The temperature inside a freezer was –18 °C when the freezer was accidentally unplugged. After that, the temperature increased by 2 °C per hour. This situation can be modeled by an equation of the form y = mx + b , where x = the time in hours that the freezer was been unplugged and y = the temperature in degrees Celsius. What is the value of b in this equation?

Answer:

A) 9841

Step-by-step explanation:

Formula of geometric sequence:

[tex]S_n=\frac{a_1*(r^n-1)}{r-1} \\[/tex]

First,  calculate the common ratio (r) of the sequence.

It can be calculated by dividing any term of the geometric sequence by the term preceding it.

[tex]r = \frac{27}{9}\\ \\r=3[/tex]

Then

[tex]Sum = \frac{1(3^9-1)}{3-1} \\\\Sum = \frac{3^9-1}{2}\\ \\Sum=\frac{19683-1}{2} \\\\Sum = \frac{19682}{2} \\\\Sum=9841[/tex]

Answer:

sine (x) / 14.9 = sine (71) / 25.5

sine (x) = 14.9 * sine (71) / 25.5

sine (x) = 14.088248 / 25.5

sine (x) = 0.5524803137

Angle (x) = arc sine(0.5524803137)

Angle (x) =  33.537 degrees

Step-by-step explanation:

The expression which represents the angle measure x with the use of Law of Sines is x=sin⁻¹[(a sin b)/c].

The law of sine is nothing but the relationship between the sides of the triangle to the angle of the triangle (oblique triangle).

It can be given as,

[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

Here (A,B,C) are the angle of the triangle and (a,b,c) are the sides of that triangle.

For the given problem it can also be given as,

[tex]x^o=\sin^{-1}\left(\dfrac{a\sin B}{c}\right)[/tex]

Put the values,

[tex]x^o=\sin^{-1}\left(\dfrac{(14.9)\sin (71)}{25.5}\right)\\x^o=\sin^{-1}\left(0.5523\right)\\x^o=33.54^o[/tex]

Thus, the expression which represents the angle measure x with the use of Law of Sines is x=sin⁻¹[(a sin b)/c].

Learn more about the sine law here;

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Answer:

Probability that the sample mean comprehensive strength exceeds 4985 psi is 0.99999.

Step-by-step explanation:

We are given that a random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength μ = 5500 psi and the standard deviation is σ = 100 psi.

Let [tex]\bar X[/tex] = sample mean comprehensive strength

The z-score probability distribution for sample mean is given by;

                          Z = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = population mean comprehensive strength = 5500 psi

            [tex]\sigma[/tex] = standard deviation = 100 psi

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, Probability that the sample mean comprehensive strength exceeds 4985 psi is given by = P([tex]\bar X[/tex] > 4985 psi)

    P([tex]\bar X[/tex] > 4985 psi) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{4985-5500}{\frac{100}{\sqrt{9} } }[/tex] ) = P(Z > -15.45) = P(Z < 15.45)

                                                                  = 0.99999

Since in the z table the highest critical value of x for which a probability area is given is x = 4.40 which is 0.99999, so we assume that our required probability will be equal to 0.99999.

Answer:

1727 students

Step-by-step explanation:

Here we have the formula for sample size given as

[tex]n = \frac{p(1-p)z^2}{ME^2}[/tex]

Where:

p = Mean

ME = Margin of error = 3

z = z score

Therefore, we have

p = 150/240 = 0.625

z  at 99 % = 2.575

ME = [tex]\pm[/tex]3%

Therefore [tex]n = \frac{0.625(1-0.625)2.575^2}{0.03^2} = 1726.73[/tex]

The number of students Professor York have to sample to estimate the proportion of all Oxnard University students who watch more than 10 hours of television each week within ±3 percent with 99 percent confidence = 1727 students.

Answer:

82°

Step-by-step explanation:

By inscribed angle theorem:

[tex]m\angle QRP = \frac{1}{2} \times 164 \degree \\ \\ \huge \red{ \boxed{\therefore \: m\angle QRP =82 \degree}}[/tex]

Answer:

3 mins 45 seconds

Step-by-step explanation:

According to the question, Michelle walks at a speed of 320 feet per minute her friend Diana Liz 400 yards from the shelves house approximately how many minutes will Michelle need to walk from her house to Diana's house and back

----First of all we have to work out in only a unit(since there are 2 units involved;feet and yards)

So,let's change the feet to yards

1 foot = 3 yards

X = 400 yards

X = 400 × 3

X = 1200 feet

Speed = distance/time

320 = 1200/x

X = 1200/320

X = 3.75 mins or 3 mins 45 secs

Answer:

y - 3 = (1/10)(x - 6)

Step-by-step explanation:

Note how x (the "run") increases by 10 and how y (the "rise") by 1.  Thus, the slope of the line connecting point (-4, 2) with point (6, 3) is

m = rise / run = 1/10.

Using the point-slope equation of a straight line, we derive the equation of this particular line as follows:

y - 3 = (1/10)(x - 6)

Answer:

Answer is 3

Step-by-step explanation:

Answer:

y ≥ 1

Step-by-step explanation:

Hence, range of given parabola is y[tex]\geq 1[/tex]

What is parabola ?

A parabola is a curve in which all points are at the same distance from two fixed points: the focus and the origin. a constant straight line (the directrix )

How to solve?

Generic equation of parabola  y=p. (x−h[tex])^{2}[/tex]+k  where (h,k) denotes the vertex. where parabola has range y[tex]\geq 0[/tex]. but as this curve is shifted  at 0,1 hence range becomes y[tex]\geq 1[/tex]

Learn more about parabola

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Answer:

11/4 or 2.75 pints

Step-by-step explanation:

We want to find the difference between the original amount of blueberries and the amount she ate

original amount-amount ate

3 1/2 -3/4

To subtract, we need common denominators

The common denominator of 2 and 4 is 4

3 1/2=7/2

Multiply by 2/2 to get a common denominator of 4

7/2*2/2=14/4

Now, we have common denominators and can subtract

14/4-3/4

Subtract the numerators, and leave the denominators as 4

11/4 =2.75

She has 11/4 or 2.75 pints left

Answer:

[tex]23,578,000 = 2.3578 \times {10}^{7} \\ [/tex]

yes, if the question is asking for a mixed number.

Answer:

5 1/2 would be a better answer or 5.5 in decimal form

hope this helps :)

Answer:

a. 3x=5  Positive Solution

Reasoning: You're working with only positives

b. 5z+7=3  Negative Solution

Reasoning: If you carry the 7 over the non-coefficient numbers will be negative thus making your answer negative

c. 7-5w=3  Positive Solution

Reasoning: both the coefficients and the non coefficients will be negative if solved and thus will result in the negatives becoming positive when dividing the 5w

d. 4a=9  Positive

Reasoning: The first step would be to divide the 9 by 4 and the resulting number would be positive

e. y=y+1 Negative Solution (No solution)

Reasoning: y can never equal itself with changing. Thats like saying 0 is 1. This has no solution but based on the rules this is negative solution

The solutions to the equations are: a. Positive solution, b. Negative solution, c. Negative solution, d. Positive solution, and e. No solution.

Let us analyze these equations one by one:

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Answer:

9.207

Step-by-step explanation:

To get the amount of starbucks for the population we can do

[tex]\frac{13 * 1629000}{100000}[/tex]

which gives us 211.77 total Starbucks in 23 miles.

To get starbucks per mile, we divide this number by 23.

This gives us 9.207

Answer:

<x = 147

Step-by-step explanation:

Supplementary angles is when the sum of the two angles are equal to 180

So the sum of angle x and angle y is equal to 180

y = 33

x + y = 180

x + 33 = 180

x = 180 - 33

x = 147

Answer:

x = 147°

Step-by-step explanation:

x ; y = suplementary =>

x + y = 180°  } => x = 180° - 33° = 147°

y = 33°

Answer:

The answer to your question is a. Infinite solution

Step-by-step explanation:

When two lines have the same slope and the same intercepts, this means that  these lines are the same so they system of equations will have infinite solutions.

If the lines do not cross, there will be no solution.

If the lines cross in one point there will be one solution

If there are a quadratic and a linear function they will cross in two points.

Answer: The rocket will reach its max after 4 seconds

Step-by-step explanation:

Hi, to find the maximum height, we have to set the first derivative of the equation equal to zero.

y=-16x^2+128x+136

0 = (2)-16x +128  

0= -32x+128

Solving for x:

32x = 128

x = 128/32

x = 4 seconds

The rocket will reach its max after 4 seconds

Feel free to ask for more if needed or if you did not understand something.

Multiply each exponent inside the parentheses by the exponent on the outside:

8^(-5 x -4) / 2^(-2 x -4)

8^20 / 2^8

The answer is C

Answer:

The speed rate of the plane in still air is 1006.67 km/h

The speed rate of the wind is 246.67 km/h

Step-by-step explanation:

To answer the question, we let the speed of the plane in still air = x  km/h

Let the speed of the wind = y km/h

Therefore,

4560/(x - y) = 6 hours and

3720/(x + y) = 3 hours

4560 = 6·x - 6·y.........(1)

3720 = 3·x + 3·y ........(2)

Multiplying equation (2) by 2 and add to (1) gives

12080 = 12·x

x = 12080/12 = [tex]1006\frac{2}{3}[/tex] km/h

Substituting the value of x in (1) gives

4560 = 6040 - 6·y

6·y = 1480

y = 1480/6 =  [tex]246\frac{2}{3}[/tex]

The speed rate of the plane in still air = 1006.67 km/h

The speed rate of the wind = 246.67 km/h.

Answer:

(x - 2)² + (y + 8)² = 121

Step-by-step explanation:

circle: (x – h)² + (y – k)² = r²   (h , k) center        r: radius

h = 2          k = - 8          r = 11

equation: (x - 2)² + (y + 8)² = 121

The equation of circle can be determine by using general equation of circle.

The equation for circle would be [tex](x - 2)^2+ (y + 8)^2 = 121[/tex].

Given:

The center of circle is [tex](2,-8)[/tex].

The radius is [tex]11[/tex].

Write the general equation of circle.

[tex](x-h)^2 + (y-k)^2= r^2[/tex]

Where, [tex](h,k)[/tex] is center of circle and [tex]r[/tex] is the radius of the circle.

Substitute [tex]2[/tex] for [tex]h[/tex], [tex]-8[/tex] for [tex]k[/tex] and [tex]11[/tex] for [tex]r[/tex] in above equation.

[tex](x - 2)^2 + (y + 8)^2 = 121[/tex]

Thus, the equation for circle would be [tex](x - 2)^2+ (y + 8)^2 = 121[/tex].

Learn more about equation of circle here:

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Answer:

Sheila earned $120 in interest.

Step-by-step explanation:

In order to calculate the interest earned by Sheila we can use the simple interest formula shown bellow:

i = P*r*t

Where i is the interested earned, P is the amount invested, r is the interest rate and t is the total time. For this case we have:

i = 800*0.03*5

i = 24*5

i = 120

Sheila earned $120 in interest.

Answer: After 5 years, Sheila earns $120

Step-by-step explanation: The calculation of simple interest is given as

Interest = P x R x T

Where P = the amount invested initially (800), R = the rate of interest earned (3% or 0.03) and T = the number of years (5) investment was held

The interest she earned can now be calculated by substituting for the known values as follows;

Interest = 800 x 0.03 x 5

Interest = 120

Therefore after 5 years, Sheila earns $120

Final answer:

To determine the age of an elephant with a shoulder height of 300 centimeters, the given formula h = 62.5t + 75.8 is used. Subtracting 75.8 from 300 and then dividing by 62.5 yields the elephant's age as approximately 3.59 years.

Explanation:

The student is asking to determine the age of an Asian elephant based on a mathematical model for its shoulder height. Given the model h = 62.5t + 75.8, and knowing the elephant's shoulder height is 300 centimeters, we can set up the equation as follows:

300 = 62.5t + 75.8

To solve for t, we first subtract 75.8 from both sides:

224.2 = 62.5t

Then, we divide both sides by 62.5:

t = 224.2 / 62.5

t = 3.5872

Therefore, the age of the elephant is approximately 3.59 years.

The elephant is about 46.16 years old.

To find the age of the elephant given its shoulder height, we need to solve the equation for  t . The equation given is:

[tex]h = 62.5\sqrt[3]{t} + 75.8[/tex]

Given  h = 300  centimeters, we substitute  h  into the equation and solve for  t :

[tex]300 = 62.5\sqrt[3]{t} + 75.8[/tex]

First, isolate the cube root term:

[tex]300 - 75.8 = 62.5\sqrt[3]{t} \\\\ 224.2 = 62.5\sqrt[3]{t}[/tex]

Next, divide both sides by 62.5:

[tex]\sqrt[3]{t} = \frac{224.2}{62.5} \\\\ \sqrt[3]{t} \approx 3.5872[/tex]

Now, to solve for  t , cube both sides:

[tex]t \approx (3.5872)^3 \\\\ t \approx 46.16[/tex]

So, the elephant is about 46.16 years old.

The complete question is:

Biologists have discovered that the shoulder height (in centimeters) of a male Asian elephant can be modeled by [tex]h = 62.5\sqrt[3]{t} + 75.8[/tex], where t is the age (in years) of the elephant. Determine the age of an elephant with a shoulder height of 300 centimeters. Round your answer to the nearest tenth.

The elephant is about ____ years old.

Answer:

This formula is in slope-intercept form. 3 is the slope (positive slope) and -2 is the y-intercept.

Hi there!

Your answer is:

The slope is 3 and the y-intercept is 2 or (0, 2).

Have a good day

~ Mqddie

Answer:

1) f(x) = x/8 - 7

2) f(x) = 1 - x/3

3) f(x) = 20 - 0.25x

4) f(x) = x + 7

Step-by-step explanation:

f^-1 = 8(x + 7)

x + 7 = y/8

x = y/8 - 7

f(x) = x/8 - 7

f^-1 = -3(x - 1)

y/-3 = x - 1

x = 1 - y/3

f(x) = 1 - x/3

f^-1 = 4(20 - x)

y/4 = 20 - x

x = 20 - y/4

f(x) = 20 - x/4

f(x) = 20 - 0.25x

f^-1 = x - 7

y = x - 7

x = y + 7

f(x) = x + 7

Answer:

The distance of the ship from the shoreline is 113 metres.

Step-by-step explanation:

Please kindly check the attached files for explanation

Answer:

The distance of the ship to the shoreline is 113 meters

Step-by-step explanation:

Here we have the following information

Location of lighthouse = 10 m back from the edge of the shoreline

Height of beacon above sea level = 52 m

Level of the eyes of Lucy above sea level = 12 m

Angle of elevation of the beacon from Lucy = 18°

Therefore, the beacon, the elevation of the eyes of Lucy and the base of the lighthouse at the same elevation with Lucy form a right triangle with opposite side to angle = 52 m and angle = 18 °

Therefore, from

[tex]Tan\theta =\frac{sin\theta }{cos\theta } = \frac{Opposite \, side \, to\, angle}{Adjacent\, side \, to\, angle}[/tex]

We have

[tex]Tan18 =\frac{52-12}{Adjacent } = \frac{40}{Adjacent}[/tex]

0.325 = [tex]\frac{40}{Adjacent}[/tex]

Where the adjacent side is the distance of the ship from the lighthouse

Adjacent side = 40/0.325 = 123.107 meters

We recall that the lighthouse is 10 m back from the edge of the shoreline, therefore the ship is 123.107 - 10 or 113.107 meters from the shore line which is 113  meters to the nearest meter.

Answer:

The number of people that attended in scientific notation is 2.25 x 10^5.

Step-by-step explanation:

Answer:

96 bricks

Step-by-step explanation:

In this question, we are asked to calculate the number of bricks which are needed by a mason given the number of bricks needed to complete each of the course.

From the question, we can identify that we have 4 rows to be filled with each of the rows being 24 bricks long.

now , to calculate the number of bricks needed to be moved by the mason, our work is pretty straightforward. what we simply need to do is to multiply the number of rows by the number of bricks per course.

According to this question specifically, this is equal to a value of 4 * 24 = 96 bricks

Answer:

6 hours

Step-by-step explanation:

Make an equation

Each hour costs $3, and there is a $12 cost regardless of the hours. We know that Lucy spent $30.

3h+12=30

Subtract 12 from both side s

3h=18

Divide both sides by 3

h=6

So, she rented  it for 6 hours

Answer: She can randomly survey 50 seventh-graders in the school.

Step-by-step explanation: To get the best result without wasting to much time means she cannot afford to survey every student. To receive the best results it should be unbiased so random is the way to go. Randomly surveying 50 girls in her school does not guarantee that those girls are all seventh graders so the best answer is She can randomly survey 50 seventh-graders in the school.

Answer:

The amount left with Valentina is $10,000.

Step-by-step explanation:

The question is:

Valentina goes shopping at the mall with $50,000. She spends 3/5 of that amount on a diver and half the rest on a skirt. How much money does Valentina have left?

The original amount Valentina had was, P = $50,000.

Compute the amount spent on a diver as follows:

D = [tex]\frac{3}{5}th[/tex] of $50,000

   [tex]=\frac{3}{5}\times 50000\\=30000[/tex]

The amount spent on a diver was, D = $30,000.

Amount left:

A = P - D

   = 50000 - 30000

   = 20000

Compute the amount spent on a skirt as follows:

S = [tex]\frac{1}{2}[/tex] of $20,000

  [tex]=\frac{1}{2}\times 20000\\=10000[/tex]

Amount left:

A₁ =  A - S

   = 20000 - 10000

   = 10000

Thus, the amount left with Valentina is $10,000.