What is the value of x in the figure below? In this diagram, ΔABD ~ ΔCAD

Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use: Step 1: Choose

TEA [102]

Answer:
Steps 3 and 4 are incorrect because
(a) An incorrect value for slope was obtained in step 3.
(b) The incorrect value for the slope was used in step 4.

Explanation:
Let us evaluate Talia's steps.

Step 1: Select (2, 5) as a point on the line.
CORRECT

Step 2: Select another point (1, 3) on the line.
CORRECT

Step 3: Count units to the right and count units up, to determine the slope.
Units right = 2 - 1 = 1
Units up = 5 - 3 = 2
Slope = (Units up)/(Units right) = 2/1 = 2
INCORRECT because Talia did not obtain a slope of 2.

Step 4: Substitute obtained values in the point-slope form.
(y - y1) = m(x - x1). If we select the point (1, 3), then
y - 2 = 2(x - 1).
Talia's equation is INCORRECT because she used an incorrect value
for the slope.

8 0

2 years ago

Read 2 more answers

In general, after a group makes a reservation at a restaurant, they do not show up 20% of the time. If a restaurant has 8 reserv

sashaice [31]

Answer:

P(more than 2 don't show up)=0.2031

Step-by-step explanation:

Multiplication rule for independent events:

If two events A and B are independent then the multiplication rule state that:

P(A and B)= P(A) x P(B)

Find the probability that more than two do not show up:

The probability that the reservations at the restaurant do not show up is 0.20 (=20%) and there were 8 reservations.

P(more than 2 don't show up)= 1- P(less than or equal to 2 don't show up)

= 1-( P(none show up) +P(one don't show up)+P(two don't show up)

=1- ((0.8⁸) +₈ C₁ (0.2¹)x(0.8⁷) +₈ C₂ (0.2²)x(0.8⁶)

=1- (0.1678 +0.3355+0.2936)= 1-0.7969

P(more than 2 don't show up)=0.2031

5 0

2 years ago

In an experiment, some diseased mice were randomly divided into two groups. One group was given an experimental drug, and one wa

damaskus [11]

Answer:

D)Yes, because the difference in the means in the actual experiment was more than two standard deviations from 0.

Step-by-step explanation:

We will test the hypothesis on the difference between means.

We have a sample 1 with mean M1=18.2 (drug group) and a sample 2 with mean M2=15.9 (no-drug group).

Then, the difference between means is:

$M_d=M_1-M_2=18.2-15.9=2.3$

If the standard deviation of the differences of the sample means of the two groups was 1.1 days, the t-statistic can be calculated as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{2.3-(0)}{1.1}=2.09$

The critical value for a two tailed test with confidence of 95% (level of significance of 0.05) is t=z=1.96, assuming a large sample.

This is approximately 2 standards deviation (z=2).

The test statistict=2.09 is bigger than the critical value and lies in the rejection region, so the effect is significant. The null hypothesis would be rejected: the difference between means is significant.

4 0

2 years ago

A bunch bowl is in the shape of a hemisphere. The top rim has a circumference of 116cm.

Tom [10]

The hemisphere is half the volume of a sphere. Since we are given the circumference, we can solve for the radius of the sphere. That is
$C=2\pi r$

$116\:cm=2\pi r$

$r=\frac{116}{2\pi }=18.462\:cm$

Part A
We can now compute for the volume of the hemisphere.
$V=\frac{1}{2}\times \frac{4}{3}\pi r^3=\frac{1}{2}\times \frac{4}{3}\pi \left(18.462\right)^3=13179\:cm^3$

Part B
We just need to convert the volume into its corresponding gallons
$13179\:cm^3\times \frac{1\:Liter}{1000\:cm^3}\times \frac{1\:gallon}{3.785\:Liters}=3.5\:gallons$

8 0

2 years ago

The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from th

bazaltina [42]

$\bf \qquad \textit{ inverse proportional variation}\\\\\\
\begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x}

&&y=\cfrac{{{ k}}}{x}
\end{array}$

"<span>The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth"

namely "w" varies inversely to </span> $\bf d^2$ or $\bf w=\cfrac{k}{d^2}$

then
"<span>A particular person weighs 192 pounds on the surface of the earth and the radius of the earth is 3900 miles. "
</span>namely when w = 192, d = 3900

so $\bf w=\cfrac{k}{d^2}\qquad 
\begin{cases}
w=192\\
d=3900
\end{cases}\implies 192=\cfrac{k}{3900^2}
\\\\\\
\textit{solve for "k", to find the}\\
\textit{"constant of variation"}\\
\textit{once you've found it, plug it back in at }w=\cfrac{k}{d^2}$

7 0

2 years ago