Differential Equations and Slope Fields

Answer:

102

Step-by-step explanation:

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:

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:

Surface area of triangular pyramid = 48 inch²

Step-by-step explanation:

Given:

Base length of triangle = 6 inches

Height of triangle = 4 inches

Find:

Surface area of triangular pyramid

Computation:

Surface area of triangular pyramid = 4 x [Surface area of triangle]

Surface area of triangular pyramid = 4 x [(1/2)(b)(h)

Surface area of triangular pyramid = 4 x [(1/2)(6)(4)

Surface area of triangular pyramid = 4 x [(1/2)(24)]

Surface area of triangular pyramid = 4 x 12

Surface area of triangular pyramid = 48 inch²

Answer:

C. Rectangle

Step-by-step explanation:

Hope it helps you in your learning process.

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:

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:

They each get 1/6

Step-by-step explanation:

Answer:

srry I can't answer this question it's kinda of hard to solve srry

Answer:

A) y = x²- x

Step-by-step explanation:

A linear function will have y equal to x, without x being manipulated by a square root, exponent, etc.

y = x²- x has x being squared.

This will create a graph of a parabola, which is not linear.

So, since it is a quadratic instead of a line, answer choice A) y = x²- x is correct.

Answer:

d

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:

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:

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:

a

Step-by-step explanation:

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:

c                                                    

Step-by-step explanation:

Answer:

first one

Step-by-step explanation:

is at least

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:

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:

4544

Step-by-step explanation:

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:

[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:

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:

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:

[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]