The value of a painting can be predicted by the expression 120 + .08t, where t is the number of years since 2014.

Answer:

Step-by-step explanation

Answer:

Hey there!

You can think of the rate of change as the slope of a quadratic function- here we see that it is 9/-3, or - 3.

Let  me know if this helps :)

Answer:

–3 meters per second

Step-by-step explanation:

Answer:

$28

Step-by-step explanation:

given that

The Principal amount is $800

The rate of interest is 3.5%

And, the time period is one year

we need to find out the simple interest

As we know that

Simple interest = Principal × rate × time period

= $800 × 3.5% × 1 year

= $28

hence, the simple interest is $28

Answer:

1. A

2. Simplification: (not sure)

\( \frac{ - 3x {}^{5} + 6x { }^{2} - 4x - 15 }{9x {}^{2} - 12x + 4 } \)

The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be 12 cupcakes, 24 cupcakes, and 50 cupcakes will cοst rοughly $2.42, $2.33, and $2.58 per cupcake, respectively.

Tο cοmplete the assignment, use the tried-and-true straightfοrward methοdοlοgy, the real variables, and any pertinent details frοm the preliminary and specialized questiοns. In respοnse, custοmers might be given anοther οppοrtunity tο range sample the prοducts. In the absence οf such changes, majοr advances in οur knοwledge οf prοgrammes will be lοst.

Here,

We must divide the tοtal cοst by the quantity οf cupcakes in οrder tο determine the unit cοst οf each οptiοn:

Twelve cupcakes:

Unit cοst is calculated as Tοtal Cοst / Cupcakes.

=>  Unit cοst: $29 fοr 12 cupcakes.

=>  $2.42 is the unit cοst per cupcake.

Tο make 24 cupcakes:

Unit cοst is calculated as Tοtal Cοst / Cupcakes.

=> 24 cupcakes equals $56 fοr the unit.

=>  $2.33 is the unit cοst per cupcake.

50 cupcakes =

Unit cοst is calculated as Tοtal Cοst / Cupcakes.

=>  $129 fοr a unit οf 50 cupcakes.

=>  Unit cοst: $2.58 fοr each cupcake

As a result, 12 cupcakes, 24 cupcakes, and 50 cupcakes will cοst rοughly $2.42, $2.33, and $2.58 per cupcake, respectively.

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This one's a special case of a right angled triangle with sides (3, 4, and 5 units)

\(\qquad\displaystyle \tt \dashrightarrow \: 5 \sin \bigg( \frac{ \pi}{3} x \bigg) = 3\)

\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \frac{3}{5} \)

Now, check the triangle, sin 37° = 3/5

therefore,

\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin(37 \degree) \)

[ convert degrees on right side to radians ]

\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin \bigg(37 \degree \times \frac{ \pi}{180 \degree} \bigg ) \)

There are three more possible values as :

\(\qquad\displaystyle \tt \dashrightarrow \: \sin( \theta) = \sin(\pi - \theta) \)

\(\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( { 2\pi}{} + \theta \bigg) \)

\(\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( \frac{ 3\pi}{} - \theta\bigg) \)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 37 \times \frac{ \cancel \pi}{180} \times \frac{3}{ \cancel \pi} \)

\(\qquad\displaystyle \tt \dashrightarrow \: x = \frac{37}{60} \)

or in decimals :

\(\qquad\displaystyle \tt \dashrightarrow \: x = 0.616666... = 0.6167\)

[ 6 repeats at third place after decimal, till four decimal places it would be 0.6167 after rounding off ]

similarly,

\(\qquad\displaystyle \tt \dashrightarrow \: \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(1 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: 1 - \frac{x}{3} = \frac{37}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 1\)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 0.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 2.385\)

\(\qquad\displaystyle \tt \dashrightarrow \: 2\pi + \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(2 + \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: 2 + \frac{x}{3} = \frac{37}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.205 - 2\)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = - 1.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times -1 .795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = -5.385\)

\(\qquad\displaystyle \tt \dashrightarrow \: 3 \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(3 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: 3 - \frac{x}{3} = \frac{37}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 3\)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 2.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 2.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 8.385\)

" x can have infinite number of values here with the same result, here are the four values as you requested "

I hope it was helpful ~

Answer:

(39,000 + 3t = 216000.)  t = 59000

Step-by-step explanation:

(How to find t) First, subtract 39000 from 216000. Divide that by 3. Your answer is 59000.

Answer:

Step-by-step explanation:

Work is said to be done when force applied to an object causes the object to move through a distance.

Work done = Force * perpendicular distance.

\(\int\limits^a_b {F} \, ds\)

Given Force F = xy i + (y-x) j and a straight line (-1, -2) to (1, 2)

First we need to get the equation of the straight line given.

Given the slope intercept form y = mx+c

m is the slope

c is the intercept

m = y₂-y₁/x₂-x₁

m = 2-(-2)/1-(-1)

m = 4/2

m = 2

To get the slope we will substtutte any f the point and the slope into the formula y = mx+c

Using the point (1,2)

2 = 2+c

c = 0

y = 2x

Substituting y = 2x into the value of the force F = xy i + (y-x) j we will have;

F = x(2x) i + (2x - x) j

Using the coordinate (1, 2) as the value of s

\(W = \int\limits^a_b ({2x^2 i + x j}) \, (i+2j)\\W = \int\limits^a_b ({2x^{2}+2x }) \, dx \\W = [\frac{2x^{3} }{3} +x^{2} ]\left \ x_2=1} \atop {x_1=-1}} \right.\\W = (2(1)^3/3 + 1^2) - (2(-1)^3/3 + (-1)^2)\\W =(2/3+1) - (-2/3+1)\\W = 2/3+2/3+1-1\\W = 4/3 Joules\)

Answer:

Step-by-step explanation:

If this is a question involving a quadratic, then the answer is

x^2 - 24x - 25

(x - 25)(x + 1)

If it is any other situation, I don't think so. Factors imply division and usually you are speaking about integers.

Given data:

Vincent turned his head 30° to the side.

The figure in the option b is the angle that he turned his head.

The equation of SQ is y = (-1/2)x + 2.

Given the coordinates of point P and point R as (-8,6) and (8,-2) respectively. Now, we need to find the equation of SQ.

Let's use the slope-intercept form of the equation of a line which is y = mx + b where m is the slope and b is the y-intercept.

Firstly, we need to find the slope of the line passing through the points P and R.

 Slope of a line through two given points (x1,y1) and (x2,y2) is given by,m = (y2 - y1) / (x2 - x1).

Hence, Slope of line PR = mPR= (-2 - 6) / (8 - (-8))= (-8) / 16= -1/2. As the line SQ is parallel to the line PR, the slope of the line SQ will be the same as the slope of line PR. The slope of line SQ = mSQ= mPR= -1/2.

Now, we need to find the equation of line SQ which passes through the point (0,2) and has slope -1/2.

Hence, using the slope-intercept form of the equation of a line, we get the equation of SQ as follows: y = mx + b 2 = (-1/2)(0) + b 2 = b.

Therefore, the equation of line SQ is y = (-1/2)x + 2, where x and y are the coordinates of the points on the line.

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Answer:

X=6 Because if you multiply 16×3= 48

and If you do it with 2 it is 2×3= 6

Step-by-step explanation:

16×3= 48

2×3=6

There is a 60% probability that a randomly selected student from the class scored either an A or B in Biostatistics.

To calculate the probability that a randomly selected student scored either an A or B in Biostatistics, we need to consider the number of students who scored A and B and divide it by the total number of students in the class.

Given that there are 25 students in the class, 5 of them scored an A and 10 scored a B. To calculate the probability, we add the number of students who scored A (5) to the number of students who scored B (10):

Number of students who scored A or B = Number of students who scored A + Number of students who scored B = 5 + 10 = 15.

Therefore, the probability that a randomly selected student scored A or B

in Biostatistics is:

Probability = Number of students who scored A or B / Total number of students = 15 / 25 = 0.6 or 60%.

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Step-by-step explanation:

Plug

\( {x}^{2} + 1\)

for x.

\(( {x}^{2} + 1) {}^{2} + 1\)

Note that

\((a + b) {}^{2} = 2ab\)

So we have

\( {x}^{4} + 2 {x}^{2} + 2\)

Answer:5SQRT61/

61

Step-by-step explanation:

Michelle's balance after two years would be $8977.50.

using the formula to find Michelle’s balance after two years:

balance = principal + (interest rate * principal * time)

where:

- principal = the initial deposit of $8750

- interest rate = 1.3% = 0.013 (as a decimal)

- time = 2 years

Substituting the values, we get:

balance = 8750 + (0.013 * 8750 * 2)

balance = 8750 + 227.5

balance = $8977.50

Therefore, Michelle's balance after two years will be $8977.50.

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Answer:

3 miles per hour

Step-by-step explanation:

Jessica is walking home from a friend's house.

After 2 minutes she is 0.8 miles from the home and after 12 minutes she is 0.3 miles away fro her house.

Her rate will be = (change in distance)/change in time

= (0.8-0.3)/(12-2)

= 0.5/10

= 0.05 miles per minute

Now we will convert timings from minutes to hour.

Or  = 0.05×60  

= 3 miles per hour

Answer:

32.4 dollars

Step-by-step explanation:

Step-by-step explanation:

step 1 = Divide 675 by 8 keeping notice of the quotient and the remainder.

step 2 =Continue dividing the quotient by 8 until you get a quotient of zero.

step 3 = Then just write out the remainders in the reverse order to get octal equivalent of decimal number 675.

Using the above steps, here is the work involved in the solution for converting 675 to octal number:

675 / 8 = 84 with remainder 3

84 / 8 = 10 with remainder 4

10 / 8 = 1 with remainder 2

1 / 8 = 0 with remainder 1

Then just write down the remainders in the reverse order to get the answer, The decimal number 675 converted to octal is therefore equal to :

1243

Answer:

B. 10x -40

Step-by-step explanation:

To rewrite the expression 5(2x-8) using the distributive property, we need to separate the expression inside the parentheses and then multiply the two expressions by 5. The answer is: 10x-40.

Answer:

Step-by-step explanation:

f(10) = 110×0.8855¹⁰

You can do the math.

Answer:

32.6045597492

Step-by-step explanation:

110(.8855)^10

This set {σ ∈ S4 : σ(1) = 3} contains the following elements of S4: (13), (23), (34), (24), (14), (12)(34), (13)(24), (14)(23) and  {σ ∈ S4 : σ(2) = 2} this set contains the following elements of S4: (12), (21), (13)(24), (24)(13).

The group S4 is the symmetric group on 4 elements and has 24 elements. We can list all of its subgroups as follows:

Now, let's consider the sets (a) and (b) and see if they are subgroups of S4:

(a) {σ ∈ S4 : σ(1) = 3}

This set contains the following elements of S4: (13), (23), (34), (24), (14), (12)(34), (13)(24), (14)(23). We can check that this set is not a subgroup of S4 because it is not closed under composition. For example, (13)(14) = (134) is not in the set.

(b) {σ ∈ S4 : σ(2) = 2}

This set contains the following elements of S4: (12), (21), (13)(24), (24)(13). We can check that this set is a subgroup of S4. It is closed under composition, inverses, and contains the identity element e. Therefore, it is a subgroup of S4 and is isomorphic to the cyclic group of order 2.

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Answer:

\(V=6912ft^3\)

Step-by-step explanation:

From the question we are told that:

Diameter  \(D=40ft\)

Radius \(r=d/2=>20ft\)

Depth at south \(d_s=3ft\)

Depth at north \(d_n=8ft\)

Average depth of the pool

 \(d_a=\frac{3+8}{2}\)

 \(d_a=5.5ft\)

Generally the equation for Volume is mathematically given by

 \(V=\pi r^2h\)

 \(V=3.142*(20)^25.5\)

 \(V=6912ft^3\)

Answer:

The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Attended the dinner speech.

Event B: Attended the breakfast forum.

70% attended the dinner speech

This means that \(P(A) = 0.7\)

40% attended both events.

This means that \(P(A \cap B) = 0.4\)

The probability that he also attended the breakfast forum is

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.7} = 0.5714\)

The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.

Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

Answer:

Step-by-step explanation:

17.

18.

f(x)=6x^2+7x-4

(a)

f(3)=6(3)^2+7(3)-4

=54+21-4

=71

(b)

f(m)=6m^2+7m-4

(c)

f(x+1)=6(x+1)²+7(x+1)-4

=6(x²+2x+1)+7x+7-4

=12x²+12x+6+7x+7-4

=12x²+19x+9

19.

(fg)(x)=f(g(x)=f(2x²+3)=2x²+3+5=2x²+8

20.

(a)

f(x)=x²+3x+4

domain:all real values

(b)

domain:all real values≥-2

(c)f(x)=log(x+7)

Domain:x≥-7

21.

x²+6x+y²-7=0

(x²+6x+6/2)²)-(6/2)²+y²=7

(x+3)²+y²=7+9

(x+3)²+y²=4²

center=(-3,0)

radius=4

22.

(x-3)²+(y-5)²=3²

or

x²-6x+9+y²-10y+25=9

x²+y²-6x-10y+25=0

Graph is for 17th question.

From the temperatures given, we have that:

a) The regression equation is: y = 2.91x + 64.61.

b) The predicted temperature at 2 pm is of 88 ºF.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

In the context of this problem, the input and the output are given as follows:

We have that an hour is 60 minutes, hence:

Thus the points are given as follows:

(0, 65), (0.75, 67), (1.5, 68), (2.5, 72), (3, 74), (3.75, 75), (4.5, 77), (5,80).

Inserting these points into the calculator, the equation is:

y = 2.91x + 64.61.

2 pm is 8 hours after 6 am, hence x = 8 and the predicted temperature, in ºF, is given by:

y = 2.91(8) + 64.61 = 88 ºF.

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Answer:

a. When the time is greater than 0, but less than 345 minutes, the temperature of the turkey is increasing at roughly a linear rate.

b. When the time ranges from 345 to 360 minutes, the temperature of the turkey stays constant, at 165 degrees.

c. When the time is greater than 360 minutes, the temperature of the turkey decreases.