What is the median for the data set? 15, 17, 8, 23, 14 <br>15 38.5 8 15.4

Solve the equation for x, where x is a real number (5 points): <br> -2x^2 + 5x + 2 = -3

Juli2301 [7.4K]

Add 3 to both sides so that the equation becomes -2x^2 + 5x + 5 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
                              x = [ -b ± √(b^2 - 4ac) ] / (2a)
                              x = [ -5 ± √(5^2 - 4(-2)(5)) ] / ( 2(-2) )
                              x = [-5 ± √(25 - (-40) ) ] / ( -4 )
                              x = [-5 ± √(65) ] / ( -4)
                              x = [-5 ± sqrt(65) ] / ( -4 )
                              x = 5/4 ± -sqrt(65)/4
The answers are 5/4 + sqrt(65)/4 and 5/4 - sqrt(65)/4..

5 0

3 years ago

$3.00 is ____ % of $1.80

natta225 [31]

1.666666666666667%

3.00/1.80

1.666666666666667 as a fraction is 5/3

8 0

3 years ago

Daniela invested a total of $50,000, some in a certificate of deposit (CD) and the remainder in bonds. The amount invested in bo

LekaFEV [45]

Answer:

The amount invested in bonds = 35,000

The amount invested in CD = 15,000.

Step-by-step explanation:

The total amount that Daniela invested is $50,000, this means if we call the amount invested in bonds $b$ , and the amount invested in CD $d$ , then we have:

$b+d=50,000$ this says the total amount Daniela invested is $50,000.

And since the amount invested in bonds $b$ is $5,000 more than twice the amount Daniela put into the CD, we have:

$b=5,000+2d$ .

Thus, we have two equations and two unknowns $b$ and $d$ :

(1). $b+d=50,000$

(2). $b=5,000+2d$ ,

and we solve this system by substituting $b$ from the second equation into the first:

$b+d=50,000\\5,000+2d+d=50,000\\3d=45,000\\\\\boxed{d=15,000}$

or, the amount invested in CD is $15,000.

With the value of $d$ in hand, we now solve for $b$ from equation(2):

$b=5,000+2d\\b=5000+2(15,000)\\\boxed{b=35,000}$

or, the amount invested in bonds is $35,000.

4 0

3 years ago

Read 2 more answers

If Store B sells 12 bottles for $3.50... What is the price for 1 bottle at Store B?

Lena [83]

Answer:

0.29 cents a bottle at store B

Step-by-step explanation:

devide the price by the amount of products. called the unit price

4 0

3 years ago

We're testing the hypothesis that the average boy walks at 18 months of age (H0: p = 18). We assume that the ages at which boys

marusya05 [52]

Answer:

II. This finding is significant for a two-tailed test at .01.

III. This finding is significant for a one-tailed test at .01.

d. II and III only

Step-by-step explanation:

1) Data given and notation

$\bar X=19.2$ represent the battery life sample mean

$\sigma=2.5$ represent the population standard deviation

$n=25$ sample size

$\mu_o =18$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean battery life is equal to 18 or not for parta I and II:

Null hypothesis: $\mu = 18$

Alternative hypothesis: $\mu \neq 18$

And for part III we have a one tailed test with the following hypothesis:

Null hypothesis: $\mu \leq 18$

Alternative hypothesis: $\mu > 18$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{19.2-18}{\frac{2.5}{\sqrt{25}}}=2.4$