4) Ella drives 60 miles per hour. How far will she drive in 2% hours?​

Answer:

degrees and the measure of angle 5 is -------- degrees. The measure of angl

Step-by-step explanation:

Answer: x = 52

Step-by-step explanation:

You'd first deal with the 4 outside the parentheses, multiplying 10x-20 by 4. This would result in 40x - 80 = 200.

You'd then further isolate x, adding 80 on both sides, resulting in 40x = 2080. Divide by 40 on both sides and You'd get your answer of x = 52.

Answer:

$1,489.88 (nearest cent)

Step-by-step explanation:

To calculate gross pay, multiply the number of hours worked by the pay per hour.

Warren worked 36.5 hours one week and 32 hours the week before.

Therefore, the total number of hours Warren worked was:

Multiply the total number of hours worked by Warren's rate of pay of $21.75 per hour:

Therefore, Warren's gross pay for the two weeks was $1,489.88 (nearest cent).

Answer:

$1489.875

Step-by-step explanation:

Warren's gross pay for 36.5 hours last week can be calculated as follows:

Gross pay for 36.5 hours = $21.75/hour * 36.5 hours = $793.875

Similarly, Warren's gross pay for 32 hours the week before can be calculated as follows:

Gross pay for 32 hours = $21.75/hour * 32 hours = $696

Adding the gross pay for the two weeks, we get:

Gross pay for 2 weeks = $793.875 + $696 = $1489.875

Answer:  10

Step-by-step explanation:

Arranged data

7,10,10,11,11,12,12,13,13,17

Range= Highest value - Lowest Vlue

Highest value=17

Lowest value =7

Range=17-7

Range=10

Answer:

\(Answer:  10

Step-by-step explanation:

Arranged data

7,10,10,11,11,12,12,13,13,17

Range= Highest value - Lowest Vlue

Highest value=17

Lowest value =7

Range=17-7

Range=10 \)

hope it is helpful to you

Answer:

127,654

Place: hundreds, Value: 600

786,540

Place: Hundred thousands, Value: 700,000

45,902

Place: ten thousands, Value: 40,000

Hope this helps!

Answer:

(8x-5y)(8x+5y)

Step-by-step explanation:

Using the square principal because the square root of 64x2 is 8x and the square root of 25y2 is 5y and +- because +times- is only minus and the equation is minus.

Answer:

190,000

190,000

190,000

Step-by-step explanation:

190,000

190,000

The expression  (x²)5 is simplified using the exponent properties to  5x².

Index forms of a number can be defined as the number written in the form of an exponential expression.

To be a single number that is raised to another number.

Numbers too large or small are written in index forms, since the law of exponents states the following;

Exponents of numbers are to be added when numbers are multiplied

We are Given the expression;

(x²)5

Using the law of exponents, we have;

5x²

Thus, the expression is simplified using the exponent properties to  5x²

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The law of cosines is used to solve a triangle when one of the following cases is given SSA, SSS, or SAS.

In the SSA (side-side-angle) case, two sides and a non-included angle are given, and we need to find the third side and remaining angles. However, there can be two possible triangles, one or none depending on the size of the non-included angle and the length of the given sides.

In the SSS (side-side-side) case, all three sides of a triangle are given, and we need to find the three angles. This can be solved using the law of cosines to find any of the angles, and then the law of sines to find the other two.

In the SAS (side-angle-side) case, two sides and an included angle are given, and we need to find the third side and remaining angles. This can be solved using the law of cosines to find the missing side and then the law of sines to find the remaining angles.

The ASA (angle-side-angle) case can be solved using the law of sines or the law of cosines, depending on the given information.

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Answer:

Answer:B AND E ARE CORRECT

Answer:B AND E ARE CORRECTStep-by-step explanation:

WE'RE SIMPLY COMPARING TWO SIMILAR SIDES OF THE FIQURES. NOTE: the pattern must be the same I mean if we start with the larger figure being on top then that is how the rest comparisons should follow. I hope this will help!

Answer:

D

Step-by-step explanation:

Let's break this down step-by-step:

1) The equation given is: 6 + 3 = 9

2) This simplifies to: 6 = 9 - 3 => 6 = 6

3) Any ordered pair (x,y) that satisfies this equation must have:

x = 6 (because x = 6)

4) Looking at the options:

a) (0,5) : x does not equal 6, so this is not the solution

b) (−2,7) : x does not equal 6, so this is not the solution

c) (0, −5) : x does not equal 6, so this is not the solution

d) (2,7) : x equals 6, so this is the solution

Therefore, the ordered pair that satisfies the equation 6 + 3 = 9 is (d) (2,7).

The correct choice is d.

As per the angle of elevation, the distance between the observation area and the balloon changing 800m

The term angle of elevation is defined as an angle that is formed between the horizontal line and the line of sight.

Here we have given that a hot-air balloon is rising straight up at 5 ft/sec. an observation area is located 80 feet from the take-off point. at the moment that the balloon reaches a height of 60 feet and we need to find the angle of elevation and the the distance between the observation area and the balloon changing

While we reading the question, we have identified that the balloon was at point D when angle of elevation was 60° i.e. ∠BAD = 60°

Now, we know that after some time, the balloon was at point E when angle of elevation was 30° i.e. ∠CAE = 30°

Therefore, the the value of BD = CE = 692 m (Height at which the balloon is flying)

As in triangle ABD the value of

=> tan BAD = BD/AB

=> tan 60° = 692/AB

=> AB = 692/3

=> AB = 692/1.73 = 400 m

As in triangle EAC, the value of

=> tan CAE = EC/AC

=> tan 30 = 692/AC

=> AC = 692 × 3

=>  AC = 692 × 1.73 = 1197.16 m

Therefore, Distance travelled by the balloon is calculated as,

=> ED = BC = AC – AB

=> 1197.16 – 400

=> 797.16 ≈ 800 m

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The best model for metronome is a rectangular pyramid.

The approximate surface area is: 500 cm².

The surface area of a rectangular pyramid = lw + l ×√[(w/2)² + h²] + w×√[(l/2)² + h²], where:

The diagram of the metronome is a: rectangular pyramid.

Given the following:

l = 9 cm

w = 11

h = 20

Surface area of a rectangular pyramid = (9)(11) + 9 ×√[(11/2)² + 20²] + 11×√[(9/2)² + 20²]

= 511.18222

Therefore, the approximate surface area is: 500 square centimeters.

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Answer: it is 500 but a metronome is a square prism and that is the right answer on edmentum, not rectangular.

Step-by-step explanation:

The standard deviation of the discrete variable is approximately 1.00.

The standard deviation for discrete variables can be calculated using the following formula:σx =√∑(x - μ)²P(x)where σx is the standard deviation for the discrete variable X, μ is the expected value (mean), x is each possible value of the variable, and P(x) is the probability associated with each value of x. The formula for the mean or expected value of a discrete variable is as follows:μ = E(X) =∑xP(x)Now we will calculate the expected value or the mean:μ = 0(0.22) + 1(0.11) + 2(0.08) + 3(0.21) + 4(0.38) = 0 + 0.11 + 0.16 + 0.63 + 1.52 = 2.42Thus, the mean is 2.42.Now, let's calculate the standard deviation:σx =√∑(x - μ)²P(x)σx = √[(0 - 2.42)²(0.22) + (1 - 2.42)²(0.11) + (2 - 2.42)²(0.08) + (3 - 2.42)²(0.21) + (4 - 2.42)²(0.38)]σx = √[(-2.42)²(0.22) + (-1.42)²(0.11) + (-0.42)²(0.08) + (0.58)²(0.21) + (1.58)²(0.38)]σx = √[0.9992]σx = 0.999Therefore, the standard deviation of the discrete variable is approximately 1.00.

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Answer:

no

Step-by-step explanation:

If x = 3 is a zero, then f(3) = 0

f(3)

= 4\((3)^{4}\) - 3³ - 52(3)² - 35(3) + 12

= 324 - 27 - 468 - 105 + 12

= - 264

Since f(3) ≠ 0 then x = 3 is not a zero of f(x)

Each model should be produced on a weekly basis to maximize net profit is $75,900.

What is Net profit?

In both business and accounting, net income or profit is an entity's revenue less cost of goods sold, costs, depreciation and amortisation, interest, and taxes for a certain accounting period.

As given,

Number of products sold:

T ≥ 1.5G

Maximize Profit Z = 150T + 130G

Labor Constraint:

Labor hours Available:

Production Department:

Number of labor hours available per day = 58 × 7 = 406

Number of days in a week = 5

Number of lobor ours available per week = 406 × 5 = 2030

Assembly Department:

Number of labor hours available per day = 25 × 7 = 175

Number of days in a week = 5

Number of labor hours available per week = 175 × 5 = 875.

Labor hours Required:

Labor hours required for G1 model:

Labor hours required at Production department = 3.5G

Labor hours required at assembly department = 2G

Labor hours required for T1 model:

Labor hours required at Production department = 4T

Labor hours required at Assembly department = 1.5T

Total labor hours required at Production department = 3.5G + 4T

Total labor hours required at Assembly department = 2G + 1.5T.

Constraint:

Labor hours required ≤ Labor hours Available.

Production department Labor constraint

3.5G + 4T ≤ 2030

Assembly department Labor constraint:

2G + 1.5T ≤ 875

The function:

Maximum Profit Z = 150T +130G

Constraint:

3.5G +4T ≤ 2030

2G + 1.5T ≤ 875

T ≥ 1.5G

Suppose that for example:

10.5G +12T = 6090

 16G + 12T = 7000

Solve both equations simultaneously,

5.5G = 7000 - 6090

5.5G = 910

    G = 910/5.5

    G = 363

Since, T > G

Hence,

T = 363,

G = 165

Calculate Profit:

150T + 130G = 150 × 363 + 130 × 165

                     = 54450 + 21450

                     = 75900

Hence, each model should be produced on a weekly basis to maximize net profit is $75,900.

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The least common denominator for the given fractions is (x+6)(x-2). Therefore, the correct answer is option B.

The given expression is \(\frac{x}{x^2+4x-12}-\frac{3}{x+6}\) and the least common denominator is (x+6)(x-2).

When two or more fractions have the same denominators, they are termed as the common denominators. The least common denominator (LCD) refers to the smallest number that is a common denominator for a given set of fractions.

Here, \(\frac{x}{x^2+6x-2x-12}-\frac{3}{x+6}\)

\(=\frac{x}{x(x+6)-2(x+6)}-\frac{3}{x+6}\)

\(=\frac{x}{(x+6)(x-2)}-\frac{3}{x+6}\)

Here, least common denominator is (x+6)(x-2)

\(=\frac{x}{(x+6)(x-2)}-\frac{3(x-2)}{(x+6)(x-2)}\)

Therefore, the correct answer is option B.

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"Your question is incomplete, probably the complete question/missing part is:"

Kelvin found that the least common denominator needed to subtract \(\frac{x}{x^2+4x-12}-\frac{3}{x+6}\) is is (x+6)(x-2). Which is the correct next step?

A) \(\frac{x-3}{x^2+3x-18}\)

B) \(\frac{x}{(x+6)(x-2)} - \frac{3(x-2)}{(x+6)(x-2)}\)

C)  \(\frac{x}{(x+6)(x-2)} - \frac{3(x+2)}{(x+6)(x-2)}\)

D) \(\frac{x(x+6)(x-2)}{(x+6)(x-2)} - \frac{3(x+6)(x-2)}{(x+6)(x-2)}\)

To determine if two normal vectors are pointing in the same general direction or opposite directions, we can compare their dot product.

A normal vector is a vector that is perpendicular (orthogonal) to a given surface or plane. When comparing two normal vectors, we want to determine if they are pointing in the same general direction or opposite directions.

To check the direction, we can use the dot product of the two vectors. The dot product of two vectors A and B is given by A · B = |A| |B| cos(θ), where |A| and |B| are the magnitudes of the vectors, and θ is the angle between them.

If the dot product is positive, it means that the angle between the vectors is less than 90 degrees (cos(θ) > 0), indicating that they are pointing in the same general direction. A positive dot product suggests that the vectors are either both pointing away from the surface or both pointing towards the surface.

On the other hand, if the dot product is negative, it means that the angle between the vectors is greater than 90 degrees (cos(θ) < 0), indicating that they are pointing in opposite directions. A negative dot product suggests that one vector is pointing towards the surface while the other is pointing away from the surface.

Therefore, by evaluating the dot product of two normal vectors, we can determine if they are pointing in the same general direction (positive dot product) or opposite directions (negative dot product).

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Answer:

degree of 8

Step-by-step explanation:

Given that f(x) is a polynomial of degree 3. The cubic function (3rd degree) can be expressed as:

\(\displaystyle{f(x) = ax^3 + bx^2 + cx + d}\)

While the g(x) is a polynomial of degree 5. It can be expressed as:

\(\displaystyle{g(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f}\)

And the problem gives us to find "\(\displaystyle{2f(x)4g(x)}\)". First, evaluate each terms:

2f(x)

2f(x) can be evaluated by multiplying 2 in every terms of function f(x):

\(\displaystyle{2f(x) = 2(ax^3+bx^2+cx+d)}\\\\\displaystyle{2f(x) = 2ax^3+2bx^2+2cx+2d}\)

4g(x)

Similar to above one except we change to multiply from f(x) to g(x) by 4:

\(\displaystyle{4g(x) = 4(ax^5 + bx^4 + cx^3 + dx^2 + ex + f)}\\\\\displaystyle{4g(x) = 4ax^5 + 4bx^4 + 4cx^3 + 4dx^2 + 4ex + 4f}\)

Since we are looking for the degree of polynomial, it's not necessary to bring all terms to multiply 2f(x) with 4g(x). We'll be multiplying both functions with the highest degree of individual polynomial.

The highest degree of 2f(x) is 3 which is term of \(\displaystyle{2ax^3}\)

The highest degree of 4g(x) is 5 which is term of \(\displaystyle{4ax^5}\)

Since we are looking for the degree, we only have to evaluate the x-term with exponent:

\(\displaystyle{x^3 \cdot x^5}\)

Apply the law of exponent - add both exponents together:

\(\displaystyle{x^8}\)

Therefore, we can conclude that the degree of polynomial is 7.

=========

In short explanation, it's not necessary to do everything. Since we are looking for degree, we only take \(\displaystyle{x^3}\) which polynomial of degree 3 and \(\displaystyle{x^5}\) which is degree of 5 then multiply both terms together which result in \(\displaystyle{x^8}\) via law of exponent.

Evaluating 2f(x)4g(x) will result with same degree anyways so it's not necessary to evaluate but in case if you want to see what is 2f(x)4g(x) then I've calculated it above.

In summary, the radius of convergence is √2 and the interval of convergence is [-√2, √2].

To find the radius of convergence and interval of convergence of the power series, we can use the ratio test.

The given power series is:

∑ ((-1)^n (x^2)^n) / (n*2^n)

Let's apply the ratio test:

lim(n->∞) |((-1)^(n+1) (x^2)^(n+1)) / ((n+1)2^(n+1))| / |((-1)^n (x^2)^n) / (n2^n)|

Simplifying and canceling terms:

lim(n->∞) |(-1) (x^2) / (n+1)*2|

Taking the absolute value and applying the limit:

|(-1) (x^2) / 2| = |x^2/2|

For the series to converge, the ratio should be less than 1:

|x^2/2| < 1

Solving for x:

-1 < x^2/2 < 1

Multiplying both sides by 2:

-2 < x^2 < 2

Taking the square root:

√(-2) < x < √2

Since the radius of convergence is the distance from the center (x = 0) to the nearest endpoint of the interval of convergence, we can take the maximum value from the absolute values of the endpoints:

r = max(|√(-2)|, |√2|) = √2

Therefore, the radius of convergence is √2.

For the interval of convergence, we consider the endpoints:

When x = √2, the series becomes:

∑ ((-1)^n (2)^n) / (n*2^n)

This is the alternating harmonic series, which converges.

When x = -√2, the series becomes:

∑ ((-1)^n (2)^n) / (n*2^n)

This is again the alternating harmonic series, which converges.

Therefore, the interval of convergence is [-√2, √2].

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Answer:

Step-by-step explanation:

Using the above conditions ; If m ∠LOM = m ∠JKI,  if m ∠MON = m ∠IKH it is proved below that m ∠LON = m ∠HKJ as are congruent angles.

An angle is known to be Congruent if its angles do have equal measure."

Note that question, In the said figure of the angles (image attached),

m ∠LOM = m ∠JKI  (congruent angles)              taken as 1      

m ∠MON = m ∠IKH  (congruent angles)             taken as 2  

The one should sum up both the side angle  of m ∠MON in (1) we obtain;

m ∠LOM + m ∠MON = m ∠JKI + m ∠MON

Then one should replace angle  m ∠MON = m ∠IKH from (eqn. 2)  on right hand side and then it will be:

m ∠LOM + m ∠MON = m ∠JKI + m ∠IKH      taken as (3)

Then:

m ∠LOM + m ∠MON = m ∠LON  ( M is said to be the interior point of ∠LON)    taken as (4)

Since m ∠JKI + m ∠IKH = m ∠HKJ  ( I is said to be the interior point of ∠HKJ)            taken as number (5)

Using Number (3) , (4) and (5)  in the image attached, we obtained:

m ∠LON = m ∠HKJ  (Congruent angles)

Therefore, Using the above conditions ; If m ∠LOM = m ∠JKI,  if m ∠MON = m ∠IKH it is proved below that m ∠LON = m ∠HKJ as are congruent angles.

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Copper oxide, often known as CuO, is the most typical natural ore of copper.

An estimated 5.6 million metric tons of copper were produced in 2021 in Chile, the world's largest copper producer.

What is copper?

A ductile, malleable, and highly efficient conductor of heat and electricity, copper is a reddish-gold colored metal. Since it was the first metal that humans worked with, copper is one of the metals that is used the most frequently today.

The two primary copper ores are copper oxide ore and copper sulfide ore. Both forms of ore may be profitably mined, although chalcopyrite, a sulfide ore mineral, is the most prevalent source of copper ore and represents nearly half of the metal's output.

The most significant and significant source of copper metal is chalcopyrite. The hue is often brassy to golden-yellow, frequently tarnished, and has a submetallic shine along with greenish-black streaks.

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To find all possible real numbers a, b, c, d ∈ R such that v = (ab), w = (cd) form a basis B = {v, w} for R2 and satisfy [(34)]B = (12), we can start by finding the transformation matrix from the standard basis to B.

Let's assume kv + lw = 0: k(ab) + l(cd) = (0, 0)= (abk, cdl) = (0, 0)
From this, we get two equations:
abk = 0
cdl = 0
Since a, b, c, and d are real numbers, k and l cannot be zero. Thus, either a = 0 or b = 0, and either c = 0 or d = 0.
If a = 0 and c = 0, then v = (0, b) and w = (0, d), which means they are not linearly independent since they lie on the same line. If a = 0 and d = 0, then v = (0, b) and w = (cd) = (c, 0), which are linearly independent and form a basis B for R2. In this case, we have [(34)]B = [(30, 40)] = (12).

Similarly, we can check the cases where b = 0, c = 0, and d = 0. Therefore, the possible choices for a, b, c, and d that ensure v and w form a basis for R2 and satisfy [(34)]B = (12) are: 1. v = (0, b) and w = (c, 0), where b ≠ 0 and c ≠ 0. In this case, a and d can be any real numbers.

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Answer:

False

Step-by-step explanation:

I would say false. The operations inside should always go by PEMDAS unless instructed otherwise

Answer:

FALSE

Step-by-step explanation:

Within a set of parentheses, the order of operations should be followed. This is because you will get the wrong answer if you don't.