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The ideal length of a particular metal rod is 30.5 cm. The measured length may vary from the ideal length by at most 0.015 cm. What is the range of acceptable lengths for the rod?

Answer:

Instantaneous rate of change = -13

Equation of tangent line : y= -2x +6

Step-by-step explanation:

the instantaneous rate of change of the function [tex]f(x) = 6x^2 - x[/tex] at the point (-1,7)

To find instantaneous rate of change we take derivative

[tex]f(x) = 6x^2 - x[/tex]

[tex]f'(x) = 12x-1[/tex]

Now we plug in  -1 for x

[tex]f'(-1) = 12(-1)-1=-13[/tex]

Instantaneous rate of change = -13

the equation of the line tangent to the function f(x) at the point (1,4)

[tex]f(x) = -x^2 + 5[/tex]

To find slope of tangent line take derivative

[tex]f'(x) = -2x[/tex]

Plug in 1 for x . given point is (1,4)

[tex]f'(1) = -2(1)=-2[/tex]

so  slope = -2

use equation [tex]y-y1=m(x-x1)[/tex]

[tex]y-4=-2(x-1)[/tex]

[tex]y-4=-2x+2[/tex]

Add 4 on both sides

y= -2x +6

ANSWER

6w = 100

EXPLANATION

The formula for calculating the perimeter of a rectangular building is P=2l +2w.

From the question, the perimeter of the garden is 100 feet.

It was given that, the length of a rectangular garden is 3 times the width.

This implies that,

[tex]l = 3w[/tex]

We substitute into the formula to get:

[tex]2(3w)+2w = 100[/tex]

[tex]6w+2w = 100[/tex]

This simplifies to:

[tex]8w = 100[/tex]

The equation that can be used to find the width of the rectangular garden is 8w = 100.

To find the width of the rectangular garden, we can set up an equation based on the given information. Let's say the width of the garden is w. If the length is 3 times the width, then the length would be 3w. The perimeter of a rectangle is calculated by adding up all the sides, so in this case, it would be 2w + 2(3w) = 100 feet. Simplifying this equation gives us 8w = 100 feet. Therefore, the equation that can be used to find the width of the garden is 8w = 100.

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Answer:

$8.10

Step-by-step explanation:

First step is to determine the tax rate, which you can easily figure out with the first sentence, since you have $4.48 tax on $56 purchase.  The tax rate is then:

TR = 4.48 / 56 = 0.08 or 8%

Now, the question can be rephrased as "What's the total difference, including taxes, between a purchase of $66.25 (A) and another of $58.75 (B)"

Let's find out the total cost for both purchases:

A = 66.25 * 1.08 = 71.55 (66.25 + 8% tax)

B = 58.75 * 1.08 = 63.45 (58.75 + 8% tax)

Difference is then 71.55 - 63.45 = 8.10

The $66.25 purchase of goods will cost $8.10 more than the $58.75 purchase of goods once the 8% tax is applied.

The area of a circle is

[tex]a = r {}^{2} \pi[/tex]

So we get

[tex]a = 2.5 {}^{2} \pi[/tex]

so we get 19.6 rounded to the nearest tenth

Now we subtract that from the area of the square which is 25

We get 5.4

So the answer shoild be 5.4ft

Hopefully this is correct and helps you!

Answer:

5.4 ft²

Step-by-step explanation:

The area of the yellow region = area of square - area of circle

area of square = 5² = 25

note that the diameter of the circle = 5, thus radius = 2.5

area of circle = π × 2.5² = 6.25π

yellow region = 25 - 6.25π ≈ 5.4 ft²

Answer:

all but the second statement are correct

Step-by-step explanation:

The n roots of unity are evenly spaced around a circle of radius 1 in the complex plane. One of the roots is always 1. If n is even, -1 will also be a root.

Answer:

Step 2

Step-by-step explanation:

Jaime did not multiply by the reciprocal of 2/5 which is 5/2 on both sides.

5*5/2=25/2

The solution to the equation 2/5n+7=12 is n = 25/2

The mistake in Jamie's simplification of the equation is in Step 2.

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is  2/5n + 7 = 12

On simplifying the equation , we get

2/5n + 7 = 12

Subtracting by 7 on both sides of the equation , we get

2/5n = 12 - 7

2/5n = 5

Now , Multiplying by 5/2 on both sides of the equation , we get

n = ( 5/2 ) x 5

The value of n = 25/2

Therefore , the value of n is 25/2

Jamie made a mistake in step 2 while simplifying the equation by cross multiplying

Hence , The solution to the equation 2/5n+7=12 is n = 25/2

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Answer:

Identity Property

Step-by-step explanation:

The property shown in the given matrix addition is identity property (of addition)

Let's define additive identity first,

For all real numbers there is exists a number zero which is when added to any real number, the number remains the same. The number is called additive identity.

Similarly, for matrices, there exists a matrix of same dimensions that is when added to the matrix, gives the same result as the original matrix.

The matrix is denoted by O and it only contains zeros..

Answer:

Identity property

Step-by-step explanation:

Answer:

Binomial Distribution. ... The mean of a binomial distribution is p and its standard deviation is sqr(p(1-p)/n). The shape of a binomial distribution is symmetrical when p=0.5 or when n is large.

Step-by-step explanation:

This is about understanding binomial distribution curve.

Statement is false.

These 2 outcomes are usually termed success and failure.

For example when a coin is tossed, chance of success of getting a head is p = ½ while failure to get a head is q = 1 - p = ½

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The r value is a number between -1 and +1.

For a negative value, the closer to -1 it would be a strong negative, if it is closer to 0, it would be a strong negative.

-0.31 is closer to 0 than -1, so it would have a strong negative association.

Answer:

b

Step-by-step explanation:

The i is is square root of -1, which can be factored out from under the square root.

Answer:

[tex]\large\boxed{\dfrac{\boxed{8}}{81}}[/tex]

Step-by-step explanation:

[tex]\text{If}\ a_1,\ a_2,\ a_3,\ a_4,\ ...,\ a_n\ \text{is the geometric sequence, then}\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...=\dfrac{a_n}{a_{n-1}}=constant=r-\text{common ration}.\\\\\text{We have}\ \dfrac{1}{2},\ \dfrac{1}{3},\ \dfrac{2}{9},\ \dfrac{4}{27},\ ...\\\\\dfrac{\frac{1}{3}}{\frac{1}{2}}=\dfrac{1}{3}\cdot\dfrac{2}{1}=\dfrac{2}{3}\\\\\dfrac{\frac{2}{9}}{\frac{1}{3}}=\dfrac{2}{9}\cdot\dfrac{3}{1}=\dfrac{2}{3}\\\\\dfrac{\frac{4}{27}}{\frac{2}{9}}=\dfrac{4}{27}\cdot\dfrac{9}{2}=\dfrac{2}{3}[/tex]

[tex]\bold{CORRECT}\\\\\dfrac{x}{\frac{4}{27}}=\dfrac{2}{3}\qquad\text{multiply both sides by}\ \dfrac{4}{27}\\\\x=\dfrac{2}{3}\cdot\dfrac{4}{27}\\\\x=\dfrac{8}{81}[/tex]

Answer:

4

Step-by-step explanation:

The first term is the value of the term when n=1. It is 3. The common ratio is is the value being raised to the power of (n-1). It is 1/4. Put these numbers into the formula and do the arithmetic

S = 3/(1 -1/4) = 3/(3/4) = 3·4/3 = 4

The sum is 4.

Answer:

B, C, D are functions

Step-by-step explanation:

Functions are those that do not share an x value.  Look at A.  x-values are used twice everywhere except the vertex.  This is not a function, it is just a relation.  B does not at any time share x-values, so this is a function.  C is also a function, and so is D.  F is a vertical line that shares the same x value throughout the whole line, so this is definitely not a function.

Answer:

bcd

Step-by-step explanation:

i got it right

Answer:

14√2

Step-by-step explanation:

Using 45 45 90 triangle properties,

b = 28/√2 = 14√2

Answer:

14√2

Step-by-step explanation:

Answer:

The correct answer option is ST.

Step-by-step explanation:

We are given a figure of a right angled triangle and we are to determine whether which of the given segments is the projection of QT on RT.

We know that:

QT = QS + ST

Therefore, on RT, ST is the projection of QT since it comes mid way from Q to T.

So the correct answer option is ST.

Answer:

ST is the projection of QT on RT

Step-by-step explanation:

To Find : What segment is the projection of QT on RT?

Solution:

We are supposed to find the projection of QT

In the projection

We draw a perpendicular on RT with point Q

So, Perpendicular on RT is QS

So, ST is the projection of QT on RT

So, Option B is true

Hence ST is the projection of QT on RT

Answer:

25

Step-by-step explanation:

The book is 420 pages long and he reads 45 pages so he has 375 pages left.

The will read equal amounts during the next 15 days so 375 ÷ 15 = 25

George reads 45 pages each day

According to the problem,

Number of pages left after reading 45 pages = (420 - 45) = 375

So number of pages he read per day = 375/15 = 25

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Answer:it’s b

Step-by-step explanation:

Answer:

[tex]t=\frac{p}{(s_1-s_2)}[/tex]

Therefore, C is the correct option.

Step-by-step explanation:

We have been given the equation [tex]p=s_1t-s_2t[/tex]

The GCF of the right hand side of the equation is t. Hence, factored out the GCF.

[tex]p=(s_1-s_2)t[/tex]

Now, [tex](s_1-s_2[/tex] is in multiplication with 't'. So in order to isolate t, we can divide both sides by [tex](s_1-s_2)[/tex]

[tex]t=\frac{p}{(s_1-s_2)}[/tex]

Therefore, C is the correct option.

ANSWER

23.6 feet

EXPLANATION

The given triangle is a right triangle.

The hypotenuse is 27 ft.

The given angle I s 29°

The unknown side x, is adjacent to the given angle.

We use the cosine ratio to get,

[tex] \cos(29 \degree) = \frac{adjacent}{hypotenuse} [/tex]

[tex] \cos(29 \degree) = \frac{x}{27} [/tex]

We multiply both sides by 27 to get;

[tex]x = 27\cos(29 \degree) [/tex]

[tex]x = 23.6ft[/tex]

to the nearest tenth.

Answer:

x = 23.6

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

To find the value of x

From the figure we can see a right angled triangle, ABC

Cos 29 = Adjacent side/Hypotenuse

 = AB/AC

 = x/27

x = 27 * Cos 29

 = 27 * 0.87

 = 23.6

Therefore x = 23.6

The answer to this question is:

y = -2x - 1

Answer:

x = 4.1

Step-by-step explanation:

The line segment from the centre to the chord is a perpendicular bisector Thus one half of the chord = 15.6 ÷ 2 = 7.8

Consider the right triangle formed with legs x and 7.8 and hypotenuse 8.8

Using Pythagoras' identity on the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other two sides, then

x² + 7.8² = 8.8²

x² + 60.84 = 77.44 ( subtract 60.84 from both sides )

x² = 16.6 ( take the square root of both sides )

x = [tex]\sqrt{16.6}[/tex] ≈ 4.1

Usually you prove the medians are concurrent way before you get the Ceva's Theorem.  But we do the problem as given.  Next time try to include the whole problem in the photo.

FA=FB, BE=EC, CG=GA

Answer: C. Definition of median

The medians go to the midpoints of the sides, so we have congruent segments from the foot.

FA/FB=1, BE/EC=1, CG/GA=1

Answer: A. Division of equal segment lengths yields 1

This one is cut off so we can't read the full justification, but we have equal segments so their ratio is 1.

(FA/FB)(BE/EC)(CG/GA)=1

Answer: E. Substitution property

Again the justification is cut off, but we have three things equal to 1, when we multiply them together we still get 1.

Medians are Concurrent

Answer: B. Ceva's Theorem

This is really the converse of Ceva's Theorem; we have the required ratio product equal to 1, so we know the medians are concurrent.   Technically they might be parallel (which is concurrent in the projective sense, meeting at infinity).  So we really need to show they're not parallel as well, which they can't be, but they left that part out.

I don't like this proof very much.

Answer:

upper right 31 middle right 24, bottom right 55

upper middle 10, center box 7, lower middle 17

upper left 41, middle left 31, bottom left 72

Step-by-step explanation:

cat and dog is the overlapping part of th diagram, 31 people like both.

dog and not cat is the left side of the

diagram, 24 people only like dogs

the total of people who like dogs is adding the left number with the the center number and 55 people all like dogs

dislikes dogs likes cats is the right side of the diagram, 10 people

not dog not cat, those who want neither are outside both bubbles, 7

the total of people who would not get a dog is 17

the total of people who like cats is the middle of the chart and the right added together 31+10 is 41

the total of people who dont like cats is the left side and the number of people who dont like anything 24+7 is 31

the total number of all the people could be gotten by adding all the number on the display together 24+31+10+7=72

or by adding the other bottom totals 55+17= 72, or by adding the other left totals together 41+31=72

The first step of factorization is done for you.  All that is needed to be done is a simplification of the factored polynomial.

5x^2(x+4)+2(x+4)

*Factor out an (x+4)*

(x+4)(5x^2+2)

Hope this helps!!

Answer:

False

Step-by-step explanation:

The angle between a tangent and radius is right.

Use the converse theorem of Pythagoras to determine.

If the square on the longest side is equal to the sum of the squares on the other two sides then the triangle is right and the segment is a tangent.

longest side = 13.1 ⇒ 13.1² = 171.61

11.3² + 6.65² = 127.69 + 44.2225 = 171.9125

Since 171.61 ≠ 171.9125 the line is not a tangent

Answer:

The current at t = 0 is

[tex]I (0) = 2[/tex] units of current

Step-by-step explanation:

If the current flowing through an electric circuit is defined as the derivative of the charge as a function of time and we have the equation of the charge as a function of time, then, to find the equation of the current, we derive the equation of the charge.

[tex]q (t) = 3t ^ 2 + 2t-5[/tex]

[tex]\frac{dq(t)}{dt} = 3 (2) t ^ {2-1} +2t ^ {1-1} -0[/tex]

Simplifying the expression we have:

[tex]\frac{dq(t)}{dt} = 6t + 2t ^0\\\\\frac{dq(t)}{dt} = 6t + 2 = I (t)[/tex]

Finally, the equation that defines the current of this circuit as a function of time is:

[tex]I (t) = 6t +2[/tex]

Now to find the current at t = 0 we make [tex]I (t = 0)[/tex]

[tex]I (0) = 6 * 0 +2[/tex]

[tex]I (0) = 2[/tex] units of current

Answer:

x= -1, y= 1

Step-by-step explanation:

2x + 6y = 4.........(1)

8x - 5y = 45........(2)

multiply equation (1) by 4

8x + 24y = 16......(3)

subtract equation (3) by (2)

29y = 29

y = 1

then substitute y=1 in equation (1)

2x + 6(1) = 4

solving for x

x = -2/2 = -1

The solution to the system of equations 2x + 6y = 4 and 8x - 5y = 45 is x = 5 and y = -1, found by using the method of elimination.

To find the solution of the system of equations containing 2x + 6y = 4 and 8x - 5y = 45, we will use the method of elimination.

First, we will manipulate the first equation to line up with the second equation regarding the x coefficient. We do this by multiplying the entire first equation by 4, giving us 8x + 24y = 16 which we will call equation (3).

Next, we subtract equation (2) from equation (3) to eliminate the x variable: (8x + 24y) - (8x - 5y) = 16 - 45, leading to 29y = -29.

Dividing both sides by 29 gives us the value of y: y = -1.

To find x, substitute y = -1 back into the original equation (1): 2x + 6(-1) = 4. Solving for x we get 2x - 6 = 4, therefore 2x = 10 and x = 5.

We can conclude that the solution to the system of equations is x = 5 and y = -1.

Answer:

(52) is the homogeneous mixture

Answer:

[tex]\sqrt{5}[/tex]

Step-by-step explanation:

in this exercise, when asking you to simplify the fraction, you are actually asking to rationalize the denominator, that is, you operate the fraction until any square root of the denominator disappears

In order to do that, the first thing to do is multiply both the denominator and the numerator by the root that you want to eliminate, that is, by [tex]\sqrt{5}[/tex] :

[tex]\frac{5}{\sqrt{5}}*\frac{\sqrt{5} }{\sqrt{5} }  =\frac{5*\sqrt{5} }{\sqrt{5} *\sqrt{5} } = \frac{5\sqrt{5} }{\sqrt{5} ^{2} } =\frac{5\sqrt{5} }{5} =\sqrt{5}[/tex]

Answer:

the answer is 7.2

Step-by-step explanation:

the square root of 5 is 2.2 that plus 5 is 7.2

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