The unknown angles are in a ratio of 7 to 13.

Let 7x represent the smaller measure.Then, 13x represents the larger measure.
7x + 13x + 140 = 180
20x + 140 = 180
20x = 40
x = 2

7x = 7 * 2 = 14

13x = 13 * 2 = 26

The measures are 14 degree and 26 degrees.

4 0

3 years ago

A store has a sale with 10% off every item. When you enter the store, you receive a coupon that states that you receive an addit

sweet [91]

Step-by-step explanation:

Step one:

We are told that the store offers off 10% of sales, this means that the store is offsetting the price down by 10% hence a price reduction.

Moreso, a coupon is a voucher entitling the holder to a discount off a particular product. the coupon is 40%, hence this is equal to a discount, that is price reduction by 40%.

Step two:

Say the price of an item is $100, a coupon if 40% will entitle the holder to only pay $60, that is

=40/100*100

=0.4*100

=$40 off

= 100-40

=$60

The total percent of reduction 10+40= 50%

This is equal to a discount on the sales price

7 0

3 years ago

A cognitive psychologist wants to know whether memory performance is changed by old age. She randomly selects 7 elderly individu

defon

Answer:

$z = \frac{418.7-465.6}{\frac{53.6}{\sqrt{7}}}= -2.340$

Now we can calculate the p value with the following probability

$p_v =2*P(z$

If we use the commonly significance level of 0.05 we see that the p value is lower than these values we can conclude that the true mean is different from the value of 465.6 at 5% of significance

Step-by-step explanation:

Data provided

$\bar X=418.7$ represent the mean score on the standardized memory test

$\sigma=53.6$ represent the population standard deviation

$n=7$ sample size

$\mu_o =465.6$ represent the value that we want to verify

z would represent the statistic

$p_v$ represent the p value

System of hypothesis

We are interested to check if the memory performance for elderly individuals differs from that of the general population (mean different from 465.6), the system of hypothesis are then:

Null hypothesis: $\mu = 465.6$

Alternative hypothesis: $\mu \neq 465.6$

Since we know the population deviation we can use the z statistic from the z test for the true mean:

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

Replacing the info given we got:

$z = \frac{418.7-465.6}{\frac{53.6}{\sqrt{7}}}= -2.340$

Now we can calculate the p value with the following probability

$p_v =2*P(z$

If we use the commonly significance level of 0.05 we see that the p value is lower than these values we can conclude that the true mean is different from the value of 465.6 at 5% of significance

6 0

4 years ago