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8090 [49]
2 years ago
7

casey ran a 75 meter race in 10 seconds her distances at certain times during the race are shown in the table . what is the doma

in for the graph of the function that would model her race[  time in seconds 0 1 2 3 4 5 6 7 8 9 10 : distance in meters 0.0 5.5 12.0 20.0 28.5 36.0 44.0 56.5 64.0 75.0
Mathematics
1 answer:
Troyanec [42]2 years ago
7 0
The domain of the graph is everything x is allowed to equal. Parentheses are used to show that x can be everything up to, but not including that number. Brackets are used to show x can be anything up to, and including, that number. The comma between the two numbers indicates that x can be anything between those two numbers.

Here, the time goes on the x axis and the distance will go on the y axis.
Time: 0 1 2 3 4 5 6 7 8 9 10
<span>Distance: 0.0 5.5 12.0 20.0 28.5 36.0 44.0 56.5 64.0 75.0
</span>
Since we are dealing with the domain, we really only need to focus on the time.
Time: 0 1 2 3 4 5 6 7 8 9 10

From this, we see that the values go from 0 to 10. This means that x can be anything from 0 to 10. Because there are y values that correlate with the numbers 0 and 10, we know that the domain will include 0 and 10. This indicates we must use brackets. 

Knowing all of this information, we can now write our domain as:
[0, 10]
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The balanced scale represents the equation: 3x + 1 = x + 3
Afina-wow [57]

<u>Given</u>:

The given balanced scale is represented by the equation

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

We need to determine the process that balance the scale.

<u>Process to balance the scale:</u>

Given that the if one x block is subtracted from the right side and three numbered blocks are subtracted from the left side.

Thus, the equation (1) becomes

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

        3x-2=3 ----- (2)

Now, to balance the scale, let us subtract one block x from the left side and subtract three numbered blocks from the right side.

Thus, the equation (2) becomes,

(3x-2)-x=3-3

        2x-2=0 ------ (3)

Thus, the equation (3) is the same as the equation (1).

Hence, the process required to balance the scale is to subtract one x block from the left side and subtract three numbered blocks from the right side.

Therefore, Option B is the correct answer.

6 0
2 years ago
Suppose the time a child spends waiting at for the bus as a school bus stop is exponentially distributed with mean 7 minutes. De
Gala2k [10]

Answer:

The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

Step-by-step explanation:

Let the random variable <em>X</em> represent the time a child spends waiting at for the bus as a school bus stop.

The random variable <em>X</em> is exponentially distributed with mean 7 minutes.

Then the parameter of the distribution is,\lambda=\frac{1}{\mu}=\frac{1}{7}.

The probability density function of <em>X</em> is:

f_{X}(x)=\lambda\cdot e^{-\lambda x};\ x>0,\ \lambda>0

Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:

P(6\leq X\leq 9)=\int\limits^{9}_{6} {\lambda\cdot e^{-\lambda x}} \, dx

                      =\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148

Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

6 0
2 years ago
A granite block in the shape of a right rectangular prism has dimensions 30 centimeters by 40 centimeters by 50 centimeters. The
Leno4ka [110]

Answer:

The mass of the block is 168,000\ g

Step-by-step explanation:

we know that

The density is equal to the mass divided by the volume

step 1

Find the volume of the granite block

we know that

The volume of a rectangular prism (granite block) is equal to

V=LWH

substitute the values

V=(30)(40)(50)=60,000\ cm^{3}

step 2

Find the mass of the block

D=\frac{m}{V}

we have

V=60,000\ cm^{3}

D=2.8\frac{g}{cm^{3}}

substitute the values and solve for the mass

2.8=\frac{m}{60,000}

m=2.8*60,000=168,000\ g

7 0
2 years ago
Suppose the government is deciding whether to create a vaccination program to prevent a potential epidemic of Zika virus. If the
Basile [38]

Answer:

Step-by-step explanation:

4 0
2 years ago
Find the measure of each acute angle.
crimeas [40]

The 3 inside angles of a triangle need to equal 180 degrees.

This is a right triangle so the bottom left corner is 90 degrees.

This means the other two angles when added need to equal 180-90 = 90 degrees.

Now you have 8x + 7x = 90

Combine like terms:

15x = 90

Divide both sides by 15

X = 6

Now you have the value for x solve the two angles:

8x = 8(6) = 48

7x = 7(6) = 42

Top left = 48 degrees

Bottom right = 42 degrees

8 0
2 years ago
Read 2 more answers
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