The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (8 pts) a) Use differentials to estimate the maximum error in the calculated area of the disk. b) What is the relative error

"can't exceed 975" means this is the largest value possible for C. So we could have C = 975 or smaller. We write this as [tex]C \le 975[/tex] which is read as "C is less than or equal to 975".

Answer:

5

Step-by-step explanation:

Answer:

0.05 inches per minute

Step-by-step explanation:

The formula for speed is [tex]Speed=\frac{Distance}{Time}[/tex]

The given distance is 6 inches and the time is 120 minutes. Plug in the components into the formula to solve for speed and reduce:

[tex]Speed=\frac{6}{120}[/tex]

[tex]Speed=\frac{1}{20}[/tex]

1/20 in decimal form is 0.05

Answer:

Step-by-step explanation:

Hope it helps.

Answer:

Answer:

data bar

Step-by-step explanation:

Answer:

chart

Step-by-step explanation:

Answer:

The difference of the functions is (f-g)(x) = 3x - 3

Step-by-step explanation:

In the problem, we are asked to find the difference of the two functions, f(x) and g(x). When we see (f-g)(x), this means that we are going to subtract g(x) from f(x).

f(x) = 5x - 2

g(x) = 2x + 1

(f-g)(x) = (5x - 2) - (2x + 1)

Distribute the negative to (2x + 1)

(f-g)(x) = 5x - 2 - 2x - 1

Combine like terms. Make sure your answer is in standard form.

(f-g)(x) = 3x - 3

So, the answer to the equation is (f-g)(x) = 3x - 3

Answer:

50 deg

Step-by-step explanation:

In an right triangle, the acute angles are complementary. That means their measures have a sum of 90 deg.

m<C + m<B = 90

7x - 20 + 4x = 90

11x = 110

x = 10

m<ACB= 7x - 20

m<ACB = 7(10) - 20

m<ACB = 70 - 20

m<ACB = 50

Answer: m<ACB = 50 deg

Answer:

y-int = C/B

Step-by-step explanation:

Ax + By = C

y-int = C/B

Answer:

I hope this helps.

Step-by-step explanation:

Answer:

A) 90

B) The individuals in the survey will be 11, 101, 191,...., 2621.

Step-by-step explanation:

Tenemos lo siguiente a partir del enuciado:

A) let, a consider a department has an alphabetical list of all 2708 employees at company and wants to conduct a systematic sample. Substitute the value as:

k = N/n

reemplanzado nos queda:

k = 2708/30 = 90.26

Lo que quiere decir que el valor de k es de aproximadamente 90 B) Randomly select the number between I and 90, Suppose the randomly selected sumber is 11. The individuals in the survey will be; need to find 30th team, hence by using the airthmetic perogression nth term formula:

30th term = 11+ (30 - 1) *90

30th term = 2621

The individuals in the survey will be 11, 101, 191,...., 2621.

The random sample is obtained

Answer:

$18

Step-by-step explanation:

Buying the jeans for $27 leaves you with ($60 - $27), or $33.

Buying the shirt for s dollar leaves you with $15.  To find s, the price of the shirt, you subtract $15 from $33:  $18.

The shirt cost you $18.

Answer:

  f(4) = g(4) and f(0) = g(0)

Step-by-step explanation:

In order for f(x) = g(x), the value of x must be the same in both functions:

  f(4) = g(4) . . . corresponds to x=4

  f(0) = g(0) . . . corresponds to x=0

The graph is not shown here, so we cannot say if these are the appropriate solutions. We can only say that the other choices are not.

f(x) = g(x) if ...

  f(4) = g(4) and f(0) = g(0)

__

Something like f(0) = g(4) is useless for finding solutions to f(x) = g(x).

Answer:

4,2,1 and 1/2

Step-by-step explanation:

The first term is 4 since A(1)=4

● A(2) = (1/2)*A(1) = (1/2)*4 = 2

So the second term is 2

● A(3) = (1/2)*A(2) = (1/2)*2= 1

The third term is 1

●A(4) = (1/2)*A(3) = (1/2) *1 = 1

Answer:show the table so I can help

Step-by-step explanation:

Answer:

Step-by-step explanation:

hello,

I assume that you mean

[tex]h(x)=\dfrac{12}{x-1}[/tex]

so first of all let's take x real different from 1 , as this is not allowed to divide by 0

[tex](hoh^{-1})(x)=x=h(h^{-1}(x))=\dfrac{12}{h^{-1}(x)-1} \ \ \ so\\h^{-1}(x)-1=\dfrac{12}{x} \\\\h^{-1}(x)=1+\dfrac{12}{x}[/tex]

and this is defined for x real different from 0

hope this helps

Answer:

The correct option is (B).

Step-by-step explanation:

The median (m) is a measure of central tendency. To obtain the median, we assemble the data in arising order. If the data is odd, the median is the mid-value. If the data is even, the median is the arithmetic-mean of the two mid-values.

The mean of a data set is:

[tex]\bar X=\frac{1}{n}\sum\limits^{n}_{x=0}{X}[/tex]

For the three kittens it is provided that the weights are in the range 147 g to 159 g.

So, the mean and median weight for the 3 kittens lies in the middle of this range.

Now a fourth kitten is born, with weight 57 g.

Now the range of the weight of 4 kittens is, 57 g to 159 g.

The mean is going to decrease as one more value is added to the data and the value is the least.

The median will also decrease because now the median will be mean of the 2nd and 3rd values.

But the mean would decrease more than the median because a smaller value is added to the data.

Thus, the correct option is (B).

Answer:

1. [tex]Area=16\,\pi=50.265[/tex]

2.- [tex]\frac{b}{a} =-8[/tex]

3.  [tex]y=\frac{1}{2} x^2+3x+\frac{5}{2}[/tex]

4.  [tex]a+b+c=\frac{17}{4}[/tex]

5.   the vertex is located at: (3, 10)

Step-by-step explanation:

1. If we rewrite the formula of the conic given by completing squares, we can find what conic we are dealing with:

[tex](x^2-2x)+(y^2+6y)=6\\\,\,\,\,\,\,+1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+9\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+10\\(x-1)^2+(y+3)^2=16\\(x-1)^2+(y+3)^2=4^2[/tex]

which corresponds to a circle of radius 4, and we know what the formula is for a circle of radius R, then:

[tex]Area=\pi\,R^2=\pi\,4^2=16\,\pi=50.265[/tex]

2.

If x=4 is the axis of symmetry of the parabola

[tex]y=ax^2+bx+c[/tex]

then recall the formula to obtain the position of the x-value of the vertex:

[tex]x_{vertex}=-\frac{b}{2a} \\4=-\frac{b}{2a}\\4\,(-2)=\frac{b}{a} \\\frac{b}{a} =-8[/tex]

3.  

From the graph attached, we see that the vertex of the parabola is at the point: (-3, -2) on the plane, so we can write the general formula for a parabola in vertex form:

[tex]y-y_{vertex}=a\,(x-x_{vertex})^2\\y-(-2)=a\,(x-(-3))^2\\y+2=a(x+3)^2[/tex]

and now find the value of the parameter "a" by requesting the parabola to go through another obvious point, let's say the zero given by (-1, 0) at the crossing of the x-axis:

[tex]y+2=a\,(x+3)^2\\0+2=a(-1+3)^2\\2=a\,2^2\\a=\frac{1}{2}[/tex]

So the equation of the parabola becomes:

[tex]y+2=\frac{1}{2} (x+3)^2\\y+2=\frac{1}{2} (x^2+6x+9)\\y+2=\frac{1}{2} x^2+3x+\frac{9}{2} \\y=\frac{1}{2} x^2+3x+\frac{9}{2} -2\\y=\frac{1}{2} x^2+3x+\frac{5}{2}[/tex]

4.

From the location of the focus of the parabola as (4, 3) and the directrix as y=1,  we conclude that we have a parabola with dominant vertical axis of symmetry, displaced from the origin of coordinates, and responding to the following type of formula:

[tex](x-h)^2=4\,p\,(y-k)[/tex]

with focus at: [tex](h,k+p)[/tex]

directrix given by the horizontal line [tex]y=k-p[/tex]

and symmetry axis given by the vertical line [tex]x=h[/tex]

Since we are given that the focus is at (4, 3), we know that [tex]h=4[/tex], and that [tex]k+p=3[/tex]

Now given that the directrix is: y = 1, then:

[tex]y=k-p\\1=k-p[/tex]

Now combining both equations with these unknowns:

[tex]k+p=3\\k=3-p[/tex]

[tex]1=k-p\\k=1+p[/tex]

then :

[tex]1+p=3-p\\2p=3-1\\2p=2\\p=1[/tex]

and we now can solve for k:

[tex]k=1+p=1+1=2[/tex]

Then we have the three parameters needed to write the equation for this parabola:

[tex](x-h)^2=4\,p\,(y-k)\\(x-4)^2=4\,(1)\,(y-2)\\x^2-8x+16=4y-8\\4y=x^2-8x+16+8\\4y=x^2-8x+24\\y=\frac{1}{4} x^2-2x+6[/tex]

therefore: [tex]a=\frac{1}{4} , \,\,\,b=-2,\,\,and\,\,\,c=6[/tex]

Then [tex]a+b+c=\frac{17}{4}[/tex]

5.

The vertex of a parabola can easily found because they give you the roots of the quadratic function, which are located equidistant from the symmetry axis. So we know that is one root is at [tex]x=3+\sqrt{5}[/tex]and the other root is at [tex]x=3-\sqrt{5}[/tex]

then the x position of the vertex must be located at x = 3 (equidistant from and in the middle of both solutions. Then we can use the formula for the x of the vertex to find b:

[tex]x_{vertex}=-\frac{b}{2a}\\3=-\frac{b}{2\,(-2)}\\ b=12[/tex]

Now, all we need is to find c, which we can do by using the rest of the quadratic formula for the solutions [tex]x=3+\sqrt{5}[/tex]  and [tex]x=3-\sqrt{5}[/tex] :

[tex]x=-\frac{b}{2a} +/-\frac{\sqrt{b^2-4\,a\,c} }{2\,a}[/tex]

Therefore the amount [tex]\frac{\sqrt{b^2-4\,a\,c} }{2\,a}[/tex],  should give us [tex]\sqrt{5}[/tex]

which means that:

[tex]\sqrt{5}=\frac{\sqrt{b^2-4\,a\,c} }{2\,a} \\5=\frac{b^2-4ac}{4 a^2} \\5\,(4\,(-2)^2)=(12)^2-4\,(-2)\,c\\80=144+8\,c\\8\,c=80-144\\8\,c=-64\\c=-8[/tex]

Ten the quadratic expression is:

[tex]y=-2x^2+12\,x-8[/tex]

and the y value for the vertex is:

[tex]y=-2(3)^2+12\,(3)-8=-18+36-8=10[/tex]

so the vertex is located at: (3, 10)

Answer:

(f * g)(x) has a final product of 16x² + 8x.

Step-by-step explanation:

When you see (f * g)(x), this means that we are going to be multiply f(x) and g(x) together.

f(x)=8x

g(x)=2x+1

Now, we multiply these terms together.

(8x)(2x + 1)

Use the foil method to multiply.

16x² + 8x

So, the product of these terms is 16x² + 8x.

Answer:

Se pagará $7200.

Step-by-step explanation:

La ecuación del costo puede descomponerse en dos factores que luego se multiplican:

1) Siendo A el area del del muro, la parte del costo que depende del área se calcula como un tercio (1/3) del doble (2) del área A. Este factor se puede escribir como:

[tex]C_1=(1/3)\cdot 2 \cdot A=(2/3)\cdot A[/tex]

2) Siendo T el número de trabajadores, el siguiente factor es el triple del numero de trabajadores T. Esto es:

[tex]C_2=3T[/tex]

Multiplicando ambos factores, tenemos la ecuacion del costo en función de A y T:

[tex]C=C_1\cdot C_2=(2/3)A\cdot 3T=2 AT[/tex]

Si se planea pintar un muro de 1200m² y se contrataran a 3 trabajadores, el costo será:

[tex]C=2AT=2(1200)(3)=7200[/tex]

Answer: D, 28 bottles.

Step-by-step explanation:

This can be translated to:

26.5 liters of water and 8.25 liters of orange juice are mixed together. All that mixture  is bottled in bottles of  1.25 liters. How many bottles are needed  to fill all the orange juice mixture?

the total mass of mixture that we have is:

26.5 L + 8.25 L = 34.75 L.

if we want to divide it into groups of 1.25 L, we have:

N = 34.75/1.25 = 27.8

So we have 27.8 groups of 1.25L this means that we need 27.8 bottles.

But we can not have a 0.8 of a bottle, so we must round it up to 28 bottles.

Then the correct option is D:

Answer:

Step-by-step explanation:

1l ........8.5 miles

x l .......6 miles

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

x=6*1/8.5

x=0.70 l

2*0.7=1.4 l petrol/day ( to work and come back home)

5*1.4=7 l/week ( 5 days works in a week)

7*1.26=8.82 L /week

8.82>8.5

The petrol costs more

So the answer is NO

Answer:

The correct answer option is: No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.

Answer:

[tex]\displaystyle x=- \frac{5}{7}[/tex]

Step-by-step explanation:

[tex]5(2x-7)+42-3x=2[/tex]

Expand brackets.

[tex]10x-35+42-3x=2[/tex]

Combine like terms.

[tex]10x-3x+42-35=2[/tex]

[tex]7x+7=2[/tex]

Subtract 7 on both sides.

[tex]7x+7-7=2-7[/tex]

[tex]7x=-5[/tex]

Divide both sides by 7.

[tex]\frac{7x}{7} =\frac{-5}{7}[/tex]

[tex]x=- \frac{5}{7}[/tex]

Answer:

[tex] \boxed{\sf x = - \frac{5}{7}} [/tex]

Step-by-step explanation:

[tex] \sf Solve \: for \: x: \\ \sf \implies 5(2x-7)+42-3x=2 \\ \\ \sf 5(2x - 7) = 10x - 35 : \\ \sf \implies \boxed{ \sf 10x - 35} - 3x + 42 = 2 \\ \\ \sf Grouping \: like \: terms, \: 10x - 35 - 3x + 42 = \\ \sf (10x - 3x) + ( - 35 + 42) : \\ \sf \implies \boxed{ \sf (10x - 3x) + ( - 35 + 42)} = 2 \\ \\ \sf 10x - 3x = 7x : \\ \sf \implies \boxed{ \sf 7x} + ( - 35 + 42) = 2 \\ \\ \sf 42 - 35 = 7 : \\ \sf \implies 7x + \boxed{ \sf 7} = 2 \\ \\ \sf Subtract \: 7 \: from \: both \: sides: \\ \sf \implies 7x + (7 - \boxed{ \sf 7}) = 2 - \boxed{ \sf 7} \\ \\ \sf 7 - 7 = 0 : \\ \sf \implies 7x = 2 - 7 \\ \\ \sf 2 - 7 = - 5 : \\ \sf \implies 7x = \boxed{ \sf - 5} \\ \\ \sf Divide \: both \: sides \: of \: 7x = - 5 \: by \: 7: \\ \sf \implies \frac{7x}{7} = \frac{ - 5}{7} \\ \\ \sf \frac{7}{7} = 1 : \\ \\ \sf \implies x = - \frac{5}{7} [/tex]

Answer:

step 1

Step-by-step explanation:

when you say three less than the quotient

you put the quotient first and then subtract 3

Answer: Step 1

Step-by-step explanation: I took it on my quiz and got an 100

Answer:

(Option A) . No, because the histogram of the data is not bell shaped, there is more than one outlier, and line points in the normal quantile plot do not lie reasonably close to a straight line.

Step-by-step explanation:

After plotting the histogram, you will see that the data does not represent the normal distribution because the histogram is not bell shaped and there are two outliers.

Answer: y=x+1

Step-by-step explanation:

y+1=1(x+2)

y+1=x+2

y=x+1

Hope this helps:)

Answer:

$1.08

Step-by-step explanation:

30 days × (2 hrs/day) × (150 W) × (1 kW / 1000 W) × (0.12 $/kWh) = $1.08

Answer:

A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1

Step-by-step explanation:

Given the sequence:

We can easily calculate the difference of terms:

As the difference of terms is same and equal to -4, it is the AP (arithmetic progression)

This sequence can be defined In the form of function as:

All the above matches the first answer choice:

Answer:

56%

Step-by-step explanation:

We have a grid with 10 columns and 10 rows making 100 equal sized squares, they tell us that 5 rows are unshaded. Therefore half is unshaded, like so:

5 rows = 50 squares

They also tell us that the sixth row has 6 squares unshaded, which means that in total they would be:

 50 + 6 = 56 squares

Knowing that the total is 100, the percentage would be:

56/100 = 0.56, that is, 56% are unshaded

Answer:

the boat is going at 3.5 mph and the current is going at .5 mph

Step-by-step explanation: