Calculate the length of edge AD in the triangle-based pyramid below.
Give your answer to 2 d.p.

The value of x  is 16 cm.

What is the equilateral triangle?

An equilateral triangle is a type of triangle that has three sides of equal length and three equal angles of 60 degrees each. All equilateral triangles are also equiangular and isosceles triangles. The sides of an equilateral triangle are congruent, and it is symmetrical in all ways, meaning that it has rotational and line symmetry.

We have given,

Lengths of sides:

16 cm,  16cm, and x cm,

we have to find the value of x.

The given triangle is an equilateral triangle,

so, The length of all three sides of an equilateral triangle is equal.

16 cm = 16cm =  x cm,

x = 16 cm

Hence, The value of x  is 16 cm.

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If vec SD, vec SE, and vec SG and if m angle DSE = 5x – 4, m angle E5G = 3x + 4, and m angle DSG = 72, m angle DSE = 90.

Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet. Two rays (half-lines) combined into an angle have a single terminal. The latter is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

An angle is a figure created by two rays or lines that have the same termination in plane geometry. The Latin word "angulus," which meaning "corner," is where the term "angle" originates. The common terminal of the two rays—known as the vertex—is referred to as an angle's sides.

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Based on the number of 60% students, the total number of students in Ms. Howard's class are 25.

Let the total number of students be x. Based on the mentioned information, we can say that 60% of total number of students ordering a hot lunch are 15. Rewriting the mentioned information as equation -

60% × x = 15

60/100 × x = 15

x = 15 × 100/60

Performing multiplication on Right Hand Side of the equation

x = 1500/60

Cancelling zero and performing division on Right Hand Side of the equation

x = 25

Therefore, there are 25 students in the class.

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Answer:

Step-by-step explanation:

always follow BODMAS or BIDMAS-

Do the multiplication, which is 15/3 and when simplifiyed becomes 5.

Then work out 6 divided by 3/2. In division for fractions, you always find the reciprocal of the 2nd number and multiply instead of divide, so its 6 x 2/3 which is 12/3, simplifiyed to be 4. 5+4=9. 9+10 is 19, and 19-4=15

Answer: The lines are only parallel if these pairs of angles are of equal size:

Angle 1 ≡ Angle 5

Angle 2 ≡ Angle 6

Angle 3 ≡ Angle 7

Angle 5 ≡ Angle 8

Step-by-step explanation:

All these angles follow a rule called corresponding angles. The rule goes that corresponding angles on parallel lines are equal. If the pairs of angles are equal, this must mean that the lines are parallel and vice versa.

Answer:

4

Step-by-step explanation:

First, substitute in g and h:

4-(0.25x10)+(0.5x5)

4-2.5+2.5

Then -2.5 and +2.5 cancel out, so you are left with:

4

Answer:

|x| = x if x >= 0, -x if x < 0

Step-by-step explanation:

On solving the provided question, we can say that Probability 8 drive to work[tex]= C(8,8) 0.77^8 * 0.23^0 = 0.77^8 = 0.123 = > 1 - 0.1236 = 0.8764[/tex]

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

x = number that drive to work alone

Likelihood that exactly eight people drive alone to work is equal to the probability that no more than seven people drive alone.

[tex]P(x < = 7) = 1 - P(x > 7) = 1- P(x = 8)[/tex]

That probability

Probability 8 drive to work

[tex]= C(8,8) 0.77^8 * 0.23^0 = 0.77^8 = 0.123\\=1 - 0.1236 = 0.8764[/tex]

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It would depend on the rate of the ferris wheel, so it is impossible to answer this question without knowing the wheel's speed.

1. The question is asking for an estimate of the time it would take for a person to get from the start of the ferris wheel to the point closest to the polar coordinate (6, 0).

2. To answer this question, we need to know the speed of the ferris wheel. Without this information, it is impossible to answer the question.

It would depend on the rate of the ferris wheel, so it is impossible to answer this question without knowing the wheel's speed.

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We can use probability to find the answers to the questions - the final answers are given below.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.

We will answer each part in detail.

Part (a)

No, there are more than 2 outcomes in this particular scenario.

Part (b)

Yes, there are two outcomes (Type A or not).

Part (c)

No, probability changes as the cards are dealt.

Part (d)

No, the trials are not independent.

Part (e)

Yes, two outcomes (more than 3 or not)

These are the final answers:

(a): No

(b): Yes

(c): Yes

(d): No

(e): Yes

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Answer:

(x-1)^3.

Step-by-step explanation:

To find the least common multiple (LCM) of two polynomials, you can factor them and take the highest exponent of each variable that appears. In this case, the LCM is (x-1)^3 because it has the highest exponent of x that appears in both polynomials. It also contains all the other terms of both polynomials.

Answer:

70⁰ is the correct answer.

El area de las bases es 628 cm^2 (ambas bases) y el area lateral es 1,256 cm^2

Tenemos un cilindro con un radio de 10 centimetros y 20 centimetros de altura.

El cilindro tiene dos tapas que son circulares, el area de estas se calcula como el area de un circulo cualquiera, esta sera:

A = 2*( pi*R^2)

Donde R es el radio y pi = 3.14, entonces tendremos:

A = 2*(3.14*(10cm)^2)

A = 628 cm^2

El area lateral será igual que el producto entre la altura y la circunferencia:

A' = 2*pi*R*H

Donde H es la altura.

Remplazando los valores que conocemos obtendremos:

A' = 2*3.14*(10cm)*20cm

A' = 1,256 cm^2

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Answer:

25÷2=12.5

Step-by-step explanation:

you put the 25 inn the division box and the 2 on the outside and 12.5 is your answer

Answer: 12.5

[tex]\frac{25}{2} =12.5[/tex]

[tex]\frac{5^{2}}{2} = 12 \frac{1}{2} = 12.5[/tex]

The correct unit of measure for the mean of the sampling distribution of I is A. Dollars.

The original distribution of prices for the car model is given in dollars, and the mean of the sampling distribution represents the average price of a random sample of 4 cars from that distribution. Hence, the correct unit of measure should be in dollars also.

In statistics, the mean is a measure of central tendency that represents the average value of a dataset. It is calculated by adding up all the values in a dataset and dividing by the number of observations. The formula for the mean of a dataset is:

mean = (sum of observations) / (number of observations)

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The bearing of H from P is 243°26′

In mathematics, an angle is a measure of the amount of rotation between two lines or planes. It is measured in units of degrees or radians. An angle is formed by two rays that have a common endpoint called the vertex. The rays are the sides of the angle and the vertex is the point where the rays meet.

An angle is defined by its measure, which is the amount of rotation between the two rays. The most common way to measure angles is in degrees, where a full rotation is equal to 360 degrees. Another way to measure angles is in radians, where a full rotation is equal to 2*pi radians.

Let the bearing of H from P be represented by x°.

tanθ=3060=0.5

θ=tan−1(0.5)=26.565°

x=180°+(90−26.565)

x=180+63.435=243.435°

= 243°26′

Hence, the bearing of H from P is 243°26′

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The formula for work is force multiplied by displacement.

Work done refers to the amount of energy used by a force to move an object. It is also a physical quantity. Its SI unit is Joule. Every time a force is applied to an object and it moves from one location to another, work has been done. The displacement is what needs to be taken into account and not the distance. Displacement is the smallest distance or straight line that connects the object's initial and final positions. Work is therefore equivalent to force times its displacement. Force is measured in newtons, and the displacement is measured in meters. Therefore, if a force of 1N is used to move a body by a displacement of 1m, then 1J of work has been completed.

                                        [tex]W=F.S[/tex]

                                         [tex]1J=1m.1N[/tex]

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The rate at which the level in the pot is rising at the instant when the coffee in the pot is 10 cm, is 16/9π cm/min.

A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface.

For cylindrical pot,

Volume, V = πr²h

dV/dt = π(r²dh/dt+h * 2r dr/dt)

Since r is constant,

Therefore, dr/dt = 0

dV/dt = 100 = πr²dh/dt

100 = π * 225/4 *dh/dt (since r = 15/2 cm)

=> dh/dt = 400/ 225π = 16/9π cm/min.

Thus, The rate at which the level in the pot is rising at the instant when the coffee in the pot is 10 cm, is 16/9π cm/min.

Correct question: Coffee is draining from a conical filter with height and diameter both 15 cm, into a cylindrical coffee pot with diameter 15 cm. The rate at which coffee drains from the filter into the pot is  100 cc/min. The rate in cm/min at which the level in the pot is rising at the instant when the coffee in the pot is 10 cm, is?

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The equation for  regression line is ŷ = -0.0192X + 39.288,

The  correlation coefficient is  -0.9817,

The population of Detroit in 2008 is 0.73 millions.

A line that, using the bivariate data gathered, summarises the linear relationship (or linear trend) between the two variables in a linear regression study.

An estimate of the line that depicts the actual, but the unidentified, linear relationship between the two variables is called a regression line. When the value of the explanatory variable is known, the regression line's equation is used to predict (or estimate) the value of the response variable.

Given table showing the population of Detroit each decade.

year                                1960   1970   1980   1990    2000

Population (millions)      1.67     1.51     1.20     1.03       0.95

A. equation for regression line,

X - Mx     Y - My     (X - Mx)²   (X - Mx)²       (X - Mx)(Y - My)

-20          -20               400          0.158              -7.96

-10           -10               100          0.057              -2.38

0              0               0          0.005                   0

10      10               100          0.059               -2.42

20     20               400           0.104               -6.44

                             Sum: 1000.00   Sum: 0.382 Sum: -19.200

Sum of X = 9900

Sum of Y = 6.36 millions

Mean X = 1980

Mean Y = 1.272

Sum of squares (SSX) = 1000

Sum of products (SP) = -19.2

Regression Equation = ŷ = bX + a

b = SP/SSX = -19.2/1000 = -0.0192

a = MY - bMX = 1.27 - (-0.02*1980) = 39.288

ŷ = -0.0192X + 39.288

B. correlation coefficient,

X Values

∑ = 9900

Mean = 1980

∑(X - Mx)² = SSx = 1000

Y Values

∑ = 6.36

Mean = 1.272

∑(Y - My)² = SSy = 0.382

X and Y Combined

N = 5

∑(X - Mx)(Y - My) = -19.2

r Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -19.2 /√((1000)(0.382)) = -0.9817

Meta Numerics

r = -0.9817

The value of R is -0.9817.

High X variable scores correlate negatively with low Y variable scores because of this strong negative connection (and vice versa).

C. population in 2008

y  = -0.0192X + 39.288  

substitute x = 2008

y = -0.0192(2008) + 39.288

y = 0.7344

population in 2008 is  0.73 millons.

Hence the equation is ŷ = -0.0192X + 39.288,

the correlation coefficient is r = -0.9817

and population of Detroit in 2008 is  0.73 millions.

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The midsegments of AABC, hypotenuse BC  is B. 15.

In a triangle, a midsegment is a line segment that connects the midpoints of two non-adjacent sides of the triangle. In this figure, DE and DF are the midsegments of AABC, which means that they connect the midpoints of the sides AB and AC, respectively. Since DE and DF are parallel, we know the triangle isosceles (both legs are congruent).

Since the angle at A is 122°, we know that the angle at B and C are 78° (180-122=58). Therefore, if we draw the altitude from B to AC, we have a 30-78-72 triangle. We have been given the length of the altitude, 8, and the angle of the base, 72. We can use the Sine Ratio to calculate the hypotenuse, BC.

sin(72) = opposite / hypotenuse = 8/BC

Solving for BC, we get 15

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Answer:

Step-by-step explanation:

So you add 1+3+7 which gives you 11

And the you divide 3300 by 11 which gives you 300 and from that you do:

1 x 300= 300

3 x 300= 900

7 x 300= 2100

And there you have it in the ratio of 1:3:7

300:900:2100

And to simplify it you find a number which you can divide them all from in this case is 100 and so:

300÷100=3

900÷100=9

2100÷100=21

3:9:21

Hope that helped.

Answer:

Step-by-step explanation:

Answer:

5x = y

10x= 5y

20x= 15y

50x= 45y

The double integral for [tex]3xy^2/x^2+1[/tex] is 8㏑(2).

[tex]3\int\limits^1_0 \int\limits^2_2 \frac{xy^2}{x^2 + 1} \, dy dx[/tex]  

3* 1/2 (㏑(2) - ㏑(1) ) * 1/3 (8+8)

8㏑(2)

A multiple integral in mathematics is a definite integral of a function with multiple real variables, such as f(x, y), or f(x, y) (x, y, z). In the real-number plane, integrals of functions of two variables over an area are referred to as double integrals, and integrals of functions of three variables over a region in real-number three-dimensional space are referred to as triple integrals.

The Cauchy formula for repeated integration can be used to calculate multiple integrals of a single-variable function.

The double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane that contains its domain, just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis.

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Answer:

i have no clue big dawg you gonna have to cheat somewhere else

Answer:

14

Step-by-step explanation:

1) "the number 35"  means 35

2) "decrease 35 by 0.6 of it"  means -(0.6)*(35)

Put them together:

35 - (0.6)*(35)

35 - 21

= 14

According to algebra, the square binomial (6 · x + 5 · y)² has the following equivalent expression: 36 · x² + 60 · x · y + 25 · y².

According to algebra, we find the case a square binomial, whose equivalent form is shown below by following rule:

(a + b)² = a² + 2 · a · b + b²

Where a, b are real coefficients.

If we know that a = 6 · x and b = 5 · y, then the equivalent form of the square binomial is:

First, write the entire expression:

(6 · x + 5 · y)²

Second, use power properties:

(6 · x)² + 2 · (6 · x) · (5 · y) + (5 · y)²

Third, perform associative and commutative properties:

6² · x² + (2 · 6 · 5) · (x · y) + 5² · y²

Fourth, multiply similar terms:

36 · x² + 60 · x · y + 25 · y²

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The number of green marbles in the box before the number of green marbles is doubled is given by [tex]$\frac{4 - 4x + 60}{2x - 30}$\\[/tex], where x is the probability of selecting a red marble before the number of green marbles is doubled.

Let the number of green marbles be 'g'.

The probability of selecting a red marble before the number of green marbles is doubled is[tex]$\frac{4}{g+4} * 100 = x\%$[/tex]

The probability of selecting one of the four red marbles from the box after the number of green marbles is doubled is [tex]$\frac{4}{2g+4} * 100 = (x - 15)\%$[/tex]

Rearranging the equations and solving for g, we get:

[tex]\frac{4}{g+4} * 100 = x$\frac{4}{2g+4} * 100 = (x - 15)$$2g+4 = \frac{4}{x-15}$$g = \frac{4 - 4x + 60}{2x - 30}$[/tex]

Therefore, the number of green marbles before the number of green marbles is doubled is [tex]$\frac{4 - 4x + 60}{2x - 30}[/tex]

The number of green marbles in the box before the number of green marbles is doubled is given by [tex]$\frac{4 - 4x + 60}{2x - 30}$\\[/tex], where x is the probability of selecting a red marble before the number of green marbles is doubled.

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the height of six glasses (24 / 6 = 4). Finally, we can multiply this by six to get the final answer, which is 30 cm.

30 cm

For two glasses, the height is 18 cm.

For eight glasses, the height is 42 cm.

Therefore, for six glasses, the height would be (42 - 18) / (8 - 2) * 6 = 30 cm.

To answer the question, we need to first determine the height of two glasses, which is 18 cm. Next, we need to find the height of eight glasses, which is 42 cm. Once we have these two values, we can calculate the height of six glasses. We can do this by finding the difference between the two heights (42 - 18 = 24), which will give us the height of six glasses (24 / 6 = 4). Finally, we can multiply this by six to get the final answer, which is 30 cm.

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