Lin is reading a 47-page book. She read the first 20 pages in 35 minutes.

If she continues to read at the same rate, will she be able to complete this book in under 1 hour?
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If so, how much time will she have left? If not, how much more time is needed?
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Answer:

[tex]A * B = \left[\begin{array}{ccc}10&-6\\8&5\\19&-10\end{array}\right][/tex]

Step-by-step explanation:

Given

[tex]A =\left[\begin{array}{cc}2&-2\\3&4\\4&-3\end{array}\right][/tex]

[tex]B = \left[\begin{array}{cc}4&-1\\-1&2\end{array}\right][/tex]

Required

[tex]AB[/tex]

To do this, we simply multiply the rows of A by the column of B;

So, we have:

[tex]A * B = \left[\begin{array}{ccc}2*4 + -2*-1&2*-1+-2*2\\3*4+4*-1&3*-1+4*2\\4*4-3*-1&4*-1-3*2\end{array}\right][/tex]

[tex]A * B = \left[\begin{array}{ccc}10&-6\\8&5\\19&-10\end{array}\right][/tex]

The study conducted in the scenario above is an experimental study because the subjects were given treatment.

Observational study involves monitoring the relationship between variables through observation without giving any treatment during the course of the study.

Experimental study on the other hand involves the introduction of a treatment or intervention in other to study the cause and effect or relationship between the variables.

In the scenario above, the research intends to demonstrate the effectiveness of a treatment(magnets) for back pain. The presence of a treatment in this research study makes it an experimental study.

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The linear equation of line passing through the (-14,-5) and (4,5) is given by -5x + 9y = 25

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -14 , -5 )

Let the second point be Q ( 4 , 5 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -5 - 5 ) / ( -14 - 4 )

Slope m = -10 / -18

Slope m = 5/9

Now , the equation of line is y - y₁ = m ( x - x₁ )

y - 5 = ( 5/9 ) ( x - 4 )

Multiply by 9 on both sides , we get

9y - 45 = 5x - 20

Adding 45 on both sides , we get

9y = 5x + 25

Subtracting 5x on both sides , we get

-5x + 9y = 25

Hence , the equation of line is -5x + 9y = 25

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Answer:

Step-by-step explanation:

Area stage = 1/2 h (ab +cd)

Area = 5(14+22)

meeting center Area = 180

room = 25*32 = 800

800-180 = 620 tile

620*$4.90 = $3038

So no not enough money....

Note: even if it was $2999 it still would not be enough because

you have to cut tiles to fit in corners and edges... Just having fun with that comment, the math problems sometimes don't take reality into account (ha ha ha)

Answer:

She has 90.96 miles of the trail to hike.

Step-by-step explanation:

Length of the trail:

The length of the trail is of 113.7 miles.

On the first day she hiked of 1/10 the distance of the trail.

Thus:

[tex]\frac{1}{10(113.7) = 11.37[/tex]

On the first day she hiked 11.37 miles.

On the second day she hiked the same distance as the first day.

Also 11.37 miles on the second day, and thus, 2*11.37 = 22.74 miles on the first two days.

How much of the trail does she have left to hike?

113.7 - 22.74 = 90.96

She has 90.96 miles of the trail to hike.

Answer:

53 degrees

Step-by-step explanation:

tan(theta)=8/6,

theta= [tex]tan^{-1} (\frac{8}{6} )=53.13 degree[/tex]

Answer:

About 34% of the weights are between 3280 grams and 3720 grams.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 3500 grams, standard deviation of 500 grams.

This means that [tex]\mu = 3500, \sigma = 500[/tex]

About 34% of the weights are between what two values?

Between the 50 - (34/2) = 33rd percentile and the 50 + (34/2) = 67th percentile.

33rd percentile:

X when Z has a p-value of 0.33, so X when Z = -0.44.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.44 = \frac{X - 3500}{500}[/tex]

[tex]X - 3500 = -0.44*500[/tex]

[tex]X = 3280[/tex]

67th percentile:

X when Z has a p-value of 0.67, so X when Z = 0.44.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.44 = \frac{X - 3500}{500}[/tex]

[tex]X - 3500 = 0.44*500[/tex]

[tex]X = 3720[/tex]

About 34% of the weights are between 3280 grams and 3720 grams.

Answer:

Amber rode for 36 minutes in total.

Step-by-step explanation:

Lets create a ratio table:

Time elpased (minutes) : Laps around park

                                    9 : 1

                                  36 : 4

Amber rode for 36 minutes in total.

đã đi 36 phút.

từng bước

                                   9: 1

                                 36: 4

Amber đã đi tổng cộng 36 phút.

Answer:  a + ( 2a - 7 ) = 41

Explanation:

Let be "a" the Nicci's age and "s" the Nicci's sister.

You know that the sum of Nicci's age and her sister's age is 41. This can be represented with the following equation:

a + 8 = 41

And knowing that Nicci's sister is 7 years less than twice Nicci's age, you can write another equation to represent this:

8 = 2a - 7

Now, substitute the second equation into the first equation in order to find the equation that represents this relationship.

Then, this is:

a + ( 2a - 7 ) = 41

Hope it helps...

Answer: 56 - 42

Step-by-step explanation: She gave 2 to EACH of her 21 students. So 2 * 21 = 42. 56 - 42

Answer:

√-2 ≈ 1.41i

Step-by-step explanation:

√-2 = i√2 = i × 1.414.. ≈ 1.41i

Answer:

nnmb cgchmfxmgfmv vb  ,  mnio qrstuvwxyz

abcdefghijklmnoprstuvxxyz

Step-by-step explanation:

now i know my abcs next time wont you sing with me

Answer:

if it takes the lorry ten hours we divide 400 by 10

40 mph

if it takes 15% longer that means it will take

10*1.15=11.5

if we divide 400 by 11.5

we get 34.7826086957

or 34.8

so the lorry travels 5.2 mph faster then the expected speed

Hope This Helps!!!

Answer:

His mark, as a percentage, was of 40%.

Step-by-step explanation:

Mark as a percentage:

His mark as a percentage is the number of questions correct multiplied by 100% and divided by the number of questions.

In this problem:

60 questions correct out of 150. So

60*100%/150 = 40%

His mark, as a percentage, was of 40%.

Answer:

7+½ = (7*2+(1))/2=15/2

Step-by-step explanation:

2+½ =5/2 and. (15/2)/(5/2)=3. this means %33.3333

Answer: 24 years

Step-by-step explanation:

Based on the information given, we've been given,

Principal = #250

Interest = #120

Interest rate = 2%

Time = Unknown

Interest = PRT/100

120 = (250 × 2 × Time)

Cross multiply

120 × 100 = (250 × 2 × T)

12000 = 500T

Time = 12000/500

Time = 24

It will take 24 years.

Answer:

Hence,

a)

Test statistic [tex]X^{2}[/tex] = 9.269.  

p value = 0.148

b)

Sunday=  15.23%, Monday= 12.62%, Tuesday= 13.10%, Wednesday=11.67%,

Thursday= 13.10%, Friday= 16.19%, Saturday= 18.09%.

Step-by-step explanation:

a)

                    relative observed    Expected       Chi square

Category   frequency(p)      [tex]O_{i}[/tex]    Ei=total*p    [tex](O-E)^{2}[/tex] [tex]R^{2}_{i} =(O_{i} -E_{i} )^{2} /E_{i}[/tex]

     1           0.142857143      64.0         60.00    16.00          0.267

    2           0.142857143      53.0       60.00     49.00         0.817

    3           0.142857143      55.0         60.00     25.00        0.417

    4           0.142857143      49.0       60.00     121.00        2.017

    5           0.142857143      55.0         60.00     25.00        0.417

    6           0.142857143      68.0         60.00     64.00        1.067

    7           0.142857143      76.0         60.00    256.00        4.267

  Total         1.000      420        420             556       9.269

Test statistic [tex]X^{2}[/tex] = 9.269.  

p value = 0.148 from excel: chidist(9.269,6)  

b)

Percentage %= Frequency of traffic occur on category x 100 / Total number of frequency given.

Category          Percentage%

Sunday                   15.23%

Monday                    12.62%

Tuesday                   13.10%

Wednesday           11.67%

Thursday           13.10%

Friday                   16.19%

Saturday                   18.09%

Answer:

f(x) = x/8

Step-by-step explanation:

f(x) = y

y = 8x

switch the x and y

x = 8y

solve for y

9514 1404 393

Answer:

  b. x = π/2, x = 3π/2

Step-by-step explanation:

The maximum is found where the argument of the cosine function is a multiple of 2π.

  2x -π = 2nπ

  2x = (2n+1)π . . . . . . . add π

  x = (2n+1) · π/2 . . . . . divide by 2

  x = {π/2, 3π/2}

Answer:

No solution is possible from the informatin provided.

Step-by-step explanation:

You didn't include the table,

Answer:

y intercept is found from the pair that has a 0 for the x variable.

Step-by-step explanation:

if a choice was (0,2) this would be the point where the line intercepts the y axis.

x=0 is the position of the vertical line, and 2 is how high up the graph the line passes through the y-axis

Answer:

6x50=300

Step-by-step explanation:

because math

Answer:

6*50

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

6*5=30*10=300

Answer:

2

Step-by-step explanation:

Value = 80

Mean = 70

Variance = 25

Standard deviation=root(Variance)=root(25)=5

z score = (value - mean)/standard deviation

            = (80-70)/5

            = 10/5

            = 2

z-score using mean 70 and variance 25 is 2

Given :

A final statistics exam had a mean of 70 and a variance of 25

First we find out standard deviation using variance

standard deviation =[tex]\sqrt{variance} =\sqrt{25} =5[/tex]

Now we find out z-score

[tex]z-score =\frac{value - mean}{standard \; deviation }[/tex]

value =80

mean=70 and standard deviation =5

substitute all the values

[tex]z-score = \frac{80-70}{5} =2[/tex]

So, his z-score using mean and variance is 2

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Answer:

Kindly check explanation

Step-by-step explanation:

Given :

Interest amount paid on loan = $90

Principal value, amount borrowed = $500

Period, t = 16 days

The equivalent annual interest :

Using the simple interest formula :

simple interest = principal * rate * time

Using, days of year = 365

Plugging in the values into the formula :

90 = 500 * rate * (16/365)

90 = 500 * rate * 0.0438356

90 = 21.917808 * rate

Rate = 90 / 21.917808

Rate = 4.10 = 4.10 * 100% = 410%

If days of year = 360 is used :

90 = 500 * rate * (16/360)

Rate = 90 / 22.222

Rate = 4.05 = 4.105 * 100% = 405%

Answer:

A= ~2.55

Step-by-step explanation:

Using Pemdos, or gemdos, you can find you do the exponent first

4^2 = 16

then to everything else in left to right order since they're all multiplication or division

22/7 = ~3.14 * 13 = ~40.86/16 = ~2.55

(I'm using "~" to mean about/rounded to)

Answer:

[tex]8.19 \times 10^{4}[/tex] different playlists are possible

Step-by-step explanation:

The order in which the songs are played is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

6 songs, so 2 reggae(from a set of 5), 2 hip hop(from a set of 15) and 2 blues(from a set of 13). So

[tex]T = C_{5,2}C_{15,2}C_{13,2} = \frac{5!}{2!3!} \times \frac{15!}{2!13!} \times \frac{13!}{2!11!} = 10*105*78 = 81900[/tex]

In scientific notations:

4 digits after the first, which is 8, so:

[tex]8.19 \times 10^{4}[/tex] different playlists are possible

Answer:

B. How many total customers were at the story today?

Step-by-step explanation:

Option 'B' is not a statistical question because there is not more than one answer.

There is only one answer to this question.

Option 'A,' 'C,' and 'D' are statistical questions because there is more than one answer.

What amounts did each person at the store spend on their purchase?

This question has more than one answer.

How long did each customer spend shopping at the store?

What are the heights of each customer who entered the store?

These questions have more than one answer as well.

Statistical questions are questions that have more than one answer. This means you can collect data.

I, therefore, believe that option 'B' is not a statistical question.

The value of the money including inflation after 6 years will be $6510.64.

The rate at which prices grow over a specific time period is known as inflation. Inflation is often measured in broad terms, such as the general rise in prices or the rise in a nation's cost of living. But it may also be computed more precisely for some products, like food, or for services, like a haircut, for instance. In any situation, inflation refers to how much more costly the pertinent collection of products and/or services has grown over a predetermined time frame, most frequently a year.

Given that, Inflation is running at 1.1% per year when you deposit $5,000 in an account earning 4.4% compounded continuously.

deposit amount (P) = $ 5000

Rate (r) = 4.4 %

Time (t) = 6 years

Compound continuously

Amount (A)= 5000 e⁰°⁰⁴⁴ˣ ⁶

A = $ 6,510.64098

A = $ 6510.64

Total accumulated money after 6 years = $ 6,510.64

value of money decreases due to inflation

The real value of money after n years with the rate of inflation i = 1.1%

yₙ = A( 1 / (1+i) )ⁿ

y₆ = 6510.64 (1 / ( 1 + 0.011))⁶

y₆ = 6,097.008

Real value of money = $ 6,097.01

Therefore, after 6 years real value of the money including inflation will be $ 6,097.01.

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Answer: Yes

Step-by-step explanation:

Work Shown:

cos(angle) = adjacent/hypotenuse

cos(64) = x/28

x/28 = cos(64)

x = 28*cos(64)

x = 12.2743921100941

x = 12.27