Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of T Q is 16 and the length of R Q is 20.
What is the length of Line segment S R?

9 units
12 units
15 units
18 units

Answer:

He completes a lap running in 3 minutes, and walking in 4 minutes.

Step-by-step explanation:

This question can be solved by a system of equations.

I am going to say that:

x is the time needed to complete a lap running.

y is the time needed to complete a lap walking.

He requires 40 minutes to do 4 laps running and 7 laps walking.

This means that:

[tex]4x + 7y = 40[/tex]

[tex]4x = 40 - 7y[/tex]

He requires 18 minutes to do 2 laps running and 3 laps walking.

This means that

[tex]2x + 3y = 18[/tex]

Multipluing everything by 2

[tex]4x + 6y = 36[/tex]

Since [tex]4x = 40 - 7y[/tex]

[tex]40 - 7y + 6y = 36[/tex]

[tex]y = 4[/tex]

And

[tex]4x = 40 - 7y[/tex]

[tex]4x = 40 - 7*4[/tex]

[tex]4x = 12[/tex]

[tex]x = \frac{12}{4}[/tex]

[tex]x = 3[/tex]

He completes a lap running in 3 minutes, and walking in 4 minutes.

Answer:

4x+8=54 this is the correct answer

Answer:

[tex]\bar x =2.53[/tex] -- Mean

[tex]Median= 2[/tex]

[tex]Mode = 2[/tex]

[tex]Range = 8[/tex]

[tex]Q_1 = 1[/tex]

[tex]Q_3 = 3[/tex]

[tex]IQR = 2[/tex]

Step-by-step explanation:

Given

n = 30

Data: 2 3 1 2 6 4 2 1 5 3 2 3 1 2 2 1 3 1 2 2 4 2 1 2 9 3 2 1 1 3

Solving (a): The mean

This is calculated as:

[tex]\bar x =\frac{\sum x}{n}[/tex]

[tex]\bar x =\frac{2 +3 +1 +2 +6 +4 +2 +1 +5 +3 +2 +3+ 1+ 2 +2 +1 +3 +1 +2 +2 +4 +2 +1 +2 +9 +3 +2 +1 +1 +3}{30}[/tex]

[tex]\bar x =\frac{76}{30}[/tex]

[tex]\bar x =2.53[/tex]

Solving (b): The median

First arrange the given data

Arranged: 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 5 6 9

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

[tex]Median =\frac{1}{2}(30+1)[/tex]

[tex]Median =\frac{1}{2}(31)[/tex]

[tex]Median = 15.5th[/tex]

This implies that the median is the average of the 15th and 16th item

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

[tex]Median = \frac{4}{2}[/tex]

[tex]Median= 2[/tex]

Solving (c): The mode

From the given data; 2 has the highest frequency of 11.

So,

[tex]Mode = 2[/tex]

Solving (d): The Range

[tex]Range = Highest\ Data - Lowest\ Data[/tex]

The highest is 9 and the lowest is 1,

So:

[tex]Range = 9 - 1[/tex]

[tex]Range = 8[/tex]

Solving (e): Lower (Q1) and Upper (Q3) quartile.

Q1 is calculated as:

[tex]Q_1 = \frac{1}{4}(n+1)th[/tex]

[tex]Q_1 = \frac{1}{4}(30+1)th[/tex]

[tex]Q_1 = \frac{1}{4}(31)th[/tex]

[tex]Q_1 = 7.75th[/tex]

[tex]Q_1 = 8th\ item[/tex]

[tex]Q_1 = 1[/tex] -- from the arranged data

Q3 is calculated as:

[tex]Q_3 = \frac{3}{4}(n+1)th[/tex]

[tex]Q_3 = \frac{3}{4}(30+1)th[/tex]

[tex]Q_3 = \frac{3}{4}(31)th[/tex]

[tex]Q_3 = 23.25th[/tex]

[tex]Q_3 = 23rd\ item[/tex]

[tex]Q_3 = 3[/tex] -- from the arranged data

Solving (f): The interquartile range (IQR)

[tex]IQR = Q_3 - Q_1[/tex]

[tex]IQR = 3-1[/tex]

[tex]IQR = 2[/tex]

Answer:

Step-by-step explanation:

Evaluate means to see what value the equation has given x is 2

substitute x for 2 (write instead of x, write 2)

5x-2 will be 5*2-2 , calculate 5*2-2= 10-2 = 8

Answer:

y = (1/4) 2^x

Step-by-step explanation:

Remark

y = a * x^n is the general equation. Let's see what that means.

Solution

Solve for x

t_12 = a x^12

1024 = a x^12

t_8 = a x^8

64 = a x^8

Now divide the two equations.

1024/64 = a x^12/a x^8       Cancel out the as

1024 / 64 = x^12 / x^8

16 = x^(12 - 8)

16 = x^4                               Take the 4th root of both sides.

[tex]\sqrt[4]{x^4}[/tex]  =  [tex]\sqrt[4]{16}[/tex]

x = 2

Go back and solve for a

y_12 = a x^12

1024 = a 2^12

1024 = a 4096                   Divide by 4096

1024 / 4096 = a

a = 1/4

Problem 7

a) First of negative numbers are probably not a good idea. It means that the population is going to decrease. That's not what will happen if you take care of the fruit flies.

So for the domain, 0 is a good starting point.

That will give you 100 flies on day 0. That's how many you bought.

I'm not a biologist so I have no idea in the world how long a fruit fly will live even with the best of care. I'm going to try 60 days and see what happens.

y = 100 * 1.05 ^60

y = 100 * 18.68

y = 1868

Is this number reasonable? Even with the biggest olive jar you can find, and the best care, I don't think that number is realistic. It's too large. Eventually all will die of disease because they are living in their own waste. So Let's try 20 days

y = 100 * 1.05^20

y = 100 * 2.65

y = 265

That's a lot more reasonable. So for convenience sake let us say that 265 flies could live for 20 days

So to answer the question

The domain would be 0 to 20

The range would be 100 to 265

b)

2 weeks = 2*7 days

2 weeks = 14 days

y = 100 * 1.05^14

y = 100 * 1.98

y = 198 fruit flies.

Answer:

I chose a box of cereal-------> rectangular prism

see the attached figure

Part 1)List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).

Length: 20 cm

Width: 8 cm

Height: 32 cm

Part 2).

Describe the shape of the cross-section when the box is cut parallel to the base

the shape of the cross-section would be a rectangle of dimensions

20 cm x 8 cm

Part 3)

What is the surface area of the box?

surface area=2*area of the base+perimeter of the base*height

area of the base=20*8=160 cm²

perimeter of the base=2*[20+8]-----> 56 cm

height=32 cm

surface area=2*160+56*32------> 2,112 cm²

the answer part 3) is

2,112 cm²

Part 4)

What is the surface area of the box if it is scaled up by a factor of 10?

we know that

surface area of the larger box=[scale factor]²*surface area original box

scale factor=10

surface area original box=2,112 cm²

so

surface area of the larger box=10²*2,112-----> 211,200 cm²

the answer part 4) is

211,200 cm²

Part 5)

What is the volume of the box?

volume of the box=L*W*H-----> 20*8*32------> 5,120 cm³

the answer Part 5) is

5,120 cm³

Part 6)

What is the volume of the box if it is scaled down by a factor of 1/10

we know that

volume of the smaller box=[scale factor]³*volume original box

scale factor=1/10

volume original box=5,120 cm³

so

volume of the smaller box=[1/10]³*5,120-----> 5.12 cm³

the answer part 6) is

5.12 cm³

Step-by-step explanation:

Answer:

541/2 square

Step-by-step explanation:

we know that

the volume of the smaller box=[scale factor]³*volume original box

scale factor=1/10

volume original box=5,120 cm³

so

volume of the smaller box=[1/10]³*5,120-----> 5.12 cm³

the answer part 6) is 541/2 square

Answer: Polynomials like to be written in standard form. This means they contain no like terms and the exponents are in descending order (largest to smallest).

Step-by-step explanation:

Answer:

The control group is the group that takes the sugar pill

Step-by-step explanation:

In drug testing, to determine the efficacy of a drug, different groups of experimental subjects are recruited, one group is given the drug to be tested (treatment group) while another group is given a placebo.

A placebo is a fake version of the drug to be tested that does not have any therapeutic effect on the test subjects that receive it. In this case, the control group receives the placebo which is the sugar pill. They serve as the baseline of measurement when the outcome of the effect of the drug testing is done. The groups that received the actual drugs are compared against the groups that received the hoax treatment, and any change occuring  in the test subjects become the changes occuring as a result of the test drug used, when the observations on the control group has been ruled out.

Answer:

its 1 and 2

Step-by-step explanation:

first find A' which is(1,2,3) since these are in the universal set but not in A.

similary B' which is (1,2,5,6)

and since (1,2) are both in A' and B' set A'nB'=(1,2)

Answer:

Step-by-step explanation:

U={1,2,3,4,5,6,7}

A={4,5,6,7}

B={3,4,7}

A'={1,2,3}

B'={1,2,5,6}

A'∩B'={1,2}

Answer:

2528839

Step-by-step explanation:

your welcome

Answer:

4kg=4m/s

8kg=?

3m/s

Step-by-step explanation:

12kgm/s/4kg

Answer:

125

Step-by-step explanation:

25 × 5 = 125

x/5 = 25 × 5 = 125

x = 125

Answer: Sorry I don't know

Step-by-step explanation:

Answer:

Step-by-step explanation:

Equation of a line  representing the relation between distance from the peak of the mountain and time is,

h = mt + b

Here, m = Slope of the line

b = y-intercept

Since, slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

From the table attached,

Slope of the line passing through (2, 2600) and (5, 950) will be,

m = [tex]\frac{2600-950}{2-5}[/tex]

   = -550

Therefore, equation of the line will be,

h = -550t + b

Since, point (2, 2600) lies on this line,

2600 = -550(2) + b

b = 2600 + 1100

b = 3700

So, equation of the line will be,

h = -550t + 3700

Input - output values for this line,

t            2             4            6  

h        2600      1500       400  

Now we can plot these points and get the graph of the line.

Answer:

21/40.

Step-by-step explanation:

Find the LCD (Least Common Denominator) of the fractions. The LCD of 5/8 and 1/10 is 40.

Convert both fractions into denominators of 40.

So then we have: 25/40 - 4/40 which is equal to: 21/40.

21/40 is the estimated value of the expression  5/8 -1/10

A number system is defined as a system of writing to express numbers.

The given expression is 5/8 -1/10

The terms in the expression are in the form of fractions, A fraction represents a part of a whole.

To find the value of expression firstly find the LCM of 8 and 10

40 is the LCM

5(5)-1(4)/40

25-4/40

The value of 25 minus 4 is twenty one.

21/40 is the value of the expression  5/8 -1/10

Hence, 21/40 is the estimated value of the expression  5/8 -1/10

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ2

Answer:

is that even a question ?

Step-by-step explanation:

3/10x=294

x=294*10/3

x=980 students

if you found my answer helpful please mark as brainliest.

Answer:

X= -6

Step-by-step explanation:

7x = -42

(÷7) (÷7)

X = -6

Answer:

Boy I'm really boutta get to yo pickle chin ahh boy, egg head like collard greens head a//ss boy, oh hell nah boy yo dirt ahh boy stank ahh boy afro head ahh, lip gloss chin ahh boy ugly ahh boi

Step-by-step explanation:

Aawdadakdaw da  awdwa dadeefdcdcs

Answer:

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]

Step-by-step explanation:

Given

[tex]\frac{x - 20}{ x^2 + x - 20}[/tex]

Required

Decompose into partial fraction

Start by factorizing the denominator:

[tex]x^2 + x - 20 =x^2 + 5x -4x- 20[/tex]

[tex]x^2 + x - 20 =x(x + 5)-4(x+5)[/tex]

[tex]x^2 + x - 20 =(x-4)(x+5)[/tex]

So, we have:

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]

Take LCM

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A(x+5)+B(x-4)}{(x-4)(x+5)}[/tex]

Cancel out the denominator

[tex]x - 20 = A(x+5)+B(x-4)}[/tex]

Open brackets

[tex]x - 20 = Ax+5A+Bx-4B[/tex]

Collect Like Terms

[tex]x - 20 = Ax+Bx+5A-4B[/tex]

[tex]x - 20 = (A+B)x+5A-4B[/tex]

By comparison;

[tex](A +B)x = x[/tex] ==>[tex]A + B = 1[/tex]

[tex]5A - 4B = 1[/tex]

Make A the subject in [tex]A + B = 1[/tex]

[tex]A = 1 - B[/tex]

Substitute 1 - B for A in [tex]5A - 4B = 1[/tex]

[tex]5(1-B) -4B = 1[/tex]

[tex]5-5B -4B = 1[/tex]

[tex]5-9B = 1[/tex]

Collect Like Terms

[tex]-9B = 1 - 5[/tex]

[tex]-9B = - 4[/tex]

[tex]B = \frac{4}{9}[/tex]

[tex]A = 1 - B[/tex]

[tex]A = 1 - \frac{4}{9}[/tex]

[tex]A = \frac{9-4}{9}[/tex]

[tex]A = \frac{5}{9}[/tex]

So:

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]

Answer: only student 2

Answer:

di ko po alam ehh

Step-by-step explanation:

sorry po

Answer:

Step-by-step explanation:

What is the question?

Price reduced by $15

Percentage reduction = 15/60 = 0.25 = 25%

Answer:

4 hours

Step-by-step explanation:

Answer:

the answer of this question is

c

Answer:

Not sure if that is "9x" or "9 times" but I will do both. I have attached a picture of me solving and explaining the steps. Hope this helps, thank you !!

Step-by-step explanation:

ssshzvecucsussddyz wksoav

Answer:

X=6 To y=-6

y=-4 TO X = 4

꧁꧁꧁꧁꧂꧂꧂꧂

꧂꧂꧂꧂꧂

Answer:

(4 × 9) / 2 = 36/2 = 18 gitu yaaa

Answer:

18

Step-by-step explanation:

plug in r and s

4(9)/2

36/2

18

Answer:

-0.756

Step-by-step explanation:

N1 = 9

N2 = 9

Sd1 = 1.5 hours

Sd2 = 1.3 hours

X1 = 5 hours

X2 = 5.5 hours

Hypothesis

H0: mu1 - mu2 = 0

H1 : mu1 - mu2 not equal to 0

Test statistic

t = (x1 - x2)/SE

SE is the standard error, which is unknown

SE = √sd1²/n1 + sd2²/n2

= √1.5²/9 + 1.3²/9

= √0.25+0.1878

= √0.4378

= 0.66166

t statistics = (5-5.5)/0.66166

= -0.5/0.66166

= -0.756