Answer:
16.1
Step-by-step explanation:
Answer: 117.6° ; 32.4° .
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Explanation:
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Note: ALL triangles, by definition, have exactly 3 (THREE) sides and exactly 3 (THREE) angles.
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We are given the following:
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We have a triangle.
Angle 1: m∡1 = (8x) ;
Angle 2: m∡2 = (2x + 3) ;
Angle 3: m∡3 = 30.
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We are asked to find: "m∡1" and " m∡2" .
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Note: In ALL TRIANGLES, the measurements of all THREE (3) angles ALWAYS add up to 180 degrees.
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So, " m∡1 + m∡2 + m∡3 = 180 " .
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Let us substitute our given values for the measurements in EACH of
the THREE (3) angles — on the left-hand side of the equation; then solve for "x" ; then substitute that solved value for "x" into the given expressions for BOTH "m∡1" AND "m∡2" ; to find the values for " m∡1" AND " m∡2 " ; which are the values asked for in this very question ;
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m∡1 + m∡2 + m∡3 = 180 ;
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8x + (2x + 3) + 30 = 180 ;
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8x + 2x + 3 + 30 = 180 ;
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Combine the "like terms" on the 'left-hand side" of the equation; to simplify:
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+8x + 2x = +10x ;
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+3 + 30 = +33 ;
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Rewrite the entire equation, as:
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10x + 33 = 180 ;
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Now, subtract "33" from EACH SIDE of the equation:
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10x + 33 − 33 = 180 −<span> 33 ;
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to get:
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10x = 147 ;
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Now, divide EACH side of the equation by "10" ; to isolate "x" on ONE SIDE of the equation; and to solve for "x" :
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10x / 10 = 147 / 10 ;
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to get:
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x = 14.7 ;
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Now, given the following, we plug in our solved value, "14.7", for "x", into the expression given for "m</span>∡1" and "m∡2"; as follows:
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Angle 1: "(8x)" = 8*(14.7) = 117.6° ;
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Angle 2: "2x + 3" = 2*(14.7) + 3 = 29.4 + 3 = 32.4° ;
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These are the two answers; that is the 2 (TWO) values asked for in the question: 117.6° ; 32.4° .
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Do they make sense? That is, do the measurements of ALL 3 (THREE) angles; that is, our two solved measurements added together, and then added to the value of the third angle (given: "m</span>∡3 = 30°); all add up to 180° ?
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Let us check:
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m∡1 + m∡2 + m∡3 = 180 ;
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Plugging in our solved values for "m∡1" and "m∡2" ; and our given value: "30" — for "m∡3 — does the equation hold true?
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→ 117.6 + 32.4 + 30 = ? 180 ??
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→ 117.6 + 32.4 = 150 ; → 150 + 30 =? 180 ? Yes!
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The answer is 120 miles , because it is a proportion
Answer: Priya practiced for <u>189 minutes
</u>
Tyler practiced for <u>123 minutes
</u>
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The Explanation: Now, Han spent 75 minutes practicing the piano over the weekend
Then, Priya practiced the violin for 152% as much time as Han practiced the piano.
Priya = 152% of 75 minutes + 75 minutes
= 152/100 × 75 + 75
= 1.52 × 75 + 75
= 114 + 75
= 189 minutes
Finally, Priya practiced for <u>189 minutes</u>
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Tyler practiced the clarinet for 64% as much time as Han practiced the piano.
Tyler = 64% of 75 minutes + 75 minutes
= 64/100 × 75 minutes + 75 minutes
= 64 / 100 × 75 + 75
= 0.64 × 75 + 75
= 48 + 75
= 123 minutes
Lastly, Tyler practiced for <u>123 minutes</u>
Answer:
Recall that probability is given as; the number of required outcome over the number of total possible outcome.
The probability that a transmitter receives the signal being sent by itself is given as 
.
when there are n transmitters, the probability will be given as 
Step-by-step explanation:
Probability simply the likelihood of an event occurring or not occurring.
Probability therefore is given as; the number of required outcome over number of possible outcome.
In the case of the first part above we have the number of required outcome to be at least one divided by the number of possible outcome which is 3.
while in the second part we have the number o possible outcome to be n.
