please answer 1 and 2 and if you can explain!!! i need help asap i’ll mark brainliest!!!

Answer:

System of equations:

[tex]x_1+2x_2+2x_3=6\\2x_1+x_2+x_3=6\\x_1+x_2+3x_3=6[/tex]

Augmented matrix:

[tex]\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right][/tex]

Reduced Row Echelon matrix:

[tex]\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right][/tex]

Step-by-step explanation:

Convert the system into an augmented matrix:

[tex]\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right][/tex]

For notation, R_n is the new nth row and r_n the unchanged one.

1. Operations:

[tex]R_2=-2r_1+r_2\\R_3=-r_1+r_3[/tex]

Resulting matrix:

[tex]\left[\begin{array}{cccc}1&2&2&6\\0&-3&-3&-6\\0&-1&1&0\end{array}\right][/tex]

2. Operations:

[tex]R_2=-\frac{1}{3}r_2[/tex]

Resulting matrix:

[tex]\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&-1&1&0\end{array}\right][/tex]

3. Operations:

[tex]R_3=r_2+r_3[/tex]

Resulting matrix:

[tex]\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&2&2\end{array}\right][/tex]

4. Operations:

[tex]R_3=\frac{1}{2}r_3[/tex]

Resulting matrix:

[tex]\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right][/tex]

Answer:

total drop per minute is 56

Step-by-step explanation:

Give data:

total capacity of bag 1 L = 1000 ml

Duration of infuse 6 hr

quantity at the time delivered is 20 gtts/ml

Drop per minute can be determined by using following relation

Drop per minute [tex]= \frac{1000 ml\times 20 gtts/ml}{6\times 60 min} = 55.55 gtt[/tex]

therefore total drop per minute is[tex] 55.55 \approx 56[/tex]

Answer:

The answer is [tex]96.851[/tex] watts.

Step-by-step explanation:

According to unit conversion,

[tex]2000\ fCal = 2\times 10^6\ Cal =8.368\times 10^6 J[/tex].

So the average power is [tex]8.368\times 10^6 J[/tex] per day.

If a day has 24 hours, and each hour has 3600 seconds, the average power in Joules/second (Watts) is

[tex]8.368 \times 10^6 Joules/day = 96.851\ Joules/second[/tex]

Answer:

The sum of the measurement is 14 feet 5 inches.

Hence, you will get the change of $8.45

The required sum is 46 minutes 5 seconds.

Step-by-step explanation:

Consider the provided information.

Add 3 feet 6 inches+8 feet 2 inches+4 inches+2 feet 5 inches.

In order to add the measurement add inches with inches and feet with feet as shown.

3 feet + 8 feet + 2 feet and 6 inches + 2 inches + 4 inches + 5 inches.

13 feet 17 inches

As we know 1 feet = 12 inches

Thus 17 inches can be written as: 1 feet 5 inches

Hence, 13 feet 17 inches = 14 feet 5 inches

The sum of the measurement is 14 feet 5 inches.

Part (B) In a grocery store, steak costs $3.85 per pound. If you buy a three-pound steak and pay for it with a $20 bill, how much change will you get?

Steak costs $3.85 per pound and you buy a three pound steak.

So, the cost will be:

$3.85×3=$11.55

You pay $20 so the change you will get is:

$20-$11.55=$8.45

Hence, you will get the change of $8.45

Part (C) Add 8 minutes 32 seconds+37 minutes 18 seconds+15 seconds.

In order to add the time add minutes with minutes and seconds with seconds as shown.

8 minutes+37 minutes and 32 seconds+ 18 seconds+15 seconds.

45 minutes 65 seconds

As we know 1 minute = 60 seconds

Thus 65 seconds can be written as: 1 minute 5 seconds

Hence, 45 minutes 65 seconds = 46 minutes 5 seconds

The required sum is 46 minutes 5 seconds.

Answer:

1.) Incorrect,

2.) Correct

Step-by-step explanation:

1.) Let x be the amount of money,

After increasing x by 20%,

New amount of money ( say y )= (100+20)% of x ( i.e. y is 20% more than x )

= 120 % of x

[tex]=\frac{120x}{100}[/tex]

⇒ y = 1.20x

[tex]\because \frac{y-x}{y}\times 100=\frac{ 1.20x-x}{1.20x}\times 100[/tex]

[tex]=\frac{0.2x}{1.2x}\times 100[/tex]

[tex]=\frac{20}{1.2}[/tex]

≈ 16.67%

Thus, x is approximately 16.67% less than y.

2.) First score = 60%,

Second score = x% ( let )

So, Average percentage score = [tex]\frac{60+x}{2}[/tex]

If [tex]\frac{60+x}{2}=70[/tex]

[tex]60+x=140\implies x = 80[/tex]

Answer: 0.3173

Step-by-step explanation:

Given : A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with

[tex]\mu=4\ cm[/tex] and [tex]\sigma=0.2\ cm[/tex]

The specifications call for corks with diameters between 3.8 and 4.2 cm.

Let x be the random variable that represents the  the diameter of the corks.

Using formula [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-score corresponding to x= 3.8 will be :_

[tex]z=\dfrac{3.8-4}{0.2}=1[/tex]

z-score corresponding to x= 4.2 will be :_

[tex]z=\dfrac{4.2-4}{0.2}=1[/tex]

Now, by using the standard normal distribution table for z, we have

[tex]\text{P value}=P(-1<z<1)=2P(z<1)-1\\\\=2(0.8413447)-1\\\\=0.6826894\approx0.6827[/tex]

∴The proportion of corks produced by this machine are meeting the specifications=0.6827

∴The proportion of corks produced by this machine are defective = [tex]1-0.6827=0.3173[/tex]

The question asks about the proportion of defective corks produced by a machine. Given that the corks diameters' are normally distributed with a mean of 4cm and a standard deviation of 0.2cm, and the specifications are between 3.8cm and 4.2cm, about 68% of corks will meet the specification. This implies that about 32% will be defective.

The subject of this question is statistics, specifically dealing with normal distribution, mean and standard deviation. To find the proportion of corks produced by the machine that are defective, we can use the properties of normal distribution where the diameters of the corks represent a normal distribution with µ (mean) = 4 cm and σ (standard deviation) = 0.2 cm.

As the corks' specification falls between 3.8 cm and 4.2 cm, these values are 1 standard deviation below and above the mean respectively. In normal distribution, the area (i.e., proportion) within one standard deviation is approximately 0.68 (or 68%). So, the proportion within the specification is 0.68.

To obtain the proportion of defective corks, you subtract the proportion within specification from 1 (the total proportion). Hence, the proportion of defective corks is 1 - 0.68 = 0.32 or 32%. This means that approximately 32% of the corks produced are outside the specification and are deemed defective.

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Answer:

$248,000.

Step-by-step explanation:

We have been given that the revenue from manufacturing and selling x units of toaster ovens is given by [tex]R(x)=-0.3x^2+200x-82,000[/tex].

To find the amount of revenue earned from selling 3,000 toaster, we will substitute [tex]x=3,000[/tex] in the given formula as:

[tex]R(3,000)=-0.03(3,000)^2+200(3,000)-82,000[/tex]

[tex]R(3,000)=-0.03*9,000000+600,000-82,000[/tex]

[tex]R(3,000)=-270,000+518,000[/tex]

[tex]R(3,000)=248,000[/tex]

Therefore, the company should expect revenue of $248,000 from selling 3,000 toaster ovens.

same as before here, the bird is up above and from there goes down, so we sum up both amounts.

[tex]\bf \stackrel{mixed}{528\frac{1}{5}}\implies \cfrac{528\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{2641}{5}}~\hfill \stackrel{mixed}{89\frac{3}{5}}\implies \cfrac{89\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{448}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{2641}{5}+\cfrac{448}{5}\implies \stackrel{\textit{using an LCD of 5}}{\cfrac{(1)2641+(1)448}{5}}\implies \cfrac{3089}{5}\implies 617\frac{4}{5}[/tex]

Answer:

[tex]617\frac{4}{5}[/tex]

Step-by-step explanation:

We have been given that a bird flies from its nest [tex]528\frac{1}{5}[/tex] to the bottom of the canyon [tex]-89\frac{3}{5}[/tex].

First of all, we will convert both mixed fractions into improper fraction.

[tex]528\frac{1}{5}\Rightarrow \frac{2640+1}{5}=\frac{2641}{5}[/tex]

[tex]89\frac{3}{5}\Rightarrow \frac{445+3}{5}=\frac{448}{5}[/tex]

To solve our given problem, we will find difference of both elevations as:

[tex]\frac{2641}{5}-(-\frac{448}{5})[/tex]

[tex]\frac{2641}{5}+\frac{448}{5}[/tex]

[tex]\frac{2641+448}{5}[/tex]

[tex]\frac{3089}{5}[/tex]

[tex]617\frac{4}{5}[/tex]

Therefore, the bird flown [tex]617\frac{4}{5}[/tex] units.

Answer:

The number of seniors who scored above 96% is 1.

Step-by-step explanation:

Consider the provided information.

Two percent of all seniors in a class of 50 have scored above 96% on an ext exam.

Now we need to find the number of seniors who scored above 96%

For this we need to find the two percent of 50.

2% of 50 can be calculated as:

[tex]\frac{2}{100}\times50[/tex]

[tex]\frac{100}{100}[/tex]

[tex]1[/tex]

Hence, the number of seniors who scored above 96% is 1.

Answer:

Step-by-step explanation:

Given that for a given paired sample data set that consists of "X" data and "Y" data, the covariance is 1000.

We know that correlation coefficient between x and y is

[tex]\frac{cov(x,y)}{s_x*s_y}[/tex]

Given that covariance =1000

and sample std dev of x = 75 and y = 100

Hence [tex]r_{xy} =\frac{1000}{25*100} \\\\=0.40[/tex]

Hence correlation coefficient is positive moderately strong with value = 0.40

Answer:

(14a+3, 21+4) = 1

Step-by-step explanation:

We are going to use the Euclidean Algorithm to prove that these two integers have a gcd of 1.

gcd (14a + 3, 21a + 4) = gcd (14a+3, 7a + 1) = gcd (1, 7a+1) = 1

Therefore,

(14a + 3, 21a + 4) = 1

Answer:

a)Total Labor Cost = $600x + $30y.

b) Total variable cost = $3000.

c) Total labor cost last month = $6000.

d) Unit cost of labor per class = $60.

e) Total variable labor cost = $30 * 150 = $4500, Total Labor Cost = $3000 + $4500 = $7500, and Unit cost of labor per class = $7500/150 = $50.

Step-by-step explanation:

a) It is given that the labor cost includes two components: cost of trainers, which is actually their salaries, and cost of a fitness class taught. Fitness trainer costs $600 and one fitness class costs $30. Assuming there are x number of trainers and y number of classes, therefore the model can be expressed as:

Total Labor Cost = Fitness Trainer Cost * number of trainers + Fitness Class Cost * number of classes.

Total Labor Cost = $600x + $30y.

b) The total variable labor cost will be the cost spent on the number of classes. Since number of classes are 100 and the cost of one class is $30, therefore:

Total variable cost = cost of one class * number of classes.

Total variable cost = $30 * 100.

Total variable cost = $3000.

c) Furthermore, last month, x = 5 and y = 100. Plug these values in the total labor cost equation:

Total labor cost last month = $600(5) + $30(100).

Total labor cost last month = $3000 + $3000.

Total labor cost last month = $6000.

d) The total labor cost is $600. Number of classes are 100. Therefore:

Unit cost of labor per class = Total Labor Cost/Number of classes.

Unit cost of labor per class = $6000/100.

Unit cost of labor per class = $60.

e) If the number of classes are increases by 50%, this means that the number of classes will be 150 instead of 100. Therefore:

Total variable labor cost = $30 * 150 = $4500.

Total Labor Cost = $3000 + $4500 = $7500.

Unit cost of labor per class = $7500/150 = $50!!!

Answer:

For the given question the correct answer is option 'C'.

Step-by-step explanation:

For a plane triangle we have:

1) Sum of the all the interior angles is 180 degrees. Hence option 'A' is correct.

2) For a right angled triangle from Pythagoras theorem we know that [tex]H^2=a^2+b^2[/tex]

where,

H is the hypotenuse of the triangle

a,b are the sides of the right angled triangle

hence the option 'B' is also correct

3) For any triangle ABC we know that

[tex]\frac{sin(A)}{BC}=\frac{sin(B)}{AC}=\frac{sin(C)}{AB}=constant[/tex]

hence option 'D' is also correct.

Thus only incorrect answer among the given option is 'C'.

Answer:

The distance between the origin and the given point is 13.9283 units.  

Step-by-step explanation:

The coordinates of origin are (0,0,0)

We are given a point R(9,7,80

The distance formula:

[tex]\sqrt{(y_1 -x_1)^2 + (y_2 -x_2)^2 + (y_3 -x_3)^2}[/tex], where [tex](x_1, x_2, x_3)[/tex] are coordinates of one point and  [tex](y_1, y_2, y_3)[/tex] are coordinates of other point.

Putting the values as:

[tex]y_1 = 9, y_2 = 7, y_3 = 8\\x_1 =0, x_2 = 0, x_3 = 0[/tex]

We get d = [tex]\sqrt{81 + 64 + 49}[/tex]

d = [tex]\sqrt{194}[/tex]

d = 13.9283

Thus, the distance between the origin and the given point is 13.9283 units.

Answer:

You can make 180 meals.

Step-by-step explanation:

We can look at this problem the following way:

For each appetizers, we can choose 3 salads.

For each salad, we can choose 5 entrees. So we already have 3 salads, each with 5 possible entrees, so there are already 3*5 = 15 possibilities.

For each entree, we can choose 4 desserts. So for each of the 15 possibilites of salad and entrees, there are 4 desserts. So there are 15*4 = 60 possibilities.

There are also 3 appetizers possible for each of the 60 possibilities of salads, entrees and desserts. So there are 60*3 = 180 possibilities.

The probability of selecting a red marble from the jar of marbles is 2/17.

To calculate the probability of selecting a red marble from the jar, we need to determine the total number of marbles in the jar and the number of red marbles.

Total number of marbles = 2 (red) + 3 (white) + 5 (blue) + 7 (green) = 17

Number of red marbles = 2

Now, the probability of selecting a red marble is given by:

Probability = (Number of red marbles) / (Total number of marbles) = 2 / 17

So, the correct probability of selecting a red marble from the jar is 2/17.

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Final answer:

The probability of selecting a red marble from the jar is [tex]\frac{2}{17}[/tex] since there are 2 red marbles out of a total of 17 marbles.

Explanation:

The probability of selecting a red marble from a jar of marbles containing two red marbles, three white marbles, five blue marbles, and seven green marbles can be calculated by dividing the number of red marbles by the total number of marbles in the jar. First, we determine the total number of marbles: 2 (red) + 3 (white) + 5 (blue) + 7 (green) = 17 marbles. Next, we calculate the probability of selecting a red marble by dividing the number of red marbles (2) by the total (17).

Therefore, the probability of selecting a red marble is [tex]\frac{2}{17}[/tex].

Answer: The attendance before the increase was 4712.

Step-by-step explanation:

Let the attendance before the increase be 'x'.

Rate of increment = 5%

so, Attendance after increment becomes

[tex]\dfrac{100+5}{100}\times x = 4948\\\\\dfrac{105}{100}\times x=4948\\\\1.05\times x=4948\\\\x=\dfrac{4948}{1.05}\\\\x=4712.38\\\\x=4712[/tex]

Hence, the attendance before the increase was 4712.

Final answer:

To find the original attendance, an equation was formulated where the original attendance (x) increased by 5% equals 4,948. By solving for x, the original attendance before the increase was determined to be approximately 4,712 when rounded to the nearest whole number.

Explanation:

The question asks to find the original attendance before a 5% increase that resulted in a final attendance of 4,948. To calculate the initial attendance, you can set up an equation where the original attendance (which we will call 'x') plus 5% of the original attendance equals the final attendance (4,948).

This can be expressed algebraically as:
x + 0.05x = 4948

Solving for x gives you:
1.05x = 4948
x = 4948 / 1.05
x = 4,712 (rounded to the nearest whole number)

Therefore, the attendance before the increase was approximately 4,712.

Answer:

look at the step by step explanation

Step-by-step explanation:

10<x=45

i dunno if this is correct

Answer:

Your column vector is:

[tex]\left[\begin{array}{c}15&10&5&0&-5&-10&-15&-20&-25\end{array}\right][/tex]

Step-by-step explanation:

The first step to solve your problem is knowing what is a column vector:

A column vector is a matrix that only has one column, and multiple rows.

The problem wants the vector to range from 15 to -25.

It means that the biggest value in the vector is 15, and the smallest is -25. Since it is from 15 to -25, the first element of your column vector is 15, and the last element is -25.

With a step size of 5

At each element, you decrease 5. So you have: 15,10,..,-20,-25.

The vector is:

[tex]\left[\begin{array}{c}15&10&5&0&-5&-10&-15&-20&-25\end{array}\right][/tex]

Answer: SERIES = 670  Ω

PARALLEL = 91.94 Ω

Step-by-step explanation:

Hi, resistors in series obey the following equation :

R1+ R2 = RT

RT is the equivalent resistance. We have the value of both resistances, so we apply the ecuation:

R1 = 110Ω, and R2 = 560Ω

110Ω+ 560Ω = 670 Ω

When resistors are in parallel, resistors obey the following equation:

1/R1 + 1/R2= 1/RT

so, in our case:

1/ 110Ω +1/560Ω = 1/rt

0.01087Ω = 1/RT

RT= 1/0.01087 Ω= 91.94 Ω

Answer:

11:3

Step-by-step explanation:

You add all the white and red marbels up which equals 11 and then add up all the marbles that are not white or red and count them up too in a seperate pile which should give you your answer of 11:3

Answer:

[tex]\left[\begin{array}{ccc}(-p)&--->&q\\f&t&t\\f&t&t\\t&t&f\\t&f&f\end{array}\right][/tex]

Step-by-step explanation:

First, we find all the possibilities for p and q in a table:

p  q

t    t

t    f

f    t

f    f

then -p:

-p  q

f    t

f    f

t    t

t    f

and we apply the operator --> (rightarrow), that is only f (false) y if the first one is t (true) and the second one is f (false)

-p    --->    q

f       t       t

f       t       f

t       t       t

t       f       f

Answer:

false

Step-by-step explanation:

Answer:

  5.  B

  6.  J

Step-by-step explanation:

5. The lower left point on the graph is (1, 5). The only answer choice containing this point is choice B.

__

6. The "range" is the list of y-values. This is also the list of second values in the ordered pairs of the answer to question 5. They are ...

 {5, 6, 10, 15} . . . . matches choice J

The shape of the distribution is positively skewed distribution as per the concept of mean and median.

In this case, the mean is 42 and the median is 37.

Since the mean is greater than the median, it suggests that the distribution is positively skewed.

This means that there are some relatively high values (outliers or extreme values) that are pulling the mean towards the higher end of the data range, which results in the median being lower than the mean.

In other words, the tail of the distribution extends more to the right (higher values) than to the left.

In a positively skewed distribution:

The mean > Median

The tail is longer on the right side (positive side).

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Final answer:

The mean age being higher than the median age in an age distribution survey with 8225 Americans indicates a right-skewed distribution. The distribution has a longer tail on the right side due to outliers or a subgroup of older individuals.

Explanation:

In the survey with a sample of 8225 Americans, the given mean age is 42, and the median age is 37. The fact that the mean is higher than the median suggests that there are outliers or a group of people who are much older than the rest skewing the average upwards. This is an indication that the age distribution is right-skewed, meaning that there is a longer tail on the right side of the distribution curve.

Statisticians commonly use the mean and median to understand the shape of a distribution. In a perfectly symmetrical distribution, these two measures would be the same. However, when there is skewness, the mean is pulled towards the tail of the distribution more so than the median. Therefore, when the mean is greater than the median, the distribution is positively skewed; conversely, if the mean is less than the median, the distribution is negatively skewed.

Understanding the skewness is important as it affects the distribution's measures of central tendency, making the mean less representative of the majority of the data points in a skewed distribution.

Answer:

The median of this set of data is 30.5 .

Step-by-step explanation:

The chart below shows how many messages he sent each day

Monday              20

Tuesday             25

Wednesday       36

Thursday            29

Now we are supposed to find the median

n = 4 (even)

[tex]Median = \frac{\frac{n}{2}th +(\frac{n}{2} +1)th}{2}[/tex]

[tex]Median = \frac{\frac{4}{2}th +(\frac{4}{2} +1)th}{2}[/tex]

[tex]Median = \frac{2nd +3rd}{2}[/tex]

[tex]Median = \frac{25+36}{2}[/tex]

[tex]Median = 30.5[/tex]

Hence The median of this set of data is 30.5 .

Answer:

27

Step-by-step explanation:

25 + 29 = 54 / 2 = 27

have fun with your answer

well, is noteworthy that an x-intercept is when y = 0 or namely is a solution or root of the quadratic, so we know then that the x-intercepts or solutions are at (-1,0) and (3,0), that simply means that

[tex]\bf (\stackrel{x}{-1},\stackrel{y}{0})\qquad (\stackrel{x}{3},\stackrel{y}{0})\qquad \begin{cases} x = -1\\ x+1=0\\ \cline{1-1} x=3\\ x-3=0 \end{cases}~\hfill \implies ~\hfill \stackrel{\textit{equation of the parabola}}{y = a(x+1)(x-3)} \\\\\\ \textit{we also know that } \begin{cases} x = 1\\ y = -8 \end{cases}\implies \underline{-8}=a(\underline{1}+1)(\underline{1}-3)[/tex]

[tex]\bf -8=a(2)(-2)\implies -8=-4a\implies \cfrac{-8}{-4}=a\implies \boxed{2=a} \\\\[-0.35em] ~\dotfill\\\\ y=2(x+1)(x-3)\implies y=2(\stackrel{\mathbb{FOIL}}{x^2-2x-3})\implies y=2x^2-4x-6[/tex]

Answer:

one

Step-by-step explanation:

these two lines are touching each other and another tow are parallel

Answer: 40.

Step-by-step explanation:

Given : The sweater department ran a sale last week and sold 95% of the sweaters that were on sale.

95% can be written as 0.95  [ by dividing 100 ]

Also, the number of sweaters sold = 38

Let x be the number of sweaters were on sale.

Then , we have the following equation :_

[tex]0.95x=38\\\\\Rightarrow\ x=\dfrac{38}{0.95}=\dfrac{3800}{95}=40[/tex]

Hence, 40 sweaters were on sale.

Answer: B

Step-by-step explanation:

twenty thousand is 20,000

10^4 is 10,000

2x10,000 = 20,000

The completed expression would be (2×10,000) + (1×100) + (9×10) which is the correct option (B) 10^4

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

The numbers on the number line increase as one moves from left to right and decrease on moving from right to left.

Juliana wants to write the numbers twenty thousand, and one hundred ninety in expanded notation.

Given the expression as (2×?)+(1×100)+(9×10)

Here (2×10,000) + (1×100) + (9×10)

Since twenty thousand is 20,000

⇒ 10⁴ is 10,000

⇒ 2×10,000

⇒ 20,000

Hence, the completed expression would be (2×10,000) + (1×100) + (9×10)

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