When an object is removed from a furnace and placed in an environment with a constant temperature of 70°F, its core temperature is 1500°F. One hour after it is removed, the core temperature is 1170°F. (a) Write an equation for the core temperature y of the object t hours after it is removed from the furnace. (Round your coefficients to four decimal places.)

Answer:

Step-by-step explanation:

Here is another example :

ii) When a polynomial f(x) is divided by (x-1) and (x+2) it leaves remainder 5 and 17 respectively. find the remainder when f(x) is divided by (x-1) (x+2)

14) The remainder when the expression  ax³ + bx² + 2x + c is divided by x-1

is twice of that when it is divided by  x + 1. Show that c = 3a - b + 6.

Answer:

ii) R(x) = -4x + 9

14) c = 3a - b + 6 ( Proved)

Step-by-step explanation:

14) The correct expression is [tex]ax^3 + bx^2 + 2x + c[/tex]

To get the remainder when the expression  [tex]ax^3 + bx^2 + 2x + c[/tex] is divided by

x - 1, let x - 1 = 0; x = 1

Remainder:

[tex]R_1(x) = a(1)^3 + b(1)^2 + 2(1) + c\\R_1(x) = a + b + 2 + c[/tex]

When  [tex]ax^3 + bx^2 + 2x + c[/tex] is divided by x + 1

Let x + 1 = 0; x = -1

Remainder:

[tex]R_2(x) = a(-1)^3 + b(-1)^2 + 2(-1) + c\\R_1(x) = -a + b - 2 + c[/tex]

According to the question, R₁(x) = 2R₂(x)

a + b + 2 + c = 2(-a + b - 2 + c)

a + 2a +b - 2b + 2 + 4 = 2c - c

c = 3a - b + 6 ( Proved)

ii)

The dividend is f(x)

(x - 1)(x + 2) is the divisor, i.e. D(x) = (x - 1)(x + 2)

Let the quotient = A(x)

Let the Remainder, R(x) = ax + b..............(1)

Therefore, f(x)  = A(x)D(x) + R(x)

f(x) = A(x)(x - 1)(x + 2) + R(x)...................(2)

When f(x) is divided by x - 1, x = 1

Put x = 1 into equation (2) knowing that R(1) = 5

f(1) = R(1) = 5

R(1) = a(1) + b = 5

a + b = 5....................(3)

When f(x) is divided by x + 2, x = -2

Put x = -2 into equation (2) knowing that R(-2) = 17

f(-2) = R(-2) = 17

R(-2) = a(-2) + b = 17

-2a + b = 17..................(4)

Subtracting equation (1) from (2)

-3a = 12

a = -12/3

a = -4

Substitute the value of "a" into equation (4)

-2(-4) + b = 17

8 + b = 17

b = 9

Since R(x) = ax + b

R(x) = -4x + 9

Answer:

[tex]\boxed{Area = 130 units^2}[/tex]

Step-by-step explanation:

Area of trapezoid = [tex]\frac{a+b}{2} h[/tex]

Where a = 7, b = 19 and h = 10

Area = [tex]\frac{7+19}{2} (10)[/tex]

Area = (26)(5)

Area = 130 units²

Answer: D) -4/3

Step-by-step explanation:

Slop can be represented as [tex]\frac{rise}{run}[/tex].  This equation rises -24 units then runs 18.  Thus, the slope is -24/18, or -4/3.

Hope it helps <3

Answer:

-4/3.

Step-by-step explanation:

To get the slope, you do the rise over the run.

In this case, the rise is going to be -24, since the track is falling. The run will be 18.

-24 / 18 = -12 / 9 = -4/3

Hope this helps!

Answer:

The correlation coefficient "tell us" that the model in question does not fit the data well (the correlation coefficient is near zero), in whose case we need to find another that can do it.

Step-by-step explanation:

Roughly speaking, the correlation coefficient "tell us" if two variables could present the following behavior:

As we can follow from the question, a correlation coefficient of 0.02 is near to zero. In this case, the correlation coefficient is "telling us" that the two variables do not follow the cases 1 and 2 above described. Instead, it follows the case 3.

Therefore, the model in question does not fit the data well, in whose case we need to find another that can do it. For example, if the model is linear, we need to test an exponential model.

It is important to remember that the correlation coefficient does not tell us anything about that one variable causes the other variable, only behaviors as described above.

Answer:

B. rotation 90° counterclockwise about the origin.

Step-by-step explanation:

Transformation is the process by which the size or orientation of a given figure is altered without any effect on its shape. Examples are; rotation, reflection, translation and dilation.

Rotation is the process of turning a figure about a reference point called the origin. While reflection is turning a figure about a line to produce its image.

In the given question, ∆ABC is  mapped onto ∆A'B'C' by rotating it at 90° counterclockwise about the origin.

The correct option is (B). rotation 90°counterclockwise about the origin.

Given, ∆ABC and ∆A'B'C' are shown in attached figure.

We have to map ∆ABC onto ∆A'B'C',.

A transformation is a general term for four specific ways to manipulate the shape and or position of a point, a line, or geometric figure.

Transformation is  also the process by which the size or orientation of a given figure is altered without any effect on its shape.

A rotation is a transformation in which the object is rotated about a fixed point.The direction of rotation can be clockwise or anticlockwise.

It is clear from the fig that the ∆ABC can be mapped over ∆A'B'C' by the rotation of  90°counterclockwise about the origin.

Hence the correct option is (B). rotation 90°counterclockwise about the origin.

For more details follow the link:

https://brainly.com/question/1571997

Explanation:

The distance we're after is the vertical distance from the point to the line. So we only care about the difference in y values from y = -19 to y = 3

You can count out the spaces or use subtraction along with absolute value

distance from P to Q = |P-Q|

distance from -19 to 3 = |-19-3|

distance from -19 to 3 = |-22|

distance from -19 to 3 = 22

The absolute value is to ensure the result is never negative.

Answer:

she needs to save up for 3 months

Step-by-step explanation:

Answer:

The unit prices will be within the range of $0.77 ≤x≤$0.78

Step-by-step explanation:

If a package 8-count AA batteries cost $6.16 and a package of same 20-count AA batteries cost $15.60, to calculate the unit price, the following steps must be carried out:

8 counts AA batteries = $6.16

A unit price (i.e 1 count) = x

Cross multiplying

8 × x = 6.16 × 1

x = 6.16/8

x = $0.77 for a unit price

Similarly, if 20-count AA batteries cost $15.60, then:

20 counta = $15.60

1 count = x

Cross multiplying

20 × x = $15.60 × 1

x = $15.60/20

x = $0.78 for a unit price

From above calculation, of can be seen that the unit price is almost similar but with a difference of $0.01 ($0.78-$0.77) which is insignificant. Based on this, we can conclude that a unit price of the battery is between the range

$0.77 ≤x≤$0.78

Answer:

The 8-count pack of AA batteries has a lower unit price of 0.77

per battery.

Step-by-step explanation:

Answer:

2/5x

Step-by-step explanation:

x% of 40= x/100×40

= 40/100x = 2/5x

Answer:

x = 37/45

Step-by-step explanation:

Here's how similar triangles work. We set up an equation as SIDE 1A/ SIDE 1B = SIDE 2A/ SIDE 2B

Ok, so these 2 triangles are similar, so we can set up a butterfly equation:

Side 1a would be 8x

Side 1b would be 5x +3

Side 2a would be 10x - 2

Side 2b would be 7x

----------------------------------------------------

Our equation would be

8x/(5x+3) = (10x-2)/7x

We cross multiply to get 8x(10x-2) = 7x(5x+3)

Instead of solving and getting squares, we can x on both sides and we get:

8(10x - 2) = 7(5x+3) ----> we simplify to get

80x - 16 = 35x + 21 ----> it's easy sailing from here.

45x = 37

x = 37/45

gosh i hope it's right...

Answer:

35 combinations

Step-by-step explanation:

The first digit cannot be 5 or 6 (Since the digits could not be in ascending order if that was the case).

If the first digit is 4, there is 1 possibility:

(4, 5, 6)

If the first digit is 3, there are 3 possibilities:

(3, 4, 5) (3, 4, 6) (3, 5, 6)

If the first digit is 2, there are 6 possibilities:

(2, 3, 4) (2, 3, 5) (2, 3, 6) (2, 4, 5) (2, 4, 6) (2, 5, 6)

If the first digit is 1, there are 10 possibilities :

(1, 2, 3) (1, 2, 4) (1, 2, 5) (1, 2, 6) (1, 3, 4) (1, 3, 5) (1, 3, 6) (1, 4, 5) (1, 4, 6) (1, 5, 6)

If the first digit is 0, there are 15 possibilities:

(0, 1, 2) (0, 1, 3) (0, 1, 4) (0, 1, 5) (0, 1, 6) (0, 2, 3) (0, 2, 4) (0, 2, 5) (0, 2, 6) (0, 3, 4) (0, 3, 5) (0, 3, 6) (0, 4, 5) (0, 4, 6) (0, 5, 6)

Therefore, he would need to try at most 35 combinations.

Answer:

first one is the right one

Step-by-step explanation:

Answer:

3x^2(3+x)

Step-by-step explanation:

Answer: 3x^2(3+1)

Because it is divisible by 3 and x^2

Answer:

The answer is

Step-by-step explanation:

(x+3)(2x-4)(x-6)

Expand

We have

(x + 3) ( 2x² - 12x - 4x + 24)

(x + 3)( 2x² - 16x + 24)

2x³ - 16x² + 24x + 6x² - 48x + 72

Simplify

Group like terms

2x³ - 16x² + 6x² + 24x - 48x + 72

We have the final answer as

Hope this helps you

Answer:

[tex]m=-\frac{13}{20.8}=-0.625[/tex]

Nowe we can find the means for x and y like this:

[tex]\bar x= \frac{\sum x_i}{n}=\frac{16}{5}=3.2[/tex]

[tex]\bar y= \frac{\sum y_i}{n}=\frac{35}{5}=7[/tex]

And we can find the intercept using this:

[tex]b=\bar y -m \bar x=7-(-0.625*3.2)=9[/tex]

So the line would be given by:

[tex]y=-0.625 x +9[/tex]

Step-by-step explanation:

We have the following data:

X: 3,3,2,1,7

Y:6,7,8,9,5

We want to find an equationinf the following form:

[tex] y= bX +a[/tex]

[tex]a=m=\frac{S_{xy}}{S_{xx}}[/tex]

Where:

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]

So we can find the sums like this:

[tex]\sum_{i=1}^n x_i = 3+3+2+1+7=16[/tex]

[tex]\sum_{i=1}^n y_i =6+7+8+9+5=35[/tex]

[tex]\sum_{i=1}^n x^2_i =72[/tex]

[tex]\sum_{i=1}^n y^2_i =255[/tex]

[tex]\sum_{i=1}^n x_i y_i =99[/tex]

With these we can find the sums:

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=72-\frac{16^2}{5}=20.8[/tex]

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=99-\frac{16*35}{5}=-13[/tex]

And the slope would be:

[tex]m=-\frac{13}{20.8}=-0.625[/tex]

Nowe we can find the means for x and y like this:

[tex]\bar x= \frac{\sum x_i}{n}=\frac{16}{5}=3.2[/tex]

[tex]\bar y= \frac{\sum y_i}{n}=\frac{35}{5}=7[/tex]

And we can find the intercept using this:

[tex]b=\bar y -m \bar x=7-(-0.625*3.2)=9[/tex]

So the line would be given by:

[tex]y=-0.625 x +9[/tex]

Answer:

52 inches

Step-by-step explanation:

Answer:

we have, 1 feet =12 inches

13/3 foot =12×13/3 inches

=52 inches.

thereforethe , the answer is 52 inches.

Answer:

y = 5x + 8

Step-by-step explanation:

Start with y = mx + b:  general slope-intercept form, equation of a line:

Replace m with 5, y with 8 and x with 0 (since the y-intercept is (0, 8):

8 = 5(0) + b.  Then b must be 8, and the desired equation is

y = 5x + 8

Answer:

its 1260°.

as by the formulae,

(n-2)×180°

we get,

sum of interior angle =(9-2)×180°

=1260°.....is anwer.

Answer:

The pyramid's height h = 12 ft

Step-by-step explanation:

Notice that the slant height of the pyramid forms a right angle triangle with the segment that joins the bottom end of the slant height with the center of the pyramid's base, and with the pyramid height (h).

The segment joining the slant height with the center of the pyramid's base is one half of the side of the base in length, so that it; 16 feet.

then we have a right angle triangle with hypotenuse given by the pyramid's slant height (20 ft), a leg given by 16 ft, and we need to find the length of the second leg (pyramid's height (h).so we use the Pythagorean theorem:

[tex]hyp^2=leg_1^2+leg_2^2\\(20\,ft)^2= (16\,ft)^2+h^2\\h^2=400\,ft^2-256\,ft^2\\h^2=144\,ft^2\\h=12 \,ft[/tex]

Answer:

C.12ft

Step-by-step explanation:

for people on edmentum

Answer:

Step-by-step explanation:

What sis line of best fit?

The line of best fit may be explained as a straight line which is drawn to pass through a set of plotted data point which gives the best and most approximate relationship between the data points. A line of best fit is required to give the best approximate value between the set of plotted data points such that it allows making inference on new data points while also ensuring the least possible deviation from the original data points.

Why do we want the sum of the residuals to be as close to zero as possible?

The line of best fit will be the line which gives the least value of residual error. The residual error is reffered to as the difference between the line drawn and the individual data point plotted. These errors are squared and summed together, the line which produces the least residual error is Considered as the leading ne of best fit for the data.

We want the sum of our residual error to be as close to zero as possible, this is to reduce the deviation between our original or plotted data and the modeled data produced by our line of best fit.

Answer:

Step-by-step explanation:

We wan the residuals to be closest to zero because they will help use later in the equation.

Answer:

24 minutes

Step-by-step explanation:

Fred can mow a lawn in 60 minutes.

Fred's Rate  [tex]=\frac{1}{60}[/tex]

Rocky can mow the same lawn in 40 minutes.

Rocky's rate [tex]=\frac{1}{40}[/tex]

Let the time it will take both of them = x minutes

Therefore:

[tex]\frac{1}{60}+\frac{1}{40}=\frac{1}{x}\\$Multiply all through by 1200$\\1200\times \frac{1}{60}+1200\times\frac{1}{40}=1200\times\frac{1}{x}\\20+30=\frac{1200}{x}\\50=\frac{1200}{x}\\$Cross multiply\\50x=1200\\Divide both sides by 50\\x=24\\[/tex]

It would take the two of them 24 minutes to mow the lawn.

Answer:

Option D and E

Step-by-step explanation:

Time for guard passes = 5G

Time for kimura arm locks = 2K

Altogether:

=> 5G+2K

If he does 7 times:

=> 7(5G+2K)

Simplified form:

=> 14K+35G

Answer:

Option D and E

Step-by-step explanation:

Time for guard passes = 5G

Time for kimura arm locks = 2K

Altogether:

=> 5G+2K

If he does 7 times:

=> 7(5G+2K)

Simplified form:

=> 14K+35G

Answer:

P = 0.3

Step-by-step explanation:

Here, we are to use the probability distribution in the table to calculate the probability that a children has 4 or more shoes in his or her closet

When we say 4 or more, what we mean by this is that the teenager has 4 shoes or 5 shoes

In probability expressions, when we use the term ‘or’ we are simply talking about adding the terms involved

So what we can do here is to add the probability that the teenager has 4 shoes to the probability that the teenager has five shoes

From the table that would be; 0.1 + 0.2 = 0.3

Answer:

the total amount is £ 756.

hope it helps..

Answer:

150 cal

Step-by-step explanation:

5x30=150

Answer:

150 calories.

Step-by-step explanation:

Assuming there is the same amount of chocolate as well as cookie dough throughout the whole cookie.

You know that 1/5 of a chocolate chip cookie has 30 calories.

Find one cookie, by multiply 5 to both numbers. Set the equation:

1/5x = 30

Isolate the variable. Multiply 5 to both sides:

(1/5x) * 5 = (30) * 5

x = 30 * 5

x = 150

150 calories is your answer.

Answer:

22.12feet

Step-by-step explanation:

the ladder becomes your hypotenuse,the wall is the height,this forms a right angled triangle and the angle of elevation forms at the base,use sine which is opposite over hypotenuse to get your answer

Answer:

5/1

Step-by-step explanation:it goes up 5 and over 1

Answer:

Solution,

Let the points be A and B

A ( 8 , 2 ) -----> (X1 , y1 )

B ( 9 , 7 ) -------> (x2 , y2)

Now,

Slope =[tex] \frac{y2 - y1}{x2 - x1} [/tex]

[tex] = \frac{7 - 2}{9 - 8} [/tex]

[tex] = \frac{ 5}{1} [/tex]

[tex] = 5[/tex]

Hope this helps..

Good luck on your assignment...

Answer:

So for the first few small values of n, we have proven by demonstration that f(n) = n / (n+1).

Our task is to prove that if it works for any positive integer value of n, then it works for n + 1. This way, it must by induction work for all subsequent values of n.

Formally said, we need to prove that if for some positive integer n we can show that f(n) = n / (n+1), then we can conclude that f(n+1) = (n + 1) / (n + 2).

We begin the real "proof" by expanding f(n + 1):

f(n + 1) = f(n) + 1 / ((n+1)((n+1)+1)) because that's based on the construction.

= n / (n+1) + 1 / ((n+1)(n+2)) because f(n) = n / (n+1); this is called "using what you know from earlier".

= n(n+2) / ((n+1)(n+2)) + 1 / ((n+1)(n+2)) because we can multiply the left fraction by (n+2)/(n+2).

= (n2 + 2n + 1) / ((n+1)(n+2)) because we have a common denominator and can combine the numerators.

= (n+1)2 / ( (n+1)(n+2)) because we can factor the numerator now; it is a perfect square.

= (n+1) / (n+2) because we can cancel the common (n+1) factor from the numerator and denominator.

Q.E.D. (which means "that which was to be proven", in other words: "voilà")

Step-by-step explanation: