Select the correct structure that

Find the x-intercept and the y-intercept of the graph of the equation.

andriy [413]

Answer:

x = 6

Step-by-step explanation:

To attain the x-intercepts you have to let y = 0.

So in this case you will be having:

4x + 2(0) = 24

4x/4 = 24/4

x = 6

Hopefully it makes sense.

:)

6 0

3 years ago

The type of triangle formed by joining the points (7,10), (-2 ,5) and (3, -4)

Arturiano [62]

A scalene triangle is formed from the three points.

5 0

3 years ago

Find four consecutive multiples of 5 whose sum is 90

STatiana [176]

Answer:

15, 20, 25, 30

Step-by-step explanation:

If want to find the first multiple, we could actually use the equation: x + (x+5) + (x+5+5) + (x+5+5+5) = 90. After simplifying this term, we would get 4x+30 = 90 which then transforms into 4x=60 which simplifys to x = 15. Plug 15 into the original equation, and you would get the multiples 15 + 20 + 25 + 30 = 90.

5 0

3 years ago

Read 2 more answers

A random sample of 100 U.S. adults were selected from a population. In the population, the probability of having hypertension is

svp [43]

Answer:

For this case we want to calculate this probability:

$P(X\leq 30)$

And for this case if we use the normal approximation we can use the z score formula given by:

$z = \frac{X -\mu}{\sigma}$

And using this formula with the correction factor of continuity we got:

$P(X\leq 30) =P(X$

And using the normal standard table or excel we got:

$P(Z \leq 1.522)= 0.936$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest "number of people with hypertension", on this case we now that:

$X \sim Binom(n=100, p=0.24)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=100*0.24=24 \geq 10$

$n(1-p)=100*(1-0.24)=76 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=100*0.24=24$

$\sigma=\sqrt{np(1-p)}=\sqrt{100*0.24(1-0.24)}=4.27$

Solution to the problem

For this case we want to calculate this probability:

$P(X\leq 30)$

And for this case if we use the normal approximation we can use the z score formula given by:

$z = \frac{X -\mu}{\sigma}$

And using this formula with the correction factor of continuity we got:

$P(X\leq 30) =P(X$

And using the normal standard table or excel we got:

$P(Z \leq 1.522)= 0.936$

7 0

3 years ago

Triangle PQR has vertices P(-3, -1), Q(-1, 7), and R(3, 3), and point A and B are midpoints of PQ and RQ, respectively. Use coor

andrezito [222]

Answer:

Part a) The figure a shows that AB is parallel to PR. Please see attached figure a.

Part b) The length of AB is half the length of PR

Step-by-step explanation:

Part A)

Let M be the midpoint formula between points A(x₁, y₁) and B(x₂, y₂)

$M=({\displaystyle {\frac {x_{1}+x_{2}}{2}}, {\frac {y_{1}+y_{2}}{2})$

Let A be the midpoint of P(-3, -1) and Q(-1, 7)

The coordinates of the midpoint of P(-3, -1) and Q(-1, 7):

$Mpq{} =({\displaystyle {\frac {-3+(-1)}{2}}, {\frac {-1+7}{2})$

$Mpq{} =(-2, 3)$

Let B be the midpoint of Q(-1, 7) and R(3, 3):

$Mqr{} =({\displaystyle {\frac {-1+(3)}{2}}, {\frac {7+3}{2})$

$Mqr{} =(1, 5)$

The figure a shows that AB is parallel to PR. Please see attached figure a.

Part B)

The point A has the coordinates: A(-2, 3)

The point B has the coordinates: B(1, 5)

The distance formula is: $d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}$

So, the length of AB $={\sqrt {(1-(-2))^{2}+(5-3)^{2}$

= $\sqrt{9+4}$

= $\sqrt{13}$

= $3.6056$

And, the length of PR $={\sqrt {(3-(-3))^{2}+(3-(-1)^{2}$

= $\sqrt{36+16}$

= $\sqrt{52}$

= $2\sqrt{13}$

= = $7.2111$

As the length of AB = 3.6056 and the length of PR = 7.2111

So, it is clear that the length of AB is half the length of PR.

Keywords: distance formula, midpoints, triangle, coordinate plane

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3 0

3 years ago