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3 years ago

If mZDEF = (7x + 4)", mZDEG = (5x + 1)', and mZGEF = 23", find each

Mathematics

1 answer:

Nataly [62]3 years ago

8 0

Answer:

Yoy answer is x=10

Step-by-step explanation:

We already know what ∠GEF is 23°

so you would have to create an equation like this $23+(5x+1)=7x+4$

you add 23+1=24 and get $5x+24=7x+4$ subtract 5x on both sides

$24=2x+4$ subtract 4 on both sides

$20=2x$ divide 2 x=10

∠DEF=7(10)=70+4=74

∠DEG=5(10)=50+1=51

To check 51+23=74

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A demographer wants to measure life expectancy in countries 1 and 2. Let μ1 and μ2 denote the mean life expectancy in countries

Art [367]

Answer:

For this case we want to test if life expectancy in country 1 is more than 10 years lower than in country 2, (alternatibe hypothesis), so then the system of hypothesis are:

Null hypothesis: $\mu_1 \leq \mu_2 -10$

Alternative hypothesis: $\mu_1 > \mu_2 -10$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 \leq 10$

Alternative hypothesis: $\mu_1 - \mu_2 >10$

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

For this case we want to test if life expectancy in country 1 is more than 10 years lower than in country 2, (alternatibe hypothesis), so then the system of hypothesis are:

Null hypothesis: $\mu_1 \leq \mu_2 -10$

Alternative hypothesis: $\mu_1 > \mu_2 -10$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 \leq 10$

Alternative hypothesis: $\mu_1 - \mu_2 >10$

7 0

3 years ago

Write the equation of the line that passes through the points (6,2) (4,1)

Alisiya [41]

Answer: y=1/2x-1

Step-by-step explanation:

To find the equation of the line that passes through the points, we need to find out slope, m.

$m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }$

We plug our points into this formula to find slope.

$m=\frac{1-2}{4-6} =\frac{-1}{-2} =\frac{1}{2}$

Our slope is 1/2. To find our y-intercept, b, we would plug any point into the equation for slope-intercept form.

y=mx+b

y=1/2x+b

1=1/2(4)+b

1=2+b

b=-1

Now that we know b, our equation is y=1/2x-1.

6 0

3 years ago

Someone please help ?

ikadub [295]

a. 1490

5 x 37.25= 186.25

186.25 x 8 = 1,490

8 0

3 years ago

How do you solve 1/2x x 3/5y=5

Anit [1.1K]

1/2 is a fraction so it is 5

8 0

3 years ago

Read 2 more answers

Math again yay!...Ew math

Sliva [168]

Answer:

The graph of g(x) is wider.

Step-by-step explanation:

Parent function:

$f(x)=x^2$

New function:

$g(x)=\left(\dfrac{1}{2}x\right)^2=\dfrac{1}{4}x^2$

Transformations:

For a > 0

$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

$f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}$

$\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of}\:a\\ & \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a\\\end{aligned}$

$\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of} \: a\\& \textsf{If }a > 1 \textsf{ it is compressed by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of}\: a\\\end{aligned}$