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Step-by-step explanation:

Mass = Volume x density

Mass = 8.4 gm

Density = 2.4 g/cc

Substituting

       8.4 = Volume x 2.4

       Volume = 3.5 cm³

[tex]\texttt{Volume of sphere =}\frac{4}{3}\pi r^3[/tex]

We need to find radius, r

Substituting volume value

              [tex]\texttt{Volume of sphere =}\frac{4}{3}\pi r^3=3.5\\\\r^3=0.836\\\\r=0.941cm=1cm[/tex]

Radius of grape = 1 cm  

To solve the problem we must know about volume.

The radius of the sphere is whose mass is 8.2 grams and has a density of 2 grams per cubic centimeter is 1 cm.

The volume can be defined as the space occupied by the three-dimensional object.

It is given by the ratio of mass(m) and density(ρ).

[tex]\text{Volume of the object} = \dfrac{m}{\rho}[/tex]

Given to us

Mass of the object, m = 8.4 grams

Density of the object, ρ = 2 gram/cm³

As it is already mentioned that the volume is equal to the ratio of its mass to density. therefore,

[tex]\text{Volume of the object} = \dfrac{m}{\rho}\\\\\text{Volume of the object} = \dfrac{8.4}{2}\\\\\text{Volume of the object} = 4.2\ cm^3[/tex]

Thus, the volume of the object is 4.2 cm³.

To find the radius of the sphere we will use the formula of the volume of the sphere.

[tex]\text{Volume of sphere} = \dfrac{4}{3}\pi r ^3[/tex]

Substitute the values,

[tex]4.2 = \dfrac{4}{3}\pi r ^3\\\\r = 1\rm\ cm[/tex]

Hence, the radius of the sphere is whose mass is 8.2 grams and has a density of 2 grams per cubic centimeter is 1 cm.

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Answer:

200

Step-by-step explanation:

8x^2 + 80x = −5

Factor out an 8

8(x^2 + 10x) = −5

Take the coefficient of the x term, divide by 2 and then square it

10/2 = 5, 5^2=25

Remember we have the 8 outside, so we are multiplying by 8

8*25 =200

Add 200 to each side

8(x^2 + 10x + 25) = −5 + 200

Answer:

Missing number is 200.

Step-by-step explanation:

In the completing the square method we follow the following steps,

Step 1 : Move constant term to the right side,

Step 2 : Make 1 as the coefficient of [tex]x^2[/tex]

Step 3 : Add square of the half of the coefficient of x in the left side and balance the equation,

Here, the given equation,

[tex]8x^2+ 80x = -5[/tex]

[tex]8(x^2 + 10x) = -5[/tex]

∵ coefficient of x = 10,

Half of 10 = 5,

Square of 5 = 25,

Thus, we need 25 inside the bracket in left side,

For this, add 200 on both side,

[tex]8(x^2 + 10x+25) = -5+200[/tex]

Hence, missing number in the last step is 200.

The correct equation representing the situation where Nancy's mother added candies to the 16 candies already in the bag is 16 + c = 32. Subtracting 16 from both sides gives the result c = 16, which is the number of candies her mother added.

The subject of this question is mathematics and it belongs to the middle school level. Nancy began with 16 candies and ended up with 32 candies after her mother added some. Nancy wants to find out how many candies her mother added.

To solve this problem, we need to use a simple addition equation. The equation that correctly represents the situation is 16 + c = 32. This equation says that Nancy's original amount of candies (16) plus the candies her mother added (c) equals the new total amount of candies (32).

To solve for c (the number of candies her mother added), we simply subtract 16 from both sides of the equation. Therefore, c = 32 - 16, which leads to c = 16, which is the number of candies her mom put in the bag.

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Final answer:

The correct equation for Nancy's chocolate candies is 16 + c = 32, solving for c reveals that 16 candies were added. Jenny initially had 14 chocolates before eating two and giving half of the remainder to Lisa.

Explanation:

The question asks to identify the correct equation to solve for the number of chocolate candies, c, that Nancy's mom put in the bag. Nancy originally had 16 chocolate candies, and her mother added some candies to the bag, increasing the total to 32 candies. The equation that represents this situation is 16 + c = 32. This equation can help Nancy find out how many candies her mother added to the bag.

To solve for c, we need to perform a subtraction operation:

This calculation gives us the number of candies Nancy's mother added, which means c = 16 candies.

Jenny's Chocolate Question

If Jenny has some chocolates, eats two, and gives half of what is left to Lisa, resulting in Lisa having six chocolates, then we must work backward to find the initial amount. Since Lisa received half of the remainder, Jenny must have had 12 chocolates after eating two. This means Jenny started with 14 chocolates as:

The correct answer for Jenny's beginning number of chocolates is 14.

Answer:

34.4°C (rounded up to nearest tenth)

Step-by-step explanation:

Given; F = [tex]\frac{9}{5}[/tex]C + 32

94°F = [tex]\frac{9}{5}[/tex]C + 32

[tex]\frac{9}{5}[/tex]C = 94 - 32 = 62

C = [tex]\frac{62 * 5}{9}[/tex] = 34.44444444°C

And is equal to: 34.4°C (rounded up to nearest tenth)

The Celsius temperature equaling 94 degrees Fahrenheit is 34.44°C.

To find the Celsius temperature equivalent to 94 degrees Fahrenheit using the formula F = (9/5)C + 32:

Substitute 94 for F: 94 = (9/5)C + 32

Then solve for C: C = (94 - 32) / (9/5) = 34.44°C

The Celsius temperature equaling 94 degrees Fahrenheit is 34.44°C.

Answer:

negative 1

2(3x-1)>4x-6

Answer:

Step-by-step explanation:

-1

Answer:

r=reduced price

r=p-200

Step-by-step explanation:

Answer:

P = P - 200$

Step-by-step explanation:

P represents the phone's original price, and the phone's original price dropped 200$. Original price minus 200$.

Answer:

3 1/2 ; 3 19/20 ; 3 39/40

Step-by-step explanation:

Find common denominators. Change all mixed fraction to improper fractions before finding common denominators.

3 1/2  = 6/2 + 1/2 = 7/2

3 19/20 = 60/20 + 19/20 = 79/20

3 39/40 = 120/40 + 39/40 = 159/40

Find the common denominators. The smallest common denominators is 40. Remember that what you do to the denominator you do to the numerator:

3 1/2 = (7/2)(20/20) = 140/40

3 19/20 = (79/20)(2/2) = 158/40

3 39/40 = (159/40) = 159/40

Least to Greatest:

3 1/2 ; 3 19/20 ; 3 39/40

~

Answer:

f(f-1(17)) = 17

f-1(f(2)) = 2

Step-by-step explanation:

Lemma;

If f(x) and g(x) are inverses, then the compositions  f(g(x)) = g(f(x)) = x.

In both situations, we are determining the composite of inverse functions;

f and f-1

Answer:

B 65

Step-by-step explanation:

The measure of the exterior angle is equal to the sum of the opposite interior angles

130 = y+y

130 = 2y

Divide by 2

130/2 = 2y/2

65= y

Answer:

(-1/2,3/2)

Step-by-step explanation:

The rule for dilation about (0,0) by a scale factor is given as:

(x,y)----------(kx,ky)

So if (4,6) was mapped to (2,3) by dilation it means;

x=4

kx=2

k=2/4 =1/2

Hence in this case, the dilation rule is ;

(x,y)---------(1/2x ,1/2y)

For (-1,3) ---------(1/2*-1, 1/2*3)

                         (-1/2, 3/2)

Answer:

[tex](-\frac{1}{2}, \frac{3}{2})[/tex].

Step-by-step explanation:

Since, the rule of dilation about origin by the scale factor k is,

[tex](x,y)\rightarrow (kx,ky)[/tex]

Given,

The dilation maps (4, 6) to (2, 3).

Let k be the scale factor for this dilation,

⇒ 4k = 2 ⇒ k = [tex]\frac{2}{4}=\frac{1}{2}[/tex],

Thus, under the dilation rule would be,

[tex](x,y)\rightarrow (\frac{1}{2}x,\frac{1}{2}y)[/tex]

Hence, (-1,3) would be mapped to [tex](-\frac{1}{2}, \frac{3}{2})[/tex].

Answer:

-3x+11

Step-by-step explanation:

f(x) = 2x-1 + 3 =2x+2

g(x) = 5x-9

(f-g)(x)=  2x+2 - (5x-9)

Distribute the minus sign

         = 2x+2 - 5x +9

Combine like terms

        = -3x+11

Answer:

375

Step-by-step explanation:

12½[30] → 25⁄2[30]

Multiply 25 by 30 [750] then divide by 2 to get 375.

I am joyous to assist you anytime.

When evaluating the expression [tex]b^2c - 1[/tex] for b = -4 and c = 2, we calculate b squared as 16, multiply by c to get 32, and subtract 1 to obtain the answer 31.

To evaluate the expression b2c - 1 for b = -4 and c = 2, we need to follow the order of operations, often referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

First, we calculate b², which is (-4)² = 16.

Next, we multiply this result by c, which gives us 16 * 2 = 32.

Finally, we subtract 1 from this product, resulting in 32 - 1 = 31.

Therefore, the evaluated expression [tex]b^2c - 1[/tex] is 31 when b = -4 and c = 2.

Answer:

In step 1, he substituted into the volume formula incorrectly.

Step-by-step explanation:

James calculated the height of a cylinder that has a volume of 324 cubic inches.

radius = 12 inches.

The formula for volume is = [tex]\pi r^{2} h[/tex]

So, James calculated wrongly by using the wrong formula.

The step 1 is wrong.

Answer:

In step 1, he substituted into the volume formula incorrectly.

Step-by-step explanation:

Answer:

Where   is the figure????

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]h(x)=x-7,\ g(x)=x^2\\\\(g\circ h)(x)=g\bigg(h(x)\bigg)-\text{exchange x to x - 7 in}\ g(x):\\\\(g\circ h)(x)=(x-7)^2\\\\(g\circ h)(5)-\text{put x = 5 to the equation}\\\\(g\circ h)(5)=(5-7)^2[/tex]

Given the functions

(a) f(x) = x³ + 5x² + x

(b) f(x) = x² + x

(c) f(x) = -x

Function (a)

f(-x) = (-x)³ + 5(-x)² + (-x)  

      = -x³ + 5x² - x

      = -(x³ - 5x² + x)

The function is neither even nor odd.

Function (b)

f(-x) = (-x)² + (-x)

       = -(-x² + x)

The function is neither even nor odd.

Function (c)

f(-x) = -(-x)  

      = x

      = -f(x)

Because f(-x) = -f(x) the function is odd.

Answer: f(x) = -x is an odd function.

Answer:

$1,475

Step-by-step explanation:

times 100 by 14 which is 1400

but then add 75 onto that

Answer:

$1475

Step-by-step explanation:

One week costs $100.

Note that:

The $75 enrollment fee is a one-time payment.

$100 per week is the amount that is paid per week, and can change depending on the amount of week they pay for.

In this case, the child would be there for 14 weeks. Set the equation. Let x = amount of weeks, and t = total cost:

100x + 75 = t

We know that the child will be there for 14 weeks, so plug in 14 for x.

(100)(14) + 75 = t

t = (100 * 14) + 75

Simplify. Remember to follow PEMDAS. Multiply first, then add:

t = (1400) + 75

t = 1475

The total cost for 14 weeks is $1475.

~

[tex]\bf \begin{cases} f(x) = x\\ g(x) = 2x+7 \end{cases}~\hspace{7em}g(x)=11\implies \stackrel{g(x)}{11}=2x+7 \\\\\\ 4=2x\implies \cfrac{4}{2}=x\implies \implies \boxed{2=x} \\\\[-0.35em] ~\dotfill\\\\ f[90x]\implies f\left[90\left( \boxed{2} \right)\right]\implies f(180)=\stackrel{x}{180}[/tex]

Answer:

10.5

Step-by-step explanation:

b=15/tan(55 degrees)=10.5

AC=10.5

Answer:

A: The value of both expressions when w=1 is 28.

D: The two expressions are not equivalent.

Step-by-step explanation:

Given expressions are:

4(3w+4)

and

16w+12

For w=1

First Expression:

4(3w+4)

= 4[3(1)+4]

=4(3+4)

=4(7)

=28

Second expression:

16w+12

= 16(1)+12

=16+12

=28

For w=3

First Expression:

4(3w+4)

= 4[3(3)+4]

=4(9+4)

=4(13)

=52

Second expression:

16w+12

= 16(3)+12

=48+12

=60

Now looking at the statements:

A: The value of both expressions when w=1 is 28.

The statement is true because our calculated values of both expressions are 28 for w=1.

B: The two expressions are equivalent.

The two expressions are not equivalent because their values at w=3 are not same.

C: The value of both expressions when w=1 is 16.

The value of both expression when w=1 is 28 so this statement is not correct

D: The two expressions are not equivalent.

We can see by comparing the values that both expressions are not equivalent.

E: The value of both expressions when w=3 is 52.

F: The value of both expressions when w=3 is 60.

Both statements are false because both expressions have different values at w=3 ..

A. The value of both expressions when w=1 is 28. D. The two expressions are not equivalent. Statements A and D are true.

To determine if the two expressions are equivalent, we need to substitute w=1 and w=3 into both expressions. The first expression is 4(3w+4) and the second expression is 16w+12.

Step-by-step:

Based on these calculations:

Answer:

I THINK IT IS THE SECOND ANSWER

Step-by-step explanation:

Answer:

it is -413 - 33h2 +31h - 3

F is the answer I did the math

Answer:

case 1) 972 in³

case 2) 1,458 in³

Step-by-step explanation:

Remember that

1 ft=12 in

case 1)

If the dimensions of the crate are

9 in x 9 in x 1 ft

Convert to inches

9 in x 9 in x 12 in

The volume is equal to

V=9*9*12=972 in³

case 2)

If the dimensions of the crate are

9 in x 9 in x 1 1/2 ft

Convert to inches

9 in x 9 in x (12*1.5) in

9 in x 9 in x 18 in

The volume is equal to

V=9*9*18=1,458 in³

Answer:

121.5

Step-by-step explanation:

9x9x1.5=121.5

Answer:

7x^2a

Step-by-step explanation:

7x^3a+7x^2a^2

7x^3a = 7 xxxa

7x^2a^2= 7 xxaa

The common terms are 7xxa

7x^2a

This is the greatest common factor

Answer:

2pi/15

Step-by-step explanation:

The intersection of y=x and y=x^2 is (0,0) and (1,1)

Washer method

Prefered this method for this one since slices are perpendicular to axis of rotation

Integrate(Big circle - Small Circle)dx

Integrate(pi*(x)^2-pi*(x^2)^2)dx on x=0..1

Integrate(pi*x^2-pi*x^4)dx on x=0..1 is 2pi/15

Shells method

So I have to solve for x since I will be integrating with respect to y

The height of the the shell will be sqrt(y)-y

The radius will be y since that is the distance between axis of rotation in a point within the shell

Integrate(2*pi*r*h ) dy

Integrate(2*pi*(sqrt(y)-y)*y) dy on y=0..1 is 2pi/15

Answer:

Answer is in the explanation

Step-by-step explanation:

I don't know exactly word from word what your choices look like...

but I can describe per each box what happened in my own words:

First box:  They multiply first equation by 3 and the second equation by 2 to obtain the equations in that first box.

Second box: They subtracted the two equations in the first box to obtain 1x+0y=2 which means 1x=2 or x=2 (this is called solving a system by elimination

Third box: They used their first original equation (before the multiplication manipulation) and plug in the value they got for x which was 2 giving them 3(2)-2y=10

Fourth box: They simplified the equation 3(2)-2y=10 by performing the multiplication 3(2) giving them 6-2y=10

Fifth box:  They subtracted 6 on both sides giving them -2y=4

Sixth box:  They divided both sides by -2 giving them y=-2

I will summarize then what I wrote above:

1st box: Multiplication Property of Equality

2nd box: Elimination

3rd box: Substitution (plug in)

4th box: Simplifying

5th box:  Subtraction Property of Equality

6th box: Division Property of Equality

Answer:

Multiply [tex] \frac { 3 } { 4 } [/tex] by 8.

Step-by-step explanation:

We are given the following expression and we are to find its quotient:

[tex] \frac { 3 } { 4 } [/tex] ÷ [tex] \frac { 1 } { 8 } [/tex]

This can also be written as:

[tex]\frac{\frac{3}{4}}{\frac{1}{8} }[/tex]

Since the two fractions are being divided so to change this division sign into a multiplication sign, we will take the reciprocal of the fraction in the denominator and multiply 3/4 by 8.

[tex]\frac{3}{4} \times 8[/tex] = 6

For this case we must find the quotient of the following expression:

[tex]\frac {\frac {3} {4}} {\frac {1} {8}} =[/tex]

Applying double C we have:

[tex]\frac {3 * 8} {4 * 1} =\\\frac {24} {4}[/tex]

This is equivalent to the following expression:

[tex]\frac {3} {4} * 8 = \frac {24} {4}[/tex]

Answer:

Option B

Step-by-step explanation:

the demonstrated property is the commutative property

The equation a + b + 7 = 7 + b + a demonstrates the commutative property of addition, which means that the order of addition does not change the sum.

The mathematical property demonstrated by the equation a + b + 7 = 7 + b + a is the commutative property of addition. This property states that the order in which two numbers are added does not affect the sum. In other words, swapping the operands does not change the result. As shown in the equation and the principles outlined, whether you add a to b or b to a, the sum remains the same. This is true for the addition of ordinary numbers as well— you get the same result whether you add 2 + 3 or 3 + 2, for example.

Answer:

B :point 2 and point 3

Step-by-step explanation:

The only interior angles are 6, 2, 3, and 7

The angles equal to each other are 6 and 7 or 2 and 3

6 and 7 is not an option so 2 and 3 are the correct answer.