Answer:
Below in bold.
Step-by-step explanation:
10,16,22,28
16-10 = 6, 22-16 = 6 and 28-22 = 6
This is an arithmetic sequence with first term a1 = 10 and common difference d = 6
General (nth) term = a1 + d(n - 1)
10th term = 10 + 6(9 -1)
= 10 + 48
= 58.
Supply a different digit for each letter so that the equation is correct. A given letter always represents the same digit. (50 pts) Explain your strategy for finding the answer. (50 pts) A B C D E X 4 __________ E D C B A
One possible solution to this puzzle is:
A=9, B=8, C=7, D=6, E=5, X=2
So the equation would look like:
58,746 X 4 = 23,494
What does this mean?This means that if you substitute the values I provided for the letters in the original equation, it would result in the equation 58,746 X 4 = 23,494 being true.
To find this solution, I used a process of elimination and logic.
First, I knew that the result of the multiplication must start with a 2, since 4 times any single-digit number results in a number between 40 and 36. Therefore, X must be either 2 or 3.
Next, I focused on the fact that the two middle digits of the result are the same, which means that either A and E are the same or B and D are the same.
If A and E are the same, they must be either 4 or 5, since they must be less than X.
However, if A and E are the same, then C must also be 4 or 5, since it cannot be higher than A or E. This means that there would be a repeated digit in the equation, which is not allowed.
Therefore, A and E cannot be the same, and B and D must be the same.
Using this information, I continued to eliminate possibilities until I found a solution that worked.
For example, since B and D must be the same and cannot be 4 or 5, they must be either 6, 7, 8, or 9.
However, if they were 6 or 7, then C would have to be 6 or 7 as well, which is not allowed. If they were 8 or 9, then A and E would have to be 4 or 5, which is also not allowed.
Therefore, B and D must be 8 or 9.
From there, I tried different combinations until I found one that worked. This process involved a lot of trial and error, but by using logic and the constraints of the puzzle, I was able to narrow down the possibilities and eventually arrive at a solution.
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Solve the following: 2x + y = 15 y = 4x + 3
[amc10b.2011.7] the sum of two angles of a triangle is $\frac{6}{5}$ of a right angle, and one of these two angles is $30^{\circ}$ larger than the other. what is the degree measure of the largest angle in the triangle?
The degree measure of the largest angle is 72° in the triangle.
We have, The sum of two angles of a triangle is 6/5 of a right angle.
One of these two angles is 30° larger than the other.
Let A and B be the two angles of the triangle such that A = B + 30°.
We know that the sum of three angles in a triangle is 180°.
⇒ A + B + C = 180°
⇒ B + 30° + B + C = 180°
⇒ 2B + C = 150°
We also know that the sum of two angles of a triangle is 6/5 of a right angle.
⇒ A + B = 6/5 × 90°
⇒ B + 30° + B = 108°
⇒ 2B = 78°
⇒ B = 39°
C = 150° - 2B ⇒ 72°
A = B + 30° ⇒ 39° + 30° ⇒ 69°
Therefore, the degree measure of the largest angle in the triangle is 72°.
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Find the surface area of the rectangular pyramid.
1 = 12 ft, w = 8 ft, sh = 10 ft
a 194 ft²
b 182 ft²
c 272 ft²
d 296 ft²
Check it
In response to the stated question, we may state that As a result, the rectangular pyramid has a surface area of 296 ft2. 296 ft2 is the correct answer.
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle" at times. A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
To determine the surface area of a rectangular pyramid, first calculate the area of each face and then add them together.
Given the rectangular pyramid's dimensions:
Slant height= 10 ft base length (l) = 12 ft base width (w) = 8 foot
Then, calculate the area of the base. The area of the base is simply l w: because it is a rectangle.
Base area = [tex]12 ft x 8 ft = 96 ft^2[/tex]
A triangle face's area equals 1/2 its base height, where base = w or l and height = sh.
[tex]1/2 *8 ft *10 ft = 40 ft^2[/tex] area of the first triangle face
[tex]1/2 *12 ft *10 ft = 60 ft^2[/tex]area of the second triangular face
Third triangular face area = [tex]1/2 *8 ft *10 ft = 40 ft^2[/tex]
The area of the fourth triangular face is equal to [tex]1/2 *12 ft *10 ft = 60 ft^2.[/tex]
Now put the areas of all the faces together to get the entire surface area:
Total surface area = base area + sum of all triangular face areas
Surface area total =[tex]96 ft^2 + (40 ft^2 + 60 ft^2 + 40 ft^2 + 60 ft^2)[/tex]
296 ft2 total surface area
As a result, the rectangular pyramid has a surface area of 296 ft2.
296 ft2 is the correct answer.
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Which of the following equations is equivalent to 2 x + 6 = 30 - x - 3 2 x + 6 = 10 - x - 3 2 x + 6 = 30 - x + 3
The equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.
What is equation?
In mathematics, an equation is a statement that two expressions are equal, usually written with an equal sign (=) between them. Equations can contain variables, which are symbols that represent unknown or unspecified values.
We can simplify and solve the equation 2x + 6 = 30 - x - 3 as follows:
2x + 6 = 30 - x - 3
Adding x and adding 3 to both sides, we get:
3x + 9 = 30
Subtracting 9 from both sides, we get:
3x = 21
Dividing both sides by 3, we get:
x = 7
So the given equation simplifies to x = 7.
We can now substitute this value of x into each of the answer choices to see which one is equivalent to the given equation:
a) 2x + 6 = 30 - x - 3
Substituting x = 7, we get:
2(7) + 6 = 30 - 7 - 3
14 + 6 = 20
20 = 20
b) 2x + 6 = 10 - x - 3
Substituting x = 7, we get:
2(7) + 6 = 10 - 7 - 3
14 + 6 = 0
20 ≠ 0
Therefore, this equation is not equivalent to the given equation.
c) 2x + 6 = 30 - x + 3
Substituting x = 7, we get:
2(7) + 6 = 30 - 7 + 3
14 + 6 = 26
20 ≠ 26
Therefore, this equation is not equivalent to the given equation.
Therefore, the equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.
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Design a cylindrical can (with a lid) to contain 1 liter (= 1000 cm3) of water, using the minimum amount of metal.
To design a cylindrical can (with a lid) to contain 1 liter (= 1000 cm3) of water, using the minimum amount of metal, we need to consider the following parameters:Height and Diameter of the canThickness of the metalMaterial used for making the canLet's assume we use Aluminium as a material. Now, let's start designing the can:Height of the can:
Volume of water = 1000 cm3Volume of cylinder = πr²hVolume of cylinder = π (d/2)² hVolume of cylinder = π (d²/4) hVolume of cylinder = 1000 cm³π (d²/4) h = 1000 cm³d²h = 4000 cm³h = (4000 cm³) / (π d²) h = (4000 cm³) / (3.14 * d²) h = (1273.24) / d²Diameter of the can:
Volume of cylinder = πr²hVolume of cylinder = π (d/2)² hVolume of cylinder = π (d²/4) hVolume of cylinder = 1000 cm³π (d²/4) h = 1000 cm³d²h = 4000 cm³d² = (4000 cm³) / h d² = (4000 cm³) / (1273.24/d²) d² = 3.1425d = 17.8 cmThickness of the metal:We can assume the thickness to be 0.5 mm.Material used for making the can:AluminiumTotal Surface Area of the can:Total Surface Area of cylinder = 2πrhTotal Surface Area of cylinder = 2π(d/2)(1273.24/d²)Total Surface Area of cylinder = 1273.24/d Total Surface Area of lid = πr²Total Surface Area of lid = π (d/2)²Total Surface Area of lid = π (17.8/2)²Total Surface Area of lid = 248.5Total Surface Area of the Can = 1273.24/d + 248.5Now, we can calculate the minimum amount of Aluminium required to make the can by minimizing the Total Surface Area of the can.Total Surface Area of the can = 1273.24/d + 248.5d (in cm)Total Surface Area of the can = 1273.24/7.09 + 248.5(7.09)Total Surface Area of the can = 584.24Therefore, the minimum amount of Aluminium required to make the can is 584.24 cm².
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I NEED HELP ON THIS ASAP!!
From the graph, the feasible region from the system of linear inequalities is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.
What is the system of linear inequalitiesa. Let x be the amount of loam soil (in tons) sold, and y be the amount of peat soil (in tons) sold. The system of inequalities representing the constraints of the problem situation is:
x ≥ 0 (non-negative amount of loam soil)
y ≥ 0 (non-negative amount of peat soil)
x + y ≤ 120 (total amount of soil sold is at most 120 tons)
x ≤ 60 (maximum amount of loam soil available is 60 tons)
y ≤ 90 (maximum amount of peat soil available is 90 tons)
To graph these inequalities, we can plot the feasible region (the region that satisfies all the inequalities) in the x-y plane, as shown below;
The feasible region is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.
b. The profit function P(x, y) for selling x tons of loam soil and y tons of peat soil is:
P(x, y) = 50x + 75y
To maximize profit, we need to find the values of x and y that satisfy the constraints of the problem situation and maximize the profit function P(x, y). One way to do this is to use the method of linear programming, which involves finding the corner points of the feasible region and evaluating the profit function at each corner point.
The corner points of the feasible region are (0, 0), (60, 0), (60, 60), (30, 90), and (0, 90). Evaluating the profit function at each corner point, we get:
P(0, 0) = 0
P(60, 0) = 3000
P(60, 60) = 9000
P(30, 90) = 6750
P(0, 90) = 6750
Therefore, the maximum profit is $9000, which occurs when the company sells 60 tons of loam soil and 60 tons of peat soil.
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anyone know the answer?
The required value of the base of the triangle is [tex]\frac{7\sqrt{3} }{3}[/tex].
What is right angled triangle?Right-angle triangles are formed when the angle formed by two of their edges is exactly 90 degrees. Obtuse angle triangle: An obtuse angle triangle is one in which the angle formed by two sides is larger than 90 degrees.
According to question:In the given triangle, we will use tangent function to find the value of x.
tan(∅) = Perpendicular/ base
tan(60°) = 7/x
x = 7/tan(60°)
x = 7/√3 ∴ (tan(60°) =√3 )
On rationalizing
x = [tex]\frac{7\sqrt{3} }{3}[/tex]
Thus, required value of x is [tex]\frac{7\sqrt{3} }{3}[/tex].
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AOC is a right-angle AOB: BOC - 2:3 what is the size of angle BOC
Angles AOB and BOC are complimentary angles if AOC is a right angle. Let's use x to represent the angle BOC's size. Next, we have: Angle AOB plus Angle BOC equals 90° (definition of complementary angles).
BOC/AOB angle equals 2/3 (given) Angle AOB may be expressed in terms of angle BOC using the second equation: (3/2) × angle BOC, where angle AOB (multiplying both sides by angle AOB) Angle BOC plus angle (3/2) equals 90 degrees. When we simplify this equation, we obtain: BOC angle (5/2) times equals 90 degrees. By multiplying both sides by 5, we obtain: BOC angle = (2/5) x 90 degrees BOC angle is 36 degrees. Hence, the angle's size Substituting this expression into the first equation, we get: (3/2) x angle BOC + angle BOC = 90 degrees Simplifying this equation, we get: (5/2) x angle BOC = 90 degrees.
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Find the slope-intercept form of the line with the slope m= 1/7 which passes through the point (-1, 4).
Answer:
y = 1/7x + 29/7
Step-by-step explanation:
Slope intercept form is y = mx + b
m = the slope
b = y-intercept
m = 1/7
Y-intercept is located at (0, 29/7)
So, the equation is y = 1/7x + 29/7
John Paszel took out a loan for 51 months but paid it in full after 25 months. Find the refund fraction he should use to
calculate the amount of his refund.
Answer: calculate the amount of his refund.
Step-by-step explanation:
At the bookstore, best-sellers are normally $19.95 each. During the store-wide 20% off sale, how much would it cost you, before tax, to buy two best-sellers?
F. $3.99
G. $7.98
H. $15 96
J. $31.92
K. $39.90
Step-by-step explanation:
20% off means you pay 80 % of the original price for two books
80% * ( 2 x 19.95 ) = .8 ( 39.90) = $ 31.92
A cylindrical tank is one-fifth full of oil. The cylinder has a base radius of 80 cm. The height of the cylinder is 200 cm. 1 litre 1000 cm3 How many litres of oil are in the tank? Round your answer to the nearest litre
The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).
The volume of any cylinder can be calculated using the formula,
V = πr²h
(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)
As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:
Volume of oil = (1/5) x Total Volume
Substituting the given values, we have:
Total Volume = π(80cm)²(200cm) = 4,031,240 cm³
Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³
Converting cm³ to litres, we have:
1 litre = 1000 cm³
Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres
Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.
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A grocer has two kinds of candies, one selling for 90 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
? pounds of 40 − cent candies, ? pounds of candies that cost $1.40 per pound
Using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
So, we have:
x + y = 100 .........A
40 × x + 140 y = 85 × 100
40 x + 140 y = 8500 ........B
Solving (A) and (B) as follows:
(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100
(40 x - 40 x) + (140 y - 40 y) = 8500 - 4000
0 + 100 y = 4500
y = 4500/100
Hence, the price per unit of grocery is $1.40 = y = 45 pounds.
Now, put the value of y in equation (A) as follows:
x + y = 100
x = 100 - y
x = 100 - 45
x = 55 pounds
The number of groceries at the 40-cent price is x = 55 pounds.
Therefore, using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
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Correct question:
A grocer has two kinds of candies, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
Could somebody help me with this?
Answer:
y = 10/3x + 130/3
Step-by-step explanation:
To find where A is, we must find where C is. C is found when plugging in 0 in for y: 0 = -1/2 x + 5, so x = 10, and y = 0.
Now that we know the length of BC, we can find A.
Subtract 10 from the x value and add 5 to the y value of B to find A: (-10, 10).
Now, find the equation of the line between (-13, 0) and (-10, 10). Solve and get the equation of a line: y = 10/3x + 130/3
Hope this helps!
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
X
The surface area of the triangular prism is 2016 [tex]feet ^2[/tex], we get to the answer by adding area of all faces in this prism.
What is surface area ?
Surface area is the sum of the areas of all the faces or surfaces of a 3D object, measured in square units.
To find the surface area of the triangular prism, we need to calculate the area of each of its faces and then add them up.
First, let's find the area of the triangular base.
Area of triangle = (1/2) x base x height
Area of triangle = (1/2) x 18 x 24
Area of triangle = 216 [tex]feet ^2[/tex]
Next, let's find the area of each rectangular face.
Area of rectangle = length x width
Area of rectangle 1 = 24 x 22 = 528 [tex]feet ^2[/tex]
Area of rectangle 2 = 18 x 22 = 396 [tex]feet ^2[/tex]
Area of rectangle 3 = 22 x 30 = 660 [tex]feet ^2[/tex]
Now, we can add up the areas of all three faces to get the total surface area of the prism:
Surface area = area of rectangle (1+2+3) + 2 x area of triangle
Surface area = 528 + 396 + 660 + 2(216)
Surface area = 2016 [tex]feet ^2[/tex]
Therefore, the surface area of the triangular prism is 2016 [tex]feet ^2[/tex].
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Question 8
Which division expression is the given figure modeling?
A
B
C
D
1
4÷3
3÷/1/1
1
12 ÷ 4
3 ÷ 1/1/
1
1
The division problem provided by the model shown here is [tex]3[/tex] ÷ [tex]\frac{1}{4}[/tex].
How are fractions divided?The first step of dividing fractions is to get the reciprocal of a second fraction, which involves flipping its numerator and denominator. Multiply all two numerators after that. Multiply the 2 denominators after that. Then finish, if required, simplify the fractions.
Simple division: What is it?Simple Division: Little numbers can be divided into groups and pieces using the simple division method in mathematics. Divide easy and basic division problems into terms that can be divided using simple division sums. Arithmetic, subtraction, multiplying, & division are the four fundamental mathematical operations.
Given:
We have three section [tex]1+ 1 + 1= 3[/tex]
[tex]= \frac{4}{12}[/tex]
[tex]= \frac{1}{3}[/tex]
In this case, the model yields the division issue.
[tex]3[/tex] ÷ [tex]\frac{1}{4}[/tex]
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given the results of the two hypothesis tests, would you reject or fail to reject your null hypotheses (assuming a 0.05 significance level)? what does your decision mean in the context of this problem? would you proceed with changing the design of the shopping cart icon, or would you stay with the original design?
Assuming a 0.05 significance level, both hypothesis tests would reject the null hypothesis. This means that there is enough evidence to suggest that the shopping cart icon's design affects the users' behavior. Therefore, the design should be changed to improve the user's experience.
Step by step explanation:
The problem is not stated, so we need to make some assumptions. We will assume that the hypothesis tests were done to determine whether a change in the shopping cart icon design would affect the users' behavior.
The null hypothesis (H0) is that the design of the shopping cart icon does not affect the users' behavior, while the alternative hypothesis (Ha) is that the design of the shopping cart icon affects the users' behavior.
The significance level is 0.05, which means that we are willing to accept a 5% chance of making a type I error (rejecting the null hypothesis when it is actually true).
If both hypothesis tests reject the null hypothesis, it means that the p-values were less than 0.05, and there is enough evidence to suggest that the design of the shopping cart icon affects the users' behavior.
Therefore, it is recommended to proceed with changing the design of the shopping cart icon to improve the user's experience.
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a normal distribution of exam scores has a standard deviation of 8. a score that is 12 points above the mean would have a z-score of: a score that is 20 points below the mean would have a z-score of:
The standard deviation of a normal distribution of exam scores is 8. A score that is 12 points above the mean would have a z-score of 1.5, and a score that is 20 points below the mean would have a z-score of -2.5.
What is the z-score?The z-score can be calculated by dividing the difference between a data value and the mean of the data set by the standard deviation of the data set.
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8.
z = (x−μ)/σ = (x−μ)/σ = (12−0)/8 = 1.5
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8 is 1.5.
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8.
z = {x-μ}/{σ} = {-20-0}/{8} = −2.5
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8 is -2.5.
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Solve the following proportion for y. 13 11 8 y Round your answer to the nearest tenth. 1 X Ú
Answer:
Were sorry! Answer is not available right now check in later.
Step-by-step explanation:
GIVING BRAINLIST SO HURRY!!!!
What is the median of the data set represented by the dot plot?
Answer:
14
Step-by-step explanation:
scores 10 10 12 13 14 15 18 19 19 Median score is the one in the middle
suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. if the population grows to 500 after one year, what will the population be after another three years?
Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, the population will be 852.78 after another three years.
What is the logistic model?A logistic model, also known as the Verhulst-Pearl model, is a type of function used to describe population growth that is limited. It’s a form of exponential growth that takes into account the carrying capacity of an environment.
Population growth that is limited and slows down as the population approaches its carrying capacity is modeled using the logistic model. It is given by this equation:
[tex]P(t) = K / (1 + Ae^{-rt})[/tex]
where P(t) is the population at time t, K is the carrying capacity, A is the constant of proportionality, and r is the growth rate.
Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, substitute this information into the logistic model: [tex]P(1) = 500[/tex], [tex]K = 2000[/tex], and [tex]P(0) = 200[/tex].
[tex]500 = 2000 / (1 + Ae^{-r(1)})[/tex]
Now, solve for A by dividing both sides by 2000 / (1 + A):
[tex]1 + A = 4A = 3[/tex]
Substitute the value of A back into the logistic model equation:
[tex]P(t) = 2000 / (1 + 3e^{-rt})[/tex]
Solve for r by using the data provided in the problem for the first year (t = 1) and second year (t = 4):
[tex]P(1) = 500 = 2000 / (1 + 3e^{-r(1)})[/tex]
[tex]P(4) = ? = 2000 / (1 + 3e^{-r(4)})[/tex]
Solve the first equation for r:
[tex]500 = 2000 / (1 + 3e^{-r})\\1 + 3e^{-r} = 4e^{-r}\\1 + 3e^r = 4e[/tex]
Solve for e using the quadratic formula to get:
e = 0.4274 and e = 1.1713
Let e = 0.4274:
[tex]1 + 3e^{-r} = 4e^{-r}\\1 + 3(0.4274)^{-r} = 4(0.4274)^{r}\\1 + 0.5746^r = 1.7166^r[/tex]
Take the natural logarithm of both sides:
[tex]ln(1 + 0.5746^r) = ln(1.7166^r) - lnr\\ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]
Use a graphing calculator to solve for r:
[tex]ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]; -0.1568 < r < 0.7534
Solve for r using the second year’s data:
[tex]2000 / (1 + 3e^{-r(4)}) = P(4)\\2000 / (1 + 3(0.4274)^{-r(4)}) = P(4)\\P(4) = 852.78[/tex]
Thus, the population will be 852.78 after another three years.
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Elise saved $184. She bought a scarf, a necklace, and a notebook. After the purchases, she still had $89. 50. The scarf cost three-fifths the cost of the necklace and the notebook cost one-sixth as much as the scarf. How much did the notebook cost?
The cost of the notebook is $4.50
Let's call the cost of the necklace "N" and the cost of the scarf "S". We know that Elise spent a total of $184 on the scarf, necklace, and notebook, so we can write:
S + N + NB = 184
We also know that after making her purchases, Elise had $89.50 left, so we can write:
89.5 = 184 - (S + N + NB)
Simplifying this equation, we get:
S + N + NB = 94.5
We're also given that the scarf cost three-fifths the cost of the necklace, so we can write
S = (3/5)N
Finally, we're told that the notebook cost one-sixth as much as the scarf, so we can write:
NB = (1/6)S
Now we can the substitution method here
(3/5)N + N + (1/6)(3/5)N = 184 - 89.5
Simplifying the right-hand side
(3/5)N + N + (1/6)(3/5)N = 94.5
Combining like terms on the left-hand side
(21/10)N = 94.5
Multiplying both sides by 10/21
N = 45
So the necklace cost $45. We can use this to find the cost of the scarf
S = (3/5)N = (3/5)($45) = $27
And we can use the cost of the scarf to find the cost of the notebook
NB = (1/6)S = (1/6)($27) = $4.50
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Jenny works at Sammy's Restaurant and is paid according to the rates in the following
table.
Jenny's weekly wage agreement
Basic wage $600.00
PLUS
$0.90 for each customer served.
In a week when Jenny serves n customers, her weekly wage, W, in dollars, is given by
the formula
W = 600+ 0.90n.
(i) Determine Jenny's weekly wage if she served 230 customers.
(ii) In a good week, Jenny's wage is $1 000.00 or more. What is the LEAST number
of customers that Jenny must serve in order to have a good week?
(iii) At the same restaurant, Shawna is paid a weekly wage of $270.00 plus $1.50 for
each customer she serves.
If W, is Shawna's weekly wage, in dollars, write a formula for calculating Shawna's
weekly wage when she serves m customers.
(iv) In a certain week, Jenny and Shawna received the same wage for serving the same
number of customers.
How many customers did they EACH serve?
Jenny works at Sammy's Restaurant and is paid according to the rates in the following
table.
Jenny's weekly wage agreement
Basic wage $600.00
PLUS
$0.90 for each customer served.
In a week when Jenny serves n customers, her weekly wage, W, in dollars, is given by
the formula
W = 600+ 0.90n.
(i) Determine Jenny's weekly wage if she served 230 customers.
(ii) In a good week, Jenny's wage is $1 000.00 or more. What is the LEAST number
of customers that Jenny must serve in order to have a good week?
(iii) At the same restaurant, Shawna is paid a weekly wage of $270.00 plus $1.50 for
each customer she serves.
If W, is Shawna's weekly wage, in dollars, write a formula for calculating Shawna's
weekly wage when she serves m customers.
(iv) In a certain week, Jenny and Shawna received the same wage for serving the same
number of customers.
How many customers did they EACH serve?
3 / 3
(i) If Jenny serves 230 customers, her weekly wage is
W = 600 + 0.90n = 600 + 0.90(230) = $807.00
Therefore, Jenny's weekly wage if she serves 230 customers is $807.00.
(ii) We want to find the least number of customers, n, that Jenny must serve in order to earn $1,000 or more. That is,
600 + 0.90n ≥ 1,000
0.90n ≥ 400
n ≥ 444.44
Since n must be a whole number, Jenny must serve at least 445 customers in order to earn $1,000 or more in a week.
(iii) Shawna's weekly wage, W, in dollars, when she serves m customers is given by the formula:
W = 270 + 1.50m
Therefore, Shawna's weekly wage when she serves m customers is $270.00 plus $1.50 for each customer she serves.
(iv) Let's assume that Jenny and Shawna received the same wage, W, for serving the same number of customers, x. Then we have:
Jenny's wage = 600 + 0.90x
Shawna's wage = 270 + 1.50x
Setting these two expressions equal to each other, we get:
600 + 0.90x = 270 + 1.50x
330 = 0.60x
x = 550
Therefore, Jenny and Shawna each served 550 customers.
-17.R Using Percents, Homework
Sarted: Mar 10 at 8:30pm
Question 1 of 9
The Quick Slide Skate Shop sells the Ultra 2002 skateboard for a price of $60.20. However, the Quick Slide
Skate Shop is offering a one-day discount rate of 45% on all merchandise. About how much will the Ultra 2002
skateboard cost after the discount?
$33.00
$87.00
$46.20
$27.00
The price after discount is $33 and option 1 is the correct answer.
What is a discount?A discount is a drop in a product's or service's price. Discounts can be provided for a variety of purposes, such as to entice consumers to make larger purchases, to get rid of excess inventory, or to draw in new clients. Discounts can be represented as a set monetary amount or as a %, as in the example above. For instance, a shop may give customers $10 off any purchase of more than $50.
Given that, one-day discount rate of 45% is applied.
Thus,
Discount = 60.20 * 0.45 = 27.09
Price after discount = 60.20 - 27.09 = 33.11
Hence, the price after discount is $33 and option 1 is the correct answer.
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. A circular fence is being used to surround a dog house. How much fencing is needed to build the fence?
45.53 ,fencing is needed to build the fence.
What is area?A solid object's surface area is a measurement of the total area that the surface of the object takes up.
The definition polyhedra of arc length for one-dimensional curves and the definition of surface area for (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.
A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.
This definition of surface area uses partial derivatives and double much simpler mathematical concepts than the definition of surface area integration and is based on techniques used in infinitesimal calculus.sought a general definition of surface area.
Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.
2*3.14*14.5/2
45.53ft
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three traffic lights on a street span 120 yards. if the second traffic light is 85 yards away from the first, how far in yards is the third traffic light from the seccond
The distance between the third traffic light from the second traffic light is 35 yards.
What is the distance?Three traffic lights on a street span 120 yards.
If the second traffic light is 85 yards away from the first.
Therefore, the third traffic light is 120 - 85 =35 yards away from the second traffic light.
This means that the third traffic light is directly adjacent to the first traffic light. The third traffic light from the second traffic light is at the same location as the first traffic light.
Thus, the distance between the third traffic light from the second traffic light is 35 yards.
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In 2008 , the population of a district was 39,700 . With a continuous annual growth rate of approximately 3%, what will the population be in 2033 according to the exponential growth function?
The population will be approximately 84,161 in 2033 according to the exponential growth function.
The given information in the problem is;Population in 2008 = 39,700
Annual growth rate = 3%
We need to find out the population in 2033.
The formula for continuous exponential growth is;P(t) = P₀e^(rt)
where;P₀ is the initial populationr is the annual growth rate (in decimal form)t is the time elapsed (in years)
We are given P₀ = 39,700r = 0.03t = 2033 - 2008 = 25 years
Put these values in the formula of continuous exponential growth;
P(25) = 39,700e^(0.03 x 25)P(25)
= 39,700e^(0.75)P(25)
= 39,700 x 2.1170000493605122P(25)
= 84,161.13
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if you have four cards and were to bet based upon suits while flipping them one at a time while trying to minimize variance, how would you do it?
The steps which can help in minimizing the variance in the four cards are correct selection of the suit with maximum number of cards.
How to minimize variance?If you have four cards and were to bet based upon suits while flipping them one at a time while trying to minimize variance, you should follow the below steps:
First, you need to check the suits of the four cards you have.
Now, you need to select the suit that has a maximum number of cards. For instance, if the four cards are 5 of hearts, 7 of spades, 2 of diamonds, and 10 of hearts, you need to select hearts as it has two cards.
After selecting the suit with the maximum number of cards, you need to start flipping the cards one at a time.
Keep a count of the number of times you get the chosen suit. For instance, if you chose hearts, you will count the number of times you get hearts after flipping each card.
Once you get the chosen suit, you can place your bet. The amount of your bet can depend on the number of times you have gotten the chosen suit so far.
So, this process doesn't guarantee that you will win every time.
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Use the graph of f(x)=−8x-2x^2 to answer the question.
Is f(x) increasing, decreasing, or constant for -2
At x = -2, which is the vertex of the quadratic function, the function f(x) is constant.
How to classify a function as increasing, decreasing or constant?To classify the graph of a function as increasing, decreasing, or constant, you need to examine the direction in which the graph is moving.
A function is considered increasing if its graph moves up and to the right as you follow it from left to right. In other words, if the y-values of the function increase as the x-values increase, then the function is increasing.A function is considered decreasing if its graph moves down and to the right as you follow it from left to right. In other words, if the y-values of the function decrease as the x-values increase, then the function is decreasing.A function is considered constant if its graph remains at the same level and does not move up or down as you follow it from left to right. In other words, if the y-values of the function do not change as the x-values increase, then the function is constant.x = -2 is the vertex of the quadratic function, which is the turning point of the function, where it changes from increasing to decreasing, hence the function is considered to be constant at x = -2, as it has a derivative of zero at x = -2.
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