A merchant bought several pieces of silk for $70. He sold all but two of them at a profit of $4 per piece. His total profit was $18. How many pieces did he originally purchase?
Let n be the number of pieces. He sold n - 2 pieces
Let p be the original price. His selling price = p + 4
Then n · p = 70.00
And (n - 2) · (p + 4) = 70.00+18.00 ---> np + 4n - 2p - 8 = 88.00
---> np + 4n - 2p = 96.00
---> 70.00 + 4n - 2p = 96.00
4n - 2p = 26.00
2n - p = 13.00
Trying some possibilities (7 & 1), (8 & 3), (9 & 5), and (10 & 7), finally gets us to the answer: n = 10 and p = 7.00.
therefore
the number of pieces was 10What are the next two terms in the sequence? 2, 12, 22, 32, ...
PLEASE HELP. I HAVE BEEN STUCK ON THIS ASSIGNMENT FOR A WHILE!! I WILL GIVE BRAINLIEST
The answer to the given question is option A that is only the first equation is an identity.
What are trigonometric identities ?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
Sin θ = 1/Csc θ or Csc θ = 1/Sin θ
Cos θ = 1/Sec θ or Sec θ = 1/Cos θ
Tan θ = 1/Cot θ or Cot θ = 1/Tan θ
1) LHS : 8 sec θ sin θ = 8 X 1/ cos θ X sin θ = 8 tan θ
RHS : 8 X sin^2 θ/ cos^2θ X cosθ / sin θ = 8 tan θ
Thus LHS = RHS and it is given above so 1st equation is an identity.
2) LHS: 11 X cot^2 θ/ cosec θ X sec^2 θ = 11 cos^2θ /sin θ
and RHS : 11 cosec^2 θ
since LHS ≠ RHS because the second equation us not an identity.
thus the correct option is A that is Only the first equation is an identity.
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Describe and correct the error a student made when graphing [tex]y+5=-\frac{3}{4}(x-8)[/tex].
Answer/Step-by-step explanation:
3
y + 5 = ( - ) ------- (x - 8)
4
3
y + 5 = ( - ) ------- x + 6
4
3
y + 5 = ( - ) ------- x + 6
-5 4 -5
3
y = ( - ) ------- x + 1
4
m = slope = (-3/4)
b = y-intercept = (0, 1)
----------------------------------------------------------------------------------------------------------
The student's first error was in step 1.
Step 1 should involve plotting a point at (0, 1).
Step 2 should involve plotting a point 3 units down and 4 units right from the point in step 1, at (4, -2).
Step 3, connecting the points with a line was correct.
----------------------------------------------------------------------------------------------------------
I hope this helps!
What is the correct conjunction identity for tan 0?
A. csc (90 ° - 0)
B. sec (90 ° - 0)
C. sin (90 ° - 0)
D.cos (90 ° - 0)
E. cot (90 ° - 0)
The correct cofunction identity for tan 0 is cot (90 ° - 0). Option E
What are cofunction identities?The cofunction identities are defined as trigonometric functions elaborates the relationship between the trigonometric identities.
These trigonometric identities includes;
SineCosineTangentCotangentSecant CosecantIt is crucial to note that the value of a trigonometric function of any specific angle is equivalent to the value of the cofunction of their complementary identities.
The cofunction identities are represented thus;
sin θ = cos(90 - θ)
cos θ = sin(90 - θ)
cot θ = tan(90 - θ)
tan θ = cot(90 - θ)
csc θ = sec(90 - θ)
sec θ = csc(90 - θ)
For tan 0, we have that its cofunction identity is expressed as;tan 0 = cot (90 ° - 0)
Thus, the identity is cot (90 ° - 0)
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The correct cofunction identity for tan 0 is cot (90 ° - 0). Option E.
What are cofunction identities?The cofunction identities are defined as trigonometric functions elaborates the relationship between the trigonometric identities.These trigonometric identities includes; sine,cosine, tangent, cotangent, secant cosecant.
It is crucial to note that the value of a trigonometric function of any specific angle is equivalent to the value of the cofunction of their complementary identities.The cofunction identities are represented thus;
sin θ = cos(90 - θ)cos θ = sin(90 - θ)cot θ = tan(90 - θ)tan θ = cot(90 - θ)csc θ = sec(90 - θ)sec θ = csc(90 - θ)For tan 0, we have that its cofunction identity is expressed as;tan 0 = cot (90 ° - 0)Thus, the identity is cot (90 ° - 0)
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susy goes to the grocery store, 3 apples cost 1.50 . find the unit rate in cost per apple
Answer:
1.50/3 Apples=0.5
That means each apple cost 0.5. If it's in rands gonna be R0.5 or 50 Cents per apple.
Thirty-five students attend a math club meeting. The number of girls at the meeting is a multiple of 13, and there are more girls than boys attending the meeting. How many boys are at the meeting?
Answer: 9 boys
Reason:
The multiples of 13 are
13, 26, 39, 52, ...
We only need to focus on the first two since they are smaller than 35
So we focus on 13 and 26
If there are 13 girls, then there are 35-13 = 22 boysIf there are 26 girls, then there are 35-26 = 9 boysThe second option has more girls than boys, so that must mean there are 26 girls and 9 boys.
Can yiu show me how to set it up and the answer please [tex]when \: k {}^{3} - 17k + 32 \: is \: divided \: by \: k + 5[/tex]
When the polynomial is divided by the linear expression we get the quotient k² -5k +8 and the remainder -8.
Polynomials are used in many areas of mathematics. For example, they are used in arithmetic and mathematical methods to approximate other functions. They are also used to describe linear combinations, which are encountered in a variety of situations, from basic physics and biology to economics and science.
From straightforward word problems to intricate scientific conundrums, polynomial equations are utilised to represent a wide range of topics. Algebraic varieties and polynomial rings, two essential concepts in algebra and computational geometry, are constructed in mathematics using harmonics.
The simplest way to do the long division is:
[tex]\begin{array}{r}k^2-5k+8\phantom{)} \\x+5{\overline{\smash{\big)}\,k^3-17k+32\phantom{)}}}\\\underline{-~\phantom{(}(k^3+5k^2)\phantom{-b)}}\\-5k^2-17k+32\phantom{)}\\\underline{-~\phantom{()}(-5k^2-25k+40)}\\ -8\phantom{)}\end{array}[/tex]
Hence the division will give quotient quotient k² -5k +8 and the remainder -8.
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Can you help me with this please!!
Let us find the third side of the right triangle using the Pythagora's theorem
The missing side is the opposite side because it is facing the angle
[tex]\begin{gathered} 13^2=5^2+x^2 \\ \\ x^2=169-25 \\ \\ x^2=144 \\ \\ x=\sqrt[]{144} \\ \\ x=12 \end{gathered}[/tex][tex]\begin{gathered} sin\theta=\frac{opposite}{hypotenuse} \\ \\ sin\theta=\frac{12}{13} \end{gathered}[/tex]Jim’s music library on his phone holds 1,900 songs. The songs have an average time of 3.5 minutes. Use scientific notation to find the total number of seconds the playlist will play. Express the answer to the exact decimal place.
We need to know about scientific notation to solve this problem. The number of seconds the playlist will play is 3.99 x 10^5.
Expressing a number in scientific notation means writing the number as a multiple of ten with ten raised to some power. We use scientific notation for numbers that are very small or very big. When writing numbers in scientific notation we always have one number other than zero before the decimal point. In this question we know that there are 1900 songs and each song has average time of 3.5 minutes, we need to convert the minutes into seconds and multiply the number of seconds of each song to 1900.
1 min=60 seconds
3.5 mins=3.5 x 60=210 seconds
210 x1900=399000 seconds
399000=3.99 x 10^5
Therefore the number of seconds that the playlist will play is 3.99x 10^5
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Identify the exponent in the term -3X²
A. 3
B. x
C. minus sign ( - )
D. 2
Find the value of x.
Answer:
x=12
Step-by-step explanation:
Express the polynomial in descending order.
4+ y4 - 9y³
y4 - 9y3 +4
Step-by-step explanation:
solo tienes que ordenarlo de mayor a menor de las variables
True or false,
In 60 min,the level in the pond increases 8 in
Answer:
True
Step-by-step explanation:
In 1 h, the level in the pond increases 1 ft. One way to find how many feet the level increases in 30 min is to multiply One way to find how many inches the level increases in 2- h is to multiply 2. 2 of 5 Completed
Answer:
True
Step-by-step explanation:
In 1 h, the level in the pond increases 1 ft. One way to find how many feet the level increases in 30 min is to multiply One way to find how many inches the level increases in 2- h is to multiply 2. 2 of 5 Completed so that is ture
3) Identify the center and radius
SOLUTION:
Case: Circle equations
Metho:
[tex](x-a)^2+(y-b)^2=r^2[/tex]Given:
[tex]\begin{gathered} (x+11)^2+(y-6)^2=9 \\ (x+11)^2+(y-6)^2=3^2 \end{gathered}[/tex][tex]\begin{gathered} Center(a,b)=(-11,6) \\ radius,r=3 \end{gathered}[/tex]Final answer:
Center (-11, 6)
radius, r= 3
Given the two rectangles below. Find the area of the shaded region.10, 2, 4, 2
Applying the formula for the area of a rectangle, the area of the shaded region is calculated as: 42 units².
What is a Rectangle?A rectangle has two pairs of opposite sides that are of equal length, one pair is the length, while the other is the width.
How to Find the Area of a Rectangle?The area of a rectangle = the product of its length and its width = (length)(width).
The area of the shaded region = area of the larger rectangle - area of the smaller rectangle
Dimensions of the larger rectangle:
Length of the larger rectangle = 10 + 2 = 12 units
Width of the larger rectangle = 9 + 2 = 11 units
Area of the larger rectangle = (12)(11) = 132 units²
Dimensions of the smaller rectangle:
Length of the smaller rectangle = 10 units
Width of the smaller rectangle = 9 units
Area of the smaller rectangle = (10)(9) = 90 units²
The area of the shaded region = 132 - 90
The area of the shaded region = 42 units²
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Write the ratio in the simplest form comparing the monetary value of 2 nickels to that os 1 quarter
The ratio of the simplest form of 2 nickels to 1 quarter is 2:5.
What is defined as the ratio?The ratio can be defined as a comparison of two amounts of the same unit to determine that much of one amount is present in the other. Ratios are divided into two types. The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groups. This ratio is represented by the fraction a/b. To simplify a ratio even further, we use the same method we used to simplify a fraction. a:b = a/b.For the given question;
The two monetary values are given as;
2 nickles and 1 quarter.
We know that;
1 nickles = 0.2 quarter.
For 2 nickles multiply both side by 2.
2 nickles = 2×0.2 quarter.
2 nickles = 0.4 quarter.
Find the ratio;
2 nickels to that of 1 quarter
2 nickels/ 1 quarter
Put the value of 2 nickle.
2 nickels/ 1 quarter = 0.4 quarter/1 quarter
2 nickels/ 1 quarter = 2/5
2 nickels: 1 quarter = 2:5
Thus, the ratio of 2 nickels to that of 1 quarter is found as 2:5.
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[3−∣∣−56−2(−13)∣∣]÷(−17)
What is the value of the expression?
The answer as a simplified fraction in the box is -1/6
Given the expression
[3-|-5/6 -2(-1/3)|] ÷ (-17)
Using PEDMAS
P is for parenthesis
[3-|-5/6+2/3)|] ÷ (-17)
[3-|2/3 - 5/6)|] ÷ (-17)
[3-|(4-5)/6)|] ÷ (-17)
[3-|-1/6)|] ÷ (-17)
Since the modulus of a negative number is equal to a positive number, the result will give:
[3 - 1/6] ÷ (-17)
[(18-1)/6] ÷ (-17)
17/6 ÷ (-17)
Next is to carry out the division operation
17/6 × (-1/17)
= -1/6
Hence, The answer as a simplified fraction in the box is -1/6
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The precipitation, in inches, Tampa normally receives each month for the last four months of the year is as follows: 6.3, 2 3/10, 1.6, and 2 1/2. Write and evaluate an expression to determine how much precipitation, in inches, Tampa receives from September through December.
Answer:
12.7 inches======================
Convert the mixed fractions into decimal and find the sum as follows:
6.3 + 2 3/10 + 1.6 + 2 1/2 = 6.3 + 2.3 + 1.6 + 2.5 = 12.7Amare drops a probe into a lake. The elevation of the probe changes
by - 11 feet every second. The probe takes 50 seconds to reach
the bottom of the lake. How deep is the lake? Show your work.
The lake is 12,250 feets deep.
The elevation is changing in the downward direction and at a rate of -11ft/s.
So it means that the downward velocity of the probe is 11ft/s.
The value of downward acceleration is 9.8?m/s² which is equal to acceleration due to gravity.
The total time taken to reach down is 50seconds.
We can use the equation of motion because the acceleration is constant,
Using,
S = ut + 1/2at²
Where,
S is the depth of the pool,
U is initial velocity,
U is zero because the probe is dropped.
S = 1/2at²
S = 1/2××9.8×50×50
S = 12250 feets.
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12.7-18.5+15+6.3-1+28.5
Answer:
43
Step-by-step explanation:
Please help I’ll mark you as brainliest if correct!!
a ) P = { a , n , c , d }
b ) {4 , 7} ⊆ { 4,7,8,12}
c ) {0,1} ⊄ { 1,4,5,6}
are the equations is mathematical symbols
What are sets and subsets ?Subsets are a component of the mathematical concept of sets. A set is anything that is contained in curly brackets, as "a,b,c,d." If set B includes the numbers 2, 4, and 6, it is said to be a subset of set A, and if set A is a collection of even integers, it is said to be the superset of set B.
Calculationa ) P = { a , n , c , d }
b ) {4 , 7} ⊆ { 4,7,8,12}
c ) {0,1} ⊄ { 1,4,5,6}
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17. Is the operation of forming Cartesian products commutative? Explain why or why not.
Choose the correct answer below.
OA. The operation of forming Cartesian products is commutative because order does not matter in
the definition of a Cartesian product.
OB. The operation of forming Cartesian products is not commutative because part of the definition of
a Cartesian product is the order of the elements generated by the two sets.
OC.
The operation of forming Cartesian products is commutative because a Cartesian product is
multiplication and multiplication is commutative.
O D. The operation of forming Cartesian products is not commutative because multiplication is not
commutative.
The operation of forming Cartesian products is not commutative because part of the definition of a Cartesian product is the order of the elements generated by the two sets.
==========================================================
Explanation:
Let's go over an example. We'll have these two sets
A = {1,2}
B = {3,4}
The cartesian product is this set of ordered pairs
A x B= {(1,3), (1,4), (2,3), (2,4)}
Each (x,y) pair has x as a value from the first set mentioned (A), and y a value from the second set mentioned (B). It might help to make a 2 by 2 table.
If we swap the order of set A and B then we have
B x A = {(3,1), (4,1), (3,2), (4,2)}
We can see that A x B does not equal B x A in this case. Therefore, the cartesian product operation is not commutative. The order matters.
Side note: Two sets are equal when they are subsets of each other.
Find the converse and determine if it is true or false.
Statement : obtuse angles are not right angles.
The converse statement is 'If an angle is not a right angles, then it is obtuse' True. Option A
What is a converse statement?The converse of a conditional statement is formed when the hypothesis and conclusion are both reversed.
In this case, the hypothesis is taken as the conclusion and the conclusion made the hypothesis.
The conditional statement is written as: a → b
The converse is written as b → a
Where;
a is the hypothesisb is the conclusionGiven that:
Original statement :Obtuse angles are not right angles
The converse statement : If an angle is not a right angles, then it is obtuse
We can see that the converse statement is true because an obtuse angle is an angle greater than 90 degrees.
Hence, the converse statement is true
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I need help finding an answer, please.
Given that ΔABC is similar to ΔDFE , the value of x = 5.83 (rounded off to hundredth place)
Comparing the given pair of similar triangles,
A ↔ D
B ↔ F
C ↔ E
Now since the ΔABC ~ ΔDFE, the ratio of their sides are equal.
=> [tex]\frac{FE}{BC} = \frac{DF}{CA}[/tex] (by property of similarity of triangles)
=> [tex]\frac{x}{15} = \frac{7}{18}[/tex] (substituting respective values)
=> x = 5.83 (simplifying the algebraic equation to hundredth place)
As per the property of similarity of triangles, the corresponding sides have fixed ratio. Thus the ratio of two sides of a triangle will be numerically equal to the ratio of two corresponding sides of its similar triangle. Moreover, the corresponding angles of two similar triangles are equal in measure.
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The sticker on Dean's new car states that the car averages 32.6 miles per gallon. If the fuel tank holds 12.3 gallons, then how far can Dean travel on one full tank of gas?
Answer:400.98 miles on one full tank
Step-by-step explanation:
you take 32.6 and multiply it by 12.3
In a recent year an author wrote 162 checks. Use the poisson distribution to find the probability that on a randomly selected day he wrote at least one check
Answer:
44.38%
Step-by-step explanation:
Becuase of 365 days a year, 162 out of 365 is 44.38% meaning that if he would selwcted a fay the probability would be 44.38% chance.
5.) Which is the better buy? Circle your answer (show supporting work)
20 cans of Mello Yello for $4.75
36 cans of Sprite for $9.50
6.)
Birth Rates and Populations around the World in 2011
Birth Rate
(per 1000 population per year)
15.53
Country
French Polynesia
Brazil
17.79
Australia
12.33
Sudan
36.12
Russia
11.05
India
20.97
Bulgaria
9.32
Source: http://www.indexmundi com/g
a.) Which country has a birth rate of 36.12?
b.) Which country has the largest birth rate?
c.) Which country has the smallest population?
Population
294,935
203,429, 800
21,766,710
45,047,500
138,739,900
1,189,173,000
7,093,635
Mello Yello
Sprite
We are spending $ 0.0263 less every Mello Yello can, therefore it is the better buy.
What is profit and loss?
Subtract the smaller value from the greater value in order to calculate the profit or loss. The selling price is always higher than the cost price when there is a profit. Selling price minus cost price is profit. In a loss scenario, the cost price is higher than the selling price. Loss = Price Cost
Given,
20 cans of Mello Yello for $4.75
Therefore cost of 1 can of Mello Yello = $4.75 / 20 = $ 0.2375
Also given,
36 cans of Sprite for $9.50
Therefore, cost of 1 can of Sprite = $9.50 / 36 = $ 0.2638
Therefore, per can we are paying $ 0.0263 less for Mello Yello.
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Complete Question:
Which is the better buy? Circle your answer (show supporting work)
20 cans of Mello Yello for $4.75
36 cans of Sprite for $9.50
There are 7 red cards, 6 blue cards, 8 purple cards, and 4 green cards in a hat. In a trial, a card is drawn from the hat and then replaced. In 640 trials a red card is drawn 240 times. How much greater is the experimental probability than the theoretical probability?
Responses
Please help:The function graphed models the profits, P(c), in thousands of dollars a store earns as a function of the number of clerks, c, working that day.Which statements are true based on the model?Select each correct answer.Maximum profits are earned when there are 4 clerks working.The store earns profits when no clerks are working.Maximum profits are earned when there are 7 clerks working.The store earns about $400,000 in profits on its best days.The store loses money when 8 or more clerks are working.
SOLUTION
The image below will help in answering the following questions
Now, from the graph, the parts above the horizontal line represents profit, while the part below the horizontal line represents loss.
(a) Maximum profits are earned when there are 4 clerks working.
From the graph, we can see that this statement is CORRECT. The maximum profit is at 400 thousand dollars and takes place at 4 on the horizontal axis, this 4 represents 4 clerks working
(b) The store earns profits when no clerks are working.
No clerks are working when we consider 0 on the horizontal plane. From the picture above, tracing 0, it shows us something below the horizontal line which represents loss. So, this statement is INCORRECT. When no clerks work, there is a loss not profit
(c) Maximum profits are earned when there are 7 clerks working.
Tracing 7 from the graph, it doesn't fall on the top part of the curve which indicates maximum profit. Hence, this statement is INCORRECT.
d) The store earns about $400,000 in profits on its best days.
From the image above, we can see that this is correct.
(e) The store loses money when 8 or more clerks are working.
When we traced 8 from the horizontal line, it fell to the part of the graph which indicated loss.
Hence this is CORRECTstatement .
So you will select the 1st, 4th and 5th options
17. The area of a square poster is 31 square inches. Find the length of one side of the poster. Explain.
PART A
To the nearest whole inch
PART B
To the nearest tenth of an inch
The length of one side of the poster, when the area of a square poster is 31 square inches is
Part A = 6 inch (To the nearest whole of an inch)
Part B = 5.6 Inch (To the nearest tenth of an inch)
As given in the question,
Area of square poster = 31 sq. inches
Let 'l' be the length of the square poster
Now according to formula
Area of square poster = Length * Length
Substitute the values in the formula we get,
31 = l × l
⇒ l² = 31
⇒ l = √31
⇒ l = 5.568
Length = 5.568
Hence, the length of one side of the poster, when the area of a square poster is 31 square inches is
Part A = 6 inch (To the nearest whole of an inch)
Part B = 5.6 Inch (To the nearest tenth of an inch)
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