Peter buys 30 apples at R5. 00 each. He sell each apple for R7. 0. How much profit does he makes?

Answer:

a=1/3

Step-by-step explanation:

First, expand the brackets by doing multiplication:

2+6a+3=3a+6

Then, move the unknown to the left and the numbers to the right:

3a=6-5

3a=1

a=1/3

The solution to the given equation is -1.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given equation is 2+3(2a+1)=3(a+2)

2+6a+3=3a+2

6a+5=3a+2

6a-3a=2-5

3a=-3

a=-1

Therefore, the solution to the given equation is -1.

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Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.

The age at which a person is qualified to receive their full retirement payment under Social Security is determined by their lifetime earnings history. The complete retirement age for anybody born in 1960 or later is 67. The complete retirement age is steadily lowered for people born before 1960, and is 65 for those born in 1937 or before.

Given that, Juanita started collecting benefits at age 65.

Thus, her benefits reduced by 13.3%.

0.133 x $2,128 = $283.10

Deducting the reduction amount from the total:

$2,128 - $283.10 = $1,844.90

Hence, Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.

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The antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.

The angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.

To get the height of the antenna, we subtract the height of the building from the height from the bottom of the building to the top of the antenna.

we shall represent the distance from the point of observation to the building with x and the height from the bottom of the building to the top of the antenna with y. so that;

tan 68° = 125/x {opposite/adjacent}

x = 125/ tan 68° {cross multiplication}

x = 50.5033

tan 71° = y/50.5033

y = 50.5033 × tan 71°

y = 144.6722

height of the antenna = 144.6722 - 125

height of the antenna = 19.6722

Therefore, the antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.

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Using the definitions of trigonometric functions for x = 0, we have tan(0) = 0 and cos(0) = 1, which simplifies to 0 * 1 = 0, and sin(0) = 0,

therefore tan(0) cos(0) = sin(0).

Define trigonometric.

Trigonometric refers to the branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles. It involves the study of trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant, and their properties and applications in various fields including mathematics, science, engineering, and navigation.

For any angle x, we have the identity:

tan(x) = sin(x) / cos(x)

Setting x = 0, we get:

tan(0) = sin(0) / cos(0)

Since tan(0) = 0 and cos(0) = 1, we can simplify this equation to:

0 = sin(0)

which is true, since the sine of 0 degrees is 0. Therefore, we have shown that:

tan(0) cos(0) = sin(0)

Therefore, the identity tan(0) cos(0) = sin(0) is proven.

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Step-by-step explanation:

No,

if the sprinkler covers a distance of 12 m meaning the 12 m is the diameter...then to find the area that it covers we use the formula for the circle since it's circular

A=πr2

A=3.142*36

A=113.112 cm3

16h^(10/2) *remove the root sign

16h^5 *simplify the exponent

Answer: 16h^5

Step-by-step explanation: im correct

Answer:

equal

Step-by-step explanation:

3BE² + 3DF²- (2AC²- AB) is the answer of the following question

The calculation is as follows

Let E and F be the feet of the perpendiculars from B and D, respectively, to AC. We can use the fact that the area of a quadrilateral is equal to half the product of the diagonals multiplied by the sine of the angle between them to find the length of the diagonal BD.

Since ABCS is a quadrilateral, we have:

Area of ABCS = (1/2) * AC * BD * sin(angle between AC and BD)

Substituting the given values, we get:

924 = (1/2) * 33 * BD * sin(angle between AC and BD)

sin(angle between AC and BD) = 924 / (16.5 * BD)

Now, consider triangles ABC and ACD. Using the Pythagorean theorem, we can write:

AB² + BC² = AC² (1)

CD²+ BC² = AC² (2)

Adding equations (1) and (2), we get:

AB² + 2BC²+ CD²= 2AC²

Substituting AC = 33 and rearranging, we get:

BC² = (2AC²- AB² - CD²) / 2

We can also write:

BE²= AB²- AE² (3)

DF² = CD²- CF²(4)

Adding equations (3) and (4), we get:

BE² + DF²= AB²+ CD² - AE²- CF²

Substituting BC²from earlier, we get:

BE²+ DF² = 2AC² - BC²- AE²- CF²

We want to find BE + DF. Squaring both sides of equation (3), we get:

BE²= AB² - AE²

AE²= AB²- BE²

Similarly, squaring both sides of equation (4), we get:

DF²= CD²- CF²

CF²= CD² - DF²

Substituting these expressions into the equation for BE²+ DF², we get:

BE²+ DF² = 2AC² - BC² - (AB² - BE²) - (CD²- DF²)

Simplifying, we get:

BE² + DF²= 2AC² - BC²- AB²- CD² + 2BE² + 2DF²

Collecting like terms, we get:

BE²+ DF²- 2BE² - 2DF²= 2AC²- BC² - AB² - CD²

Simplifying, we get:

BE²- DF² = 2AC²- BC²- AB²- CD²- 2BE² - 2DF²

Substituting the values we know, we get:

BE²- DF²= 2(33)²- BC²- AB² - CD²- 2BE²- 2DF²

Rearranging, we get:

3BE²+ 3DF² - BC²- AB²- CD²= 2(33)² - 924

Substituting BC^2 from earlier, we get:

3BE²+ 3DF² - (2AC²- AB)

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Answer:

Step-by-step explanation:

Given:

Side a and Side b are 6 and 5.

The angle C is 131.

This is an obtuse scalene triangle as identified.

Area = ab * sin (C)/2  = 11.32064

Answer: Do not agree.

Step-by-step explanation:

To determine if we agree with Marcus, we need to verify if the percentages he used on rides, video games, and batting cage add up to 100%.

Marcus used 25% of the tickets on rides and 1/2 on video games. So, the total percentage of tickets he used is:

25% + 1/2 × 100% = 25% + 50% = 75%

This means that Marcus should have used 25% of the tickets in the batting cage. If he said he used 23% of the tickets in the batting cage, then we do not agree with him.

Answer: 1.1. The donation per learner cannot be determined from the given table.

1.2. TABLE 1: INCOME IN RANDS OF FUNDRAISING

Number of learners that paid Income (R)

1 200

1.3. To calculate the missing value A, we need to add up all the given incomes and subtract it from the total income for 45 learners, which is 45 x A. Then we can solve for A:

Total income = 200 + 150 + 10(2,000) + 20(45) + A + 4,000 + 9,000

Total income = 45A

45A = 25,150

A = 558.89

Therefore, the missing value A is R558.89.

1.4. The dependent variable in the table is the income received from fundraising.

To find the ratio of income received from 10 learners to income received from 45 learners, we need to divide the income received from 10 learners by the income received from 45 learners and simplify the fraction:

Income from 10 learners = R1,100 (since each learner donates R110)

Income from 45 learners = R215

Ratio = Income from 10 learners : Income from 45 learners

= 1,100 : 215

= 20 : 3 (in its simplest form)

The total number of learners enrolled at the school is 1,100. If 80% of the learners paid, then the number of learners who paid is:

80% of 1,100 = 0.8 x 1,100 = 880 learners

The minimum income that the school can raise if 80% of the learners paid is when each of the 880 learners paid the minimum donation, which is R150:

Minimum income = 880 x 150 = R132,000

Since R132,000 is less than R170,000, the SGB chairperson's statement is not valid.

Step-by-step explanation:

Answer:

169 - 144p²

Step-by-step explanation:

(13 - 12p) × (13 + 12p)

each term in the second factor is multiplied by each term in the first factor

13(13 + 12p) - 12p(13 + 12p) ← distribute parenthesis

= 169 + 156p - 156p - 144p² ← collect like terms

= 169 - 144p²

The value of m∠JKL is 34°

An angle formed by a tangent and a secant intersecting outside a circle is equal to one-half the difference of the measures of the intercepted arcs.

Based on the theorem above, we can say:

m∠JKL = 1/2 * (159 - 91)

m∠JKL = 1/2 * 68

m∠JKL = 34°

Therefore, the value of m∠JKL in the circle is 34°.

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Answer:

ames have 18 litres of water. He poured unequally into 3 tank

I. Poured three quarter of water from tank one into tank 2

II. Poured half of the water that is now in tank 2 into tank 3

III. Poured one third of water that is now in tank 3 into tank 1

Find how much water is in each tanks

Step-by-step explanation:

Let's start with the amount of water in tank 1 as x liters.

I. Poured three quarter of water from tank one into tank 2, so tank 1 now has 1/4 of x liters and tank 2 has 3/4 of x liters.

II. Poured half of the water that is now in tank 2 into tank 3, so tank 2 now has 3/8 of x liters and tank 3 has 3/8 of x liters.

III. Poured one third of water that is now in tank 3 into tank 1, so tank 3 now has 1/3 * 3/8 * x = 1/8 * x liters and tank 1 has 1/4 * x + 1/8 * x = 3/8 * x liters.

We know that James poured 18 liters of water into the three tanks, so the sum of the water in the three tanks must be 18 liters.

3/8 * x + 3/8 * x + 1/8 * x = 18

Simplifying the equation, we get:

7/8 * x = 18

x = 18 * 8 / 7 = 20.57 (rounded to two decimal places)

Therefore, the amount of water in each tank is:

Tank 1: 3/8 * x = 7.71 liters

Tank 2: 3/8 * x = 7.71 liters

Tank 3: 1/8 * x = 2.57 liters

In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.

The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.

The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.

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According to the image, we can infer that the shapes which have at least 1 pair of perpendicular sides are the top leftmost trapezium and the bottom-center rectangle.

Perpendicular sides is a term to refer to a shape with a special characteristic. These shapes have two sides connected through an angle or vertex of 90°. So, to select the correct shapes we have to take into account this feature. According to the above, the correct shapes would be:

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The data we get from the question is a random experiment can result in one of the outcomes {a,b,c,d} with probabilities from that information, P(A U B U C) = 0.8.
         

The given probabilities of events and outcomes are:

       P({a}) = 0.4,P({b}) = 0.1,P({c}) = 0.3,P({d}) 0.2

 So the given events are:

        A = {a,b},B = {b,c,d},C = {d}

   We have to find P(A U B U C) Using the formula of the probability of the union of two events,

    we get:

          P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)

Now we will find the values of all probabilities:

                  P(A) = P({a}) + P({b})

                         = 0.4 + 0.1

                         = 0.5

                   P(B) = P({b}) + P({c}) + P({d})

                          = 0.1 + 0.3 + 0.2

                           = 0.6

                   P(C) = P({d})

                            = 0.2

                      P(A ∩ B) = P({b})

                                     = 0.1

                      P(A ∩ C) = P({d})

                                     = 0.2

                      P(B ∩ C) = P({d})

                                     = 0.2

               P(A ∩ B ∩ C) = 0

 (No common event) Put all the above values in the formula:

           P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) +

                                     P(A ∩ B ∩ C)

                                 = 0.5 + 0.6 + 0.2 - 0.1 - 0.2 - 0.2 + 0

                                 = 0.8

         Therefore, P(A U B U C) = 0.8 is the required probability.

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By answering the question the answer is Therefore, landscapers should equation use 35 gallons of an 80% pesticide solution.

In mathematics, an equation is a statement that two expressions are equal. The equation consists of her two sides divided by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of solving an equation is to find the values ​​of the variables to make the equation true. Simple or complex equations, regular or nonlinear, and equations involving one or more factors are all possible. For example, the expression "[tex]x2 + 2x - 3 = 0\\[/tex]" squares the variable x. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.  

Let's say a landscaper needs to use x gallons of an 80% pesticide solution.

The amount of pesticide for an 80% solution is 0.8 x gallons and the amount of pesticide for a 30% solution is 0.3 (35) = 10.5 gallons.

After mixing the two solutions, the total amount of pesticides in the mixture is 0.8 x + 10.5 gallons and the total volume of the mixture is x + 35 gallons.

Since we need a 55% pesticide solution, we can set the following formula:

[tex]0.8x10.5 0.55(x+35)0.8x10.5 0.55x+19.250.25x = 8.75x = 35[/tex]

Therefore, landscapers should use 35 gallons of an 80% pesticide solution.

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Answer:

Step-by-step explanation:

You want to know the cost of corn dogs and the cost of chili-cheese fries when 2 dogs and 3 fries cost $13, while 4 dogs and 1 fries cost $8.50.

The cost of each purchase can be represented by the equations ...

Subtracting the second equation from twice the first gives ...

  2(2d +3f) -(4d +f) = 2(13) -(8.50)

  5f = 17.50 . . . . . .  simplify

  f = 3.50 . . . . . . . divide by 5

  4d = 8.50 -f = 5.00 . . . . use the second equation to find d

  d = 1.25 . . . . . . divide by 4

Corn dogs cost $1.25; chili-cheese fries cost $3.50.

__

Additional comments

Many calculators provide a number of methods of solving systems of equations. The use of an augmented matrix of the equation coefficients is perhaps one of the simplest.

The second equation is a good choice for writing an expression for f in terms of d: f = 8.50 -4d. This expression can be substituted into the first equation if you want to solve the system by substitution, rather than elimination. Making that substitution gives 2d +3(8.50 -4d) = 13, and that simplifies to -10d = -12.50 after subtracting 25.50 from both sides.

Answer:

285°

Step-by-step explanation:

x + x + 2x + 2x + 40 + 2x + 10 = (5 - 2)180

8x + 50 = 540

8x = 490

x = 61.25

2x + 40 = 2(61.25) + 40 = 285

Answer:

Step-by-step explanation:

Interior angles in a pentagon equal 540°.

Simplify

x°,x°,2x°, (2x+40) and (2x+10) = 8x+50

Calculate x

8x + 50 = 540

8x = 540 - 50 = 490

x = 490/8

x = 61.25°

Calculate largest angle

2x + 40, where x = 61.25°

=162.5°

Answer:

The simplified expression is sec^2a

Step-by-step explanation:

We can start by using the trigonometric identities:

cot^2 a + 1 = csc^2 a

tan^2 a + 1 = sec^2 a

Using these identities, we can rewrite the expression as:

(cos^2 a - cot^2 a)/(sin^2 a - tan^2 a)

= (cos^2 a - (csc^2 a - 1))/(sin^2 a - (sec^2 a - 1))

= (cos^2 a - csc^2 a + 1)/(sin^2 a - sec^2 a + 1)

Now we can use the identity:

sin^2 a + cos^2 a = 1

to rewrite the expression further:

= (1/sin^2 a - 1/sin^2 a cos^2 a)/(1/cos^2 a - 1/cos^2 a sin^2 a)

= (1 - cos^2 a)/(sin^2 a - sin^2 a cos^2 a)

= sin^2 a / sin^2 a (1 - cos^2 a)

= 1 / (1 - cos^2 a)

= sec^2 a

Therefore, the simplified expression is sec^2 a.

All of the reasons that the range is an appropriate measure of variability to describe the variation in the hours slept by eighth graders include the following:

A. The data are evenly distributed between 7 hours and 9 hours.

D. There is no outlier in the data.

In Mathematics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.

Mathematically, the range of a data set can be calculated by using the following mathematical equation;

Range = Highest number - Lowest number

By critically observing the double box-and-whisker plots or box plot for the variation in the hours slept by eighth graders, we can logically deduce that there is no outlier in the data because they are evenly distributed and centered about the mean.

In conclusion, the box-and-whisker plot or box plot is symmetrical.

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Answer:

Step-by-step explanation:

Yeah what the other guy said

Let f be a continuous function in c[a, b] such that f(a) = 200. Then for all real numbers c, the scalar multiple cf is also a continuous function in c[a, b]. Specifically, cf(a) = c(200) = 200c.

To demonstrate that c[a, b] is a subspace, the following facts must be proved:
1. If f and g are both continuous functions in c[a, b], then the sum f + g is also a continuous function in c[a, b].
2. If f is a continuous function in c[a, b], then the scalar multiple cf is also a continuous function in c[a, b], where c is a real number.
3. The zero vector of c[a, b] is the constant zero function.

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Answer:

X

Step-by-step explanation:

We first must check the total amount of breakfast. Y happens to have 130 instead of 125. Now, we see that W and Z have a majority on strawberries with oatmeal, which is not what we are looking for. The last answer we have is X, where there is a majority of oatmeal + blueberries and there is a total of 125 breakfasts.

Hope this helps!

The following is the correct sequence of steps to prove that if n is a perfect square, then n + 2 is not a perfect square:

Step 1: Assume n = m², for some non-negative integer m.

Step 2: If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)².

Step 3: Expand (m + 1)² to obtain (m + 1)² = m² + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.

Step 4: Let's assume m ≥ 1.

Step 5: Hence, n + 2 is not a perfect square.

The first step in the sequence involves making an assumption to start the proof. The second step entails the derivation of the smallest perfect square greater than n. In the third step, we expand the (m + 1)² expression to get n + 2m + 1. The fourth step is an important one, as it shows that m must be greater than or equal to 1.

In the final step, we conclude that n + 2 is not a perfect square.

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The bearing of part A from part B is 254 degrees.

22 gallons of the first brand (35% pure antifreeze) and 88 gallons of the second brand (60% pure antifreeze) to make 110 gallons of a mixture that contains 55% pure antifreeze.

Let x be the number of gallons of the first brand (35% pure antifreeze) needed, and y be the number of gallons of the second brand (60% pure antifreeze) needed to make the desired mixture.

We know that the total volume of the mixture is 110 gallons and the desired concentration of antifreeze is 55%.

We can set up two equations based on the amount of antifreeze and the total volume of the mixture:

0.35x + 0.6y = 0.55(110) (amount of antifreeze)

x + y = 110 (total volume)

Simplifying the first equation, we get:

0.35x + 0.6y = 60.5

Now we can use substitution or elimination to solve for x and y. Here's one way to use substitution method

x + y = 110 (equation 1)

x = 110 - y (solve for x)

0.35x + 0.6y = 60.5 (equation 2, substitute x)

0.35(110 - y) + 0.6y = 60.5 (substitute x into equation 2)

38.5 - 0.35y + 0.6y = 60.5 (distribute 0.35)

0.25y = 22 (combine like terms)

y = 88 (divide both sides by 0.25)

So we need 88 gallons of the second brand (60% pure antifreeze). To find the amount of the first brand (35% pure antifreeze), we can substitute y back into equation 1:

x + y = 110

x + 88 = 110

x = 22 gallons

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Answer:

Step-by-step explanation:

only the 1st and 5th statements are true