The regular price of one baseball bat is $80.40.
How is a discount calculated? What is a discount?A discount is a drop in a product's or service's price. It is often provided by the vendor as an inducement to lure customers into making a purchase. Often, the discount is indicated as a percentage or a dollar amount off the list price.
The standard price and the discount rate must be known in order to determine a discount. Often, the discount rate is expressed as a percentage. We multiply the usual price by the discount rate to determine the discount amount.
Given that, coach buys 5 identical baseball bats for a total of $327.45.
Thus,
5P = 327.45
P = 65.49
So one bat cost him 65.90.
Now, the regular cost of the bat will be:
Price = 65.90 + 14.50
Price = 80.40
Hence, the regular price of one baseball bat is $80.40.
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He following data points represent the number of quesadillas each person at Toby's Tacos ate.
Sort the data from least to greatest.
00
0
0
12\dfrac12
2
1
start fraction, 1, divided by, 2, end fraction
00
0
0
11
1
1
12\dfrac12
2
1
start fraction, 1, divided by, 2, end fraction
22
2
2
11
1
1
14\dfrac14
4
1
start fraction, 1, divided by, 4, end fraction
54\dfrac54
4
5
start fraction, 5, divided by, 4, end fraction
22
2
2
11
1
1
Find the interquartile range (IQR) of the data set
To get the interquartile range (IQR) of the data set, we must first determine the median [tex](Q2). 00 0 0 12\dfrac12 2 1 begin fraction,[/tex] divide by 2, end fraction.
[tex]00 0 011 1 1 12\dfrac12 2 1 begin fraction,[/tex]divide by 2, end fraction 22 2 2 11 1 1 14\dfrac14 4 1 begin fraction, divide by 4, end fraction 54\dfrac 5 4 5 end fraction, 5, divided by 4, start fractio When the data is sorted in order, the median is the middle value, thus we must locate the value that is exactly in the centre[tex]0 0 0 11] 1 12\dfrac12 2 1 begin fraction,[/tex] divide by 2, end fraction 22 2 11 1 1 14\dfrac14 4 1 begin fraction, divide by 4, end fraction 54\dfrac54 4 5 end fraction, 5, divided by 4, start fraction The median is (1 + 1)/2 = 1 since the middle two numbers are 1 and 1. The median of the lower half of the data (Q1) and the median of the upper half of the data (Q2) must then be determined (Q3) For the bottom half: 00 0 0 11 1 1 Q1 = 0 since the intermediate value is 0. For the top half: 12\dfrac12.
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A multivitamin constaions. 17g of vitamin C. How much vitamin c does 60 tablets contain? answer in milligrams
60 tablets of the multivitamin, with 17g (17,000mg) of vitamin C per tablet, contains 1,020,000mg of vitamin C in total.
If one tablet of the multivitamin contains 17g of vitamin C, then 60 tablets would contain 60 times that amount:
60 tablets x 17g of vitamin C per tablet = 1020g of vitamin C
However, it is more common to express vitamin C (and other nutrients) in milligrams (mg) rather than grams (g). To convert from grams to milligrams, we can multiply by 1000:
1020g of vitamin C x 1000 mg/g = 1,020,000 mg of vitamin C
Therefore, 60 tablets of the multivitamin contain 1,020,000 mg of vitamin C.
Just to clarify, in the answer above, I made a mistake in the units. 17g is actually 17,000mg, not 17mg. So the correct calculation is:
If one tablet of the multivitamin contains 17,000mg of vitamin C, then 60 tablets would contain 60 times that amount:
60 tablets x 17,000mg of vitamin C per tablet = 1,020,000mg of vitamin C
Therefore, 60 tablets of the multivitamin contain 1,020,000mg of vitamin C.
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She walked 30 minutes a day for 5 days. The next 3 days she walked an average of 46 minutes. What was the average time she spent walking?
She took five days of daily 30-minute walks. She walked for 46 minutes each day for the following three days. 36 minutes per day was the average time she spent walking.
To find the average time she spent walking, we need to add up the total time she spent walking and divide it by the number of days she walked.
For the first 5 days, she walked for a total of:
30 minutes/day x 5 days = 150 minutes
For the next 3 days, she walked for an average of 46 minutes/day, so she walked a total of:
46 minutes/day x 3 days = 138 minutes
The total time she spent walking over 8 days is:
150 minutes + 138 minutes = 288 minutes
The average time she spent walking is:
288 minutes / 8 days = 36 minutes/day
Therefore, the average time she spent walking is 36 minutes per day.
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Benjamin owns a food truck that sells tacos and burritos. He only has enough supplies to make 120 tacos or burritos. He sells each taco for $3.75 and each burrito for $8.25. Benjamin must sell at least $660 worth of tacos and burritos each day. If � x represents the number of tacos sold and � y represents the number of burritos sold, write and solve a system of inequalities graphically and determine one possible solution.
one possible solution is to sell 60 tacos and 60 burritos. To graph these inequalities, we can start by graphing the boundary lines for each inequality, which are obtained by replacing the inequality signs with equal signs.
Let x be the number of tacos sold and y be the number of burritos sold. Then we can write the following system of inequalities:
x + y ≤ 120 (since Benjamin only has enough supplies to make 120 tacos or burritos)
3.75x + 8.25y ≥ 660 (since Benjamin must sell at least $660 worth of tacos and burritos each day)
To graph these inequalities, we can start by graphing the boundary lines for each inequality, which are obtained by replacing the inequality signs with equal signs.
For the first inequality, we have:
x + y = 120
This is the equation of a straight line passing through the points (0, 120) and (120, 0). We can graph this line by plotting these two points and connecting them with a straight line.
For the second inequality, we have:
3.75x + 8.25y = 660
This is the equation of a straight line in slope-intercept form, y = (-3.75/8.25)x + 80. We can graph this line by plotting the y-intercept (0, 80) and using the slope (-3.75/8.25) to find additional points on the line.
Next, we need to shade the feasible region, which is the region that satisfies both inequalities. This is the region below the line x + y = 120 and above the line 3.75x + 8.25y = 660.
One possible solution is the point where these two lines intersect, which we can find by solving the system of equations:
x + y = 120
3.75x + 8.25y = 660
Solving for x and y, we get:
x = 60
y = 60
Therefore, one possible solution is to sell 60 tacos and 60 burritos.
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Roy’s Toys Company received a huge shipment of rubber duckies from a factory. The factory guaranteed Roy that the percentage of defective toys won’t exceed 1.5%, but Roy suspects it does. He took a random sample of 200 duckies, and found that 3% of them were defective. Let's test the hypothesis that the actual percentage of defective duckies is 1.5% versus the alternative that the actual percentage is higher than that. Roy finds the probability of getting a sample with 3% defective duckies or more to be 7.8%. Which of the following do you have for rejecting H0?
a. Insufficient evidence b. Some evidence c. Strong evidence d. Very strong evidence
The above question, we may state that As a result, the null hypothesis answer is (a) inadequate evidence.
What is null hypothesis?A null hypothesis is a sort of statistical hypothesis that asserts that a certain set of observations has no statistical significance. Sample data is used to assess the feasibility of ideas. H0 represents what is referred to as "zero" on occasion. The researchers make the premise that there may be a link between the parameters. The null hypothesis, on the other hand, claims that no such association exists. While it may not appear to be relevant, the null hypothesis is a crucial aspect of research.
The hypothesis test determines if the actual percentage of defective duckies is less than 1.5% (null hypothesis) or more (alternative hypothesis).
Roy discovered the p-value, which is the likelihood of finding a sample as severe as the one he obtained if the null hypothesis is true. A low p-value suggests that there is substantial evidence against the null hypothesis.
The p-value in this situation is 7.8%, which is not very tiny. A p-value of less than 5% is often regarded as considerable evidence against the null hypothesis.
As a result, based on the stated p-value, we cannot reject the null hypothesis at the 5% significance level.
As a result, the answer is (a) inadequate evidence.
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Evaluate the expression when b=3 and c=-2. -9c+b
Given:-
b = 3c = - 2[tex] \: [/tex]
Solution:-
-9c + b-9 ( -2 ) + 318 + 321_________
hope it helps ⸙
Maths question. Please explain how you got your answer.
Thank you :)
Answer:5/2=2.5
Step-by-step explanation:
[tex]\sqrt{27}=\sqrt{3^{3}}=3^\frac{3}{2}\\\\we \ can \ show \ \sqrt{3^{3}} \ as \ 3^\frac{3}{2}\\3^{1}*3{\frac{3}{2}}=3^{1+\frac{3}{2}}=3^{\frac{5}{2}}\\n=\frac{5}{2}[/tex]
Answer:
[tex]n=\dfrac{5}{2}[/tex]
Step-by-step explanation:
Rewrite 27 as the product of prime numbers:
[tex]\implies 27 = 3 \cdot 3 \cdot 3 = 3^3[/tex]
Therefore, replace 27 with 3³ in the given equation:
[tex]\implies 3 \times \sqrt{3^3}=3^n[/tex]
[tex]\textsf{Apply the exponent rule:} \quad \sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]
[tex]\implies 3 \times 3^{\frac{3}{2}}=3^n[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 3^1 \times 3^{\frac{3}{2}}=3^n[/tex]
[tex]\implies 3^{1 +\frac{3}{2}}=3^n[/tex]
[tex]\implies 3^{\frac{2}{2} +\frac{3}{2}}=3^n[/tex]
[tex]\implies 3^{\frac{5}{2}}=3^n[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]
[tex]\implies \dfrac{5}{2}=n[/tex]
Therefore, the value of n is 5/2.
Two bags contain white and yellow balls. Bag 1 contains two white balls and four yellow balls. Bag 2 contains four white balls and five yellow balls. A ball is drawn at random from each container. What is the probability that both balls are white?
A. 1/9
B. 1/6
C. 4/27
D. 10/201
Answer:
C. 4/27
Step-by-step explanation:
Let's use the multiplication rule of probability to calculate the probability that both balls drawn are white:
P(white ball from Bag 1) = 2/6 = 1/3
P(white ball from Bag 2) = 4/9
Therefore, the probability of drawing a white ball from each bag is:
P(white from Bag 1 and white from Bag 2) = P(white from Bag 1) * P(white from Bag 2)
= (1/3) * (4/9)
= 4/27
So, the answer is C. The probability that both balls are white is 4/27.
find the surface area = sq.cm
6cm 5cm 3cm 5cm 3cm
Answer: To find the surface area of this object, we need to find the area of each of its faces and add them together.
The object has two faces that are 6 cm by 5 cm, which gives an area of:
6 cm x 5 cm = 30 sq. cm
The object also has two faces that are 5 cm by 3 cm, which gives an area of:
5 cm x 3 cm = 15 sq. cm
Finally, the object has two faces that are 3 cm by 3 cm, which gives an area of:
3 cm x 3 cm = 9 sq. cm
Adding up the areas of all six faces, we get:
30 sq. cm + 30 sq. cm + 15 sq. cm + 15 sq. cm + 9 sq. cm + 9 sq. cm = 108 sq. cm
Therefore, the surface area of the object is 108 square centimeters.
Step-by-step explanation:
An initial investment of $5000 grows at 7% per year. Write the function represents the
value of the investment after t years.
Answer: V(t) = 5000 * (1.07)^t
Step-by-step explanation:
In particular, you will compare the AVERAGE PROFITABILITY for customers with INCOME < 40,000 with customers whose income > = 40,000. Ignore missing values in this analysis (leave them as they are as you complete this analysis and do NOT eliminate records with INCOME missing) and let the EXCEL IF function treat missing values by default. Which of the following is a FIRST STEP towards completing this analysis?
The formulas will calculate the average profitability for customers with income < 40,000 and those with income >= 40,000 respectively.
The first step towards completing the given analysis is to create two groups of customers based on their income levels. The groups should consist of customers with income < 40,000 and those with income > = 40,000. The detailed explanation is provided below:Step-by-step explanation:Here, we need to compare the average profitability of two groups of customers based on their income levels, one with income less than 40,000 and the other with income greater than or equal to 40,000.The first step towards completing this analysis is to create two groups of customers based on their income levels. The groups should consist of customers with income < 40,000 and those with income > = 40,000. This can be achieved using the following steps:1. Open a new Excel workbook and import the dataset that needs to be analyzed.2. Once the data is imported, create a new column named 'Income Group' that will classify customers into the two groups based on their income level. To do this, we can use the following formula: =IF(B2<40000,"<40,000",">=40,000")Here, B2 is the cell that contains the income value of the first customer.3. Drag the formula down to the last cell in the column to apply it to all customers. This will create two groups of customers based on their income levels.4. Now, we need to calculate the average profitability of each group. To do this, we can use the following formula: =AVERAGEIF(C2:C11,"<40,000",D2:D11) and =AVERAGEIF(C2:C11,">=40,000",D2:D11)Here, C2:C11 contains the income group values, D2:D11 contains the profitability values, and "<40,000" and ">=40,000" are the criteria for each group. These formulas will calculate the average profitability for customers with income < 40,000 and those with income >= 40,000 respectively.
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Diners at several restaurants were surveyed to see what day of the week they prefer to go out to eat. The following table gives some of the data collected by the restaurants.
Restaurant Number of Customers
Who Prefer Saturdays Number of
Customers Surveyed
A 26 30
B 35 72
C 38 143
D 15 64
E 63 74
If each restaurant selects one customer from the group of people surveyed, selecting a customer who prefers to go out to eat on Saturday is an unlikely event for
.
If each restaurant selects one customer from the group of people surveyed, selecting a customer who prefers to go out to eat on Saturday is a likely event for
.
If each restaurant selects one customer from the group of people surveyed, selecting a customer who prefers to go out to eat on Saturday is neither a likely event nor an unlikely event for
If each restaurant selects one customer from the group of people surveyed, selecting a customer who prefers to go out to eat on Saturday is an unlikely event for Restaurants C and D.
If each restaurant selects one customer from the group of people surveyed, selecting a customer who prefers to go out to eat on Saturday is a likely event for Restaurants A and E.
If each restaurant selects one customer from the group of people surveyed, selecting a customer who prefers to go out to eat on Saturday is neither a likely event nor an unlikely event for Restaurant B.
How to find the likelihood ?Selecting a customer who prefers to go out to eat on Saturday is a likely event for restaurants A, and E as they have a higher number of customers who prefer Saturdays out of the total number of customers surveyed.
Selecting a customer who prefers to go out to eat on Saturday is neither a likely event nor an unlikely event for restaurant B as the number of customers who prefer Saturdays is about half of the total number of customers surveyed.
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Numeros que multiplicados den 30 y sumados o restados den -11
Los dos números que multiplicados den 30 son 5 y 6. Para encontrar dos números que sumados o restados den -11, debemos verificar todas las posibles combinaciones. Al hacerlo, descubrimos que -5 y -6 sumados dan -11. Por lo tanto, los dos números son 5 y -6.
Elliott is standing 32 feet from the base of a tree. The angle of elevation measured from a point on the ground to the tops of the tree is 61 degrees. How tall is the tree? Round your answer to the nearest foot. Sketch a picture and show all of your work in the workspace for full credit.
Hence, the tree is roughly 67 feet tall (rounded to the nearest foot) as the angle of elevation being 61 degrees.
what is angles ?Angles are polygons created when two rays intersect at a location known as the vertex. The rays might alternatively be referred as legs or sides. Angles are used to describe how much rotation or turning there is between two rays and are often measured in minutes or radians. Acute lengths, right angles, acute angles, and linear angles are the four most typical angles. Obtuse angles are those that are higher than 90 degrees, acute angles are those that are less than 90 °, and straight sides are those that are precisely 180 degrees.
given
The height of the tree serves as one side of a right triangle, the distance between Elliott and the tree serves as the other side, and the hypotenuse serves as the line of sight from Elliott to the top of the tree. Trigonometry is what we'll need in order to determine the tree's height.
We can rearrange the letters to get: since we know that tan() = opposite/adjacent.
inverse = nearby * tan(θ)
With the next side being 32 feet and the angle of elevation being 61 degrees, we have the following:
opposition is equal to 32 * tan(61°) 66.87 feet.
Hence, the tree is roughly 67 feet tall (rounded to the nearest foot) as the angle of elevation being 61 degrees.
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Can someone help me out?
In a class of 100 students, 60 like sports, 50 like music and 25 like both. show it in Venn-diagram and find the number of students who do not like any of them. find the number of students who like only one item
Answer:
Step-by-step explanation:
n(u)=100
n(s)=60
n(m)=50
n(snm)=25
n(sum)=85
n(sum)compliment = n(u)-n(sum)
= 100-85
= 15
Liquid A has a density of 1.09 g/cm³.
Liquid B has a density of 1.53 g/cm³.
43 cm³ of liquid A and 166 cm³ of liquid B are mixed to make liquid C.
Work out the density of liquid C.
Give your answer correct to 2 decimal places.
g/cm³
The density of the mixture (liquid C) is 1.44 g/cm³ (rounded to 2 decimal places).
What is density ?
Density is a physical property of matter that describes how much mass is contained within a given volume. It is defined as the amount of mass per unit volume of a substance. In other words, density tells us how tightly packed the molecules or particles of a substance are.
The formula for density is:
density = mass / volume
where mass is the amount of matter in an object or substance, and volume is the amount of space it occupies.
According to the question:
To find the density of the mixture, we need to use the formula:
density of mixture = (mass of liquid A + mass of liquid B) / (volume of liquid A + volume of liquid B)
We can find the masses of the liquids by using their densities and volumes:
mass of liquid A = density of A x volume of A = 1.09 g/cm³ x 43 cm³ = 46.87 g
mass of liquid B = density of B x volume of B = 1.53 g/cm³ x 166 cm³ = 254.58 g
Now we can substitute the values into the formula:
density of mixture = (mass of liquid A + mass of liquid B) / (volume of liquid A + volume of liquid B)
density of mixture = (46.87 g + 254.58 g) / (43 cm³ + 166 cm³)
density of mixture = 301.45 g / 209 cm³
Therefore, the density of the mixture (liquid C) is 1.44 g/cm³ (rounded to 2 decimal places).
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Solve the following equation.
5x = 60
x =
Group of answer choices
5
12
1
60
Answer:
x=12
Step-by-step explanation:
You have to do 60/5 which is 12
so x=12
Answer:
x=12
Step-by-step explanation:
5x=60
divide both sides by 5
x=12
answer: x=12
A jar of dimes and quarters contains $2. 55. There are 15 coins in all. How many of each coin are there?
06.02 LC) What best describes the expression y/3?
Group of answer choices
A) 3 less than some number
B) 3 more than some number
C) Some number divided by 3
D) Some number times 3
Answer:
C) Some number divided by 3
Step-by-step explanation:
y is an unknown variable and is being divided by 3.
Find the area of the triangle with vertices (10, 1), (7, 11), and (7, 1).
The area of the triangle is 15 square units.
What is area of triangle?The area of a triangle is a measure of the size of the region enclosed by the three sides of the triangle. The formula for finding the area of a triangle depends on the length of its base and height, which are usually denoted by "b" and "h", respectively.
We can find the area of the triangle with vertices (10, 1), (7, 11), and (7, 1) by using the formula for the area of a triangle:
area = (1/2) * base * height
where the base is the distance between the two points with the same y-coordinate, and the height is the distance from the third point to the line that contains the base.
The base is a vertical line segment with length 11 - 1 = 10, since the two points (7, 11) and (7, 1) have the same y-coordinate.
The height is the distance from the point (10, 1) to the line that contains the base. Since the line is vertical and passes through the point (7, 1), the distance is simply the difference between the x-coordinates of the two points: 10 - 7 = 3.
Substituting these values into the formula, we get:
area = (1/2) * 10 * 3
= 15
Therefore, the area of the triangle is 15 square units.
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Use this tax table to find how much tax you need to pay on a taxable income of $25,000.
If taxable income is over-- But not over-- The tax is:
$0 $7,825 10 percent of the amount over $0
$7,825 $31,850 $782. 50 plus 15 percent of the amount over 7,825
$31,850 $77,100 $4,386. 25 plus 25 percent of the amount over 31,850
$77,100 $160,850 $15,698. 75 plus 28 percent of the amount over 77,100
$160,850 $349,700 $39,148. 75 plus 33 percent of the amount over 160,850
$349,700 no limit $101,469. 25 plus 35 percent of the amount over 349,700
The second tax bracket can be used to determine the amount of tax due for taxable income of $25,000: $7,825 (maximum amount for the first bracket) (maximum amount for the first bracket)
$25,000 (taxable income) minus $7,825 (first bracket's limit) equals $17,175 (amount in the second bracket)
15% of $17,175 (the tax amount for the second bracket) plus $782.50 (the tax amount for the first bracket) equals $3,178.75.
The total tax on a taxable income of $25,000 is therefore $3,178.75.
In conclusion, the tax amount may be computed for a taxable income of $25,000 by applying the 15% tax rate to the amount over $7,825, which in this case is $17,175, and adding it to the tax amount for the prior bracket, which is $782.50. The total tax due as a consequence is $3,178.75.
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if anyone could help, would be much appreciated
Answer:
f(x+h)-f(x)/h=5h+10x-6
Step-by-step explanation:
f(x)=5x²-6x+1
f( x+h )=5( x+h )²-6(x+h)+1
=5(x²+h²+2hx)-6x-6h+1
=5x²+5h²+10xh-6x-6h+1
f(x+h)-f(x)=(5x²+5h²+10xh-6x-6h+1-(5x²-6x+1)
=5x²+5h²+10xh-6x-6h+1-5x²+6x-1
=5h²+10hx-6h
f(x+h)-f(x)/h=(5h²+10hx-6h)/h
=5h+10x-6
can someone help me solve the area of this composite figure please
Therefore, the area of the composite figure is 65 square centimeters. Therefore, the area of the composite figure is approximately 150.8 square centimeters.
What is area?In mathematics, the area is the measure of the size of a two-dimensional surface or shape. It is the amount of space inside the boundary of a flat object, such as a triangle, rectangle, circle, or any other polygon. The standard unit of measurement for area is square units, such as square meters (m²), square centimeters (cm²), or square feet (ft²). To calculate the area of a shape, we usually use a formula that depends on the shape's geometry and dimensions, such as its length, width, radius, or height. Area has many applications in everyday life, such as calculating the size of a room, the amount of paint needed to cover a wall, or the area of land required to build a house or grow crops. In mathematics and science, area is also used to solve problems in geometry, physics, engineering, and other fields.
Here,
1. Combination of Square and Rectangle
To find the area of this composite figure, we need to break it down into simpler shapes and add up their areas. The figure consists of a square with sides of 5 cm, a rectangle with sides of 4 cm and 9 cm, and a square with sides of 2 cm.
The area of the square with sides of 5 cm is:
A1 = (side)²
= (5 cm)²
= 25 cm²
The area of the rectangle with sides of 4 cm and 9 cm is:
A2 = length x width
= (9 cm) x (4 cm)
= 36 cm²
The area of the square with sides of 2 cm is:
A3 = (side)²
= (2 cm)²
= 4 cm²
To find the total area of the composite figure, we add up the areas of these three shapes:
A = A1 + A2 + A3
A = 25 cm² + 36 cm² + 4 cm²
A = 65 cm²
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2. Verify the following identity, using the elementary trigonometric identities you have learned. Carefully lay out all steps in your computation. cos 2θ−cotθsin 2θ−tanθ=tan 2θ
The trigonometric identities cos 2θ − cotθ sin 2θ − tanθ= tan 2θ, is verified below with the help of elementary trigonometric identities.
Describe Trigonometric Identities?Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables in the equation. They are useful in solving trigonometric equations, simplifying expressions involving trigonometric functions, and evaluating integrals in calculus.
There are several types of trigonometric identities, including:
Pythagorean identities: These involve the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. The Pythagorean identities express this relationship in terms of trigonometric functions, such as sin²θ + cos²θ = 1.
Reciprocal identities: These involve the reciprocals of trigonometric functions, such as csc θ = 1/sin θ and sec θ = 1/cos θ.
We will start with the left-hand side of the identity and simplify it using the trigonometric identities:
cos 2θ − cotθ sin 2θ − tanθ
= cos 2θ − (cosθ/sinθ)(2sinθcosθ) − (sinθ/cosθ)
= cos 2θ − 2cosθsinθ − sin²θ/cosθ
= cos²θ − sin²θ − 2cosθsinθ − sin²θ/cosθ
= (cos²θ - sin²θ) - (sin²θ/cosθ) - 2cosθsinθ
= cos²θ - sin²θ - sin²θ/cosθ - 2sinθcosθ
= cos²θ - sin²θ - sin²θ/cos²θ - 2sinθcosθ/cos²θ (since cosθ ≠ 0)
= cos²θ - sin²θ - (sin²θ + 2sinθcosθ)/cos²θ
= cos²θ - sin²θ - sin(2θ)/cos²θ
= (cos²θ - sin²θ)/cos²θ - sin(2θ)/cos²θ
= (cos²θ/cos²θ) - (sin²θ/cos²θ) - sin(2θ)/cos²θ
= 1 - tan²θ - sin(2θ)/cos²θ
= (1 - tan²θ) - sin(2θ)/cos²θ
= (sec²θ) - (2sinθcosθ)/cos²θ
= (sec²θ) - (2sinθ/cosθ)
= (sec²θ) - 2tanθ
= tanθ + 1 - 2tanθ - 2tanθ (using the identity sec²θ = tan²θ + 1)
= tan²θ - 4tanθ + 1
= (tanθ - 1)²
= tan²θ - 2tanθ + 1
Therefore, we have shown that:
cos 2θ − cotθ sin 2θ − tanθ = tan 2θ
This verifies the given identity.
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michael has $85 in his bank account. He deposits $10 each week. write an equation representing the number of weeks, it will take him to save $400.
as a special case in which the error of the backward euler method can be analyzed directly, we consider the model problem (4.3) again, with x an arbitrary real constant. the backward euler solution of the problem is given by the formula (4.10).
This equation can be used to analyze the error of the backward Euler method directly for the model problem (4.3) with x an arbitrary real constant. The backward Euler method is a numerical method for solving ordinary differential equations (ODEs). It is an implicit method, meaning that it requires the solution of a nonlinear equation at each time step.
The error of the backward Euler method can be analyzed directly for the model problem (4.3) with x an arbitrary real constant. The backward Euler solution of the problem is given by the formula (4.10).
The backward Euler method is given by:
y_n+1 = y_n + h*f(t_n+1, y_n+1)
Where h is the time step, f is the function defining the ODE, t_n is the current time, and y_n is the current solution. The backward Euler method is an implicit method because it requires the solution of the nonlinear equation f(t_n+1, y_n+1) = 0 at each time step.
The error of the backward Euler method can be analyzed directly for the model problem (4.3) with x an arbitrary real constant. The model problem is given by:
y' = x*y
The exact solution of this problem is given by:
y(t) = y_0*exp(x*t)
The backward Euler solution of the problem is given by the formula (4.10):
y_n+1 = y_n/(1 - h*x)
The error of the backward Euler method is given by the difference between the exact solution and the numerical solution:
e_n = y(t_n) - y_n
By substituting the exact solution and the numerical solution into the error equation, we can analyze the error of the backward Euler method directly:
e_n = y_0*exp(x*t_n) - y_n
By rearranging the terms and using the formula for the numerical solution, we can obtain an equation for the error:
e_n = (y_0*exp(x*t_n) - y_n)/(1 - h*x)
This equation can be used to analyze the error of the backward Euler method directly for the model problem (4.3) with x an arbitrary real constant.
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Brianna bought two pounds of strawberries for 4.80 What is the price of dollars ounce per strawberries 1 pound = 16 ounces
Answer:
There are 16 ounces in 1 pound, so Brianna bought 2 x 16 = <<2*16=32>>32 ounces of strawberries.
The total cost was 4.80 dollars for 32 ounces.
To find the price per ounce, we divide the total cost by the number of ounces:
4.80 / 32 = 0.15
Therefore, the price of dollars per ounce for strawberries is $0.15.
Step-by-step explanation:
Levi Hempke wants to buy a car costing $21,000. He will finance the pu rchase with an installment loan from the bank, but he would like to finance no more than$14,280. What percent of the car's total cost should his down payment be?
Therefore , the solution of the given problem of percentage comes out to be down payment is 32% of the overall cost of the vehicle.
What is percentage, exactly?In statistics, a% is a number or value that is expressed as a fraction of 100. The terms "pct.," "pct.," but also "pc" are also infrequently used. Nevertheless, the symbol "%" is frequently used to indicate it. The percentage sum is flat; there are no dimensions. Since the numerator of a percentage is always 100, percentages truly constitute integers. Either the percent symbol (%) or the word "percent" must come before a number to denote that it is a percentage.
Here,
Levi Hempke wishes to borrow a maximum of $14,280 to finance a $21,000 vehicle. Consequently, he intends to put down:
=> $21,000 - $14,280 = $6,720
We must divide his down payment by the total cost of the car, multiply by 100 to convert to a percentage, and
then determine the percentage of the total cost of the car that he should put down:
=> ($6,720 ÷ $21,000) × 100 = 32%
Levi's down payment should therefore equal 32% of the overall cost of the vehicle.
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-6 inches per second it takes her 4 minutes to reach the bottom what is the cliff's height in feet
The height of the cliff from which Oletha rappels is 1,440 feet. We simply used the speed, distance, and time formulas.
To find the height of the cliff, we can use the formula:
distance = rate x time
In this case, the rate is -6 inches per second (negative because Oletha is descending), and the time is 4 minutes or 240 seconds.
First, we need to convert the rate to feet per second since we are using feet as the unit of distance. There are 12 inches in a foot, so:
-6 inches per second = -0.5 feet per second
Now we can use the formula to find the distance:
distance = (-0.5 feet per second) x (240 seconds)
distance = -120 feet
The negative sign indicates that Oletha has descended 120 feet below the starting point. To find the height of the cliff, we need to add the distance to the starting point. Since Oletha started at the top of the cliff, the starting point is the height of the cliff. Therefore:
height of cliff = starting point + distance
height of cliff = 0 feet + 120 feet
height of cliff = 120 feet
Therefore, the height of the cliff is 1,440 feet since there are 12 inches in a foot and 1,440 = 12 x 120.
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Complete Question:
Oletha rappels from the top of a cliff at a rate of -6 inches per second. It take Oletha 4 minutes to reach the bottom of the cliff. What is the height of the cliff in feet?