What is the place value of 7 in 0.724 rounded.

Answer:

well, okay. its basically what you wrote. assuming there was missing information.

let's dive right into it.

we'll assume that the problem asks for integers, whole numbers.

if x would be 0,

we would get 9 numbers out, 0, -1, -2, -3, -4, -5, -6, -7 and -8

if x would one, the range would be from 7 to -8, giving us 16 numbers

if x would be 2, the range would be from 14 to -8, giving us 23 numbers (7 more each time we increasex by one)

so the answer isn't a fixed value, but a function.

7x+9

the plus nine is true when x=0 and is still relevant for every other scenario

Answer:

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

Apply the Triangle Inequality Theorem.

It states that:

We'll take the sum of two shortest sides and compare with the longest:

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).

The extreme values of the function subject to the given constraint is 512.

Apply Lagrange multipliers

f(x,y,z) = xy²z

g(x,y,z) = x² + y² + z² - 64 condition

F(x,y,z,λ) = xy²z - λ(x² + y² + z² - 64)

Calculate first order derivatives

Fx = y²z - 2xλ

Fy = 2xyz - 2yλ

Fz = y²x - 2zλ

Fλ = -( x² + y² + z² - 64 )

Apply the critical points conditions(Match previous derivatives to zero)

y²z - 2xλ = 0                                    equation 1

2xyz - 2yλ = 0                                  equation 2

y²x - 2zλ = 0                                     equation 3

-( x² + y² + z² - 64 ) = 0                     equation 4

Clearing λ in the first three equations

λ = y²z/2x

λ = xz

λ = y²x/2z

y²z/2x =  y²x/2z

x² = z²

z = ±x

y²z/2x = xz

y² = 2x²

y = ±\(\sqrt 2x\)

Substituting in the equation 4

z = ±x     y = ±\(\sqrt 2x\)

x² + y² + z² - 64  = 0

x² + (    \(\sqrt{2x}\))²+ z² - 64 = 0

x² + 2x² + x² = 64

4x² = 64

x = 4

y = ±4√2

z = ±4

The critical points are:

P1(4,4√2,4)

P2(4,-4√2,-4)

P3(4,-4√2,4)

P4(4,-4√2,-4)

P5(-4,-4√2,-4)

P6(-4,4√2,4)

P7(-4,-4√2,4)

P8(-4,4√2,-4)

Evaluate the points in the function to determine conditional maximums and minimums

f(x,y,z) = xy²z

P1(4,4√2,4) = 512 = maximum point

P2(4,-4√2,-4) = -512 = minimum point

P3(4,-4√2,4) = 512 = maximum point

P4(4,-4√2,-4) = -512 = minimum point

P5(-4,-4√2,-4) = 512 = maximum point

P6(-4,4√2,4) = -512 = minimum point

P7(-4,-4√2,4) = -512 = minimum point

P8(-4,4√2,-4) = 512 = maximum point

So,

Minimum points

(4,-4√2,-4)

(4,-4√2,-4)

(-4,4√2,4)

(-4,4√2,4)

Minimum value of function = -512

Maximum points

(4,4√2,4)

(4,-4√2,4)

(-4,-4√2,-4)

(-4,4√2,-4)

Maximum value of function = 512

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Answer:

The minimum cost is $17.30c

Step-by-step explanation:

Given

\(V = 288\) --- Volume

\(C_1 = 0.06\) --- cost of wall paint

\(C_2 = 0.16\) ---cost of ceiling paint

Required

Minimum cost of paint

The volume is calculated as:

\(V =xyz\)

Substitute 288 for V

\(288 =xyz\)

Make z the subject

\(z = \frac{288}{xy}\)

The surface area is calculated as:

\(Area = 2(yz + xz) + xy\)

Because xy represent the dimension of the ceiling and the opposite of the ceiling (the floor) will not be painted. Hence, it does not require a coefficient of 2

The cost is:

\(C = 0.06 * 2(yz + xz) + 0.16 * xy\)

Substitute \(z = \frac{288}{xy}\)

\(C = 0.06 * 2(y*\frac{288}{xy} + x*\frac{288}{xy}) + 0.16 * xy\)

\(C = 0.06 * 2(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy\)

\(C = 0.12(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy\)

\(C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 * xy\)

\(C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy\)

Differentiate w.r.t x and y

\(C_x = -\frac{34.56}{x^2} + 0.16y\)

\(C_y = -\frac{34.56}{y^2} + 0.16x\)

By comparison: \(x = y\)

Set them equal to 0

\(C_y = -\frac{34.56}{y^2} + 0.16x=0\)

\(-\frac{34.56}{y^2} + 0.16x=0\\\)

Substitute x for y

\(-\frac{34.56}{x^2} + 0.16x=0\)

\(0.16x=\frac{34.56}{x^2}\)

Cross multiply

\(0.16x^3 = 34.56\)

\(x^3 = \frac{34.56}{0.16}\)

\(x^3 = 216\)

Take the cube root of both sides

\(x = \sqrt[3]{216}\)

\(x = 6\)

\(x=y= 6\)

Substitute 6 for x and for y in \(C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy\)

\(C = (\frac{34.56}{6} + \frac{34.56}{6}) + 0.16 * 6* 6\)

\(C = (\frac{2*34.56}{6}) + 5.76\)

\(C = 11.52 + 5.76\)

\(C = 17.28\)

\(C = 17.3\) --- approximated

Answer:

One hour

Step-by-step explanation:

48 miles in 48 minutes

X miles. In 60minutes

48/48 = x/60 (cross multiplication)

(48*60)/48 = 60 minutes

Answer:

y=1.5

x=-3.5

Our answer is (-3.5,1.5)

Step-by-step explanation:

y-5=x

x=-2-y

y=?

--------

Using substitution,

y-5=-2-y

Solve:

2y-5=-2

2y=3

y=1.5

We can enter 1.5 into the equation:

1.5-5=x

-3.5=x

Since the values on both sides are difference, hence the system of equation has no solution

Given the following system of equation

x + y = 7

2x + 2y = 8

The solution by graphing is the point where the two lines intersect on the xy-plane

From equation 1;

x = 7 - y

Substitute into equation 2 to have:

2x + 2y = 8

x + y = 4

7 - y + y = 4

7 =4

Since the values on both sides are difference, hence the system of equation has no solution

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Answer:

(x,y) is in the Quadrant II.

Step-by-step explanation:

The Quadrant II contains the x-values that are less than 0 (negative x-values), while the y-values are greater than 0 (positive y-values). Therefore, if x < 0 and y > 0, then point (x, y) must be somewhere in Quadrant II of the Cartesian Plane.

Please mark my answers as the Brainliest if my explanations were helpful :)

Therefore , the solution of the given problem of expression comes out to be for addition +2 and subtraction -2.

Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.

Here,

Given :

So, for addition expression:

=> -5 + 2 = -3

So , for the subtraction expression:

=> -5 -(-2) = -3

Therefore , the solution of the given problem of expression comes out to be for addition +2 and subtraction -2.

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Answer: d- they are not perpendicular because their slopes are not negative reciprocals.

Step-by-step explanation:

The statement best explains the relationship between lines FG and HJ is They are not perpendicular because their slopes are not negative reciprocals, the correct option is D.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

We are given that;

The graph of line FG and HJ

Now,

The slope of line FG can be found by using the points (-4, 1) and (0, -2):

m = (-2 - 1) / (0 - (-4)) = -3 / 4

The slope of line HJ can be found by using the points (-4, -2) and (0, 4):

m = (4 - (-2)) / (0 - (-4)) = 6 / 4 = 3 / 2

The slopes of lines FG and HJ are not negative reciprocals of each other, since -3/4 is not equal to -1/(3/2) or 2/3. So, lines FG and HJ are not perpendicular.

Therefore, the answer will be they are not perpendicular because their slopes are not negative reciprocals.

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Explanation

Step 1

do the product of the functions:( apply distributive property)

so, the answer is

I hope this helps you

The result of the multiplication in scientific notation is given by:

\(6 \times 10^{6}\)

A number in scientific notation is given by:

\(a \times 10^b\)

With the base being \(a \in [1, 10)\).

When we multiply two numbers in scientific notation, we multiply the bases and add the exponents.

For this problem, the numbers are given by:

\(3 \times 10^{-4}, 2 \times 10^{10}\)

The result of the multiplication is given by:

\(3 \times 10^{-4} \times 2 \times 10^{10} = 6 \times 10^{-4 + 10} = 6 \times 10^{6}\)

The result of the multiplication in scientific notation is given by:

\(6 \times 10^{6}\)

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Answer:

y= 11x

Step-by-step explanation:

find the slope: 22-11/2-1= 11/1 or 11

To find the y-intercept you can use the slope by subtracting 11 (inverse operation) from the y value of (1,11). So the y- intercept is (0,0). To write the equation plug in 11 for m and 0 for b. Since 0 has no value the equation would be y= 11x

Answer:

A) \(I=\frac{P}{4\pi r^2}\)

Step-by-step explanation:

To isolate \(I\), we need to divide both sides by \(4\pi r^2\). Therefore, the answer is \(I=\frac{P}{4\pi r^2}\).

Based on an equation, the amount that Isabel spent on bread was $2.42.

To solve the equation for the amount spent on bread, we determined the total amount Isabel spent by subtracting the change from the total bills she had.

An equation is a mathematical statement of the equality or equivalence of two or more mathematical expressions.

The amount Isabel spent on vegetables = $15.91

The amount she spent on fruits = $11.22

Let the amount she spent on bread = x

The total amount she went with = $30 (3 x $10)

The change she got after giving the cashier $30 = $0.45

The total amount Isabel spent for vegetables, fruits, and bread = $29.55 ($30.00 - $0.45)

x = $2.42 ($29.55 - $15.91 - $11.22)

Check:

Vegetables = $15.91

Fruits = $11.22

Bread = $2.42

Total expenses = $29.55

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Answer:

12/55

Step-by-step explanation:

Probability is the ratio of the number of possible outcomes to the number of total outcomes.

Given that the bag contains 8 red balls and 3 white balls, the probability of picking a red ball

p(r) = 8/(8+3) = 8/11

Probability of picking a white ball

= 3/11

when a red ball is picked first, the total number of balls reduces to 10 hence the probability that the second ball is white, given that the first ball is red

=8/11 * 3/10

= 24/110

= 12/55

Answer:

1/17

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

17

To take the reciprocal of the number, we simply take its fraction form and flip it:

17 = 17/1

Flip

1/17

Answer:

Step-by-step explanation:

6x

Answer:

Based on the information given, we know that angles 3 and 4 are supplementary (they add up to 180 degrees) and angles 2 and 4 are vertical angles (they are congruent). Therefore, we can write:

m∠4 + m∠3 = 180 (since angles 3 and 4 are supplementary)

m∠4 = m∠2 (since angles 2 and 4 are vertical angles)

Substituting m∠4 = m∠2 into the first equation, we get:

m∠2 + m∠3 = 180

Now we can solve for m∠2 and m∠3:

m∠3 = 43 (given)

m∠2 = 180 - m∠3 = 180 - 43 = 137

Since angles 1 and 2 are also supplementary, we can find m∠1 by subtracting m∠2 from 180:

m∠1 = 180 - m∠2 = 180 - 137 = 43

Therefore, m∠1 = 43 degrees and m∠2 = 137 degrees.

Answer:

P(A∩B) = 0

P(A) = 0.1667

P(B) = 0.8333

=================================================

Explanation:

The events

are mutually exclusive. There isn't any overlap. This is because event B involves "at least 2 rolls", meaning we cannot get 5 on the first roll. Either event A happens, or B does, but not both at the same time.

This allows us to say P(A∩B) = 0

In a venn diagram, the overlapped region between circles A and B would have probability 0 marked inside.

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

P(A) = 1/6 since there is exactly one side labeled "5" out of 6 sides total. This converts to the approximate decimal form 1/6 = 0.1667 when rounding to four decimal places. The 6's go on forever, but of course we have to round at some point.

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

We found that P(A) = 1/6. The complement to this is 1-(1/6) = 5/6, which is the probability of rolling anything but a "5". This fraction represents the scenario "at least 2 rolls are needed for the 1st '5' to show up" since we forced the first roll to be anything but 5.

Put another way, we have two options:

The two probabilities 1/6 and 5/6 add to 6/6, aka 1, to represent 100% of all possible cases. This means P(A)+P(B) = 1 for this scenario.

The fraction 5/6 converts to the approximate decimal form of 5/6 = 0.8333; use a calculator or long division to determine this value.

Answer:

Step-by-step explanation:

5 ≤ - 3x- 3 ≤ 10

x

few notes about inequality

the direction of the inequality doesn't change if you

the direction of the inequality does change

if you

\(step - 1 : difine\)

\(5 \leqslant - 3x - 3 \leqslant 10\)

\(step - 2 : \\ add \: 3 \: in \: each \: sides\)

\(5 + 3 \leqslant - 3x - 3 + 3 \leqslant 10 + 3\)

\(8 \leqslant - 3x \leqslant 13\)

\(step - 3 : \\ divide \: - 3\: from \: each \: sides \: \\ and \: swap \: the \: inequalily\)

\( \therefore - \frac{8}{3} \geqslant x \geqslant - \frac{13}{3} \)

Answer:

c

Step-by-step explanation:

it is c because it said girls to boys, then explained girls to boys, while b was out of order. a and d said 5 first, contrary to the original question

Answer:

C because all the other options are from boys to girls or 5 to 2 and were looking for girls to boys or 2 to 5.

Step-by-step explanation:

The coefficient of variation for A is 20.37% and for B is 15.98%.

What is coefficient of variation?

In statistics, the relative standard deviation (RSD), commonly referred to as the coefficient of variation formula (CV), is a standardized way to assess how widely spaced out a probability distribution or frequency distribution is. Lower values of the coefficient of variation indicate that the data is highly stable and less variable.

We know that formula for coefficient of variation is

CV = Standard Deviation / Mean

A. $31,100, $25,800, $36,300, $30,200, $30,000, $19,800, $22,300, $22,600, $34,900, $21,700, $36,900, $30,800, $31,700, $37,100

Mean = 411200 / 14

Mean = $29371.42

Similarly,

Standard Deviation = $5984.52

So,

CV = 5984.52 / 29371.42 * 100

CV = 20.37%

B. 3.18, 4.24, 4.27, 4.38, 3.87, 4.75, 3.43, 3.35, 4.16, 4.81, 2.98

Mean = 43.42 / 11

Mean = $3.94

Similarly,

Standard Deviation = $0.63

So,

CV = 0.63 / 3.94 * 100

CV = 15.98%

Hence, the coefficient of variation for A is 20.37% and for B is 15.98%.

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Answer:

The perimeter of the pentagon ≅ 19 units (approximately)

Step-by-step explanation:

Clockwise, starting from the base of the pentagon, we have:

The base of the pentagon or bottom side ≅ 4 units

2nd side ≅ 3.75 units

3rd side ≅ 3.75 units

4th side ≅ 3.75 units

5th side ≅ 3.75 units

In consequence,

Perimeter of the pentagon ≅ 4 + 3.75 + 3.75 + 3.75 + 3.75

The perimeter of the pentagon ≅ 19 units

The solution to the algebraic problem is \(x^{2}\)

What is an Algebraic Equation?

An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.

Solution:

(\(x^{3}\) – 1) = (x+2)

On dividing (\(x^{3} - 1\)) by (x+2)

The first term of the quotient will be x^2 by following the Long Division Method of Algebraic Division.

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Answer:

B

Step-by-step explanation:

Stage 1: 10 exterior faces

Stage 2: 18 exterior faces

Stage 3: 26 exterior faces

Difference between stage 2 and stage 1: 18 - 10 = 8

Difference between stage 3 and stage 3: 26 - 18 = 8

The constant difference is 8. The first term (Stage 1) is 10.

Answer: B

Answer:

8+2\(\sqrt{20\\}\\\)

Step-by-step explanation:

2+2+2+2+\(\sqrt{20\\}\\\)+\(\sqrt{20\\}\\\)=8+2\(\sqrt{20\\}\\\)

4^2+2^2=h^2

20=h^2

h=\(\sqrt{20\\}\\\)

Answer:

\(\displaystyle \frac{cd^6}{a^4b^2}\)

Step-by-step explanation:

\(\displaystyle \frac{a^{-4}b^{-2}cd^6}{e^{-7}}\\\\=a^{-4}b^{-2}cd^6e^7\\\\=\frac{cd^6}{a^4b^2}\)

Notice that the variables with negative exponent that were originally in the denominator went to the numerator (like with \(e^{-7}\)) and became positive, and vice versa with those originally in the numerator went in the denominator (like with \(a^{-4}b^{-2}\)) and also became positive.

Step-by-step explanation:

a‐⁴b‐²cd⁶

_______

e‐⁷

cd⁶e⁷

_____

a⁴b²

Answer:

2

Step-by-step explanation:

The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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