A plane flies 1.4 hours at 150 mph on a bearing of 10. It then turns and flies hours at the same speed on a bearing of . How far is the plane from its starting​ point?

Answer:

a) k = 0.00012491389

b) The Shroud of Turin was 755 years old at the time of this data.

Step-by-step explanation:

(a) Find the value of the constant k in the differential equation C' = -kC.

First we find the differential equation, by separation of variables. So

[tex]\int \frac{C^{\prime}}{C} dt = -\int k dt[/tex]

So

[tex]\ln{C} = -kt + K[/tex]

In which K is the constant of integration, representing the initial amount of substance. So

[tex]C(t) = C(0)e^{-kt}[/tex]

Half-life of 5549 years.

This means that [tex]C(5549) = 0.5C(0)[/tex]. We use this to find k. So

[tex]C(t) = C(0)e^{-kt}[/tex]

[tex]0.5C(0) = C(0)e^{-5549k}[/tex]

[tex]e^{-5549k} = 0.5[/tex]

[tex]\ln{e^{-5549k}} = \ln{0.5}[/tex]

[tex]-5549k = \ln{0.5}[/tex]

[tex]k = -\frac{\ln{0.5}}{5549}[/tex]

[tex]k = 0.00012491389[/tex]

So

[tex]C(t) = C(0)e^{-0.00012491389t}[/tex]

(b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained 91% of the amount of carbon-14 contained in freshly made cloth of the same material. How old was the Shroud of Turin at the time of this data?

This is t for which [tex]C(t) = 0.91C(0)[/tex]

So

[tex]C(t) = C(0)e^{-0.00012491389t}[/tex]

[tex]0.91C(0) = C(0)e^{-0.00012491389t}[/tex]

[tex]e^{-0.00012491389t} = 0.91[/tex]

[tex]\ln{e^{-0.00012491389t}} = \ln{0.91}[/tex]

[tex]-0.00012491389t = \ln{0.91}[/tex]

[tex]t = -\frac{\ln{0.91}}{0.00012491389}[/tex]

[tex]t = 755[/tex]

The Shroud of Turin was 755 years old at the time of this data.

Answer:

P( fraction) = 1/2

P ( percent) = 50%

P ( decimal) = .5

Step-by-step explanation:

The possible outcomes on  a six sided cube are 1,2,3,4,5,6

Multiples of 2 are  2,4,6

P( multiple of 2) = number of multiples of 2 / total outcomes

                           = 3/6 = 1/2

P( fraction) = 1/2

P ( percent) = 50%

P ( decimal) = .5

Answer:

B

Step-by-step explanation:

When we reflect something across the y axis, the y axis stays the same but the x values change by a factor of -1.

B is the Answer

Answer:

c. switch the x-values and y-values in the table

Step-by-step explanation:

For any table or graph reflection over the line y=x

The rule is (x,y) ----> (y,x)

f(x) is reflected over the line y=x, so the coordinates of f(x) becomes

(-2,-31) becomes (-31,-2)

(-1,0) becomes (0,-1)

(1,2) becomes (2,1)

(2,33) becomes (33,2)

As per the rule, we switch the x-values and y-values in the table

For reflection over the line y=x , the coordinate becomes

(-31,-2)

(0,-1)

(2,1)

(33,2)

Answer:

w= 103.5 inches

Step-by-step explanation:

384=w+3w-30

414=4w

w=414/4=103.5 inches

Answer:

first drop box 384

second drop box 3

third drop boc 30

384 = 3 [tex]w^{2}[/tex] – 30 w

Step-by-step explanation:

Correct answer on Plato/Edmentum test

Answer/Step-by-step explanation:

2. a. 5y - 3 = -18

Add 3 to both sides

5y - 3 + 3 = -18 + 3

5y = -15

Divide both sides by 5

5y/5 = -15/5

y = -3

b. -3x - 9 = 0

Add 9 to both sides

-3x - 9 + 9 = 0 + 9

-3x = 9

Divide both sides by -3

-3x/-3 = 9/-3

x = -3

c. 4 + 3(z - 8) = -23

Apply the distributive property to open the bracket

4 + 3z - 24 = -23

Add like terms

3z - 20 = -23

Add 20 to both sides

3z - 20 + 20 = - 23 + 20

3z = -3

Divide both sides by 3

3z/3 = -3/3

z = -1

d. 1 - 2(y - 4) = 5

1 - 2y + 8 = 5

-2y + 9 = 5

-2y + 9 - 9 = 5 - 9

-2y = -4

-2y/-2 = -4/-2

y = 2

3. First, find the sum of 3pq + 5p²q² + p³ and p³ - pq

(3pq + 5p²q² + p³) + (p³ - pq)

3pq + 5p²q² + p³ + p³ - pq

Add like terms

= 3pq - pq + 5p²q² + p³ + p³

= 2pq + 5p²q² + 2p³

Next, subtract 2pq + 5p²q² + 2p³ from 3p³ - 2p²q² + 4pq

(3p³ - 2p²q² + 4pq) - (2pq + 5p²q² + 2p³)

Apply distributive property to open the bracket

3p³ - 2p²q² + 4pq - 2pq - 5p²q² - 2p³

Add like terms

3p³ - 2p³ - 2p²q² - 5p²q² + 4pq - 2pq

= p³ - 7p²q² + 2pq

4. Perimeter of the rectangle = sum of all its sides

Perimeter = 2(L + B)

L = (5x - y)

B = 2(x + y)

Perimeter = 2[(5x - y) + 2(x + y)]

Perimeter = 2[5x - y + 2x + 2y]

Add like terms

Perimeter = 2(7x + y)

Substitute x = 1 and y = 2 into the equation

Perimeter = 2(7(1) + 2)

Perimeter = 2(7 + 2)

Perimeter = 2(9)

Perimeter = 18 units

5. First let's find the quotient to justify if the value we get is greater than or less than 2.25

7⅙ ÷ 3⅛

Convert to improper fraction

43/6 ÷ 25/8

Change the operation sign to multiplication and turn the fraction by the left upside down.

43/6 × 8/25

= (43 × 8)/(6 × 25)

= (43 × 4)/(3 × 25)

= 172/75

≈ 2.29

Therefore, the quotient of 7⅙ ÷ 3⅛ is greater than 2.25

Answer:

The circumference and diameter of a circle

Step-by-step explanation:

Proportional relationships can be written as [tex]y=kx[/tex], where [tex]k[/tex] is some constant of proportionality. The formula for a circumference of a circle can be written as [tex]C=d\pi[/tex], where [tex]d[/tex] is the diameter of the circle. Therefore, the constant of proportionality is [tex]\pi[/tex] and the circumference and diameter of a circle are in a proportional relationship.

Answer:

w = 5

y = 4

Step-by-step explanation:

w+y=9

3w-y=11

4w = 20

w = 5

y = 4

Answer:

a AND ~c

Step-by-step explanation:

you can find the full explanation in wikipedia:

https://en.m.wikipedia.org/wiki/Material_conditional

under "Negated conditionals"

Answer:

0.0228 = 2.28% probability that a one-month old girl will be categorized as having microcephaly

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.

Medscape defines microcephaly (small head syndrome) as a head circumference that is more than two standard deviations below the mean. What is the probability that a one-month old girl will be categorized as having microcephaly?

Probability of a z-score of -2 or less, which is the p-value of Z = -2.

Looking at the z-table, Z = -2 has a p-value of 0.0228.

0.0228 = 2.28% probability that a one-month old girl will be categorized as having microcephaly

Answer:

Step-by-step explanation:

A). Volume of a rectangular prism = Length × Width × Height

                                                        = lwh

1). Volume of a rectangular prism if the measures of the sides are,

    Length (l) = 9 cm

    Width (w) = 4 cm                                              

    Height (h) = 3 cm                                            

    Therefore, volume = lwh

                                   = 9 × 4 × 3

                                   = 108 cm³

2). Length = 10 cm

     Width = 7 cm

     Height = 15 cm

     Volume = lwh

                   = 10 × 7 × 15

                   = 1050 cm³

3). Length = 14 cm

    Width = 10 cm

    Height = 9 cm

    Volume = 14 × 10 × 9

                  = 1260 cm³

B. Volume of a cube = (Side)³

4). If the measure of one side = 12 cm

    Volume of the cube = (12)³

                                      = 1728 cm³

5). If the measure of one side = 6 cm

   Volume of the cube = (6)³

                                     = 216 cm³

Answer:

4/3

Step-by-step explanation:

Substitute in 4.

(1/3)4

Multiply

4/3

I hope this helps!

Answer:

36

Step-by-step explanation:

2x is an exterior angle

Exterior angles = the sum of the two remote (unconnected - non supplementary interior angles).

Put symbolically

<LEG = <EGF + <EFG

<EFG = 180 - 4x           In this case you need to find the supplemtnt

<LEG = x + 180 - 4x

2x = 180 - 3x                Add 3x to both sides

5x = 180                       Divide by 5

x = 36

Answer:

[tex]-\dfrac{2}{17} + \dfrac{9}{17}i[/tex]

Step-by-step explanation:

[tex] (2 + i) \div (1 - 4i) = [/tex]

[tex] = \dfrac{2 + i}{1 - 4i} [/tex]

[tex] = \dfrac{2 + i}{1 - 4i} \times \dfrac{1 + 4i}{1 + 4i} [/tex]

[tex] = \dfrac{(2 + i)(1 + 4i)}{(1 - 4i)(1 + 4i)} [/tex]

[tex] = \dfrac{2 + 8i + i + 4i^2}{1 + 16} [/tex]

[tex] = \dfrac{2 + 9i - 4}{17} [/tex]

[tex] = \dfrac{-2 + 9i}{17} [/tex]

[tex]= -\dfrac{2}{17} + \dfrac{9}{17}i[/tex]

Answer:

Our fourth number is 52.

Step-by-step explanation:

Let our first even number be x.

Then the second even number must be (x + 2), the third (x + 4), fourth (x + 6), and the fifth (x + 8).

They sum to 250. Hence:

[tex]x+(x+2)+(x+4)+(x+6)+(x+8)=250[/tex]

Solve for x. Combine like terms:

[tex]5x+20=250[/tex]

Subtract 20 from both sides:

[tex]5x=230[/tex]

And divide both sides by five. Hence:

[tex]x=46[/tex]

Thus, our sequence is 46, 48, 50, 52, and 54.

Hence, our fourth number is 52.

Answer: B. Cannot be determined

Explanation:

We can't use SAS since we don't have two pairs of proportional sides. We only know one pair of sides. This also rules out SSS as well since we'd need 3 pairs of proportional sides.

We can't use AA because we don't have two pairs of congruent angles.

Currently, we simply don't have enough information to determine if the triangles are similar or not.

Answer:

x = 2

Step-by-step explanation:

The minimum point of the curve is (2, 0). Hence, axis of symmetry is x = 2

Answer:

2 < x < 6

Step-by-step explanation:

x/10

1/5 = 2/10

.6 = 6/10

2 < x < 6

Answer:

Terms:

Like Terms:

Coefficients:

Constants:

You simplify the expression by combining like terms:

-5x + 4 - x - 1 = -6x + 5

(7b - 4) + (-2b + a + 1) = 7b - 4 - 2b + a + 1 = 5b + a - 3

Answer:

Step-by-step explanation:

so let the equation equal 13

13 = 3[tex]x^{3}[/tex]-12x+13

so when ever 3[tex]x^{3}[/tex]-12x=0  then this is equation is true, soooo

x (3[tex]x^{2}[/tex] - 12) =0

so when x = 0  this is true, but also when

3[tex]x^{2}[/tex]-12=0   also

3[tex]x^{2}[/tex] = 12

[tex]x^{2}[/tex] = 4

x = 2

so when x = 2  or -2  or 0  ,  then this is true

Answer:

Hence the correct option is 3rd option. 40

Step-by-step explanation:

If two figures are similar, then the ratio of the corresponding sides is proportional.

[tex]\frac{15}{30} =\frac{20}{n} \\\\n=\frac{30 \times 20}{15} \\\\n= 40.[/tex]

Answer:

There is no significance evidence that students who completed two years of college had a higher average than students who had only completed high school.

Step-by-step explanation:

The hypothesis :

H0 : μ1 = μ2

H1 : μ1 > μ2

Given :

n1 = 35 ; x1 = 75.1 ; s1 = 12.8

n2 = 50 ; x2 = 72.1 ; s2 = 14.6

Pooled variance = Sp² = (df1*s1² + df2*s2²) ÷ (n1 + n2 - 2)

df1 = n1 - 1 = 35 - 1 = 34

df2 = n2 - 1 = 50 - 1 = 49

(x1 - x2) ÷ Sp(√(1/n1 + 1/n2))

Sp² = (34*12.8^2 + 49*14.6^2) / (35+50-2)

Sp² = (5570.56 + 10444.84) / 83

Sp² = 192.95662

Sp = √192.95662

Sp = 13.89

Test statistic = (75.1 - 72.1) / 13.89 * √(1/35 + 1/50)

Test statistic = 3 / (13.89 * 0.2203892)

Test statistic = 0.980

df = n1 + n2 - 2

df = 35 + 50 - 2 = 83

Using the Pvalue calculator :

Pvalue(0.980, 83) = 0.165

α = 0.1

Pvalue > α ; We fail to reject the H0; and conclude that there is no significance evidence that students who completed two years of college had a higher average than students who had only completed high school.

Answer:

(x - 3)^2 + (x + 2)^2 = 4

Step-by-step explanation:

Equation of circle:

(x - h)^2 + (x - k)^2 = r^2

(h, k) = (3, -2)

r = 2

(x - 3)^2 + (x - (-2))^2 = 2^2

(x - 3)^2 + (x + 2)^2 = 4

Answer:

[tex]{ \tt{y = 8 - 3x}} - - - (i) \\ \\ = > 7x - 4(8 - 3x) = 6 \\ 7x - 32 + 12x = 6 \\ 19x - 32 = 6 \\ 19x = 38 \\ x = 2 \\ \\ = > y = 8 - 3(2) \\ y = 2[/tex]

Answer:

Yes

Step-by-step explanation:

If you replace each x with -3 and each y with 2 you get:

1) 2<-4*(-3)

2<12

True

2) -3+8*2>7

13>7

True

Therefore the point is part of the solution set

Answer:

Length of the rectangle:

[tex]x = \frac{4800}{106} = \frac{2400}{53} [/tex]

Breadth of the rectangle:

[tex]60\%(x) = \frac{60}{100} \times \frac{4800}{106} \: \: \: \: \: \: \: \: \: \: \: \\ =60 \times \frac{48}{106} \\ = \frac{2880}{106} [/tex]

Step-by-step explanation:

Longer side of the rectangle(length) = x

Shorter side of the rectangle(breadth) = (60%)x

Perimeter of the rectangle = 2(l+b) = 96 inches

Hence,

[tex]96 = 2(x + 60\%(x))[/tex]

[tex]96 = 2(x + \frac{6}{100 } x)[/tex]

[tex]96 = 2( \frac{100}{1 00} x + \frac{6}{100} x)[/tex]

[tex]96 = 2( \frac{106}{100} x)[/tex]

[tex]96 = \frac{106}{50} x[/tex]

[tex]96 \div \frac{106}{50} = x[/tex]

[tex]96 \times \frac{50}{106} = x[/tex]

[tex] \frac{4800}{106} = x[/tex]

Answer:

Well, divide the shape into rectangles,

triangles or other shapes after that, you can find the area of and then add the areas back together.

Step-by-step explanation:

The area of composite shapes is defined as the area covered by any composite shape. A composite shape is made up of basic shapes put together. Thus, the area of the composite shape is found by individually adding all the basic shapes.

To calculate the area of a composite shape you must divide the shape into rectangles, triangles or other shapes you can find the area of and then add the areas back together.es

Answer:

1st blank=[tex]y_{1}[/tex]

2nd blank=[tex]x_{1}[/tex]

3rd blank= [tex]y_{2}[/tex]

3*27=81

so 1*[tex]y_{1}[/tex]=81

hence [tex]y_{1}[/tex]=81

9* [tex]x_{1}[/tex]= 81

[tex]x_{1}[/tex]=9

27*[tex]y_{2}[/tex]=81

[tex]y_{2}[/tex]=3

Thus solved.

Hope this helps.

Please mark me as brainliest.

Answer:

Step-by-step explanation:

Answer:

A. 8h=m

Step-by-step explanation:

$8* h= total money m earned.

Answer:

15

Step-by-step explanation: