<span>It is given that m ∥ n, m∠1 = 50</span>°<span> , and m∠2 = 42</span>°<span>. By the triangle sum theorem, m∠3 = 88</span>°<span>. Because corresponding angles formed by two parallel lines and a transversal are congruent, ∠3 ≅ ∠4. By the angle congruence theorem, m∠3 =m∠4. Using substitution, 88</span>°<span>=m. Angles 4 and 5 form a linear pair, so by the linear pair postulate, m∠4 + m∠5=180</span>°<span>. Substituting gives 88</span>° <span>+ m∠5=180</span>°<span>. Finally, by the subtraction property of equality, m∠5 = 92</span>°<span>.</span>
Now Tim gets $500 after it $45 was added to what he had last week
That means that
"What Tim earned last week" + $45 = $500
Subtract $45 from $500
$500-$45= $455
If you're not sure check your work
If I make $455 now and next week I get $45 more next week
$455+$45=$500
Next week I make $500
Answer:
12083.929
Step-by-step explanation:
First step: find the mean of the data.
mean = <u>3</u><u>+</u><u>3</u><u>3</u><u>+</u><u>3</u><u>0</u><u>3</u><u>+</u><u>2</u><u>3</u><u>3</u><u>+</u><u>3</u><u>+</u><u>7</u><u>3</u><u>+</u><u>8</u><u>3</u><u>+</u><u>6</u><u>3</u>
8
= <u>7</u><u>9</u><u>4</u>
8
= 99.25
Second step: Now we calculate each dog's difference from the Mean.
Example : 3–99.25=96.25
Answer: (-96.25)+(-66.25)+203.75+133.75+(-96.25)+(-26.25)+(-16.25)+(36.25)
Third step: To calculate the Variance, take each difference, square it, and then average the result.
s² = <u>(-96.25)</u><u>²</u><u>+(-66.25)</u><u>²</u><u>+203.75</u><u>²</u><u>+133.75</u><u>²</u><u>+(-96.25)</u><u>²</u><u>+(-26.25)</u><u>²</u><u>+(-16.25)</u><u>²</u><u>+(36.25)</u><u>²</u>
8–1
=<u> </u><u>9</u><u>2</u><u>6</u><u>4</u><u>.</u><u>0</u><u>6</u><u>3</u><u>+</u><u>4</u><u>3</u><u>8</u><u>9</u><u>.</u><u>0</u><u>6</u><u>3</u><u>+</u><u>4</u><u>1</u><u>5</u><u>1</u><u>4</u><u>.</u><u>0</u><u>6</u><u>3</u><u>+</u><u>1</u><u>7</u><u>8</u><u>8</u><u>9</u><u>.</u><u>0</u><u>6</u><u>3</u><u>+</u><u>9</u><u>2</u><u>6</u><u>4</u><u>.</u><u>0</u><u>6</u><u>3</u><u>+</u><u>6</u><u>8</u><u>9</u><u>.</u><u>0</u><u>6</u><u>3</u><u>+</u><u>2</u><u>6</u><u>4</u><u>.</u><u>0</u><u>6</u><u>3</u><u>+</u><u>1</u><u>3</u><u>1</u><u>4</u><u>.</u><u>0</u><u>6</u><u>3</u>
7
=<u> </u><u>8</u><u>4</u><u>5</u><u>8</u><u>7</u><u>.</u><u>5</u>
7
= 12083.929
Variance Formula:
<u> </u><u> </u>
Variance = s² =<u>Σ(</u><u>x</u><u>i−</u><u> </u><u>x</u><u> </u><u>)</u><u>²</u>
n−1
Mean (μ) = 11.5 feet
Standard deviation (σ) = 1.7 feet
First we need to find the z-score for less than 13.5 feet.
The formula of z-score is : z = (X - μ)/σ
Here X= 13.5, so z = 
z =
= 1.18
P(X < 13.5) = P(z< 1.18) =P(z< (1.1 + .08)) = 0.8810 (from z-score table)
P(X< 13.5) = 88.1% (for making percentage from decimal, we need to multiply by 100)
So, the probability that a randomly selected tree is less than 13.5 feet tall = 88.1%