Evaluate 5x3 - 21 + 7 when x = -2.

Answer:

Bionic Woman wins by 4 seconds.

Step-by-step explanation:

Given:

Speed of Batman = 3 km/min

Speed of Bionic woman = 5 km/min

Total distance = 2 km

Start given to Batman = 12 seconds

To find:

Winner of the race and by how many seconds?

Solution:

Start given to Batman = 12 second start

Let us find the Distance traveled by Batman in 12 second.

12 seconds = [tex]\frac{1}{5}[/tex] minutes

[tex]Distance = Speed \times Time[/tex]

[tex]Distance = 3 \times \frac{1}{5} = 0.6\ km[/tex]

Hence, distance left for batman to be traveled = 2 - 0.6 = 1.4 km

Time taken by Batman = [tex]\frac{1.4}{3} \times 60[/tex] seconds = 28 seconds

Distance for Bionic woman to be traveled = 2 km with 5 km/min

Time taken by Bionic Woman = [tex]\frac{2}{5}[/tex] minutes = 24 seconds

Bionic woman is taking lesser time, So the winner of the race will be Bionic woman.

She will win by 28-24 = 4 seconds

So, answer is:

Bionic Woman wins by 4 seconds.

Answer:

2√3

Step-by-step explanation:

5√3 - √27

= 5√3 - √9√3

= 5√3 - 3√3

=2√3

Answer:

The probability that more than half of these babies are female is closest to 0.53.

Step-by-step explanation:

We are given that at a certain hospital, the probability of a child being born female is 0.5. 80 babies are born on a certain day.

Let X = Number of babies that are female

The above situation can be represented through binomial distribution which means X ~ Binom(n = 80, p = 0.51)

Here, n = number of samples taken and p = probability of success

For finding the probability we will use the normal approximation because the sample size is greater than 30 (n > 30), i.e;

Mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex]

                    = 80 [tex]\times[/tex] 0.51 = 40.8

Standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p\times (1-p)}[/tex]

                                         = [tex]\sqrt{80 \times 0.51 \times (1-0.51)}[/tex]  = 4.5

So, X ~ Normal([tex]\mu=40.8, \sigma^{2} = 4.5^{2}[/tex])

Now, the probability that more than half of these babies are female is given by = P(X > 40) = P(X > 40.5)  {using continuity correction}

      P(X > 40.5) = P( [tex]\frac{X-\mu}{{\sigma}} }[/tex] > [tex]\frac{40.5-40.8}{{4.5} } }[/tex] ) = P(Z > -0.07) = P(Z < 0.07)

                                                          = 0.5279 ≈ 0.53

The above probability is calculated by looking at the value of x = 0.07 in the z table which has an area of 0.5279.

Hence, the probability that more than half of these babies are female is closest to 0.53.

Answer:

yes

Step-by-step explanation:

|-12| = |12| they always equal to 12

Answer:

true

Step-by-step explanation:

when you put the 2 lines on the left and right side of a (negative) number, it instantly becomes a positive

Answer:

  M = (-1, 0) on the x-axis

Step-by-step explanation:

You know the midpoint is the average of the coordinates of the end points:

  M = (S +T)/2

  M = ((-4, -3) +(0, 3))/2 = (-4+0, -3+3)/2 = (-2, 0)/2

  M = (-1, 0)

The midpoint is (-1, 0). It lies on the x-axis because the y-coordinate is 0.

3x - 2 = 4

Move the -2 to the other side of the equals sign to make it 4 + 2, it is now a positive because when you moved it to the other side of the equals sign the negative always changes to a positive.

Now;

3x = 4 + 2

3x = 6, divide each side by 3.

x = 2.

Answer:

y = -1/2x + 5/2 or y = -0.5x + 2.5

Step-by-step explanation:

perpendicular lines have reciprocated slopes (opposite signs and values)

y = 2x + 1 → y = (-1/2x) + b

plug in (3,1) to find b

1 = -1/2(3) + b

1 = -1.5 + b

2.5 = b

y = -1/2x + 5/2 or y = -0.5x + 2.5

Answer:

y = -1/2 x +5/2

Step-by-step explanation:

y = 2x+1 is in slope intercept form ( y = mx+b) where 2 is the slope

We want a line perpendicular

Perpendicular lines have slopes that multiply to -1

m * 2 = -1

Divide by 2

m = -1/2

The slope of the perpendicular line is -1/2

y = mx+b

y = -1/2x +b

Using the point (3,1)

1 = -1/2 *3 +b

1 = -3/2 +b

Add 3/2 to each side

2/2 +3/2 = b

5/2 = b

y = -1/2 x +5/2

Answer:

15

Step-by-step explanation:

3x+4x+8=5x+10

7x+8=5x+10

7x-5x=10-8

2x=2

x=1

AC=5x+10=5(1)+10=15

Answer:

Area of the field = 384

Step-by-step explanation:

Given:

diagonal  = d = 32 m

perpendiculars dropped on it from the remaining opposite vertices:

h1 = 10 m

h2 = 14 m

Sum of perpendiculars:

h1 + h2 = 10  + 14

           = 24

Area of the field = 1/2 x d x (h1 + h2)

                           = 0.5(32)(24)

Area of the field = 384 m²

Answer:

250 cm³

Step-by-step explanation:

The volume of a box will always be the value of multiplying its 3 dimensions. Since the dimensions of this box are 5, 5, and 10, the volume is:

[tex]5\cdot5\cdot10=250[/tex] cm³.

Hope this helped!

Answer:

250 cm^3

Step-by-step explanation:5x5x10

Answer: x = 2, x = 3 ( whichever is m and whichever is n )

Step-by-step explanation: h

x^2 + 6x - 5 = 0

( x - 2 ) ( x - 3 ) you take the x^2 and you split it into separate groups

the negatives will give you a positive 6, but also a negative 5. you want to use multiples of 6 to add up to -5. so you do ( x - 2 ) and ( x - 3 ) and it doesn't matter what order you do the numbers!! both are negative trying to add up to a negative.

then you want to get x.

x - 2 = 0

add two to the 0 and x = 2

then the other x

x - 3 = 0

add the three to the 0 and x = 3

Answer:

x=-3+[tex]\sqrt{x} 14[/tex]

Step-by-step explanation:

I got it right on plato

Answer:

So the ratio of shirts before the purchase to the total number of shirts after the purchase is 1:3

Step-by-step explanation:

In this question we have to find the ratio of before and after so It will be written like this

Before : After

11: 33

Dividing both sides with 11

11/11:33/11

1: 3

So the ratio of shirts before the purchase to the total number of shirts after the purchase is 1:3

Which means that if we have total of 4 shirts then the number of shirts before the purchase were 1 and after the purchase were 4 meaning there are 3  new shirts in place for every single old shirt.

Answer:

The fraction is [tex]\frac{7}{9}[/tex].

Step-by-step explanation:

The division problem provided is:

7 ÷ 9

The fraction representing the division problem is:

[tex]7\div 9=\frac{7}{9}[/tex]

As the denominator is greater than the numerator the fraction cannot be converted into a mixed fraction.

Thus, the fraction is [tex]\frac{7}{9}[/tex].

Answer:

7/9

Step-by-step explanation:

The division problem is as follows:

7 ÷ 9

The fraction that represents the difficulty of division is:

7 ÷ 9=7/9

The fraction cannot be converted to a mixed fraction since the denominator is bigger than the numerator.

As a result, the fraction is 7/9.

Answer:

Step-by-step explanation:

-1 appears once

0 appears once

3 appears twice

4 appears once

1 appears once

Answer: -1

Step-by-step explanation: -1

occurs the most.

Answer:

Step-by-step explanation:

I am not sure if this is correct but I hope it helps

Answer:

36

Step-by-step explanation:

[tex](x {}^{2} - 6)(x {}^{2} - 6)[/tex]

then we get,

[tex]x {}^{2} - 12x + 36[/tex]

Answer:

You need 10 of those numbers to be whole numbers, decimals, or fractions (THESE ARE RATIONAL)

You need the other 10 of those numbers to radicals, or numbers similar to pi (THESE ARE IRRATIONAL)

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

I took the test.

Answer:

answer of question 28 is 8/13(D)

Answer:

8

Step-by-step explanation:

2x + 6y = 4

Since, graph passes through (x, - 2)

Therefore, plug y = - 2 in the above equation.

2x + 6*(-2) = 4

2x - 12 = 4

2x = 12 + 4

2x = 16

x = 16/2

x = 8

Answer:

Dr Carter

Step-by-step explanation:

I would want to visit Dr. Carter for an orthodontis appointment for multiple reasons. One, he can prove that he doesn’t do his work sloppily as his office is clean, and two, he can prove that his treatments work. since his teeth are now perfectly straight, that shows that his Braces really work, whereas Dr. Shuman’s treatments either don’t work or take a lot longer for results to appear.

I got 60 as my answer

you ALWAYS do your parentheses first

then you do 8+5 and that equals 13•6-9

13 times 6 is 78. then you subtract 9 which will leave you with 60. hope that helped ☺️

Answer:

h = -9

Step-by-step explanation:

Distribute the 2 to the parentheses:

5h + 2(11 - h) = -5

5h + 22 - 2h = -5

Add like terms:

3h + 22 = -5

3h = -27

h = -9

Answer:

h = -4.5

Step-by-step explanation:

5h + 2(11-h) = -5

5h + 2(11-h)

+h          +h

6h + 2 x 11 = -5

6h + 22 = -5

    - 22     -22

6h = -27

/6     /6

h = -4.5

I hope this helps, I know the explanation is kinda confusing but I tried my best to explain :))

Answer:

1/7

Step-by-step explanation:

In order to determine the slope, we must find the change in y over the change in x:

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } = \frac{8-6}{10--4}[/tex] = 2/14= 1/7.

Therefore, the slope between these two points is 1/7.

Answer:

1/7

Step-by-step explanation:

To find the slope when given two points, use the slope formula. The slope formula is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let (-4,6) be x₁ and y₁ and let (10,8) be x₂ and y₂:

[tex]m=\frac{(8)-(6)}{(10)-(-4)} =2/14=1/7[/tex]

Therefore, the slope of the line passing through the two points is 1/7.

Answer:  price of total notebooks = p(a+b+c) or pa+pb+pc= price of total notebooks

Step-by-step explanation:

you have to add all the number of notebooks or a b and c and then multiply it by the price of each notebook. there are multiple ways to do this but those are the ways I could think of.

 if a=2, b=3 and c=6 then you have to add 2+3+6 to equal 11 then multiply 11 by the price of each notebook, say p=$4.50  your equation would be 4.50*11 which is $49.50, and that would be the total of all the notebooks. these numbers metaphorical of course, but hope that puts it into perspective.

Answer:

No.

Step-by-step explanation:

There are two different ways to do this - solve for x in the given equation or substitute the value for x and see if you get a true statement.

3x + 7 = 13 subtract 7 from both sides

3x = 6 divide by 3 on both sides

x = 2

3(3) + 7 = 13

9 + 7 = 13

16 ≠ 13

Therefore, x = 3 is not a solution for 3x + 7 = 13.

Answer:

a = -10

Step-by-step explanation:

6a+40=2a

Subtract 6a from each side

6a-6a+40=2a-6a

40 = -4a

Divide each side by -4

40/-4 = -4a/-4

-10 = a

Answer: y<1x-2

Step-by-step explanation:

Find some coordinates on the line to write a slope intercept form equation for the line and turn it into inequality.

First we need to find the slope and the y-intercept. The y intercept is when x is 0 and as we can see it  already indicates that the y intercept is -2 .

(0,-2)

(2,0)   Use these points o the find the slope.

0- 2 = -2

-2 -0 = -2

-2/-2 = 1   The slope is one so the equation will be y = 1x - 2   But since this is not an inequality we have to change the equal to sign to an inequality sign.

Looking at the line, it is a dashed line so the inequality sign will be > or <  

The painted side of the graph represents the solutions of the graph  and that is all underneath the graph so the inequality will be   y < 1x-2