If a block has a mass of 10 g and a
volume of 5 cm3, what is the density
of the block?

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=60\\ k=50 \end{cases}\implies y=a(x-60)^2+50\qquad \textit{we also know that} \begin{cases} x=0\\ y=30 \end{cases} \\\\\\ 30=a(0-60)^2 + 50\implies -20=a(-60)^2\implies -20=3600a \\\\\\ \cfrac{-20}{3600}=a\implies -\cfrac{1}{180}=a\hspace{5em}\boxed{y=-\cfrac{1}{180}(x-60)^2+50} \\\\\\ \textit{when x = 80, what is "y"?}\qquad y=-\cfrac{1}{180}(80-60)^2+50 \\\\\\ y=-\cfrac{20^2}{180}+50\implies y=-\cfrac{20}{9}+50\implies y=\cfrac{430}{9}\implies y=47\frac{7}{9}\)

Answer: 14 gallons of gasoline.

Step-by-step explanation:

given data:

25(x + 3) = 424

where x is the number of gallon of gasoline needed to purchase.

Solution.

25(x + 3) = 424

first we open the bracket

25x + 75 = 424

collect like terms

25x = 424 – 75

25x = 349

divide both sides by 25

25x/25 = 349/25

x = 13.96

x = 14

mathew needs to get 14 gallons of gasoline.

Answer:n=−2

Step-by-step explanation:

Answer:

-9.4

Step-by-step explanation:

Answer:

the next shipment of ornaments are 16

The probability is approximately 0.4253.

To find the probability that a person talked less than 600 minutes given that the person is a man, we need to use conditional probability.

The total number of men surveyed is 37 + 14 + 17 + 19 = 87.

The number of men who talked less than 600 minutes is 37.

Therefore, the probability that a randomly selected person talked less than 600 minutes given that the person is a man is:

P(Less than 600 | Man) = Number of men who talked less than 600 minutes / Total number of men surveyed

P(Less than 600 | Man) = 37 / 87

P(Less than 600 | Man) ≈ 0.4253

Rounding to four decimal places, the probability is approximately 0.4253.

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Answer: I don't get the question? Can you please explain the question?

Answer: 0.799 is grater

Step-by-step explanation:

The letters in full are given as L, C C, C C, L, L, A, L, L, O, and M. They are identified by either reflecting them or rotating them. See below which of the elements gives the result for each.

Rotation in mathematics is defined as the act of turning an element by one or more degrees about one fixed axis or central point such that the object faces different directions each time.

According to the rules of geometry, a reflection occurs when an object is flipped into its mirror image. See the attached as an example.

Both reflections and rotation are known as transformation.

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The zeroes of the function f(x) = x (x – 8) will be 0 and 8.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The function is given below.

f(x) = x (x – 8)

The zeroes of the function f(x) is given by the factor equals to zero.

Then we have

      f(x) = 0

x(x – 8) = 0

          x = 0, 8

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Step-by-step explanation:

7x-8y = - 5     arrange to   y = mx+ b  form    m is the slope of this line

8y = 7x+5

y = 7/8 x = 5/8     <======   m, slope = 7/8  

           perpendicular slope =  - 1/m  =  - 8/7

Now use point ( -7,3)   slope (-8/7)  form:

  y-3   = - 8/7 ( x - - 7)     simplify

   y = -8/7 x  + 5          re-arrange ,   add  8/7 x to both sides of the equation

   8/7 x  + y = 5                 multiply through by 7 to get integer values

      8x + 7y =  - 35  

Answer:

let the number be x

representing the equation...

it will be....

2 times (the number- 10)=42

2 times(x-10)= 42

2(x-10)=42

what's up? to convert this into a fraction, simply multiply 12.3/1 by 10 in order to get 123/10. you can also do it by seeing .3 is in tenths, so it would be 3/10. you are left with 12 (whole number) so 12 3/10 which is also 123/10

best of luck with your studies

The correct answer is a)True  c)True The order of the cyclic group is determined by the number of elements in the group, whereas the order

a. True. If a nonempty subset H of a group G is closed under the binary operation of G, contains the identity element of G, and contains the inverse of each of its elements, then H is a subgroup of G.

c. A is true but B is false. Every cyclic group is indeed abelian, but the order of the cyclic group is not necessarily the same as the order of its generator. The order of the cyclic group is determined by the number of elements in the group, whereas the order of the generator refers to the smallest positive exponent that generates all elements of the group.

a. Zero has no inverse. In the set of real numbers under the usual multiplication operation, the element zero does not have a multiplicative inverse. Every nonzero real number has an inverse, but zero itself does not. In a group, every element should have an inverse, so the set of all real numbers under multiplication does not form a group.

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Answer:

ok but with what

Step-by-step explanation:

Answer:

i go to k12 we got the same sience class want to be pen pals? we help eachother

Step-by-step explanation:

It is correct to say that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.

Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. What is a perpendicular bisector? A perpendicular bisector is a line that intersects a line segment and forms a 90-degree angle. It divides the line segment into two equal halves.Each point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment. This means that the distance from any point on the line to one endpoint of the segment is the same as the distance to the other endpoint of the segment.

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The rate at which the shadow of the man is increasing in length is 1/5 m/s.

We can solve this problem using similar triangles. Let x be the length of the shadow, and let y be the distance between the man and the base of the lamppost. Then, we have the following equation:

(1.4 + x)/y = 1/5

Solving for x, we get:

x = (y/5) - 1.4

Differentiating both sides with respect to time t, we get:

dx/dt = (1/5) dy/dt

We are given that dy/dt = 1 m/s, so substituting that in, we get:

dx/dt = (1/5) m/s

Finally, we are asked for the rate at which the shadow length is increasing, which is just dx/dt. Thus, the rate is (1/5) m/s.

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Answer:

The dependent variable is the time taken to run 100 metres

Step-by-step explanation:

A dependent variable is simply one that is being measured or sometimes tested in an experiment.

Now, in this case, what is being determined is the time each group of participants will take to run a 100-meter race.

Thus, the dependent variable is the time each group of participants will take to run a 100-meter race.

Answer:

3

Step-by-step explanation:

17.35 * 3

Answer:

A = (q + z / 2)m

Step-by-step explanation:

9 + z / 2 . m =A

(q + z)m / 2 = A

(q + z)m/2 / m = A / m

2(q + z / 2) =  2(a / m)

Simplify Left:

q + z = 2(a / m)

Simplify right:

q + z = 2A / m

Subtract z from both sides

q = 2A / m -z

A = (q + z / 2)m

Answer:

Step-by-step explanation:

Given

Natoy's rectangular swimming pool has the length of 3m more than thrice its

width.

Width=w

Length =3w+3

So

Area of the rectangular swimming pool=length×width

216=(3w+3)×w

216=3w^2+3w

3w^2+3w-216=0

3(w^2+w-72)=0

W^2+w-72=0

W^2+(9-8)w-72=0

W^2+9w-8w-72=0

W(w+9)-8(w+9)=0

(W+9)(w-8)=0

Sotwo value of w are 8,-9

We take positive value for rectangular swimming so we take w=8m

Width=8m

Length=3×8+3

= 24+3

=27m

Answer:

Slope Calculator

Step-by-step explanation:

Search up slope calculator and put in those expressions

We cannot determine the convergence or divergence of the given series based solely on the Alternating Series Test.

To determine the convergence or divergence of the series, we can use the Alternating Series Test. The Alternating Series Test states that if a series has the form ∑[k=1 to ∞] (-1)^(k+1)*b_k, where b_k is a positive sequence that decreases as k increases, then the series converges.

In our case, the series is ∑[k=1 to ∞] 5(-1)^(k+1)*k^0.4. Here, b_k = 5k^0.4, which is a positive sequence. Now, let's check if this sequence decreases as k increases.

We observe that as k increases, k^0.4 also increases. However, since the alternating (-1)^(k+1) term changes sign with each term, the overall sequence (-1)^(k+1)*k^0.4 oscillates between positive and negative values.

Since the sequence 5k^0.4 does not strictly decrease, the conditions of the Alternating Series Test are not met. Therefore, we cannot determine the convergence or divergence of the given series based solely on the Alternating Series Test. Further analysis or tests are required to determine its convergence or divergence.

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The probability that Linda randomly selects a peanut butter cookie, eats it, and then randomly selects an oatmeal cookie is 2/43.

1. First, we need to find the total number of cookies in the bag. The bag contains:
  - 8 chocolate chip cookies
  - 5 peanut butter cookies
  - 9 sugar cookies
  - 8 oatmeal cookies

  Total cookies = 8 + 5 + 9 + 8 = 30 cookies

2. Next, we find the probability of Linda randomly selecting a peanut butter cookie:
  Probability of peanut butter = (Number of peanut butter cookies) / (Total number of cookies)
  Probability of peanut butter = 5/30

3. After eating the peanut butter cookie, there are now 29 cookies left in the bag (and 4 peanut butter cookies remaining).

4. Now, we find the probability of Linda randomly selecting an oatmeal cookie:
  Probability of oatmeal = (Number of oatmeal cookies) / (Total number of remaining cookies)
  Probability of oatmeal = 8/29

5. To find the overall probability of both events occurring, we multiply the individual probabilities:
  Probability of both events = (Probability of peanut butter) * (Probability of oatmeal)
  Probability of both events = (5/30) * (8/29)

6. Simplify the fraction:
  Probability of both events = 40/870

7. Reduce the fraction to its lowest terms:
  Probability of both events = 2/43

So the probability that Linda randomly selects a peanut butter cookie, eats it, and then randomly selects an oatmeal cookie is 2/43.

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Answer:

c = -22, 22

Step-by-step explanation:

\( {(x - 11)}^{2} = {x}^{2} - 22x + 121\)

\( {(x + 11)}^{2} = {x}^{2} + 22x + 121\)

Answer: If n>1, then any positive number raised to the power of n will always be greater than 1. Therefore, any number greater than 1 raised to the power of n, such as 2^n, 3^n, etc., will also always be greater than 1.

Step-by-step explanation:

1. The solution to the system of linear equations2x + 3y = 9 and x + 5y = 8 is (x, y) = (37/9, 1)through elimination method.

2. 3x + y= 5 and 2x-2y =-2 is x = 3, y = -6.

The elimination method is a method for solving systems of linear equations, which are set of two or more linear equations with the same variables. The goal of the elimination method is to eliminate one of the variables from the equations, so that you are left with an equation in one variable that can be easily solved.

The elimination method works by multiplying one or both of the equations by constants so that the coefficients of one of the variables are the same in both equations, and then adding or subtracting the equations to eliminate that variable. The resulting equation in one variable is then solved, and the value of the eliminated variable is found by substituting back into one of the original equations.

1. Solve the system of linear equations using the elimination method:

2x + 3y = 9

x + 5y = 8

Multiply the first equation by a constant so that the coefficients of one of the variables are the same in both equations and add or subtract the two equations to eliminate that variable:

2x + 3y = 9

x + 5y = 8

Multiply the first equation by 5:

10x + 15y = 45

x + 5y = 8

Subtract the second equation from the first:

10x + 15y = 45

x + 5y = 8

9x + 10y = 37

Solve for one of the variables in one of the equations, and then substitute that expression into the other equation:

9x + 10y = 37

x = (37 - 10y) / 9

Solve for the other variable:

x = (37 - 10y) / 9

y = (37 - 9x) / 10

Substitute the expression for x found in step 2 into the equation found in step 3:

y = (37 - 9((37 - 10y) / 9)) / 10

y = (37 - 37 + 10y) / 10

y = 10y / 10

y = y

So, the solution to the system of linear equations is (x, y) = (37/9, 1).

2. Solve the given system of equations 3x+y= 5 and 2x-2y=-2

First, multiply the first equation by 2 to make the coefficients of y equal:

6x + 2y = 10

Next, subtract the second equation from the first equation to eliminate y:

6x + 2y = 10

2x - 2y = -2

4x = 12

Finally, solve for x:

x = 3

Now that we have x, we can substitute it back into either of the original equations to find y:

3x + y = 5

3 * 3 + y = 5

y = -6

So, the solution to the system of equations is x = 3, y = -6.

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