if you dig a 6 foot hole, how deep is that hole?

Answer:

- 14

Step-by-step explanation:

[tex]f(x) = - 5 {x}^{2} - 4x + 19 \\ plug \: x = - 3 \\ f( - 3) = - 5 {( - 3)}^{2} - 4( - 3) + 19 \\ f( - 3) = - 5 \times 9 + 12 + 19 \\ f( - 3) = - 45 + 31 \\ f( - 3) = -14[/tex]

Answer:

first term (a) = 54

Second term (b) = 18

common ratio = b/a = 18/54 = 1/3

Answer:

the first and second car seats are appropriate for a 33 lb. child. The first seat suits children up to 34 lb. The second seat suits children that weight between 16 to 40 lb.

The only seat that is not appropriate would be the third one that is too large, since children between 34 to 90 lb. should use it.

seat 1 ≤ 34 lb ⇒ simple inequality

16 lb < seat 2 and seat 2 < 40 lb ⇒ compound inequality

34 lb < seat 3 and seat 3 ≤ 90 lb ⇒ compound inequality

Answer:

The mean exam scores in the second section is greater than the mean exam scores in the first section

Step-by-step explanation:

Here, we are interested in making a conclusion.

Mathematically;

z-score = (score - mean)/SD

so basically, what determines the sign of the z-score is dependent entirely on the mean.

If the mean is larger than the score, we will have a negative z-score. If the mean is smaller than the score, then will have a positive z-score

So basically what drives the sign is the mean value since the scores are the same for both students in this case, irrespective of the standard deviation in both classes.

So, for the first girl with a positive z-score, we can conclude that her score is larger than the mean; while for the second girl with a negative z-score, her score is smaller to the mean.

Thus, what we conclude here is that the mean score of the second section with the professor is greater than the mean score of the first section with the professor.

Answer:

Step-by-step explanation:

y - 8 = 6(x + 2)

y - 8 = 6x + 12

y = 6x + 20

Answer:

6^-2 =0.02777777777

Step-by-step explanation:

Divide 30 by 25% to find the full amount:

30/0.25 = 120

Now multiply the full amount by 40%:

120 x 0.40 = 30

Answer:

La lancha y el bote se encontrarán a 70 metros de distancia del puente.

Step-by-step explanation:

Sea el punto debajo del puente el punto de referencia y que ambas lanchas se desplazan a velocidad a continuación, las ecuaciones cinemáticas para cada embarcación son presentadas a continuación:

Bote a 7 metros por segundo

[tex]x_{A} = x_{o}+v_{A}\cdot t[/tex] (Ec. 1)

Lancha a 10 metros por segundo

[tex]x_{B} = x_{o}+v_{B}\cdot (t-3\,s)[/tex] (Ec. 2)

Donde:

[tex]x_{o}[/tex] - Posición debajo del puente, medido en metros.

[tex]x_{A}[/tex], [tex]x_{B}[/tex] - Posición final de cada embarcación, medido en metros.

[tex]v_{A}[/tex], [tex]v_{B}[/tex] - Velocidad de cada embarcación, medida en metros por segundo.

[tex]t[/tex] - Tiempo, medido en segundos.

Para determinar la posición en la que ambas embarcaciones se encuentran, se debe determinar el instante en que ocurre a partir de la siguiente condición: [tex]x_{A} = x_{B}[/tex]

Igualando (Ec. 1) y (Ec. 2) se tiene que:

[tex]v_{A}\cdot t = v_{B}\cdot (t-3\,s)[/tex]

Ahora despejamos el tiempo:

[tex]3\cdot v_{B} = (v_{B}-v_{A})\cdot t[/tex]

[tex]t = \frac{3\cdot v_{B}}{v_{B}-v_{A}}[/tex]

Si sabemos que [tex]v_{B} = 10\,\frac{m}{s}[/tex] y [tex]v_{A} = 7\,\frac{m}{s}[/tex], entonces:

[tex]t = \frac{3\cdot \left(10\,\frac{m}{s} \right)}{10\,\frac{m}{s}-7\,\frac{m}{s}}[/tex]

[tex]t = 10\,s[/tex]

Ahora, la posición de encuentro es: ([tex]x_{o} = 0\,m[/tex], [tex]v_{A} = 7\,\frac{m}{s}[/tex] y [tex]t = 10\,s[/tex])

[tex]x_{A} = 0\,m + \left(7\,\frac{m}{s} \right)\cdot (10\,s)[/tex]

[tex]x_{A} = 70\,m[/tex]

La lancha y el bote se encontrarán a 70 metros de distancia del puente.

Answer:

min = (4, -136) ; max = (-2,80)

Step-by-step explanation:

The option is B

The (-2, 80) is a relative minimum, (4, -136) relative maximum option (C) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The cubic function:

f(x) = 2x³ - 6x² - 48x + 24

Find f'(x):

f'(x) = 6x² - 12x - 48

Equate f'(x) to zero:

6x² - 12x - 48 = 0

Find the roots of the quadratic equation:

x = -2

x = 4

Find f''(x):

f''(x) = 12x - 12

Plug x = -2

f''(-2) = -24 - 12 = -36 < 0

At x = -2 f(x) is minimum

f(-2) = 80

Plug x = 4

f''(4) = 48 - 12 = 36 > 0

At x = 4 f(x) is maximum

f(4) = -136

Thus, the (-2, 80) is a relative minimum, and (4, -136) relative maximum option (C) is correct.

Learn more about the function here:

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Answer: 0.08192

Step-by-step explanation:

Given: Probability of free throws = 0.80

Then, probability of missing the free throw = 1-0.80=0.20

Now, According to the negative binomial probability distribution, the probability that the rth success is achieved in xth trial is given by ;-

[tex]P(X=x)= pC_{r-1}^{x-1}p^{r-1}(1-p)^{(x-r}[/tex]

Put p = 0.20 , x=5 and r =1, we get

The probability of this player missing a free throw for the first time on the fifth attempt as [tex](0.20)\ ^{5-1}C_{1-1}(0.20)^{1-1}(1-0.20)^{5-1}[/tex]

[tex]= (0.20)\ ^{4}C_{0}(0.20)^{0}(0.80)^{4}\\\\=(0.20)(1)(0.80)^4\\\\=(0.20)(0.4096)\\\\=0.08192[/tex]

hence the required probability =0.08192

Answer:0.08912

Step-by-step explanation:

Answer:

x=16

Step-by-step explanation:

I hope this helps you

Answer:

34

Step-by-step explanation:

1. if to guess the Caleb's age is 'x' years and Linda's age is 'y' years now, then

2. according to the 'sum of the ages of Caleb and Linda is 55 years' it may be written: x+y=55 - the first equation of the system;

3. according  to the condition '8 years ago, Caleb's age was 2 times Linda's age' it may be written: (x-8)(y-8)=2 - the second equation of the system;

4. if to make up the system of two equation and calculate the values of 'x' and 'y':

5. if x=34, then Caleb is 34 old now.

Answer:

Step-by-step explanation:

the answer is .25 because i got it right and it makes alot of sense

23.67 X 2.03 = 48.0501

Hope this helps! :)

Answer:

48.0501

Step-by-step explanation:

The terminal point on the unit circle determined by π radians is (-1, 0).

To find the terminal point on the unit circle determined by π radians, we can use the properties of the unit circle.

The unit circle is a circle with a radius of 1 unit centered at the origin (0, 0) in a coordinate plane. The point on the unit circle determined by an angle θ is given by (cosθ, sinθ).

Since we want to find the terminal point determined by π radians, we can substitute π into the formulas for cosine and sine:

x = cos(π) = -1

y = sin(π) = 0

The terminal point on the unit circle determined by π radians is (-1, 0).

It's important to note that on the unit circle, π radians corresponds to half of the circumference of the circle. In other words, it represents a point on the circle that is diametrically opposite to the point (1, 0) which corresponds to 0 radians.

By understanding the relationship between angles and their corresponding points on the unit circle, we can easily determine the coordinates of terminal points for various angles.

For more such questions on terminal point on the unit circle

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Answer:

The box plot

Step-by-step explanation:

Answer:

No, they are not equivalent.

Step-by-step explanation:

2^5 means 2 to the 5th power, so we multiply it by itself 5 times.

2x2x2x2x2=32

Same as 5^2

5x5=25

32>25

There is your answer, no.

Answer:

Step-by-step

i) a² - 2ab + b² = (a + b)²

a² = p² ;     a  = p

b² = 16 = 4²  ;        b = 4

2ab = 2*p*4 = 8p

p² - 8p + 16 = (p - 4)²

ii) a² + 2ab + b² = (a +b)²

a² = 121x² = (11x)²                 ;  b² = 4y² = (2y)²

2ab = 2 * 11x * 2y = 44xy

121x² + 44xy + 4y² = (11x + 2y)²

Answer:

i think it is b .

Step-by-step explanation:

Answer:

1            2                  3             4            5       6

2 ÷ 15   1 ÷ 6           1 ÷ 6        1 ÷ 6     1 ÷ 6    1 ÷ 5

Step-by-step explanation:

As it is mentioned in the question that the probability of faces like 2,3,4,5 are not affected so in this case

P(2) = P(3) = P(4) = P(5) = 1 ÷ 6

And,  P(6) = 0.2

As we know that

P(1) + P(2) +P(3) +P(4) +P(5) +P(6) = 1

This results P(1) = 2 ÷ 15

So,

1            2                  3             4            5       6

2 ÷ 15   1 ÷ 6           1 ÷ 6        1 ÷ 6     1 ÷ 6    1 ÷ 5

Hence, the correct option is 2nd

Answer:

C≈31.42

r Radius 5

Answer:

Step-by-step explanation:

Perimeter = Circumference

Step 1. Know and recognize what you have

C = pi*d

pi = 3.142

d = 10

Step 2. Solve for the circumference of whole circle

C = 3.142*10

C = 31.42

Step 3. Solve for the questions answer

C of semicircle = 31.42/2

Hope this helped,

Kavitha

To get the percent, divide 27 by 150 then multiply the quotient by 100.

(27 / 150) * 100 = 18%

Answer:

2.8

Step-by-step explanation:

2.8*10=28

Also, when you multiply 2.8 by 10, you can just move the decimal to the right once, giving you 28.

Dear student,

I request you to make you question more clear.

thank you,

________ ___________________________________

Answer:

  4,152,842.53301 cm³ ≈ 4.1528 m³

Step-by-step explanation:

The volume of a rectilinear room of those dimensions will be the product of those dimensions:

  (144.78 cm)(198.12 cm)(144.78 cm) = 4,152,842.53301 cm³

A more appropriate unit for such a volume is cubic meters. There are a million cubic centimeters in a cubic meter, so the volume (to 5 significant digits) is ...

  4.1528 m³

_____

We assume that any oxygen is uniformly distributed in the space, so the volume of oxygen will be the same as the volume of the room.

_____

Additional comment

These dimensions correspond to those of a room that is 57 inches square and 78 inches high.