Answer:
Step-by-step explanation:
So the ratio is 5:4:2
there are 11 parts to this ratio (5+4+2)
the 5 is for the $2, the 4 is for the $1 and the 2 is for the 50 cents
he has 30 of the 50 cents
so you divide 30 by 2 to get one part of this ratio
1 part of this ratio is equal to 15 coins
multiply 15 by 5 to get the number of $2 coins: 75
multiply 15 by 4 to get the number of $1 coins: 60
add all of those parts together
30+60+75 = 165
If he uses a $1 coin to buy the sundae he will have 75 $2 coins and 59 $1 coins left
however, if he uses two 50 cents coins to buy the sundae he will have 75 $2 coins and 60 $1 coins left
The third box plot is your answer
The correct graph to the inequality is a number line with open dot at <em>negative 3</em> with shading to the left and an open dot at 6 with shading to the right. The correct option is the second option
<h3>Linear Inequalities </h3>
From the question, we are to determine the graph for the given compound inequality
The given compound inequality is
4p + 1 < −11 or 6p + 3 > 39
Solve the inequalities separately
4p + 1 < −11
4p < -11 - 1
4p < -12
p < -12/4
p < -3
OR
6p + 3 > 39
6p > 39 - 3
6p > 36
p > 36/6
p > 6
Thus,
p < -3 OR p > 6
Hence, the correct graph to the inequality is a number line with open dot at <em>negative 3</em> with shading to the left and an open dot at 6 with shading to the right. The correct option is the second option
Learn more on Linear Inequalities here: brainly.com/question/5994230
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Using linear function concepts, it is found that the slopes and intercepts of the functions are given as follows:
a) -4.
b) P = 25.
c) 2.
d) P = 5.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The demand is given by:
D = 100 - 4P.
Hence the slope is of -4. The demand is equals to zero when:
100 - 4P = 0 -> P = 25.
The supply is given by:
QS = -10 + 2P.
Hence the slope is of 2. The supply is equals to zero when:
-10 + 2P = 0 -> P = 5.
More can be learned about linear function concepts at brainly.com/question/24808124
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Part (a)
<h3>Answer: 12.1</h3>
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Work Shown:
We'll apply the sine rule since we have a known opposite side of AB = 10 and an unknown hypotenuse we want to find BD.
Focus on triangle ABD
sin(angle) = opposite/hypotenuse
sin(D) = AB/BD
sin(56) = 10/x
x*sin(56) = 10
x = 10/sin(56)
x = 12.062179
x = 12.1
Make sure your calculator is in degree mode.
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Part (b)
<h3>
Answer: 15.1</h3>
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Work Shown:
Draw an xy coordinate grid.
Place point A at the origin (0,0).
Point B is 10 units above this, so B is at (0,10).
Point C is at (18,10) since we move 18 units to the right of B.
Point D is at approximately (6.745085, 0). The 6.745085 is from solving tan(56) = 10/x for x.
Refer to the diagram below.
Apply the distance formula for the points C and D.
Segment CD is roughly 15.1 cm long.
