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2 years ago

4

Lili has saved $2,500 money from her part time job at a bakery. Since she will not need this money for a few years, she decides

to put the money in a 3-year CD (Certificate of Deposit) at a local credit union. The credit union offers Lili 2.75% APR, compounded quarterly. How much will Lili's CD be worth at the end of the 3 years?

1 answer:

alukav5142 [94]2 years ago

5 0

Answer:

Lili's CD be worth at the end of 3 years is $2714.23

Step-by-step explanation:

Lili deposit $2500 at the Annual percent rate 2.75% and for 3 years compounded quarterly.

Let's use formula

A = p $(1+\frac{r}{n} )^{n*t}$

From the given information

p=2500

r =0.0275

t=3

n=4

Plug in these values into the formula

A=2500 $(1+\frac{0.0275}{4})^{4*3}$

Simplify the right side of the equation,

A=$2714.23

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Answer:

5 feet

Step-by-step explanation:

The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation,

$y=-0.4x^2+3x$

where y is the height above water and x is the horizontal distance in feet.

If a beam of light is shone upward at an angle modeled by the equation

$x+y=10$

A beam of light hit the dolphin.

So, line must be intersect path of dolphin.

Using substation method,

Substitute y=10-x into dolphin equation.

$10-x=-0.4x^2+3x$

$-0.4x^2+4x-10=0$

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$x=5\text{ feet }$

$y=5\text{ feet }$

Hence, The beam hit dolphin at 5 feet.

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2 years ago

What is the common ratio between successive terms in the sequence 1.5, 1.2, 0.96, 0.768

Pani-rosa [81]

Answer:

To determine the common ratio of a geometric sequence. You just need to divide any two consecutive terms on it. You can see below that all of them have the same quotient.

1.2 / 1.5 = 0.8

0.96 / 1.2 = 0.8

0.768 / 0.96 = 0.8

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Decimal form = 0.8

Fraction form = 4/5

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Check:

1.5 x 0.8 = 1.2

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2 years ago

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%

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Answer:

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This is a right triangle shown in the picture.

To solve for $x$ , we can use trigonometry.

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The ratio that relates opposite and hypotenuse is sine.

<em>We know that,</em>

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<em>Thus we can write:</em>

$sin(35)=\frac{250}{x}$

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Second answer choice is right: 435.9 ft

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