards?
Final answer:
The area of a rectangle floor that is 24 feet long and 9 feet wide is 216 square feet, which is equivalent to 24 square yards when converted using the fact that there are 9 square feet in a square yard.
Explanation:
The student is asking about the area of a rectangle when the dimensions are given in feet and the answer is required in square yards. To convert the area from square feet to square yards, we need to know the conversion factor between these two units of measurement.
It's established that 1 square yard is equal to 9 square feet. Thus, the area of the floor in square feet is calculated by multiplying the length by the width:
Area in square feet = Length in feet × Width in feet
= 24 ft × 9 ft
= 216 square feet
Next, we convert the area into square yards by dividing by 9:
Area in square yards = Area in square feet ÷ Conversion factor
= 216 sq ft ÷ 9 (sq ft/sq yd)
= 24 square yards
Therefore, the area of the floor in square yards is 24 square yards.