Simplify , using the law of exponents

Answer:

5/10

Step-by-step explanation:

5/7 x 7/10

35/70

5/10

Answer:

To find the circumference you need to use C= 2πr but since you started with the diameter you need to divide it by 2 and you will get 3963.2. After you get the radius use the formula C= 2πr and you will get 24901.52

The equation would be written as 2 x π x 3963.2 = 24901.52

Al-Fatihah is an Islamic prayer recited during the five daily prayers. Comparing radio and television in reading Al-Fatihah from its beginning requires an analysis of how each medium conveys the prayer to its audience. Radio precedes television in reading Al-Fatihah from its beginning.

This is because radio broadcasting began in the early 1900s while television broadcasting began in the late 1940s.

This delay can range from a few seconds to a few minutes depending on several factors such as the geographical location of the audience, the strength of the signal, and the quality of the receiver. Therefore, the time difference between radio and television in reading Al-Fatihah can vary depending on the factors mentioned above.

Mathematically, the time difference between radio and television can be calculated using the formula: d = s / tWhere d is the distance between the transmitter and the receiver, s is the speed of the signal, and t is the time it takes for the signal to reach the receiver.

In this case, d is the distance between the broadcasting station and the audience, s is the speed of the signal which is constant (i.e., the speed of light), and t is the time it takes for the signal to reach the audience. Since the speed of light is approximately 299,792,458 m/s, the time it takes for the signal to reach the audience can be calculated using the following formula:t = d / s

Therefore, the time difference between radio and television in reading Al-Fatihah can be calculated by subtracting the time it takes for the radio signal to reach its audience from the time it takes for the television signal to reach its audience. This difference can range from a few milliseconds to a few minutes depending on the factors mentioned above.

In network concepts, the time difference between radio and television in reading Al-Fatihah can be affected by the bandwidth of the network. The bandwidth is the amount of data that can be transmitted over a network in a given time. If the bandwidth is low, it can cause a delay in the transmission of the signal which can affect the time difference between radio and television.

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The weighted-average unit contribution margin is $46.20.

The weighted-average unit contribution margin can be calculated by multiplying the unit contribution margin of each model by its respective sales mix percentage, and then summing up the results.

To find the weighted-average unit contribution margin, we first calculate the unit contribution margin for each model by subtracting the unit variable costs from the selling price:

For Model A12:

Unit contribution margin = Selling price - Unit variable cost

                     = $60 - $42

                     = $18

For Model B22:

Unit contribution margin = Selling price - Unit variable cost

                     = $120 - $84

                     = $36

For Model C124:

Unit contribution margin = Selling price - Unit variable cost

                     = $480 - $360

                     = $120

Next, we multiply each unit contribution margin by its respective sales mix percentage:

Weighted contribution margin for Model A12 = 60% * $18 = $10.80

Weighted contribution margin for Model B22 = 15% * $36 = $5.40

Weighted contribution margin for Model C124 = 25% * $120 = $30.00

Finally, we sum up the weighted contribution margins:

Weighted-average unit contribution margin = $10.80 + $5.40 + $30.00 = $46.20. Therefore, the weighted-average unit contribution margin is $46.20.

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The point of collision is θ = π/6.

A curve's polar equation is often stated with r as a function of θ and represented in polar coordinates.

The given equations are r = √3 + 2cosθ and r = 4cosθ.

The characters will collide at the intersection of these paths, the intersection of the two equations is given by:

√3 + 2cosθ = 4cosθ

4cosθ - 2cosθ = √3

2cosθ = √3

cosθ = √3/2

θ = cos⁻¹(√3/2)

θ = π/6

Hence, the point of collision is θ = π/6.

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Answer:

A rectangle have 2 equal sides whilst the other 2 is also equal

So we can make length “l”

Whilst we can make width “w”

So the formula for a perimter is

2l+2w=p

In this case it’s 70

Now the length is 3 in longer then the width.

So l= 3+w

We can subsitute that in so we can solve the equation now

2(3+w) + 2w = 70

4w+6=70

Now solve

4w+6=70

4w= 64

w= 16

So width is 16

Lenght is 3 more then with so 16+3=19

Width is 16

Length is 19

Answer:

To make students question their existence

Step-by-step explanation:

The area of the figure is 50 square feet.

We are given a figure. The figure is formed with straight lines. We have to find the area of the figure. We can split the figure into two rectangles.

The length and breadth of the first rectangle are 3 feet and 2 feet, respectively. The area of the first rectangle is calculated below.

A1 = L1×B1

A1 = 3×2

A1 = 6 square feet

The length and breadth of the second rectangle are 11 feet and 4 feet, respectively. The area of the first rectangle is calculated below.

A2 = L2×B2

A2 = 11×4

A2 = 44 square feet

The area of the figure is the sum of the areas of both rectangles.

A = A1 + A2

A = 6 + 44

A = 50 square feet

Hence, the area of the figure is 50 square feet.

The complete question is given below.

Find the area of the figure. (Sides meet at right angles.) The side lengths are 3 ft, 2 ft, 2 ft, 4 ft, 4 ft, 4 ft, and 4 ft.

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No, the Normal/large sample condition is not met for constructing at confidence interval. Option C.

To estimate the amount of carbon emissions released by cars, the mean weight of cars must be estimated. In this case, a random sample of 20 cars is selected and their mean weight is calculated. The conditions for constructing a confidence interval are met if the following conditions are satisfied:
1. Random Condition: The sample is randomly selected.
2. 10% Condition: The sample size is less than 10% of the population size.
3. Normal/Large Sample Condition: The sample size is large enough (usually n≥30) for the Central Limit Theorem to apply, or the population distribution is approximately normal.
In this scenario, the random condition is met since the cars are randomly selected. The 10% condition is also met, assuming there are more than 200 cars in the population. However, the Normal/large sample condition is not met since the sample size of 20 is less than the recommended threshold of 30.
Therefore, the answer is: No, the Normal/large sample condition is not met.

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The required value of arcDF from the figure shown is 30 degrees.

In mathematics, an arc is characterized as a piece of the limit of a circle or a bend. It can likewise be alluded to as an open bend. The limit of a circle is the border or the distance around a circle, otherwise called the boundary.

In light of the evenness of the figure given, we can say that the action of<DEF is equivalent to the minor curve DF

Given the accompanying boundaries

m∠DEF=30 degrees

Since m∠DEF = arcDF, consequently the proportion of bend DF is 30degrees

Thus, The proportion of arcDF from the figure shown is 30 degrees.

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Answer:

83.75%

Step-by-step explanation:

67/80 = 83.75%

Answer:

Step-by-step explanation:

ok, so this is an infinitly repeating function, so you can write it as:

sqrt(12-x)

Although, x is also equal to sqrt(12-x), so

x = sqrt(12-x), and

x^2 = 12-x

x^2-12+x = 0

now just apply the quadratic formula and you're good

hope i helped :D

Answer:

The answer to your question is choice a

The calculated value of the tenth term, b₁₀ of the sequence is 78732

From the question, we have the following parameters that can be used in our computation:

b₁ = -4

bₙ = 3bₙ₋₁

The above means that

We multiply the current term by 4 to get the next term

So, we have

b₂ = 3 * 4 = 12

b₃ = 3 * 12 = 36

b₄ = 3 * 36 = 108

b₅ = 3 * 108 = 324

b₆ = 3 * 324 = 972

b₇ = 3 * 972 = 2916

b₈ = 3 * 2916 = 8748

b₉ = 3 * 8748 = 26244

b₁₀ = 3 * 26244 = 78732

Hence, the tenth term, b₁₀ of the sequence is 78732

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Answer:

(1, - 1.5 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then

midpoint = ( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

here (x₁, y₁ ) = (4, 0 ) and (x₂, y₂ ) = (- 2, - 3 ) , then

midpoint = ( \(\frac{4-2}{2}\) , \(\frac{0-3}{2}\) ) = ( \(\frac{2}{2}\) , \(\frac{-3}{2}\) ) = (1, - 1.5 )

(1, -1.5).

Step-by-step explanation:

The midpoint of a segment with endpoints (x1, y1) and (x2, y2) is given by the following formula:

((x1 + x2)/2, (y1 + y2)/2)

So, for the given endpoints (4,0) and (-2,-3), the midpoint is:

((4 + (-2))/2, (0 + (-3))/2) = (1, -1.5)

The midpoint of the segment is (1, -1.5).

Integrate (ax)2 − b2 3/2 with respect to x. The result is (2/5)ax5/2 − (b2/5)x3/2 + c, where c is the constant of integration.

Integrate (ax)2 − b2 3/2 with respect to x.

First, use the power rule to rewrite the integrand as

(2/5)ax5/2 − (b2/5)x3/2.

Next, use the integration by parts formula to integrate the expression:

∫(2/5)ax5/2 − (b2/5)x3/2 dx

= (2/5)ax5/2 − (b2/5)x3/2 + c,

where c is the constant of integration.

Integrating (ax)2 − b2 3/2 with respect to x involves using the power rule and the integration by parts formula. The power rule states that when integrating a function to the nth power, the exponent is reduced by one and the coefficient is multiplied by the original exponent divided by the reduced exponent. Therefore, the integrand is rewritten as (2/5)ax5/2 − (b2/5)x3/2. The integration by parts formula is then used to integrate the expression, resulting in (2/5)ax5/2 − (b2/5)x3/2 + c, where c is the constant of integration.

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Complete question is;

A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas. During one particular week, the two cars went a combined total of 1850 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?

Answer:

Car 1 consumed 30 gallons of gas.

Car 2 consumed 20 gallons of gas.

Step-by-step explanation:

Let x be number gallons consumed by car 1

Let y be number of gallons consumed by car 2

We are told that total gas consumption of 50 gallons. Thus;

x + y = 50 - - - - - eq(1)

We are told that the first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas and they went a combined total of 1850 miles. Thus;

35x + 40y = 1850 - - - - eq2

Let's make y the subject in eq(1),

y = 50 - x - - - - eq(3)

Putting 50 - x for y in eq 2 gives;

35x + 40(50-x) = 1850

35x + 2000 - 40x = 1850

-5x + 2000 = 1850

-5x = -150

x = 150/5

x = 30 gallons

Substitute 30 for x into eq 3,we have;

y = 50 - 30

y = 20 gallons

Thus;

Car 1 consumed 30 gallons of gas.

Car 2 consumed 20 gallons of gas.

Answer:

15.24m

Step-by-step explanation:

1-foot=0,304m then 50-foot=0,304*50=15,2 m

Answer:

Large box = 31/2 = 15.5 kgs

Small box = 27/2 = 13.5 kgs.

Step-by-step explanation:

Let x be large box

Let y be small box

5x + 3y = 118

5x = 118 - 3y

x = 118/5 - 3/5y

2x + 12y = 193

2(118/5 - 3/5y) +12y = 193

y = 27/2 = small box

Large box

5x + 3(27/2)=118

x = 31/2 = large box

Answer:

2

Step-by-step explanation:

Use BODMAS(bracket, of, division, multiplication, addition and subtraction)

72/8=9

(6*4)=24

24/12+9-9

2+0

=2

The solution for the given operations of numbers is 2.

PEMDAS rule is the same as BODMAS rule.

PEMDAS is the abbreviation for Parenthesis, Exponents, Multiplication, Division, Addition and Subtraction.

We are using BODMAS rule here to solve the given operations.

6 * 4 ÷ 12 + 72 ÷8 - 9

According to the rule, first we should do multiplication.

6 × 4 = 24

6 * 4 ÷ 12 + 72 ÷8 - 9 = 24 ÷ 12 + 72 ÷8 - 9

Next do the division.

24 ÷ 12 = 2 and 72 ÷8 = 9

24 ÷ 12 + 72 ÷8 - 9 = 2 + 9 - 9

Now do the addition and subtraction.

2 + 9 - 9 = 2

Hence the final answer for the given operation is 2.

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Given:

Chandra get a bonus if average quarterly sales for an year exceeds $70000.

From the bar diagram, we can find the sales for each quarter.

The height of each bar gives the sales for each quarter.

Since the data in the vertical column is given in thousands of dollars, multiply the height of the bar by 1000 to get the correct sales value.

The sales for the first quarter is $40000.

The sales for the second quarter is $100000.

The sales for the third quarter is $80000.

Let x be the sales for the fourth quarter.

Now, the average of the quarterly sales is,

Put A=70000 and solve the equation for x to obtain the sales for the fourth quarter so that Chandra gets bonus.

So, the sales of the fourth quarter must be $60000 in order for Chandra to earn the bonus.

Hence, option D is correct.

The measures in the circle given in the image above are calculated as:

1. m<PSQ = 130°;   2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.

In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.

1. m<PSQ = m<PAQ

Substitute:

m<PSQ = 130°

2. Find m<PBQ:

m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]

Substitute:

m<PBQ = 1/2(130 + 2(35))

m<PBQ = 100°

m<AQS = 180 - [m<BAQ + m<PBQ]

Substitute:

m<AQS = 180 - [(180 - 130) + 100]

m<AQS = 30°

3. m(QR) = m<QAR

Substitute:

m(QR) = 100°

4. m(PS) = 180 - m(RS)

Substitute:

m(PS) = 180 - 2(35)

m(PS) = 110°

5. m(RS) = 2(35)

m(RS) = 70°

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The error involved in approximating the sum of the given series by the sum of the first five terms of the series is `R5 = 1/6³ + 1/7³ + ...`.

To estimate the error that is made by approximating the sum of the given series by the series the first 5 terms 1/k³, we can use the remainder term of a convergent series.

The given series is ∑ 1/k³ from k = 1 to infinity.We have to find the error involved in approximating the sum of the given series by the sum of the first five terms of the series.

That is, we need to find the difference between the actual sum of the series and the sum of the first five terms of the series.

The sum of the series is given by: `S = 1/1³ + 1/2³ + 1/3³ + 1/4³ + ... + 1/n³ + ...` We can use the remainder term of the series to find the error in approximation.

The remainder term `Rn` is given by: `Rn = Sn - S` where `Sn` is the sum of the first `n` terms of the series. Thus, we have to find the remainder term for `n = 5`.

The remainder term `Rn` is given by: `Rn = S - Sn = 1/6³ + 1/7³ + ...` Since the given series is convergent, the remainder term `Rn` tends to zero as `n` tends to infinity.

So, if we take the sum of the first five terms of the series, the error involved in approximation is given by the remainder term `R5`.

The error involved in this approximation is very small and can be neglected.

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Answer:

\(63\sqrt{2}\)

Step-by-step explanation:

\(7\sqrt{6}* \sqrt{27} \\=7\sqrt2\sqrt{3} * \sqrt{9} \sqrt{3}\\ =7\sqrt{2}\sqrt{3} *3\sqrt{3}\\ =\sqrt{2} *3*3*7\\=63\sqrt{2}\)

Answer:

\(\sqrt{53}\)

Step-by-step explanation:

Answer: 1.8 cubic cm

Step-by-step explanation:

Answer:

(2, -3)

Step-by-step explanation:

The  x-axis is the perpendicular bisector of a segment with an endpoint of (2,3).

A perpendicular bisector is a line which is perpendicular to a segment, dividing the segment into two equal parts. The perpendicular bisector passes through the midpoint of the segment.

Since the x axis bisects a segment with an endpoint of (2,3) perpendicularly, hence a point on the x axis is the midpoint of the segment. The midpoint would have the same x coordinate as the endpoint.

Hence, the midpoint is (2, 0).

Let (x, y) be the other endpoint, then:

(2, 0) is the midpoint of the segment joining (2, 3) and (x, y). we find the value of x and y using:

(2 + x) / 2 = 2;  and (3 + y) / 2 = 0

2 + x = 4;  and 3 + y = 0

x = 4 - 2 ;    and y = 0 - 3

x = 2; and y = -3

Hence the other endpoint is at (2, -3)

Because the x-axis is the perpendicular bisector of a segment with an endpoint of (2, 3), we will see that the other endpoint must be at (2, -3).

First, we know that the x-axis is perpendicular to our segment, so our segment must be a vertical segment. This means that there can't be a variation in the x-values between the endpoints.

So, if one endpoint is (2, 3), then the other must be (2, y).

To find the value of y we use the fact that the x-axis is also a bisector, so it divides the segment in two equal parts, then we must have y = -3

In this way, we can conclude that the other endpoint is (2, -3)

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Once we have categorized an object, our memory of the object increasingly resembles the category is B) prototype. This means that when we categorize an object, our memory of it begins to resemble the prototype or typical example of that category. For example, if we categorize a bird as a robin, our memory of the bird will increasingly resemble the characteristics of a typical robin.

This happens because our brain uses prototypes as a shortcut to process information and make sense of the world around us. We use prototypes to quickly identify objects and make assumptions about their characteristics based on their category.

our memory of an object after categorization is influenced by the prototype of the category. This helps us to quickly process and make sense of information, but it can also lead to errors and biases in our thinking.


A prototype is a mental image or best example of a category. When we categorize an object, our memory of the object increasingly resembles the prototype because we tend to recall the most representative or typical example of the category.

Once we categorize an object, our memory of the object becomes more like the prototype, which is the best example of the category. This is because we tend to remember the most representative or typical examples of a category.

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