What is the solution to this system of equations 5x+2y=29
X+4y=13

Answer:

a) [tex]\frac{450}{100}[/tex] x 45 = 202.5g of sugar is in the can

b)[tex]\frac{4}{100}[/tex] x 80 = 3.2L is left

c)[tex]\frac{2400}{100}[/tex] x 70 = 1480 acres were planted with wheat

a. 202.5g

Since 45% of the energy drink is sugar

⇒ 45% of the total 450 grams will be made up of sugar

∴ sugar = [tex]\frac{45}{100}[/tex] * 450

             = 202.5g

Thus, the can contains 202.5g of sugar

b. 3.2L

Since Simon used up 20% of the paint, the paint left in the can will now be 80% of the original 4 liters

∴ paint left = [tex]\frac{80}{100}[/tex] * 4

                  = 3.2L

Thus, the can has 3.2 liters of paint left.

c. 1680 acres

Here, 30% of the farmer's crop is and the rest is wheat

⇒ 70% is wheat

Total acres of land planted= 2400

∴ Acres planted with wheat = [tex]\frac{70}{100}[/tex] *2400

                                              = 1680 acres

Thus 1680 acres is planted with wheat

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Answer:

Hakim's share = 2 x 12 = 24 guppies

Edmund's share = 3 x 12 = 36 guppies

Paul's share = 6 x 12 = 72 guppies

Step-by-step explanation:

We will have Hakim's share as the base unit.

Hakim : Edmund = 2:3

Edmund : Paul = 1:2

Hakim : Edmund : Paul = 2:3:3x2 = 2:3:6

Total units = 2+3+6 = 11 units

11 units = 132 guppies

1 unit = 132/11 = 12 guppies

Hakim's share = 2 x 12 = 24 guppies

Edmund's share = 3 x 12 = 36 guppies

Paul's share = 6 x 12 = 72 guppies

Answer:

D

Step-by-step explanation:

Passes through the x-axis at r and k

Answer:

[tex]\boxed {f(x) = x^{2} - 6x + 1}[/tex]

Step-by-step explanation:

Substituting each x value and checking it corresponds to the table :

x = -6

⇒ f(-6) = (-6)² - 6(-6) + 1

⇒ f(-6) = 36 + 36 + 1

⇒ f(-6) = 73

x = -2

⇒ f(-2) = (-2)² - 6(-2) + 1

⇒ f(-2) = 4 + 12 + 1

⇒ f(-2) = 17

x = 2

⇒ f(2) = (2)² - 6(2) + 1

⇒ f(2) = 4 - 12 + 1

⇒ f(2) = -7

x = 6

⇒ f(6) = (6)² - 6(6) + 1

⇒ f(6) = 36 - 36 + 1

⇒ f(6) = 1

x = 10

⇒ f(10) = (10)² - 6(10) + 1

⇒ f(10) = 100 - 60 + 1

⇒ f(10) = 41

Answer:

Step-by-step explanation:

A. Correct

B. Correct

C. Correct

D. False

2.

A. Correct

B. Correct

C. Correct

D. False

Hope I helped!

Using matrix algebra, the material cost of making one of each product at each location is as follows:​

                       Product X    Product Z

Location A        birr 38          birr 50

Location B        birr 38          birr 49.5

Matrix algebra involves the arrangement of numbers in a rectangular array.

Matrices are arranged in columns and rows to express some mathematical values.

                      Steel    Glass    Plastic

Product X         3            1             2

Product Z         4          0.5           3

                      Steel    Glass    Plastic

Location A      10           2           3

Location B       9           3           4

                      Steel    Glass    Plastic   Total

Location A     30           2           6          38

Location B     27           3           8          38

                      Steel    Glass    Plastic   Total

Location A     40          1             9          50

Location B     36          1.5         12         49.5

Thus, Product X costs birr 38 at locations A and B, respectively, while Product Z costs birr 50 and birr 49.5 at locations A and B, respectively.

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=========================================================

Reason:

We have "1" in the upper left corner and "2" in the direct middle. This means "3" goes to the left of the "2" since each row and column cannot use repeats. Just below that "3" will go "2".

In summary so far, the first column has 1, 3, 2 in that order when moving from top to bottom. Refer to the values in green in the diagram below.

For identical reasoning, the first row has 1, 3, 2 in that order when moving from left to right. These are the values in light blue.

Once the first row is filled out, we can determine the middle entry of the bottom row, which is "1" marked in pink. This item helps us determine that M = 3 which in turn leads to N = 1.

Therefore, N+M = 1+3 = 4 is the final answer.

Side note: This square has symmetry along the northwest diagonal

Answer:

3

Step-by-step explanation:

Cardinalities are the number of elements in a set.

(A∩B∩C) is the very middle part of the circle, and there are 3 elements there.

Answer:

050°

Step-by-step explanation:

The bearing of D from C is the angle between the north pole and the line joining C and D when moving in a clockwise direction.

From the diagram, the angle is 050°

Find volume

Density=12g/cm³

We know

mAss=Density ×Volume

Answer:

6032 g

Step-by-step explanation:

The battery can be modeled as a cylinder.

Volume of a cylinder

  [tex]\sf V=\pi r^2 h[/tex]

where:

Given:

Substitute the given values into the formula and solve for v:

[tex]\begin{aligned}\textsf{Volume of a cylinder} & =\sf \pi r^2 h \\ \implies \textsf{Volume of the battery} & = \sf \pi (4)^2(10)\\ v& = \sf 160 \pi\:\:cm^3\end{aligned}[/tex]

Density equation

  [tex]\rho =\dfrac{m}{v}[/tex]

where:

Given:

   [tex]\rho = 12 \dfrac{\text{g}}{\sf cm^3}[/tex]

   [tex]v=160 \pi \sf \:\:cm^3[/tex]

Substitute the given values into the Density equation and solve for m:

[tex]\begin{aligned}\rho & =\dfrac{m}{v}\\\implies 12 \dfrac{\text{g}}{\sf cm^3} & = \dfrac{m}{160 \pi \sf \:\:cm^3}\\m & = 12 \dfrac{\text{g}}{\sf cm^3} \cdot 160 \pi \sf \:\:cm^3\\m & = 12 \cdot 160 \pi \:\text{g}\\ m & = 1920\pi\:\text{g}\\ m & = 6031.857895...\:\text{g}\end{aligned}[/tex]

Therefore, the total mass of the battery to the nearest gram is 6032 g.

The probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

41% of adults say cashews are their favorite kind of nut.

P = 41% = 0.41

Q = 1 - P = 1 - 0.41 = 0.59

n = 2

From the binomial distribution:

[tex]\rm P(X = r) = C(n, r) P^r(1-P)^{n-r}[/tex]

a) Exactly​ three

[tex]P(X=3) = C(12, 3) (0.41)^3(0.59)^9[/tex]

P(X = 3) = 0.131

b) At least​ four:

P(X≥4) = P(X=4)+ P(X=5)+ P(X=6)+..............+ P(X=13)

[tex]\rm P(X\geq 4)=C(12, 4) (0.41)^4(0.59)^9+C(12, 5) (0.41)^5(0.59)^8+...............+C(12, 3)(0.41)^3(0.59)^9[/tex]

P(X ≥ 4) = 0.795

c) At most two:

P(X≤2) =P(X=0)+ P(X=1)+ P(X=2)

[tex]\rm =C(12, 0) (0.41)^0(0.59)^12+C(12, 1) (0.41)^1(0.59)^1^1+C(12, 2)(0.41)^2(0.59)^1^0[/tex]

P(X ≤ 2) = 0.0733

Thus, the probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.

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Answer:

the first answer y = 20x - 15

Step-by-step explanation:

since the correct tangent line must share the same point with the originated function, only a line function that delivers y = 25 for x = 2 can be correct.

only the first answer option provides this (20×2 - 15 = 25).

so, we know, this line goes through the given point, but does it have the correct slope for the tangent ?

the correct slope we get from the first derivative of the original function.

f(x) = (1 + 2x)² = 1 + 4x + 4x²

f'(x) = 4 + 8x

for x = 2 we get the tangent slope at that point as

4 + 8×2 = 20

and the provided line is again

y = 20x - 15

with the slope being the factor of x (20).

so, it fits, and indeed, answer 1 is correct.

There are 210 different three-digit whole numbers that can be formed with the digits 2, 3, 4, 5, 6, 7, 8 if the digits cannot be repeated.

To calculate how many different three-digit whole numbers can be formed with the digits 2, 3, 4, 5, 6, 7, 8 if the digits cannot be repeated, we need to use the permutation formula.

The number of permutations of n objects taken r at a time, where order matters and objects cannot be repeated, is given by:

P(n,r) = n! / (n-r)!

In this case, we have 7 digits to choose from, and we want to form a three-digit number, so r = 3. Therefore, the number of different three-digit whole numbers that can be formed is:

P(7,3) = 7! / (7-3)! = 7! / 4! = 7 x 6 x 5 = 210

Each of these numbers will be unique, as we are not allowed to repeat any of the digits.

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Answer:

D

Step-by-step explanation:

0.0378÷0.21=0.18

this is 18 hundredths

but its 180 thousandths

Explanation:

Now--this is an awfully odd way to word a question.

BUT, it is solvable!

digits have "place values" in numbers, let's focus on after the decimal point:

_ . _ _ _ _ _ '

we know this can go on forever, but we don't need it to (for this problem, that is)

_ . _ _ _

_ . {tenths} {hundredths} {thousandths} ........

we want to know how many thousandths we have:

the answer to this problem (0.0378 / 0.21) is 0.18

{let's consider what we know about place values:}

"10" can be thought of as ten-ones

and "1" can be thought of as ten tenths

{the reason it's always ten __ is that we use a base-ten system, and there are only ten options for each digit [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] }

so, 10 could be thought of as ten ones, which could each be thought of as ten tenths--meaning that 10 is the same thing as 100 tenths

[if you ignore the decimal point, it becomes more clear]:

10.0 [100]

likewise, 10.00 is 1000 hundredths; and 10.000 is 10,000 thousandths

--------

okay, back to our problem:

how many thousandths make up 0.18?

Let's write this out to the thousandths place:

0.180

if we use our tactic of ignoring the decimal, we are left with 0180 [of course, a "0" before a number has no value, so we can rewrite it as 180], or 180

so, 0.18 is really composed of 180 thousandths, which is how option D is the answer

hope this helps!! :)

{let me know if there's anything else you would like me to explain about this!}

Answer:

3041.06

Step-by-step explanation:

The formula of a cone is [tex]\pi r^{2} \frac{h}{3}[/tex] , so plugging both the height and radius will result in the answer!

Answer: Peyton

Step-by-step explanation:

Michelle: Greatest common factor is 1

Naomi: Greatest common factor is abc

Olivia: Greatest common factor is 2ab

Peyton: Greatest common factor is ab

Answer:

Non-Homogeneous Recurrence Relation and Particular Solutions

A recurrence relation is called non-homogeneous if it is in the form. Fn=AFn−1+BFn−2+f(n) where f(n)≠0.

The range of the function will be (-9, 7). Then the correct option is D.

The domain means all the possible values of x and the range means all the possible values of y.

The function is given in the form of the pair of points.

{(-2, 0), (-4,-3), (2, -9), (0, 5), (-5, 7)}

Then the range of the function will be (-9, 7).

Then the correct option is D.

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Remember that for a given angle θ, any point on the unit circle is written as:

(cos(θ), sin(θ)).

And remember that:

cos(45°) = sin(45°) = √2/2

Then the angle θ = 45° is a solution.

To find another positive solution, we just add the period of the circle, which is 360°.

θ = 45° + 360° = 405°

Adding the period again:

θ = 405° + 360° = 765°

So the 3 positive solutions can be:

{45°, 405°, 765°}

To get the negative angles we just subtract the period:

45° - 360° = -315°

We can do that again:

-315° - 360° = -675°

So the two negative angles are:

{-315°, -675°}

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Finding the percent increase, it is found that the correct option is given by:

C. The Master Program and the Excel Program are both effective, but Math is more effective because of the greater percent increase.

The percent increase is given by the difference between the final and the initial score, divided by the initial score and multiplied by 100%.

Researching the problem on the internet, we have that:

The percent increases are given as follows:

Hence the correct option is given by:

C. The Master Program and the Excel Program are both effective, but Math is more effective because of the greater percent increase.

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In the case above about Samuel, one can say that Samuel's calculator has display option A.  2.5 E (- 13)

The function was  [tex]\frac{5E (-9) }{2E(4) }[/tex] :

We know that, E implies 10 to rise to power.

So, The equation above is Converted from scientific notation into standard form.

 [tex]\frac{5 x 10^-9 }{2 x 10^ 4 }[/tex]

= 5/2  x 10 ⁻⁹⁻⁴

=2.5 x 10⁻¹³

Therefore, In the case above about Samuel, one can say that Samuel's calculator has display option A.  2.5 E (- 13)

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The decimal value that express the total percent markdown for the given scenerio are 0.5,0.31,0.09.

Given the total percent markdown for the following scenario, after being rounded to the nearest percent:50%, 31%,and 9%

Percentage is a ratio of the numbers expressed as a fraction of 100.

We have to just convert the percentages into decimal number which will be done as under:

To convert percentages into decimals we need to divide the number by 100. In this way the percentages will become:

50%=50/100

=0.5

31%=31/100

=0.31

9%=9/100

=0.09

Hence the decimal value of 50% ,31 % and 9% in percentages are 0.5,0.31,0.09.

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Answer:0.69

Step-by-step explanation:

Answer:

1/a+ 1/b = 1/2

Adding the fractions we get

b+a/ab=1/2

cross Multiplying the denominator we get,

b+a=ab/2

a= ab/2 -b

Answer:

a = 1/(1/2 + 1/b)

Step-by-step explanation:

1/a + 1/b = 1/2

1/a = 1/2 - 1/b

1 = a(1/2 - 1/b)

1/(1/2 + 1/b) = a

Answer:

833.25 or 877.59

Step-by-step explanation:

I solved this in two different ways because I wasn't sure on how the question was meant to be read.

Attempt 1:

(833.3/1)-(1+0.00833)^-360

(1+0.00833)^-360 = 0.0505

so:

833.3 - 0.0505 = 833.25

Attempt 2:

833.3/(1-(1+0.00833)^-360)

1- 0.0505 = 0.9495

833.3/0.9495 = 877.59

Step-by-step explanation:

1). (3+1)=4

2).5(1+11)

3).4+3(4)

4).5+2(4)

5).5(2+2)

6).1+4^2

7).6-(5-5)

8).4×5×2=40

9).2(2+3)

10).5+3+3=11

11)6+(4-4)

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Answer:

a) Cat

b) 4 (unless there is a key that says otherwise)

c) 3 more people

Step-by-step explanation:

a) It has the least number of shapes (only 5)

b) Cat has 1 small square which stands for 1 person and 4 small squares put together make a big square so a big square is 4 people. Unless a key says that a small square is more or less 1, then it should be 4.

c) If one big square is 4 people, then there are 10 people for giraffes and 7 people for dogs. 10 - 7 = 3 more people.

Fundamental Trigonometric Identities are listed below:

Fundamental Trigonometric Identities can be defined as the basic identities or variables that can be used to proffer solutions to any problem relating to angles and trigonometry.

In conclusion, A few Fundamental Trigonometric Identities are listed above.

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The equation that represents the given data is  [tex]\RM \\f(x) = -\sqrt[3]{-x} ,[/tex] Option D is the correct answer.

It is a statement where two variables , one dependent and one independent are related.

It is given that

a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).

The equation given in the options are

[tex]\rm f(x) = -\sqrt[3]{x} \\f(x) = -\sqrt[3]{x-1} \\f(x ) =-\sqrt[3]{-x} -1 \\f(x) = -\sqrt[3]{-x}[/tex]

The function goes through (8,2)

Substituting the values

f(x) = -2

f(x) = [tex]\sqrt[3]{7}[/tex]

f(x) = -3

f(x) = 2

The equation that represents the given data is

[tex]\RM \\f(x) = -\sqrt[3]{-x} ,[/tex] Option D is the correct answer.

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Answer:

D

Step-by-step explanation:

Answer:

11,812.5

Step-by-step explanation:

25% = 0.25

(YEAR ONE)

[tex]28,000*0.25 -- > 21,000[/tex]

↓ (why?)

28,000 * 0.25 = 7,000

[tex]28,000 - 7,000 = 21,000[/tex]

(YEAR TWO)

[tex]21,000 * 0.25 -- > 15,750[/tex]

↓ (why?)

[tex]21,000 * 0.25 = 5250[/tex]

[tex]21,000 - 5,250 = 15,750[/tex]

(YEAR THREE)

[tex]15,750 * 0.25 -- > 11,812.5\\[/tex]

↓ (why?)

[tex]15,750 * 0.25 = 3,937.5\\15,750 - 3,937.5 = 11,812.5[/tex]

Answer = 11, 812.5