A local boys club sold 176 bags of mulch and made a total cost of $520.They sold hardwood mulch for $3.50 per bag and pine bark mulch for $2.75 per bag.How bags of each type of mulch did they sell?

Rena's answer is correct.

To evaluate whether Rena's answer is correct, we need to perform the division of the two fractions 3/4 and 2/5. To divide one fraction by another, you multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping its numerator and denominator.
Here is a step-by-step solution:
Step 1: Write down the problem.
\[ \frac{3}{4} \div \frac{2}{5} \]
Step 2: Find the reciprocal of the second fraction.
The reciprocal of \( \frac{2}{5} \) is \( \frac{5}{2} \).
Step 3: Multiply the first fraction by the reciprocal of the second.
\[ \frac{3}{4} \times \frac{5}{2} \]
Step 4: Multiply the numerators together and the denominators together.
\[ \frac{3 \times 5}{4 \times 2} \]
\[ \frac{15}{8} \]
Step 5: Simplify the fraction if necessary.
In this case, \( \frac{15}{8} \) is an improper fraction because the numerator is larger than the denominator. We can convert it into a mixed number.
The whole number part of the mixed number is obtained by dividing the numerator by the denominator:
\[ 15 \div 8 = 1 \text{ with a remainder of } 7 \]
So, the mixed number is \( 1 \frac{7}{8} \).
Conclusion:
Rena's answer of \( 1 \frac{7}{8} \) is correct. The statement about her answer is true; she correctly evaluated the division of \( \frac{3}{4} \) by \( \frac{2}{5} \).

Answer:

x=0.8, y=2.2 (0.8, 2.2).

Step-by-step explanation:

y+x=3

y=1.5x+1

-------------

1.5x+1+x=3

2.5x=3-1

2.5x=2

x=2/2.5

x=0.8

y+0.8=3

y=3-0.8

y=2.2

To solve the given system of equations by substitution, we substitute the second equation into the first, solve for x, and then substitute x back into the second equation to solve for y, which yields x=0.8 and y=2.2 as the solution.

To solve the system of equations using substitution, we start by isolating one variable in one of the equations. Here, the second equation already gives us y in terms of x: y = 1.5x + 1.

Next, we substitute this expression for y into the first equation y + x = 3. This gives us:

Combine like terms to solve for x:

Now that we have the value of x, we can find the value of y by substituting x back into the equation y = 1.5x + 1:

Hence, the solution to the system of equations is x = 0.8 and y = 2.2.

As a final step, you may want to check your solution by plugging the values back into the original equations to confirm that they satisfy both equations.

Answer:

1. The ladder forms 71.8° with the ground.

2. The top of the ladder will reach 18.79 feet up the wall.

3. Height = 8.66 cm and area = 21.65 sq. cm.

Step-by-step explanation:

1. If the angle of elevation of the ladder is [tex]\theta[/tex] then we can write  

[tex]\sin  \theta = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} = \frac{19}{20}[/tex]

⇒ [tex]\theta = \sin ^{-1}(\frac{19}{20}) = 71.8[/tex] Degrees.

Therefore, the ladder forms 71.8° with the ground. (Answer)

2.  Now, if the ladder formed a 70 degree angle with the ground and the length of the ladder remains the same as 20 feet, then we can write  

[tex]\sin 70 = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} =  \frac{x}{20}[/tex]

⇒ x = 20 sin 70 = 18.79 feet.

Therefore, the top of the ladder will reach 18.79 feet up the wall.

3. See the attached figure.

We have, [tex]\tan 60 = \frac{BC}{CD} = \frac{BC}{5}[/tex]

⇒ Height = BC = 5 tan 60 = 8.66 cm.

Therefore, the area of the triangle BCD will be = [tex]\frac{1}{2} \times CD \times BC =  \frac{1}{2} \times 5 \times 8.66 = 21.65[/tex] sq. cm. (Answer)

Answer:

x³ - 5x² + 81x - 405 = 0

Step-by-step explanation:

Complex roots occur in conjugate pairs.

Thus given x = - 9i is a root then x = 9i is also a root

The factors are then (x - 5), (x - 9i) and (x + 9i)

The polynomial is the the product of the roots, that is

f(x) = (x - 5)(x - 9i)(x + 9i) ← expand the complex factors

    = (x - 5)(x² - 81i²) → note i² = - 1

    = (x - 5)(x² + 81) ← distribute

    = x³ + 81x - 5x² - 405, thus

x³ - 5x² + 81x - 405 = 0 ← is the polynomial equation

The required polynomial equation is x³ - 5x² + 81x - 405 = 0 with roots 5 and -9i.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

As we know that complex roots occur in conjugate pairs.

Thus given x = - 9i is a root then x = 9i is also a root

The factors are then (x - 5), (x - 9i) and (x + 9i)

The polynomial is the product of the roots, that is

f(x) = (x - 5)(x - 9i)(x + 9i)

Expand the complex factors in the above equation

f(x) = (x - 5)(x² - 81i²)   [∵ i² = - 1]

f(x) = (x - 5)(x² + 81)

f(x) = x³ + 81x - 5x² - 405

This is equating to zero.

f(x) = 0

Thus, the required polynomial is x³ - 5x² + 81x - 405 = 0

Learn more about the polynomial here:

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Answer:

c=4

Step-by-step explanation:

Answer:

C=4

Step-by-step explanation:

when solving these equations you have to get the letter by itself and in this case the 4 is being multiplied by the c so you have to do the opposite and divide the 4 from the c and divide 16 by 4 because what you do to one side of the equal sign you have to do to the other side.

The correct solution for the equation 3x + 6 = 34 is x = 9.33 (repeating). The provided options do not match this solution, indicating an error in the given choices.

To solve the equation 3x + 6 = 34, start by subtracting 6 from both sides to isolate the term with the variable x on one side. You get 3x = 28. Next, divide both sides by 3 to solve for x, which gives you x = 28 / 3 or 9.33 (repeating). None of the provided options A, B, C, or D matches the solution, indicating a potential error in the question or the options provided.

Step-by-step explanation:

2x²-4x=0

2x²=4x

[tex] \frac{2x {}^{2} }{x} = 4[/tex]

2x=4

x=2

Answer:

No solution

Step-by-step explanation:

we have

[tex]7x-7(x+6)=10[/tex]

Solve for x

Apply distributive property left side

[tex]7x-7x-42=10[/tex]

Combine like terms left side

[tex]-42=10[/tex] ----> is not true

therefore

The equation has no solution

Final answer:

To find the product, multiply 400 by 9.460730473, then multiply the result by 2/3.

Explanation:

To find the product of 400 and 9.460730473 times 10/15, we need to multiply the three numbers together. First, let's simplify 10/15 to 2/3. Then, multiply 400 by 9.460730473 to get the product. Finally, multiply the result by 2/3 to find the final answer.

400 x 9.460730473 = 3784.2921892

3784.2921892 x 2/3 = 2522.8614595

The product of 400, 9.460730473, and 10/15 is approximately 2522.8614595.

Answer:

The sign of h must be negative, and the sign of k must be positive.

the answer is c

Step-by-step explanation:

12

23

34

56

512

the answer is c

Step-by-step explanation:

12

23

34

56

Your answer is A. $485

200 – 130 = 70

70 – 25 = 45

45 + 240 = 285

285 + 225 = 510

510 – 100 = 410

410 + 75 = 485

Answer:

36 more students of grade 7 went on a trip than students of grade 6

Step-by-step explanation:

60 % of 110 students= 60/100*110= 66 students

85 % of 120 students= 85/100 * 120= 102 students

No of students of grade 7th more than 6th grade students= 102-66= 36

60% of the 6th grade band members and 85% of the 7th grade band members went on a trip Disney World trip. Then 36 more 7th graders went on the trip than 6th graders

percentage, a relative value indicating hundredth parts of any quantity.

Given,

The number of students in 6th grade=100

The number of students in 7th grade=120

60% of the 6th grade band members

60%×110

60/100×110=0.6×110=66

85% of the 7th grade band members

85%×120=85/100×120

=0.85×120=102

We need to find how many more 7th graders went on the trip than 6th graders

For this we need to find difference of 7th and 6th grade

102-66=36

Hence 36 more 7th graders went on the trip than 6th graders

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Answer:

Step-by-step explanation:

3x+4y=5

6x+8y=10

---------------

-2(3x+4y)=-2(5)

6x+8y=10

----------------

-6x-8y=-10

6x+8y=10

------------------

0=0

Answer: Infinitely many solutions.

------------------------------------------------------

7x-2y=9

7x-2y=13

--------------

-1(7x-2y)=-1(9)

7x-2y=13

---------------------

-7x+2y=-9

7x-2y=13

-------------

0=4

Answer: NO Solution.

-------------------------------------

2x-y=-11

-2x+y=11

-----------------

0=0

Answer: Infinitely many solutions.

-----------------------

3x+6y=1

x+y=0

x=0-y=-y

3(-y)+6y=1

-3y+6y=1

3y=1

y=1/3

x=-y=-1/3

Answer: x=-1/3, y=1/3. (-1/3, 1/3).

Answer:69

Step-by-step explanation:

69

Answer:

2.3 × [tex]10^{-4}[/tex] is 20,000 times greater than 1.15 × [tex]10^{-8}[/tex]

Step-by-step explanation:

Given as :

The first number= x = 2.3 × [tex]10^{-4}[/tex]

The second number= y = 1.15 × [tex]10^{-8}[/tex]

Let The first number is z times greater than second number

i.e x = z × y

Or, z = [tex]\dfrac{x}{y}[/tex]

Or, z = [tex]\dfrac{2.3\times 10^{-4}}{1.15\times 10^{-8}}[/tex]

Or, z = 2 × [tex]10^{4}[/tex]

∴  z = 20,000

So,The first number is 20,000 times greater than second number

Hence, 2.3 × [tex]10^{-4}[/tex] is 20,000 times greater than 1.15 × [tex]10^{-8}[/tex] . Answer

Answer:

a. true

b. false

c. true

d. false

Step-by-step explanation:

a. A product raised to a power is equivalent to each of the multiplicand raised to that power as well. Example:

  (xyz)ⁿ = xⁿyⁿzⁿ

  (1·3·7)² = 1²(3²)(7²)

b. Is wrong. When you have addition/subtraction inside a parentheses, you have to foil. Example:

  (a + b)² = (a + b)(a + b)

               = a² + 2ab + b²

  (1 + 3)² = (1 + 3)(1 + 3)

               = 1² + 2(1)(3) + 3²

               = 16

c. Numbers with the same root can be merged when you're multiplying/dividing them. Example:

  √(a)√(b) = √(ab)

  √(2)√(3) = √(2·3) = √(6)

d. You can only merge or split the root when multiplying/dividing.

You CANNOT merge the root when adding/subtracting.

  √(a ± b) ≠ √(a) + √(b),    this is NOT allowed

e. I already gave examples in the previous parts.

Answer:

[tex]g(x)=\frac{1}{4}x-3[/tex]

Step-by-step explanation:

we have

[tex]f(x)=4x+12[/tex]

Find the inverse

step 1

Let

y=f(x)

[tex]y=4x+12[/tex]

step 2

Exchange the variables  (x for y and y for x)

[tex]x=4y+12[/tex]

step 3

Isolate the variable y

we have

[tex]x=4y+12[/tex]

Subtract 12 both sides

[tex]x-12=4y[/tex]

Divide by 4 both sides

[tex]y=\frac{x-12}{4}[/tex]

simplify

[tex]y=\frac{1}{4}x-3[/tex]

step 4

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{1}{4}x-3[/tex]

we have that

[tex]g(x)=f^{-1}(x)[/tex]

therefore

[tex]g(x)=\frac{1}{4}x-3[/tex]

Yes!

This would be in-fact a linear equation!

This equation is set up in y=mx+b form, therefore we know it is a linear equation.

y=12x+2

The 12 is the mx in the equation.

And the 2 is the B in the equation! :)

That is how we solve that.

Any questions?

Have a great day!

The expression in terms of "n" for how much of the fire they will extinguish in 1 minute when both hoses are turned on together is [tex]\frac{n + 14}{7n + 49}[/tex]

Solution:

Given that,

Hose A, when turned on alone, can extinguish the fire in 7 minutes

Hose B takes "n" minutes more time than hose A

Hose takes (n + 7) minutes to extinguish the fire

STEP 1: Calculate how much work (here work is to extinguish the fire) each person does in one minute

[tex]Hose A = \frac{1}{7}th \text{ of the work }\\\\Hose B = \frac{1}{n+7}th \text{ of the work }[/tex]

STEP 2: Add up the amount of work done by each person in one minute

Work done in one minute when both are working together:

[tex]\rightarrow \frac{1}{7} + \frac{1}{n + 7}\\\\\rightarrow \frac{n + 7 + 7}{7n + 49}\\\\\rightarrow \frac{n + 14}{7n + 49}[/tex]

Therefore, the expression in terms of "n" for how much of the fire they will extinguish in 1 minute when both hoses are turned on together is:

[tex]\frac{n + 14}{7n + 49}[/tex]

The total rate in 1 minute is [tex]\frac{1}{7} + \frac{1}{7+n}[/tex].

To find the expression for how much of the fire they will extinguish in 1 minute when both Hose A and Hose B are turned on together, we need to determine their individual rates first.

Hose A can extinguish the fire in 7 minutes, so its rate is:

⇒ Rate of Hose A = 1 fire ÷ 7 minutes = [tex]\frac{1}{7}[/tex].

Hose B takes 'n' minutes more than Hose A. Therefore, it takes (7 + n) minutes to extinguish the fire, so its rate is:

⇒ Rate of Hose B = 1 fire ÷ (7 + n) minutes = [tex]\frac{1}{7+n}[/tex].

When both hoses are operating together, their combined rate is the sum of their individual rates:

⇒ Combined Rate = [tex]\frac{1}{7} + \frac{1}{7+n}[/tex]

We need the combined rate per minute:

⇒ Combined Rate per Minute = [tex]\frac{1}{7} + \frac{1}{7+n}[/tex]

This fraction represents the portion of the fire they will extinguish in 1 minute when both hoses are used together.

Answer:

No, we can't.

Step-by-step explanation:

Let x be the amount of time it takes each machine to make 1 cockpit, and y be the amount of time it takes each machine to make 1 propulsion system.

For machine A: 22 hours to produce 3 cockpits and 5 propulsion system.

For machine B: 44 hours to produce 6 cockpits and 10 propulsion system.

So, this will produce the following system of equations:

3x + 5y = 22  ⇒(1)

6x + 10y = 44  ⇒(2)

We can note that the second equation is two times the first equation.

So, the two equation are actually represent one equation.

OR, by another way the two equation have the same slope and y-intercept

So, the two equation are identical, therefore, we can't solve one equation with two variables.

Also, see the attached figure.

equation (1) with blue color and the second equation with red color.

Answer:

19/2

Step-by-step explanation:

8 3/2=19/2

Answer:

19/2

Step-by-step explanation:

Answer:

16. Disagree because 0.1 0f 0.1 is 0.01

17. the whale swam for 19 to 21.7 hours. Because 152/8=19 and 152/7=21.7

18. Meg can use 15,000 / 50 because 14,270 rounded up to by the thousand will be 15,000.

19. 61.5 because 3016/7 = 430.8   430.8/7=61.5

Step-by-step explanation:

Answer:

.85 or 85/100

Step-by-step explanation:

Answer:

0.85 is your decimal. 85 / 100 - not simplified.

17 / 20 - simplified.

Step-by-step explanation:

For the decimal, all you gotta do is move your decimal to the left 2 times.

-Hope this helps.

For the fraction, 85% is per 100, so it's 85 / 100. To simplify, the answer is 17 / 20.

Answer:

If you wanted the intersecting points there is only one and It's (12, 14)

Hope that could help.

Answer:

Dimensions of printed area

x   =  7.58     the length

y   =  31.40  cm   the height

Step-by-step explanation:

Printed region    P(a)  =  238 cm²

Let call x  and y dimensions of printed area then:

A  =  238  =  x*y       ⇒    y  = 238/x

And the area of the advertisement   is

A(a)  =  L *  W        where     L  =  x  + 6       and   W  =  y  + 5

A(x)  =  (x  +  6  ) * (  y  +  5 )

Area as a function of x                         y  =  238/ x

A(x)  =  (x  +  6  ) * ( 238/x  +  5 )

A(x)  = 238  + 5x  + 1428/x  +  30

A(x)   =  268  +   5x    + 1428/x

Taking derivatives on both sides of the equation

A´(x)   =   5  -  1428/x²

A´(x)   =  0         ⇒   5x²   =  1428       ⇒ x²   =  57.12

x  = 7.58 cm         and         y  =  238/ 7.58       y  =  31.40 cm

Answer:

46 and 47.

Step-by-step explanation:

If x is one of the integers then the other is x+1.

x + x + 1 = 93

2x = 92

x = 46.

Answer:

2 times

Step-by-step explanation:

Mai biked [tex]7\frac{1}{4} = \frac{29}{4}[/tex] miles today and Noah biked [tex]3\frac{5}{8} = \frac{29}{8}[/tex] miles  today.

We are asked how many times the length of Noah's bike ride was Mai's bike ride.

Therefore, the length of Mai's bike ride was [tex](\frac{29}{4} \div \frac{29}{8})  = 2[/tex] times the length of Noah's bike ride.  

Therefore, we will take option B will be correct. ( Answer )

Answer:

2.15

×

10

−

3

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

The answer is 2.15 * 10^-3

Step-by-step explanation:

I got this answer from Khan Academy.

Hope this helps! :)

Answer: 18%

Step-by-step explanation:

The percentage spent on book = cost of books / total cost x 100

% spent on book = 504/2800 x 100

= 18

Therefore , the percentage spent on book is 18