Which function f (x) , graphed below, or g (x) , whose equation is g (x) = 3 cos 1/4 (x + x/3) + 2, has the largest maximum and what is the value of this maximum?

f(x), and the maximum is 3.

g(x), and the maximum is 5.’

f(x), and the maximum is 2.

g(x), and the maximum is 2.

To solve this problem, we can set up a system of equations to represent the given information. Solving this system of equations, we find that each small candle holder holds 2 candles and each large candle holder holds 8 candles.

To solve this problem, let's represent the number of candles each small candle holder holds as x and the number of candles each large candle holder holds as y. We can set up a system of equations to represent the given information:

We can solve this system of equations by eliminating one variable. Subtracting the equations, we get 8x = 16. Dividing both sides by 8, we find that x = 2. Substituting this value back into one of the equations, we can solve for y. Using the first equation, we have 10(2) + 4y = 52, which simplifies to 20 + 4y = 52. Subtracting 20 from both sides, we obtain 4y = 32. Dividing by 4, we find that y = 8. Therefore, each small candle holder holds 2 candles and each large candle holder holds 8 candles.

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To find out how many candles each candle holder holds, set up a system of equations using the given information and solve for the variables. Each small candle holder holds 2 candles and each large candle holder holds 8 candles.

To find out how many candles each candle holder holds, we need to set up a system of equations using the given information. Let's say the number of candles a small candle holder can hold is 's' and the number of candles a large candle holder can hold is 'l'.

From the east side, we have the equation 10s + 4l = 52. From the west side, we have the equation 2s + 4l = 36. Solving these equations, we can find the values of 's' and 'l', which will give us the number of candles each candle holder can hold.

We can eliminate 'l' by multiplying the first equation by 2 and the second equation by 5. This gives us 20s + 8l = 104 and 10s + 20l = 180. By subtracting the second equation from the first, we get 10l = 76. Dividing both sides by 10, we find that l = 7.6. Since we cannot have a fraction of a candle, we can approximate l to the nearest whole number, which is 8.

Substituting the value of l back into one of the original equations, we can find the value of s. Using the first equation, we have 10s + 4(8) = 52. Simplifying this equation gives us 10s + 32 = 52. Subtracting 32 from both sides, we find that 10s = 20. Dividing both sides by 10, we find that s = 2. Therefore, each small candle holder holds 2 candles and each large candle holder holds 8 candles.

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Answer:

A

Step-by-step explanation:

Taking the square root of both sides, you get

[tex]\sqrt{x^2} = \pm\sqrt{180}[/tex]

which simplifies to

[tex]x = \pm\sqrt{180}[/tex]

The square root of 180 is approximately 13.42 and since it is the plus or minus square root, the answer is A, -13.42, 13.42.

Final answer:

The equation x²=180 is solved by taking the square root of both sides, yielding two solutions: x = 13.42 and x = -13.42. Thus, option A is corect.

Explanation:

To solve the equation x² = 180 algebraically, we need to take the square root of both sides of the equation. This gives us two solutions, since both a positive and negative number squared will yield 180. The square root of 180 once calculated is approximately 13.42. Therefore, the two solutions are x = 13.42 and x = -13.42.

It takes 5 meters per second.

If you divide 250 by 50 you would get his average speed

The average speed of Ahmed is 5 meters per second.

Important information:

We need to find the average speed of Ahmed.

Formula for average speed is:

[tex]\text{Average Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

Using this formula, the average speed of Ahmed is:

[tex]\text{Average Speed}=\dfrac{250}{50}[/tex]

[tex]\text{Average Speed}=5[/tex]

Thus, the average speed of Ahmed is 5 meters per second.

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Answer:

The only possible groups that could be made if each group have the same number of people is 2 groups of 14 or 4 groups of 7. Since each group cannot have more than 10 people, the only group left is 4 groups of 7.

Answer:

[tex]\boxed{\text{b. \$1845 a month}}[/tex]

Step-by-step explanation:

   Amount if retired at 66 = $2460/mo

Less 25 % = 0.25 × 2460 =    -615

   Amount if retired at 62 = $1845/mo

John would receive [tex]\boxed{\text{\$1845/mo}}[/tex] if he retired at 62.

Answer:

Blank 1. Professional engineer

Blank 2. ABET( Accreditation Board for Engineering and Technology)

Answer:

Option D. [tex]x=10[/tex]

Step-by-step explanation:

step 1

Find the midpoint of the given line segment

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

we have

[tex]A(5,10),B(15,10)[/tex]

substitute the values

[tex]M=(\frac{5+15}{2},\frac{10+10}{2})[/tex]

[tex]M=(10,10)[/tex]

step 2

Find the equation of the perpendicular bisector

we know that

The equation of a perpendicular bisector is equal to the x-coordinate of the midpoint, because is a vertical line (parallel to the y-axis)

therefore

the equation is equal to

[tex]x=10[/tex]

Answer:

10

Step-by-step explanation:

Answer: The length of EF=15 cm.

Step-by-step explanation:

Answer: A: there is not enough evidence to support a relationship between lunch preference and role at school

The relationship between poll result and the student preference is: option A, not enough evidence

This due to the fact that the statistics in the question is incomplete. W do not have sufficient data that would be used for hypothesis testing.

Due to the fact above, we conclude that there is insufficient evidence to get the relationship between variables.

In conclusion, there is not enough evidence to support a relationship between lunch preference and role at school

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For this case we have that the figure shown is composed of a cylinder and a cone.

We have that the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

A: It's the radio

h: It's the height

Substituting the values:

[tex]V = \pi * (5) ^ 2 * 10\\V = \pi * 25 * 10\\V = 250 \pi \ m ^ 3[/tex]

On the other hand, the volume of a cone is given by:

[tex]V = \frac {\pi * r ^ 2 * h} {3}[/tex]

Where:

A: It's the radio

h: It's the height

Substituting the values:

[tex]V = \frac {\pi * (5) ^ 2 * 4} {3}\\V = \frac {\pi * 25 * 4} {3}\\V = \frac {100 \pi} {3} \ m ^ 3[/tex]

Then, the total volume is:

[tex]V_ {t} = 250 \pi \ m ^ 3 + \frac {100 \pi} {3} \ m ^ 3[/tex]

Taking [tex]\pi = 3.14[/tex], we have to:

[tex]V_ {t} = 889.67 \ m ^ 3[/tex]

Answer:

Option D

Answer:

Quadrant II

Step-by-step explanation:

I attached an image of the quadrants system.

You'll see that the scenario where we have a point with a negative X value and a positive Y value, it belongs to Quadrant II.

Quadrant I

Degrees: 0-90

X values: positive (+)

Y values: positive (+)

Quadrant II

Degrees: 90-180

X values: negative (-)

Y values: positive (+)

Quadrant III

Degrees: 180-270

X values: negative (-)

Y values: negative (-)

Quadrant IV

Degrees: 270-360

X values: positive (+)

Y values: negative (-)

Answer:

x = 1+12z, y = -1+10z, and z = z

Step-by-step explanation:

Step 1: Convert the system into the augmented matrix form:

• 3 -4 4 | 7  

• 1 -1 -2 | 2

• 2 -3 6 | 5

Step 2: Multiply row 2 with -2 and add it into row 3:

• 3 -4 4 | 7  

• 1 -1 -2 | 2

• 0 -1 10 | 1

Step 3: Multiply row 2 with -3 and add it into row 1:

• 0 -1 10 | 1  

• 1 -1 -2 | 2

• 0 -1 10 | 1

Step 4: Replace row 1 with row 2 and multiply the updated row 2 with -1 and add it into row 3:

• 1 -1 -2 | 2

• 0 -1 10 | 1  

• 0 0 0 | 0

Step 5: Multiply row 2 with -1 and add it in row 1:

0 1 -10 -1

• 1 0 -12 | 1

• 0 -1  10 | 1  

• 0 0  0 | 0

Step 6: It can be seen that there are infinite solutions of this system since the last row is all zeroes. It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• x - 12z = 1

• -y + 10z = 1

Step 7: Make x and y the subject of their respective equations:

• x = 1 + 12z

• y = -1 + 10z

So final answer is x = 1+12z, y = -1+10z, and z = z!!!

Answer:

D. [tex]y=\frac{7}{x}[/tex]

Step-by-step explanation:

Let y varies inversely with x.

Then we can write the variation equation:

[tex]y\propto \frac{1}{x}[/tex]

We introduce the constant of proportionality, k and obtain the inverse variation equation:

[tex]y=\frac{k}{x}[/tex]

From the given options, the only equation in this form is

[tex]y=\frac{7}{x}[/tex]

In this case, k=7 is the constant of proportionality or constant of variation.

Answer: 4

Step-by-step explanation: I Am Almost Sure The Answer Is 4. I Did The Math Out And That Is What I Got.

ABC is a right triangle, so AC has length given by

[tex]AC^2=(6\,\mathrm m)^2+(8\,\mathrm m)^2\implies AC=\sqrt{100\,\mathrm m^2}=10\,\mathrm m[/tex]

Then the circumference of circle M is [tex]10\pi\,\mathrm m[/tex].

Answer:

Step-by-step explanation:

A=BH/2

A=9x12/2

A=54

Answer: 54

Step-by-step explanation:

A = base * height ÷ 2

A = 12 * 9 ÷ 2

A = 108 ÷ 2

A = 54

Final answer:

After removing one bulb of each type, the probability of the next customer getting an amaryllins bulb is 5/16, which is 31.25%. Thus, the closest answer provided is 31%, option B.

Explanation:

The question asks for the probability of the next customer getting an amaryllins bulb after four bulbs of different types have been removed from a basket containing miscellaneous flower bulbs. Initially, there were 6 amaryllins, 7 daffodils, 4 lilies, and 3 tulips. Since one bulb of each type was bought by the previous customer, we now have 5 amaryllins, 6 daffodils, 3 lilies, and 2 tulips remaining.

To find the probability of selecting an amaryllins bulb, we divide the number of amaryllins bulbs left by the total number of bulbs remaining:

Probability of selecting an amaryllins = Number of amaryllins bulbs remaining / Total number of bulbs remaining

Probability = 5 / (5 + 6 + 3 + 2) = 5 / 16

To convert this to a percentage, we multiply it by 100: (5 / 16) * 100 = 31.25%

Therefore, the probability is closest to 31%, which corresponds to option B.

Answer:

7

Step-by-step explanation:

In similar triangles, corresponding elements are proportional. Then we get,

(2x + 1)/(x-1) = 10/4

4(2x +1)       = 10(x-1)

8x + 4         = 10x - 10

8x               = 10x - 14

2x               = 14

x                 = 7

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Answer:

7

both sides are corresponding so triangleABC AB=AC.

Answer:

Final answer is approx [tex]\cos\left(H\right)=0.4235[/tex].

Step-by-step explanation:

using given information from the attached picture, we need to find the value of cos(H) so let's apply the formula of cosine.

[tex]\cos\left(\theta\right)=\frac{adjacent}{hypotenuse}[/tex]

[tex]\cos\left(H\right)=\frac{GH}{FH}[/tex]

[tex]\cos\left(H\right)=\frac{36}{85}[/tex]

[tex]\cos\left(H\right)=0.423529411765[/tex]

Hence final answer is approx [tex]\cos\left(H\right)=0.4235[/tex].

Using the cosine ratio, the value of cos H to 4 decimal places is: A. 0.4235.

Cosine ratio is expressed as, cos ∅ = adjacent/hypotenuse of a right triangle.

Given:

Therefore:

Cos H = 36/85

Cos H = 0.4235

Therefore, using the cosine ratio, the value of cos H to 4 decimal places is: A. 0.4235.

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Answer:

option C is correct

Step-by-step explanation:

We need to find the determinant.

= -1(7*9 - 3*9)-( -3)(4*9 - 3*3) -2(4*9 -7*3)

= -1(63-27) +3 (36 - 9) -2( 36- 21)

= -1(36)+3(27)-2(15)

= -36+81-30

= 15

Option C is correct

Question :- Eight less then seven times a number is the same as for l four more than three times a number. Find the number.

Answer :-

Let the number be x

Therefore,

[tex]=> 8-7x = 4+3x[/tex]

[tex]=> 8-4 = 3x+7x[/tex]

[tex]=> 4 = 10[/tex]

[tex]=> X = 5/4[/tex]

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There was 23.29 inches used on a headband for each player.

And 8.54 inches used on a wristband for each player.

To find out how much fabric for headbands and would beused for each player/person you would do

[tex]total \: fabric \: used \: \div \: total \: amount \: of \: people[/tex]

So, if you substitute the values in it is

[tex]791.86÷34=23.29 \: inches \: for \: 1 \: headband. \: [/tex]

And finally, to find how much fabric is used on a wristband for each player/person you would use the same formula.

[tex]273.28 \: \div 32 = 8.54 \: inches[/tex]

To find (ƒ + g)(x) for the given functions ƒ(x) = 5x² + 4 and g(x) = 6x² - x, we add the like terms to get

(ƒ + g)(x) = 11x² - x + 4.

To find (ƒ + g)(x) where ƒ(x) = 5x²  + 4, and g(x) = 6x²  – x, we simply add the two functions together. We combine like terms to calculate the sum.

By adding the corresponding terms:

Combining these, we get

(ƒ + g)(x) = f(x) + g(x)

(f + g)(x) = 11x² - x + 4.

Answer:

Option A. [tex]30\ pounds[/tex]

Step-by-step explanation:

step 1

Find the volume of the sphere ( medicine ball)

The volume is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter

Convert inches to feet

Remember that

1 ft=12 in

[tex]r=5\ in=5/12\ ft[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(5/12)^{3}[/tex]

[tex]V=0.3029\ ft^{3}[/tex]

step 2

Find the weight of the ball

Multiply the volume in cubic foot by 100

[tex]0.3029*100=30.29\ pounds[/tex]

Round to the nearest pound

[tex]30.29=30\ pounds[/tex]

The medicine ball would be A. 30 pounds

Since the medicine ball is a sphere, its volume is

V = πd³/6 where d = diameter of medicine ball = 10 in = 10 in × 1 ft/12 in = 0.8333 ft

So, substituting the value of the variable into the equation, we have

V = πd³/6

V = π(0.8333 ft)³/6

V = π(0.5787 ft³)/6

V = 1.818 ft³/6

V = 0.303 ft³

The mass of the medicine ball = mass of sand per cubic foot × volume of medicine ball

where

So,

mass of the medicine ball = 100 lb/ft³ × 0.303 ft³

= 30.3 lb

≅ 30 pounds

So, the medicine ball would be A. 30 pounds

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Answer:

A) - 39,991

Step-by-step explanation:

Sum of geometric sequence formula is

[tex]S = a(\frac{1 -r^n}{1-r} )\\a=-1, r=6/(-1)=-6, n=7\\\\S = -1(\frac{1 -(-6)^7}{1-(-6)} )= -\frac{279937}{7} = -39991[/tex]

Answer:

The correct answer option is A) -39,991.

Step-by-step explanation:

We know that the sum of the geometric sequence is given by the formula:

[tex] S _ n = \frac { a _ 1 ( 1 - r ^ n ) } { 1 - r } [/tex]

where [tex]a_1[/tex] is the first term, [tex]r[/tex] is the common ratio and [tex]n[/tex] is the number of terms.

Here,

[tex]a_1 = -1[/tex]

[tex]r = -6[/tex]

[tex]n=7[/tex]

Substituting these values in the above formula to get:

[tex] S _ 7 = \frac { -1 ( 1 - (-6) ^ 7 ) } { 1 - (-6) } [/tex]

S_n = -39,991

Answer:

C.1/6

Step-by-step explanation:

Initially the box has four $1 and six $5 bills. The probability of selecting a $5 bill in the first trial would be given as;

(number of $5 bills) / (total number of bills)

= (6)/(4+6) = 3/5

If in the first attempt we actually pick a $5 bill, the number of $5 bills will reduce by one to 5. Now, the probability of picking a $5 bill in the second attempt will be given as;

(new number of $5 bills) / (new total number of bills)

= (5)/(4+5) = 5/9

The new number of $5 bills will now be; 6 - 2 = 4 since we have already picked 2 without replacing them.

Now, the probability of picking a $5 bill in the third attempt will be given as;

(new number of $5 bills) / (new total number of bills)

= (4)/(4+4) = 1/2

Since the three attempts are independent, the probability of picking  all three $5 bills is;

3/5 * 5/9 * 1/2 = 1/6

The probability of drawing three $5 bills from a box containing four $1 bills and six $5 bills, when the bills are drawn without replacement, is 1/6.

The question is asking for the probability of drawing three $5 bills from a box containing four $1 bills and six $5 bills, given that the bills are drawn without replacement. This is a problem of combinatorial probability. We first find the total ways of selecting three bills from the box, then find the ways of selecting three $5 bills.

The total ways of selecting three bills is given by combination formula C(n, r) = n! / (r!(n-r)!), where n is the total number of bills and r is the number selected. In this case, n=10 (4 $1 bills and 6 $5 bills) and r=3. So, C(10,3) = 120.

The ways of selecting three $5 bills is C(6,3) = 20,

So the probability of drawing three $5 bills is 20/120 = 1/6.

Therefore, the correct answer is C. 1/6.

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Answer:

28

Step-by-step explanation:

7*4

Answer:

28

Step-by-step explanation:

7*4

Answer:

A = 48x + 24 (square units)

Step-by-step explanation:

L = 6x + 3

W = 8

A = L * W

A = 8(6x + 3)

A = 48x + 24

Answer:

e = 8x + 0.1y

Step-by-step explanation:

If Gustavo makes no sales at all, he still gets $8 per hour worked (x).  We can model this part with this equation:

e = 8x

But then, if he sells something, he makes extra money.. He makes 10% (0.1) of every sale (y).  So the equation becomes:

e = 8x + 0.1y

or you can express it this way:

e = 8x + y/10

which is the same thing just written differently.