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2 years ago

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A lab worker monitors the growth of a bacteria colony starting at 9:00 a.m. At that time, there are 100 bacteria. According to t

he exponential function f(x) = 100(4)x, the bacteria quadruple every hour. What is the value of f(0)? A) 0 B) 4 C) 100 D) 400

1 answer:

zzz [600]2 years ago

8 0

Answer:

Step-by-step explanation:

D)hope it helpef

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The U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions (BLS website, January 2014). Suppose a s

andrezito [222]

Answer:

a) Null hypothesis: $p \leq 0.113$

Alternative hypothesis: $p > 0.113$

b) $z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing we got:

$z=\frac{0.13 -0.113}{\sqrt{\frac{0.113(1-0.113)}{400}}}=1.074$

The p value for this case would be given by:

$p_v =P(z>1.074)=0.141$

c) For this case we see that the p value is higher than the significance level of 0.05 so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion workers belonged to unions is significantly higher than 11.3%

Step-by-step explanation:

Information given

n=400 represent the random sample taken

X=52 represent the workers belonged to unions

$\hat p=\frac{52}{400}=0.13$ estimated proportion of workers belonged to unions

$p_o=0.113$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic

$p_v$ represent the p value

Part a

We want to test if the true proportion of interest is higher than 0.113 so then the system of hypothesis are.:

Null hypothesis: $p \leq 0.113$

Alternative hypothesis: $p > 0.113$

Part b

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing we got:

$z=\frac{0.13 -0.113}{\sqrt{\frac{0.113(1-0.113)}{400}}}=1.074$

The p value for this case would be given by:

$p_v =P(z>1.074)=0.141$

Part c

For this case we see that the p value is higher than the significance level of 0.05 so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion workers belonged to unions is significantly higher than 11.3%

8 0

2 years ago

Which values of m and b will create a system of equations with no solution? Select two options. y = mx + b y = –2x + A system of

Nuetrik [128]

Answer:

m = -2 and b = -1/3

m = -2 and b = -2/3.

Step-by-step explanation:

y = -2x - 1/3

y = -2x - 2/3

This system has no solutions because y cannot be 2 different values at once.

5 0

2 years ago

Read 2 more answers

Which statement shows how two polynomials 4x + 6 and 2x2 − 8x demonstrate the closure property when multiplied?

steposvetlana [31]

Answer:

$8x^{3} -20x^{2} -48x$ is a polynomial

Step-by-step explanation:

Given : polynomials $4x+6$ and $2x^{2} -8x$

Solution:

$(4x+6)*(2x^{2} -8x)$

$4x(2x^{2} -8x)+6(2x^{2} -8x)$

$8x^{3} -32x^{2}+12x^{2} -48x$

$8x^{3} -20x^{2} -48x$

Polynomial :An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable.

Thus $8x^{3} -20x^{2} -48x$ is a polynomial

Hence option A is correct.

7 0

2 years ago

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In a trapezoid the lengths of bases are 11 and 18. The lengths of legs are 3 and 7. The extensions of the legs meet at some poin

FrozenT [24]

Answer: The length of segments between this point and the vertices of greater base are $7\frac{5}{7}$ and 18.

Step-by-step explanation:

Let ABCD is the trapezoid, ( shown in below diagram)

In which AB is the greater base and AB = 18 DC= 11, AD= 3 and BC = 7

Let P is the point where The extended legs meet,

So, according to the question, we have to find out : AP and BP

In Δ APB and Δ DPC,

∠ DPC ≅ ∠APB ( reflexive)

∠ PDC ≅ ∠ PAB ( By alternative interior angle theorem)

And, ∠ PCD ≅ ∠ PBA ( By alternative interior angle theorem)

Therefore, By AAA similarity postulate,

$\triangle APB\sim \triangle D PC$

Let, DP =x

⇒ $\frac{3+x}{18} = \frac{x}{11}$

⇒ 33 +11x = 18x

⇒ x = 33/7= $4\frac{5}{7}$

Thus, PD= $4\frac{5}{7}$

But, AP= PD + DA

AP= $4\frac{5}{7}+3 =7\frac{5}{7}$

Now, let PC =y,

⇒ $\frac{7+y}{18} = \frac{y}{11}$

⇒ 77 + 11y = 18y

⇒ y = 77/7 = 11

Thus, PC= 11

But, PB= PC + CB

PB= 11+7 = 18

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2 years ago

a contractor needs to purchase 500 bricks. the dimensions of each brick are 5.1 cm by 10.2 by 20.3 cm, and the density of each b

AveGali [126]

No, the trailer cannot hold the weight of the bricks. It is beyond the 900kg capacity of the trailer. The total weight of the bricks is 1,013.77 kilograms. The total weight was derived from getting the volume of the brick (0.051m x 0.102m x 0.203m), then multiplying the volume to the density of each brick (1.056 x 10^3m^3 x 1920kg/m^3). The weight of each brick is 2.03kg. Lastly, multiply the total number of bricks to the weight of each brick to get the total weight.

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2 years ago