A, B, C and D form the vertices of a
quadrilateral. Calculate the area of the
quadrilateral rounded to 1 DP.
AB = 23.6m
AD = 7.8m
BC = 9.7m
CD = 14.9m
Angle ABC = 59⁰

Answer:

1. 4hrs and 10mnts

2. 13 builders

3. 25 walls

4. 52 toy soldiers

Step-by-step explanation:

1. then, one man can do it in 16hrs and 40mnts, so, 4 men would take 4hrs and 10mnts

2. one builder can build 4 houses in a year, so 13 builders are needed to build 52 houses

3. they can do it at a rate of 2 walls per person for 3 days, so 10 ppl can make 25 walls in 3.75 days

4. 4 toys per person for 2 weeks, so 7 makers can make 52 toys for 3 weeks

There are 20 combinations of boxes that can be used for the customer's 15 chocolate pieces.

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression. When the coefficients are themselves variables, they may also be called parameters.

It is given that a customer ordered 15 pieces of gourmet chocolate. The order can be packaged in small boxes that contain 1, 2 or 4 pieces of chocolate. Any box that is used must be full.

The coefficient of \(x^{15}\) from the steps shown in the image is 20.

Hence, there are 20 possibilities.

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Answer:

16

Step-by-step explanation:

ABC is isosceles, CA=CB=5

CD⊥ AB, AD = BD

D ( 7,3)   , A (4,3)        AB = 10-4 = 6

perimeter = 5+5+6 = 16

Answer:   \(\sqrt{6}\)

This is the same as typing in sqrt(6)

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

Explanation:

The square has all four sides the same length, which in this case is \(\sqrt{3}\) units.

The diagonal of the square splits it into two identical right triangles.

Use the Pythagorean Theorem to find the hypotenuse x, aka the diagonal.

\(a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\x = \sqrt{\left(\sqrt{3}\right)^2+\left(\sqrt{3}\right)^2}\\\\x = \sqrt{3+3}\\\\x = \sqrt{6}\\\\\)

Or you can take the shortcut

\(\text{hypotenuse} = (\text{leg})*\sqrt{2}\\\\x = \sqrt{3}*\sqrt{2}\\\\x = \sqrt{3*2}\\\\x = \sqrt{6}\\\\\)

Which applies to 45-45-90 right triangles.

let's recall that a square has four equal sides, Check the picture below.

Answer: 30

Step-by-step explanation: 26 rounded to the nearest ten is 30!      

I know  this will not help!

Answer:

False

Step-by-step explanation:

When you are squaring a number, you multiply the number by itself (7*7 or 12*12), so if you were to reverse that and find the square root of the number (let's say 49), you'd have to do some guess and check and figure out which number, when multiplied with itself, would equal that number (7*7 = 49).

The square roots of a number are the number by which multiply with the same number we will get the number thus the given statement is completely False.

The number system is a way to represent or express numbers.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number b.

Consider the number 9.

The square root of it is given as,

√(9) = 3

Now, if we multiply 3 by 3 then we get 9 as,

3 x 3 = 9

If we divide 3 by 2 then 3/2 = 1.25 is not 9.

Hence "The square roots of a number are the number by which multiply with the same number we will get the number thus the given statement is completely False".

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The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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Answer:

no they are not equivalent

Step-by-step explanation:

0.4/15 = 0.026

so for every minute they travel 0.026km

0.6/20 = 0.03

so for every minute they travel 0.03km

so they are not the same/equivalent

The Quadratic equation -x² = 8x + 20 does not have real roots.

Given that:

Quadratic equation, -x² = 8x + 20

The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,

D = b² - 4ac

If D > 0, then the roots are real and distinct root.

If D = 0, then the roots are real and equal roots.

If D < 0, then the roots are imaginary roots.

Simplify the equation, then we have

-x² = 8x + 20

x² + 8x + 20 = 0

The discriminant is calculated as,

D = 8² - 4 × 1 × 20

D = 64 - 80

D = - 16

D < 0

The Quadratic equation -x² = 8x + 20 does not have real roots.

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Answer:

Step-by-step explanation:

Angle FEH is obtuse; its measure is 105 degrees.

The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Answer:

= -3

Step-by-step explanation:

The absolute value signs in the expression cancel out any negative value inside. Therefore, substituting x = 13 into the expression:

\(\frac{1}{3}|-(13)+4|-6 = \frac{1}{3}|-9|-6\)

the negative and absolute value signs cancel out, and thus:

\(=\frac{1}{3}(9)-6=3-6 =-3\)

Answer:

Step-by-step explanation:

The sum of a triangle’s angles is always 180 degrees so

x+x+25=180

2x+25=180

2x=155

x=77.5 degrees

Step-by-step explanation:

Step 1:  Convert degrees into radians

\(\frac{degrees}{1}*\frac{\pi }{180}\)

\(\frac{52}{1}*\frac{\pi}{180}\)

\(\frac{52\pi}{180}\)

\(\frac{13\pi}{45}\)

Step 2:  Find the arc length

\(S = r\theta\)

\(S=(3)(\frac{13\pi}{45})\)

\(S = \frac{39\pi}{45}\)

\(S=\frac{13\pi}{15}\)

Answer: Option B

The rule that describes a reflection across the line y = x is given as (x, y) ⇒ (y, x)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right on the coordinate plane.

The rule that describes a reflection across the line y = x is given as (x, y) ⇒ (y, x)

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The first quartile of the distribution of the semiconductor lifetime is 3266 hours

Given the mean of a normal distribution is 5000 hours and a standard deviation of 1000 hours. We need to find the first quartile of the distribution of the semiconductor lifetime.

Quartiles are dividing points of a set of observations into quarters. Therefore, the first quartile is denoted as Q1, which means that one-quarter of the data is less than Q1, and three-quarters are more than Q1. We know that a normal distribution is symmetrical, the 50th percentile is the same as the mean.So, we need to calculate the z-score for the first quartile.

z-score for the first quartile=  (25th percentile/100) = 0.25  => -0.674

z-score equation isz = (x - μ) / σ

Where x = score of interest, μ = mean, and σ = standard deviation

Here, we have μ = 5000, σ = 1000, and z = -0.674

Rearranging the above z-score equation, we get x = (z * σ) + μ

Putting all the given values into the above equation, we get

x = (-0.674 * 1000) + 5000x =  $ 3265.62

Therefore, the first quartile of the distribution of the semiconductor lifetime is 3265.62 or 3266 (approx).

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Answer:

Always is the answer I believe.

Using the given data, the average percent score for the 100 students is 77\(\%\).

Average, also known as mean, is one of the measures of central tendency and is the ratio of the sum of all observations to the total number of observations. It is very useful to summarize a probability distribution.

Let the average percent score for the 100 students be N.

As it is known that the average is the ratio of the sum of all observations to the total number of observations, therefore:

\(N = \dfrac{100\times7+90\times18+80\times35+70\times25+60\times10+50\times3+40\times2}{100}\)

   \(= \dfrac{7700}{100}\\= 77\)

Thus, the average percent score for the 100 students, using the given data is calculated as 77\(\%\).

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The complete question is as follows:

Mrs. Riley recorded this information from a recent test taken by all of her students. Using the data, what was the average percent score for these 100 students?

\(\%\) Score  Number of students

100                  7

90                   18

80                   35

70                   25

60                   10

50                   3

40                   2

Answer: Yes, it'll be approved

Step-by-step explanation:

To solve this, we.need to calculate 2/9 of 78 states. This will be:

= 2/9 × 78

= 17 states

Since 21 states approve an​ amendment, then the constitution will be​ amended because the number of states is more than 2/9 of the 78 states

The potential function f(x,y,z) for which fx(x,y,z)= is zero, exists, and hence f is conservative.

Given that all components of curl(f) are zero, we can conclude that f is a conservative vector field. Therefore, a potential function f(x,y,z) exists such that the gradient of f, denoted by ∇f, is equal to f(x,y,z). As fx(x,y,z) = ∂f/∂x, it follows that ∂f/∂x = 0.

This implies that f does not depend on x, so we can take f(x,y,z) = g(y,z), where g is a function of y and z only. Similarly, we can show that ∂f/∂y = ∂g/∂y and ∂f/∂z = ∂g/∂z are zero, so g is a constant. Thus, f(x,y,z) = C, where C is a constant. Therefore, the potential function f(x,y,z) for which fx(x,y,z) = 0 is f(x,y,z) = C.

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Answer:

c part is the answer of this question

im like 99% sure the answer is b

Answer:

b. To find the probability a customer who ordered pancakes came to thediner late, we need to look at the intersection of the "pancakes" row and the "late" column. This gives us a probability of 0.1, or 10%

c. To determine whether breakfast choice and meal time are independent, we need to see if the probability of one event changes based on the occurrence of the other event. In this case, it seems that breakfast choice and meal time are not independent, as the probability of being late seems to differ based on what breakfast item the customer chose. For example, the probability of being late is higher for customers who ordered pancakes compared to those who ordered cereal. Therefore, the choice of breakfast item appears to be related to the probability of being late, and so breakfast choice and meal time are not independent.

Step-by-step explanation:

Answer:

For question 7a, James and Liu will NOT have the same amount of money saved.

Step-by-step explanation:

Completing the table we have:

Deposit Balance in James' Balance in Liu's

0 300 200

1 30 40

2 30 40

3 30 40

4 30 40

5 30 40

6 30 40

7 30 40

8 30 40

9 30 40

10 30 40

11 30 40

12 30 40

660 680

Therefore, they won't be able to save up the same amount of money.

7b. The graghs representing James and Liu end as parallel graghs therefore the both of them will never be able to save the same amount.

(Using 50 units on the vertical axis and 1 unit on the horizontal axis)

Answer:

6x^2-39x+2/3x

Based on the information given the average speed for his trip is 64 miles.

Using this formula

d=rt

r=d/t

Where:

r=rate=?

d=distance=512 miles

t=time=8 hours

Let plug in the formula

r=512/8

r=64 miles

Inconclusion the average speed for his trip is 64 miles.

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Answer:

In order to solve this, we need to transform the equation into R = D/T

Plug in the numbers into this equation

R = 512/8

So after we divide these two numbers, we get an answer of 64 mph as Adam's average speed.

To find the area of the region R bounded above by the parabola y = 4 - \(x^2\) and below by the line y = 1, we need to determine the points of intersection between these two curves.

Setting y = 4 -\(x^2\) equal to y = 1, we have:

4 - \(x^2\) = 1

Rearranging the equation, we get:

\(x^2\) = 3

Taking the square root of both sides, we have:

\(x\)= ±√3

Since we are only interested in the region in the first quadrant, we consider \(x\) = √3 as the boundary point.

Now, we can set up the integral to calculate the area:

A =\(\int\limits^_ \,\)[0 to √3]\((4 - x^2 - 1)\) dx  \(\sqrt{3}\)  

Simplifying, we have:

A =\(\int\limits^_ \,\)[0 to √3] \((3 - x^2)\)dx

Integrating, we get:

A =\([3x - (x^3)/3]\) evaluated from 0 to √3

Substituting the limits, and simplifying further, we have:

A = 3√3 - √3

Therefore, the area of region R is 3√3 - √3 square units.

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a) The size of the sample space is 133,784,560.

b) The probability that at least 4 of the cards drawn are red is approximately 0.6835.

a) The size of the sample space can be calculated by determining the number of possible combinations of 7 cards drawn from a standard deck of 52 cards. This can be calculated using the combination formula: nCr = n! / (r!(n-r)!), where n is the total number of cards (52) and r is the number of cards drawn (7). Therefore, the size of the sample space is 52C7.

b) To calculate the probability that at least 4 of the cards drawn are red, we need to consider the different possibilities: drawing exactly 4 red cards, drawing exactly 5 red cards, drawing exactly 6 red cards, and drawing all 7 red cards. For each case, we calculate the probability and sum them up to get the total probability. The probability of drawing exactly k red cards can be calculated using the combination formula: (26Ck * 26C(7-k)) / 52C7. Finally, we sum up the probabilities for k = 4, 5, 6, and 7 to get the probability that at least 4 cards are red.

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Answer:

  3.56 kg

Step-by-step explanation:

You want the mass of a model that is 45 cm tall and has a density of 1200 kg/m³ when the statue it is modeling is 270 cm tall, has a density of 2500 kg/m³, and a mass of 1600 kg.

The ratio of volumes of the model to the statue is the cube of the ratio of their heights:

  Vm/Vs = (Hm/Hs)³

  Vm = Vs(Hm/Hs)³ = (1600 kg)/(2500 kg/m³)·((45 cm)/(270 cm))³

  Vm ≈ 0.002963 m³

The mass of the model is the product of its volume and its density:

  Mm = Vm·ρ = (0.002963 m³)(1200 kg/m³) ≈ 3.56 kg

The mass of Justin's model is about 3.56 kg.

__

Additional comment

The relationship between density, volume, and mass is ...

  ρ = mass/volume

This can be rearranged to ...

  volume = mass/ρ

Which is the expression we used for Vs in the first section above.

(We used V and H for volume and height with 'm' and 's' signifying the model and the statue, respectively.)

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The mass of Justin's model is approximately 3.57 kg., rounded to 3 significant figures.

To find the mass of Justin's model, we can use the concept of mathematical similarity.

Mathematical similarity means that corresponding dimensions of two objects are proportional. In this case, Since the densities are also given, we can use the volume ratio to find the mass ratio.

Let's calculate the volume ratio first:

Volume ratio = (Height of model / Height of statue)^3

            = (45 cm / 270 cm)^3

            = (0.1667)^3

            = 0.00463

Now, using the density ratio:

Density ratio = Density of model / Density of statue

            = 1200 kg/m³ / 2500 kg/m³

            = 0.48

Finally, we can find the mass of Justin's model by multiplying the mass of the statue by the volume ratio and density ratio:

Mass of Justin's model = Mass of statue * Volume ratio * Density ratio

                     = 1600 kg * 0.00463 * 0.48

                     = 3.5712 kg

Rounding to 3 significant figures, the mass of Justin's model is approximately 3.57 kg.

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a) she put the numbers in the wrong place, V2 ≠2

b) V32= 4V2

The surface area of the prism is 240cm²

A prism is a solid shape that is bound on all its sides by plane faces. The surface area of a prism is given by ;

SA = 2B + pH

where B is the base area

P is the perimeter of the base

h is the height of the prism

Therefore, Base area = 1/2 bh

= 1/2 × 8 × 3

= 4× 3

= 12cm²

perimeter = 5+5+8

= 18cm

SA = 2(12) + 18× 12

SA = 24 + 216

SA = 240cm²

therefore the surface area of the prism is 240cm²

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The surface area of the figure which comprises of two identical triangles and a rectangle is equal to 120 square centimeters

area of a triangle = 1/2 × base × height

area for one of the triangles = 1/2 × 8 cm × 3 cm

area for one of the triangles = 12 cm²

area of the two identical triangles = 2 × 12 cm²

area of the two identical triangles = 24 cm²

area of rectangle = length × width

area of the rectangle = 12 cm × 8 cm

area of the rectangle = 96 cm²

Total surface area of the figure = 24 cm² + 96 cm²

Total surface area of the figure = 120 cm²

Therefore, the surface area of the figure which comprises of two identical triangles and a rectangle is equal to 120 square centimeters.

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