Find the volume of this composite solid.

A. addition:

[tex]3x^{2}  + 2x - 6\\2x^{2}  - 2x + 10\\------\\5x^{2} + 4[/tex]

B. subtraction:

[tex]3x^{2} + 2x - 6\\2x^{2} - 2x + 10\\-------\\x^{2} + 4x - 16[/tex]

Answer:

1. 5x²+4         2.-x²-4x+16

Step-by-step explanation:

The question is on operations in quadratic equations

1. Addition

P=3x²+2x-6

Q= 2x²-2x+10

P+Q= 3x²+2x-6 +2x²-2x+10

Collect like terms

3x²+2x²+2x-2x-6+10

5x²+4

2.Subtraction

Q-P

(2x²-2x+10) -(3x²+2x-6)

open brackets

2x²-2x+10-3x²-2x+6

collect like terms

2x²-3x²-2x-2x+10+6

-x²-4x+16

-x²+4x+16

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

Answer:

There are 7 milliliters of water in each of the first 7 beakers

Step-by-step explanation:

* At first lets read the problem

- There are 86 milliliters of water to pour into tiny beakers

- Jerry has 8 tiny beakers

- He pours same amount in seven of them

- He pours 16 milliliters in the 8th one

- we want to know how many milliliters in each of the 7 beakers

* Look to the attached drawing

- There are 8 shapes represent the tiny beakers

- Seven of them have same amount x

- The last one has amount 16 milliliters

- All of them have 86 milliliters

* Now lets write the steps to answer the problem

∵ The amount of water is 86 milliliters

∵ The 8th tiny beaker has 16 milliliters

∴ The amount of water in the 7 beakers = 86 - 16 = 70 milliliters

∵ Each one of the 7 beakers has x milliliters of water

∴ 7 × (x) = 70 ⇒ divide each side by 7

∴ x = 7 milliliters

* There are 7 milliliters of water in each of the first 7 beakers

Each of the first 7 beakers contains 10 milliliters of water.

1. First, we identify the total amount of water Jerry poured, which is 86 milliliters.

 2. We know that the eighth beaker contains 16 milliliters of water.

3. To find out how much water was poured into the first 7 beakers, we subtract the amount in the eighth beaker from the total amount:

[tex]\[ \text{Water in first 7 beakers} = \text{Total water} - \text{Water in 8th beaker} \] \[ \text{Water in first 7 beakers} = 86 \text{ ml} - 16 \text{ ml} \] \[ \text{Water in first 7 beakers} = 70 \text{ ml} \][/tex]

4. Now, we divide the total water in the first 7 beakers by 7 to find out how much water is in each beaker:

[tex]\[ \text{Water per beaker} = \frac{\text{Water in first 7 beakers}}{\text{Number of beakers}} \] \[ \text{Water per beaker} = \frac{70 \text{ ml}}{7} \] \[ \text{Water per beaker} = 10 \text{ ml} \][/tex]

Therefore, each of the first 7 beakers contains 10 milliliters of water.

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

Hope it helps and if it does, please mark me brainliest...

Answer:

7

both sides are corresponding so triangleABC AB=AC.

Answer:

5040

Step-by-step explanation:

at least thats what it is on GP

Answer:

The symbol ∩ signifies the intersection of the left operand and the right operand. Here, it means "and", as it often does.

Step-by-step explanation:

The solution to the left inequality is x < -1.

The solution to the right inequality is x > -3.

The intersection symbol (∩) means you are interested in the interval where these solutions overlap—the intersection of the solutions: -3 < x < -1; (-3, -1) in interval notation.

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:

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:

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 = 48x + 24 (square units)

Step-by-step explanation:

L = 6x + 3

W = 8

A = L * W

A = 8(6x + 3)

A = 48x + 24

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.

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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I believe the answer is c. I hope that’s right! Good luck!

The parametric equation is : [tex]\frac{x-13}{4}[/tex]

The correct option is (a).

In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

Given parametric equation:

x= 4t+1 and y=t-3

From, y=t-3

         t= y+3

put t in x= 4t+1

x= 4(y+3) +1

x= 4y +12+1

x= 4y  + 13

x-13=4y

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

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Answer:

623168

Step-by-step explanation:

749x832=623168

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

Transformations are important subjects in geometry. In this exercise, these are the correct transformation rules:

Consider the point [tex](x,y)[/tex], if you reflect this point across the x-axis you should multiply the y-coordinate by -1, so you get:

[tex]\boxed{(x,y)\rightarrow(x,-y)}[/tex]

Consider the point [tex](x,y)[/tex], if you reflect this point across the y-axis you should multiply the x-coordinate by -1, so you get:

[tex]\boxed{(x,y)\rightarrow(-x,y)}[/tex]

Consider the point [tex](x,y)[/tex]. To rotate this point by 90° around the origin in counterclockwise direction, you can always swap the x- and y-coordinates and then multiply the new x-coordinate by -1. In a mathematical language this is as follows:

[tex]\boxed{(x,y)\rightarrow(-y,x)}[/tex]

Consider the point [tex](x,y)[/tex]. To rotate this point by 180° around the origin, you can flip the sign of both the x- and y-coordinates. In a mathematical language this is as follows:

[tex]\boxed{(x,y)\rightarrow(-x,-y)}[/tex]

Rotate a point 270° counter-clockwise about origin is the same as rotating the point 90° in clock-wise direction. So the rule is:

[tex]\boxed{(x,y)\rightarrow(y,-x)}[/tex]

Answer:Transformations are important subjects in geometry. In this exercise, these are the correct transformation rules:

Step-by-step explanation:

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.

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]

Hope it helps!

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: The length of EF=15 cm.

Step-by-step explanation:

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:

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:

Blank 1. Professional engineer

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

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: option a

Step-by-step explanation:

The volume of a cylinder can be calculated with this formula:

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

Where the radius is "r" and the height is "h"

Calculate the volume of the Cylinder A:

[tex]V_A=\pi (1m)^2(4m)\\\\V_A=4\pi\ m^3[/tex]

Calculate the volume of the Cylinder B:

[tex]V_B=\pi (1m)^2(8m)\\\\V_B=8\pi\ m^3[/tex]

Now, the ratio of the volume of the Cylinder A to the volume of the Cylinder B can be calculated with:

[tex]ratio=\frac{V_A}{V_B}[/tex]

Substituting values, you get:

[tex]ratio=\frac{4\pi\ m^3}{8\pi\ m^3}[/tex]

[tex]ratio=\frac{1}{2}[/tex] or 1:2

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]

Seems like it would be

[tex]\displaystyle\int_5^9x^4\,\mathrm dx[/tex]

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.