Find the distance using the modulus of the difference between z1 = -8 + 3i and z2 = 7 - 4i.

Answer:

88/27 or 3 7/27  in^2

Step-by-step explanation:

Multiply the length and width together:

2 2 /3 times 1 2 /9

We could either convert these measurements to improper fractions and then multiply, or we could use a calculator:  2+(2/3) ENTER x (1 + 2/9) ENTER.

Result:  3.259 in^2 (approximately) or 88/27 in^2 (exact answer)

Answer:

Area of circle = 201.09 ft²

Step-by-step explanation:

Given the following data;

Radius, r = 8 ft

To find the area of the circular area;

Area of circle = πr²

Area of circle = 3.142 * 8²

Area of circle = 3.142 * 64

Area of circle = 201.09 ft²

Therefore, the measurement which is closest to the area is 201.09 square feet.

Answer:

7/25

Step-by-step explanation:

In simpler words, the problem wants us to find the probability of choosing a student that both play a sport and takes a foreign language.

To find this, we need to locate the intersection in the Venn diagram which is

14.

The intersection represents the number of students that both play a sport and take a foreign lang.

We have our favorable outcomes of 14.

Our total outcomes can be found by adding all the numbers like so:

23+14+10+3=50

The theoretical probability theorem is:

Number of favorable outcomes/number of total outcomes.

So our answer is 14/50, or simplified as 7/25!

Hope it helps! :))

Answer:

a

Step-by-step explanation:

Answer:

[tex]b = 90[/tex]

[tex]c=80[/tex]

[tex]d =100[/tex]

Step-by-step explanation:

Given

See attachment

Required

Find b, c and d

First, we solve for b using:

[tex]b + 10 + b - 10 = 180[/tex] --- base angles of a parallelogram

Collect like terms

[tex]b + b =180+10-10[/tex]

[tex]2b = 180[/tex]

Solve for b

[tex]b = 180/2[/tex]

[tex]b = 90[/tex]

Then, we have:

[tex]d =b + 10[/tex]

[tex]c = b - 10[/tex] --- opposite angles

So, we have:

[tex]d =90 + 10[/tex]

[tex]d =100[/tex]

[tex]c = 90 - 10[/tex]

[tex]c=80[/tex]

Answer:

2/3 > 2/5 > 1/4

Step-by-step explanation:

Lucia - 2/3 - 40/60

Allie - 1/4 - 15/60

Carolina -  2/5 - 24/60

( in this case 60 is the LCM)

least to greatest

15/60 < 24/60 < 40/60

Hope this helps!

Answer:

2308.39 m³

Step-by-step explanation:

The formula of volume of sphere

[tex] = \frac{4}{3} \pi {r}^{3} [/tex]

The volume of the sphere

[tex] = \frac{4}{3} \times 3.14 \times {(16.4 \div 2)}^{3} [/tex]

[tex] = \frac{4}{3} \times 3.14 \times {8.2}^{3} [/tex]

[tex] = \frac{6925.18208}{3} [/tex]

[tex] = 2308.394027...[/tex]

= 2308.39 m³ (rounded to the nearest hundredth)

Answer:

A

Step-by-step explanation:

area = [tex]\pi r^{2}[/tex]

circumference = [tex]2\pi r[/tex]

[tex]r^{2} = 4\\\sqrt{r^{2}} =\sqrt{4} \\r = 2[/tex]

[tex]2\pi (2) = 4\pi[/tex] [tex]yd[/tex]

Answer:

Sum of Squares=50.5

Treatment Sum of Squares, 4.5

Error Mean Squares, 0.3

Treatment Mean Squares 0.9

Error Sum of Square = 3

Step-by-step explanation:

Given data

Observation A B C

1                8 7 10

2                7 7 11

3                6 6 10

4                7 6 9

5               8 7 10

6                6 6 10

A B C Row total (xr)

1 8 7 10 25

2 7 7 11 25

3 6 6 10 22

4 7 6 9 22

5 8 7 10 25

6 6 6 10 22

Col total (xc) 42 39 60 141

Using calculator for summarizing data

∑x²=1155 ⇒(A)

∑x²c/r=16(42²+39²+60²)

=1/6(1764+1521+3600)

=1/6(6885)

=1147.5⇒(B)

∑x²r/c=13(25²+25²+22²+22²+25²+22²)

=1/3(625+625+484+484+625+484)

=1/3(3327)

=1109⇒(C)

(∑x)²/n=(141)²/18

=19881/18

=1104.5⇒(D)

Sum of squares total

SST=∑x²-(∑x)²/n=(A)-(D)

=1155-1104.5

=50.5

Sum of squares between rows

SSR=∑x²r/c-(∑x)²/n=(C)-(D)

=1109-1104.5

=4.5

Sum of squares between columns

SSC=∑x²c/r-(∑x)²n=(B)-(D)

=1147.5-1104.5

=43

Sum of squares Error (residual)

SSE=SST-SSR-SSC

=50.5-4.5-43

=3

ANOVA table

Source                     Sums         Degrees of           Mean Squares

of Variation        of Squares          freedom                                 F- value

                                      SS                DF                  MS              

Between Treatments SSR=4.5      r-1=5        MSR=0.9              3

Between Blocks          SSC=43     c-1=2       MS =21.5      71.6667

Error (residual)         SSE=3    (r-1)(c-1)=10        MSE=0.3  

Total                    SST=50.5      rc-1=17                                  

Answer:

7 meters by 5 meters, or vice versa

Step-by-step explanation:

p = 24 meters

a = 35 meters²

Formula for perimeter = l + l + w + w

Formula for area = l · w

7 and 5 are the only values where the rules are satisfied.

x + x + y + y = 24

7 + 7 + 5 + 5 = 24

14 + 10 = 24

x · y = 35

7 · 5 = 35

Answer:

The answers are 47 &12 for "q" & "△" respectively

Answer:

24 hours

Step-by-step explanation:

2+4+2 hours on Friday, Saturday, Sunday =8 hours per weekend

8 hours per weekend x 3 weekends = 24 total hours.

Answer:

102

Step-by-step explanation:

Answer:

Height of triangle = 16 meter

Step-by-step explanation:

Given:

Area of given triangle = 96 squares meter

Base length of triangle = 12 meter

Find:

Height of triangle

Computation:

Area of triangle = (1/2)(b)(h)

Area of given triangle = (1/2)(Base length of triangle)(Height of triangle)

96 = (1/2)(12)(Height of triangle)

96 = (6)(Height of triangle)

Height of triangle = 96 / 6

Height of triangle = 16 meter

Answer:

535.29

Step-by-step explanation:

If you multiply 400 by 1.06 five times, you get 535.29.

400*1.06=424

424*1.06=449.44

449.44*1.06=476.4

476.4*1.06=504.99

504.99*1.06=535.29

Hope that this helps!

Answer:

See the arrangement below

Step-by-step explanation:

Given the expression

2x^2+x - 9 = 4x

Step 1: Write in standard form

2x^2 + x - 9 - 4x = 0

2x^2 + x - 4x - 9 = 0

2x^2 - 3x - 9 = 0

Step 2; identify the coefficients

The standard quadratic expression is ax^2+bx+c = 0

a = 2, b = -3, c = -9

Step 3: Using the general formula to find the roots

x = -b±√b²-4ac/2a

x = -(-3)±√(-3)²-4(2)(-9)/2(2)

Step 4: simplify

x =  -(-3)±√(-3)²-4(2)(-9)/2(2)

x = 3 ±√9+72/4

Step 5; Find the roots

x = 3 ±√81/4

x = 3 ±9/4

x = 3+9/4 and 3-9/4

x = 12/4 and -6/4

x = 3 and -3/2

Answer:

d

Step-by-step explanation:

Answer:

[tex]2 \times \pi \: \times r[/tex]

is the circumference of the circle

Answer:

Step-by-step explanation:

If the radius of a circle is r cm then

circumference = 2πr

Answer:

The value of X is 4, and the area of the triangle is [tex]60^2 units[/tex].

Step-by-step explanation:

First we need to add up all the sides. Doing so will give us the equation [tex]8x+8=40[/tex]. Subtracting 8 from both sides will give us [tex]8x=32[/tex]. Next we divide both sides by 8 in order to isolate the variable, which gives us [tex]x=4.[/tex]

This gives us 4 as our value of x.

Now we need to find the area. Substituting x into the values for base and height will give us 8+7 = 15 for our height, and 4+4=8 for our base. 15*8 is 120, and divided by two gives us 60 as out area.

Thus, x=4 and area=60.

Good day from NightyKnight.

Answer:

The calculated χ² = 21.455       falls in the critical region χ² ≥  7.815  so we reject the null hypothesis that the type of hard drive and the store where the computers were bought are dependent and accept the claim the type of hard drive and the store where the computers were bought are independent.

Step-by-step explanation:

1) We set up our null and alternative hypothesis as

H0: the type of hard drive and the store where the computers were bought are dependent

against the claim

Ha: the type of hard drive and the store where the computers were bought are independent

2) the significance level alpha is set at 0.05

3) the test statistic under H0 is

χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency

which has an approximate chi square distribution with ( 4-1) (2-1)=  3 d.f

4) Computations:

Using the calculator we summarize the results as

Under H0 , the observed frequencies are :

Observed         Expected  E        χ²= (O-E)²/E

13                          (23.58)            [4.75]                

11                           (10.63)             [0.013]                  

19                          (14.69)              [1.264]

9                            (3.09)              [11.282]

109                       (98.42)              [1.138]

44                          (44.37)            [0.003]

57                           (61.31)               [0.303]

7                             (12.91)               [2.703]                            

∑                                                            21.455        

5) Conclusion:

The calculated χ² = 21.455       falls in the critical region χ² ≥  7.815  so we reject the null hypothesis that the type of hard drive and the store where the computers were bought are dependent and accept the claim the type of hard drive and the store where the computers were bought are independent.

The p-value is .000085.

The result is significant at p < .05 meaning the claim is accepted.

Answer:

first one

Step-by-step explanation:

is at least

Answer:

4544

Step-by-step explanation:

Answer:

They each get 1/6

Step-by-step explanation:

Answer:

[tex](a)\ (1,5)[/tex]

Step-by-step explanation:

Given

[tex](x + 9)^2 + (y - 4)^2 = 101[/tex]

Required

Which of the points does it pass through

To do this, we simply substitute the values of x and y in the above equation.

So, we have:

[tex](a)\ (1,5)[/tex]

[tex](x + 9)^2 + (y - 4)^2 = 101[/tex]

[tex](1 + 9)^2 + (5 - 4)^2 = 101[/tex]

Solve each bracket

[tex]10^2 + 1^2 = 101[/tex]

[tex]100 + 1 = 101[/tex]

[tex]101 = 101[/tex]

The above equation is true,

Hence, it passed through [tex](1,5[/tex])

We do not need to check for others

Answer:

C. Rectangle

Step-by-step explanation:

Hope it helps you in your learning process.

Answer:

c                                                    

Step-by-step explanation:

Answer:

3.5944

Step-by-step explanation:

first the fraction is mixed and you need to change the fraction to proper or improper fraction

the denominator 4 is multiply 16

16×4=64

then the numerator 3 is add to 64

64+3=67

the fraction will be

=====67/4

the denominator is not change from the first part

》》do the same thing by the other mixed fraction

the final answer would be 3.5944

first calculate 67÷4=16.75

the second calculate 14÷3=4.66

in the second part i get 14/3 that means i change the mixed fraction to the normal fraction

calculate 16.75÷4.66=3.5944