rounding to 1 significant figure, estimate the answers to these questions:
a)
78 x 92
b)
615 x 38
c)
423 x 764

A linear function because the data has a common ratio of 70 miles per hour. The answer is C.

The rate of change of a linear function is constant, which means it doesn't change as the input variable increases or decreases.

This rate of change is also known as the slope of the line, and it represents how steeply the line is inclined.

The formula for calculating the slope of a line is:

slope = (change in y) / (change in x)

For the table, the rate of change is constant and the value is:

slope = change in distance / change in time

slope = (360 - 430)/(2 - 1) = 70 miles per hour

Therefore,  the data can model a linear function because the data has a common ratio of 70 miles per hour.

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Answer:

If its all multiplying its 1644.032 but if it's not all multiplying then that will be wrong

Answer:

Proportionate to whatever length the corresponding segment for the similar triangle.

Answer:

Here is the ans...Hope it helps :)

So, the probability of rolling two consonants is 1/1.

The probability of rolling two consonants when rolling a six-sided cube with the letters S, O, L, V, E and D, we first need to determine the number of consonants and the total number of outcomes.

The given letters are S, O, L, V, E, and D. Out of these, the consonants are S, L, V and D.

So, there are 4 consonants in total.

The cube has 6 sides, meaning there are 6 possible outcomes when rolling it.

To find the probability, we divide the number of favorable outcomes (rolling two consonants) by the total number of outcomes.

The number of favorable outcomes is given by the number of ways we can choose 2 consonants out of the 4 available.

This can be calculated using combinations, denoted as "C."

The number of ways to choose 2 consonants out of 4 is written as C(4, 2) or 4C2.

C(4, 2) = 4! / (2! × (4 - 2)!)

= 4! / (2! × 2!)

= (4 × 3 × 2 × 1) / (2 × 1 × 2 × 1)

= 6

So, there are 6 ways to choose 2 consonants out of the 4 available.

The total number of outcomes is 6, as there are 6 sides on the cube.

Now, we can calculate the probability:

Probability of rolling two consonants = Number of favorable outcomes / Total number of outcomes

Probability of rolling two consonants = 6 / 6 = 1

The probability of rolling two consonants is 1.

Expressing it as a fraction in simplest form, we have:

1/1

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The surface with the given vector equation, r(s, t) = (s cos(t), s sin(t), s), is a circular cone.

The vector equation r(s, t) = (s cos(t), s sin(t), s) represents a surface in three-dimensional space. Let's analyze the equation to determine the nature of the surface.

In the equation, we have three components: s, cos(t), and sin(t). The presence of s indicates that the surface expands or contracts radially from a central point. The trigonometric functions cos(t) and sin(t) determine the angle at which the surface extends in the x and y directions.

By observing the equation closely, we can see that as s increases, the radius of the surface expands uniformly in all directions, while the height remains constant. This behavior is characteristic of a circular cone. The circular base of the cone is defined by s cos(t) and s sin(t), and the vertical component is determined by s.

Therefore, the surface described by the vector equation r(s, t) = (s cos(t), s sin(t), s) is a circular cone.

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Answer:

7

Step-by-step explanation:

7 square is 49. 44 is 5 less than 49.

so the correct answer is 7

The missing term in the equation (x + 9)² = x² + 18x + is 81. The simplified form of the (x + 9 )² = x² + 18x + 81. The correct option is C.

Given

(x + 9)² =  x² + 18x +----

Required to find the missing term =?

It is given the form of ( a + b)² = a² + 2ab + b²

Putting the given values in the above form we get the value of the missing term from the equation

(x + 9 )² = x² + 2 × x ×9 + 9 × 9

              = x² + 18x + 81  

A quadratic equation is a second-order polynomial equation in one variable that goes like this: x ax2 + bx + c=0, where a 0. Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.

Thus, we get the value of the missing term as 81.

Thus, the ideal selection is option C.

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$16,200

1) Coletando los datos

Valor presente: 5,000

rate: 9%

Tiempo: 36 meses

2) Escribindo la formula y despues aplicando los datos, tienemos:

Mira que subtraemos de lo Valor Futuro, el Principal. A -P = i

3) Entonces el interés simple és $16,200

A matrix consisting entirely of zeros is called a zero matrix, or an all-zero matrix.

It is denoted with the symbol O and can be written in a matrix form, such as O = [0 0 0 0] where the number of columns and rows depends on the size of the matrix. A zero matrix is a matrix which has all its elements equal to zero. It has a number of special properties that make it useful in linear algebra. For instance, the sum of any two zero matrices is a zero matrix, and any scalar multiple of a zero matrix is a zero matrix. Additionally, the product of two zero matrices is a zero matrix, and the product of a zero matrix and an identity matrix is a zero matrix. These properties make it useful in solving systems of linear equations where all the coefficients are zero. Finally, the inverse of a zero matrix does not exist since its determinant is zero.

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The third length of the acute triangle is calculated by suing the formula ∠A + ∠B + ∠C = 180°.

The term acute triangle is defined as a type of triangle in which all the three internal angles of the triangle are acute and they are also called acute-angled triangles.

Here we know that the length of the sides of acute triangles differs, but the value of interior angles are never more than 90°.

Here we need to find the way to find the third length of acute triangle.

In order to find the third angle of an acute triangle, then we have to add the other two sides and then subtract the sum from 180°.

Therefore, the formula to find the third angle is written as,

=> ∠A + ∠B + ∠C = 180°.

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Answer:

$2.72

Step-by-step explanation:

To calculate the amount to be paid as tax, we simply find 13.6% of the amount before tax

Mathematically, that would be;

13.6/100 * 16 = $2.716

To the nearest hundredth is $2.72

According to the given information, the noise level in a restaurant is normally distributed with an average of 30 decibels. To find the value below which 99% of the time the noise level is, we need to use the Z-table.

We know that 99% of the area under the normal curve is below a Z-score of 2.33 (found from the Z-table).

To find the corresponding noise level value, we use the formula:

Z-score = (X - μ) / σ

where X is the noise level value we want to find, μ is the average (30 decibels), and σ is the standard deviation (which is not given in this question).

However, we can use the empirical rule (68-95-99.7 rule) to estimate the standard deviation. According to the rule, 99.7% of the data falls within 3 standard deviations of the mean. So, if 99% of the time the noise level is below a Z-score of 2.33, then we can estimate that the standard deviation is approximately:

(2.33 x σ) = 3

Solving for σ, we get:

σ = 3 / 2.33 = 1.29 (approx.)

Now we can use the formula above to find the noise level value below which 99% of the time the noise level is:

2.33 = (X - 30) / 1.29

X - 30 = 2.33 x 1.29

X = 33.01

So, 99% of the time, the noise level in the restaurant is below 33.01 decibels (rounded to two decimal places).

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Answer:

P(B and B) = 1/9

Step-by-step explanation:

There are 4+3+5 = 12 tiles in total

The probability of selecting a B would be 4/12=1/3

When you are replacing a B tile, planning to pick a B tile again, the total tile count doesn't change. Therefore, because the two events are independent, their probabilities are multiplied and so P(B and B) = P(B) * P(B) = 1/3 * 1/3 = 1/9

Answer:

(-3, -7)

Step-by-step explanation:

2x - y =  7                 multiply by -1  ⇔     -2x + y = -7

1x - y = 10                Do not change ⇔     1x -  y =  10  

                                                                     -x   = 3

                                                                      x = -3

Use the second equation to solve on y when x = -3

-1x - y = 10

-1(-3) - y = 10

 3 - y = 10

    -y = 10 - 3

    -y  = 7

     y = -7                         Solution:  (-3, -7)

A change in production from x = 10 to x = 70 boxes would add $2,038.77 to the total cost. This can be answered by the concept of integration.

To find the added cost of a change in production from x = 10 to x = 70 boxes, we need to calculate the total cost of producing each quantity and then find the difference between the two.

The total cost of producing x boxes is given by the integral of the marginal cost function:

C(x) = ∫(7 + x²/1000) dx = 7x + (x³/3000) + C

where C is the constant of integration.

To find the value of C, we can use the initial condition that the cost of producing 10 boxes is $100:

C(10) = 7(10) + (10³/3000) + C = 100
C = 30.33

Therefore, the total cost of producing x boxes is:

C(x) = 7x + (x³/3000) + 30.33

The added cost of producing 70 boxes instead of 10 is:

C(70) - C(10) = (7(70) + (70³/3000) + 30.33) - (7(10) + (10³/3000) + 30.33)
= $2,038.77

Therefore, a change in production from x = 10 to x = 70 boxes would add $2,038.77 to the total cost.

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The correct arrangement of the areas of the figures from the least to the greatest is Y < X < Z.

The area of the figures is calculated as follows;

area of the triangle;

Area = ¹/₂ x base x height

Area = ¹/₂ x 14 m x 22.5 m

Area = 157.5 m²

area of the circle is calculated as follows;

Area = πr²

where;

Area = π x ( 7 m )²

Area = 153.94 m²

The area of the parallelogram is calculated as follows;

Area = base x height

Area = 15.5 m x 10.9 m

Area = 168.95 m²

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Answer:

z = -8

Step-by-step explanation:

I'm guessing you want to find out what z is equal to, so here you go.

2z - 1 = -9 + z

2z = -8 + z

z = -8

Answer:

z = -8

Step-by-step explanation:

let's simplify the equation by getting the like terms together.

2z-1 = -9+z

first get the z's on the same side:

2z-z-1 = -9

z-1 = 9

then the constants:

z = -9+1

z = -8

Answer:

i love ur art its amazeballs and an asteroid thing

Step-by-step explanation:

Given:

To find:

The correct statements

Explanation:

Since the angles PCQ and SCR are vertically opposite angles.

So, we can write it as,

Therefore, the arc PQ is congruent to arc SR.

So, the first statement is correct.

Since the angles PCQ and SCR are vertically opposite angles and the angles QCR and PCS are vertically opposite angles.

So, we can write it as,

Since the central angle of a circle is 360 degrees.

Therefore,

Therefore, the measure of an arc QR is 150 degrees.

So, the second statement is correct.

Let us find the circumference of the circle.

Using the circumference formula,

Therefore, the circumference of the circle is,

So, the third statement is wrong.

Let us find the arc length of PS.

Here,

Using the formula,

Therefore, the arc length of PS is 13.1cm.

So, the fourth statement is correct.

Let us find the arc length of QS.

Here,

Using the formula,

Therefore, the arc length of QS is 15.7cm.

So, the fifth statement is correct.

Final answer: The statements 1, 2, 4, and 5 are correct.

The Elementary Matrix E is \(\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right]\).

We know that the Matrix

\(A = \left[\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right] , B = \left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right]\)

\(EA = B\)

⇒ \(E = B A^{-1}\)

\(A^{-1} = \frac{1}{|A|} \times \left[\begin{array}{ccc}A_{11}&A_{12}&A_{13}\\A_{21}&A_{22}&A_{23}\\A_{31}&A_{32}&A_{33}\end{array}\right]\)

\(|A| = \left|\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right|\)

\(= 2 \times4\times4-2\times5\times1 - 1\times(-2)\times4+1\times5\times3+3\times(-2)\times1 - 3\times4\times3\\= 32 -10+8+15-6-36 = 3\)

\(A^{-1} = \frac{1}{3} \left[\begin{array}{ccc}11&-1&-7\\23&-1&-16\\-14&1&10\end{array}\right] \\A^{-1} = \left[\begin{array}{ccc}\frac{11}{3} &\frac{-1}{3}&\frac{-7}{3}\\\frac{23}{3}&\frac{-1}{3}&\frac{-16}{3}\\\frac{-14}{3}&\frac{1}{3}&\frac{10}{3}\end{array}\right]\)

\(\therefore E =\left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right] \times \left[\begin{array}{ccc}\frac{11}{3} &\frac{-1}{3}&\frac{-7}{3}\\\frac{23}{3}&\frac{-1}{3}&\frac{-16}{3}\\\frac{-14}{3}&\frac{1}{3}&\frac{10}{3}\end{array}\right]\)

\(E = \left[\begin{array}{ccc}\frac{22+23-42}{3}&\frac{2+1-3}{3}&\frac{-14-16+30}{3}\\\frac{33+23-56}{3}&\frac{-3-1+4}{3}&\frac{-21-16+41}{3}\\\frac{-22+92-70}{3}&\frac{2-4+5}{3}&\frac{14-64+50}{3}\end{array}\right]\)

\(E = \left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right]\)

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The amount of oil required for 1 liter of fuel is 111.11 mL.

Fraction is the portion of a total amount where the above part of the fraction is the denominator and the bottom part of the fraction is called the numerator.

Given that the fuel is the mixture where 8 parts are petrol and 1 part is oil in the whole part of the fuel.

The total part of the fuel is 8+1=9

the portion of the petrol is = parts of petrol/total parts of the fuel= 8/9

the portion of the oil = parts of oil /total parts of the fuel= 1/9

Now we have to calculate the amount of oil required for 1 liter of fuel.

As discussed before, 1/9 parts of the fuel is oil.

So the amount of oil is= (1/9)*1 liter= (1/9)litre= 1/9* 1000 mL= 111.11 mL

Similarly, we can calculate the amount of petrol which will be

the amount of petrol= (8/9)*1 liter= (8/9) liter= 8/9*1000 mL= 888.88 mL

Therefore the amount of oil required for 1 liter of fuel is 111.11 mL.

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Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

Substitute these values into the equation: cos(7π/12) = (√2/2)(1/2) - (√2/2)(√3/2) = √2/4 - √6/4 = (√2 - √6)/4. Therefore, cos(7π/12) = (√2 - √6)/4.

To compute cos[7W/12), we can use the sum formula for cosine:

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

In this case, let a = pi/4 and b = pi/3, so that a + b = 7pi/12:

cos(7pi/12) = cos(pi/4)cos(pi/3) - sin(pi/4)sin(pi/3)

cos(7pi/12) = (sqrt(2)/2)(1/2) - (sqrt(2)/2)(sqrt(3)/2)

cos(7pi/12) = (sqrt(2) - sqrt(6))/4

For the second question, we can use the Pythagorean identity to find cos(a):

cos^2(a) + sin^2(a) = 1

cos^2(a) = 1 - sin^2(a)

cos(a) = -sqrt(1 - (3/5)^2) = -4/5

Then, we can use the fact that sin(pi - a) = sin(a) to find sin(B - a):

sin(B - a) = sin(pi/2 - a - B) = cos(a + B)

sin(B - a) = cos(a)cos(B) - sin(a)sin(B)

sin(B - a) = (-4/5)(12/13) - (3/5)(5/13)

sin(B - a) = -63/65

To compute cos(7π/12) without using a calculator, we can use the sum formula for cosine and the given fact that π/4 + π/3 = 7π/12. Let angle A be π/4 (second quadrant) with sin(A)=3/5, and angle B be π/3 (first quadrant) with cos(B)=12/13. We want to compute sin(A-B).

The sum formula for cosine is cos(A ± B) = cos(A)cos(B) ∓ sin(A)sin(B). Since we want to compute cos(7π/12), we have:

cos(7π/12) = cos(π/4 + π/3) = cos(π/4)cos(π/3) - sin(π/4)sin(π/3).

Now we need to find the cosine and sine values for the given angles:
cos(π/4) = √2/2,
sin(π/4) = √2/2,
cos(π/3) = 1/2,
sin(π/3) = √3/2.

Substitute these values into the equation:

cos(7π/12) = (√2/2)(1/2) - (√2/2)(√3/2) = √2/4 - √6/4 = (√2 - √6)/4.

Therefore, cos(7π/12) = (√2 - √6)/4.

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Answer:

Step-by-step explanation:

boody boody

Answer:

Step-by-step explanation:

The chosen topic is not meant for use with this type of problem. Try the examples below.

5

3

y

+

5

2

=

5

x

3

=

2

x

−

1

=

2

y

Answer: x=-1

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    3*x+3-(8*(5*x+5))=0

 Pull out like factors :

  5x + 5  =   5 • (x + 1) 3x + 3) -  40 • (x + 1)  = 0

-37   =  0 but nozero's can't be converted so

 Solve  :    x+1 = 0  

Subtract  1  from both sides of the equation :  

                     x = -1

Answer:

  x = 3

Step-by-step explanation:

We don't know what equation you think is wrong.

__

The solution to the problem is ...

  x/2 +x/6 = 2

  x(1/2 +1/6) = 2 . . . . working using the given fractions

  x(3/6 +1/6) = 2

  x(4/6) = 2

  x(2/3) = 2

  x = (3/2)(2)

  x = 3

__

We can also work this by eliminating fractions first.

  x/2 +x/6 = 2

  3x +x = 12 . . . . multiply the equation by 6

  4x = 12 . . . . . . .collect terms

  x = 3 . . . . . . . . .divide by 4

Complete question is;

The city just assigned a second garbage truck to empty the bins in Kat’s neighborhood on trash day. The crew from the first garbage truck used to empty all the bins by themselves in 5 hours. In their training, it took the crew from the second garbage truck 8 hours to empty all the bins. When the two crews start working together, what part of all the garbage bins will the first garbage truck empty? To the nearest tenth, the first garbage truck will empty about of all the bins.

Answer:

Part of all bins first garbage truck will empty = 0.6

Step-by-step explanation:

Let the total number of bins emptied be denoted by n.

We are told that the crew from the first garbage truck empties all the bins in 5 hours. Thus

Work rate = (n/5) bins/hr

We are told the second garbage truck empties in 8 hours. Thus;

Work rate = (n/8) bins/hr

When both garbage trucks work together, the total amount of time spent will be denoted by x. Thus;

((n/5) + (n/8))x = n

Divide through by n to get;

x/5 + x/8 = 1

Multiply through by 40 to gwt;

8x + 5x = 40

13x = 40

x = 40/13 hrs

To find the part of all the garbage bins the first garbage truck empty when they work together, we will simply multiply the value of x by the work rate of the first garbage truck. Thus;

Part = (n/5) × (40/13)

Part = (40/65)n = 0.615 of n

To the nearest tenth gives 0.6 of n