A regular triangular pyramid has a base and lateral faces that are congruent equilateral triangles. It has a lateral surface area of 57 square centimeters. What is the surface area of the regular triangular pyramid?

The equation of the line passing through point C and perpendicular to line AB is: y = -6/5x - 20/5 + 2

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

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

Where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Using the coordinates of points A and B, we have:

m = (4 - 9) / (8 - 2) = -5 / 6

The slope of a line perpendicular to this line would be the negative reciprocal of this slope, so:

m= -1 / m = -6 / 5

Next, we can use the point-slope form of a line to find the equation of the line, which is:

y - y1 = m * (x - x1)

Substituting the values for m, x1, and y1 (where x1 and y1 are the coordinates of point C), we have:

y - (-2) = -6/5 * (x + 3)

Simplifying and solving for y, we get:

y = -6/5 * x - 20/5 + 2

So, the equation of the line passing through point C and perpendicular to line AB is: y = -6/5x - 20/5 + 2

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The average rate of change from x=1 to x=5 is -1.325.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

at x=1 the value of y is 8.5

x=5 the value of y is 3.2

slope=3.2-8.5/5-1

=-5.3/4

m=-1.325

Hence,  the average rate of change from x=1 to x=5 is -1.325.

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The number of months during which the company is not making a profit 18.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

C(x) = 17 - 8x - 2x²

R(x) = 5 - 3x

If there is no profit it means,

R(x) - C(x) = 0

Now,

5 - 3x - ( 17 - 8x - 2x²) = 0

5 - 3x - 17 + 8x + 2x² = 0

2x² + 5x - 12 = 0

Solve for x.

2x² + 5x - 12 = 0

2x² + (8 - 3)x - 12 = 0

2x² + 8x - 3x - 12 = 0

2x(x + 4) - 3(x + 4) = 0

(x + 4)(2x - 3) = 0

x = -4 (rejected) and x = 3/2

Now,

x = 3/2 = 1.5

This means,

1.5 years = 18 months

Thus,

The number of months is 18.

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Answer:

383

Step-by-step explanation:

37 - 29 = 6

59 x 6 = 353

353 + 29

Answer:

Step-by-step explanation:

[tex]4x+\frac{1}{2}x = (4+\frac{1}{2} )x[/tex]

             [tex]=(\frac{8}{2} +\frac{1}{2} )x[/tex]

            [tex]=\frac{9}{2}x[/tex]

The study described is a randomized experiment.

A randomized experiment is a typical experimental study design. It is a study design in which the researcher or investigator is in complete control of the research environment. For example, an investigator may wish to assess the effects of certain treatments on some experimental units.

The investigator decides the type of treatment, the type of experimental unit to use, and the allocation and assessment procedures of the treatments and effects, respectively, while in an observational study, the researcher or investigator is usually a passive observer as he only observes and analyses facts and events as they occur naturally.

In experimental studies, the researcher is in complete control of the exposure, and the result should therefore provide stronger evidence of an association or lack of association between exposure and a health problem than would an observational study.  

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"Determine whether the study described below is a randomized experiment or an observational study.

A medical researcher wants to determine whether exercise can lower blood pressure. She recruits 100 people with high blood pressure to participate in the study. She assigns a random sample of 50 of them to pursue an exercise program that includes daily swimming and jogging. She assigns the other 50 to refrain from vigorous activity. She measures the blood pressure of each of the 100 individuals both before and after the study."--

The surface area of the pyramid is A = 265.23 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of hexagonal pyramid be represented as A

Surface area of hexagonal pyramid = Area of base + area of lateral surface

Area of the base = 93.5 inches²

Now , the Area of the lateral surface = 3a √ ( h² + ( 3a²/4 ) )

where a = 6 inches

h = 8 inches

Substituting the values in the equation , we get

Area of the lateral surface = ( 3 x 6 ) √ ( 64 + ( 3 x 36 / 4 ) )

On simplifying the equation , we get

Area of the lateral surface = 171.7 inches²

So , Surface area of hexagonal pyramid = Area of base + area of lateral surface

Surface area of hexagonal pyramid A = 93.5 inches² + 171.7 inches²

Surface area of hexagonal pyramid A = 265.23 inches²

Hence , the surface area of hexagonal pyramid is 265.23 inches²

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The probability that the disposal of such capacitors can be regulated is

0.2266.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values.

Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

Given:

Population mean μ = 47.9

Standard deviation σ = 5

Sample size n = 39

Event to compute its probability [tex]\bar X[/tex] = [tex]\bar X[/tex] ≥ 48.5.

z = X₁ - μ / σ /√n

Substituting the values,

z = (48.5 - 47.9)/5 / √39

z = 0.6 / 0.800640769.

z = 0.75

From the normal distribution table,

the probability can be calculated as,

P = Pr (Z > 0.75)

P = 1 - 0.7734

P = 0.2266

Therefore, the probability is 0.2266.

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Answer:

h = 13 ft

Step-by-step explanation:

The cross-sectional area of the first story is the area of a rectangle with width 30 ft and height 8 ft.  The area of a rectangle is the product of its width and height.

[tex]\begin{aligned}\implies \textsf{Cross-sectional area of first story}&=30 \times 8\\&=240\; \sf ft^2\end{aligned}[/tex]

The cross-sectional area of the second story is made up of a rectangle with width 30 ft and height 3 ft, and a triangle with base 30 ft and height (h - 3).  The area of a triangle is half the product of its base and height.

[tex]\begin{aligned}\implies \textsf{Cross-sectional area of second story}&=(30 \times 3)+\dfrac{1}{2} \times 30 \times (h-3)\\&=90+15(h-3)\\&=90+15h-45\\&=(15h+45)\; \sf ft^2\end{aligned}[/tex]

If the second story has the same cross-sectional area as the first story, then:

[tex]\implies 15h+45=240[/tex]

To find h, solve the equation:

[tex]\begin{aligned}\implies 15h+45&=240\\15h&=195\\h&=13\; \sf ft\end{aligned}[/tex]

Therefore, the value of h such that the second story will have the same cross-sectional area as the first story is 13 ft.

Answer:

b) 15/7

Step-by-step explanation:

The frequency of a signal is a measure of how often the signal repeats over time. In this case, x(t) is a complex exponential signal, represented by the equation x(t) = e^(30πit/7). The variable "t" represents time, and the variable "i" represents the imaginary unit, which is equal to the square root of -1.

The "30πi" term in the exponent represents the angular frequency of the signal, which is a measure of how rapidly the signal oscillates. The "t/7" term in the exponent represents the time scaling of the signal, which determines how quickly or slowly the signal repeats over time.

When we combine these two factors, we can see that the signal repeats every 7 units of time. Therefore, the frequency of the signal is 1/7, which is equivalent to 15/7 in decimal form. Therefore the answer is (b) 15/7

Answer:

give a list and then I can help

Answer:

Bangalore

Step-by-step explanation:

new York..

make me brainleast

The inequality  4(2.8z + 1.75) > -26.6  has 5 as a solution and its solution is, z > - 3.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The inequalities are,

⇒ 4(2.8z + 1.75) > -26.6

⇒ 2(1.9z + 1.5) ≤ 18.2

Now, We can solve the inequalities as;

1) ⇒ 4(2.8z + 1.75) > -26.6

Divide by 4;

⇒ 2.8z + 1.75 > - 6.65

Subtract 1.75 both side,

⇒ 2.8z > - 6.65 - 1.75

⇒ 2.8z > - 8.4

Divide by 2.8;

⇒ z > - 8.4/2.8

⇒ z > - 3

Clearly, z = 5 is the solution of the above inequality.

2) 2(1.9z + 1.5) ≤ 18.2

Divide by 2;

⇒ 1.9z + 1.5 ≤ 9.1

Subtract 1.5 both side,

⇒ 1.9z ≤ 9.1 - 1.5

⇒ 1.9z ≤ 7.6

Divide by 1.9;

⇒ z ≤ 7.6/1.9

⇒ z ≤ 4

Clearly, z = 5 is not the solution of the above inequality.

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The complete question is this,

Solve each of the given inequalities for z. Which of the inequalities has 5 as a solution?

   Inequality 1                                 Inequality 2

4(2.8z + 1.75) > -26.6                2(1.9z + 1.5) ≤ 18.2

The fence's shortest overall length is 808 meters.

Describe the rectangle.

A quadrilateral having all four interior angles at 90 degrees is a rectangle.

Given that the square field has an area of 800 m2.

Let the rectangle's length and breadth be x and y.

The rectangle's area is then:

A= xy

Or, xy = 800

x = 800/y (1) (1)

The triangle's perimeter is:

2x +2y

The total length of the fence is equal to the perimeter of the triangle plus twice the length or width of the triangle since the fence divides the triangle into three equal portions.

Consequently, the fence's overall length is:

L = 2x + 2y + 2x

L = 4x +2y

the equation above with x = 800/y as a replacement:

L = 4(800/y) + 2y

L = 3200/y +2y         (2)

Differentiate the equation with respect to y:

L' = -3200/y² +2

Substitute L'= 0 into the above equation:

0 = -3200/y² + 2

y² = 3200/2

y² = 1600

y = 400

Substitute y = 400 into equation (2):

L = 3200/400 + 2(400)

L = 8 + 800

L = 808

Hence, The fence's shortest overall length is 808 meters

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The given expression becomes 5.35-2b.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 7j+5-8kb.

Here,  j = 0.5 and k = 0.25

Now, substitute j = 0.5 and k = 0.25 in the given expression, we get

7×0.5+5-8×0.25×b

= 0.35+5-2b

= 5.35-2b

Therefore, the expression is 5.35-2b.

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Answer:

6.5

Step-by-step explanation:

Answer:

if 1cm-10grams

what Abt 640 grams=64cm

Answer: The recursive equation for this sequence is t(n+1)=t(n) - 3.

Step-by-step explanation:

The recursive equation for the given sequence is t(n+1) = t(n) - 3. This means that to find the next term in the sequence, we take the previous term and subtract 3 from it.

For example:

t(1) = 8 (first term in the sequence)

t(2) = t(1) - 3 = 8 - 3 = 5 (second term in the sequence)

t(3) = t(2) - 3 = 5 - 3 = 2 (third term in the sequence)

t(4) = t(3) - 3 = 2 - 3 = -1 (fourth term in the sequence)

In general, the recursive equation t(n+1) = t(n) - 3 will give the nth term of the sequence.

It should be noted that the initial condition provided in the question t(0)=-3, t(n+1)=t(n) +11 is incorrect and will not give the same sequence.

The mean of X can be calculated using the expected value formula, E(X) = sum of all possible values of X * probability of each value.

Since Jenny has to admit exactly 14 applicants, the possible values of X can be 0 to 14.

The probability of each value can be calculated using the binomial distribution formula, P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where n = 14 (number of applicants Jenny has to admit), k = number of domestic applicants, and p = probability of a domestic applicant (55/100).

So, the expected value of X can be calculated as:

E(X) = sum of P(X=k) * k, for k = 0 to 14

= (0 choose 0) * (55/100)^0 * (45/100)^(14-0) * 0 + (14 choose 1) * (55/100)^1 * (45/100)^(14-1) * 1 + ... + (14 choose 14) * (55/100)^14 * (45/100)^(14-14) * 14

= 7

So, the mean of X, M = E(X) = 7

The standard deviation of X can be calculated using the formula, o(X) = sqrt(E((X-M)^2))

= sqrt(E(X^2) - M^2)

= sqrt((sum of P(X=k) * k^2) - M^2)

= sqrt((0 choose 0) * (55/100)^0 * (45/100)^(14-0) * 0^2 + (14 choose 1) * (55/100)^1 * (45/100)^(14-1) * 1^2 + ... + (14 choose 14) * (55/100)^14 * (45/100)^(14-14) * 14^2 - M^2)

= sqrt(3.65)

So, the standard deviation of X, o(X) = 1.91 (rounded to nearest three decimal places).

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Answer:

y =  -3/4 x + 3                                                                                                            

Step-by-step explanation:

y = mx + b  You need the m value (slope) and the b (y-intercept value) to the write the equations.

Slope:

Look that the two intercepts of x (4,0) and the y intercept of (0,3).  If you start and (4,0) and go up 3 and left 4, you will land back on the line at the point (0,3).  Slope is the rise over the run.  The rise is up and positive 3.  The run is left and negative -4

3/-4 is the same as -3/4

-3/4 is the slope.

y-intercept:

The y intercept is at the point (0,b)  In this case, the point is (0,3).

3 is the y-intercept.

y = mx + b  Substitute -3/4 for m and 3 for b

y = -3/4 x + 3

Answer:

d

Step-by-step explanation: using logic of dimension analysis , since y represent distance and x represent hours of traveling in train means time then 60 must be speed for equality i.e distance traveled by train per hour , for correcting dimensionaly

More than once a week: 0.11

Once a week: 0.51

Every other week: 0.26

Every three weeks: 0.05

Less often than every three weeks: 0.07

To make a relative frequency distribution, follow these steps:

Count the number of occurrences of each category in the data. In this case, 11% of the 251 participants responded "more than once a week", so the number of occurrences for this category is 0.11 * 251 = 27.61 (rounded to 28). Similarly, 51% of the participants responded "once a week", so the number of occurrences for this category is 0.51 * 251 = 127.51 (rounded to 128). And so on for the other categories.

Divide the number of occurrences for each category by the total number of participants. In this case, the total number of participants is 251, so the relative frequency for "more than once a week" is 28 / 251 = 0.11. The relative frequency for "once a week" is 128 / 251 = 0.51. And so on for the other categories.

And that's it! These are the relative frequencies for each category in the data.

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The required coordinate of the midpoint C is given as (2, 5), as per the given conditions.

Midpoint is that point on the line whose distance from both ends of the line is equal.

Here,
The coordinates of the endpoints of AB are A(–4,8) and B(8,2).

Let the coordinate of point C be (x, y)

Now,
x = x₁ + x₂ / 2    ; y = y₁ + y₂/2

Substitute value in the above expression,
x = -4 + 8 / 2    ; y = 8 + 2 / 2
x = 2                 , y = 5

Thus, the required coordinate of the midpoint C is given as (2, 5), as per the given conditions.

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On solving the provided question we can say that the equation when factorization we have is (4x³ - 6x³ + 6x - 7)/(-2x + 3) on diving we will have, the quotient will be (-2x² + 6x -7)/(-2x + 3).

A number or other mathematical object is factored, or written as the product of numerous factors—typically smaller or simpler things of the same kind—in mathematics. For instance, the integer 15 is factorized as 3 5, which is the factorization of the polynomial x² – 4. Factorization in mathematics refers to the breakdown of a number into smaller numbers that are multiplied together to produce the original number. Factorization is the division of a number into its factors or factors. 12 is multiplied by 3 and 4 as an example.

the equation we have is

(4x³ - 6x³ + 6x - 7)/(-2x + 3)

on diving we will have

(-2x² + 6x -7)/(-2x + 3)

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The quadratic function for the height of the player, h(t) = -16·t² + 12·t indicates the following

The player starts going up at 0 seconds

The player stops going up at 0.375 seconds

The player would be rising in the interval [0, 0.375)

A quadratic function is a function that can be expressed as; f(x) = a·x² + b·x + c, with the values of a, (a ≠ 0) b, and c representing numbers.

The function for the height is; h(t) = -16·t² + 12·t

The time the player starts going up can be found as follows;

The minimum height = -1

When h(t) = -1, we get; -1 = -16·t² + 12·t

-16·t² + 12·t + 1 = 0

Therefore, t = (3 ± √13)/8

t ≈ 0.826 and t ≈ -0.076

However, the value of the time is a natural number, therefore;

The player stops going up at the maximum height, which can be obtained from the value of the maximum point of a quadratic function, which is; t = -12/(2 × (-16)) = 3/8 = 0.375

In mathematical terms the player will be rising between the interval, 0 ≤ t < 0.375, which can be expressed as; [0, 0.375)

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The domain of d(x) = -(x+7)^2 + 9 are the set of all real numbers and the function is d(x) = -(x+7)^2 + 9

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

d(x) = -(x+7)^2 + 9

This means that the function is d(x) = -(x+7)^2 + 9

There is no restriction on the input values, x

So, the domain of d(x) = -(x+7)^2 + 9 is all real numbers, since there is no restriction on the input (x).

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The exponential function for the graph at the end of the answer is defined as follows:

y = -1.5(2)^x.

The definition of an exponential function is given as follows:

y = ab^x

In which the parameters are defined as follows:

When x = 0, y = -1.5, hence the parameter a is given as follows:

a = -1.5.

When x = 2, y = -6, hence the parameter b is obtained as follows:

-1.5b² = -6

b² = 4.

b = 2.

Then the function is defined as follows:

y = -1.5(2)^x.

The function is given by the image presented at the end of the answer.

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Answer:

Below

Step-by-step explanation:

four more than h   is     h+4

no less than 27 means it is greater than or equal to 27

h+4 >= 27

Answer:

3x+12 because of the bracket it makes the 3 multiply the x and

The fewest number of trips Trisha takes to walk all 13 dogs is of

Five trips.

The fewest number of trips is obtained applying the proportions in the context of this problem.

To minimize the number of trips, we must maximize the number of trips with three dogs, hence:

13/3 = 4 with a remainder of 1.

Hence she needs five trips, divided as follows:

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Answer:

Step-by-step explanation:

You want the interest rate and account balance after 10 years if the investment of $700 doubles in 9 1/2 years with interest compounded continuously. And, you want the interest rate and doubling time if a $900 investment has a value of $1405 after 10 years with continuous compounding.

These problems are solved by making use of the compound interest formula for continuously compounded interest. In each case, you fill in the values you know, and solve for the one you don't know.

  A = Pe^(rt)

The investment doubles after 9.5 years, so we have ...

  2·700 = 700e^(9.5r)

Dividing by 700 and taking natural logs, we find the rate to be ...

  ln(2) = 9.5r

  r = ln(2)/9.5 ≈ 0.072963 ≈ 7.30%

Using the exact value in the computation of the balance, we get ...

  A = 700e^(10·(ln(2)/9.5)) = 700·2^(10/9.5) = 700·2^(20/19)

  A = 1452.02

The annual rate is 7.30%; the balance in 10 years is $1452.02.

The balance after 10 years is ...

  1405 = 900e^(r·10)

  ln(1405/900) = 10r

  r = ln(1405/900)/10 ≈ 0.0445398 ≈ 4.45%

As we found above, the relation between r and doubling time is ...

  r = ln(2)/t   ⇒   t = ln(2)/r

  t = ln(2)/0.0445398 ≈ 15.56 . . . . years

The annual rate is about 4.45%; the doubling time is about 15.56 years.

__

Additional comment

In the first problem, we could find the account balance after 10 years using the found interest rate. In that case, it would be $1452.56. Instead, we chose the doubling time to be the exact value in the problem.

There is a "rule of 70" or sometimes the "rule of 72" that tells you the approximate doubling time in years (y) for an interest rate of r%. It is ...

  y = 70/r

The amount of error depends on the interest rate and the way interest is compounded.

When the interest is compounded continuously, a slightly different rule gives the exact doubling time:

  y = 100·ln(2)/r ≈ 69.31472/r

This is effectively the rule we used above.