Select the correct answer.

A pair of pliers is an example of a simple machine with two levers. Which part of the pliers is the fulcrum?

Answer:

The distance between Toronto and Helsinki is 4110 miles, and the distance between Helsinki and Moscow is 558 miles.

Step-by-step explanation:

Let's assign variables to the unknown distances:

Distance from Toronto to Helsinki = x

Distance from Helsinki to Moscow = x - 3552

According to the given information, the total distance flown from NY to Moscow is 5015 miles, and the distance from NY to Toronto is 347 miles. Using these values, we can set up the equation:

347 + x + (x + x - 3552) = 5015

Simplifying the equation:

347 + 2x - 3552 = 5015

Combining like terms:

2x - 3205 = 5015

Adding 3205 to both sides:

2x = 8220

Dividing both sides by 2:

x = 4110

Therefore, the distance between Toronto and Helsinki is 4110 miles, and the distance between Helsinki and Moscow is 4110 - 3552 = 558 miles.

Answer: X is equal to 62

The solution of 4+√3 x+5=7  is x = ( - 2 ) / \(\sqrt{3}\) .

Linear Equation : An equation ( containing equal to = sign ) is called a linear equation if the highest power of variable is 1 . In order to solve linear equation in 1 variable 1 equation is enough .

Solving linear eq . in 1 variable

4+√3 x+5=7

√3 x = 7 - 5 - 4

x = ( - 2 ) / \(\sqrt{3}\)

Hence , the solution of 4+√3 x+5=7  is x = ( - 2 ) / \(\sqrt{3}\) .

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Answer:

Step by step

Step-by-step explanation:

Since we have the endpoints of the diameter, the midpoint coordinates of the line segment joining them gives the centre of the circle.

That is, centre (a,b) = ( [1+(-3)]/2, [4+2]/2) = (-1,3)

Distance between the given points give the diameter and half of that is the radius length.

So, radius r = (1/2)* sqrt ( [1-(-3)]^2 + [4–2]^2) = sqrt(5)

Thus equation required is: (x-a)^2 + (y-b)^2 = r^2

So, (x+1)^2 + (y-3)^2 = 5

The equation of the circle is (x + 1)² + (y - 3)² = 5

The endpoints of the diameter are given as:

(1, 4) and (−3, 2)

Start by calculating the midpoint using:

Midpoint = 0.5 * (x₁ + x₂, y₁ + y₂)

So, we have:

Midpoint = 0.5 * (1 - 3, 4 + 2)

Evaluate

Midpoint = (-1, 3)

So, the center (a,b) of the circle is:

(a,b) = (-1,3)

Calculate the length of the diameter using:

D² =(x₁ - x₂)² + (y₁ - y₂)²

This gives

D² = (1 + 3)² + (4 - 2)²

D² = 20

Take the square roots

D = 2√5

Divide by 2 to calculate the radius

r = √5

Square both sides

r² = 5

The equation of the circle is then represented as:

(x - a)² + (y - b)² = r²

This gives

(x + 1)² + (y - 3)² = 5

Hence, the equation of the circle is (x + 1)² + (y - 3)² = 5

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The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

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Answer:

Step-by-step explanation:

3 has two outputs in a

Answer:

3.5355 inches

Step-by-step explanation:

Area should be same the concentric circle and rest piece .

let's consider the radius of concentric circle as r

so it's area is π r²

area of whole circle is π (5)" ( because diameter is 10 inches)

so the area of rest piece is π (5)² - π r²

π (5)² - π r² = π r²

5² = 2r²

r² = 25/2

r = √(25/2)

r = 3.5355 inches

Answer: 6*4 or 8*3

Step-by-step explanation:

12^2=24

a rule in quadratic equ states that

if summation of the roots should be -b/a of the equa

comparing the equ x² - 6x + y=0

with. ax² + bx +c =0

we see that in the equ, a= 1, b=-6

so the sum of the roots is -(-6)/1= +6

looking the the option the only one that agreed is option A

-2 + 8= 6

there fore the values of x are -2 or 8

Answer:

x=17 degrees

Step-by-step explanation:

All 3 angles = 180 degrees

So 90 + 54 + (x+19) = 180

Combine like terms

163 + x = 180

Subtract 163 from both sides

x = 180-163

x = 17

Answer:

19.5/3=6.5 centimeters

Step-by-step explanation:

The correct order of statements to prove that modus ponens is a valid argument form is as follows: ~p V -(p = q) V q = (Tp V q) v -(Tp V q).

To prove the validity of the modus ponens argument form, we need to arrange the statements in the correct order. Here is the correct order of statements:

The first statement is given, and we begin by commuting the disjunction in the second statement. Then, we use the logical equivalence between ~p and Tp to rewrite the third statement. This allows us to express the conditional statement (p = q) -> (Tp V q) in the fourth statement. Finally, we apply the law of excluded middle in the last statement.

It's important to note that the correctness of each step has not been explicitly specified, so we assume that all the steps in the proof are correct and belong to the final valid argument form.

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Answer: if a column contains a leading 1 then the rest of the entries in that column are zeroes

Step-by-step explanation:

Answer:

y=26

Step-by-step explanation:

2(3y+7+5)=196-16 do the () first and then subtract 16 from 16

6y+24=180 subtract 24 from both sides

6y=156  divide by 6

y=26

Answer:

26

Step-by-step explanation:

6y+14+10=180

6y=180-24

6y=156

y=26

Answer:

(9, 5)

Step-by-step explanation:

First, we can use the axis of symmetry formula to find the x value of the vertex.

This formula is: -b/2a

Plug in the b and a values:

-b/2a

-(-18) / 2(1)

18/2

= 9

Then, plug in 9 as x into the equation, and solve for y:

f(x) = x² - 18x + 86

f(9) = 9² - 18(9) + 86

f(9) = 81 - 162 + 86

f(9) = 5

y = 5

So, the vertex is at (9, 5)

Hello !

\(a - (a - b) - b - (b - a)\\\\= a - a + b - b - b+a\\\\\boxed{= a - b}\)

Answer:

Step-by-step explanation:

a - ( a - b ) - b - ( b - a )

= a - a + b - b - b + a

= a - b

Answer:

h(5) = 20

Step-by-step explanation:

Assume that '2' is an exponent.

So the question for you should be:-

\( \displaystyle \large{h(x) = {x}^{2} - x}\)

We want to find h(5); we substitute x = 5 in.

\( \displaystyle \large{h(x) = {5}^{2} - 5}\)

5^2 is 5•5 = 25.

\( \displaystyle \large{h(x) = 25 - 5} \\ \displaystyle \large{h(x) = 20}\)

Therefore, h(5) is 20.

Answer:

it should be 1 hour 30 min long (maybe)

Step-by-step explanation:

a) The null hypothesis H sub 0 is that the mean time for the mice to complete the maze with the loud noise is equal to 18 seconds, or H sub 0: µ = 18. The alternative hypothesis H sub a is that the mean time for the mice to complete the maze with the loud noise is less than 18 seconds, or H sub a: µ < 18. A Type I error would occur if the researcher rejects the null hypothesis and concludes that the loud noise causes the mice to complete the maze faster when in fact it does not. A Type II error would occur if the researcher fails to reject the null hypothesis and concludes that the loud noise does not cause the mice to complete the maze faster when in fact it does.

b) The null hypothesis H sub 0 is that the mean score for the teaching assistant's students is equal to 50, or H sub 0: µ = 50. The alternative hypothesis H sub a is that the mean score for the teaching assistant's students is greater than 50, or H sub a: µ > 50. A Type I error would occur if the teaching assistant rejects the null hypothesis and concludes that his students have a higher mean score than the class as a whole when in fact they do not. A Type II error would occur if the teaching assistant fails to reject the null hypothesis and concludes that his students do not have a higher mean score than the class as a whole when in fact they do.

c) The null hypothesis H sub 0 is that the mean percent of total spending on housing for households in the Cleveland metropolitan area is equal to 31%, or H sub 0: µ = 31%. The alternative hypothesis H sub a is that the mean percent of total spending on housing for households in the Cleveland metropolitan area is not equal to 31%, or H sub a: µ ≠ 31%. A Type I error would occur if the homebuilders association rejects the null hypothesis and concludes that the national finding does not apply in their area when in fact it does. A Type II error would occur if the homebuilders association fails to reject the null hypothesis and concludes that the national finding does apply in their area when in fact it does not.

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In a population growth model for rabbits, foxes, and humans, the sum norm of the coefficient matrix is 4.5 and the max norm is 4.4. Using these norms, we can bound the size of the population vector after one period.

(a) To find the coefficient matrix A, we identify the coefficients of the variables R, F, and H in the given model equations. Once we have A, we can calculate its sum norm by adding up the absolute values of its elements and its max norm by taking the maximum absolute value among its elements. (b) Given the population vector p = [10, 10, 10], we can calculate p'Ap by multiplying p' (transpose of p) with A and then with p. The resulting value will provide the bounds for the size of p'Ap in both sum and max norms. Comparing this value with the norm bounds will indicate how close they are. (c) To determine the sum norm bound for the population vector after four periods, p(4), we need to multiply A by itself four times and calculate the sum of the absolute values of its elements. This sum will give us the desired sum norm bound.

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Step-by-step explanation:

6×(2.5)+1.5

15+1.5

16.5

or

f(x)= 6x+1.5

f(2.5)= 6(2.5)+15

f(2.5)=16.5

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The plot that represents the data in the table is:A dot plot line labeled Ice Cream Flavors and titled Ice Cream. Four tick marks labeled Chocolate, Pistachio, Strawberry, and Vanilla. There is 1 dot above Chocolate, 3 above Pistachio, 2 above Strawberry, and 4 above Vanilla.

This plot accurately represents the number of friends who like each type of ice cream, with the corresponding number of dots above each flavor. In the given table, we have four different types of ice cream (Chocolate, Pistachio, Strawberry, and Vanilla) and the corresponding number of friends who like each flavor.

The plot that represents this data is a dot plot. A dot plot is a type of graph where dots are used to represent the frequency or count of a specific value. In this case, we are using dots to represent the number of friends who like each type of ice cream.

The dot plot has a horizontal line labeled "Ice Cream Flavors" and titled "Ice Cream". This line represents the x-axis. Above the line, there are four tick marks labeled with the names of the ice cream flavors (Chocolate, Pistachio, Strawberry, and Vanilla). These tick marks represent the different categories or values being plotted.

For each flavor, the plot shows the corresponding number of dots above it. The dots represent the count or frequency of friends who like that particular flavor. According to the table, there is 1 dot above Chocolate, 3 dots above Pistachio, 2 dots above Strawberry, and 4 dots above Vanilla.

By visualizing the dots above each flavor on the dot plot, we can easily compare the frequencies and see the distribution of ice cream preferences among the student's friends.

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The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.

When an equation is given in this format, finding both intercepts is rather simple (x and y). Additionally, when resolving systems of two linear equations, this form is highly helpful.

It is possible to determine the x- and y-intercepts of the corresponding line when we have a linear equation in standard form.

In some circumstances, we might want to convert an equation written in a different form to standard form (for instance, while solving systems of equations).

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By using the slope intercept form of equation of line, it can be calculated that-

a) Equation of the graph

\(y = -\frac{5}{3}x +10\)

b) Slope = \(-\frac{5}{3}\)

It represents the ounces of ice cream reducing per minute when Katie has been eating the ice cream

c) y - intercept is 10.

It means Katie started eating with 10 ounces of ice cream

d) When y = 0, x = 6

It means Katie finished eating the ice cream in 6 minutes.

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If \(\theta\)  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = \(tan\theta\)

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

a) From the figure, it is clear that the graph passes through (6, 0) and (0, 10)

Slope = \(-\frac{10}{6}\)

Slope = \(-\frac{5}{3}\)

Equation of the graph

\(y - 0 = -\frac{5}{3}(x - 6)\\\\y = -\frac{5}{3}(x - 6)\\\\y = -\frac{5}{3}x +10\)

b) Slope = \(-\frac{5}{3}\)

It represents the ounces of ice cream reducing per minute when Katie has been eating the ice cream

c) y - intercept is 10.

It means Katie started eating with 10 ounces of ice cream

d) When y = 0, x = 6

It means Katie finished eating the ice cream in 6 minutes.

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Answer:

this is a long shot( like rly long) but try either -6 or -3

Step-by-step explanation:

Don't co.e for me if I'm wrong im just a poor girl in year 8

Answer:

-2a +4

Step-by-step explanation:

-6a + 2(2a + 2)

Distribute

-6a +4a +4

Combine like terms

-2a +4

Answer:

Answer A is correct

Step-by-step explanation:

First Solve the brackets

\( - 6a + 2(2a + 2) \\ - 6 a+ 4a + 4\)

Then combine like terms

\( - 6 a+ 4a + 4 \\ - 2 a + 4\)