10. Explain why log328 is between 3 and 4.

Answer:

Determinant = -12

Step-by-step explanation:

rewrite the system as

-2 =  2x - 3y  + 0z

0 =  0x +  y - 2z

1 =  -3x + 2y   - z

then the coefficient matrix is

{  [2,  -3,   0]

  [0,   1,    -2]

  [-3,  2,   -1]  }

to find determinant

{  [2,  -3,   0]    ,   2,    -3

  [0,   1,    -2]   ,    0,     1

  [-3,  2,   -1]  },     -3,     2

determinant  =   2*1*-1  +  (-3 * -2 * -3)  +   (0*0*2)  -  0  -  (2*-2*2)  - 0

determinant = -2  - 18  + 0  - 0 + 8 =   -12

The area of the cake that is frosted is 464 in²

What is the area of the cake that is frosted?

Bottom cake = 10 inches

Top cake = 6 inches

The lateral area of the bottom cube is 4 faces, each of which is a 10-inch square.

Lateral area = 4 × s²

= 4 × (10 in)²

= 400 in²

Top cube

The top area is the difference in area between a 10-inch square and a 6-inch square;

= (10 in)² - (6 in)²

= (100 -36) in²

= 64 in²

Therefore,

Area of the cake frosted = the sum of the lateral area and the top frosted area.

Area of the cake frosted = 400 in² +64 in²

= 464 in²

Answer:

45

Step-by-step explanation:

Taking into account the definition of equation and percentage, 30 percent of 120 is the same as 80 percent of 45.

An equation is defined as an established equality between two expressions, in which there may be one or more unknowns or variables.

So solving an equation consists of finding the value or values ​​of the variables so that they fulfill the equality represented in the equation. That is, when changing the variable for the solution found, the equality must be true.

On the other side, the percentage is a value that represents the proportionality between two established quantities. That is, the percentage tells what part of a total represents a quantity.

Mathematically, the percentage is the division between an initial quantity and the total quantity, all multiplied by one hundred.

And to calculate the percentage of a quantity, the quantity is multiplied by the percentage and divided by 100. Then, 30 percent of 120 can be expressed as: (30×120)÷100

On the other hand, 80 percent of a number can be expressed as: (80×number)÷100

Since 30 percent of 120 must be the same as 80 percent of an unknown number, the following equation can be expressed:

(30×120)÷100= (80×number)÷100

Solving:

3600 ÷100= (80×number)÷100

36= (80×number)÷100

36×100= 80×number

3600= 80× number

3600÷ 80= number

45= number

The, 30 percent of 120 is the same as 80 percent of 45.

Learn more about percentage with this examples:

Answer:

1. D & F

2. A, C, D

Step-by-step explanation:

DID ON EDGE

None of the given graphs are identical. Their differences arise from the distinct characteristics of their specific square root or cube root functions, as well as the range of x-values they apply to.

None of the aforementioned graphs are identical. The syntax y=√x corresponds to the graph of the square root function, which is always positive and only defined for x≥0. On the other hand, the syntax y=-√x describes the graph that's a reflection of y=√x in the x-axis. However, y=∛x and y=-∛x both entail the cube root function, which is distinguishable from the square root function by its shape and the fact it includes values for negative x. Lastly, y=√-x and y=∛-x are not properly defined real functions, since taking square or cube roots of negative x values leads to complex numbers.

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Answer: 54

Step-by-step explanation:

Answer:

The teacher will have to give out 54 pencils

Step-by-step explanation:

there 9 children in the class. each student gets 6 pencils.

9 times 6 = 54

Answer:

Therefore it will take 28 years.

Step-by-step explanation:

To find the years, we use the following formula,

[tex]A=P(1+r)^n[/tex]

A= Total balance after n years

P= Initial amount.

r= Rate of interest per year.

n = Time in years.

Given that, Josh's grandparents put $3,000 into a college saving account when he was born. The account earn 6% interest per years.

Here A=$15,000,P=$3,000, r=6%=0.06 ,n=?

[tex]\therefore 15,000=3,000(1+0.06)^n[/tex]

[tex]\Rightarrow (1.06)^n=\frac{15,000}{3,000}[/tex]

[tex]\Rightarrow (1.06)^n=5[/tex]

Taking ln both sides

[tex]\Rightarrow ln(1.06)^n=ln(5)[/tex]

[tex]\Rightarrow n=\frac{ln(5)}{ln(1.06)}[/tex]

[tex]\Rightarrow n\approx 28[/tex]

Therefore it will take 28 years.

Marian and Robin, by combining their efforts, can weed a garden together in approximately 1 hour and 43 minutes by adding their individual work rates and calculating the time taken to complete one whole task at this combined rate.

The question involves discovering the collective work rate of Marian and Robin when weeding a garden. To solve, we first identify the individual rates: Marian can weed a garden in 3 hours, which means her rate is 1/3 of the garden per hour. Robin's rate is 1/4 of the garden per hour, as he can complete it in 4 hours. To find the rate at which they can weed the garden together, we add their individual rates: (1/3) + (1/4) = 4/12 + 3/12 = 7/12.

Thus, their combined rate is 7/12 of the garden per hour. To find the total time taken, we divide the whole task (1 garden) by their collective rate (7/12). Hence, the time taken for them to complete the weeding together is 12/7 hours, which can be simplified to approximately 1 hour and 43 minutes.

Answer:

Kidnappers

Step-by-step explanation:

Answer:

kidnappers

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

1/4 divided by 2

Final answer:

Each friend received 1/8 of the original pie after equally sharing 1/4 that was left over.

Explanation:

Marge and Kimo equally shared 1/4 of a pie that was left over. To determine the fraction of the original pie that each friend got, we divide that 1/4 by two, since there are two people sharing it. So, each friend received 1/8 of the original pie.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

edg

Answer:

4

Step-by-step explanation:

i just got it right

Answer:

1 1/4

Step-by-step explanation:

For the strawberries, we will have to multiply 3 by 1/4 to get the total amount of strawberries used.

1/4 * 3 = 3/4

For the blueberries, we will have to multiply 2 by 1/4 to get the total amount of blueberries used.

1/4 * 2 = 2/4

Simplify that to get 1/2

Now we need to add 3/4 and 1/2

3/4 + 1/2 = 5/4

Simplify that and we get our answer;

1 1/4

The known acute angle of the triangle is 46 degrees, so the unknown acute angle of that triangle is 90-46 = 44 degrees. In other words, the two acute angles of any right triangle must add to 90, so 46+44 = 90.

The 44 degree angle is adjacent to angle ADC, and it adds to angle ADC to form 180 degrees.

If x is the measure of angle ADC, then

44+(angleADC) = 180

44+x = 180

x = 180-44

x = 136

angle ADC = 136 degrees

For any parallelogram, the opposite angles are always congruent. Therefore, angle ABC is equal to angle ADC = 136, making ABC = 136 as well.

Answer: C. 136 degrees

Step-by-step explanation:

From the diagram, angle C is a right angle because it is formed by a perpendicular line. It means that

Angle BCD + 46 = 90

angle BCD = 90 - 45 = 44 degrees

The opposite angles in a parallelogram are equal while the adjacent angles are supplementary. Angle ABC and angle BCD are supplementary and the sum of supplementary angles is 180 degrees. Therefore,

Angle ABC + 44 = 180

Angle ABC = 180 - 44

Angle ABC = 136 degrees

Answer:

9x8=72 and 25+2=27

Step-by-step explanation:

1x9=9

2x9=18

3x9=27

4x9=36

5x9=45

6x9=54

7x9=63

8x9=72

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To simplify the expression, first rewrite the fractions:[tex]\( \frac{2y}{y - 3} \) and \( \frac{2(y - 3)}{y + 3} \)[/tex]. Then, divide the first fraction by the reciprocal of the second, yielding[tex]\( \frac{2y}{y - 3} \).[/tex]

let's simplify the expression:

[tex]\[ \frac{\frac{2y}{y - 3}}{\frac{4y - 12}{2y + 6}} \][/tex]

First, we'll simplify the fractions within the larger fractions:

[tex]\[ \frac{2y}{y - 3} = \frac{2y}{y - 3} \times \frac{(y - 3)}{(y - 3)} = \frac{2y(y - 3)}{(y - 3)^2} = \frac{2y^2 - 6y}{y^2 - 6y + 9} \][/tex]

[tex]\[ \frac{4y - 12}{2y + 6} = \frac{4(y - 3)}{2(y + 3)} = \frac{2(y - 3)}{y + 3} \][/tex]

Now, we'll divide the first fraction by the second fraction. This is equivalent to multiplying by the reciprocal:

[tex]\[ \frac{\frac{2y^2 - 6y}{y^2 - 6y + 9}}{\frac{2(y - 3)}{y + 3}} = \frac{2y^2 - 6y}{y^2 - 6y + 9} \times \frac{y + 3}{2(y - 3)} \][/tex]

Now, let's cancel out common factors:

[tex]\[ = \frac{2y(y + 3)}{(y - 3)(y + 3)} \times \frac{y + 3}{2(y - 3)} \][/tex]

[tex]\[ = \frac{2y}{y - 3} \][/tex]

So, the simplified expression is [tex]\( \frac{2y}{y - 3} \).[/tex]

Answer:

We use Simultaneous Equation to express the problem

From the equation, a bag of popcorn will cost $5

Step-by-step explanation:

We can represent drink with d and bad of popcorn with p

If Tristan spent $38.75 on 5 drinks and 2 bags of popcorn, the we can interpret it as

5d + 2p = 38.75 ....................... eqn 1

And if Noah spent $37.25 on 3 drinks and 4 bags of popcorn, we can interpret it also as

3d + 4p = 37.25 ........................ eqn 2

This is now a Simultaneous Equation

Since we are to state the price of a bag of popcorn, then we can use the elimination method to eliminate d and solve for p

To do this, Multiply eqn 1 by 3 and eqn 2 by 5

(5d + 2p = 38.75)*3

(3d + 4p = 37.25)*5

The we will have

15d + 6p = 116.25 .......................... eqn 3

15d + 20p = 186.25 ...................... eqn 4

If we subtract eqn 3 from eqn 4, we will have

14p = 70

Divide both sides by 14 to get the value of p, and we will have

p = 70/14

p = 5

Therefore a bag of popcorn equals to $5

Answer:

SAS

Step-by-step explanation:

The sides have the same ratio and the angle between them is congruent, so it's SAS

Answer:

The answer to your question is Volume = 80000 cm³

Step-by-step explanation:

Data

height = 50 cm

radius = 20 cm

Process

1.- The smallest dimensions of the prism must have the same dimensions that the cylinder.

Radius = 20 cm then the length of a side = 2 x radius = 40 cm

2.- Calculate the area of the base

     Area = 40 x 40

              = 1600 cm²

3.- Calculate the volume of the prism

    Volume = Area x height

                  = 1600 x 50

                  = 80000 cm²

Answer:

V = [tex]\frac{15}{2x}[/tex]

Step-by-step explanation:

Using the volume formula

V = [tex]\frac{12}{x}[/tex] × [tex]\frac{x+4}{4}[/tex] × [tex]\frac{5}{2x+8}[/tex] ← cancel 12 and 4 by 4 and factor 2x + 8

   = [tex]\frac{3}{x}[/tex] × [tex]\frac{x+4}{1}[/tex] × [tex]\frac{5}{2(x+4)}[/tex] ← cancel (x + 4) on numerator/denominator

  = [tex]\frac{3}{x}[/tex] × 1 × [tex]\frac{5}{2}[/tex]

  = [tex]\frac{15}{2x}[/tex]

Answer:

55 and 7.5 for number 3

Step-by-step explanation:

The zeros of the function f(x) = (x + 4)(x – 7) are x = -4 and x = 7. These values are where the function intersects the x-axis and can be expressed as points (-4, 0) and (7, 0) on a graph.

To find the zeros of the function f(x) = (x + 4)(x – 7), we need to determine the values of x that make f(x) equal to zero. This means each factor in the product must be set equal to zero and solved for x individually.

Setting the first factor equal to zero gives us x + 4 = 0, which simplifies to x = -4.

Similarly, setting the second factor equal to zero gives us x – 7 = 0, which simplifies to x = 7. Thus, the zeros of the function are x = -4 and x = 7.

These can be written as the ordered pairs (-4,0) and (7,0) when we consider them as points on the Cartesian plane where the function intersects te x-axis.

The correct choice from the options provided would be -4 and 7, which corresponds to the first option.

It is not necessary to provide the y-coordinates when identifying the zeros of a function, as by definition, they are points where the y-value is zero.

Final answer:

John's new balance after 6 years with an original investment of $18,000 at a 4.5% annual compound interest rate will be approximately $23,362.65.

Explanation:

To calculate John's new balance after 6 years with a principal investment of $18,000 at an annual compound interest rate of 4.5%, we use the formula for compound interest:

A = P[tex](1+r/n)^{(nt)}[/tex]

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time the money is invested for, in years.

In this case, P = $18,000, r = 0.045 (4.5%), n = 1 (since it's compounded annually), and t = 6 years.

Now we plug the values into the formula:

A = 18000(1 + 0.045/1)⁶

A = 18000(1 + 0.045)⁶

A = 18000(1.045)⁶

Calculating this, we get:

A ≈ 18000(1.297925)

A ≈ $23,362.65

Therefore, after 6 years, John will have approximately $23,362.65 in his account.

Answer:

The width of the framing material is 3 inches

Step-by-step explanation:

we know that

The area of the frame and photograph combined is given by the expression

[tex]156=(7+2x)(6+2x)[/tex]

solve for x

Expanded the expression

[tex]156=42+14x+12x+4x^2\\4x^2+26x+42-156=0[/tex]

[tex]4x^2+26x-114=0[/tex]

solve the quadratic equation by graphing

using a graphing tool

The solution is x=3 in

see the attached figure

therefore

The width of the framing material is 3 inches

The width of the framing material is [tex]\( x = 3 \)[/tex] inches

Given:

- Length of the photograph = 7 inches

- Width of the photograph = 6 inches

- Width of framing material = x inches

- Area of frame and photograph combined = 156 square inches

The total length of the framed photograph would be [tex]\( 7 + 2x \)[/tex] inches, and the total width would be [tex]\( 6 + 2x \)[/tex] inches.

So, the area of the framed photograph is the product of its total length and total width:

[tex]\[ \text{Area of framed photograph} = (7 + 2x)(6 + 2x) \][/tex]

Given that the area of the framed photograph is 156 square inches, we set up the equation:

[tex]\[ (7 + 2x)(6 + 2x) = 156 \][/tex]

Expanding and simplifying:

[tex]\[ 42 + 14x + 12x + 4x^2 = 156 \][/tex]

[tex]\[ 4x^2 + 26x + 42 = 156 \][/tex]

[tex]\[ 4x^2 + 26x - 114 = 0 \][/tex]

Now, let's solve this quadratic equation for x . We can simplify it by dividing all terms by 2:

[tex]\[ 2x^2 + 13x - 57 = 0 \][/tex]

Using the quadratic formula:

[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

Where:

- a = 2

- b = 13

- c = -57

Plugging in the values:

[tex]\[ x = \frac{{-13 \pm \sqrt{{13^2 - 4(2)(-57)}}}}{{2(2)}} \][/tex]

[tex]\[ x = \frac{{-13 \pm \sqrt{{625}}}}{{4}} \][/tex]

[tex]\[ x = \frac{{-13 \pm 25}}{{4}} \][/tex]

So, we have two possible solutions for x:

[tex]\[ x_1 = \frac{{-13 + 25}}{{4}} = 3 \][/tex]

[tex]\[ x_2 = \frac{{-13 - 25}}{{4}} = -9 \][/tex]

Since the width of the framing material cannot be negative, we discard [tex]\( x_2 \).[/tex]

Therefore, the width of the framing material is [tex]\( x = 3 \)[/tex] inches.

Answer:

The answer is A

Step-by-step explanation:

Answer: 144

Step-by-step explanation: To find a value of c that would make this a perfect square, take -24 and divide it by 2 to get -12. Next, simply square -12 to get 144.

x^2 - 24x + 144 can be factored into (x - 12)(x - 12)

Answer:

144 is the correct answer

Answer:

$50

Step-by-step explanation:

Let's write an equation to solve:

We can represent the profit as "p"

In that case, we have:

(p - 25) = 35

Adding 25:

p = 25.

If you charge 50, you will get 25 dollars back.

If you charge 10, you will get no profit.

Thus, the answer is $50.

Answer:

3 1/2 pounds or 3.5 pounds

Step-by-step explanation:

Two ingredients are measured in pounds while one is measured in ounces.  Recall that 1 pound = 16 ounces.  Thus, 12 ounces of cocoanut comes out to

(12/16) pound.  Next, we sum up 1 1/2 pounds of flour, 12/16 pound of cocoanut and 1 1/4 pounds of sugar, after rewriting these mixed numbers with the same denominator (4):

1 1/2 pounds       stays 1 2/4 pounds;

12 ounces becomes       3/4 pound; and

1 1/4 pounds stays        1 1/4 pounds

Summing up the fractions results in 6/4 pounds, or 1 1/2 pounds; and summing up the integers results in 2 pounds.

The final sum is 1 1/2 pounds + 2 pounds, or 3 1/2 pounds.

Dwayne buys 3 1/2 pounds of ingredients.

Alternatively, we could convert all of these measurements to decimal fractions and then add up those fractions:

1.5 pounds + 0.75 pounds + 1.25 pounds = 3.5 pounds (same as before).

Given:

The given triangle is a right angled triangle.

One of the angle is 64° and the length of one of the leg is x.

The length of the hypotenuse is 28.

We need to determine the value of x.

Value of x:

The value of x can be determined using the trigonometric ratio.

Thus, we have;

[tex]cos \ \theta=\frac{adj}{hyp}[/tex]

where [tex]\theta= 64[/tex], adj = x and hyp = 28

Substituting the values, we get;

[tex]cos\ 64=\frac{x}{28}[/tex]

Multiplying both sides by 28, we have;

[tex]cos \ 64 \times 28=x[/tex]

 [tex]0.438\times 28=x[/tex]

       [tex]12.264=x[/tex]

Rounding off to the nearest hundredth, we get;

[tex]12.26=x[/tex]

Therefore, the value of x is 12.26

U means "Union" or all the numbers from one set and all the numbers from the other set combined.  So your answer is any of the numbers included in one set or the other or both.

Final answer:

By using the ratio of 4:5 for the amounts that Jamie and her sister save, we calculate that since Jamie has $20, her sister has $25 in her account.

Explanation:

To find out how much money Jamie's sister has in her account, we need to first understand the ratio of the amounts they save. For every four dollars that Jamie saves, her sister saves five dollars. This gives us a ratio of 4:5.

Since Jamie has $20 in her account, we can determine how many times four dollars fits into twenty dollars to find out how many 'units' of savings Jamie has made. We do this by dividing 20 by 4, which equals 5. So, Jamie has saved 5 units of 4 dollars each.

Knowing that each unit for Jamie's sister is $5, we calculate the total amount for her sister by multiplying 5 units with the sister's $5, which equals $25. Therefore, Jamie's sister has $25 in her account.

Final answer:

For every $4 Jamie saves, her sister saves $5. Jamie has $20, which is equal to 5 units of $4. Therefore, Jamie's sister has saved 5 units of $5, which amounts to $25.

Explanation:

The question asks how much money Jamie's sister would have in her account, given that Jamie has $20 and for every four dollars that Jamie saves, her sister saves five dollars. To find the amount Jamie's sister has saved, we use the ratio of their savings. Since Jamie has $20 and saves $4 for every $5 her sister saves, we can calculate the amount Jamie's sister has saved using the following steps:

First, determine how many 'four dollar' units Jamie has saved. She has saved $20, so that's $20/$4 = 5 units.

Since Jamie's sister saves $5 for each of these units, we multiply the number of units by $5 to find her savings, which is 5 units * $5/unit = $25.

Therefore, Jamie's sister has $25 in her account.

Answer:

Step-by-step explanation:

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 3

θ = π/6

2π = 360 degrees

π = 360/2 = 180

Therefore,

θ = 180/6 = 30 degrees

Therefore,

Length of arc = 30/360 × 2 × 3.14 × 3

Length of arc = 1.6 to the nearest tenth

Final answer:

To find the length of the intercepted arc on a circle with radius 3 and a central angle of π/6, calculate using the formula s = rθ. The result is approximately 1.6 units after rounding to the nearest tenth.

Explanation:

The question asks to find the length of the intercepted arc given a central angle of measure θ=π/6 on a circle with radius r = 3 and to round the answer to the nearest tenth. To calculate the arc length (θ), we use the formula s = rθ, where θ is measured in radians. Given θ=π/6 and r=3, the arc length s is therefore 3*(π/6)= π/2. To get a numerical answer, substitute π with approximately 3.14159, resulting in s = (3*3.14159)/6 which simplifies to s ≈ 1.57. Rounding to the nearest tenth gives us an arc length of 1.6 units.