Practice Final Apex Unit 4 Linear Equations
How many solutions does 5 - 3x = 4 + x + 2 -4x
One solution
Two solutions
No solution
Infinitely many solutions

Answer:

y = 3x + 3

Step-by-step explanation:

m = 3 because the slope rises 3 and runs 1, therefore 3/1 = 3

b = 3 because the y-intercept is (0,3), therefore y-int = 3

y = 3x + 3

Answer:

I would use addition, subtraction, multiplication, and division in terms of taxes, interest rates, my fixed salaries, and so forth. And dividing rational numbers would be like 10% of the interest rate or 11% of the interest rate. I can also simplify the algebraic expressions to make the terms easier for me in my head.

Step-by-step explanation:

I would use addition, subtraction, multiplication, and division in terms of taxes, interest rates, my fixed salaries, and so forth. And dividing rational numbers would be like 10% of the interest rate or 11% of the interest rate. I can also simplify the algebraic expressions to make the terms easier for me in my head.

Answer:

.2 maybe but I don't know how to do this

Answer:

neither one of those are a dot plot

Step-by-step explanation:

Answer:

height of kids in class is the dot plot

Step-by-step explanation:

Answer:

The answer is (3×7) + (12×2) .

\((3 \times 7) + (12 \times 2)\)

\( = 21 + 24\)

\( = 45\)

Answer:

7:8

Step-by-step explanation:

First, convert their times to common units. You'll want to put it in seconds:

5 minutes and 50 seconds = 350 seconds

- multiply 5 minutes by 60 to get it into seconds and then add the other 50 seconds to it

- for Elizabeth's time, multiply 6 by 60 seconds and add 40 to it

To get the ratio of their times, divide Alison's time by Elizabeth's time:

350 ÷ 400 = 7:8

Answer:

a) 7:8

Step-by-step explanation:

Alison: 5 minutes and 50 seconds = 355 seconds

Elizabeth: 6 minutes and 40 seconds = 400 seconds

355:400, reduces to 71:80 or 7:8

Both \(det(s^(-1)as) and det(sas^(-1))\)are equal to 3.

To compute \(det(s^(-1)as) and det(sas^(-1))\), we can utilize the following properties and theorems:

The determinant of a product of matrices is equal to the product of their determinants: det(AB) = det(A) * det(B).

The determinant of the inverse of a matrix is the inverse of the determinant of the original matrix: \(det(A^(-1)) = 1 / det(A)\).

Using these properties, let's compute the determinants:

\(det(s^(-1)as)\):

Applying property 1, we have \(det(s^(-1)as) = det(s^(-1)) * det(a) * det(s).\)

Since s is invertible, its determinant det(s) is nonzero, and using property 2, we have \(det(s^(-1)) = 1 / det(s)\).

Combining these results, we get:

\(det(s^(-1)as) = (1 / det(s)) * det(a) * det(s) = (1 / det(s)) * det(s) * det(a) = det(a) = 3.\)

det(sas^(-1)):

Again, applying property 1, we have \(det(sas^(-1)) = det(s) * det(a) * det(s^(-1)).\)

Using property 2, \(det(s^(-1)) = 1 / det(s)\), we can rewrite the expression as:

\(det(sas^(-1)) = det(s) * det(a) * (1 / det(s)) = det(a) = 3.\)

Therefore, both \(det(s^(-1)as) and det(sas^(-1))\)are equal to 3.

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(a) The variable educ might be endogenous

(b) The variable brthord is birth order (one for the first-born child, two for a second-born child and so on) could be used as an instrument for educ in equation

a) The variable instruction might be endogenous because as compensation increases the income expansions which additionally make able to an individual more educating himself. So there is an opportunity for the instruction might be an endogenous variable.

The indigeneity may involve the 32 the coefficient of knowledge as well different variables like married, black, south, urban, etc.

b) There is a substantial high relationship exists between birth order and the status of teaching. it is more possible to have higher schooling with less the order of child-born and the birth order is autonomous of the error term as well with wage. So the variable "birth order" is a good variable to use as an agency for the endogenous variable instruction.

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Answer:

8v

Step-by-step explanation:

Answer:

610.9 km

Step-by-step explanation:

For the plane that is flying at 520km/h:

520km/h * 45minutes * 1h/60minutes = 390 km

For the plane that is flying at 480km/h:

480km/h * 45minutes * 1h/60minutes= 360 km

This is a SAS triangle which means Side angle Side

the formula for this is: a^2 = b^2 + c^2 − 2bc cosA

for this problem it should be:

a^2= (390^2) +(360^2) - 2(390*360)*cos(115)

a should be approximately 610.9 km

Explanation:

The adjacent angle to the right of the (6x+1) angle is 180-(6x+1). Simply subtract it from 180 to get its supplementary counterpart.

The three inner angles of any triangle must add to 180, so,

(inner angle 1) + (inner angle 2) + (inner angle 3) = 180

[ 180-(6x+1) ] + (79) + (2x+10) = 180

180 - 6x - 1 + 79 + 2x + 10 = 180

(-6x+2x) + (180-1+79+10) = 180

-4x+268 = 180

-4x = 180 - 268

-4x = -88

x = -88/(-4)

x = 22

Answer:

x = 22

Step-by-step explanation:

2x + 10 + 79 = 6x + 1

Think alternate interior angles

2x + 10 + 79  makes up one of the alternate interior angles

6x + 1 is the other.

Combine like terms.

Subtract 2x both sides.

Subtract 1 from both sides.

Divide by 4 both sides.  

The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

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Answer:

slope = - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x + 3 ← is in slope- intercept form

with slope m = - 2

Answer:

Place compass point on the vertex of the angle (point B).

Stretch the compass to any length that will stay ON the angle.

Swing an arc so the pencil crosses both sides (rays) of the given angle.

Place the compass point on one of these new intersection points on the sides of the angle.

Answer:

AE - 3, EB - 2, EC - 5

Step-by-step explanation:

Use the Pythagorean theorem and you'll find that these are the answers.

I'll answer problem 19

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

Part (a)

The tickmarks on segments DE and DC indicate they are the same length. We're also told that |DC| = |DE| = 5.

So DE is also 5 cm long. Triangle DAE is a right triangle with the 90 degree angle at angle A. Let x be the length of segment AE.

We'll use the pythagorean theorem to find x

a^2 + b^2 = c^2

(AE)^2 + (AD)^2 = (DE)^2

x^2 + 4^2 = 5^2

x^2 + 16 = 25

x^2 = 25-16

x^2 = 9

x = sqrt(9)

x = 3

Segment AE is 3 cm long

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

Part (b)

For any rectangle, the opposite sides are parallel and the same length. This means AB = DC = 5 cm.

We found earlier that AE = 3 cm, so,

AE+EB = AB

3+EB = 5

EB = 5-3

EB = 2

Segment EB is 2 cm long

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

Part (c)

We know that AD = BC = 4 cm, because the opposite sides are the same length.

Earlier in part (b), we found that segment EB was 2 cm long.

Triangle EBC is a right triangle with legs EB = 2 and BC = 4. Let's apply the pythagorean theorem to find EC. Let y = EC.

a^2 + b^2 = c^2

(EB)^2 + (BC)^2 = (EC)^2

2^2 + 4^2 = y^2

4 + 16 = y^2

20 = y^2

y^2 = 20

y = sqrt(20)

y = sqrt(4*5)

y = sqrt(4)*sqrt(5)

y = 2*sqrt(5)

y = 4.4721359

As an exact value, EC is sqrt(20) or 2*sqrt(5) cm long.

As an approximate value, EC is roughly 4.4721359 cm long.

I would ask your teacher if you should use the exact or approximate value.

Answer:

The absolute value for x = 1/6

Step-by-step explanation:

Leave |x + 3| alone

2/3|x + 3| = 11/6 + 1/2 ➡ 2/3|x + 3| = 14/6

|x + 3| = 14/6 ÷ 2/3 ➡ |x + 3| = 7/2 now we write two equations

x + 3 = 7/2 or x + 3 = -7/2 first we subtract 3 from all

x = 1/6 or x = -13/6 since we are asked to find the absolute value, the answer would be 1/6

The distance traveled by a passenger on each rotation of the Ferris wheel is 1635.2 feet.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

The expression is given in the question as:

⇒ 3.14d

The circumference of the Ferris wheel can be determined by multiplying the diameter, d, by (3.14).

Thus, the circumference of the Ferris wheel is:

⇒ 3.14 × 520 = 1635.2 feet.

Since the Ferris wheel makes one full rotation in one ride, the distance traveled by a passenger on each rotation of the Ferris wheel is 1635.2 feet.

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The series diverges with an integral of 1/ln(16) and the series converges with an integral of 1/4 and a sum of 1/2.

We can use the integral test to determine the convergence of the series ∑n=1∞ 1/6n. The integral of the function f(x) = 1/6x is:

\(∫f(x) dx = (1/6) ln(x) + C\)

Using the limits of integration from 1 to ∞, we get:

∫1∞ f(x) dx = (1/6) ln(∞) - (1/6) ln(1) = ∞

Since the integral diverges, the series also diverges.

We can use the integral test to determine the convergence of the series ∑n=1∞ \((n+4)/(n^2+8n+4\)). The integral of the function f(x) = \((x+4)/(x^2+8x+4)\) is:

∫f(x) dx = (1/2) ln(x^2 + 8x + 4) + 3 ln|x + 4| + C

Using the limits of integration from 1 to ∞, we get:

∫1∞ f(x) dx = (1/2) ln(∞) + 3 ln(∞ + 4) - (1/2) ln(13) - 3 ln(5) = ∞

Since the integral diverges, the series also diverges.

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Answer:

a = 14

b = 15

c = 15

d = 18

e = 18

Step-by-step explanation:

The stratified sampling works as follows:

stratified sampling = (Population of subgroups)*(total sample size)/(entire population)

in this case, sample size = 80

entire population = 140 + 150 + 150 + 180 + 180 = 800

Population sample is the number of students of each year (for year 7, the population of subgroup is 140, and so on)

whith this equation we can find all the missing values:

a = (140)*(80/800) = 14

b = (150)*(80/800) = 15

c = (150)*(80/800) = 15

d = (180)*(80/800) = 18

e = (180)*(80/800) = 18

Answer:

No mode

Step-by-step explanation:

Just no mode cause no number appears more than once.

The areas of the four triangular sections in the trapezoidal cornfield in Iowa are: Section 1: 7200 sq m, Section 2: 10800 sq m, Section 3: 10800 sq m, Section 4: Approximately 14988.86 sq m

To find the areas of the triangular sections, we need to first find the lengths of the diagonals IW and OA.
Given that IO is parallel to WA, we can use the properties of trapezoids to find the length of the diagonal IW.
Since the area of the trapezoidal field is 18000 sq m, we can use the formula for the area of a trapezoid:
Area = (a + b) * h / 2
where a and b are the lengths of the parallel sides, and h is the height (the distance between the parallel sides).
In this case, a = 100 m, b = 150 m, and the area = 18000 sq m. We can plug these values into the formula and solve for the height:
18000 = (100 + 150) * h / 2
36000 = 250 * h
h = 36000 / 250
h = 144 m
Now that we have the height, we can use the properties of triangles to find the length of the diagonal IW.
In a right triangle with one leg being the height (h) and the hypotenuse being the diagonal (IW), we can use the Pythagorean theorem:
IW² = h² + b²
IW² = 144² + 100²
IW² = 20736 + 10000
IW² = 30736
IW ≈ 175.21 m
Similarly, we can find the length of the diagonal OA using the same steps:
OA² = h² + a²
OA² = 144² + 150²
OA² = 20736 + 22500
OA²= 43236
OA ≈ 207.93 m
Now, we can find the areas of the triangular sections.
Section 1: Triangle IOW
The base is IO, which is 100 m, and the height is h, which is 144 m. Using the formula for the area of a triangle:
Area1 = (base * height) / 2
Area1 = (100 * 144) / 2
Area1 = 7200 sq m
Section 2: Triangle IWA
The base is WA, which is 150 m, and the height is h, which is 144 m. Using the formula for the area of a triangle:
Area2 = (base * height) / 2
Area2 = (150 * 144) / 2
Area2 = 10800 sq m
Section 3: Triangle OWA
The base is WA, which is 150 m, and the height is h, which is 144 m. Using the formula for the area of a triangle:
Area3 = (base * height) / 2
Area3 = (150 * 144) / 2
Area3 = 10800 sq m
Section 4: Triangle OAI
The base is OA, which is approximately 207.93 m, and the height is h, which is 144 m. Using the formula for the area of a triangle:
Area4 = (base * height) / 2
Area4 = (207.93 * 144) / 2
Area4 ≈ 14988.86 sq m
The areas of the triangular sections are as follows:
- Section 1: 7200 sq m
- Section 2: 10800 sq m
- Section 3: 10800 sq m
- Section 4: Approximately 14988.86 sq m
To find the areas of the triangular sections in the trapezoidal cornfield in Iowa, we first need to find the lengths of the diagonals IW and OA. By using the formula for the area of a trapezoid, we can determine the height of the trapezoid, which is 144 m. Using the Pythagorean theorem, we can find the lengths of the diagonals IW and OA. IW is approximately 175.21 m, while OA is approximately 207.93 m. Next, we can calculate the areas of the triangular sections. Section 1 has a base of 100 m and a height of 144 m, resulting in an area of 7200 sq m. Section 2 and Section 3 both have a base of 150 m and a height of 144 m, resulting in areas of 10800 sq m each. Finally, Section 4 has a base of approximately 207.93 m and a height of 144 m, resulting in an area of approximately 14988.86 sq m.
In conclusion, the areas of the four triangular sections in the trapezoidal cornfield in Iowa are:
- Section 1: 7200 sq m
- Section 2: 10800 sq m
- Section 3: 10800 sq m
- Section 4: Approximately 14988.86 sq m

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Answer:

192

Step-by-step explanation:

It’s the answer

Answer:

The total mechanical energy is 0.712 J.

Step-by-step explanation:

A blue 573 g mobile is moving on a metal rail. If on the mobile, the spring exerts a force to the right of modulus 0.85 N and in the indicated position the kinetic energy of the mobile-spring system is 0.47 J and its elastic potential energy is 0.242 J. Determine the mechanical energy of the system mobile-spring in the position shown as indicated in the figure.

The total mechanical energy is given by the sum of the kinetic energy and the potential energy.

Kinetic energy = 0.47 J

Potential energy = 0.242 J

The total mechanical energy is

T = 0.47 + 0.242 = 0.712 J

P's coordinates are (0.6, 0.1), with each box denoting 0.1, Point Q may be found at the coordinates (0.8, 0.7).

When a coordinate plane is made, we are free to select the unit that we want to give to one step in any particular axis of the plane. Now here in this case, the point is given to be located at the coordinate point (0.6,0.1).

This reveals two things to us. Because the point p is one box above the x-axis and six boxes distant from the y axis, the distance is 0.1. So, just counting the number of boxes for Q's location yields (0.8, 0.7).

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Answer:

if you need help with some subjects you can come here in brainly it helps me a lot i just started grad 6 so yeah

like if you have a math question just go to ask question you and someone will help

The sample standard deviation Sₓ for these measurements is 155.8846 and the actual confidence level for the given interval is unknown.

Standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

Given that, a report gives the results in the form "mean plus or minus the standard error of the mean."11 Data for 12 subjects are summarized as 251 ± 45

SE = 45, x = 251, n = 12,

Confidence level =

SE = Sₓ/√n

Sₓ = 45 × √12

Sₓ = 155.8846

The confidence interval is calculated by using the formula,

x ± (t* × E),

The interval in the problem is (t* × E),

And, t* is unknown.

As a result, the provided interval is not a confidence interval.

Hence, the sample standard deviation Sₓ for these measurements is 155.8846 and the actual confidence level for the given interval is unknown.

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40% should be the correct answer! ;D

Please mark brainiest if I'm correct!

Hope this helped!

Answer:

40%

Step-by-step explanation:

40% of 50 shirts would be 20.

To solve you can use 10% of 50, to find 10% of any number simply move the decimal one point to the left. So in this case, 50.0 becomes 5.0. Therefore, 5 is 10% of 50. Then multiply 5 times 4 to get 20. Since 5 is 10% of 50, 20 is four 10% of 50, or simply 40%.