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3 years ago

Kara and Sonny went to see a movie at the local theater.

Mathematics

1 answer:

CaHeK987 [17]3 years ago

8 0

Answer:

popcorn=4$

soft drink=4.5$

Step-by-step explanation:

if we used omitting method:

1-we multiply (p+s=8.5) by (-2) so we could get rid of (s) and be leftover with (p)

so: (-2p-2s= -17)

2- we subtract this equation from (p+2s=13) and the result will be (-p= -4)

3- divide them by (-1) and the result is (p=4)

4-(p+s=8.5) ,substitute (p) with (4) and make it go to the other side with negative sign and the result of (s) is (8.5-4=4.5)

if we used substituting method:

1-(p+s=8.50), we will make (s) go to the other side with negative sign so the result is (p=8.50-s)

2-(p+2s=13.00), substitute (p) with (8.50-s):

(8.50-s+2s=13)

3- make (8.50) go to the other side with negative sign:

(s=13-8.50=4.5) and then you could get (p)

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Determine the arithmetic sequence if the fourth term is negative six and the eleventh term is negative thirty four

ICE Princess25 [194]

An arithmetic sequence takes the form

$a_n=a_{n-1}+d$

where $d$ is the common difference between terms. You can solve for $a_n$ in terms of any of the previous terms of the sequence:

$a_n=a_{n-1}+d\implies~a_n=a_{n-2}+2d\implies~a_n=a_{n-3}+3d\implies\cdots\implies~a_n=a_{n-k}+kd$

for some integer $1\le k\le n-1$

Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term $a_1$

$a_n=a_1+(n-1)d$

Given that the 4th term is $a_4=-6$ and the 11th term is $a_{11}=-34$ , you have the following system of equations.

$\begin{cases}-6=a_1+(4-1)d\\-34=a_1+(11-1)d\end{cases}$

Solving this system for the two unknowns yields $a_1=6$ and $d=-4$ .

So, the sequence is given explicitly by

$a_n=6+(n-1)(-4)=-4n+5$

3 0

2 years ago

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Aleks04 [339]

The answer is none of the lines intersect each other, because they are at the same slope, and they do not have a different slope for the lines to be intersected.

3 0

2 years ago

Lasers can provide highly accurate measurements of small movements. To determine the accuracy of such a laser, it was used to ta

sp2606 [1]

Answer: $p-value \approx 0.01$

Step-by-step explanation:

Hypothesis testing

$\\\left\{\begin{matrix}H_0 : \mu_0 =0\\ H_1: \mu_0 \neq 0\end{matrix}\right.\\$

For this problem, we need to use the t-student distribution to make inference about the data. We calculate the t-statistics as below:

$\bar{X} = 20\:\mu m\\S.E. = 60\:\mu m\\n=82\\t_{stat} = \frac{\bar{X}-\mu_0}{S.E/\sqrt{n}}=\frac{20-0}{60/\sqrt{82}}=3.0185$

Using a t-statistics table, or using the function TDIST in Microsoft Excel with $t_{stat} = 3.0185,\: df (degree\: of\: freedom) = 14 - 1 = 13$ with two-tailed distribution, we obtain $p-value \approx 0.01$ .

4 0

2 years ago

The function F described by F(x)equals=2.75xplus+71.48 can be used to estimate the height, in centimeters, of a woman whose h

Kryger [21]

Answer:

156.5375 cm

Step-by-step explanation:

The function used to estimate the height is F(x)

F(x) = 2.75x + 71.48

The humerus is xcm long. When x = 30.93cm, we put x = 30.93 into the function F(x)

F(30.93) = 2.75(30.93) + 71.48

= 85.0575 + 71.48

= 156.5375 cm(4 decimal places)

3 0

3 years ago

A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test c

Alja [10]

As the question is unable to be understood/incomplete hence let's discuss the complete question (most probable question) and the answer for that.

Updated Question:

"A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100"

Answer:

Correct answer for this question is first option because it satisfies the first inequality but not the second one.

Step by Step Explanation:

$NO,\\4c+6a\leq 120\\ and\\4c+4a\leq 100$

<u>First Inequality:</u>

4(20)+6(6)≤120

80+36≤120

116≤120 ⇒ TRUE

<u>Second Inequality:</u>

4(20)+4(6)≤100

80+24≤100

104≤100 ⇒ FALSE

5 0

3 years ago