Angle 1 and Angle 2 are supplementary angles. Find x and the measure of Angle 1.

Jeremy will roll a number cube, numbered 1-6, twice. What is the probability of rolling an even number than the number 3?

andreyandreev [35.5K]

There are 6 possible outcomes on a dice. Meaning when you roll it it could be any of them. Because 3 is one of the 6 the answer would be 1/6

3 0

3 years ago

Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.<br> g(x)<br> f(x)

vlada-n [284]

Answer:

k = 4

Step-by-step explanation:

First, find the equations of each function.

f(x) = x/3 - 3

g(x) = x/3 + 1

Then plug these values for g(x) = f(x) + k.

x/3 + 1 = x/3 - 3 + k subtract x/3 on both sides

1 = -3 + k add -3 on both sides

k = 4 we're done!

and this makes sense because g(x) is just a translation of f(x) 4 units up.

5 0

2 years ago

Help simplify the answer. In the picture

Paul [167]

rounding to nearest 10 to any number follow these rules

1. if number ends 0 , 1 , 2 ,3 4 , 5 take number down to nearset multiple of 10

2. if number ends with above 5 take the upper number multiple of 10

so here

413 + 35.6 + 998.5 + 376 + 85.3

= 410 + 40 + 1000+ 380 + 90

= 1920

5 0

4 years ago

Expand the exppresion -7(k-3)

Lana71 [14]

Answer:

-7k+21

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

An auto company claims that the fuel efficiency of its sedan has been substantially improved. A consumer advocate organization w

zzz [600]

Answer:

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.983 -0}{\frac{1.685}{\sqrt{12}}}=2.021$

$df=n-1=12-1=11$

$p_v =P(t_{(11)}>2.021) =0.0342$

If we compare the the p value with the significance level provided $\alpha=0.1$ , we see that $p_v < \alpha$ , so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.

Step-by-step explanation:

Previous concepts

A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.

Let put some notation :

x=test value 2017 , y = test value 2019

x: 28.7 32.1 29.6 30.5 31.9 30.9 32.3 33.1 29.6 30.8 31.1 31.6

y: 31.1 32.4 31.3 33.5 31.7 32.0 31.8 29.9 31.0 32.8 32.7 33.8

Solution to the problem

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x \leq 0$

Alternative hypothesis: $\mu_y -\mu_x >0$

Because if we have an improvement we expect that the values for 2019 would be higher compared with the values for 2017

The first step is calculate the difference $d_i=y_i-x_i$ and we obtain this:

d: 2.4, 0.3, 1.7,3,-0.2, 1.1, -0.5, -3.2, 1.4, 2, 1.6, 2.2

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{11.8}{12}=0.983$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =1.685$

We assume that the true difference follows a normal distribution. The 4th step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.983 -0}{\frac{1.685}{\sqrt{12}}}=2.021$

The next step is calculate the degrees of freedom given by:

$df=n-1=12-1=11$

Now we can calculate the p value, since we have a right tailed test the p value is given by:

$p_v =P(t_{(11)}>2.021) =0.0342$

If we compare the the p value with the significance level provided $\alpha=0.1$ , we see that $p_v < \alpha$ , so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.

4 0

3 years ago