Answer:
= The exponent is 12
Step-by-step explanation:
(9.1 × 10^9)(7.5 × 10^2)
When multiplying terms in scientific notation, we multiply the numbers in front and add the exponents
(a* 10^b) (c* 10^d) = ac * 10^(b+d)
(9.1 × 10^9)(7.5 × 10^2) = (9.1*7.5) * 10^(9+2)
=68.25 * 10^11
But this is not proper scientific notation. We can only have 1 number in front of the decimal. We need to move the decimal 1 place to the right. That adds 1 to the exponent.
=68.25 * 10^11 = 6.825 * 10^(11+1)
= 6.825 * 10^12
Answer:
Mean = 44.
Mean is the average.
Add all numbers:
(43 × 3) + (44 × 5) + (45 × 2) + 46
(129) + (220) + (90) + 46
= 485
Divide by number of points:
485 ÷ 11 = 44.090909 (09 repeating)
Round to 44.
Median = 44
Median is the middle-most number.
Line all the values up:
43, 43, 43, 44, 44, 44, 44, 44, 45, 45, 46
'Cross' numbers off from each side until you reach the middle- 44.
Mode = 44
Mode is the number that appears most often. 43 appears three times, 44 appears five, 45 appears twice, and 46 appears once. Five was the greatest reoccurrence. Therefore, 44 is the mode.
Range = 3
Range is the distance between the smallest value and the largest value.
Smallest number: 43
Largest number: 46
46 - 43 = 3
A. The scores in order are: 10, 12, 13, 14, 14, 16, 18, 23, 24, 26. The range is 26 - 10 = 16. The mean is the sum divided by 10, which is 17. The median is between 14 & 16, which is 15. The mode is 14, since it is repeated twice.
B. The variance is calculated by subtracting each score from the mean, squaring, and adding all such squares. Then divide by the number of terms (10) to get 27.6 Take the square root to get the standard deviation, which is 5.25.
C. This is for a population, since these are all 10 games that Jason played. (If it were a sample, we would divide by 9 only)
D. The mean of 17 is higher than the median of 15 and the mode of 14. This implies a left-skewed distribution. However, the SD of 5.25 is quite high relative to the mean of 17, so the distribution is not that clearly defined yet (more data points would make it clearer).
Answer:
(2,3)
Step-by-step explanation:
y = 90°
Solution:
The reference image for the answer is attached below.
The sum of opposite interior angles is equal to the exterior angles.
m∠BAC + m∠ACB = 110°
m∠BAC + 70° = 110°
m∠BAC = 110° – 70°
m∠BAC = 40°
m∠BAD + m∠DAC = 40°
x + x = 40°
2x = 40°
Divide by 2 on both sides of the equation.
x = 20°
In triangle DAC,
Sum of all the angles of a triangle = 180°
m∠DAC + m∠ACD + m∠CDA = 180°
20° + 70° + m∠CDA = 180°
90° + m∠CDA = 180°
m∠CDA = 180° – 90°
m∠CDA = 90°
∠CDA and y lies on the straight line. So they form a linear pair.
y + m∠CDA = 180°
y + 90° = 180°
y = 180° – 90°
y = 90°
The value of y is 90°.
