What is the current through a 2.5 ohm resistor that is connected across a 6.0 V potential difference?

a + 26 = 180 (linear pair)

a = 180 - 26

a = 154°

We can conclude that the equation of the line of best fit is -

ŷ = 713.70516X + 1077.04596. Also, the slope {m} is 713.70516 and {y} -

intercept is 1077.04596.

Given is a table as shown in the image.

-6.6

-5.6

-3.6

-1.6

-0.6

0.4

2.4

3.4

5.4

6.4

-4887.5

-3887.5

-2587.5

-1287.5

-637.5

962.5

1762.5

2312.5

3737.5

4512.5

43.56

31.36

12.96

2.56

0.36

0.16

5.76

11.56

29.16

40.96

{SS} : 178.4

32257.5

21770

9315

2060

382.5

385

4230

7862.5

20182.5

28880

{SP} : 127325

Sum of {X} = 66

Sum of {Y} = 57875

Mean {X} = 6.6

Mean {Y} = 5787.5

Sum of squares {SSₓ} = 178.4

Sum of products {SP} = 127325

Regression Equation -

ŷ = bX + a

b = SP/SSₓ = 127325/178.4 = 713.70516

a = MY - bMₓ = 5787.5 - (713.71*6.6) = 1077.04596

ŷ = 713.70516X + 1077.04596

Slope -

{m} = 713.70516

{y} - intercept = 1077.04596

Therefore, we can conclude that the equation of the line of best fit is -

ŷ = 713.70516X + 1077.04596. Also, the slope {m} is 713.70516 and {y} -

intercept is 1077.04596.

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Answer:

A. The number of actual outcomes is 6 (since there are 6 sides to the block).

B. The number of all possible outcomes would be the number of ways the block could land on the table, which is also 6 (since each of the 6 sides is equally likely to face up).

C. The probability that the block will land with either the T, C or R facing up is the probability of landing on any one of those 3 sides. Since there are 3 such sides, and each side is equally likely to face up, the probability is 3/6 or 1/2.

Step-by-step explanation:

the point and goal is to come up with a series of multiplications of terms that is equivalent to the original sum of terms.

in doing so, we try to find the same common factors in the sub-groups we are building.

so, the error was to use "-" with the last term, as this "destroyed" the common factor.

it should have been

3x(2x - 3) + 4(2x - 3)

which gives us via the common terms

(2x - 3)(3x + 4)

that is the correct factoring.

The Cartesian equation y = 3x^2 as a polar equation can be write as r(θ) = 3 sec(θ) / (1 + tan²(θ)).

To rewrite the Cartesian equation y = 3x² as a polar equation, we need to use the conversion formulas between Cartesian coordinates (x, y) and polar coordinates (r, θ):

x = r cos(θ)
y = r sin(θ)

Substituting these formulas into the Cartesian equation gives us:

r sin(θ) = 3(r cos(θ))²

Dividing both sides by r and rearranging terms gives us:

r = 3 cos²(θ) / sin(θ)

Using the identity 1 + tan²(θ) = sec²(θ), we can rewrite the equation in terms of tan(θ) and sec(θ):

r = 3 (1 / (1 + tan²(θ))) / (1 / sec(θ))

Simplifying gives us the final polar equation:

r(θ) = 3 sec(θ) / (1 + tan²(θ))

Therefore, the Cartesian equation y = 3x²can be rewritten as the polar equation r(θ) = 3 sec(θ) / (1 + tan²(θ)).

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Answer:

He realizes the casino is a trap when he found out people from 1977 are in the casino. They wasted five days in the casino.

Answer:

B

Step-by-step explanation:

The correct answer is Option C - Type 1 and Type 2. The power of a test is the probability of rejecting the null hypothesis when it is false; in other words, it is the probability of avoiding a type II error.

The power may also be thought of as the likelihood that a particular study will detect a deviation from the null hypothesis given that one exists. A Type 1 error occurs when a hypothesis test results in rejecting a true null hypothesis, and a Type 2 error occurs when a hypothesis test fails to reject a false null hypothesis.

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Answer:

-24x^8y^6+32x^2y^5

Step-by-step explanation:

The amount Suzy must repay at the end of the period is R2 682.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

In this case, we have:

P = R2 400

r = 0.047 (since the annual interest rate is 4.7%)

t = 2.5 years (since the period is two years and six months)

Substituting these values into the formula, we get:

I = 2400 * 0.047 * 2.5

I = 282

Therefore, the interest is R282.

The total amount to be repaid is the sum of the principal and the interest, which is:

2400 + 282 = R2 682

Therefore, by the simple interest the answer will be  R2 682.

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Answer:

Step-by-step explanation:

f(x)=x^4−x^2+9

To factor the trinomial 2x²+7x-4, you could rewrite it as 2x²+8x-2x-4, and then factor by grouping. The factor pairs of ac are (x+4), (2x-1).

To factor the trinomial 2x²+7x-4 by grouping, we need to find a factor pair of ac that sums to b. In this case, ac = (2)(-4) = -8 and b = 7.

The factor pair of -8 that sums to 7 is 8 and -1. Therefore, we can rewrite the trinomial as follows:

2x²+7x-4 = 2x²+8x-x-4

Next, we can group the first two terms and the last two terms:

(2x²+8x)+(-x-4)

Now, we can factor out the greatest common factor from each group:

2x(x+4)-1(x+4)

Finally, we can factor out the common factor of (x+4):

(x+4)(2x-1)

Therefore, the factored form of the trinomial 2x²+7x-4 is (x+4)(2x-1).

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Answer:

option (1)

Step-by-step explanation:

rearrange making x the subject, then x is the inverse

y = [tex]\frac{3}{2}[/tex] x ( multiply both sides by 2 to clear the fraction )

2y = 3x ( isolate x by dividing both sides by 3 )

[tex]\frac{2}{3}[/tex] y = x

change y back into terms of x , then inverse is

[tex]f^{-1}[/tex] (x) = [tex]\frac{2}{3}[/tex] x , or

y = [tex]\frac{2}{3}[/tex] x

The slide does not meet safety requirements.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

As per the given data:

maximum average slope = 30°

height of the slide = 6 ft

length of the slide = 11.7 ft

For calculating slope (θ):

sinθ = (P/H) {P is perpendicular and H is hypotunese}

sinθ = (height/length)

sinθ = (6/11.7)

sinθ = 0.512

Using sin inverse:

θ = 30.8°

θ > maximum average slope

Hence, the slide does not meet safety requirements.

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The amount that Beth borrowed at the annual interets of 30% is found to be  £4880.

We can use the relation to find the original borrowed which is,

original amount x (1 + interest rate)² = total amount to be paid

The interest in annual so the value of interest of the loan that Beth took is 30% and the amount to be paid is £8112. Let x be the borrowed amount,

Now, putting all the values in the relation above-mentioned,

Based on the given conditions, formulate:

x+(1+30%)² = 8112

x(1.3)² = 8112

Divide both sides of the equation by the coefficient of variable,

x = 8112/(1.30)²

Calculated value of x = 4800

The original amount that Beth borrowed is £4880.

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Answer:1 and 2/3 lb per person

Step-by-step explanation:

5 pund divided by 3 ppl = 5/3

Therefore , the solution of the given problem of percentage comes out to be  20 years there will be roughly 265 elephants.

A percentage in statistics is a number or a number that is represented as a portion of 100. Additionally, "pct.," "pct," and "pc" are infrequently employed. However, the "%" symbol is frequently used to indicate it. The percentage sum is flat; there are no dimensions. Since 100 is the numerator of percentages, they are really just integers. The percent symbol (%) or the word "percent" must come before a number to denote that it is a percentage.

Here,

Elephant population after each year is 97% of the population after the preceding year if the population is declining at a rate of 3% per year.

We can use the following equation to determine the number of elephants in 20 years:

Population after 20 years is equal to the initial population multiplied by (1 - rate of decline/100) years.

Inputting the numbers provided yields:

=> 20-year population = 486 * (1 - 3/100)

=> 20 People after 20 years= 486*0.97.

=> 20 Years Later, Number = 486 x 0.5459

=> 20 years later, the population is 265,26.

Consequently, in 20 years there will be roughly 265 elephants.

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Therefore, the lengths of the sides of quadrilateral HIJK are √(65),  13, √(65), and √(52).

A quadrilateral is a polygon with four sides and four vertices. The sum of the interior angles of a quadrilateral is always equal to 360 degrees. There are many different types of quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombuses, and kites. Each type of quadrilateral has its own unique properties, such as having four equal sides (square), having opposite sides parallel (parallelogram), or having two pairs of equal adjacent sides (kite). Quadrilaterals can be classified based on their sides, angles, or both.

Here,

The point H has coordinates (-5, 6), which means it is located 5 units to the left of the y-axis and 6 units above the x-axis. The point I has coordinates (3, 4), which means it is located 3 units to the right of the y-axis and 4 units above the x-axis. The point J has coordinates (0, -8), which means it is located at the intersection of the x-axis and the y-axis, but 8 units below the x-axis. Finally, the point K has coordinates (-7, -2), which means it is located 7 units to the left of the y-axis and 2 units below the x-axis.

We can see that HIJK is a general quadrilateral, meaning that it does not have any special properties like being a rectangle or a parallelogram. We can find the lengths of its sides and the measures of its angles by using the distance formula and the slope formula, respectively. The distance formula gives us the distance between any two points (x1, y1) and (x2, y2):

distance = √((x2 - x1)² + (y2 - y1)²)

The slope formula gives us the slope of a line passing through two points (x1, y1) and (x2, y2):

slope = (y2 - y1) / (x2 - x1)

Using these formulas, we can find that the lengths of the sides of HIJK are:

HI = √((3 - (-5))² + (4 - 6)²) = √(65)

IJ = √((0 - 3)² + (-8 - 4)²) = √(169) = 13

JK = √((-7 - 0)² + (-2 - (-8))²) = √(65)

KH = √((-7 - (-5))² + (-2 - 6)²) = √(52)

We can also find the slopes of the lines passing through each pair of adjacent vertices:

The slope of line segment HI passing through points H and I is:

(4 - 6) / (3 - (-5)) = -1/2.

The slope of line segment IJ passing through points I and J is:

(-8 - 4) / (0 - 3) = 4/3.

The slope of line segment JK passing through points J and K is:

(-2 - (-8)) / (-7 - 0) = 6/7.

The slope of line segment KH passing through points K and H is:

(6 - (-2)) / (-5 - (-7)) = 4/3.

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Complete question:

Quadrilateral HIJK has vertices at H(-5,6), I(3,4), J(0,-8), and K(-7,-2). find the length of sides as well as the slopes.

The 14th term of the given geometric sequence is -40,960.

A geometric progression is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a constant factor called the common ratio. It is a type of exponential growth or decay.

The given sequence is a geometric sequence with the first term (a₁) as 5 and the common ratio (r) as -2. To find the 14th term, we can use the formula for the nth term of a geometric sequence, which is:

[tex]a_n = a_1 \times r^{(n-1)}[/tex]

Substituting the values of a₁ and r, we get:

[tex]a_n = 5\times -2^{(n-1)}[/tex]

To find the 14th term, we can substitute n = 14 and simplify:

[tex]a_{14} = 5 \times (-2)^{(14-1)}[/tex]

[tex]a_{14} = 5 \times (-2)^{(13)}[/tex]

[tex]a_{14} = 5 \times -8192[/tex]

a₁₄ = -40,960

Therefore, the 14th term of the given geometric sequence is -40,960.

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The value of a₄ is,

⇒ a₄ = 108

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The value is,

⇒ a₁ = - 4

And, [tex]a_{n} = - 3a_{n - 1}[/tex]

Now, We can put n = 2;

⇒ a₂ = - 3 a₁

⇒ a₂ = - 3 x - 4

⇒ a₂ = 12

Put n = 3;

⇒ a₃ = - 3 a₂

⇒ a₃ = - 3 x 12

⇒ a₃ = - 36

Put n = 4;

⇒ a₄ = - 3 a₃

⇒ a₄ = - 3 x - 36

⇒ a₄ = 108

Thus, The value of a₄ is,

⇒ a₄ = 108

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Value of a₄ in sequence is -108.

In mathematics, geometric sequence, also known as a a geometric progression, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Given,

a₁ = 4 and aₙ = -3aₙ₋₁

a₂ = -3a₂₋₁

a₂ = -3a₁

a₂ = -3(4)

a₂ = -12

a₃ =  -3(-12)

a₃ = 36

a₄ = -3a₄₋₁

a₄ = -3a₃

a₄ = -3(36)

a₄ = -108

Hence, -108 is value of a₄ of the sequence.

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C. The dog's body temperature is regarded normal because the range for a healthy adult is 101°F to 102.5°F.

What exactly is value?

Value is the appraised, monetary, or material worth of a good, service, or asset. Several ideas are associated with the word "value," including shareholder value, company value, fair value, and selling price.

The phrase to assess whether a dog's body temperature is acceptable or not is:

|t - 101.75| ≤ 0.75

When we replace the specified value for the dog's body temperature, we obtain:

|101.2 - 101.75| = |-0.55| = 0.55

The body temperature of the dog is regarded as normal because 0.55 is less than 0.75.

Option C, however, is the one that accurately depicts the dog's core body temperature:

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No solution is the answer because the equation cannot be solved because both sides of the equation do not have the same denominator. To solve the equation, we can cross-multiply and simplify the terms to get a quadratic equation.

Then we can use the quadratic formula to find the solutions. The denominator of the left side is w, while the denominator of the right side is (w² - 4).

Here are the steps:

1. Cross-multiply to get rid of the fractions: (w)(w² - 4) = (w + 2)(w + 25) - (5)(w + 2)(w - 2)
2. Distribute the terms: w³ - 4w = w² + 27w + 50 - 5w² + 10w
3. Combine like terms and rearrange to get a quadratic equation: w³ - 6w² - 41w - 50 = 0
4. Use the quadratic formula to find the solutions: w = (-(-6) ± √((-6)² - 4(1)(-41)(-50)))/(2(1))
5. Simplify the terms inside the square root: w = (6 ± √(36 - 8200))/2
6. Simplify further: w = (6 ± √(-8164))/2
7. Since the square root of a negative number is not a real number, there are no real solutions to this equation.

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All four statements are logically equivalent.

The statements (a), (b), (c), and (d) are all logically equivalent because they all describe the same concept: that the matrix A has a solution for every possible vector b.

Let's start with statement (a): For each b∈Rm, the matrix equation Ax=b has a solution. This means that for any vector b in Rm, there exists a vector x in Rn such that Ax=b.

Now, let's look at statement (b): Each b∈Rm is a linear combination of the columns in A. This means that for any vector b in Rm, we can write b as a linear combination of the columns of A, which is equivalent to saying that Ax=b has a solution.

Statement (c) says that the columns of A span Rm. This means that the columns of A can be combined in a linear combination to produce any vector in Rm, which is equivalent to saying that Ax=b has a solution for any vector b in Rm.

Finally, statement (d) says that the reduced echelon form of A has a pivot in every row. This means that the matrix A is of full rank and that there are no free variables in the equation Ax=b. This implies that there is a unique solution for every vector b in Rm, which is equivalent to saying that Ax=b has a solution for any vector b in Rm.

Therefore, all four statements are logically equivalent because they all describe the same concept: that the matrix A has a solution for every possible vector b.

The solution to this question is to understand that all four statements are logically equivalent because they all describe the same concept: that the matrix A has a solution for every possible vector b.

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The value of fy(1,1) is 5.5 with one decimal digit on the right side of the decimal point.

To find the value of fy(1,1), we need to first find the partial derivative of f(x,y) with respect to y. This is done by treating x as a constant and taking the derivative with respect to y.

The partial derivative of f(x,y) with respect to y is:
fy(x,y) = (1/2)(4x2 - 2y + 7x4y5)-1/2 (-2 + 35x4y4)

Now we can plug in the values of x=1 and y=1 into the partial derivative to find the value of fy(1,1):
fy(1,1) = (1/2)(4(1)2 - 2(1) + 7(1)4(1)5)-1/2 (-2 + 35(1)4(1)4)
fy(1,1) = (1/2)(4 - 2 + 7)-1/2 (-2 + 35)
fy(1,1) = (1/2)(9)-1/2 (33)
fy(1,1) = (1/2)(1/3)(33)
fy(1,1) = 5.5

Therefore, the value of fy(1,1) is 5.5 with one decimal digit on the right side of the decimal point.

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`u−2u2u0u3 = u^3`

(a) 1 / 34 * 4 = 4 / 34

(b) 6y * (1 / (53xy2))3 = 6y / 53xy2

(c) x * (1 / 9y) * (1 / 14x2) * (1 / (x−8)) = x / (9y * 14x2 * (x−8))

(d) (u−2 * u2) / (u0 * u3) = u−4 / u3
(a) Rewrite the given expression without negative exponents and simplify:(a)- (34)- 4Let us first use the law of exponents that says `(a^m)^n = a^(m*n)`The negative exponent `−4` means the denominator, so we can move the base `3` to the denominator and change the exponent to `+4`.Thus, `(a)−(34)−4 = a*(3^4) = 81a`Therefore, `(a)- (34)- 4 = 81a`(b) Rewrite the given expression without negative exponents and simplify:(b)(6y-5/3xy2)3Let us first use the law of exponents that says `(a^m)^n = a^(m*n)`We have to remove the negative exponent from `y^-5`, we can write it as `1/y^5`.Thus, `(6y-5/3xy2)3 = 6^3 * y^-15 * x^3 * y^6`Moving the base `y` with the negative exponent to the denominator and change the exponent to `+15`.Therefore, `(6y-5/3xy2)3 = 216x^3/ y^9`(c) Rewrite the given expression without negative exponents and simplify:(c) x-9y-14x2x-8We can rewrite `x^-9` as `1/x^9` and `x^-8` as `1/x^8`. Therefore, we get `(1/x^9 * y^-14 * x^2 * 1/x^8)`.Simplifying the above expression we get `(y^-14/x^15)`Therefore, `x-9y-14x2x-8 = y^-14/x^15` (d) Rewrite the given expression without negative exponents and simplify:(d) u−2u2u0u3Here we can observe that `u^0 = 1`. Hence, `u−2u2u0u3 = u^-2*u^2*1*u^3`We can simplify the expression by multiplying the coefficients and adding the exponents. Thus, `u^-2*u^2*1*u^3 = u^(2-2+3) = u^3`Therefore, `u−2u2u0u3 = u^3`

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Answer:

tan A= 8/15

draw triangle where A and B are legs and C is hypotenuse

A=8 and C=17, meaning that you need to find B by using Pythagorean theorem (a^2+b^2=c^2)

8^2+b^2=17^2

64+b^2=289

b^2=225

b=15

tan= opposite/adjacent

tan A=8/15

The linear equation that shows the interest earned from each investment is (d): "4a + 6b + 5c = 950"

Investment refers to the act of allocating money or other resources to an asset or venture with the expectation of generating a profit or some other form of return over a period of time.  The primary goal of investing is to use the available resources to generate a return that is greater than the initial investment, thus growing wealth over time.

A linear equation is an algebraic equation in which the highest power of the variable is one. In other words, a linear equation is a polynomial of degree one. It represents a straight line when plotted on a graph. The general form of a linear equation with one variable, x, is:

ax + b = 0

In the given question,

Let's assume that Mr. Silverstone invested a dollars in the first annuity with an interest rate of 2%, b dollars in the second annuity with an interest rate of 4%, and c dollars in the bond with an interest rate of 5%. The interest earned from each investment can be calculated as follows:

Interest earned from the first annuity = 0.02a

Interest earned from the second annuity = 0.04b

Interest earned from the bond = 0.05c

The total interest earned from all three investments together is given as $950. Therefore, we can write the equation:

0.02a + 0.04b + 0.05c = 950

This is the same as option (c) given in the question: "0.04a + 0.06b + 0.05c = 950". However, option (c) has some errors in the coefficients, as the interest rates for the annuities were given as 2% and 4%, not 4% and 6%.

Therefore, the linear equation that shows the interest earned from each investment if the total was $950 is:

0.02a + 0.04b + 0.05c = 950

This can also be simplified as:

2a + 4b + 5c = 95000 (by multiplying both sides by 100 to remove the decimals)

So, the correct option is (d): "4a + 6b + 5c = 950".

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Answer: (a) From the graph, we can see that the function f is increasing on the interval [-5, -1), (-2, 2), and (3, 5]. Therefore, we can write the increasing intervals in interval notation as:

[-5, -1) ∪ (-2, 2) ∪ (3, 5]

(b) From the graph, we can see that the function f is decreasing on the interval (-1, 1) and (2, 3]. Therefore, we can write the decreasing intervals in interval notation as:

(-1, 1) ∪ (2, 3]

(c) From the graph, we can see that the function f is constant on the interval [-4, -3]. Therefore, we can write the constant interval in interval notation as:

[-4, -3]

Step-by-step explanation:

The answer choice which represents the solution to the inequality given as required is; b > -90.

Quotient refers to a number resulting from the division of one number by another.

As evident in the task content; the given inequality is;

Eight more than the quotient of a number b and 45 is greater than 6.

The symbols of inequalities are;

Greater than >

Less than <

Equal to =

Greater than or equal to ≥

Less than or equal to ≤

Therefore, the algebraic expression is;

b/45 + 8 > 6

Therefore; b/45 > -2

b > -90.

Ultimately, the required inequality is; b/45 + 8 > 6 and it's solution is; b > -90.

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