If mCD = 60 and m
find mAB!

Answer:

n = 7

Step-by-step explanation:

Varies directly

w/n² = k

---------------------------

when n = 3, W = 117

k =117/3²

k = 117/9

k = 13

-------------------------

Find n when W = 637

637/n² = 13

637 /13 = n²

49 = n²

7 = n

Answer:

the 99% confidence interval for the true mean number of mosquitos caught in all mosquito traps is ( 667.81, 732.19 )

Step-by-step explanation:

Given the data in the question;

sample mean x' = 700

sample size n = 64

the standard deviation σ = 100

99% confidence interval for the true mean number of mosquitos caught in all mosquito traps = ?

significance level ∝ = 1 - 99% = 1 - 0.99 = 0.01

∝/2 = 0.01 / 2 = 0.005

Z-critical [tex]Z_{\alpha /2[/tex] = 2.575 { from table }

So, to get the 99% confidence interval;

⇒ x' ± [tex]Z_{\alpha /2[/tex] ( σ / √n )

we substitute

⇒ 700 ± 2.575 ( 100 / √64)

⇒ 700 ± 2.575( 12.5 )

⇒ 700 ± 32.1875

⇒ ( 700 - 32.1875 ), ( 700 + 32.1875 )

⇒ ( 667.81, 732.19 )

Therefore,  the 99% confidence interval for the true mean number of mosquitos caught in all mosquito traps is ( 667.81, 732.19 )

Answer:

[tex]c=\frac{ab}{a+b}[/tex]

Step-by-step explanation:

To solve for [tex]c[/tex], our goal is to isolate it.

Start by multiply both sides by [tex]ab[/tex]. That way, we'll still have only one term with [tex]c[/tex], but we'll be able to get rid of two messy fractions.

[tex]b+a=\frac{ab}{c}[/tex]

Taking the reciprocal of both sides:

[tex]\frac{1}{a+b}=\frac{c}{ab},\\c=\boxed{\frac{ab}{a+b}}[/tex]

*Note: You cannot take the reciprocal of both sides if you're adding fractions. This is why we can't just take the reciprocal of both sides in the initial equation.

Alternate solution:

[tex]\frac{1}{a}+\frac{1}{b}=\frac{b}{ab}+\frac{a}{ab}=\frac{1}{c},\\\\\frac{b+a}{ab}=\frac{1}{c},\\\\c=\frac{ab}{b+a}=\boxed{\frac{ab}{a+b}}[/tex]

Answer:

c=ab

a+b

Step-by-step explanation:

1 + 1= 1

a. b. c

a+b = c

ab

a+b= ab

c

ac+bc=ab

c(a+b)=ab

c(a+b)=ab

a+b. a+b

c=ab

a+b

Answer:

2 times length of AB

Step-by-step explanation:

Given

[tex]AB =50\%[/tex]

Required

Length of line with 100%

To get the length of line segment that is 100%, simply multiply AB by 2

i.e.

[tex]2 * AB =2 * 50\%[/tex]

[tex]2 AB =100\%[/tex]

Assume AB = 5cm (at 50%). The length at 100% will be 10cm i.e. 2 * 5cm

Answer:

twenty-four nights

Step-by-step explanation:

597 divided by 25 will give you 23.88 which i rounded up to 24.

Answer:

450 foe

Step-by-step explanation:

Answer:

33.30 units²

Step-by-step explanation:

Central angle = m<BCD = 106°

Radius (r) = 6 units

Area of sector BCD = central angle/360° × πr²

Plug in the values into the formula

Area of sector BCD = 106/360 × π × 6²

Area of sector BCD = 106/360 × π × 36

Area of sector BCD = 33.3008821

Area of sector BCD = 33.30 units² (nearest hundredth)

Answer:

20

Step-by-step explanation:

[tex]15^2+b^2=25^2\\225+b^2=625\\625-225=b^2\\b^2=400\\\sqrt{400}=20[/tex]

Answer:

Option B

Step-by-step explanation:

It's clear from the graph attached,

ΔABC has been dilated and shifted downwards.

Length of segment AB = 2 units

Length of segment DE = 4 units

Scale factor by which the dilation has been done = [tex]\frac{\text{Dimension of the image triangle}}{\text{Dimension of the original triangle}}[/tex]

Scale factor = [tex]\frac{DE}{AB}[/tex]

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

                    = 2

Therefore, triangle ABC is dilated by a scale factor of 2 about the origin.

Lets consider a point B(0, 0) from the given graph and analyze the transformations done.

If a point B(0, 0) is shifted to point E(0, -10) which follows the rule,

B(0, 0) → E(0 + h, 0 + k)

Here, 'h' and 'k' are the translations of the given point over x-axis and y-axis.

Therefore, (0 + h) = 0 ⇒ h = 0

0 + k = -10

k = -10

Hence, triangle ABC has been dilated by a scale factor of 2 centered at origin and followed by the translation (x, y - 10)

Option B is the correct option.

Answer:

c

Step-by-step explanation:

I think it is c

Answer:

21.142

Step-by-step explanation:

not sure it's correct

Answer:

1,406

Step-by-step explanation:

p = a(1 + r)^t

p = 1,236(1.013)^10

p = 1,406.4131692427

p = 1,406

Answer:

40π in^2

Step-by-step explanation:

360°/72°=5

so, each of the two shaded regions are 1/5 of the circle.

the formula for finding the area of a circle is πr^2, so:

area for one of the shaded regions:

1/5πr^2

1/5π(10)^2

1/5π100

20π in^2

this means that the area for one of the shaded regions is 20π. however, since there are two of them:

2(20π)=40π

so, the area of the shaded regions is 40πin^2

Answer:

24.4

Step-by-step explanation:

Given the data :

Month (X) : 0, 1, 2, 4, 6

Weight (Y) : 7.2, 9.4, 10.5, 13.2, 15.9

To obtain the predicted weight at 1 year, we fit the data to obtain the regression model. Using technology, the regression model obtained is :

y = 7.6 + 1.4X1

Substituting x = 1 year into the regression model, we obtained the predicted weight at 1 year ;

1 year = 12 months, hence, x = 12

y = 7.6 + 1.4(12)

y = 7.6 + 16.8

y = 24.4

Answer:

Area of the sector : D.

3π cm²

Answer:

0=0  1=1   2=0  3=0  4=1   5=3   6=1   7=0   8=0   9=1   10=2   11=1   12=2   13=0   14=0   15=3   16=0

Step-by-step explanation:

There was no question so here above is the Dollars spent graph in numbers not dots!

- 3 is for vertical displacement sis.

( Sorry about my bad graphing and bad quality of the pic )

Answer: Alice returns on Wednesday, 3 pm.

Step-by-step explanation: One day is 24 hours long. 55 hours is 2 days and 7 hours. So Alice comes back home on Wed  , add 8 am 7 hours and you get 3 pm

The time that Alice would arrive home from the sponsored walk given the the time she starts the walk is Wednesday by 3pm.

The first step is to divide 55 hours into days. This can be done by dividing 55 hours by 24.

55/24 = 2 days 7 hours

The second step is to add 2 days 7 hours to 8am: Monday 8am + 2 days 7 hours = Wednesday 3pm

To learn more about how to calculate time, please check: https://brainly.com/question/26290873

Answer:

[tex] {f}^{ - 1} (x) = 2x - 8[/tex]

[tex] {f}^{ - 1} (4) = 0[/tex]

Step-by-step explanation:

[tex] y = \frac{1}{2} x + 4 = = = > \\y - 4 = \frac{1}{2} x = = = > \\ 2y - 8 = x = = > {f}^{ - 1} (x) = 2x - 8[/tex]

[tex] \frac{1}{2} x + 4 = 4 = = = > \\ \frac{1}{2} x = 0 = = = > x = 0[/tex]

Answer:

What are the original demensions?

Step-by-step explanation:

Answer:

40 cookies was sold

Step-by-step explanation:

Let x represent the number of cakes baked, y represent the number of cookie baked and z represent the number of buns baked.

He made 270 cakes. Therefore x = 270

28% of the total baked products where cookies, hence:

0.28(270 + y + z) = y

75.6 + 0.28z = 0.72y

0.72y - 0.28z = 75.6      (1)

The number of cakes was three times the number of buns. Hence:

x = 3z

3z = 270

z = 90

Put z = 90 in equation 1:

0.72y - 0.28(90) = 75.6

0.72y -25.2 = 75.6

y = 140

Therefore 270 cakes was baked, 140 cookies was baked and 90 buns was baked.

He sold 40 buns and 120 cakes, the number of buns and cakes left is 50 buns and 150 cakes. Let us assume that number of cookies left was a. Since the ratio of left buns to cakes to cookies is 1:3:2. Hence:

(1/6) * (50 + 150 + a) = 50

300 = 200 + a

a = 100

Therefore 100 cookies was left. The number of sold cookies = 140 - 100 = 40

Answer:

i know there's a lot of explanation. but it helps u for sure :)

Step-by-step explanation:

1)

[tex]-7 \ and \ \frac{1}{3} = \frac{-7}{1} \ and \ \frac{1}{3}\\\\LCM \ of \ 1 \ and\ 3 = 3\\\\\frac{-21}{3} \ and \ \frac{1}{3}\\\\To \ find \ rational \ numbers \ between \ \frac{-21}{3} \ and \ \frac{1}{3} \ write \ any \ number \ between \ -21 \ and \ 1 \ with \ denominator \ 3. \\\\That \ is, \ \frac{-20}{3}, \frac{-19}{3}, \frac{-18}{3}.....[/tex]

2)

[tex]\frac{5}{9} \ and \ \frac{2}{3}\\\\Similarly \ take \ LCM \ of \ 9 \ and \ 3 = 9\\\\Since \ it \ is \ still \ complicated \ to \ find \ rational \ number \ between \ \frac{5}{9} \ and \ \frac{6}{9},[/tex]

[tex]because \ there \ exists \ no\ natural \ number \ between \ 5 \ and \ 6.[/tex]

[tex]We \ will \ multiply \ numerator \ and \ denominator\ by\ 10. \\\\Therefore\ \frac{5}{9} \ and \ \frac{6}{9} \ becomes \ \frac{50}{90} \ and \ \frac{60}{90}.[/tex]

[tex]Keeping \ denominator \ 90 \ write \ numbers \ from \ 50 \ to \ 60 \ in \ the\ numerator.\\\\That \ is , \frac{51}{90}, \frac{52}{90}, \frac{53}{90}, \frac{54}{90}, .\ .\ .[/tex]

3)

[tex]LCM \ of \ 5 \ and \ 7 = 35\\\\\frac{-2}{5} \ and \ \frac{-3}{7}\ becomes \ \frac{-14}{35} \ and \ \frac{-15}{35}\\\\Now \ multiply \ denominator \ and \ numerator \ by \ 10\\\\\frac{-140}{350} \ and \ \frac{-150}{350}.\\\\Rational \ numbers \ are \frac{-141}{350}, \frac{-142}{350}, \frac{-143}{350}, . \ . \ . \[/tex]

Tip :

1. Make the denominator same.

2. Multiply numerator and denominator by 10 , 100 or 1000

3. Just write the natural numbers between the 2 numerators keeping denominator same.

Answer:

0.2005

Step-by-step explanation:

Mean, m = 65000

Standard deviation, σ= 7000

Sample size, n = 25

Let X = random variable of salary

Recall:

Z = (μ - x) /(σ/√n)

P(62500 ≤ x ≤ 64000) =?

Pr((65000 - 62500)/7000/√25 ≤ z ≤ (65000 - 64000) / 7000/√25)

P(2500 / 1400 ≤ z ≤ 1000/1400)

P = (1.79 ≤ z ≤ 0.714)

Using the normal distribution table or a Z probability calculator

0.4633 - 0.2624

= 0.2009

Answer:

2 gallons and 1/2

Step-by-step explanation:

You just have to subtract 1/2 from 3.

3 - 1/2 = 2 1/2

or

3 - .5 = 2.5

And 2 1/2 is how much more he served.

Answer: 5 times more hot chocolate

Step-by-step explanation:

The entire group about which you want to draw conclusions is referred to as a population. A sample is a subset of the population from which you will collect data. The sample size is always smaller than the population's total size. A population in research does not always refer to people.

Answer:

B) 2meter line segment

Step-by-step explanation:

3.28ft=1m

Then an easy way to find the answer is to multiply 3.28 by 2

to if the 6.3ft line is under or over 2m

3.28 multiplied by 2 equals 6.56

6.56>6.3

therefore, the 6.3ft. line segment is just a little shorter than 2m

Answer:

C 4:7 and 12:21

Step-by-step explanation:

4×3 => 12

7×3 => 21

Answer:

One hundred thousand

Step-by-step explanation:

It would be one hundred thousand because 10*10*10*10*10 is 100,000, hence 100,000 would be, well, one hundred thousand.

Answer:

ten times ten times ten times ten times ten or one hundred thousand

Step-by-step explanation: