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velikii [3]
3 years ago
11

Pi High School ordered 40 science books. The next week, the school ordered 30 algebra books. The bill for the first order was $3

60 greater than the bill for the second order. The two bills together totaled $3960. Find the price of an algebra book.
Mathematics
1 answer:
maria [59]3 years ago
4 0

Answer:

Each algebra book costs $60.

Step-by-step explanation:

A=bill for algebra books; S=bill for science books=A+$360

S+A=$3960 Substitute for S

A+$360+A=$3960 Subtract $360 from each side.

2A=$3600 Divide each side by 2.

A=$1800 The order for 30 algebra books cost $1800.

Individual book=A/30

individual book=$1800/30=$60 ANSWER: Each algebra book cost $60.

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igomit [66]
15 is exact answer because in combination or does not matter<span />
5 0
3 years ago
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Surveys of students' parents born in Michigan. Are the students independent or not. <br>​
Allushta [10]

Answer:

a. No, they are not independent

Step-by-step explanation:

The probability that a student's father was born in Michigan is:

48 / 100 = 48%

For students' whose mother was born in Michigan, the probability that their father was also born in Michigan is:

29 / 73 = 40%

Since these probabilities are not the same, the events are not independent.  The probability of one event is affected by the occurrence of the other event.

8 0
4 years ago
Given that tan ∅=-1/2, lies in quad 4 and sin α=-4/5, α lies in quad 3 find...
Aleksandr [31]

3)

we know that θ is the IV quadrant, well, there the sine(y) is negative and the cosine(x) is positive, we have a tangent(sine/cosine) of -1/2, so one of those is the negative, in the IV Quadrant it has to be the sine, so the 1 is negative, so the fraction is (-1)/2.

\bf tan(\theta )=\cfrac{\stackrel{opposite}{-1}}{\stackrel{adjacent}{2}}\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad  \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}

\bf c=\sqrt{2^2+(-1)^2}\implies c=\sqrt{5} \\\\\\ \stackrel{\textit{double-angle identities}}{cos(2\theta )=2cos^2(\theta )-1}\implies 2[cos(\theta )]^2-1\implies 2\left[ \cfrac{\stackrel{adjacent}{2}}{\stackrel{hypotenuse}{\sqrt{5}}} \right]^2-1 \\\\\\ 2\cdot \cfrac{2^2}{(\sqrt{5})^2}-1\implies 2\cdot \cfrac{4}{5}-1\implies \cfrac{8}{5}-1\implies \cfrac{3}{5}

4)

recall that the hypotenuse is just a length unit, and is never negative, therefore on that sine ratio of opposite/hypotenuse, the negative is the 4, so the fraction is really (-4)/5,

also let's recall that the cosine(x) is also negative in the III Quadrant.

\bf sin(\alpha )=\cfrac{\stackrel{opposite}{-4}}{\stackrel{hypotenuse}{5}}\impliedby \textit{let's find the \underline{adjacent}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad  \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}

\bf \sqrt{5^2-(-4)^2}=a\implies \sqrt{25-16}=a\implies \pm 3=a\implies \stackrel{III~quadrant}{-3=a} \\\\\\ \stackrel{\textit{double-angle identities}}{sin(2\alpha)= 2sin(\alpha)cos(\alpha)}\implies 2\left( \cfrac{-4}{5} \right)\left( \cfrac{-3}{5} \right) \implies  \cfrac{24}{25}

8 0
3 years ago
Find the slope of the line through the pair of points. A(2, –3), P(2, 9)
laiz [17]
9- -3=12
2-2=0.
Slope is 12/0
5 0
4 years ago
Read 2 more answers
8
Nata [24]

Answer: 15, -8

Step-by-step explanation:

u_2=7\\u_2=u_1+r\\u_3=u_1+2r\\u_4=u_1+3r\\\\u_1+u_2+u_3+u_4=4u_1+6r=12\\u_1+r=7\\\\

\left \{ \begin {array} {ccc|c|c}u_1+r&=&7&-4&-6\\4u_1+6r&=&12&1&1\\\end {array} \right.\\\\\\\left \{ \begin {array} {ccc}2r&=&-16\\-2u_1&=&-30\\\end {array} \right.\\\\\\\left \{ \begin {array} {ccc}r&=&-8\\u_1&=&15\\\end {array} \right.\\\\\\Proof:\\u_1=15\\u_2=7\\u_3=-1\\u_4=-9\\sum=12\\

6 0
3 years ago
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