Angelique had 20 tokens to use for games at the arcade. She lost some of them. Her dad tripled the tokens she had left. Angeliqu
2 answers:
Answer: Both the expressions are exactly same . Both are representing the number of tokens she has now.
Step-by-step explanation:
Given: The total number of tokens Angelique has= 20
Since, she lost some of them, let the number of lost tokens be t.
Then, The remaining tokens she has = 20-t
Then her father triples the tokens she has.
now, the number of token she has=....>Angelique's expression
By using distributive property,
The number of token she has=
⇒The number of token she has=...> Dante's expressions
Hence, both are the same expressions. Both are representing the number of tokens she has now.
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Answer: 0.9332.
Step-by-step explanation:
Claim : College Algebra final exam score of engineering majors equal to 88.
Given that : The test statistic is z equals to 1.50.
To find the p-value (Probability value), we use standard normal distribution table, and search the p-value corresponds to the z-score.
In a Standard Normal Distribution Table below, the p-value corresponds z equals 1.5 is 0.9332.
Hence, the p-value is 0.9332.
Answer:
5 trees should be planted to maximize the yield per acre,
The maximum yield would be 1250
Step-by-step explanation:
Given,
The original number of trees per acre = 20,
Average pounds of nuts by a tree = 60,
Let x be the times of increment in number of trees,
So, the new number of trees planted per acre = 20 + x
∵ for each additional tree planted per acre, the average yield per tree drops 2 pounds,
So, the new number of pounds of nut = (60 - 2x)
Thus, the total yield per acre,
Differentiating with respect to t ( time ),
Again differentiating with respect to t,
For maxima or minima,
⇒ 20 - 4x = 0
⇒ 20 = 4x
⇒ x = 5,
For x = 5, Y''(x) = negative,
Hence, Y(x) is maximum for x = 5,
And, maximum value of Y(x) = (20+5)(60 - 10) = 25(50) = 1250,
i.e. 5 trees should be planted to maximize the yield per acre,
and the maximum yield would be 1250 pounds
Answer:
a). x = 11
b). m∠DMC = 39°
c). m∠MAD = 66°
d). m∠ADM = 36°
e). m∠ADC = 18°
Step-by-step explanation:
a). In the figure attached,
m∠AMC = 3x + 6
and m∠DMC = 6x - 49
Since "in-center" of a triangle is a points where the bisectors of internal angles meet.
Therefore, MC is the angle bisector of angle AMD.
and m∠AMC ≅ m∠DMC
3x + 6 = 8x - 49
8x - 3x = 49 + 6
5x = 55
x = 11
b). m∠DMC = 8x - 49
= (8 × 11) - 49
= 88 - 49
= 39°
c). m∠MAD = 2(m∠DAC)
= 2(30)°
= 60°
d). Since, m∠AMD + m∠ADM + m∠MAD = 180°
2(39)° + m∠ADM + 66° = 180°
78° + m∠ADM + 66° = 180°
m∠ADM = 180° - 144°
= 36°
e). m∠ADC =
=
= 18°